<s>
The	O
Bueno-Orovio	B-Algorithm
–	I-Algorithm
Cherry	I-Algorithm
–	I-Algorithm
Fenton	I-Algorithm
model	I-Algorithm
,	O
also	O
simply	O
called	O
Bueno-Orovio	O
model	O
,	O
is	O
a	O
minimal	O
ionic	O
model	O
for	O
human	O
ventricular	O
cells	O
.	O
</s>
<s>
It	O
belongs	O
to	O
the	O
category	O
of	O
phenomenological	O
models	O
,	O
because	O
of	O
its	O
characteristic	O
of	O
describing	O
the	O
electrophysiological	B-Algorithm
behaviour	O
of	O
cardiac	O
muscle	O
cells	O
without	O
taking	O
into	O
account	O
in	O
a	O
detailed	O
way	O
the	O
underlying	O
physiology	O
and	O
the	O
specific	O
mechanisms	O
occurring	O
inside	O
the	O
cells	O
.	O
</s>
<s>
This	O
mathematical	O
model	O
reproduces	O
both	O
single	O
cell	O
and	O
important	O
tissue-level	O
properties	O
,	O
accounting	O
for	O
physiological	O
action	B-Algorithm
potential	I-Algorithm
development	O
and	O
conduction	B-Algorithm
velocity	I-Algorithm
estimations	O
.	O
</s>
<s>
It	O
also	O
provides	O
specific	O
parameters	O
choices	O
,	O
derived	O
from	O
parameter-fitting	O
algorithms	O
of	O
the	O
MATLAB	B-Language
Optimization	B-Application
Toolbox	I-Application
,	O
for	O
the	O
modeling	O
of	O
epicardial	O
,	O
endocardial	O
and	O
myd-myocardial	O
tissues	O
.	O
</s>
<s>
In	O
this	O
way	O
it	O
is	O
possible	O
to	O
match	O
the	O
action	B-Algorithm
potential	I-Algorithm
morphologies	O
,	O
observed	O
from	O
experimental	O
data	O
,	O
in	O
the	O
three	O
different	O
regions	O
of	O
the	O
human	O
ventricles	O
.	O
</s>
<s>
The	O
Bueno-Orovio	B-Algorithm
–	I-Algorithm
Cherry	I-Algorithm
–	I-Algorithm
Fenton	I-Algorithm
model	I-Algorithm
is	O
also	O
able	O
to	O
describe	O
reentrant	O
and	O
spiral	O
wave	O
dynamics	O
,	O
which	O
occurs	O
for	O
instance	O
during	O
tachycardia	B-Application
or	O
other	O
types	O
of	O
arrhythmias	B-Application
.	O
</s>
<s>
One	O
PDE	O
,	O
similar	O
to	O
the	O
monodomain	B-Algorithm
model	I-Algorithm
,	O
for	O
an	O
adimensional	O
version	O
of	O
the	O
transmembrane	O
potential	O
,	O
and	O
three	O
ODEs	O
that	O
define	O
the	O
evolution	O
of	O
the	O
so	O
called	O
gating	O
variables	O
,	O
i.e.	O
</s>
<s>
The	O
adimensional	O
transmembrane	O
potential	O
can	O
be	O
rescaled	O
in	O
mV	O
by	O
means	O
of	O
the	O
affine	B-Algorithm
transformation	I-Algorithm
.	O
</s>
<s>
Different	O
parameters	O
sets	O
,	O
as	O
shown	O
in	O
Table	O
1	O
,	O
can	O
be	O
used	O
to	O
reproduce	O
the	O
action	B-Algorithm
potential	I-Algorithm
development	O
of	O
epicardial	O
,	O
endocardial	O
and	O
mid-myocardial	O
human	O
ventricular	O
cells	O
.	O
</s>
<s>
In	O
order	O
to	O
trigger	O
the	O
action	B-Algorithm
potential	I-Algorithm
development	O
in	O
a	O
certain	O
position	O
of	O
the	O
domain	O
,	O
a	O
forcing	O
term	O
,	O
which	O
represents	O
an	O
externally	O
applied	O
density	O
current	O
,	O
is	O
usually	O
added	O
at	O
the	O
right	O
hand	O
side	O
of	O
the	O
PDE	O
and	O
acts	O
for	O
a	O
short	O
time	O
interval	O
only	O
.	O
</s>
<s>
The	O
Bueno-Orovio	B-Algorithm
–	I-Algorithm
Cherry	I-Algorithm
–	I-Algorithm
Fenton	I-Algorithm
model	I-Algorithm
can	O
be	O
rewritten	O
in	O
the	O
compact	O
form	O
:	O
</s>
<s>
To	O
obtain	O
the	O
weak	B-Algorithm
formulation	I-Algorithm
:	O
</s>
<s>
perform	O
an	O
integration	O
by	O
parts	O
of	O
the	O
diffusive	O
term	O
of	O
the	O
first	O
monodomain-like	O
equation	O
:	O
</s>
<s>
Finally	O
the	O
weak	B-Algorithm
formulation	I-Algorithm
reads	O
:	O
</s>
<s>
There	O
are	O
several	O
methods	O
to	O
discretize	O
in	O
space	O
this	O
system	O
of	O
equations	O
,	O
such	O
as	O
the	O
finite	B-Application
element	I-Application
method	I-Application
(	O
FEM	O
)	O
or	O
isogeometric	B-Algorithm
analysis	I-Algorithm
(	O
IGA	O
)	O
.	O
</s>
<s>
Time	O
discretization	O
can	O
be	O
performed	O
in	O
several	O
ways	O
as	O
well	O
,	O
such	O
as	O
using	O
a	O
backward	B-Algorithm
differentiation	I-Algorithm
formula	I-Algorithm
(	O
BDF	O
)	O
of	O
order	O
or	O
a	O
Runge	B-Algorithm
–	I-Algorithm
Kutta	I-Algorithm
method	I-Algorithm
(	O
RK	O
)	O
.	O
</s>
<s>
Let	O
be	O
a	O
tessellation	B-Algorithm
of	O
the	O
computational	O
domain	O
by	O
means	O
of	O
a	O
certain	O
type	O
of	O
elements	O
(	O
such	O
as	O
tetrahedrons	O
or	O
hexahedra	O
)	O
,	O
with	O
representing	O
a	O
chosen	O
measure	O
of	O
the	O
size	O
of	O
a	O
single	O
element	O
.	O
</s>
<s>
In	O
the	O
framework	O
of	O
SVI	O
,	O
by	O
denoting	O
with	O
and	O
the	O
quadrature	B-Algorithm
nodes	O
and	O
weights	O
of	O
a	O
generic	O
element	O
of	O
the	O
mesh	O
,	O
both	O
and	O
are	O
evaluated	O
at	O
the	O
quadrature	B-Algorithm
nodes	O
:	O
</s>
<s>
The	O
equations	O
for	O
the	O
three	O
gating	O
variables	O
,	O
which	O
are	O
ODEs	O
,	O
are	O
directly	O
solved	O
in	O
all	O
the	O
degrees	O
of	O
freedom	O
(	O
DOF	O
)	O
of	O
the	O
tessellation	B-Algorithm
separately	O
,	O
leading	O
to	O
the	O
following	O
semidiscrete	O
form	O
:	O
</s>
