A cylindrical model of contraction of left ventricle of the heart
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A cylindrical model of contraction of left ventricle of the heart. Syomin F.A., Tsaturyan A.K. Institute of Mechanics, Lomonosov Moscow State University. C ardiac tissue as elastic continuum. Assumed deformations of the ventricle. D λ H⋅ R/r. λ H. H. ρ r In. r In.

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A cylindrical model of contraction of left ventricle of the heart

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A cylindrical model of contraction of left ventricle of the heart

Syomin F.A., Tsaturyan A.K.

Institute of Mechanics, Lomonosov Moscow State University


Cardiac tissue as elastic continuum


Assumed deformations of the ventricle

DλH⋅ R/r

λH

H

ρrIn

rIn


Fiber orientation within the ventricle wall

α(r)


Stress equilibrium equations

  • T33

  • T33

p0


Boundary conditions


Windkessel model for hemodynamic processes

Ri, Li

LV

Pa, C

Qin

P0

Pv

Rper


Computational modeling

V, mL

P0, mm Hg

Pa, mm Hg


λ

ρ

D*z


L, μm

rIn

rIn + 0.5*(rOut- rIn)

L, μm

rOut


Radial distribution of sarcomere lengths

L, μm

L, μm

r, cm

t, s

r, cm

t, s

1.706

2.39

1.61

2.51


Hypertrophic cardiomyopathy

V, mL

2x

2x

F

P0, mm Hg

Pa, mm Hg


λ

ρ

D*z


Dilated cardiomyopathy

V, mL

1.2x

2x

1.5x

vmax

V0

P0, mm Hg

Pa, mm Hg


λ

ρ

D*z


Summary

A kinetic model of cardiac muscle was used to simulate contraction of the left ventricle using a cylindrical approximation of its shape.

  • Computational results are in good agreement with the time course of hemodynamic and geometrical parameters during a heart beat.

  • The model shows the importance of the change in fiber orientation within the ventricle wall. The ventricle twist leads to more uniform distribution of sarcomere length.

  • The model confirms that the changes in ventricle geometry found in hearts with hypertrophic and dilated cardiomyopathies result in the maintenance of the stroke volume in spite of decreased contractile force or shortening velocity, respectively.


Syomin FyodorInstitute of Mechanics, Lomonosov Moscow State Universitysan@aviel.ru


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