Electrophysiological properties of computational human ventricular
cell action potential models under acute ischemic conditions
Sara Dutta
a
,
*
, Ana Minchol
e
a
, T. Alexander Quinn
b
, Blanca Rodriguez
a
a
Department of Computer Science, University of Oxford, Oxford, UK
b
Department of Physiology and Biophysics, Dalhousie University, Halifax, Canada
article info
Article history:
Received 1 August 2016
Received in revised form
30 December 2016
Accepted 15 February 2017
Available online 20 February 2017
Keywords:
Arrhythmias
Action potential duration
Conduction velocity
Myocardial ischemia
Human ventricular cell models
Refractory period
abstract
Acute myocardial ischemia is one of the main causes of sudden cardiac death. The mechanisms have been
investigated primarily in experimental and computational studies using different animal species, but
human studies remain scarce. In this study, we assess the ability of four human ventricular action po-
tential models (ten Tusscher and Panfilov, 2006; Grandi et al., 2010; Carro et al., 2011; O'Hara et al., 2011)
to simulate key electrophysiological consequences of acute myocardial ischemia in single cell and tissue
simulations. We specifically focus on evaluating the effect of extracellular potassium concentration and
activation of the ATP-sensitive inward-rectifying potassium current on action potential duration, post-
repolarization refractoriness, and conduction velocity, as the most critical factors in determining
reentry vulnerability during ischemia. Our results show that the Grandi and O'Hara models required
modifications to reproduce expected ischemic changes, specifically modifying the intracellular potassium
concentration in the Grandi model and the sodium current in the O'Hara model. With these modifica-
tions, the four human ventricular cell AP models analyzed in this study reproduce the electrophysio-
logical alterations in repolarization, refractoriness, and conduction velocity caused by ac ute myocardial
ischemia. However, quantitative differences are observed between the models and overall, the ten
Tusscher and modified O'Hara models show closest agreement to experimental data.
© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
(
http://creativecommons.org/licenses/by/4.0/).
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ 41
2. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ 41
2.1. Human ventricular cell models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........................................41
2.2. Ischemic electrophysiological changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......................................41
2.3. Modifications to the ORd and GPB models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......................................42
2.4. Stimulation protocols and electrophysiological measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................42
2.5. Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........................................42
3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ 42
3.1. AP and ionic currents under control and ischemic conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................42
3.2. APD and resting membrane potential under varying ischemic conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................45
3.3. PRR under varying ischemic conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......................................45
3.4. CV, upstroke velocity and peak voltage under varying ischemic conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........................46
3.5. APD and CV restitution curves under control and ischemic conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................47
3.6. Comparison to experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........................................47
4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ 49
4.1. All models reproduce ischemia-induced changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......................................49
4.2. Comparison between experimental and simulation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................50
* Corresponding author. Department of Computer Science, University of Oxford,
Parks Road, OX1 3QD, Oxford, United Kingdom.
E-mail address:
sara.dutta@cs.ox.ac.uk (S. Dutta).
Contents lists available at ScienceDirect
Progress in Biophysics and Molecular Biology
journal homepage: www.elsevier.com/locate/pbiomolbio
http://dx.doi.org/10.1016/j.pbiomolbio.2017.02.007
0079-6107/© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Progress in Biophysics and Molecular Biology 129 (2017) 40e52
5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................. 50
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................50
Supplementary data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................. 50
Disclosures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................. 50
Funding sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................. 50
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................50
1. Introduction
One of the major causes of sudden cardiac death is acute
myocardial ischemia, resulting from an imbalance in the supply and
demand of oxygen and nutrients to the heart. During the first
10e15 min of ischemia, metabolic and electrophysiological changes
occur rapidly and vary spatially, resulting in a shortening of action
potential duration (APD), a prolongation of effective refractory
period (ERP) beyond APD (termed post-repolarization refractori-
ness, PRR), and a reduction of AP upstroke and conduction velocity
(CV) compared to normal tissue (
Sutton et al., 2000; Taggart, 2000).
The resulting electrophysiological heterogeneities between normal
and ischemic tissue provide the substrate for reentrant arrhyth-
mias, as demonstrated in experimental and simulation studies
(
Dutta et al., 2016; Janse and Wit, 1989; Pogwizd and Corr, 1987;
Tice et al., 2007
). Previous research has shown that these changes
are mainly caused by: hyperkalemia (increased extracellular po-
tassium concentration, [K
þ
]
o
)(Pandit et al., 2010; Schaapherder
et al., 1990
), which results in an increase in cell resting mem-
brane potential and decreased cell excitability; hypoxia (inadequate
supply of oxygen) (
Van Wagoner and Lamorgese, 1994; Weiss et al.,
1992
), which results in an opening of ATP-sensitive inward-recti-
fying potassium current (I
K(ATP)
) channels; and acidosis (reduced
intracellular pH) (
Sato et al., 1985; Yatani et al., 1984), which de-
creases the conductance of the sodium (I
Na
) and L-type calcium
(I
CaL
) currents (Carmeliet, 1999). However, ischemia is a complex
and dynamic process, which needs to be further investigated for a
better understanding of ischemia-induced arrhythmia
mechanisms.
Most research on ischemia has been carried out in animals
(Carmeliet, 1999; Coronel et al., 1988; Fiolet et al., 1985; Furukawa
et al., 1991; Ma and Wang, 2007; Pandit et al., 2011;
Schaapherder et al., 1990; Wilensky et al., 1986
), and data from
human is scarce (
Sutton et al., 2000; Taggart, 2000). Therefore,
extrapolation of mechanisms from animal to human is challenging,
but can be facilitated by computational modeling using multi-scale
human-specific models (
Rodriguez et al., 2016). These computa-
tional models provide a flexible platform to impose specific
changes not possible in experimental studies and dissect mecha-
nisms with high spatio-temporal resolution, to increase our un-
derstanding of ischemia-induced arrhythmic mechanisms in
human. Most human models, however, have been created and
evaluated using data from healthy cells and their applicability for
simulations of ischemia is currently unknown. Therefore, it is
important to assess their behavior under varied ischemic condi-
tions, as the ischemic changes described above vary through time
and space in and around the ischemic area (
Coronel et al., 1988;
Fiolet et al., 1985; Schaapherder et al., 1990; Wilensky et al.,
1986
). Furthermore, even species-specific (e.g., human) models
are based on experimental data acquired from different species
(e.g., rabbit, pig, etc.) (
Niederer et al., 2009); a comparison and
assessment between the different model outputs and to experi-
mental data is thus necessary, especially under varying conditions
such as ischemia, as has been done in previous studies (Cherry and
Fenton, 2007; Gemmell et al., 2016; O'Hara and Rudy, 2012; ten
Tusscher et al., 2006
).
The aim of this study is to investigate the response of the four
most recent computational human-specific ventricular action po-
tential (AP) models (the
ten Tusscher and Panfilov, 2006; Grandi
et al., 2010; Carro et al., 2011; O'Hara et al. 2011
models) to varied
ischemic conditions by comparing electrophysiological properties
in single cell and tissue simulations in order to assess their utility
for studying mechanisms of arrhythmogenesis during the initial
phase of acute myocardial ischemia.
2. Methods
2.1. Human ventricular cell models
Four human ventricular models were investigated in this study:
the ten Tusscher et al., the Grandi et al., the Carro et al., and the
O'Hara et al. models (
Carro et al., 2011; Grandi et al., 2010; O'Hara
et al., 2011; ten Tusscher and Panfilov, 2006
); a detailed descrip-
tion of the models can be found in the original publications. The ten
Tusscher et al. (TP06) model is the most widely used and studied
human model, it is based on a previous human model from the
same group (
ten Tusscher et al., 2004). However, the model does
not adequately reproduce AP response to frequency changes and
block of potassium currents. The Grandi et al. model (GPB), based
on a previously developed rabbit cell model (
Shannon et al., 200 4),
overcomes limitations of the TP06 model. However, based on an
analysis of GPB APD restitution and rate adaptation shortcomings,
Carro et al. (CRLP) modified and reformulated various currents,
including I
CaL
and the inward rectifying potassium current, I
K1
;
although the CRLP calcium dynamics still needs further improve-
ment compared to the TP06 calcium dynamics. Finally, the most
recent human cell model is the
O'Hara et al., 2011 model (ORd)
(
O'Hara et al., 2011), based on human data obtained from over 100
undiseased human hearts. Most notably, the model incorporates
the effects of Ca
2þ
/calmodulin-dependent protein kinase II (CaMK)
on known ionic currents. Nonetheless, the model is limited in
simulating hyperkalemia in tissue, as the model does not reproduce
propagation of excitation for [K
þ
]
o
6 mM; an issue that we
address in this study.
2.2. Ischemic electrophysiological changes
The I
K(ATP)
current:I
KðATPÞ
¼ G
KðATPÞ
f
KðATPÞ
½K
þ
o
½K
þ
o;n
!
0:24
ðV
m
E
K
Þ;
was based on a previous formulations (
Ferrero et al., 1996;
Michailova et al., 2007; Shaw and Rudy, 1997
) and added to the
cell models using COR (
Garny et al., 2003). The amplitude of the
current depends on the ratio of the present [K
þ
]
o
, and the control
value of [K
þ
]
o
([K
þ
]
o,n
). It also depends on the membrane potential
of the cell, V
m
, and the Nernst potential of potassium, E
K
. We used
the value estimated by
Michailova et al. (2007). for the channel
conductance (G
K(ATP)
¼ 0.05 mS/
m
F) and used f
K(ATP)
as a scaling
factor to vary peak I
K(ATP)
conductance in the models.
We simulated the electrophysiological consequences of the
S. Dutta et al. / Progress in Biophysics and Molecular Biology 129 (2017) 40e52 41
initial phase of acute myocardial ischemia (first 10e15 min), the
time period with highest arrhythmic risk following the onset of
ischemia (
Carmeliet, 1999; Janse and Wit, 1989; Kazbanov et al.,
2014; Tr
enor et al., 2005
), as in previous computational
(
Heidenreich et al., 2012; Tice et al., 2007; Tr
enor et al., 2005) and
experimental (
Irisawa and Sato, 1986; Sato et al., 1985; Yatani et al.,
1984
) studies. Hyperkalemia and hypoxia are the two major
ischemic conditions affecting APD and PRR, important de-
terminants of reentry during ischemia, and were simulated through
changes in [K
þ
]
o
and I
K(ATP)
. They were varied to cover the range of
values observed experimentally from control to ischemic condi-
tions (
Carmeliet, 1999; Coronel, 1994; Van Wagoner and
Lamorgese, 1994; Weiss and Shine, 1982
) and to reproduce gradi-
ents that are observed at the border zone between the ischemic
central area and healthy tissue (
Coronel, 1994; Schaapherder et al.,
1990; Wilensky et al., 1986
); a highly heterogeneous region that is
prone to ectopic beats and plays an important role in arrhythmo-
genesis (
Bernus et al., 2005; Coronel et al., 1991). [K
þ
]
o
was
increased from 4 to 9 mM, in steps of 1 mM, and I
K(ATP)
peak
conductance (varied through f
K(ATP)
) was increased from 0 to 0.2, in
steps of 0.02 in single cell and 0.04 in tissue. Peak I
Na
and I
CaL
conductances were decreased by 25% in all simulations and were
not varied, as they play a smaller role in modulating APD and PRR
compared to [K
þ
]
o
and I
K(ATP)
(Tice et al., 2007; Yatani et al., 1984).
2.3. Modifications to the ORd and GPB models
The original versions of the ORd and GPB models display certain
limitations when simulating ischemia: the ORd model does not
reproduce PRR in single cell, nor propagation of excitation during
hyperkalemia in tissue, while the GPB model does not show exci-
tation propagation for [K
þ
]
o
greater than 8 mM. In order to over-
come the limitations of these two models for simulations of
ischemia, the I
Na
formulation and the intracellular potassium con-
centration ([K
þ
]
i
) were modified in the ORd and the GPB models,
respectively. As suggested by O'Hara in a comment on the ORd
model, the I
Na
formulation was replaced by the TP06 I
Na
formula-
tion (referred to here as the ORd (TP06 I
Na
) model). Under normal
conditions, as described by Elshrif and Cherry, the ORd (TP06 I
Na
)
model reproduces a more physiologic CV compared to the original
ORd model, while leaving the main other action potential features
unchanged (Elshrif and Cherry, 2014). In addition, we developed an
adaptation of the original ORd model (referred to as ORd (modified
I
Na
) model), which preserves the CaMK effects on I
Na
included in the
original ORd model (
Wagner et al., 2006), by only changing the I
Na
inactivation gates. Specifically, we changed the steady state of the
inactivation h gate as in (
Passini et al., 2016) and further improved
tissue propagation under hyperkalemia by modifying the time
constants of the inactivation gates to match the TP06 I
Na
formula-
tion (see supplemental material). These changes allow the new
versions of the ORd model to overcome limitations of the original
model, namely to reproduce the observed increase in PRR under
ischemic conditions in single cell, as well as to allow activation
propagation in tissue with elevated [K
þ
]
o
. Finally, the [K
þ
]
i
of the
original GPB model was changed from 120 to 138 mM as in the
CRLP model, allowing the new GPB model to show propagation of
excitation in tissue for [K
þ
]
o
¼ 9 mM (this is not the case with the
original GPB model).
2.4. Stimulation protocols and electrophysiological measurements
Single cell simulations were run to steady state for 1000 beats
with a 1 ms stimulus of 50
m
A/
m
F applied every 1000 ms, set at
two times control diastolic threshold as in (Sutton et al., 200 0).
Tissue simulations were run in a 5 cm long strand of tissue for 5
beats with a 0.5 ms stimulus of 10
6
m
A/cm
3
(equivalent
to 71 4
m
A/
m
F given a surface area to volume ratio of 1400 cm
1
and a capacitance of 1
m
F/cm
2
) applied every 1000 ms to the cell at
position x ¼ 0 cm. Both in single cell and tissue simulations the
electrophysiological properties were calculated using the last beat.
AP amplitude (APA) was calculated as the difference between the
peak and resting membrane potential (V
rest
) during the last beat.
APD was calculated as the difference between the time of
maximum upstroke velocity and the time when the cell repolarizes
to 90% of its APA. ERP was calculated once the cell was at steady
state by applying a stimulus at progressively shorter coupling in-
tervals (S2), with 10 ms precision. In single cell, ERP was defined as
the minimum S2 coupling interval (greater than the APD) that
triggered an AP (defined as having a plateau above 20 mV). In
tissue simulations, ERP was defined by the minimum S2 coupling
interval that triggered an AP in the cell at position x ¼ 3 cm. The
PRR was calculated as the difference between ERP and APD. CV was
calculated between the cell at position 1 cm and the cell at position
3 cm as the difference in time of maximum upstroke velocity (dV/
dt
max
) at each position divided by the distance between the two
cells. APD and CV restitution curves were calculated in tissue by
pacing for 5 beats with a coupling interval of 1000 ms and then
delivering a progressively shorter S2 coupling interval (in 100 ms
increments) until propagation failure. Convergence of tissue sim-
ulations results was assessed by comparing metrics after 5, 10 and
100 beats under ischemic conditions ([K
þ
]
o
¼ 9 mM and
f
K(ATP)
¼ 0.2); all models showed a change of less than 3% in CV,
APD90 and V
rest
when 5 and 100 beats were compared.
2.5. Numerical methods
Single cell simulations were run in MATLAB for all models.
Equations were solved using ode15s with a maximum time step of
1 ms, and a relative and absolute tolerance of 10
7
and 10
9
to
ensure numerical convergence. Tissue simulations were run using
Chaste (
Pitt-Francis et al., 2009) with a space discretization of
0.01 cm. The ODE and PDE time steps were set to 0.001 ms and
0.01 ms for all the models, which ensured convergence of results.
The forward Euler method was used to solve the set of ODEs and the
monodomain model described the electrical activity of the
myocardium through a parabolic differential equation, which was
solved using the finite element method (
Bernabeu et al., 2014,p.
20;
Pathmanathan et al., 2010).
3. Results
3.1. AP and ionic currents under control and ischemic conditions
Fig. 1 shows the AP, transient outward potassium current (I
to
),
rapid (I
Kr
) and slow (I
Ks
) delayed rectifier potassium current, I
Na
and
I
CaL
traces for all models under control ([K
þ
]
o
¼ 4 mM and
f
K(ATP)
¼ 0) and ischemic ([K
þ
]
o
¼ 9 mM and f
K(ATP)
¼ 0.2) condi-
tions. We notice that all models display different AP and current
morphologies in both control and ischemic conditions. For
example, the GPB and CRLP models have a longer control APD than
the other models, due to a lower I
Kr
current; however, under
ischemic conditions all models show similar APDs. Furthermore,
the TP06 AP has a more pronounced notch and plateau phase
compared to the other models, due to its higher I
CaL
and I
to
currents,
both in control and ischemia. There are no clear differences in AP
morphology between the original ORd model and the ORd (TP06
I
Na
) and ORd (modified I
Na
) models, apart from the AP peak
amplitude due to the changes in I
Na
. Finally, as expected under
ischemic conditions, in all models, the APD decreases and V
rest
increases.
S. Dutta et al. / Progress in Biophysics and Molecular Biology 129 (2017) 40e5242
Fig. 1. Action potential (AP), slow (I
Ks
) and rapid (I
Kr
) delayed rectifier potassium current, L-type calcium current (I
CaL
), peak sodium current (I
Na
) and transient outward potassium
current (I
to
) traces in single cell under (A.) control ([K
þ
]
o
¼ 4 mM; f
K(ATP)
¼ 0) and (B.) ischemic ([K
þ
]
o
¼ 9 mM; f
K(ATP)
¼ 0.2) conditions for all the models: ten Tusscher (TP06; black
solid line), Grandi (GPB; yellow solid line), Carro (CRLP; green solid line), original O'Hara (original ORd; purple dotted line), O'Hara with TP06 I
Na
(ORd (TP06 I
Na
); red dotted line)
and O'Hara with modified I
Na
(ORd (modified I
Na
); blue dotted line). The same x- and y-axis limits were applied for the respective plots in (A.) and (B.); and inset plots were added to
(B.).
S. Dutta et al. / Progress in Biophysics and Molecular Biology 129 (2017) 40e52 43
Fig. 2. AP traces (A.) and range of AP duration (APD) and resting membrane potential (V
rest
) (B.) under varying ischemic conditions ([K
þ
]
o
is varied from 4 to 9 mM; f
K(ATP)
is varied
from 0 to 0.2) in single cell (A.) and both single cell and tissue (B.) for all models. The green AP trace and cross represent control conditions ([K
þ
]
o
¼ 4 mM; f
K(ATP)
¼ 0) and the red AP
trace and cross represent the most ischemic conditions ([K
þ
]
o
¼ 9 mM; f
K(ATP)
¼ 0.2). In (A.), Arrow 1 emphasizes the decrease in APD mainly due to f
K(ATP)
increasing from 0 (green)
to 0.2 (red). Arrow 2 emphasizes the increase in V
rest
mainly due to [K
þ
]
o
increasing from 4 mM (green) to 9 mM (red). *Original ORd model does not enable tissue simulations for
varied [K
þ
]
o
due to the I
Na
formulation (see Methods).