In this work features of propagation of electrical excitation waves in inhomogeneous anisotropic moving myocardium is considered. The conductivity values in different directions differ by an order of magnitude. The orientation of anisotropy axes significantly changes across the heart wall. Accounting for changes in the macroconductivity of the myocardium during its deformation is based on the analysis of its microstructure. The strain-activated channel (SAC) model is generalized for the case of triaxial strain under the following assumptions: the channels are evenly distributed over the cell surface or in t-tubules; the channels respond to a local increase in the area of the intercellular membrane site; the formula that uses elongation along the fiber is true for one-dimensional stretching along the fiber. Formulas are obtained for the cases of the arrangement of channels on the outer surface of the cell and in tubules. The fraction of stretched membrane regions where SAC can be activated was found.

The reported study was funded by RFBR and Perm Krai according to the research project N 19-41-590002

1.
P.E.
Hand
,
B.E.
Griffith
, and
C.S.
Peskin
, “
Deriving macroscopic myocardial conductivities by homogenization of microscopic models
,”
Bulletin of Mathematical Biology
71
,
1707
1726
(
2009
).
2.
G.
Richardson
and
S.J.
Chapman
, “
Derivation of the bidomain equations for a beating heart with a general microstructure
,”
SIAM Journal on Applied Mathematics
71
,
657
675
(
2011
).
3.
J.
Sundnes
,
G.T.
Lines
,
X.
Cai
,
B.F.
Nielsen
,
K-A.
Mardal
, and
A.
Tveito
,
Computing the Electrical Activity in the Heart
(
Springer-Verlag
,
2006
).
4.
M.
Potse
,
B.
Dube
,
J.
Richer
,
A.
Vinet
, and
R.M.
Gulrajani
, “
A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart
,”
IEEE Transactions on Biomedical Engineering
53
,
2425
2435
(
2006
).
5.
B.J.
Roth
, “
How to explain why unequal anisotropy ratios is important using pictures but no mathematics
,” in
Proc. of the 2006 Int. Conf. of the IEEE Engineering in Medicine and Biology Society
.
New York, USA
,
August 30-September 3, 2006
. (
2006
) pp.
580
583
.
6.
A. R.
Wikswo
J.P.,
Lin
S.-F.
, “
Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation
,”
Biophys. J.
69
,
2195
2210
(
1995
).
7.
A.
Logg
,
K.-A.
Mardal
,
G. N.
Wells
, et al.,
Automated Solution of Differential Equations by the Finite Element Method
, edited by
A.
Logg
,
K.-A.
Mardal
, and
G. N.
Wells
(
Springer
,
2012
).
8.
H. P.
Langtangen
and
A.
Logg
,
Solving PDEs in Python–The FEniCS Tutorial I
(
Springer
,
2017
).
9.
I.J.
Le Grice
,
P.J.
Hunter
, and
B.H.
Smaill
, “
Laminar structure of the heart: a mathematical model
,”
Am. J. Physiol.
272
,
H2466
H2476
(
1997
).
10.
F.J.
Vetter
,
S.B.
Simons
,
S.
Mironov
,
C.J.
Hyatt
, and
A.M.
Pertsov
, “
Epicardial fiber organization in swine right ventricle and its impact on propagation
.”
Circulation Research
96
,
244
251
(
2005
).
11.
I.N.
Vasserman
,
V.P.
Matveenko
,
I.N.
Shardakov
, and
A.P.
Shestakov
, “
Numerical simulation of the propagation of electrical excitation in the heart wall taking its fibrous laminar structure into account
.”
Biophysics
60
,
613
621
(
2015
).
12.
I.N.
Vasserman
,
V.P.
Matveenko
,
I.N.
Shardakov
, and
A.P.
Shestakov
,
“The mechaism of the initiation of cardiac arrhythmias due to a pathological distribution of myocardial conductivity.
”.
13.
I.N.
Vasserman
,
V.P.
Matveenko
,
I.N.
Shardakov
, and
A.P.
Shestakov
, “
Derivation of the macroscopic intracellular conductivity of deformed myocardium on the basis of microstructure analysis
,”
Biophysics
63
(
3
),
455
462
(
2018
).
14.
I.N.
Vasserman
,
I.N.
Shardakov
, and
A.P.
Shestakov
, “
Influence of the deformation on the propagation of waves of excitation in the heart tissue
,”
Russian Journal of Biomechanics
22
(
3
),
332
342
(
2018
).
15.
P.
Kohl
and
F.
Sachs
, “
Mechanoelectric feedback in cardiac cells
,”
Phil. Trans. R. Soc. Lond. A.
359
,
1173
1185
(
2001
).
16.
J.
Keener
and
J.
Sneyd
,
Mathematical Physiology
(
Springer
,
2009
).
17.
J.B.
Youm
 et al, “
Role of stretch-activated channels on the stretch-induced changes of rat atrial myocytes
,”
Prog Biophys Mol Biol.
90
,
186
206
(
2006
).
18.
N.H.
Kuijpers
 et al, “
Mechanoelectric feedback leads to conduction slowing and block in acutely dilated atria: a modeling study of cardiac electromechanics
.”
Am. J. Physiol.
292
,
H2832
H2853
(
2007
).
19.
C.R.
Kong
,
N.
Bursac
, and
L.
Tung
, “
Mechanoelectrical excitation by fluid jets in monolayers of cultured cardiac myocytes
,”
J. Appl. Physiol.
98
,
2328
2336
(
2005
).
20.
P.
Wiggins
and
R.
Phillips
, “
Mechanoelectrical excitation by fluid jets in monolayers of cultured cardiac myocytes
,”
J. Appl. Physiol.
88
,
880
902
(
2005
).
21.
H.
Sackin
, “
Stretch-activated ion channels
.”
Kidney International
48
,
1134
1177
(
1995
).
22.
B.F.
Guharay
and
F.
Sachs
, “
Stretch-activated single ion channel currents in tissue-cultured embriolitic chick skeletal muscle
,”
J.Physiol.
352
,
685
701
(
1984
).
23.
A.
Reed
,
P.
Kohl
, and
R.
Peyronnet
, “
Molecular candidates for cardiac stretch-activated ion channels
.”
Glob. Cardiol. Sci. Pract.
2014
,
9
25
(
2014
).
This content is only available via PDF.
You do not currently have access to this content.