mechanical function from tissue model to organ model Vladimir Zverev Sergey Pravdin Leonid Katsnelson Olga Solovyova Ural Federal University Institute of Immunology and Physiology ID: 931567
Download Presentation The PPT/PDF document "Modeling of myocardial" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Modeling of myocardial mechanical function: from tissue model to organ model
Vladimir Zverev, Sergey Pravdin, Leonid Katsnelson, Olga Solovyova
Ural Federal University,
Institute of Immunology and Physiology,
Ekaterinburg
Slide2Schematic representation of heart and MRI of the heart
BIOMECHANICS IN THE HEART: AN INTRODUCTION, COMMAS SUMMER SCHOOL Universitat Stuttgart, DE, 2013
Abbreviations: L.A. left atrium, L.V. left ventricle, R.A. right atrium, R.V. right ventricle
Pressures and volumes during the cycle
2
Right atrium
Left atrium
Right ventricle
Heart cycle
Left ventricle
Slide3Reference configuration
Current configuration
displacement
3
is right Cauchy tensor
, where
Notations for kinematic
Slide44
P is first
Piola
-Kirchhoff stress tensor(relates forces in the current configuration with areas in the reference )
BIOMECHANICS
IN THE HEART: AN INTRODUCTION
,
COMMAS SUMMER SCHOOL
Universitat
Stuttgart
, DE
, 2013
Mechanical equation
Holzapfel
, Ogden// Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2009,
Adapted
from
Dokos
et
al
. (2002)
shear stress (
kPa
)
amount of shear
(
adapted
from Dokos et al. ,
2002)
Le
Grice
et
al
. (1995)
Slide55
is transmembrane potential
is
diffusion tensor
is
vector of other state
variables (
T
is element
of
S
)
Equations. Active forces
Phenomenological model
of the electrical activity
Detailed
model
of the
electrical-mechanical
activity
approximately 30 equations
Katsnelson
L.B.
et al //
Russ. J.
Numer
. Anal
.
Math. Model. 2014.
V
.
29. № 5.
p
.
1–26.
Aliev
R.R.,
Panfilov
A. V
. //
Chaos, Solitons and Fractals.
1996
.
v.
7.
p.
293–301.
3
equations
,
,
,
,
,
are parameters of model
initial fiber direction
6Numerical approximation:
key pointsNewton method for solving nonlinear equationsLagrange extrapolation
in order to find initial point for newton iterationWe decrease the time step
when iteration process does not converge
Finite element
method (
FEniCS
framework)
Operator splitting
scheme
M. S.
Alnæs
, J.
Blechta
, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E.
Rognes
and
G. N. Wells (2015).
The
FEniCS
Project Version 1.5
, Archive
of
Numerical
Software, 3(100)
Slide77
Electrical function in 1D Domain
We also emulated the 1D case on
bar-shaped
geometry using an adaptive mesh.
Red color correspond the hugest value of v (transmembrane potential)
Arrival time is first moment
when time when
position [dimensionless]
Study of scalability
of the LV simulation in 3d (electrical function only)
Detailed model
of the electrical activity
Katsnelson L.B. et al // Russ. J.
Numer
. Anal
.
Math. Model. 2014.
v
.
29. № 5. p. 1–26.Sozykin A. et al//Mathematical and
Information Technologies, MIT-2016 7178 points, 26156 tetrahedrons
8
Slide99Simulation of the electrical and mechanical function in 3D model
fibers are parallel to the longest side
Slide1010
Model a wedge preparation of the LV free wallwith the characteristic fiber rotation
fiber orientation
I
. J.
LeGrice
et al //
Am
. J. Physiol.
, vol. 269, no. 2 Pt 2, pp. H571–H582, 1995.
Slide1111
Simulation of the LV diastolic filling
Slide12My deeply acknowledge
to colleges
Sergey Pravdin,
Alexandr Kursanov,
Natalya Vikulova, Anastasya
Khohlova
Pavel
Konovalov
, Tatyana
Chumarnya
,
and prof. Leonid Katsnelson, prof
. Olga SolovyovaThe work is supported by Russian
Science Foundation
Slide13Thank you for your interest