Original Article

A Combined In Vivo, In Vitro, In Silico Approach for Patient-Specific

Haemodynamic Studies of Aortic Dissection

MIRKO BONFANTI ,1 GAIA FRANZETTI ,2 SHERVANTHI HOMER-VANNIASINKAM ,1,2,3

VANESSA DIAZ-ZUCCARINI ,1,2 and STAVROULA BALABANI2

1Wellcome/EPSRC Centre for Interventional and Surgical Sciences (WEISS), Department of Medical Physics and BiomedicalEngineering, University College London, 43-45 Foley Street, London W1W 7TS, UK; 2Department of Mechanical Engineering,University College London, Torrington Place, London WC1E 7JE, UK; and 3Leeds Teaching Hospitals NHS Trust, Great

George Street, Leeds LS1 3EX, UK

(Received 18 June 2020; accepted 2 September 2020; published online 14 September 2020)

Associate Editor Lakshmi Prasad Dasi oversaw the review of this article.

Abstract—The optimal treatment of Type-B aortic dissection(AD) is still a subject of debate, with up to 50% of the casesdeveloping late-term complications requiring invasive inter-vention. A better understanding of the patient-specifichaemodynamic features of AD can provide useful insightson disease progression and support clinical management. Inthis work, a novel in vitro and in silico framework to performpersonalised studies of AD, informed by non-invasive clinicaldata, is presented. A Type-B AD was investigated in silicousing computational fluid dynamics (CFD) and in vitro bymeans of a state-of-the-art mock circulatory loop andparticle image velocimetry (PIV). Both models not onlyreproduced the anatomical features of the patient, but alsoimposed physiologically-accurate and personalised boundaryconditions. Experimental flow rate and pressure waveforms,as well as detailed velocity fields acquired via PIV, areextensively compared against numerical predictions at dif-ferent locations in the aorta, showing excellent agreement.This work demonstrates how experimental and numericaltools can be developed in synergy to accurately reproducepatient-specific AD blood flow. The combined platformpresented herein constitutes a powerful tool for advancedhaemodynamic studies for a range of vascular conditions,allowing not only the validation of CFD models, but alsoclinical decision support, surgical planning as well as medicaldevice innovation.

Keywords—Aortic dissection, Particle image velocimetry,

Blood flow, Computational fluid dynamics, Pulsatile flow,

Patient-specific.

ABBREVIATIONS

AD Aortic dissectionFL False lumenTL True lumenIF Intimal flapCFD Computational fluid dynamicsPIV Particle image velocimetry3WK 3-Element Windkessel modelWSS Wall shear stressBC Boundary conditionR ResistanceC ComplianceRI Refractive indexTAWSS Time-averaged wall shear stressFSI Fluid structure interactionPC-MRI Phase-contrast magnetic resonance

imagingCT Computed tomographyLSA Left subclavian arteryBT Brachiocephalic trunkLCC Left common carotidDA Descending aortaCO Cardiac outputSV Stroke volumeSST Shear stress transportRANS Reynolds-averaged Navier–Stokes

Mirko Bonfanti and Gaia Franzetti have contributed equally to

this work.

Address correspondence to Vanessa Dıaz-Zuccarini, and

Stavroula Balabani, Department of Mechanical Engineering,

University College London, Torrington Place, London WC1E 7JE,

UK. Electronic mails: v.diaz@ucl.ac.uk, s.balabani@ucl.ac.uk

Annals of Biomedical Engineering, Vol. 48, No. 12, December 2020 (� 2020) pp. 2950–2964

https://doi.org/10.1007/s10439-020-02603-z

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0090-6964/20/1200-2950/0 � 2020 The Author(s)

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INTRODUCTION

Aortic dissection (AD) is a life-threatening vascularcondition in which an intramural tear results in bloodflowing within the medial layer of the aortic wallleading to the development of an intimal flap (IF). TheIF separates the true lumen (TL), the physiologicalpathway of blood, from a false lumen (FL), the newpathological route within the aortic wall.

The optimal treatment of Type-B dissections—thoseinvolving the arch and descending aorta—is still de-bated; when uncomplicated, they are commonly man-aged medically, but up to 50% of the cases will developcomplications requiring invasive intervention. Cur-rently, some anatomical predictors of AD growth areused to customise the follow-up and treatment plan-ning; however, haemodynamic information such asflow patterns, pressures, velocity and wall shear stress(WSS) indices can provide a more comprehensiveunderstanding of the condition, adding prognosticvalue.11

There is a great amount of evidence that haemo-dynamics plays an important role in AD progression.For example, high intra-luminal pressure and pressureimbalance between the lumina are key drivers of FLdilation and distal extension of the dissection, whileWSS greatly affects aortic remodelling.28 Elevatedtime-averaged WSS (TAWSS) has been associated withretrograde Type-A dissections and tear initiation,19

while low and oscillatory WSS and vortical flow havebeen correlated with FL shrinkage and thrombosis.29

However, accurate haemodynamic measurements aredifficult to obtain non-invasively in vivo.

In the last decade, personalised computational fluiddynamics (CFD) models have been investigated as atool to improve the understanding and clinical out-come of AD.13 Advances in modelling and simulationhave allowed for increasingly realistic AD models.Geometrical accuracy has improved from the repre-sentation of only the dissected aorta with the upperbranches9 to the inclusion of the abdominal and vis-ceral vessels.21 Simplified ‘static’ outlet boundaryconditions (BCs), such as constant pressure or pre-scribed flow splits, have been replaced by more phys-iologically-accurate ‘dynamic’ three-elementWindkessel models (3WKs).12 Recently, the limitationof the rigid wall assumption has also been overcome,with the implementation of fluid structure interaction(FSI) models able to simulate the motion of the aorticwall and IF.1,2,4

Experimental investigations of flow in simplifiedmodels of AD have increased the general understand-ing of the pathology and highlighted the influence of

morphological features on the involved fluid dynamicvariables.3,23 However, patient-specific, complex flowfields have not been measured in physical AD modelsyet. Currently, there are no AD experimental modelsable to accurately reproduce personalised haemody-namics conditions, by using both anatomically-accu-rate phantoms and physiologically-correct BCs.

Complementing CFD simulations with experimen-tal flow measurements can allow extensive validationof computational results, increasing the confidence inthe numerical predictions. Validation of patient-specificCFD simulations of AD is currently based on in vivo,2D and 4D phase-contrast magnetic resonance imag-ing (PC-MRI) data.21 However, these modalities, whenused in a clinical setting, have poor resolution and areoften subject to noise. Few studies have attempted tocombine in vitro and in silico approaches for the studyof AD hitherto. Chen et al.8 developed a 3D FSI modelof an idealised AD and validated the results againstin vitro ultrasound measurements in a porcine ADmodel in a pulse duplicator system; however, clinicalultrasound measurements exhibit limited resolution.An established flow diagnostics technique, particleimage velocity (PIV), can provide high temporal andspatial resolution velocity fields for visualisation andquantification of vascular flows. The use of an exper-imental technique, such as PIV, allows the validationof numerical models in a highly-controlled environ-ment, with a level of reproducibility and accuracy notpossible in vivo.22 PIV was recently used to study theimpact of tear size on the flow in an idealised model ofAD using computations and experiments.30 However,to date, PIV has not been used in any patient-specificin vitro AD work.

The main aim of this work is to develop a combinedin vitro, in silico approach for the study of the patient-specific haemodynamics of AD informed by non-in-vasive in vivo data. This work presents several novelaspects:

1. For the first time an experimental mock circula-tory loop for AD investigations was developedalongside state-of-the-art CFD simulations, thatincludes not only an anatomically-accurate phan-tom, but also physiologically-accurate and per-sonalised BCs.

2. This allowed the study of a Type-B AD with bothnumerical and experimental tools, informed byclinical data to accurately reproduce patient-specific haemodynamic conditions.

3. Experimental PIV acquisitions, alongside pressureand flow rate measurements, allowed an extensivecomparison between measured and predicted

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haemodynamic parameters and the validation ofthe CFD model.

4. A new paradigm to guide clinical decisions isintroduced.

MATERIALS AND METHODS

Figure 1 provides an overview of the in vivo - in vitro- in silico approach developed in this work, which isdetailed in the following sections.

Clinical Data and Vessel Segmentation

The study is based on a clinical dataset of a 77-year-old male subject with a chronic Type-B AD. The da-taset was acquired as part of an ethically-approvedprotocol at the Leeds General Infirmary (NHS HealthResearch Authority, ref: 12/YH/0551; Leeds TeachingHospitals NHS Trust, ref: 788/RADRES/16) andconsent was obtained from the patient.

The dataset included a computed tomography (CT)scan of the entire aorta and 2D PC-MRI scans atseveral locations of the aorta and upper branches, asindicated in Fig. 1a. Systolic and diastolic brachialpressure values were also acquired with a sphygmo-manometer. Flow information was extracted from thePC-MRI sequences using the software GTFlow (Gy-roTools, Switzerland), while the AD geometry wassegmented from the CT scan with Simpleware ScanIP(Synopsys, USA). Full details on the image acquisitionand segmentation procedures are reported in Bonfantiet al.5

The dissection originated distal to the left subcla-vian artery (LSA) and extended to the celial trunk.Only one entry tear located approximately 10 mmdistal to the proximal end of the dissection was evidentfrom the clinical images, while no re-entry tears weredetected (Fig. 1a).

Experimental Setup

A 3D phantom of the patient-specific AD wasmanufactured by 3D printing technology (MaterialiseNV, Belgium) to obtain a rigid, transparent model(Fig. 1b).

The abdominal aortic branches were excluded fromthe phantom, which terminated just after the distal endof the dissection, in order to simplify the geometry ofinterest. Connectors were added to the inlet and bra-chiocephalic trunk (BT), left common carotid (LCC),LSA, and descending aorta (DA) outlets of the phan-tom to facilitate the connection to the experimentalsetup.

A pulsatile flow circuit was developed14 comprisinga computer-controlled piston pump and left ventriclesimulator, the AD phantom, a tunable 3WK model ateach aortic outlet and an atrial reservoir. A schematicof the experimental arrangement used is shown inFig. 2. A detailed description of the components can befound in Franzetti et al.14 Pressure (P) and flow rate(Q) waves were acquired in real time using pressuretransducers (Omega Engineering, UK) and an ultra-sound flow meter (Sonotec, Germany), respectively, atthe inlet and outlets of the phantom, as indicated inFig 2a. The signals were acquired via a custom madeLabVIEW virtual instrument using a CompactRIOcontroller (cRIO-9040, 1.3 GHz Dual-Core, 70T,FPGA, RT, 4-Slot; National Instruments, USA) with asampling sequence of 200 Hz. A Savitzky-Golay low-pass filter was employed to attenuate high frequenciesin the pressure signals. The experimental platform wastuned in order to reproduce patient-specific conditionsusing the personalisation procedures described in Sec-tion ‘‘Model Personalisation’’.

For PIV measurements, the flow was seeded withfluorescent polymer particles (PMMA-RhB-10, 1–20 lm ; Dantec Dynamics, Denmark) with a meandiameter of 10 lm, injected into the flow upstream ofthe phantom and allowed to disperse uniformly withinthe aortic model.

The tracing particles were illuminated by a pulsedNd:YAG laser (Litron Lasers, Bernoulli, UK) emitting@ 532 nm wavelength light. Pairs of particle imageswere recorded with a charge-coupled device camera(Imperx, USA) at a sampling rate of 22 Hz with aresolution of 4000 � 3000 pixels and a time interval of1 ms. An optical cut-off filter @ 550 nm was used toallow only the particles’ fluorescent signal through thecamera.

Two separate measurements were taken to acquirethe flow field in the aortic arch—section 1—and in theproximal part of the TL and FL in the descendingaorta—section 2—as shown in Fig. 2b.

Image acquisition was performed using the TSI In-sight4G software (TSI, USA), that was also used tosynchronise the camera and the laser pulses via a La-ser-Pulse synchroniser (TSI, Model 610006).

The acquired images were subsequently processed inPIVlab.27 Velocity fields were generated using the fastFourier transform based cross-correlation algorithm,implemented with a three-pass technique, starting withan interrogation area of 64 � 64 pixels and ending withan area of 32 � 32 pixels, overlapping by 50%. Thenormalised median test was applied after each pass,evaluating the velocity fluctuations with respect to themedian value in a 5 � 5 neighbourhood around thevector. Lastly, a smoothing filter was applied to thevelocity fields after each iteration in order to decrease

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FIGURE 1. (a) Geometry of the dissected aorta as extracted from the CT scan. The dotted lines indicate the sections where 2D PC-MRI data was acquired. (b) In vitro phantom with physical boundary conditions. (c) In silico 3D fluid domain and correspondingboundary conditions. (d) Schematic of the in vivo, in vitro and in silico approach developed and implemented in this work. Clinicalnon-invasive data (2D PC-MRI derived flow rate and brachiocephalic pressure) is used to inform both the experimental andcomputational models. In vitro results are compared with in vivo data to assess that the fluid dynamic conditions meet the patient-specific criteria, while in silico results are compared with in vitro measurements to validate the computational simulation. Theposition of the four lines where velocity profiles have been extracted from both PIV data and CFD results for comparison purposesare shown in (b) and (c).

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the amount of noise introduced by the algorithm andincrease the quality of the velocity estimation.22 Post-processing was performed to extract the parameters ofinterest with custom developed MATLAB (Math-Works, USA) routines.

Phase-averaged velocity fields huðx; y; tÞi were ex-tracted from the instantaneous velocity data uðx; y; tÞ.Convergence was evaluated by plotting the phase-av-eraged velocity in small regions as a function of thenumber of cycles considered; 10 cardiac cycles werefound to be sufficient to reach converged average val-ues with variation <1:6%.

In order to quantify the error in the velocity mea-surements, the flow rate was calculated from the phase-averaged velocity field at 28 successive sections of theaortic inlet (grey area highlighted in Fig. 1b) by per-forming double integration under the assumption ofaxial-symmetrical flow. Using the mass conservationprinciple, the difference between the flow rate valuesled to an error of 5.32%.26

The working fluid was selected in order to match therefractive index (RI) of the phantom material as closelyas possible ðRI ¼ 1:50� 1:51Þ. In the present study, apotassium thiocyanate (KSCN) water solution (63%by weight) was selected as a Newtonian blood mim-icking fluid as in previous works.15,18 Since it was notpossible to create a test fluid with the same viscosityand density of blood while matching the RI of thephantom wall, a compromise had to be made inaccepting a higher fluid density (q = 1310 Kg/m3) anda lower viscosity ðl ¼ 2:2 cPÞ. However, the nondi-mensional parameters characterising the experimental

flow remained in the physiological range (see Sec-tion ‘‘Numerical Simulations’’). The impact of thisapproximation was further investigated with the insilico model, as reported in Section ‘‘Limitations’’.

Model Personalisation

The experimental and numerical BCs were tuned toreproduce the patient under investigation as follows.

The protocol described in Franzetti et al.14 wasadopted to obtain the analytical waveform reproduc-ing as closely as possible the aortic flow rate of thepatient, which was measured with 2D PC-MRI. First,the main physiological parameters were extracted fromthe in vivo waveform (i.e. stroke volume (SV) = 107.6mL, cycle length (T) = 0.8 s and mean flow rate = 134mL/s). Second, the parameters were adjusted forcompatibility with the image acquisition rateðf ¼ 22HzÞ; in particular, T was increased to 0.82 s tobe a multiple of 1/f whilst maintaining the same SVand mean flow rate. Finally, the correct analyticalwaveform was generated through a computer routine.

The parameters of the 3WK models were selectedfollowing the procedure described in Bonfanti et al.5

with the aim to obtain the patient-specific systolic anddiastolic pressure values and correct cardiac output(CO) distribution amongst the aortic branches. Thetarget values for the calibration procedure are listed inTable 1.

The estimated resistance (R) and compliance (C)values were used to tune the physical components ofthe experimental rig14 and to set the outflow BCs of the

FIGURE 2. (a) Schematic illustration of the experimental platform highlighting the positions where flow rate and pressure curveswere acquired and PIV was performed. (b) Detail of the aortic phantom showing the imaged sections for the PIV acquisitions.

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numerical model, described in the following sec-tion. The set experimental and computational 3WKvalues differ slightly due to the latter including thehydraulic resistance contribution of connectors andtubes between the phantom and the physical 3WK,which were not included in the 3D computationaldomain. Such discrepancy is although negligible. Thevalues of the 3WK parameters used in the numericalmodel are listed in Table 2.

Numerical Simulations

The Navier–Stokes and continuity equations for 3Dtime-dependent flows were solved with the CFD solverANSYS-CFX 19.0 (ANSYS, USA). The equationswere spatially and temporally discretised with a high-resolution advection scheme and a second order im-plicit backward Euler scheme, respectively, using auniform time-step of 1 ms, small enough for time-stepsize-independent results. The fluid was treated asNewtonian and incompressible with l and q matchingthose of the KSCN solution used in the experiments, asreported in Section ‘‘Experimental Setup’’.

The in silico 3D fluid domain comprised the lumenof the aortic phantom (Fig. 1c). The BCs adopted inthe CFD model are shown schematically in Fig. 1c.The experimental flow rate waveform was prescribed atthe inlet with a flat velocity profile. WK3s were cou-pled to the outlets with parameters listed in Table 2.

The 3D model walls were assumed rigid with a no-slipBC, to reproduce the in vitro phantom.

Based on the inlet cross-sectional area of the aortaand the inlet flow rate, the mean ðRemÞ and peak ðRepÞReynolds numbers were equal to 3472 and 11581,respectively, while the Womersley number (Wo) was32. Since Rep was higher than the critical Reynolds

number ðRecÞ for transition to turbulent flow (calcu-lated following Kousera et al.17 as Rec ¼ 250�Wo),the Shear Stress Transport (SST) turbulence modelwas employed in the simulation. The SST model is aReynolds-Averaged Navier-Stokes (RANS) approachwhich combines the k� x model for the inner regionof the boundary layer with the k� � model for theouter region, and it is commonly used in CFD modelsof AD flows.1 An inflow turbulence intensity (Tu)equal to 1% was applied, in agreement with the find-ings of Kousera et al.17 The sensitivity of the results tothis parameter was tested by also running a simulationwith a Tu of 5%; the comparison against the resultsobtained with a Tu of 1% showed only minor changesin the calculated velocity field (maximum and meandifference in the fluid domain at peak systole equal to7.3 and 0.1%, respectively). The fluid domain wasdiscretised with Fluent meshing (ANSYS), adopting atetrahedral grid in the core region and ten prism layersat the walls. The dimensionless height (y+) of the celladjacent to the wall was kept less than 2 for an accu-rate resolution of the near-wall velocity profile with theemployed turbulence model. A sensitivity analysis wasperformed to guarantee the independence of the resultsto the mesh. Three computational meshes of 2.3M,4.1M and 6.1M cells were tested. Comparison ofnumerical results showed that the relative difference interms of peak velocity, pressure and flow rate at theboundaries were less than 2.0, 1.1 and 1.9%, respec-tively, between the coarse and medium mesh, and lessthan 0.5, 0.1 and 0.5%, respectively, between themedium and fine mesh. Therefore, the medium meshwith 4.1M elements was selected for the analysis.Simulations were run for three cycles in order to reachthe periodic steady-state on the high-performancecomputing cluster of UCL Computer Science Depart-ment (computational time: 11 h/cycle). The conver-gence of the solution was controlled by specifying a

TABLE 2. Parameters of the three-element Windkessel models (3WK) coupled to the outlets of the numerical aortic model.

3WK R1 [mmHg s mL21] R2 [mmHg s mL21] C [mL mmHg21]

BT 0.25 6.00 0.30

LCC 0.63 10.00 0.07

LSA 0.57 10.00 0.07

DA 0.01 1.15 0.30

TABLE 1. Systolic ðPsysÞ and diastolic ðPdiaÞ blood pressurevalues and mean flow rate ð �QÞ at the aortic branches used as

target values for the personalisation procedure.

Parameter Value Unit Source

Psys 150 mmHg Sphygmomanometer

Pdia 80 mmHg Sphygmomanometer�QIN 134.5 mL/s 2D PC-MRI�QBT 22.5 mL/s 2D PC-MRIa

�QLCC 8.9 mL/s 2D PC-MRI�QLSA 9.8 mL/s 2D PC-MRIa

�QDA 93.3 mL/s 2D PC-MRI

aThe value of these parameters were calculated based on patient-

specific 2D PC-MRI data and physiological considerations as

explained in Bonfanti et al.4.

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maximum root-mean square residual of 10�5. Post-processing was performed using CFD-Post (ANSYS)and MATLAB.

In Vivo, In Vitro, In Silico Comparison

Experimental and numerical P and Q waveformswere first compared to the clinical systolic and diastolicpressures and patient-specific CO distribution to verifythat the models met the in vivo condition. Then, ADhaemodynamics was analysed using the in vitro and insilico aortic velocity fields in two sections of interest(i.e. Sections 1 and 2 shown in Fig. 2b). The aortic archand proximal part of TL and FL—where the tear islocated—were selected as deemed more appropriate toillustrate our approach in this patient-specific case ofAD. A qualitative comparison was performed betweenthe in-plane velocity magnitudes. Quantitatively,computational and experimental velocity profiles overthe four lines shown in Figs. 1b and 1c were extractedby calculating the in-plane axial velocity (i.e. normal tothe section line, un) at four instants of the cardiac cycle(i.e. acceleration, peak systole, deceleration and dias-tole). The percentage difference ðDÞ between theexperimental and computational profiles was calcu-lated as

D ¼ 1

N

XN

i¼1

uen;i � ucn;i

������

maxj ucn;j

������

ð1Þ

where uen;i and ucn;i are the experimental and computa-tional velocity profiles, respectively, and N is the totalnumber of data points per line (in this case equal to1000).

RESULTS

Flow Rate and Pressures

The personalisation procedures employed to cali-brate the model BCs allowed the reproduction of thein vivo condition. The experimental inlet flow rate wascharacterised by T = 0.82 s, corresponding to a heartfrequency of 73 bpm, mean flow rate of 137.4 ± 5.4mL/s, and SV of 106 ± 4.4 mL, closely matching theparameters extracted from the 2D PC-MRI. Compar-isons between target clinical pressure and mean flowrate values, and experimental and computational re-sults are shown via histograms in Fig. 3. The clinicalsystolic/diastolic pressure values and mean flow rate atthe outlets are within the experimental range with theonly exception of BT, where the clinical value exceedsthe upper experimental bound by 1.5 mL/s, equivalentto an error of 6%. These results indicate that thepersonalisation procedure of the experimental plat-form was successful in reproducing the patient-specifichaemodynamic features of the case under investiga-tion. The obtained computational predictions comparewell with the experimental results, meeting the cali-bration targets (Fig. 3).

Flow rate and pressure waveforms acquired exper-imentally at the four outlets of the phantom are com-pared against the corresponding numerical results inFig. 4. Good agreement is found between the in vitroand in silico results, both in terms of values and shapeof the waveforms.

The oscillations observed in the measured pressurewaveforms—whose amplitude decreases along the flowdirection—are a consequence of the mechanical valveand correspond to its opening and closing phases at thebeginning of systole and diastole, respectively. The

FIGURE 3. Comparison between mean flow rate (Q) values at the aortic outlets and systolic (Psys) and diastolic (Pdia) pressures atthe inlet obtained with the experimental and computational models against the target clinical values. Error bars are reported for theexperimental data, which include the standard deviation (SD) due to inter-cycle variability as well as the amplitude of theexperimental oscillations due to the mechanical action of the aortic valve for the systolic pressure value.

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filtered experimental curves were considered in thequantitative comparison against the results of thecomputational model, since the latter did not includethe action of the mechanical valve. As shown in Fig. 4,numerical predicted diastolic pressure values are sys-tematically higher than those measured experimentally.The rate of decay of the diastolic pressure is describedby the time constant, or decay time ðs ¼ RCÞ, char-

acterising the 3WKs coupled to the aortic outlets.Lower values of s are observed in the experi-ments when compared to the simulations, which maybe explained by smaller R and/or C values in thephysical 3WKs with respect to the nominal ones.However, the pressure range observed in vitro and insilico is very similar as indicated by the very goodagreement between the minimum and maximum pres-

FIGURE 4. Comparison between flow rate (Q) and pressure (P) waveforms obtained from numerical and experimental results atthe outlets of the aortic domain. The experimental data is reported with standard deviation (SD) intervals. The filtered experimentalpressure waveforms are also shown to facilitate the comparison against the computational results.

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sure values, with the highest difference of 2 2.3% forthe peak value at LCC, and 10.7% for the minimumdiastolic value at DA (Fig. 4).

Velocity Fields and Profiles

The velocity fields in the ascending aorta and aorticarch obtained by numerical simulations and PIVmeasurements are presented in Fig. 5. The results showthe flow development during a cardiac cycle. Due tooptical constraints and light refraction, the PIV-der-ived phase-averaged velocities are restricted to a regionof the imaged plane. Highly organised motion isobserved during the acceleration and systolic phases(Figs. 5a and 5b) reaching a maximum velocity of 0.95and 0.74 m/s towards the inner wall of the aortic archfor CFD and PIV, respectively. A flow separation re-gion at the inner curvature of the aorta forms duringthe deceleration phase (Fig. 5c), while disorganisedstreamlines characterise the flow in the aortic archduring diastole, with velocity values up to 0.31 and0.28 m/s for CFD and PIV respectively. The 3D natureof the flow is illustrated by the 3D streamlines obtainedwith the computational model (Fig. 5, right column):ordered streamlines can be observed during the systolicphase in the ascending aorta, where the fluid flows inparallel layers, while disturbed, 3D flow is evident indiastole. The numerical and experimental velocitydistributions are qualitatively and quantitatively simi-lar throughout the cardiac cycle. Slight discrepanciescan be observed in diastole (Fig. 5d) where experi-mental error is expected to be higher.

A closer comparison between the experimental andcomputational results is provided in Fig. 6 by plottingaxial velocity profiles ðunÞ over the four selected linesshown in Fig. 5. The predicted and measured velocitiesagree remarkably well. Skewed velocity profiles can beobserved during systole (Fig. 6b), with highest velocityvalues towards the inner wall of the arch, while bidi-rectional velocity profiles are evident at early diastole(Fig. 6d), characterised by retrograde flow along theinner wall and anterograde flow along the outer wall ofthe arch.

The percentage difference between the experimentaland computational profiles are reported in Fig. 6. Amaximum difference of 30% is noted at early diastolefor the profile in line 1 which can be attributed to thelower velocity values and associated PIV errors, asdiscussed in the following section.

Figure 7 shows a comparison between PIV-derivedvelocity fields and corresponding numerical results inthe proximal part of the TL and FL. The increase ofthe velocity peak value due to the narrowing of the TLcan be observed in both PIV and CFD results (Fig. 7a)reaching a maximum value of 0.9 m/s. Complex

recirculating flow patterns are observed throughout thecardiac cycle in the FL, as illustrated by the 3Dstreamlines in Fig. 7. Unlike the TL, no significant flowstructure and velocity magnitude variations areobserved in the FL during the cardiac cycle. Interest-ingly, slightly higher velocity values are captured in theFL during diastole, both in the PIV and CFD results.This behaviour is due to the particular location of theimaged plane (see Fig. 2b), which does not include theentry tear and is oriented perpendicularly to its crosssection. Therefore, the flow is mainly out of the imagedplane during systole, and hence the measured velocitiesare lower, whereas during diastole, in-plane recircu-lating flows develop increasing the velocities measuredherein.

DISCUSSION

The purpose of this work was to develop a robustframework for accurate experimental and numericalhaemodynamic studies of AD informed by non-inva-sive clinical data. The state-of-the-art models includedcomputer-controllable pulsatile flow and finely-ad-justable dynamic BCs as well as a patient-specificaortic domain.

Aortic Dissection Haemodynamics

The experimental platform developed in this studyevaluated physiological and patient-specific blood flowin an AD model with a high level of accuracy. This wasachieved by properly tuning the inlet and outlet BCs ofa patient-specific aortic phantom. In particular, thecomputer-controlled pulsatile pump—driving the flowin the mock circulation loop—produced an inlet flowrate with the characteristic features of the in vivowaveform acquired via 2D PC-MRI for the studiedpatient. The bespoke pump offers a higher degree ofcustomisation and flexibility allowing the reproductionof patient-specific conditions with an unprecedentedlevel of detail and accuracy compared to commercialsystems20,24; moreover, the chosen flow configuration(i.e. piston-pump and left ventricle simulator) is moresuitable to create physiological aortic flow waves,characterised by a systolic and a diastolic phase, thansolutions that comprise only a displacement pump.3

The physical 3WK models coupled to the outlets of thephantom successfully reproduced the hydraulic im-pedance of the distal vasculature of the aorta, allowingfor physiological pressure/flow relationships, as evi-denced by the realistic waveforms acquired in theexperiment. By tuning the R and C components of the3WK for each outlet, it was possible to personaliseimportant haemodynamic quantities, such as the flow

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distribution among the aortic branches and the sys-tolic/diastolic pressure values in the aortic model.These quantities typically provide a measure of thepersonalisation achieved in blood flow simulations6;the experimentally derived flow distribution and pres-sures demonstrate that the same personalisation can beachieved by the developed in vitro platform.

High-definition PIV allowed the visualisation of thevelocity fields in the aortic phantom. Axial velocityprofiles at four different instants of the cardiac cyclewere extracted at four selected locations in the

ascending aorta/aortic arch accurately quantifying thehaemodynamics therein, and reliably capturing thephysiological features of the flow at all phases ofthe cardiac cycle. During the acceleration and peaksystolic phases, the velocity profiles were skewed to-wards the inner curvature of the arch, in agreementwith in vitro observations on healthy aortic phan-toms.16 Flow separation was detected at the inner wallduring the deceleration phase, while a bidirectionalvelocity profile with back-flow along the inner wall wasmeasured at early diastole. This behaviour matchedvery well the in vivo measurements of blood velocity inthe human ascending aorta reported by Segadal andMatre.25

PIV measurements in the proximal dissectiondemonstrated organised and high-velocity flow in thenarrowed TL during the systolic phase. On the otherhand, the FL was dominated by vortical and complexflow structures during both the systolic and diastolicphases. This is a common feature for AD flow as

FIGURE 6. Experimental and numerical axial velocity profiles ðunÞ at (a) acceleration, (b) peak systole, (c) deceleration and (d)early diastole. For the position of lines 1–4 refer to Fig. 5. The average percentage difference ðDÞ between the two curves calculatedaccording to Eq. (1) is reported in the bottom-right corner of the plots.

bFIGURE 5. Comparison between experimental PIV-derivedphase-averaged velocity magnitude fields (left column) andcorresponding numerical predictions (middle column) in theaortic arch. The 3D streamlines obtained with the CFDsimulation is reported in the right column. The comparisonis shown for four different instants of the cycle: (a)acceleration, (b) peak systole, (c) deceleration and (d)diastole. The dashed lines indicate the position for theextraction of the velocity profiles reported in Fig. 6.

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widely reported by computational studies.9 The ab-sence of secondary tears in this patient led to a zeronet-flow entering the FL via the entry tear. Conse-quentially, low-velocity and disturbed flow wasobserved in the region next to the tear throughout thecardiac cycle, while stagnant flow characterised theremaining part of the FL.

In Vitro and In Silico Comparison

This study is the first to validate a patient-specificAD CFD model with dynamic BCs and pulsatile flow,and the first to employ PIV to investigate the haemo-dynamics of a personalised AD model. A comprehen-sive comparison between the numerical predictionsand experimental results demonstrated the consistencyand accuracy of the blood flow patterns obtained in theaortic domain.

FIGURE 7. Comparison between experimental PIV-derived phase-averaged velocity magnitude fields (left column) andcorresponding numerical predictions (middle column) in the proximal part of the true (TL) and false (FL) lumen. The 3Dstreamlines obtained with the CFD model are shown on the right. The comparison is shown at (a) peak systole and (b) earlydiastole. It should be noted that the colour scales between the TL and FL differ for clarity purposes.

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Given the complexity of the pathology underinvestigation, the exceptional agreement achieved is atestament of the level of sophistication in our experi-mental platform and the potential of our combinedapproach. Nevertheless, small discrepancies betweennumerical and experimental flow fields were observedin certain regions, attributed to various, well docu-mented,22 sources of error in PIV measurements, suchas inaccuracies in the location of the laser sheet, con-struction of the physical model and near-wall refrac-tion.

The largest differences between the experimentalresults and numerical predictions were found in the FLthroughout the cycle and in the TL during diastole,which were characterised by disorganised and low-ve-locity flows. In these regions, the phase-averaged flowmeasurements fluctuate more, with standard deviationvalues comparable to the magnitude of the in-planevelocity. These standard deviation values includeexperimental inter-cycle variations, PIV errors andsmall scale turbulent motions in the flow. In addition,the accumulation of seeding particles in the areas oflow-velocity or stagnant flow, such as the FL, increaseslaser light reflections and hence the optical noise inthese regions.

As evidenced by the comparison between the PIVand CFD velocity profiles, experimental near-wallvelocity gradients—necessary for WSS calcula-tion—are prone to errors and represent a limitation onthe information that can be obtained from the in vitromodel. However, in line with the aim of this work, suchlimitation is complemented by the use of a validatedcomputational model, and highlights the potential ofcombining experimental and numerical tools as de-scribed in the following Section.

Clinical Relevance

This work demonstrates how in vitro and in silicotools can be developed in synergy to accuratelyreproduce the patient-specific haemodynamics ofcomplex AD cases introducing a new paradigm in thetreatment planning of AD or other vascular condi-tions.

As the recent literature shows, fluid dynamicmarkers, such as WSS and intra-luminal pressures,have a significant impact on the long-term progressionof AD, and an informed clinical planning cannot relyonly on geometric information, but must take thepathological and complicated haemodynamic envi-ronment that characterises complex AD cases intoaccount.6

The value of such a synergistic approach to ADresearch and clinical translation cannot be underesti-mated. Ensuring that simulations are valid and accu-

rate is an important step to transfer suchmethodologies to the clinic. The experimental toolsdeveloped in this research provide a benchmark for thevalidation of the in silico results. Once validated, CFDmodels can be used to estimate with high detailhaemodynamic markers, such as WSS, that would bedifficult to measure experimentally and impossiblein vivo. In silico models can also be used for the virtualsimulation of different interventional scenarios (e.g.fenestration, tear occlusions). On the other hand,experimental facilities allow the performance testing ofnovel and possibly personalised medical device proto-types, such as stent-grafts, that would require compu-tationally expensive numerical models, as recentlydemonstrated by Birjiniuk et al.3 Realistic phantomsand flow conditions can also be used for surgicaltraining and pre-procedural planning for AD.

Limitations

This work was carried out under the assumption ofrigid wall of the aortic phantom. This approximationwas numerically investigated by Bonfanti et al.4 for thesame case-study highlighting the impact of aorticcompliance on the transmural pressure between the TLand FL. However, the wall displacement was less that0.75 mm for this chronic AD, consequently, the rigidwall approximation was deemed acceptable.Nonetheless, this assumption is not always appropriate(especially for the acute stage of AD as highlighted byBaumler et al.2) and the manufacturing of phantomswith physiological mechanical properties will be ad-dressed in future work.

In the present study a compromise had to be madewith regards to the rheology of the blood mimickingfluid. In vitro haemodynamic works commonly employNewtonian fluids, either water3 or blood analoguesolutions.20 Since RI matching is a requirement forPIV applications, compromises must be made and qand l values different from those of blood have beenaccepted in several studies.7 In order to evaluate theimpact of these approximations, a simulation with therheological properties of a non-Newtonian bloodmodel (i.e. Carrau-Yasuda viscosity model with

parameters from Clarion et al.10 and q = 1060 kg/m3)was compared against the results obtained with theKCSN solution. A maximum and mean difference of25.9 and 1.0%, respectively, was found when com-paring the velocity fields at peak systole in the wholefluid domain, while a maximum difference of 3.6 and4.3% was found between the P and Q waveforms atthe boundaries. Therefore, the approximation of theworking fluid was considered acceptable.

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Conclusions

A novel, personalised approach combining experi-mental and numerical tools informed by clinical datawas introduced. For the first time, both in vitro and insilico models included an anatomically-accurate ADgeometry, and physiologically-accurate and person-alised pulsatile flow and dynamic BCs. As highlightedin Fig. 1, both models were developed with high inte-gration of information at several levels, and were in-formed by clinical data.

The developed platform can be used to assess clin-ically-relevant haemodynamic markers and planinterventions as well as support the development ofnovel or personalised medical devices. Overall, thepresented combined approach is a powerful tool forthe haemodynamic investigation of AD, with a level ofdetail impossible to achieve hitherto. It thus representsa significant advance of the state-of-the-art on patient-specific modelling and simulation of AD haemody-namics and can be generalised and applied to othervascular conditions changing the current paradigm inclinical practise.

ACKNOWLEDGMENTS

This project was supported by the Wellcome/EPSRC Centre for Interventional and Surgical Sci-ences (WEISS) (203145Z/16/Z); and the British HeartFoundation (GA FS/15/22/31356). The authors wouldalso like to thank Prof John P. Greenwood and DrSapna Puppala for the clinical dataset, and theDepartment of Computer Science of University Col-lege London for the high-performance computingcluster resources used to perform the simulations.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

OPEN ACCESS

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