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Nonlinear dynamics modeling of mechanical periodicity of end diastolic volume of left ventricle

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Abstract

The cardiovascular system with a lumped parameter model is treated, in which the Starling model is used to simulate left ventricle and the four-element Burattini & Gnudi model is used in the description of arterial system. Moreover, the feedback action of arterial pressure on cardiac cycle is taken into account. The phenomenon of mechanical periodicity (MP) of end diastolic volume (EDV) of left ventricle is successfully simulated by solving a series of one-dimensional discrete nonlinear dynamical equations. The effects of cardiovascular parameters on MP is also discussed.

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Abbreviations

X n +1:

The EDV of the (n+1)th heartbeat

X n :

The EDV of thenth heartbeat

Y n :

The eject volume of thenth heartbeat

U n :

The mass of the blood through vein to heart

P s :

The systolic pressure of left ventricle

P d :

The diastolic pressure of left ventricle

P v :

The pressure

P a :

The arterial pressure

P n :

The average arterial pressure

ΔP :

The increment of arterial pressure

F d :

Coefficient of diastolic LV

L d :

Coefficient of diastolic LV

F s :

Coefficient of systolic LV

L s :

Coefficient of systolic LV

V s :

The volume of systolic LV

T :

The cardiac cycle

k :

The ratio of ejection time to the whole cardiac cycle

R a :

The resistance of the arterial valve

R m :

The resistance in vein flow

R :

The external resistance

Q :

The volume of blood throughR in a cardiac cycle

Q 1 :

The volume of blood throughL in a cardiac cycle

C :

The compliance

L :

The inertia

T s :

The minimum value of cardiac cycle

T m :

The maximum value of cardiac cycle

α:

The coefficient of feedback

γ:

The coefficient of feedback

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Authors and Affiliations

  1. Mechanics and Engineering Science Department, Fudan University, 200433, Shanghai, P R China

    Xu Shi-xiong & Mao Xiao-chun

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  1. Xu Shi-xiong
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  2. Mao Xiao-chun
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Communicated by DAI Shi-qiang

Biography: XU Shi-xiong (1943-), Professor

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Shi-xiong, X., Xiao-chun, M. Nonlinear dynamics modeling of mechanical periodicity of end diastolic volume of left ventricle. Appl Math Mech 22, 1183–1191 (2001). https://doi.org/10.1007/BF02436454

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  • DOI: https://doi.org/10.1007/BF02436454

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