Post on 13-Feb-2021
Application of engineering models of the cardiovascular system in studies of high blood pressure
Alberto Avolio
Professor of Biomedical Engineering Australian School of Advanced Medicine Macquarie University, Sydney, Australia
alberto.avolio@mq.edu.au
Joint Electrical Institutions Sydney Engineers Australia, IEEE, IET
14 August 2014
Biomedical Engineering brief interdisciplinary journey
1968-69 Eng 1, Eng 2 (Townsville University College) 1970-71 Eng 3, Eng 4 (UNSW) – Biology for Engineers [Peter Bason]) 1972-76 PhD “Haemodynamc Studies and Modelling of the Mammalian Arterial System” (UNSW; Peter Bason [Elec Eng], Michael O’Rourke [Med]) 1976-78 Post Doc. Dept. Physiology, University of Leiden, The Netherlands. Studies in the coronary circulation (John Laird – Aeronautical Engineering; Avco Everett) 1979-86 Research Fellow (NHMRC;NHF; St V Hospital - O’Rourke) 1986-2007 Center/Graduate School of Biomedical Engineering- UNSW 2007-present Australian School of Advanced Medicine Macquarie University
Arterial Blood Pressure
New (emerging, evolving) paradigms for treatment and management of arterial blood pressure (BP) • Office BP; Ambulatory (24h) BP; Home BP; Tele BP
• Conventional brachial cuff BP + pulse waveform - Central aortic BP (close to the heart)
Arterial Blood Pressure
What is arterial blood pressure?
(Laplace)
Wall Tension ( terms: “hypertension”, “hypotension” )
The Circulation of Blood
Early Ideas Natural Spirits
- food; liver; blood; flow in veins (back and forth); right ventricle; exhale impurities; passages to left ventricle (LV)
Vital Spirits
-blood in LV, mixing with inhaled air; flow in arteries (back and forth).
[artery: ‘air duct’]
Animal Spirits
- flow to brain; mixing with spirits, exit through nerves (hollow) to all parts of the body
William Harvey (1578-1657)
Father of modern physiology
“ Experimentation
and
Reason ”
First annotation of the circulation of blood- 1616
So it is proved that a continual movement of the blood in a circle is caused by the beat of the heart.
“On the motion of the heart and blood in animals” - 1628
The circulation of blood - 1628
...by reason and experiment
• Presence of valves
• Blood flows back towards the heart
The Circulation of Blood - pulsatility Pressure (output)
CV
CV
R
Flow (input)
CV
CV
R C CV
C
R C
R: Resistance; C: Compliance
Non-Uniform Transmission Line
Wave Velocity = 1
√𝐿𝐿𝐿𝐿
• wave distortion • amplitude amplification
The Circulation of Blood- arterial pressure
Pressure (mmHg)
Distance from Heart
Arterial pressure pulse
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Arterial pressure pulse
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
John Womersley
Donald McDonald
Michael Taylor
Arterial Haemodynamics ~ 1950-60’s
English
Australian 1960 (1st Edition) Blood flow in Arteries (Physiological Society, Monograph
No 7)
2011 (July) 6th Edition
Michael O’Rourke
Pressure and Flow in arteries
Harmonic decomposition
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
ZR(ω) = R ZL(ω) = jωL ZC(ω) = 1/jωC
Impedance (Zin) = Pressure / Flow
Z1 = P1/Q1
Z2 = P2/Q2
...
Vascular impedance
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Blood Vessel Electric Equivalent
▪ Blood flow (fin) ▪ Electric current (Iin) ▪ Blood volume (ΔV) ▪ Electric charge (Q) ▪ Blood pressure (Pout - Pin) ▪ Electric potential (Vout - Vin) ▪ Young’s modulus (E) ▪ Capacitance (C) ▪ Blood flow friction (F) ▪ Resistance (R) ▪ Leak flow resistance ▪ Resistance (r1)
▪ Pressure-dependent compliance (C (P)) ▪ Frequency-dependent compliance (C (ω); Ed) ▪ Viscoelasticity of blood vessel (r (ω); η(ω))
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Windkessel Model
Lumped parameter representation
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Input impedance of the human arterial tree
Evolution of arterial models
Randomly branching network of elastic tubes
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Input Impedance – dependence on branching structure
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Pulse Wave Analysis
and
The Arterial Pulse
Rowell LB, et al. 1968. Disparities between aortic and peripheral pulse pressures induced by upright exercise and vasomotor changes in man. Circulation. 1968; 37(6):954-64. [A:Rest; B:28.2%; C:47.2%; D:70.2% of maximal oxygen uptake]
Arterial Blood Pressure
Radial artery
Aorta
Blood Pressure Measurement non-invasive; indirect
• Sphygmomanometer – Systolic (max) – Diastolic (min)
• Brachial pressures
• No waveform information
Arterial Blood Pressure invasive, direct measurements
Pauca, A. et al, Chest 1992;102:1193-1198. [ N=51 (46M, 5F), age 48-77 yrs; external transducers]
closed circles: Diastolic Pressure; open squares: Mean Pressure; open circles: Systolic Pressure
Bars: 2 SD
Central aortic blood pressure
Central Aortic Pressure (i) Systolic/Diastolic values
- peak load on the left ventricle
- improved accuracy for aortic stress calculation [aneurysms]
(ii) Waveform - additional parameters
- rate or rise [ dp/dt – myocardial fibre shortening ]
- late systolic augmentation [ augmentation index – myocardial stress ]
- systolic/diastolic area [ perfusion of the myocardium ]
(Subendocardial Viability Ratio – SEVR)
- end-systolic pressure [ myocardial contractility ]
Non-invasive measurement of central (aortic) blood pressure
Estimation of central systolic pressure (cSBP)
cSBP = (brachial)SBP – constant (~12 mmHg)
1. Non-Waveform Methods (conventional cuff measures)
Error ~ +/- 18 mmHg
How many in “acceptable”
range?
19%
cSBP = (brachial)SBP – constant (~12 mmHg)
Non-invasive measurement of central blood pressure
The Arterial Pulse and Non-invasive Assessment of Arterial Function
Applanation Tonometry
Frederick Akbar Mahomed ~ 1870’s
Effects of vasoactive agents Nitroglycerin
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
The Arterial Pulse and Haemodynamics
Arterial pressure and wave propagation
Simulation
Wave Reflection Phenomena
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Nichols W and O’Rourke M. McDonalld’s Blood flow in Arteries. 5th Ed
Wave propagation - Strings
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Nichols W and O’Rourke M. McDonalld’s Blood flow in Arteries. 5th Ed
Wave propagation - Tubes
Complete occlusion
Incomplete occlusion
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Nichols W and O’Rourke M. McDonalld’s Blood flow in Arteries. 5th Ed
Wave reflection – effects on pressure and flow
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Nichols W and O’Rourke M. McDonalld’s Blood flow in Arteries. 5th Ed
Human Kangaroo
Wave reflection – modification of pressure pulse
- Peak pressure in SYSTOLE - Peak pressure in DIASTOLE
Importance of measuring waveform features Augmentation Index (AIx)
AIx = ΔP/P1
Peak Systolic Pressure due to ‘Arterial function’
Peak Systolic Pressure due to ‘Cardiac function’
’
AORTIC FLOW
Importance of measuring waveform features Augmentation Index (AIx)
AIx = ΔP/P1
Late systolic augmentation and left ventricular mass
SJ Marchais et al.Wave reflections and cardiac hypertrophy in chronic uremia. Influence of body size. Hypertension. 1993;22:876-883
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Balloon Inflation
Relaxation time (TAU)
Arterial Pulse • Measurement of arterial
pulse waveform
• Central aortic pressure
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Arterial Pulse Waveform Features
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Takazawa K et al Assessment of Vasoactive Agents and Vascular Aging by the Second Derivative of Photoplethysmogram Waveform . Hypertension. 1998;32:365-370
Blood Pressure Measurement
• Sphygmomanometer – Systolic (max) – Diastolic (min)
• Brachial pressures
• No waveform information
Pulse detection
2. Cuff methods
1. Tonometric methods
SphygmoCor Aortic Pressure
Radial Tonometer
Brachial Cuff
SphygmoCor TF
Estimated TF
Transfer Function (mathematical model)
Radial Aortic
Forward
Reverse (no timing
information)
Peripheral Pulse (Measured) Central Pulse (Measured)
Model
Arterial Pressure Pulse – Waveform Features
Inverse Transfer Function (obtain whole wave)
Peripheral Pulse (Measured) Central Pulse ( DERIVED )
Arterial Pressure Pulse – Waveform Features Peripheral Pulse (Measured) Central Pulse ( DERIVED )
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
SBP2
SBP1
SBP2 cSP
Transfer Function (mathematical model)
Radial Aortic
Forward
Reverse (no timing
information)
Model
1. Frequency (ω) Domain : H(ω) = Prad(ω)/Pao(ω) 2. Auto Regressive Model, (ARX):
A(z)y(k) = B(z)u(k - n) + e(k)
u(k): system inputs; y(k): system outputs : n: system delay e(k): system disturbance; A(z) , B(z): polynomials; z : shift operator
Frequency (Hz)
Transfer Function
Transfer function between central and peripheral pulse is frequency dependent
Amplitude
Phase (deg)
3
4
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
2
1
200
0
-200
-400
Rowell LB, et al. 1968. Disparities between aortic and peripheral pulse pressures induced by upright exercise and vasomotor changes in man. Circulation. 1968; 37(6):954-64. [A:Rest; B:28.2%; C:47.2%; D:70.2% of maximal oxygen uptake]
Arterial Blood Pressure
Radial artery
Aorta
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Chen, C.-H. et al. Circulation 1997;95:1827-1836
Validation of brachial transfer function
Measured Derived
Generalized Transfer Function
B.P. measurement with waveform information
? 90 mmHg
144 mmHg
90 mmHg
144 mmHg
Patient 1 ≠ Patient 2
Central Brachial
122 mmHg
136 mmHg
Radial Pressure Aortic Pressure
McEneiry et al, Hypertension. 2008:51:1-7
“70% of individuals with high normal brachial pressure had similar aortic pressures as those with stage 1 hypertension”
Central Aortic Pressure : a re-assessment of categories of hypertension?
males females
* *
( N ~ 10,000 )
JACC, 54(10): 1730-1743, October, 2009
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Booysen HL et al. Journal of Hypertension 2013; 31:1124-1134
Central Aortic Blood Pressure
Central Aortic Blood Pressure
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Central Aortic Pressure
1. Non-invasive measurement of central aortic blood pressure from the peripheral pulse
2. End-organ function
Heart - Left Ventricular Hypertrophy
- Heart Failure
HEART
Regression of Left Ventricular Hypertrophy
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Central Aortic Pressure and End-Organ Function
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
The Losartan Intervention For Endpoint Reductionin Hypertension Study
An investigator-initiated, prospective, community-based, multinational, double-blind, double-dummy, randomised, active-controlled, parallel-group study from 945 centres
Dahlöf B et al Lancet 2002;359:995-1003.
Steering CommitteeChair: Co-chair:
B. Dahlöf R.B. Devereux
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Brachial
Central
Use of models for optimization of cardiac resynchronization therapy (CRT)
Cardiac Resynchronization Therapy ● Cardiac resynchronization therapy (CRT) - biventricular pacing - coordination of L and R ventricular contraction - improve the symptoms of heart failure ● Assessment: ejection fraction (echocardiography)
● A CRT device has a left ventricular pacemaker lead, and under X-ray guidance, this specialized left ventricular pacing lead is placed into the “coronary sinus”
● Electrical activity can be
coordinated with the right ventricle via the right ventricular pacing lead which can reduce the right and left ventricular electrical delay
Chest X-ray of a CRT device in the chest
Echo results in CRT responder ● Circumferential 2D strain before (A)
and after (B) 4 years of CRT in a responder. Parasternal short axis view at the level of the papillary muscles
● Before CRT, there is asynchronous
circumferential contraction with postsystolic shortening and passive movement of the inferior and posterior segments, which are scar tissue. After 4 years of CRT, there is increased synchronous contraction, a reduction of postsystolic shortening; the scarred segments (inferior and posterior) show no circumferential contraction
(Circumferential 2D-Strain Imaging for Predicting long term Response to CRT: Results, www. medscape.com/viewarticle/577484_3)
CRT optimization
Empiric: Fixed delays : VV : 0 ms; AV: 120 ms Patient Specific: Search for AV and VV delay to maximise hemodynamc parameters (eg cardiac output; ejection fraction; arterial pressure)
Model for specific optimization of CRT
● The electric circuit representation of the closed loop cardiovascular model. The left and right heart are represented by variable capacitors and systemic and pulmonary arterial section and systemic pulmonary venous sections are represented by Windkessel components. This model was made for simulation under the PLECS® platform.
● Two mechanisms inherent in the simulation are Frank-Starling mechanism affected by venous return and the association of the reduction in maximum ventricular contractility and the VV delay.
Model for specific optimization of CRT
AS
TPR
Hemodynamic effects investigation
● Illustration of the alterations in the effects of the optimal VV delay maximizing cardiac output (CO) parabolic curve due to changes of total arterial compliance (Cas, inverse of arterial stiffness) and peripheral resistance (Ras, TPR)
In arterial stiffness (AS) and total peripheral resistance (TPR)
“ Right bundle branch block (RBBB) ”
Simulation results (Linear)* ● The responses of
maximal CO and SBP with respect to VV delay as functions of Cas and Ras. Functions are fit with linear regression (Cas) or polynomials (Ras) seen in left pannels.
● The trend of the
responses of optimal AV delay for changes in Cas and Ras. A much smaller effect is observed.
VV delay AV delay
Simulation results (Nonlinear, VV) Effect of increasing aortic stiffness
Effect of increasing peripheral resistance
Simulation results (Nonlinear, AV) Effect of increasing aortic stiffness
Effect of increasing peripheral resistance
Simulation results – pressure dependency
Pure effect of pressure-dependency of arterial compliance to VV delay, which shows the reverse influence comparing with that from compliance value. This implies the equivalent of left bundle branch block if large arteries loose the property of pressure-dependency. Larger range changes for the value of CO or SBP because of the nonlinear feature of arterial compliance with blood pressure
●
●
“ Left bundle branch block (LBBB) ”
Australian School of Advanced Medicine Macquarie University, Sydney, Australia
Conclusion • Increased recognition of importance of pulsatile
function in the circulation of blood .
• Engineering models have been highly significant in enhancing understanding of cardiovascular dynamics.
• Models in improving measurement of arterial blood pressure:
conventional cuff + arterial pulse waveform
- provides significant enhancement for non-invasive assessment of cardiovascular function
Application of engineering models of the cardiovascular system in studies of high blood pressureSlide Number 2Arterial Blood PressureArterial Blood PressureThe Circulation of BloodEarly IdeasSlide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11The Circulation of Blood - pulsatilitySlide Number 13The Circulation of Blood- arterial pressureArterial pressure pulseArterial pressure pulseSlide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Blood Vessel Electric EquivalentSlide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Blood Pressure Measurement�non-invasive; indirect Arterial Blood Pressure �invasive, direct measurementsSlide Number 41Slide Number 42Slide Number 43Slide Number 44Applanation TonometrySlide Number 46Effects of vasoactive agentsSlide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Slide Number 58Slide Number 59Slide Number 60Blood Pressure Measurement Slide Number 62Slide Number 63Slide Number 64Slide Number 65Slide Number 66Slide Number 67Slide Number 68Slide Number 69B.P. measurement with waveform informationSlide Number 71Slide Number 72Slide Number 73Slide Number 74Central Aortic Blood PressureCentral Aortic Blood PressureSlide Number 77HEART��Regression of Left Ventricular HypertrophySlide Number 79Slide Number 80Slide Number 81Slide Number 82Slide Number 83Use of models for optimization of cardiac resynchronization therapy (CRT) �Cardiac Resynchronization Therapy Chest X-ray of a CRT device in the chestEcho results in CRT responderCRT optimizationModel for specific optimization of CRT Model for specific optimization of CRT Hemodynamic effects investigationSimulation results (Linear)*Simulation results (Nonlinear, VV)Simulation results (Nonlinear, AV)Simulation results – pressure dependency Slide Number 96