One of the most important characteristics of red blood cells is their elasticity and ability to return to original biconcave shape after external forces stop acting on them. There are several conservation laws that together govern this return and one of them is the area conservation. In this paper, we focus on local area conservation and introduce a new way of modeling it using a spring network model. We take into account the current shape of the network triangles and find the proportional allocation of area conservation forces, which would for individual triangles preserve their shapes. Since the force contributions in each node are combined from all adjacent triangles, the final resulting shape might not be the same, but overall effect on the triangulations is positive in the sense that this approach tends to regularize them.

1.
P.
Gaehtgens
,
C.
Duhrssen
, and
A.
K.H.
,
Blood Cells
6
,
799
817
(
1980
).
2.
X.
Xu
,
P.
Sarder
,
Z.
Li
, and
A.
Nehorai
,
Biomicrofluidics
7
, – (
2013
).
3.
N.
Mohandas
, and
P.
Gallagher
,
Blood
112
,
3939
3948
(
2008
).
4.
M.
Dupin
,
I.
Halliday
,
C.
Care
, and
L.
Alboul
,
Phys Rev E
75
,
066707
(
2007
).
5.
B.
Dunweg
, and
A. J. C.
Ladd
,
Advances in Polymer Science
221
,
89
166
(
2009
).
6.
Z.
Feng
, and
E.
Michaelides
,
Journal of Computational Physics
195
,
602
628
(
2004
).
7.
I.
Cimrák
,
M.
Gusenbauer
, and
T.
Schrefl
,
Computers and Mathematics with Applications
64
,
278
288
(
2012
).
8.
I.
Cimrák
,
I.
Jančigová
,
K.
Bachratá
, and
H.
Bachratý
, “
On elasticity of spring network models used in blood flow simulations in ESPResSo
,” in
III International Conference on Particle-based Methods – Fundamentals and Applications PARTICLES 2013
, edited by
M.
Bisschoff
,
E.
Oñate
,
D.
Owen
,
E.
Ramm
, and
P.
Wriggers
,
2013
, pp.
133
144
.
9.
I.
Jancčigová
, and
R.
Tóthová
, “
Scalability of forces in mesh-based models of elastic objects
,” in
ELEKTRO 2014: 10th International Conference
,
IEEE
,
2014
, pp.
562
566
.
10.
R.
Tóthová
,
I.
Jančigová
, and
I.
Cimrák
, “
Energy contributions of different elastic moduli in mesh-based modeling of deformable objects
,” in
ELEKTRO 2014: 10th International Conference
,
IEEE
,
2014
, pp.
634
638
.
11.
A.
Arnold
,
O.
Lenz
,
S.
Kesselheim
,
R.
Weeber
,
F.
Fahrenberger
,
D.
Roehm
,
P.
Košovan
, and
C.
Holm
, “ESPResSo 3.1 - Molecular Dynamics Software for Coarse–Grained Models,” in
Meshfree Methods for Partial Differential Equations VI
,
Lecture Notes in Computational Science and Engineering
, edited by
M.
Griebel
, and
M.
Schweitzer
,
2013
, vol.
89
, pp.
1
23
.
12.
A.
Henderson
,
ParaView guide, A Parallel Visualization Application
,
Tech. rep
.,
Kitware Inc
. (
2007
).
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