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Modelling of Passive Blood Flow Stimulation

S.S. Simakov, T.M. Gamilov

Mathematical and Computational Modelling in Cardiovascular Problems, 15.04.2014

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Moscow Institute of Physics and Technology1

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Review

1) “Passive” blood flow stimulation

2) Blood flow circulation model• Wall state equation

3) Modelling of EECP

• EECP

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Blood flow stimulation

“active”

Skeletal-muscle pump

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“passive”

Blood flow stimulation

Enhanced External Counterpulsation (EECP)

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Blood flow stimulation

“passive”

Intra-aortic balloon pump Vessels rings

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Enhanced External Counterpulsation (EECP)

Heart failure

Ishemia

…

EECPAngina

Increased blood supply

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Blood flow circulation model

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Blood flow circulation model

0

uSSt x

02

020

0

2,16 ... ,

,2

S SSu u P u S S S S St x Sd

S S

1) Mass balance

2) Momentum balance

1 ,...,

0, 1,M

m mk k k k k k

k k k

Q Q u S

, , 0,node mk k m k k k k kp t x p t R Q x L

3) Bifurcations3.1

3.2

Compatibility conditions3.3

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The network of vessels

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Wall state equation

4) Vessel wall elasticity

Pedley, Luo, 1998

2,extP S P t x c f S

0 0

0 0

exp 1 1,

ln ,

S S S Sf S

S S S S

2,extP S P t x c f S

0 0

0 0

exp 1 1,

ln ,

S S S Sf S

S S S S

Analytic approximation

,extP t x external pressure

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2

0

exp 1 1SP cS

Wall state adaptation:

t

PP

T T

newPoldP

Physiological reactions: autoregulation

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new new

old old

c Pc P

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Wall state equation. EECP

t

t

tCardiac cycle

,extP t x external pressure

0.2 s

E.T. Ozawa, K.E. Bottom, X. Xiao, R.D. Kamm, Numerical Simulation of EnhancedExternal Counterpulsation, Ann Biomed Eng 29, pp 284–297 (2001)

150 mm Hg

100 mm Hg

200 mm Hg

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EECP regimes

tCardiac cycle

extP

Standard procedure

tCardiac cycle

extP

Procedure with rest phases

1/0 (1 cycle – work, 0 cycles - rest)

1/2 (1 cycle – work, 2 cycles - rest)

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EECP. Blood pressure in a terminal coronary artery

1/0

10/100

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EECP. Blood flow and pressure (during “work phase”)in a terminal coronary artery

Terminal artery

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EECP. Systolic pressure

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EECP. Shifted timing

0.2 s

Normal timing

t

0.35 s

Shifted timing

Shifted timing, 1/0

Cardiac cyclet

Normal timing, 1/0

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Thank You!