Modelling of Passive Blood Flow Stimulation
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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!