Research ArticleComputational Fluid Dynamics Characterization of TwoPatient-Specific Systemic-to-Pulmonary Shunts beforeand after Operation

Neichuan Zhang 1 Haiyun Yuan 2 Xiangyu Chen 1 Jiawei Liu 1 Qifei Jian 1

Meiping Huang 3 and Kai Zhang 4

1School of Mechanical and Automotive Engineering South China University of Technology Guangzhou 510640Guangdong China2Department of Cardiac Surgery Guangdong Cardiovascular InstituteGuangdong Provincial Key Laboratory of South China Structural Heart Disease Guangdong Provincial Peoplersquos HospitalGuangdong Academy of Medical Sciences Guangzhou China3Department of Catheterization Lab Guangdong Cardiovascular InstituteGuangdong Provincial Key Laboratory of South China Structural Heart Disease Guangdong Provincial Peoplersquos HospitalGuangdong Academy of Medical Sciences Guangzhou China4Guangdong Cardiovascular Institute Guangdong Provincial Key Laboratory of South China Structural Heart DiseaseGuangdong Provincial Peoplersquos Hospital Academy of Medical Sciences School of MedicineSouth China University of Technology Guangzhou China

Correspondence should be addressed to Qifei Jian tcjqfscuteducn and Meiping Huang huangmeiping126com

Received 22 November 2018 Accepted 6 January 2019 Published 3 February 2019

Academic Editor Maria N DS Cordeiro

Copyright copy 2019 Neichuan Zhang et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Studying the haemodynamics of the central shunt (CS) and modified BlalockndashTaussig shunt (MBTS) benefits the improvement ofpostoperative recovery for patients with an aorta-pulmonary shunt Shunt configurations including CS and MBTS are virtuallyreconstructed for infants A and B based on preoperative CTdata and three-dimensional models of A 11months after CS and B 8months after MBTS are reconstructed based on postoperative CT data A series of parameters including energy loss wall shearstress and shunt ratio are computed from simulation to analyse the haemodynamics of CS andMBTS Our results showed that theshunt ratio of the CS is approximately 30 higher than the MBTS and velocity distribution in the left pulmonary artery (LPA) andright pulmonary artery (RPA) was closer to a natural development in the CS than the MBTS However energy loss of the MBTS islower and the MBTS can provide more symmetric pulmonary artery (PA) flow than the CS With the growth of infants A and Bthe shunt ratio of infants was decreased but maximumwall shear stress and the distribution region of high wall shear stress (WSS)were increased which raises the probability of thrombosis For infant A the preoperative abnormal PA structure directly resultedin asymmetric growth of PA after operation and the LPARPA ratio decreased from 049 to 025 Insufficient reserved length ofthe MBTS led to traction phenomena with the growth of infant B on the one hand it increased the eddy current and on the otherhand it increased the flow resistance of anastomosis promoting asymmetric PA flow

1 Introduction

Systemic-to-pulmonary shunts (SPSs) consisting of an ar-tificial shunt connecting the aorta to the pulmonary arteryare palliative operations for neonates with cyanotic con-genital heart disease such as Tetralogy of Fallot pulmonary

artery hypoplasia and hypoplastic left heart syndrome [1 2]For patients with diminished pulmonary blood flow anartificial systemic-to-pulmonary artery shunt has frequentlybeen used to provide blood flow from systemic circulation topulmonary circulation MBTS with a shunt connecting theinnominate artery (IA) to the right pulmonary artery (RPA)

HindawiComputational and Mathematical Methods in MedicineVolume 2019 Article ID 1502318 10 pageshttpsdoiorg10115520191502318

and CS with a shunt connecting the ascending aorta (AAO)to the main pulmonary artery (MPA) are commonly usedSPS in clinical settings

Currently computer fluid dynamics have been in-creasingly used to study the postoperative haemodynamicsof SPS [3] ey allow for the comparison of the haemo-dynamic characteristics of different shunt configurations [4]and studying the effects of different anastomosis methods onthe haemodynamics of the MBTS [5] Mathematical mod-elling is used to predict the postoperative haemodynamicparameters [6] Based on mathematical models such as thelumped parameters model (LPM) there are many studiescovering the effects of the shunt diameterrsquos size and itsorientation in SPS haemodynamics [7ndash9]

is study utilized clinical data from two infants A andB born with pulmonary artery stenosis Infant A presentedwith CS in the clinic when he was three months old and CTdata were collected before and 11 months after surgeryinfant B presented with MBTS in the clinic when he was 12days old and CT data were collected before and 8 monthsafter surgery Notably we reconstructed shunt configura-tions including CS and MBTS virtually based on the CTdataof preoperative patients to analyse the haemodynamiccharacteristics of CS and MBTS Furthermore we recon-structed three-dimensional postoperative models by post-operative CT data of A and B to compare thehaemodynamics of two infants before and after surgery andanalyse the effects of CS and MBTS on the postoperativedevelopment of the pulmonary artery

2 Materials and Methods

21 Diameters of Shunts e decision about shunt size ismostly based on clinical experience through the patientrsquosbody weight [10] 3mm grafts are used for infants weighinglt3 kg and ge35mm shunts for 3sim6 kg patients Consideringthe specific condition of patients a shunt with a diameter of35mm was selected for our study

22 3D Reconstruction 3D anatomical data from a 155multislice CTof infant A and a 138 multislice CTof infant Bwere provided by the Guangdong Provincial PeoplersquosHospital As is shown in Figure 1 model A representsthree-dimensional neonatal arterial model of infant A andA-CS (A-MBTS) indicates that CS (MBTS) location con-figurations was created virtually for model A Model Brepresents the three-dimensional neonatal arterial model ofinfant B and B-CS (B-MBTS) indicates that CS (MBTS)location configurations were restructured virtually formodel B

23 CalculationMethods Several numerical studies indicatethat the influence of shear thinning properties of blood is notsignificant for the flow in large arteries under steady flowconditions [11ndash13] Additionally studies showed that understeady flow conditions the Newtonian model is certainly agood approximation in regions of midrange to high shearwith the debate centring on whether the fact that it

underestimates WSS in regions of low shear is biologicallysignificant [14] Non-Newtonian properties of blood wereexhibited by blood typically only at shear rates lower than100 sminus1 [15] In this study regions of interest are large ar-teries and the shear rate in the region of interest is greaterthan 100 sminus1 for systemic-to-pulmonary shunt [16] ere-fore the blood was assumed to be an incompressibleNewtonian fluid with a density of 1060 kgm3 and viscosityequal to 00035 kg(mmiddots) [17] with 3D domains being rigidwalled [18 19] To compute haemodynamic variables fordifferent shunt configurations LPM was built up based onthe relevant studies [5 20 21] Postoperative LPM (Figure 2)can be divided into four parts cardiac systemic circulationand pulmonary circulation and shunt

e LPM consists of resistors (R) inductors (L) andcapacitors (C) which represent the viscous resistanceinertance and the compliance of the vessel [22] and diodesin the circuit were used to simulate the cardiac valves

Atria are represented in terms of a constant compliance(C14 and C15) since atrial contractility is discarded [20]Cardiac pressures are considered to be composed of activeand passive parts In order to represent the rhythmic con-traction of cardiac circulation the relation function betweenpressure and volume was described as follows

E(t) Psv(t)

Vsv(t)minusV0 (1)

where E(t) [23] meant time-varying elastance function withunit mmHgmL Psv(t) and Vsv(t) represents time-varyingventricle pressure and time-varying volume of ventriclerespectively V0 was the initial value of ventricular volume(t) can be computed by the following function

E(t) Emax minusEmin( 1113857 middot En tn( 1113857 + Emin (2)

where Emax and Emin were related with ventricle pressure andvolume in end systole and diastasis respectively In thisstudy Emax 25118 and Emin 00458 [5]ese values werekept constant during the subsequent calculations E(tn)

(double Hill function [24]) was described as follows

En tn( 1113857 155 middottn07( 1113857

19

1 + tn07( 111385719

⎡⎣ ⎤⎦ middot1

1 + tn117( 1113857219

⎡⎣ ⎤⎦ (3)

where tn t(02 + 015 tc) (tc was one cardiac cycle in-terval and it was set as 05 s according to the specificpatient)

e values of the LPN elements that refer to relevantstudies [5 17 21] are shown in Table 1 Also Ren and Ding[5 17] utilized clinical data and proved the rationality of thevalues of the parameters in LPM

For physiologic circulation it is observed that the time-averaged velocity field of pulsatile flow does not show re-markable differences to steady-state results [25] eboundary condition was set as the average over a cardiaccycle with boundary conditions of CS and MBTS shown inTables 2 and 3 In addition the boundary condition wasassumed to be the same for infants A and B enablingcomparison of haemodynamics in a different three-dimensional anatomy

2 Computational and Mathematical Methods in Medicine

(a) (c) (e)

(b) (d) (f)

Central

Central Righ

t mbt

inR

ight

mbt

in

IA

LCA

LSA

RPA

LPA

DAO

MPA

AAO

IALCA

LSA

DAO

LPA

RPA

AAO

MPA

Figure 1 ree-dimensional neonatal arteries model of infants A ((a) model A) and B ((b) model B) and central shunt (CS) configurationestablished for infants A ((c) A-CS) and B ((d) (B-CS)) modified BlalockndashTaussig shunt (MBTS) configuration established for infants A ((e)A-MBTS) and B ((f) B-MBTS) In order to simplify the model we neglected independent branching vessels e remaining vessels includeascending aorta (AAO) innominate artery (IA) left carotid artery (LCA) left subclavian artery (LSA) descending aorta (DAO) mainpulmonary artery (MPA) left pulmonary artery (LPA) and right pulmonary artery (RPA) e central shunts are placed between AAO andMPA e right-modified BlalockndashTaussig (MBT) innominate shunt connects IA to RPA

PC

L11

L13

R11

R13 C13

C11 C10

C12

C14R14

R15 C15

CardiacCv

R16

R17

IVC C9

R

CSRight MBT in

C1AAO

R1

LEA C8

R18

C2

L2R2 R5

C5

LCA

C3

IA

LUA

LSA

C6

R7

R21

L7

C7SVC

R6 L6

C4

R3 L3

L5

R19

R20 R4 L4L8 R8L9 R9

L1

L10 R10R12L12

RUA

Figure 2 Lumped parameters model LPM is made up of cardiac and pulmonary circulation (PC) ascending aorta (AAO) innominateartery (IA) left carotid artery (LCA) left subclavian artery (LSA) right upper extremity artery (RUA) left upper extremity artery (LUA)superior vena cava (SVC) lower extremities artery (LEA) and inferior vena cava (IVC)

Computational and Mathematical Methods in Medicine 3

24 Energy Loss LPARPA Ratio and Shunt Ratio efundamental purpose of a systemic-to-pulmonary arteryshunt is to provide the appropriate blood flow from systemiccirculation to pulmonary circulation to promote the devel-opment of PA LPARPA ratio (RLPARPA) and shunt ratio (η)are important parameters to evaluate shunt configurations

RLPARPA QLPA

QRPA

η QShunt

QAAO1113888 1113889 times 100

(4)

whereQLPAQPRAQShunt andQAAO indicate the volumetricflow rate at LPA RPA shunt and AAO

Energy loss Wloss is an indicator for evaluating hae-modynamic efficiency e smaller the energy loss thehigher the energy conversion efficiency of shunt configu-rations [26 27]

W Qv P +12ρv

21113874 1113875

Wloss 1113944 Winlet minus 1113944 Woutlet

(5)

where Qv P ρ and v indicate the volumetric flow rate staticpressure density andmean velocity1113936 Winlet is the sum of theinlet energy and 1113936 Woutlet is the sum of the outlet energy

3 Result

3D blood flow streamlines clearly show the flow state of SPS inFigures 3 and 4 A velocity vector diagram at corresponding

sections and partial enlargement of streamline of LPA andRPA are shown to describe the complex flow structures in PAwhich is closely related to abnormal growth of PA [4]

In Figure 3 aortic blood with high pressure and flow rateflows through the shunt and mixes with pulmonary blood inMPA e turbulence intensity in MPA is high and swirlsoccurred near anastomosis of MPA Velocity distribution inLPA and RPA is relatively uniform which is close to naturaldevelopment e blood flow rate of RPA in A-CS was 100higher than that of LPA and the blood flow rate of RPA inB-CS was 5 lower than that of LPA which indicated thatthe preoperative PA structure has an important influence onsymmetrical flow of LPA and RPA for patients with CSerefore the arterial structure of specific patients should beconsidered when LPARPA is an important parameter af-fecting shunt operation e shunt ratios of A-CS and B-CSare 3461 and 3419 respectively e ratio for infants Aand B was similar when CS was performed for two infantsdue to an identical shunt size

In Figure 4 aortic blood with high pressure and flow rateflows through the shunt and mixes with pulmonary blood inRPA which leads to high vorticity regions in RPA Velocitydistribution in LPA is relatively uniform while high vorticityregions in RPA result in an uneven velocity distribution inRPA Pulmonary blood flow of RPA in A-MBTS was 66higher than that of LPA and pulmonary blood flow of RPAin B-MBTS was 1 higher than that of LPA which dem-onstrates that the arterial structure also has an importanteffect on flow distribution of LPA and RPA for MBTS Eventhough the length and curvature of shunts are different theshunt ratio of A-MBTS and B-MBTS are close the shuntratios of A-MBTS and B-MBTS were 2529 and 2614respectively which indicated that the main factors affectingthe shunt ratio of MBTS is the diameter of the shunt Energyloss of CS was greater than that of MBTS for two infants Forinfant A energy loss of CS and MBTS was 016W and013W respectively for infant B energy loss of CS andMBTS was 011W and 008W respectively It is notable thatthe flow state of SPS without additional pulmonary bloodflow (APBF) [4] is different from the flow state of SPS withAPBE When there is still APBE energy loss of MBTS islower than that of CS while the conclusion is just the op-posite when MPA was transected [4] When CS (MBTS) wasperformed for patient A the LPARPA ratio was 049 (059)when CS (MBTS) was performed for patient B the LPARPAratio was 105 (099) is shows that the RPALPA ratio ofMBTS approaches unity when compared with CS that isMBTS can provide a more symmetrical flow between LPAand RPAe shunt ratio of CS is approximately 30 higherthan that of MBTS for infants A and B which indicates thatCS has a greater chance of congestive heart failure ere isanother point that the diameter of the MBT shunt is limitedby the size of the RPA CS could be preferred for patientswith narrow PA to prevent thrombosis due to small sizeshunts [10]

Infant A was presented with CS in the clinic Figure 5(a)shows the preoperative arterial geometry of infant A andFigure 5(b) shows the arterial geometry of patient A 11months after operation Blood flow in RPA was 50 higher

Table 1 Values of parameters in LPM

Block R(mmHgmiddotsml)

C(mlmmHg)

L(mmHgmiddots2

ml)AAQ R1 012 C1 0127 L1 00013IA R2 169 C2 00962 L2 000038LCA R3 1858 C3 008911 L3 000047LSA R4 1858 C4 008911 L4 000047RUA R5 1065 C5 01399 L5 000213LUA R6 05751 C6 01463 L6 000107SVC R7 1235 C7 07233 L7 00005LEA R8 0863 C8 001995 L8 0001248IVC R9 1453 C9 08571 L9 0000977

PC

R10 00075 C10 002394 L10 000049R11 01002 C11 000465 L11 0000488R12 00075 C12 002394 L12 000049R13 01002 C13 000465 L13 0000488

Cardiaccirculation

R14 0015 C14 00409R15 0135 C15 0009975R16 345R17 00213

Shunt Rcs 30075Rmbts 26316R18 00676R19 00676R20 00676R21 00133

4 Computational and Mathematical Methods in Medicine

than blood flow in LPA after the creation of the central shuntvirtually in simulation results of A-CS Prediction based onsimulation results indicated that when CS was performed forinfant A RPA tends to develop better than LPA After 11months the cross-sectional area of MPA increased by 70

and the cross-sectional area of RPA and LPA increased by290 and 90 respectively e results of PA growth after11 months were that the development of RPA was betterthan LPA which is consistent with the prediction based onthe simulation results of A-CS

Table 2 Haemodynamic variables of CS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Mean value 06 01 7852 7866 7857 7853 3085 3085

Table 3 Haemodynamic variables of MBTS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Meanvalue 06 01 7768 7751 7746 777 3132 3132

StreamlineLPA

RPA 2-2

11

22

35 26 18 09 0

Velocity (mmiddotsndash1)

1-1

(a)

StreamlineLPA

11

22

32 24

Velocity (mmiddotsndash1)

16 08 0

RPA

1-1

2-2

(b)

Figure 3 Streamline and velocity vector plots at CS (a) A-CS (b) B-CS

StreamlineLPA

RPA2-2

11

22

33 24 16 08 0

Velocity (mmiddotsndash1)

1-1

(a)

Streamline

11

22

30 23

Velocity (mmiddotsndash1)

15 08 0

RPA

LPA1-1

2-2

(b)

Figure 4 Streamline and velocity vector plots at MBTS (a) A-MBTS (b) B-MBTS

Computational and Mathematical Methods in Medicine 5

e boundary condition of CS postsurgery was set as thesame in Table 1 On being subjected to high pressure gradientsand varying ow pulsatility SPS often develops unevenintraluminal narrowing or curvature distortion during therst months after implantation [28] As is shown in Figure 6maximum velocity in the shunt increases and shunt ratiodecreases from 3461 to 1817 due to distortion of theshunt In addition increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] after dis-tortion of the shunt Abnormal preoperative PA structure forCS such as size dierences between LPA and RPA bending ofMPA and sharp angle between RPA and MPA will lead toasymmetric LPARPA ow ere is a vicious spiral asym-metric LPARPA ow results in asymmetric development ofLPA and RPA in turn asymmetric development of LPA andRPA will lead to more asymmetric LPARPA ow e bloodow rate of RPA was 100 higher than that of LPA in A-CSWith the growth of the patients the blood ow rate of RPAwas 300 higher than that of LPA after 11 months

Infant B received an MBTS in the clinic Figure 7(a)shows the preoperative arterial geometry of infant B andFigure 7(b) shows the arterial geometry of patient B 8months after operation It can be seen from Figure 7 thatwith the growth of infant B IA gradually grows upward andtraction occurred in RPA which resulted in the bending ofthe RPA Preoperative B-MBTS simulation results showedthat there is a symmetric pulmonary artery ow after MBTSwas performed for infant B and therefore LPA and RPA candevelop symmetrically after operation However the cross-sectional area of MPA increased by 60 and LPA and RPAincreased by 500 and 30 after 8 months e develop-ment of LPA was being obviously better than that of RPAwhich is inconsistent with the simulation results of B-MBTS

ere are many factors aecting the development of PAin patients some of which are hard to predict for specicpatients In this study the ow statersquos changes before andafter surgery and factors aecting the growth of PA were

analysed from the perspective of haemodynamics eboundary condition of MBTS after surgery was set as thesame in Table 2 As is shown in Figure 8 inhomogeneousintraluminal stenosis occurs in the shunt as infant B growsleading to an increase in shunt resistance and a decrease inshunt ratio the shunt ratio decreased from 2614 to2055 Meanwhile intraluminal stenosis leads to the in-crease in wall shear stress which is an important cause ofthrombosis e formation of PA vortices and complex owstructures of PA were highly related to T-junction topologyof shunt anastomosis in MBTS which may result in ab-normal PA growth [4] Comparing the ow states of PAbefore deformation of RPA the vorticity of PA is higherwhen the PRA is bending as is shown in Figure 8 With thegrowth of patients on the one hand the eddy current in PAmay increase signicantly due to the traction phenomenoncaused by insucient reserved length of the shunt on theother hand the inhomogeneous narrowing of the shunt andbending of anastomosis increase ow resistance leading topulmonary ow and ow of RPA decreasing For patientswith MBTS the traction phenomenon is unfavourable forsymmetric development of LPA and RPA erefore theprediction of PA development based on patients with MBTSshould take into account not only the inuence of the PAstructure on symmetric development of LPA and RPA butalso the inuence of traction phenomenon when the lengthof a reserved shunt is insucient Although increasing thelength of the shunt will lead to an increase in energy loss anda decrease in shunt ratio a sucient reserved length ofMBTS according to patientrsquos preoperative specic condi-tions could prevent the occurrence of traction phenomenonand is conducive to symmetrical development of LPA andRPA after operation

e infants A and B selected in our study showedasymmetrical development of PA after operation For infantA with CS asymmetric ow of LPA and RPAwas induced byan abnormal PA structure before operation which resultedin asymmetric development of LPA and RPA after

RPA (A = 281cm2)

LPA (A = 185cm2)

MPA (A = 377cm2)

PA structure

(a)

PA structure

LPA (A = 352cm2)

MPA (815cm2)

RPA (A = 110cm2)

(b)

Figure 5 Arterial structure of infant A before (a) and after (b) surgery

6 Computational and Mathematical Methods in Medicine

operation e structure of PA is symmetrical before op-eration in patients B treated with MBTS but the tractionphenomenon of MBTS has a negative impact on post-operative symmetrical development of PA

4 Discussion

e common problem for the prognosis of SPS is highlyrelated to overflow and underflow Overflow means exces-sive shunt ratio and reduction in systemic circulation whichmay bring about complications such as congestive heart

failure Underflow indicated that PA flow is insufficient andoxygen saturation in the blood is too low to reach the idealresult of operation Our results demonstrated that CS hashigher PA blood flow rate compared to MBTS To ensuresufficient PA flow and prevent complications such as con-gestive heart failure CS could be preferred for cases withvery low PA overflow risk and MBTS for high PA overflowrisk e complex flow structures observed in RPA and LPAmay lead to abnormal PA growth Simulation results showsthat velocity distribution in LPA and RPA was relativelyuniform in CS which is consistent with the study by Bao

156(pa)

(mmiddotsndash1)

117

1 1

35 26 17 080

Velocity

78 39 WSS

WSS

Streamline Velocity

1-1

(a)

2 2

171(pa)

(mmiddotsndash1)

128

45 34 23 130

Velocity

86

WSS

Streamline Velocity

2-2

43 WSS

(b)

Figure 6 Streamline velocity contour and wall shear stress (WSS) plots at CS before (a) and after (b) surgery for infant A

RPA (A = 94cm2)LPA (A = 73cm2)

MPA (A = 373cm2)

PA structure

(a)

PA structure

RPA (A = 102cm2)LPA (A = 441cm2)

MPA (A = 618cm2)

(b)

Figure 7 Arterial structure of infant B before (a) and after (b) surgery

Computational and Mathematical Methods in Medicine 7

et al [31] Nevertheless an obvious swirling phenomenonoccurred at the RPA in MBTS resulting in formation of highvorticity regions

Whether to retain the MPA depends on the specificcondition of the patient It is notable that the flow state ofSPS with APBF is different from the flow state of SPS withoutAPBF Energy loss of CS is higher than that of MBTS whenthere is still APBF while the conclusion is opposite whenMPA was transected [4] For patients with underdevelopedmyocardium energy loss is an important evaluation pa-rameter erefore whether to retain MPA has certain in-fluence on the choice of an optimal operation plan

With the growth of infants who are affected by highpressure gradients and varying flow pulsatility SPS oftendevelops uneven intraluminal narrowing or curvature dis-tortion during the first months after implantation [28] Forinfants treated with CS and MBTS the stenosis or de-formation of the shunt after operation will lead to an in-crease in shunt resistance and a decrease in the shunt ratioIn addition the increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] afterdistortion of the shunt

Postoperative development of PA is the most commonconcern of SPS e development of LPA and RPA forpatients treated with CS is closer to natural developmentand the probability of LPA and RPA distortion is very smallin the long term However abnormal preoperative PAstructure will lead to asymmetric development of LPA andRPA after surgery like infant A in our study e LPARPA

ratio of MBTS approaches unity when compared with CSNevertheless when the length of reserved MBTS shunt isinsufficient traction phenomenon may occur leading toasymmetrical development of PA as seen in infant B in ourstudy

Although the lumped parameter method has been widelyused and recognized in biomechanics it still has somedeviations due to lack of clinical experiments In additionthe elasticity of the vascular wall was neglected in this studyand the fluid-solid couplingmethod will be considered in thenext work

5 Conclusion

For specific patients the selection of shunt configurationsshould take into account the shunt ratio energy loss LPARPA split flow ratio and other parameters Because of thehigh shunt ratio CS could be preferred for patients with verylow PA overflow risk

MBTS could be preferred for cases with underdevelopedmyocardium owing to low energy loss With the growth ofinfants the shunt ratio of infants decreases but maximumshear stress and distribution regions of high shear stress willincrease which raise the probability of thrombosis Velocitydistribution of CS in LPA and RPA is uniform which iscloser to natural development however the symmetricaldevelopment of LPA and RPA is greatly influenced by thepreoperative PA structure e LPARPA ratio of MBTSapproaches unity compared with CS but an insufficientlength of reserved MBTS shunt will lead to traction

Streamline WSS

WSS(Pa)

198 148 99 49 0

(a)

Streamline WSS

WSS(Pa)

214 161 107 54 0

(b)

Figure 8 Streamline and wall shear stress (WSS) plots at MBTS before (a) and after (b) surgery for infant B

8 Computational and Mathematical Methods in Medicine

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

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Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

(a) (c) (e)

(b) (d) (f)

Central

Central Righ

t mbt

inR

ight

mbt

in

IA

LCA

LSA

RPA

LPA

DAO

MPA

AAO

IALCA

LSA

DAO

LPA

RPA

AAO

MPA

Figure 1 ree-dimensional neonatal arteries model of infants A ((a) model A) and B ((b) model B) and central shunt (CS) configurationestablished for infants A ((c) A-CS) and B ((d) (B-CS)) modified BlalockndashTaussig shunt (MBTS) configuration established for infants A ((e)A-MBTS) and B ((f) B-MBTS) In order to simplify the model we neglected independent branching vessels e remaining vessels includeascending aorta (AAO) innominate artery (IA) left carotid artery (LCA) left subclavian artery (LSA) descending aorta (DAO) mainpulmonary artery (MPA) left pulmonary artery (LPA) and right pulmonary artery (RPA) e central shunts are placed between AAO andMPA e right-modified BlalockndashTaussig (MBT) innominate shunt connects IA to RPA

PC

L11

L13

R11

R13 C13

C11 C10

C12

C14R14

R15 C15

CardiacCv

R16

R17

IVC C9

R

CSRight MBT in

C1AAO

R1

LEA C8

R18

C2

L2R2 R5

C5

LCA

C3

IA

LUA

LSA

C6

R7

R21

L7

C7SVC

R6 L6

C4

R3 L3

L5

R19

R20 R4 L4L8 R8L9 R9

L1

L10 R10R12L12

RUA

Figure 2 Lumped parameters model LPM is made up of cardiac and pulmonary circulation (PC) ascending aorta (AAO) innominateartery (IA) left carotid artery (LCA) left subclavian artery (LSA) right upper extremity artery (RUA) left upper extremity artery (LUA)superior vena cava (SVC) lower extremities artery (LEA) and inferior vena cava (IVC)

Computational and Mathematical Methods in Medicine 3

24 Energy Loss LPARPA Ratio and Shunt Ratio efundamental purpose of a systemic-to-pulmonary arteryshunt is to provide the appropriate blood flow from systemiccirculation to pulmonary circulation to promote the devel-opment of PA LPARPA ratio (RLPARPA) and shunt ratio (η)are important parameters to evaluate shunt configurations

RLPARPA QLPA

QRPA

η QShunt

QAAO1113888 1113889 times 100

(4)

whereQLPAQPRAQShunt andQAAO indicate the volumetricflow rate at LPA RPA shunt and AAO

Energy loss Wloss is an indicator for evaluating hae-modynamic efficiency e smaller the energy loss thehigher the energy conversion efficiency of shunt configu-rations [26 27]

W Qv P +12ρv

21113874 1113875

Wloss 1113944 Winlet minus 1113944 Woutlet

(5)

where Qv P ρ and v indicate the volumetric flow rate staticpressure density andmean velocity1113936 Winlet is the sum of theinlet energy and 1113936 Woutlet is the sum of the outlet energy

3 Result

3D blood flow streamlines clearly show the flow state of SPS inFigures 3 and 4 A velocity vector diagram at corresponding

sections and partial enlargement of streamline of LPA andRPA are shown to describe the complex flow structures in PAwhich is closely related to abnormal growth of PA [4]

In Figure 3 aortic blood with high pressure and flow rateflows through the shunt and mixes with pulmonary blood inMPA e turbulence intensity in MPA is high and swirlsoccurred near anastomosis of MPA Velocity distribution inLPA and RPA is relatively uniform which is close to naturaldevelopment e blood flow rate of RPA in A-CS was 100higher than that of LPA and the blood flow rate of RPA inB-CS was 5 lower than that of LPA which indicated thatthe preoperative PA structure has an important influence onsymmetrical flow of LPA and RPA for patients with CSerefore the arterial structure of specific patients should beconsidered when LPARPA is an important parameter af-fecting shunt operation e shunt ratios of A-CS and B-CSare 3461 and 3419 respectively e ratio for infants Aand B was similar when CS was performed for two infantsdue to an identical shunt size

In Figure 4 aortic blood with high pressure and flow rateflows through the shunt and mixes with pulmonary blood inRPA which leads to high vorticity regions in RPA Velocitydistribution in LPA is relatively uniform while high vorticityregions in RPA result in an uneven velocity distribution inRPA Pulmonary blood flow of RPA in A-MBTS was 66higher than that of LPA and pulmonary blood flow of RPAin B-MBTS was 1 higher than that of LPA which dem-onstrates that the arterial structure also has an importanteffect on flow distribution of LPA and RPA for MBTS Eventhough the length and curvature of shunts are different theshunt ratio of A-MBTS and B-MBTS are close the shuntratios of A-MBTS and B-MBTS were 2529 and 2614respectively which indicated that the main factors affectingthe shunt ratio of MBTS is the diameter of the shunt Energyloss of CS was greater than that of MBTS for two infants Forinfant A energy loss of CS and MBTS was 016W and013W respectively for infant B energy loss of CS andMBTS was 011W and 008W respectively It is notable thatthe flow state of SPS without additional pulmonary bloodflow (APBF) [4] is different from the flow state of SPS withAPBE When there is still APBE energy loss of MBTS islower than that of CS while the conclusion is just the op-posite when MPA was transected [4] When CS (MBTS) wasperformed for patient A the LPARPA ratio was 049 (059)when CS (MBTS) was performed for patient B the LPARPAratio was 105 (099) is shows that the RPALPA ratio ofMBTS approaches unity when compared with CS that isMBTS can provide a more symmetrical flow between LPAand RPAe shunt ratio of CS is approximately 30 higherthan that of MBTS for infants A and B which indicates thatCS has a greater chance of congestive heart failure ere isanother point that the diameter of the MBT shunt is limitedby the size of the RPA CS could be preferred for patientswith narrow PA to prevent thrombosis due to small sizeshunts [10]

Infant A was presented with CS in the clinic Figure 5(a)shows the preoperative arterial geometry of infant A andFigure 5(b) shows the arterial geometry of patient A 11months after operation Blood flow in RPA was 50 higher

Table 1 Values of parameters in LPM

Block R(mmHgmiddotsml)

C(mlmmHg)

L(mmHgmiddots2

ml)AAQ R1 012 C1 0127 L1 00013IA R2 169 C2 00962 L2 000038LCA R3 1858 C3 008911 L3 000047LSA R4 1858 C4 008911 L4 000047RUA R5 1065 C5 01399 L5 000213LUA R6 05751 C6 01463 L6 000107SVC R7 1235 C7 07233 L7 00005LEA R8 0863 C8 001995 L8 0001248IVC R9 1453 C9 08571 L9 0000977

PC

R10 00075 C10 002394 L10 000049R11 01002 C11 000465 L11 0000488R12 00075 C12 002394 L12 000049R13 01002 C13 000465 L13 0000488

Cardiaccirculation

R14 0015 C14 00409R15 0135 C15 0009975R16 345R17 00213

Shunt Rcs 30075Rmbts 26316R18 00676R19 00676R20 00676R21 00133

4 Computational and Mathematical Methods in Medicine

than blood flow in LPA after the creation of the central shuntvirtually in simulation results of A-CS Prediction based onsimulation results indicated that when CS was performed forinfant A RPA tends to develop better than LPA After 11months the cross-sectional area of MPA increased by 70

and the cross-sectional area of RPA and LPA increased by290 and 90 respectively e results of PA growth after11 months were that the development of RPA was betterthan LPA which is consistent with the prediction based onthe simulation results of A-CS

Table 2 Haemodynamic variables of CS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Mean value 06 01 7852 7866 7857 7853 3085 3085

Table 3 Haemodynamic variables of MBTS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Meanvalue 06 01 7768 7751 7746 777 3132 3132

StreamlineLPA

RPA 2-2

11

22

35 26 18 09 0

Velocity (mmiddotsndash1)

1-1

(a)

StreamlineLPA

11

22

32 24

Velocity (mmiddotsndash1)

16 08 0

RPA

1-1

2-2

(b)

Figure 3 Streamline and velocity vector plots at CS (a) A-CS (b) B-CS

StreamlineLPA

RPA2-2

11

22

33 24 16 08 0

Velocity (mmiddotsndash1)

1-1

(a)

Streamline

11

22

30 23

Velocity (mmiddotsndash1)

15 08 0

RPA

LPA1-1

2-2

(b)

Figure 4 Streamline and velocity vector plots at MBTS (a) A-MBTS (b) B-MBTS

Computational and Mathematical Methods in Medicine 5

e boundary condition of CS postsurgery was set as thesame in Table 1 On being subjected to high pressure gradientsand varying ow pulsatility SPS often develops unevenintraluminal narrowing or curvature distortion during therst months after implantation [28] As is shown in Figure 6maximum velocity in the shunt increases and shunt ratiodecreases from 3461 to 1817 due to distortion of theshunt In addition increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] after dis-tortion of the shunt Abnormal preoperative PA structure forCS such as size dierences between LPA and RPA bending ofMPA and sharp angle between RPA and MPA will lead toasymmetric LPARPA ow ere is a vicious spiral asym-metric LPARPA ow results in asymmetric development ofLPA and RPA in turn asymmetric development of LPA andRPA will lead to more asymmetric LPARPA ow e bloodow rate of RPA was 100 higher than that of LPA in A-CSWith the growth of the patients the blood ow rate of RPAwas 300 higher than that of LPA after 11 months

Infant B received an MBTS in the clinic Figure 7(a)shows the preoperative arterial geometry of infant B andFigure 7(b) shows the arterial geometry of patient B 8months after operation It can be seen from Figure 7 thatwith the growth of infant B IA gradually grows upward andtraction occurred in RPA which resulted in the bending ofthe RPA Preoperative B-MBTS simulation results showedthat there is a symmetric pulmonary artery ow after MBTSwas performed for infant B and therefore LPA and RPA candevelop symmetrically after operation However the cross-sectional area of MPA increased by 60 and LPA and RPAincreased by 500 and 30 after 8 months e develop-ment of LPA was being obviously better than that of RPAwhich is inconsistent with the simulation results of B-MBTS

ere are many factors aecting the development of PAin patients some of which are hard to predict for specicpatients In this study the ow statersquos changes before andafter surgery and factors aecting the growth of PA were

analysed from the perspective of haemodynamics eboundary condition of MBTS after surgery was set as thesame in Table 2 As is shown in Figure 8 inhomogeneousintraluminal stenosis occurs in the shunt as infant B growsleading to an increase in shunt resistance and a decrease inshunt ratio the shunt ratio decreased from 2614 to2055 Meanwhile intraluminal stenosis leads to the in-crease in wall shear stress which is an important cause ofthrombosis e formation of PA vortices and complex owstructures of PA were highly related to T-junction topologyof shunt anastomosis in MBTS which may result in ab-normal PA growth [4] Comparing the ow states of PAbefore deformation of RPA the vorticity of PA is higherwhen the PRA is bending as is shown in Figure 8 With thegrowth of patients on the one hand the eddy current in PAmay increase signicantly due to the traction phenomenoncaused by insucient reserved length of the shunt on theother hand the inhomogeneous narrowing of the shunt andbending of anastomosis increase ow resistance leading topulmonary ow and ow of RPA decreasing For patientswith MBTS the traction phenomenon is unfavourable forsymmetric development of LPA and RPA erefore theprediction of PA development based on patients with MBTSshould take into account not only the inuence of the PAstructure on symmetric development of LPA and RPA butalso the inuence of traction phenomenon when the lengthof a reserved shunt is insucient Although increasing thelength of the shunt will lead to an increase in energy loss anda decrease in shunt ratio a sucient reserved length ofMBTS according to patientrsquos preoperative specic condi-tions could prevent the occurrence of traction phenomenonand is conducive to symmetrical development of LPA andRPA after operation

e infants A and B selected in our study showedasymmetrical development of PA after operation For infantA with CS asymmetric ow of LPA and RPAwas induced byan abnormal PA structure before operation which resultedin asymmetric development of LPA and RPA after

RPA (A = 281cm2)

LPA (A = 185cm2)

MPA (A = 377cm2)

PA structure

(a)

PA structure

LPA (A = 352cm2)

MPA (815cm2)

RPA (A = 110cm2)

(b)

Figure 5 Arterial structure of infant A before (a) and after (b) surgery

6 Computational and Mathematical Methods in Medicine

operation e structure of PA is symmetrical before op-eration in patients B treated with MBTS but the tractionphenomenon of MBTS has a negative impact on post-operative symmetrical development of PA

4 Discussion

e common problem for the prognosis of SPS is highlyrelated to overflow and underflow Overflow means exces-sive shunt ratio and reduction in systemic circulation whichmay bring about complications such as congestive heart

failure Underflow indicated that PA flow is insufficient andoxygen saturation in the blood is too low to reach the idealresult of operation Our results demonstrated that CS hashigher PA blood flow rate compared to MBTS To ensuresufficient PA flow and prevent complications such as con-gestive heart failure CS could be preferred for cases withvery low PA overflow risk and MBTS for high PA overflowrisk e complex flow structures observed in RPA and LPAmay lead to abnormal PA growth Simulation results showsthat velocity distribution in LPA and RPA was relativelyuniform in CS which is consistent with the study by Bao

156(pa)

(mmiddotsndash1)

117

1 1

35 26 17 080

Velocity

78 39 WSS

WSS

Streamline Velocity

1-1

(a)

2 2

171(pa)

(mmiddotsndash1)

128

45 34 23 130

Velocity

86

WSS

Streamline Velocity

2-2

43 WSS

(b)

Figure 6 Streamline velocity contour and wall shear stress (WSS) plots at CS before (a) and after (b) surgery for infant A

RPA (A = 94cm2)LPA (A = 73cm2)

MPA (A = 373cm2)

PA structure

(a)

PA structure

RPA (A = 102cm2)LPA (A = 441cm2)

MPA (A = 618cm2)

(b)

Figure 7 Arterial structure of infant B before (a) and after (b) surgery

Computational and Mathematical Methods in Medicine 7

et al [31] Nevertheless an obvious swirling phenomenonoccurred at the RPA in MBTS resulting in formation of highvorticity regions

Whether to retain the MPA depends on the specificcondition of the patient It is notable that the flow state ofSPS with APBF is different from the flow state of SPS withoutAPBF Energy loss of CS is higher than that of MBTS whenthere is still APBF while the conclusion is opposite whenMPA was transected [4] For patients with underdevelopedmyocardium energy loss is an important evaluation pa-rameter erefore whether to retain MPA has certain in-fluence on the choice of an optimal operation plan

With the growth of infants who are affected by highpressure gradients and varying flow pulsatility SPS oftendevelops uneven intraluminal narrowing or curvature dis-tortion during the first months after implantation [28] Forinfants treated with CS and MBTS the stenosis or de-formation of the shunt after operation will lead to an in-crease in shunt resistance and a decrease in the shunt ratioIn addition the increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] afterdistortion of the shunt

Postoperative development of PA is the most commonconcern of SPS e development of LPA and RPA forpatients treated with CS is closer to natural developmentand the probability of LPA and RPA distortion is very smallin the long term However abnormal preoperative PAstructure will lead to asymmetric development of LPA andRPA after surgery like infant A in our study e LPARPA

ratio of MBTS approaches unity when compared with CSNevertheless when the length of reserved MBTS shunt isinsufficient traction phenomenon may occur leading toasymmetrical development of PA as seen in infant B in ourstudy

Although the lumped parameter method has been widelyused and recognized in biomechanics it still has somedeviations due to lack of clinical experiments In additionthe elasticity of the vascular wall was neglected in this studyand the fluid-solid couplingmethod will be considered in thenext work

5 Conclusion

For specific patients the selection of shunt configurationsshould take into account the shunt ratio energy loss LPARPA split flow ratio and other parameters Because of thehigh shunt ratio CS could be preferred for patients with verylow PA overflow risk

MBTS could be preferred for cases with underdevelopedmyocardium owing to low energy loss With the growth ofinfants the shunt ratio of infants decreases but maximumshear stress and distribution regions of high shear stress willincrease which raise the probability of thrombosis Velocitydistribution of CS in LPA and RPA is uniform which iscloser to natural development however the symmetricaldevelopment of LPA and RPA is greatly influenced by thepreoperative PA structure e LPARPA ratio of MBTSapproaches unity compared with CS but an insufficientlength of reserved MBTS shunt will lead to traction

Streamline WSS

WSS(Pa)

198 148 99 49 0

(a)

Streamline WSS

WSS(Pa)

214 161 107 54 0

(b)

Figure 8 Streamline and wall shear stress (WSS) plots at MBTS before (a) and after (b) surgery for infant B

8 Computational and Mathematical Methods in Medicine

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

24 Energy Loss LPARPA Ratio and Shunt Ratio efundamental purpose of a systemic-to-pulmonary arteryshunt is to provide the appropriate blood flow from systemiccirculation to pulmonary circulation to promote the devel-opment of PA LPARPA ratio (RLPARPA) and shunt ratio (η)are important parameters to evaluate shunt configurations

RLPARPA QLPA

QRPA

η QShunt

QAAO1113888 1113889 times 100

(4)

whereQLPAQPRAQShunt andQAAO indicate the volumetricflow rate at LPA RPA shunt and AAO

Energy loss Wloss is an indicator for evaluating hae-modynamic efficiency e smaller the energy loss thehigher the energy conversion efficiency of shunt configu-rations [26 27]

W Qv P +12ρv

21113874 1113875

Wloss 1113944 Winlet minus 1113944 Woutlet

(5)

where Qv P ρ and v indicate the volumetric flow rate staticpressure density andmean velocity1113936 Winlet is the sum of theinlet energy and 1113936 Woutlet is the sum of the outlet energy

3 Result

3D blood flow streamlines clearly show the flow state of SPS inFigures 3 and 4 A velocity vector diagram at corresponding

sections and partial enlargement of streamline of LPA andRPA are shown to describe the complex flow structures in PAwhich is closely related to abnormal growth of PA [4]

In Figure 3 aortic blood with high pressure and flow rateflows through the shunt and mixes with pulmonary blood inMPA e turbulence intensity in MPA is high and swirlsoccurred near anastomosis of MPA Velocity distribution inLPA and RPA is relatively uniform which is close to naturaldevelopment e blood flow rate of RPA in A-CS was 100higher than that of LPA and the blood flow rate of RPA inB-CS was 5 lower than that of LPA which indicated thatthe preoperative PA structure has an important influence onsymmetrical flow of LPA and RPA for patients with CSerefore the arterial structure of specific patients should beconsidered when LPARPA is an important parameter af-fecting shunt operation e shunt ratios of A-CS and B-CSare 3461 and 3419 respectively e ratio for infants Aand B was similar when CS was performed for two infantsdue to an identical shunt size

In Figure 4 aortic blood with high pressure and flow rateflows through the shunt and mixes with pulmonary blood inRPA which leads to high vorticity regions in RPA Velocitydistribution in LPA is relatively uniform while high vorticityregions in RPA result in an uneven velocity distribution inRPA Pulmonary blood flow of RPA in A-MBTS was 66higher than that of LPA and pulmonary blood flow of RPAin B-MBTS was 1 higher than that of LPA which dem-onstrates that the arterial structure also has an importanteffect on flow distribution of LPA and RPA for MBTS Eventhough the length and curvature of shunts are different theshunt ratio of A-MBTS and B-MBTS are close the shuntratios of A-MBTS and B-MBTS were 2529 and 2614respectively which indicated that the main factors affectingthe shunt ratio of MBTS is the diameter of the shunt Energyloss of CS was greater than that of MBTS for two infants Forinfant A energy loss of CS and MBTS was 016W and013W respectively for infant B energy loss of CS andMBTS was 011W and 008W respectively It is notable thatthe flow state of SPS without additional pulmonary bloodflow (APBF) [4] is different from the flow state of SPS withAPBE When there is still APBE energy loss of MBTS islower than that of CS while the conclusion is just the op-posite when MPA was transected [4] When CS (MBTS) wasperformed for patient A the LPARPA ratio was 049 (059)when CS (MBTS) was performed for patient B the LPARPAratio was 105 (099) is shows that the RPALPA ratio ofMBTS approaches unity when compared with CS that isMBTS can provide a more symmetrical flow between LPAand RPAe shunt ratio of CS is approximately 30 higherthan that of MBTS for infants A and B which indicates thatCS has a greater chance of congestive heart failure ere isanother point that the diameter of the MBT shunt is limitedby the size of the RPA CS could be preferred for patientswith narrow PA to prevent thrombosis due to small sizeshunts [10]

Infant A was presented with CS in the clinic Figure 5(a)shows the preoperative arterial geometry of infant A andFigure 5(b) shows the arterial geometry of patient A 11months after operation Blood flow in RPA was 50 higher

Table 1 Values of parameters in LPM

Block R(mmHgmiddotsml)

C(mlmmHg)

L(mmHgmiddots2

ml)AAQ R1 012 C1 0127 L1 00013IA R2 169 C2 00962 L2 000038LCA R3 1858 C3 008911 L3 000047LSA R4 1858 C4 008911 L4 000047RUA R5 1065 C5 01399 L5 000213LUA R6 05751 C6 01463 L6 000107SVC R7 1235 C7 07233 L7 00005LEA R8 0863 C8 001995 L8 0001248IVC R9 1453 C9 08571 L9 0000977

PC

R10 00075 C10 002394 L10 000049R11 01002 C11 000465 L11 0000488R12 00075 C12 002394 L12 000049R13 01002 C13 000465 L13 0000488

Cardiaccirculation

R14 0015 C14 00409R15 0135 C15 0009975R16 345R17 00213

Shunt Rcs 30075Rmbts 26316R18 00676R19 00676R20 00676R21 00133

4 Computational and Mathematical Methods in Medicine

than blood flow in LPA after the creation of the central shuntvirtually in simulation results of A-CS Prediction based onsimulation results indicated that when CS was performed forinfant A RPA tends to develop better than LPA After 11months the cross-sectional area of MPA increased by 70

and the cross-sectional area of RPA and LPA increased by290 and 90 respectively e results of PA growth after11 months were that the development of RPA was betterthan LPA which is consistent with the prediction based onthe simulation results of A-CS

Table 2 Haemodynamic variables of CS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Mean value 06 01 7852 7866 7857 7853 3085 3085

Table 3 Haemodynamic variables of MBTS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Meanvalue 06 01 7768 7751 7746 777 3132 3132

StreamlineLPA

RPA 2-2

11

22

35 26 18 09 0

Velocity (mmiddotsndash1)

1-1

(a)

StreamlineLPA

11

22

32 24

Velocity (mmiddotsndash1)

16 08 0

RPA

1-1

2-2

(b)

Figure 3 Streamline and velocity vector plots at CS (a) A-CS (b) B-CS

StreamlineLPA

RPA2-2

11

22

33 24 16 08 0

Velocity (mmiddotsndash1)

1-1

(a)

Streamline

11

22

30 23

Velocity (mmiddotsndash1)

15 08 0

RPA

LPA1-1

2-2

(b)

Figure 4 Streamline and velocity vector plots at MBTS (a) A-MBTS (b) B-MBTS

Computational and Mathematical Methods in Medicine 5

e boundary condition of CS postsurgery was set as thesame in Table 1 On being subjected to high pressure gradientsand varying ow pulsatility SPS often develops unevenintraluminal narrowing or curvature distortion during therst months after implantation [28] As is shown in Figure 6maximum velocity in the shunt increases and shunt ratiodecreases from 3461 to 1817 due to distortion of theshunt In addition increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] after dis-tortion of the shunt Abnormal preoperative PA structure forCS such as size dierences between LPA and RPA bending ofMPA and sharp angle between RPA and MPA will lead toasymmetric LPARPA ow ere is a vicious spiral asym-metric LPARPA ow results in asymmetric development ofLPA and RPA in turn asymmetric development of LPA andRPA will lead to more asymmetric LPARPA ow e bloodow rate of RPA was 100 higher than that of LPA in A-CSWith the growth of the patients the blood ow rate of RPAwas 300 higher than that of LPA after 11 months

Infant B received an MBTS in the clinic Figure 7(a)shows the preoperative arterial geometry of infant B andFigure 7(b) shows the arterial geometry of patient B 8months after operation It can be seen from Figure 7 thatwith the growth of infant B IA gradually grows upward andtraction occurred in RPA which resulted in the bending ofthe RPA Preoperative B-MBTS simulation results showedthat there is a symmetric pulmonary artery ow after MBTSwas performed for infant B and therefore LPA and RPA candevelop symmetrically after operation However the cross-sectional area of MPA increased by 60 and LPA and RPAincreased by 500 and 30 after 8 months e develop-ment of LPA was being obviously better than that of RPAwhich is inconsistent with the simulation results of B-MBTS

ere are many factors aecting the development of PAin patients some of which are hard to predict for specicpatients In this study the ow statersquos changes before andafter surgery and factors aecting the growth of PA were

analysed from the perspective of haemodynamics eboundary condition of MBTS after surgery was set as thesame in Table 2 As is shown in Figure 8 inhomogeneousintraluminal stenosis occurs in the shunt as infant B growsleading to an increase in shunt resistance and a decrease inshunt ratio the shunt ratio decreased from 2614 to2055 Meanwhile intraluminal stenosis leads to the in-crease in wall shear stress which is an important cause ofthrombosis e formation of PA vortices and complex owstructures of PA were highly related to T-junction topologyof shunt anastomosis in MBTS which may result in ab-normal PA growth [4] Comparing the ow states of PAbefore deformation of RPA the vorticity of PA is higherwhen the PRA is bending as is shown in Figure 8 With thegrowth of patients on the one hand the eddy current in PAmay increase signicantly due to the traction phenomenoncaused by insucient reserved length of the shunt on theother hand the inhomogeneous narrowing of the shunt andbending of anastomosis increase ow resistance leading topulmonary ow and ow of RPA decreasing For patientswith MBTS the traction phenomenon is unfavourable forsymmetric development of LPA and RPA erefore theprediction of PA development based on patients with MBTSshould take into account not only the inuence of the PAstructure on symmetric development of LPA and RPA butalso the inuence of traction phenomenon when the lengthof a reserved shunt is insucient Although increasing thelength of the shunt will lead to an increase in energy loss anda decrease in shunt ratio a sucient reserved length ofMBTS according to patientrsquos preoperative specic condi-tions could prevent the occurrence of traction phenomenonand is conducive to symmetrical development of LPA andRPA after operation

e infants A and B selected in our study showedasymmetrical development of PA after operation For infantA with CS asymmetric ow of LPA and RPAwas induced byan abnormal PA structure before operation which resultedin asymmetric development of LPA and RPA after

RPA (A = 281cm2)

LPA (A = 185cm2)

MPA (A = 377cm2)

PA structure

(a)

PA structure

LPA (A = 352cm2)

MPA (815cm2)

RPA (A = 110cm2)

(b)

Figure 5 Arterial structure of infant A before (a) and after (b) surgery

6 Computational and Mathematical Methods in Medicine

operation e structure of PA is symmetrical before op-eration in patients B treated with MBTS but the tractionphenomenon of MBTS has a negative impact on post-operative symmetrical development of PA

4 Discussion

e common problem for the prognosis of SPS is highlyrelated to overflow and underflow Overflow means exces-sive shunt ratio and reduction in systemic circulation whichmay bring about complications such as congestive heart

failure Underflow indicated that PA flow is insufficient andoxygen saturation in the blood is too low to reach the idealresult of operation Our results demonstrated that CS hashigher PA blood flow rate compared to MBTS To ensuresufficient PA flow and prevent complications such as con-gestive heart failure CS could be preferred for cases withvery low PA overflow risk and MBTS for high PA overflowrisk e complex flow structures observed in RPA and LPAmay lead to abnormal PA growth Simulation results showsthat velocity distribution in LPA and RPA was relativelyuniform in CS which is consistent with the study by Bao

156(pa)

(mmiddotsndash1)

117

1 1

35 26 17 080

Velocity

78 39 WSS

WSS

Streamline Velocity

1-1

(a)

2 2

171(pa)

(mmiddotsndash1)

128

45 34 23 130

Velocity

86

WSS

Streamline Velocity

2-2

43 WSS

(b)

Figure 6 Streamline velocity contour and wall shear stress (WSS) plots at CS before (a) and after (b) surgery for infant A

RPA (A = 94cm2)LPA (A = 73cm2)

MPA (A = 373cm2)

PA structure

(a)

PA structure

RPA (A = 102cm2)LPA (A = 441cm2)

MPA (A = 618cm2)

(b)

Figure 7 Arterial structure of infant B before (a) and after (b) surgery

Computational and Mathematical Methods in Medicine 7

et al [31] Nevertheless an obvious swirling phenomenonoccurred at the RPA in MBTS resulting in formation of highvorticity regions

Whether to retain the MPA depends on the specificcondition of the patient It is notable that the flow state ofSPS with APBF is different from the flow state of SPS withoutAPBF Energy loss of CS is higher than that of MBTS whenthere is still APBF while the conclusion is opposite whenMPA was transected [4] For patients with underdevelopedmyocardium energy loss is an important evaluation pa-rameter erefore whether to retain MPA has certain in-fluence on the choice of an optimal operation plan

With the growth of infants who are affected by highpressure gradients and varying flow pulsatility SPS oftendevelops uneven intraluminal narrowing or curvature dis-tortion during the first months after implantation [28] Forinfants treated with CS and MBTS the stenosis or de-formation of the shunt after operation will lead to an in-crease in shunt resistance and a decrease in the shunt ratioIn addition the increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] afterdistortion of the shunt

Postoperative development of PA is the most commonconcern of SPS e development of LPA and RPA forpatients treated with CS is closer to natural developmentand the probability of LPA and RPA distortion is very smallin the long term However abnormal preoperative PAstructure will lead to asymmetric development of LPA andRPA after surgery like infant A in our study e LPARPA

ratio of MBTS approaches unity when compared with CSNevertheless when the length of reserved MBTS shunt isinsufficient traction phenomenon may occur leading toasymmetrical development of PA as seen in infant B in ourstudy

Although the lumped parameter method has been widelyused and recognized in biomechanics it still has somedeviations due to lack of clinical experiments In additionthe elasticity of the vascular wall was neglected in this studyand the fluid-solid couplingmethod will be considered in thenext work

5 Conclusion

For specific patients the selection of shunt configurationsshould take into account the shunt ratio energy loss LPARPA split flow ratio and other parameters Because of thehigh shunt ratio CS could be preferred for patients with verylow PA overflow risk

MBTS could be preferred for cases with underdevelopedmyocardium owing to low energy loss With the growth ofinfants the shunt ratio of infants decreases but maximumshear stress and distribution regions of high shear stress willincrease which raise the probability of thrombosis Velocitydistribution of CS in LPA and RPA is uniform which iscloser to natural development however the symmetricaldevelopment of LPA and RPA is greatly influenced by thepreoperative PA structure e LPARPA ratio of MBTSapproaches unity compared with CS but an insufficientlength of reserved MBTS shunt will lead to traction

Streamline WSS

WSS(Pa)

198 148 99 49 0

(a)

Streamline WSS

WSS(Pa)

214 161 107 54 0

(b)

Figure 8 Streamline and wall shear stress (WSS) plots at MBTS before (a) and after (b) surgery for infant B

8 Computational and Mathematical Methods in Medicine

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

than blood flow in LPA after the creation of the central shuntvirtually in simulation results of A-CS Prediction based onsimulation results indicated that when CS was performed forinfant A RPA tends to develop better than LPA After 11months the cross-sectional area of MPA increased by 70

and the cross-sectional area of RPA and LPA increased by290 and 90 respectively e results of PA growth after11 months were that the development of RPA was betterthan LPA which is consistent with the prediction based onthe simulation results of A-CS

Table 2 Haemodynamic variables of CS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Mean value 06 01 7852 7866 7857 7853 3085 3085

Table 3 Haemodynamic variables of MBTS computed by lump parameters model

Boundarycondition

AAO(ms)

MPA(ms)

LSA(mmHg)

IA(mmHg)

LCA(mmHg)

DAO(mmHg)

LPA(mmHg)

RPA(mmHg)

Meanvalue 06 01 7768 7751 7746 777 3132 3132

StreamlineLPA

RPA 2-2

11

22

35 26 18 09 0

Velocity (mmiddotsndash1)

1-1

(a)

StreamlineLPA

11

22

32 24

Velocity (mmiddotsndash1)

16 08 0

RPA

1-1

2-2

(b)

Figure 3 Streamline and velocity vector plots at CS (a) A-CS (b) B-CS

StreamlineLPA

RPA2-2

11

22

33 24 16 08 0

Velocity (mmiddotsndash1)

1-1

(a)

Streamline

11

22

30 23

Velocity (mmiddotsndash1)

15 08 0

RPA

LPA1-1

2-2

(b)

Figure 4 Streamline and velocity vector plots at MBTS (a) A-MBTS (b) B-MBTS

Computational and Mathematical Methods in Medicine 5

e boundary condition of CS postsurgery was set as thesame in Table 1 On being subjected to high pressure gradientsand varying ow pulsatility SPS often develops unevenintraluminal narrowing or curvature distortion during therst months after implantation [28] As is shown in Figure 6maximum velocity in the shunt increases and shunt ratiodecreases from 3461 to 1817 due to distortion of theshunt In addition increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] after dis-tortion of the shunt Abnormal preoperative PA structure forCS such as size dierences between LPA and RPA bending ofMPA and sharp angle between RPA and MPA will lead toasymmetric LPARPA ow ere is a vicious spiral asym-metric LPARPA ow results in asymmetric development ofLPA and RPA in turn asymmetric development of LPA andRPA will lead to more asymmetric LPARPA ow e bloodow rate of RPA was 100 higher than that of LPA in A-CSWith the growth of the patients the blood ow rate of RPAwas 300 higher than that of LPA after 11 months

Infant B received an MBTS in the clinic Figure 7(a)shows the preoperative arterial geometry of infant B andFigure 7(b) shows the arterial geometry of patient B 8months after operation It can be seen from Figure 7 thatwith the growth of infant B IA gradually grows upward andtraction occurred in RPA which resulted in the bending ofthe RPA Preoperative B-MBTS simulation results showedthat there is a symmetric pulmonary artery ow after MBTSwas performed for infant B and therefore LPA and RPA candevelop symmetrically after operation However the cross-sectional area of MPA increased by 60 and LPA and RPAincreased by 500 and 30 after 8 months e develop-ment of LPA was being obviously better than that of RPAwhich is inconsistent with the simulation results of B-MBTS

ere are many factors aecting the development of PAin patients some of which are hard to predict for specicpatients In this study the ow statersquos changes before andafter surgery and factors aecting the growth of PA were

analysed from the perspective of haemodynamics eboundary condition of MBTS after surgery was set as thesame in Table 2 As is shown in Figure 8 inhomogeneousintraluminal stenosis occurs in the shunt as infant B growsleading to an increase in shunt resistance and a decrease inshunt ratio the shunt ratio decreased from 2614 to2055 Meanwhile intraluminal stenosis leads to the in-crease in wall shear stress which is an important cause ofthrombosis e formation of PA vortices and complex owstructures of PA were highly related to T-junction topologyof shunt anastomosis in MBTS which may result in ab-normal PA growth [4] Comparing the ow states of PAbefore deformation of RPA the vorticity of PA is higherwhen the PRA is bending as is shown in Figure 8 With thegrowth of patients on the one hand the eddy current in PAmay increase signicantly due to the traction phenomenoncaused by insucient reserved length of the shunt on theother hand the inhomogeneous narrowing of the shunt andbending of anastomosis increase ow resistance leading topulmonary ow and ow of RPA decreasing For patientswith MBTS the traction phenomenon is unfavourable forsymmetric development of LPA and RPA erefore theprediction of PA development based on patients with MBTSshould take into account not only the inuence of the PAstructure on symmetric development of LPA and RPA butalso the inuence of traction phenomenon when the lengthof a reserved shunt is insucient Although increasing thelength of the shunt will lead to an increase in energy loss anda decrease in shunt ratio a sucient reserved length ofMBTS according to patientrsquos preoperative specic condi-tions could prevent the occurrence of traction phenomenonand is conducive to symmetrical development of LPA andRPA after operation

e infants A and B selected in our study showedasymmetrical development of PA after operation For infantA with CS asymmetric ow of LPA and RPAwas induced byan abnormal PA structure before operation which resultedin asymmetric development of LPA and RPA after

RPA (A = 281cm2)

LPA (A = 185cm2)

MPA (A = 377cm2)

PA structure

(a)

PA structure

LPA (A = 352cm2)

MPA (815cm2)

RPA (A = 110cm2)

(b)

Figure 5 Arterial structure of infant A before (a) and after (b) surgery

6 Computational and Mathematical Methods in Medicine

operation e structure of PA is symmetrical before op-eration in patients B treated with MBTS but the tractionphenomenon of MBTS has a negative impact on post-operative symmetrical development of PA

4 Discussion

e common problem for the prognosis of SPS is highlyrelated to overflow and underflow Overflow means exces-sive shunt ratio and reduction in systemic circulation whichmay bring about complications such as congestive heart

failure Underflow indicated that PA flow is insufficient andoxygen saturation in the blood is too low to reach the idealresult of operation Our results demonstrated that CS hashigher PA blood flow rate compared to MBTS To ensuresufficient PA flow and prevent complications such as con-gestive heart failure CS could be preferred for cases withvery low PA overflow risk and MBTS for high PA overflowrisk e complex flow structures observed in RPA and LPAmay lead to abnormal PA growth Simulation results showsthat velocity distribution in LPA and RPA was relativelyuniform in CS which is consistent with the study by Bao

156(pa)

(mmiddotsndash1)

117

1 1

35 26 17 080

Velocity

78 39 WSS

WSS

Streamline Velocity

1-1

(a)

2 2

171(pa)

(mmiddotsndash1)

128

45 34 23 130

Velocity

86

WSS

Streamline Velocity

2-2

43 WSS

(b)

Figure 6 Streamline velocity contour and wall shear stress (WSS) plots at CS before (a) and after (b) surgery for infant A

RPA (A = 94cm2)LPA (A = 73cm2)

MPA (A = 373cm2)

PA structure

(a)

PA structure

RPA (A = 102cm2)LPA (A = 441cm2)

MPA (A = 618cm2)

(b)

Figure 7 Arterial structure of infant B before (a) and after (b) surgery

Computational and Mathematical Methods in Medicine 7

et al [31] Nevertheless an obvious swirling phenomenonoccurred at the RPA in MBTS resulting in formation of highvorticity regions

Whether to retain the MPA depends on the specificcondition of the patient It is notable that the flow state ofSPS with APBF is different from the flow state of SPS withoutAPBF Energy loss of CS is higher than that of MBTS whenthere is still APBF while the conclusion is opposite whenMPA was transected [4] For patients with underdevelopedmyocardium energy loss is an important evaluation pa-rameter erefore whether to retain MPA has certain in-fluence on the choice of an optimal operation plan

With the growth of infants who are affected by highpressure gradients and varying flow pulsatility SPS oftendevelops uneven intraluminal narrowing or curvature dis-tortion during the first months after implantation [28] Forinfants treated with CS and MBTS the stenosis or de-formation of the shunt after operation will lead to an in-crease in shunt resistance and a decrease in the shunt ratioIn addition the increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] afterdistortion of the shunt

Postoperative development of PA is the most commonconcern of SPS e development of LPA and RPA forpatients treated with CS is closer to natural developmentand the probability of LPA and RPA distortion is very smallin the long term However abnormal preoperative PAstructure will lead to asymmetric development of LPA andRPA after surgery like infant A in our study e LPARPA

ratio of MBTS approaches unity when compared with CSNevertheless when the length of reserved MBTS shunt isinsufficient traction phenomenon may occur leading toasymmetrical development of PA as seen in infant B in ourstudy

Although the lumped parameter method has been widelyused and recognized in biomechanics it still has somedeviations due to lack of clinical experiments In additionthe elasticity of the vascular wall was neglected in this studyand the fluid-solid couplingmethod will be considered in thenext work

5 Conclusion

For specific patients the selection of shunt configurationsshould take into account the shunt ratio energy loss LPARPA split flow ratio and other parameters Because of thehigh shunt ratio CS could be preferred for patients with verylow PA overflow risk

MBTS could be preferred for cases with underdevelopedmyocardium owing to low energy loss With the growth ofinfants the shunt ratio of infants decreases but maximumshear stress and distribution regions of high shear stress willincrease which raise the probability of thrombosis Velocitydistribution of CS in LPA and RPA is uniform which iscloser to natural development however the symmetricaldevelopment of LPA and RPA is greatly influenced by thepreoperative PA structure e LPARPA ratio of MBTSapproaches unity compared with CS but an insufficientlength of reserved MBTS shunt will lead to traction

Streamline WSS

WSS(Pa)

198 148 99 49 0

(a)

Streamline WSS

WSS(Pa)

214 161 107 54 0

(b)

Figure 8 Streamline and wall shear stress (WSS) plots at MBTS before (a) and after (b) surgery for infant B

8 Computational and Mathematical Methods in Medicine

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

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Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

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Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

e boundary condition of CS postsurgery was set as thesame in Table 1 On being subjected to high pressure gradientsand varying ow pulsatility SPS often develops unevenintraluminal narrowing or curvature distortion during therst months after implantation [28] As is shown in Figure 6maximum velocity in the shunt increases and shunt ratiodecreases from 3461 to 1817 due to distortion of theshunt In addition increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] after dis-tortion of the shunt Abnormal preoperative PA structure forCS such as size dierences between LPA and RPA bending ofMPA and sharp angle between RPA and MPA will lead toasymmetric LPARPA ow ere is a vicious spiral asym-metric LPARPA ow results in asymmetric development ofLPA and RPA in turn asymmetric development of LPA andRPA will lead to more asymmetric LPARPA ow e bloodow rate of RPA was 100 higher than that of LPA in A-CSWith the growth of the patients the blood ow rate of RPAwas 300 higher than that of LPA after 11 months

Infant B received an MBTS in the clinic Figure 7(a)shows the preoperative arterial geometry of infant B andFigure 7(b) shows the arterial geometry of patient B 8months after operation It can be seen from Figure 7 thatwith the growth of infant B IA gradually grows upward andtraction occurred in RPA which resulted in the bending ofthe RPA Preoperative B-MBTS simulation results showedthat there is a symmetric pulmonary artery ow after MBTSwas performed for infant B and therefore LPA and RPA candevelop symmetrically after operation However the cross-sectional area of MPA increased by 60 and LPA and RPAincreased by 500 and 30 after 8 months e develop-ment of LPA was being obviously better than that of RPAwhich is inconsistent with the simulation results of B-MBTS

ere are many factors aecting the development of PAin patients some of which are hard to predict for specicpatients In this study the ow statersquos changes before andafter surgery and factors aecting the growth of PA were

analysed from the perspective of haemodynamics eboundary condition of MBTS after surgery was set as thesame in Table 2 As is shown in Figure 8 inhomogeneousintraluminal stenosis occurs in the shunt as infant B growsleading to an increase in shunt resistance and a decrease inshunt ratio the shunt ratio decreased from 2614 to2055 Meanwhile intraluminal stenosis leads to the in-crease in wall shear stress which is an important cause ofthrombosis e formation of PA vortices and complex owstructures of PA were highly related to T-junction topologyof shunt anastomosis in MBTS which may result in ab-normal PA growth [4] Comparing the ow states of PAbefore deformation of RPA the vorticity of PA is higherwhen the PRA is bending as is shown in Figure 8 With thegrowth of patients on the one hand the eddy current in PAmay increase signicantly due to the traction phenomenoncaused by insucient reserved length of the shunt on theother hand the inhomogeneous narrowing of the shunt andbending of anastomosis increase ow resistance leading topulmonary ow and ow of RPA decreasing For patientswith MBTS the traction phenomenon is unfavourable forsymmetric development of LPA and RPA erefore theprediction of PA development based on patients with MBTSshould take into account not only the inuence of the PAstructure on symmetric development of LPA and RPA butalso the inuence of traction phenomenon when the lengthof a reserved shunt is insucient Although increasing thelength of the shunt will lead to an increase in energy loss anda decrease in shunt ratio a sucient reserved length ofMBTS according to patientrsquos preoperative specic condi-tions could prevent the occurrence of traction phenomenonand is conducive to symmetrical development of LPA andRPA after operation

e infants A and B selected in our study showedasymmetrical development of PA after operation For infantA with CS asymmetric ow of LPA and RPAwas induced byan abnormal PA structure before operation which resultedin asymmetric development of LPA and RPA after

RPA (A = 281cm2)

LPA (A = 185cm2)

MPA (A = 377cm2)

PA structure

(a)

PA structure

LPA (A = 352cm2)

MPA (815cm2)

RPA (A = 110cm2)

(b)

Figure 5 Arterial structure of infant A before (a) and after (b) surgery

6 Computational and Mathematical Methods in Medicine

operation e structure of PA is symmetrical before op-eration in patients B treated with MBTS but the tractionphenomenon of MBTS has a negative impact on post-operative symmetrical development of PA

4 Discussion

e common problem for the prognosis of SPS is highlyrelated to overflow and underflow Overflow means exces-sive shunt ratio and reduction in systemic circulation whichmay bring about complications such as congestive heart

failure Underflow indicated that PA flow is insufficient andoxygen saturation in the blood is too low to reach the idealresult of operation Our results demonstrated that CS hashigher PA blood flow rate compared to MBTS To ensuresufficient PA flow and prevent complications such as con-gestive heart failure CS could be preferred for cases withvery low PA overflow risk and MBTS for high PA overflowrisk e complex flow structures observed in RPA and LPAmay lead to abnormal PA growth Simulation results showsthat velocity distribution in LPA and RPA was relativelyuniform in CS which is consistent with the study by Bao

156(pa)

(mmiddotsndash1)

117

1 1

35 26 17 080

Velocity

78 39 WSS

WSS

Streamline Velocity

1-1

(a)

2 2

171(pa)

(mmiddotsndash1)

128

45 34 23 130

Velocity

86

WSS

Streamline Velocity

2-2

43 WSS

(b)

Figure 6 Streamline velocity contour and wall shear stress (WSS) plots at CS before (a) and after (b) surgery for infant A

RPA (A = 94cm2)LPA (A = 73cm2)

MPA (A = 373cm2)

PA structure

(a)

PA structure

RPA (A = 102cm2)LPA (A = 441cm2)

MPA (A = 618cm2)

(b)

Figure 7 Arterial structure of infant B before (a) and after (b) surgery

Computational and Mathematical Methods in Medicine 7

et al [31] Nevertheless an obvious swirling phenomenonoccurred at the RPA in MBTS resulting in formation of highvorticity regions

Whether to retain the MPA depends on the specificcondition of the patient It is notable that the flow state ofSPS with APBF is different from the flow state of SPS withoutAPBF Energy loss of CS is higher than that of MBTS whenthere is still APBF while the conclusion is opposite whenMPA was transected [4] For patients with underdevelopedmyocardium energy loss is an important evaluation pa-rameter erefore whether to retain MPA has certain in-fluence on the choice of an optimal operation plan

With the growth of infants who are affected by highpressure gradients and varying flow pulsatility SPS oftendevelops uneven intraluminal narrowing or curvature dis-tortion during the first months after implantation [28] Forinfants treated with CS and MBTS the stenosis or de-formation of the shunt after operation will lead to an in-crease in shunt resistance and a decrease in the shunt ratioIn addition the increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] afterdistortion of the shunt

Postoperative development of PA is the most commonconcern of SPS e development of LPA and RPA forpatients treated with CS is closer to natural developmentand the probability of LPA and RPA distortion is very smallin the long term However abnormal preoperative PAstructure will lead to asymmetric development of LPA andRPA after surgery like infant A in our study e LPARPA

ratio of MBTS approaches unity when compared with CSNevertheless when the length of reserved MBTS shunt isinsufficient traction phenomenon may occur leading toasymmetrical development of PA as seen in infant B in ourstudy

Although the lumped parameter method has been widelyused and recognized in biomechanics it still has somedeviations due to lack of clinical experiments In additionthe elasticity of the vascular wall was neglected in this studyand the fluid-solid couplingmethod will be considered in thenext work

5 Conclusion

For specific patients the selection of shunt configurationsshould take into account the shunt ratio energy loss LPARPA split flow ratio and other parameters Because of thehigh shunt ratio CS could be preferred for patients with verylow PA overflow risk

MBTS could be preferred for cases with underdevelopedmyocardium owing to low energy loss With the growth ofinfants the shunt ratio of infants decreases but maximumshear stress and distribution regions of high shear stress willincrease which raise the probability of thrombosis Velocitydistribution of CS in LPA and RPA is uniform which iscloser to natural development however the symmetricaldevelopment of LPA and RPA is greatly influenced by thepreoperative PA structure e LPARPA ratio of MBTSapproaches unity compared with CS but an insufficientlength of reserved MBTS shunt will lead to traction

Streamline WSS

WSS(Pa)

198 148 99 49 0

(a)

Streamline WSS

WSS(Pa)

214 161 107 54 0

(b)

Figure 8 Streamline and wall shear stress (WSS) plots at MBTS before (a) and after (b) surgery for infant B

8 Computational and Mathematical Methods in Medicine

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

operation e structure of PA is symmetrical before op-eration in patients B treated with MBTS but the tractionphenomenon of MBTS has a negative impact on post-operative symmetrical development of PA

4 Discussion

e common problem for the prognosis of SPS is highlyrelated to overflow and underflow Overflow means exces-sive shunt ratio and reduction in systemic circulation whichmay bring about complications such as congestive heart

failure Underflow indicated that PA flow is insufficient andoxygen saturation in the blood is too low to reach the idealresult of operation Our results demonstrated that CS hashigher PA blood flow rate compared to MBTS To ensuresufficient PA flow and prevent complications such as con-gestive heart failure CS could be preferred for cases withvery low PA overflow risk and MBTS for high PA overflowrisk e complex flow structures observed in RPA and LPAmay lead to abnormal PA growth Simulation results showsthat velocity distribution in LPA and RPA was relativelyuniform in CS which is consistent with the study by Bao

156(pa)

(mmiddotsndash1)

117

1 1

35 26 17 080

Velocity

78 39 WSS

WSS

Streamline Velocity

1-1

(a)

2 2

171(pa)

(mmiddotsndash1)

128

45 34 23 130

Velocity

86

WSS

Streamline Velocity

2-2

43 WSS

(b)

Figure 6 Streamline velocity contour and wall shear stress (WSS) plots at CS before (a) and after (b) surgery for infant A

RPA (A = 94cm2)LPA (A = 73cm2)

MPA (A = 373cm2)

PA structure

(a)

PA structure

RPA (A = 102cm2)LPA (A = 441cm2)

MPA (A = 618cm2)

(b)

Figure 7 Arterial structure of infant B before (a) and after (b) surgery

Computational and Mathematical Methods in Medicine 7

et al [31] Nevertheless an obvious swirling phenomenonoccurred at the RPA in MBTS resulting in formation of highvorticity regions

Whether to retain the MPA depends on the specificcondition of the patient It is notable that the flow state ofSPS with APBF is different from the flow state of SPS withoutAPBF Energy loss of CS is higher than that of MBTS whenthere is still APBF while the conclusion is opposite whenMPA was transected [4] For patients with underdevelopedmyocardium energy loss is an important evaluation pa-rameter erefore whether to retain MPA has certain in-fluence on the choice of an optimal operation plan

With the growth of infants who are affected by highpressure gradients and varying flow pulsatility SPS oftendevelops uneven intraluminal narrowing or curvature dis-tortion during the first months after implantation [28] Forinfants treated with CS and MBTS the stenosis or de-formation of the shunt after operation will lead to an in-crease in shunt resistance and a decrease in the shunt ratioIn addition the increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] afterdistortion of the shunt

Postoperative development of PA is the most commonconcern of SPS e development of LPA and RPA forpatients treated with CS is closer to natural developmentand the probability of LPA and RPA distortion is very smallin the long term However abnormal preoperative PAstructure will lead to asymmetric development of LPA andRPA after surgery like infant A in our study e LPARPA

ratio of MBTS approaches unity when compared with CSNevertheless when the length of reserved MBTS shunt isinsufficient traction phenomenon may occur leading toasymmetrical development of PA as seen in infant B in ourstudy

Although the lumped parameter method has been widelyused and recognized in biomechanics it still has somedeviations due to lack of clinical experiments In additionthe elasticity of the vascular wall was neglected in this studyand the fluid-solid couplingmethod will be considered in thenext work

5 Conclusion

For specific patients the selection of shunt configurationsshould take into account the shunt ratio energy loss LPARPA split flow ratio and other parameters Because of thehigh shunt ratio CS could be preferred for patients with verylow PA overflow risk

MBTS could be preferred for cases with underdevelopedmyocardium owing to low energy loss With the growth ofinfants the shunt ratio of infants decreases but maximumshear stress and distribution regions of high shear stress willincrease which raise the probability of thrombosis Velocitydistribution of CS in LPA and RPA is uniform which iscloser to natural development however the symmetricaldevelopment of LPA and RPA is greatly influenced by thepreoperative PA structure e LPARPA ratio of MBTSapproaches unity compared with CS but an insufficientlength of reserved MBTS shunt will lead to traction

Streamline WSS

WSS(Pa)

198 148 99 49 0

(a)

Streamline WSS

WSS(Pa)

214 161 107 54 0

(b)

Figure 8 Streamline and wall shear stress (WSS) plots at MBTS before (a) and after (b) surgery for infant B

8 Computational and Mathematical Methods in Medicine

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

et al [31] Nevertheless an obvious swirling phenomenonoccurred at the RPA in MBTS resulting in formation of highvorticity regions

Whether to retain the MPA depends on the specificcondition of the patient It is notable that the flow state ofSPS with APBF is different from the flow state of SPS withoutAPBF Energy loss of CS is higher than that of MBTS whenthere is still APBF while the conclusion is opposite whenMPA was transected [4] For patients with underdevelopedmyocardium energy loss is an important evaluation pa-rameter erefore whether to retain MPA has certain in-fluence on the choice of an optimal operation plan

With the growth of infants who are affected by highpressure gradients and varying flow pulsatility SPS oftendevelops uneven intraluminal narrowing or curvature dis-tortion during the first months after implantation [28] Forinfants treated with CS and MBTS the stenosis or de-formation of the shunt after operation will lead to an in-crease in shunt resistance and a decrease in the shunt ratioIn addition the increase of maximum shear stress and highshear stress region may lead to thrombosis and a series ofcomplications such as intimal hyperplasia [29 30] afterdistortion of the shunt

Postoperative development of PA is the most commonconcern of SPS e development of LPA and RPA forpatients treated with CS is closer to natural developmentand the probability of LPA and RPA distortion is very smallin the long term However abnormal preoperative PAstructure will lead to asymmetric development of LPA andRPA after surgery like infant A in our study e LPARPA

ratio of MBTS approaches unity when compared with CSNevertheless when the length of reserved MBTS shunt isinsufficient traction phenomenon may occur leading toasymmetrical development of PA as seen in infant B in ourstudy

Although the lumped parameter method has been widelyused and recognized in biomechanics it still has somedeviations due to lack of clinical experiments In additionthe elasticity of the vascular wall was neglected in this studyand the fluid-solid couplingmethod will be considered in thenext work

5 Conclusion

For specific patients the selection of shunt configurationsshould take into account the shunt ratio energy loss LPARPA split flow ratio and other parameters Because of thehigh shunt ratio CS could be preferred for patients with verylow PA overflow risk

MBTS could be preferred for cases with underdevelopedmyocardium owing to low energy loss With the growth ofinfants the shunt ratio of infants decreases but maximumshear stress and distribution regions of high shear stress willincrease which raise the probability of thrombosis Velocitydistribution of CS in LPA and RPA is uniform which iscloser to natural development however the symmetricaldevelopment of LPA and RPA is greatly influenced by thepreoperative PA structure e LPARPA ratio of MBTSapproaches unity compared with CS but an insufficientlength of reserved MBTS shunt will lead to traction

Streamline WSS

WSS(Pa)

198 148 99 49 0

(a)

Streamline WSS

WSS(Pa)

214 161 107 54 0

(b)

Figure 8 Streamline and wall shear stress (WSS) plots at MBTS before (a) and after (b) surgery for infant B

8 Computational and Mathematical Methods in Medicine

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

phenomenon and increased eddy current in PA which is notconducive to symmetrical development of LPA and RPA

Data Availability

Previously reported data were used to support this study andare available at R7265 R31801 R31801 101152ajpheart20012805H2076 ese prior studies (and data-sets) are cited at relevant places within the text as references[5 17 21]

Disclosure

Neichuan Zhang and Haiyun Yuan are the co-first authors

Conflicts of Interest

e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Neichuan Zhang and Haiyun Yuan contributed equally tothis work

Acknowledgments

is study was supported by the Union of National NaturalScience Foundation of China-Guangdong Province(U1401255) the Natural Science Foundation of GuangdongProvince (2018A030313785) the National Key Research andDevelopment Program (2018YFC1002600) the Science andTechnology Planning Project of Guangdong Province (Nos2014A050503048 2017A070701013 2017B090904034 and2017B030314109)

References

[1] E Rodrıguez R Soler R Fernandez and I Raposo ldquoPost-operative imaging in cyanotic congenital heart diseases part1 normal findingsrdquo American Journal of Roentgenologyvol 189 no 6 pp 1353ndash1360 2007

[2] J J AmatoM LMarbey C Bush R J Galdieri J V Cotroneoand J Bushong ldquoSystemic pulmonary polytetrafluoroethyleneshunts in palliative operations for congenital heart surgeryRevival of the central shuntrdquo Journal of 5oracic and Car-diovascular Surgery vol 95 no 1 pp 62ndash69 1988

[3] Z Malota Z Nawrat and P Kostka ldquoComputer and physicalmodeling of blood circulation pump support for a new field ofapplication in palliative surgeryrdquo International Journal ofArtificial Organs vol 30 no 12 pp 1068ndash1074 2007

[4] S Piskin H F Altin O Yildiz I Bakir and K PekkanldquoHemodynamics of patient-specific aorta-pulmonary shuntconfigurationsrdquo Journal of Biomechanics vol 50 pp 166ndash1712017

[5] X C Ren Hemodynamic Geometrical Multiscale NumericalStudy on Modified Blalock Taussing Surgery with DifferentAnastomosis Beijing University of Technology BeijingChina 2014

[6] T-Y Hsia D Cosentino C Corsini et al ldquoUse of mathe-matical modeling to compare and predict hemodynamic ef-fects between hybrid and surgical norwood palliations for

hypoplastic left heart syndromerdquo Circulation vol 124 no 11pp S204ndashS210 2011

[7] P G G Pennati G Dubini and E L Bove ldquoModeling ofsystemic-to-pulmonary shunts in newborns with a uni-ventricular circulation state of the art and future directionsrdquoProgress in Pediatric Cardiology vol 30 no1-2 pp 23ndash29 2010

[8] S-M Kim and P Sung-Yun ldquoA study of systemic-to-pulmonary artery shunt deformation shape by CFD (com-putational fluid dynamics)rdquo International Journal of PrecisionEngineering and Manufacturing vol 11 no 1 pp 137ndash1432010

[9] F Migliavacca G Dubini G Pennati et al ldquoComputationalmodel of the fluid dynamics in systemic-to-pulmonaryshuntsrdquo Journal of Biomechanics vol 33 no 5 pp 549ndash557 2000

[10] E Sisli O N Tuncer S Senkaya et al ldquoBlalock-taussig shuntsize should it be based on body weight or target branchpulmonary artery sizerdquo Pediatric Cardiology 2018

[11] F J H Gijsen E Allanic F N van de Vosse and J D Janssenldquoe influence of the non-Newtonian properties of blood onthe flow in large arteries unsteady flow in a 90deg curved tuberdquoJournal of Biomechanics vol 32 no 7 pp 705ndash713 1999

[12] Y I Cho and K R Kensey ldquoEffects of the non-Newtonianviscosity of blood on flows in a diseased arterial vessel Part 1steady flowsrdquo Biorheology vol 28 no 3-4 pp 241ndash262 1991

[13] K Perktold R O Peter M Resch et al ldquoPulsatile non-Newtonian blood flow in three-dimensional carotid bi-furcation models a numerical study of flow phenomenaunder different bifurcation anglesrdquo Journal of BiomedicalEngineering vol 13 no 6 pp 507ndash515 1991

[14] B M Johnston P R Johnston S Corney and D KilpatrickldquoNon-Newtonian blood flow in human right coronary ar-teries steady state simulationsrdquo Journal of Biomechanicsvol 37 no 5 pp 709ndash720 2004

[15] S A Berger and L-D Jou ldquoFlows in stenotic vesselsrdquo AnnualReview of Fluid Mechanics vol 32 no 1 pp 347ndash382 2000

[16] M Esmaily-Moghadam T-Y B Murtuza and A MarsdenldquoSimulations reveal adverse hemodynamics in patients withmultiple systemic to pulmonary shuntsrdquo Journal of Bio-mechanical Engineering vol 137 no 3 article 031001 2015

[17] J Ding Numerical Study on Hemodynamics of CardiovascularSurgical Planning Beijing University of Technology BeijingChina 2013

[18] P Evegren L Fuchs and J Revstedt ldquoWall shear stressvariations in a 90-degree bifurcation in 3D pulsating flowsrdquoMedical Engineering amp Physics vol 32 no 2 pp 189ndash2022010

[19] K Perktold and G Rappitsch ldquoComputer simulation of localblood flow and vessel mechanics in a compliant carotid arterybifurcation modelrdquo Journal of Biomechanics vol 28 no 7pp 845ndash856 1995

[20] G Pennati F Migliavacca G Dubini R PietrabissaR Fumero andM R de Leval ldquoUse of mathematical model topredict hemodynamics in cavopulmonary anastomosis withpersistent forward flowrdquo Journal of Surgical Research vol 89no 1 pp 43ndash52 2000

[21] F Migliavacca G Pennati G Fumero et al ldquoModeling of theNorwood circulation effects of shunt size vascular re-sistances and heart raterdquo American Journal of Physiology-Heart and Circulatory Physiology vol 280 no 5pp H2076ndashH2086 2001

[22] R Pietrabissa S Mantero T Marotta and L Menicanti ldquoAlumped parameter model to evaluate the fluid dynamics of

Computational and Mathematical Methods in Medicine 9

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

different coronary bypassesrdquo Medical Engineering amp Physicsvol 18 no 6 pp 477ndash484 1996

[23] A L Goldberger L A N Amaral L E Glass et al ldquoPhys-ioBank PhysioToolkit and PhysioNetrdquo Circulation vol 101no 23 pp e215ndashe220 2000

[24] N Stergiopulos J J Meister and N Westerhof ldquoDe-terminants of stroke volume and systolic and diastolic aorticpressurerdquo American Journal of Physiology-Heart and Circu-latory Physiology vol 270 no 6 pp H2050ndashH2059 1996

[25] A C Benim A Nahavandi A Assmann D SchubertP Feindt and S H Suh ldquoSimulation of blood flow in humanaorta with emphasis on outlet boundary conditionsrdquo AppliedMathematical Modelling vol 35 no 7 pp 3175ndash3188 2011

[26] T-Y Hsia F Migliavacca S Pittaccio et al ldquoComputationalfluid dynamic study of flow optimization in realistic models ofthe total cavopulmonary connectionsrdquo Journal of SurgicalResearch vol 116 no 2 pp 305ndash313 2004

[27] F Migliavacca G Dubini E L Bove and M R de LevalldquoComputational fluid dynamics simulations in realistic 3-Dgeometries of the total cavopulmonary anastomosis the in-fluence of the inferior caval anastomosisrdquo Journal of Bio-mechanical Engineering vol 125 no 6 pp 805ndash813 2003

[28] M Bonnet J Petit V Lambert et al ldquoCatheter-based in-terventions for modified Blalock-Taussig shunt obstruction a20-year experiencerdquo Pediatric Cardiology vol 36 no 4pp 835ndash841 2015

[29] S K Shanmugavelayudam D A Rubenstein and W YinldquoEffects of physiologically relevant dynamic shear stress onplatelet complement activationrdquo Platelets vol 22 no 8pp 602ndash610 2011

[30] C Celestin M Guillot N Ross-Ascuitto and R AscuittoldquoComputational fluid dynamics characterization of blood flowin central aorta to pulmonary artery connections importanceof shunt angulation as a determinant of shear stress-inducedthrombosisrdquo Pediatric Cardiology vol 36 no 3 pp 600ndash6152014

[31] M Bao H Li G Pan Z Xu and Q Wu ldquoCentral shuntprocedures for complex congenital heart diseasesrdquo Journal ofCardiac Surgery vol 29 no 4 pp 537ndash541 2014

10 Computational and Mathematical Methods in Medicine

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

Stem Cells International

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Disease Markers

Hindawiwwwhindawicom Volume 2018

BioMed Research International

OncologyJournal of

Hindawiwwwhindawicom Volume 2013

Hindawiwwwhindawicom Volume 2018

Oxidative Medicine and Cellular Longevity

Hindawiwwwhindawicom Volume 2018

PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Computational and Mathematical Methods in Medicine

Hindawiwwwhindawicom Volume 2018

Behavioural Neurology

OphthalmologyJournal of

Hindawiwwwhindawicom Volume 2018

Diabetes ResearchJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Research and TreatmentAIDS

Hindawiwwwhindawicom Volume 2018

Gastroenterology Research and Practice

Hindawiwwwhindawicom Volume 2018

Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom