14 august 2014 application of engineering models of the ......14 august 2014. biomedical engineering...

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

[email protected]

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)


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

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


ZR(ω) = R ZL(ω) = jωL ZC(ω) = 1/jωC

Impedance (Zin) = Pressure / Flow

Z1 = P1/Q1

Z2 = P2/Q2

...

Vascular impedance

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))


Windkessel Model

Lumped parameter representation

Input impedance of the human arterial tree

Evolution of arterial models

Randomly branching network of elastic tubes


Input Impedance – dependence on branching structure


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]


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


The Arterial Pulse and Haemodynamics

Arterial pressure and wave propagation

Simulation

Wave Reflection Phenomena



Nichols W and O’Rourke M. McDonalld’s Blood flow in Arteries. 5th Ed

Wave propagation - Strings



Wave propagation - Tubes

Complete occlusion

Incomplete occlusion



Wave reflection – effects on pressure and flow



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


Balloon Inflation

Relaxation time (TAU)

Arterial Pulse • Measurement of arterial

pulse waveform

• Central aortic pressure


Arterial Pulse Waveform Features


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 )


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]


Radial artery

Aorta


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


Booysen HL et al. Journal of Hypertension 2013; 31:1124-1134

Central Aortic Blood Pressure


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


Central Aortic Pressure and End-Organ Function


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


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) ”


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

14 august 2014 application of engineering models of the ......14 august 2014. biomedical engineering...

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