Electrophysiological properties of computational human ventricular cell action potential models under acute ischemic conditions Progress in Biophysics and Molecular Biology

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 Pan ﬁ lov, 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 speci ﬁ cally 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 modi ﬁ cations to reproduce expected ischemic changes, speci ﬁ cally modifying the intracellular potassium concentration in the Grandi model and the sodium current in the O'Hara model. With these modi ﬁ ca- tions, the four human ventricular cell AP models analyzed in this study reproduce the electrophysiological alterations in repolarization, refractoriness, and conduction velocity caused by acute myocardial ischemia. However, quantitative differences are observed between the models and overall, the ten Tusscher and modi ﬁ ed O'Hara models show closest agreement to experimental data. © 2017 The


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 refractoriness, 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 arrhythmias, as demonstrated in experimental and simulation studies 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 potassium concentration, [K þ ] o ) (Pandit et al., 2010;Schaapherder et al., 1990), which results in an increase in cell resting membrane 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-rectifying potassium current (I K(ATP) ) channels; and acidosis (reduced intracellular pH) (Sato et al., 1985;Yatani et al., 1984), which decreases 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 . These computational models provide a flexible platform to impose specific changes not possible in experimental studies and dissect mechanisms with high spatio-temporal resolution, to increase our understanding 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 conditions, 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 experimental 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 potential (AP) models (the ten 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.

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;ten Tusscher and Panfilov, 2006); a detailed description 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., 2004), 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 improvement compared to the TP06 calcium dynamics. Finally, the most recent human cell model is the 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.

Ischemic electrophysiological changes
The I K(ATP) current: 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/mF) 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 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 determinants 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 conditions (Carmeliet, 1999;Coronel, 1994;Van Wagoner and Lamorgese, 1994;Weiss and Shine, 1982) and to reproduce gradients 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 arrhythmogenesis (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).

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 excitation propagation for [K þ ] o greater than 8 mM. In order to overcome the limitations of these two models for simulations of ischemia, the I Na formulation and the intracellular potassium concentration ([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 formulation (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  and further improved tissue propagation under hyperkalemia by modifying the time constants of the inactivation gates to match the TP06 I Na formulation (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).

Stimulation protocols and electrophysiological measurements
Single cell simulations were run to steady state for 1000 beats with a 1 ms stimulus of À50 mA/mF applied every 1000 ms, set at two times control diastolic threshold as in (Sutton et al., 2000). Tissue simulations were run in a 5 cm long strand of tissue for 5 beats with a 0.5 ms stimulus of À10 6 mA/cm 3 (equivalent to À714 mA/mF given a surface area to volume ratio of 1400 cm À1 and a capacitance of 1 mF/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 intervals (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 À20 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 simulations 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.

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 À7 and 10 À9 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).

AP and ionic currents under control and ischemic conditions
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.

APD and resting membrane potential under varying ischemic conditions
Figs. 2 and 3 show AP morphology, APD, and V rest for all models 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 both single cell (Fig. 2) and tissue (Fig. 3). As is shown in Figs. 2A and 3A, all models produce slightly different AP morphologies due to their different ionic formulations. As in single cell, the GPB and CRLP models have a longer control APD than the other models in tissue: 304 and 335 ms for the GPB and CRLP models vs approximately 280 ± 5 ms for the other models. In contrast, in single cell and tissue the differences in APD between the original ORd, the ORd (TP06 I Na ), and the ORd (modified I Na ) models are small (less than 8 ms), except for the ORd (TP06 INa) model, which displays a 16 ms longer APD under tissue ischemic conditions compared to the other models.
All models produce the expected changes in AP morphology under ischemic conditions: a decrease in APD (such as 282 to 138 ms for the TP06 model in single cell) and a less negative resting membrane potential (V rest ) (such as À93 to À73 mV for the TP06 model in single cell). Furthermore, as shown in Fig. 3B, APD decreases as [K þ ] o and f K(ATP) increase. However, the amount of change is different between the models. In fact, the GPB and CRLP models show the biggest change in APD between the control and the ischemic conditions (both in single cell and tissue simulations; as shown in Fig. 2B, single cell APD decreases by 51% and 53% for TP06 and ORd (TP06 I Na ) models vs 61% and 64% for GPB and CRLP models). This difference is due to the smaller repolarizing currents in the GPB and CRLP models (i.e., I Kr and I Ks , as shown in Fig. 1), so that the same amount of I K(ATP) current has a larger effect in the GPB and CRLP models than in the other models. Fig. 4 shows the PRR under varying [K þ ] o and f K(ATP) ischemic conditions for all models both in single cell and tissue, along with the activation and inactivation gates of I Na in single cell. As is shown in Fig. 4, PRR is close to 0 in all cases for [K þ ] o < 7 mM, and as the ischemic conditions become more pronounced, PRR increases. Furthermore, PRR is more sensitive to [K þ ] o than f K(ATP) , due to its increased effects on the excitability of the cell (Carmeliet, 1999;Janse and Wit, 1989). Nonetheless, the greatest PRR for all models (apart from the original ORd and ORd (TP06 I Na ) models in tissue) occurs at the most pronounced ischemic conditions (marked with a red cross in Fig. 4A and 4B) with [K þ ] o ¼ 9 mM and f K(ATP) ¼ 0.2 (in single cell TP06: 75 ms; GPB: 104 ms; CRLP: 115 ms; ORd (TP06 I Na ): 82 ms; ORd (modified I Na ): 49 ms). In Fig. 4B, we notice that ischemic conditions in the ORd (TP06 I Na ) tissue model (represented by the red cross) do not result in the greatest PRR compared to the maximum PRR observed for [K þ ] o ¼ 9 mM and f K(ATP) ¼ 0 (82 vs 160 ms, respectively); therefore, PRR for the ORd (TP06 I Na ) model is more sensitive to changes in f K(ATP) than for the other models.

PRR under varying ischemic conditions
As for APD, the amount of change in PRR induced by ischemia varies from model to model. The TP06, GPB and CRLP models show the greatest increase in PRR, due to a delayed recovery of the I Na current (Fig. 4C), as the activation and inactivation gates recover later and reach a lower steady state than in the other models (apart from the original ORd model). The original ORd model, on the other hand, does not display an increase in PRR in single cell and does not propagate activation in tissue with increased [K þ ] o . This is due to a faster recovery and lower steady state of the I Na inactivation gates (Fig. 4C) than in other models under ischemic conditions. This is improved in the ORd (TP06 I Na ) and ORd (modified I Na ) models; under ischemic conditions the h and j gate steady state value is higher and slower than the original ORd (Fig. 4C), hence, those models reproduce the expected increase in PRR. However, the change is smaller than in the TP06, GPB and CRLP models due to a faster recovery of the activation and inactivation I Na gates. In addition, Fig. 4B shows that PRR in tissue is more pronounced than in single cell. This is due primarily to differences in the method for calculation of ERP between single cell and tissue simulations. In the tissue simulations, the extra stimulus must be strong enough to trigger a wave of activation that will reach the end of the 5 cm strand of tissue to be counted as successful, while in single cells the stimulus only needs to be strong enough to activate a single cell.
Furthermore, studies have shown that differences between single cell and tissue occur due to cell coupling via gap junctions, for example specific conditions are needed in tissue for a single cell's activation to propagate to the neighboring tissue (Joyner et al., 1991;Xie et al., 2010). Fig. 5 shows CV, dV/dt max , and peak V m (V max ) under varying ischemic conditions for all models in single cell and tissue (apart from CV that is calculated in tissue only). Fig. 5A shows that CV, under control conditions, is similar in all models (0.067, 0.077, 0.074, 0.069 and 0.059 cm/ms for the TP06, GPB, CRLP, ORd (TP06 I Na ) and ORd (modified I Na ) models). However, the ORd (modified I Na ) model displays smaller changes in CV during ischemia (0.15 vs 0.4 cm/ms for the TP06, GPB and CRLP models). Fig. 5A also shows that CV becomes slower as [K þ ] o increases, due to reduced I Na availability caused by a less negative resting potential. However, CV is unchanged with variations of f K(ATP) , as the repolarizing current I K(ATP) primarily affects repolarization. Fig. 5B shows that dV/dt max and V max are decreased in all models ) Activation (m gate) and inactivation (j gate) gates of I Na under control and ischemic conditions for all the models (as in Fig. 1). *(as in Fig. 2).

CV, upstroke velocity and peak voltage under varying ischemic conditions
for the most ischemic conditions (red cross). For example, TP06 single cell dV/dt max decreases from 348.5 to 98.9 mV/ms between control and ischemic conditions (green and red cross). Both of these properties are also affected primarily by [K þ ] o , showing little to no change for varying f K(ATP) (data not shown). We notice that the original ORd and ORd (modified I Na ) models display a smaller dV/ dt max than the other models due to a smaller I Na current (Fig. 1). Both dV/dt max and V max for the TP06, GPB, CRLP and ORd (TP06 I Na ) models show greater values in single cell than in tissue, due to the stimulus current being applied directly to the cell in the single cell simulations, while in tissue the stimulus comes from the excitation of the neighboring cells. Nonetheless, both in single cell and tissue, the models reproduce the expected ischemic changes: a decrease in dV/dt max and V max . Fig. 6 shows CV and APD restitution curves for all models under control ([K þ ] o ¼ 4 mM and f K(ATP) ¼ 0) and ischemic conditions ([K þ ] o ¼ 9 mM and f K(ATP) ¼ 0.2). We notice that overall, under ischemic conditions, the restitution curves are flattened (for example TP06 APD restitution slope is decreased from 0.559 in control to 0.015 in ischemia), as shown experimentally (Kurz et al., 1994). In fact, the TP06 and ORd (modified I Na ) models display the flattest APD restitution curve under ischemic conditions, with no change in APD for varying diastolic intervals. On the other hand, the ORd (TP06 I Na ) and GPB models do not display the expected flattening in APD restitution and show a slight increase in slope, while the CRLP model displays alternans for shorter diastolic intervals, as observed experimentally (Kurz et al., 1994). However, for the CV restitution curves under ischemic conditions, the GPB model displays the flattest restitution curve, and all other models show a slight decrease in CV for decreasing cycle length. Table 1 summarizes ischemia-induced changes in electrophysiological properties (APD, PRR, CV, V rest , AP amplitude (APA) and dV/dt max ) in clinical human and experimental animal studies. Sutton et al. and Taggart et al. investigated effects of occlusion of the left anterior descending artery for 3 min in patients while they were undergoing open chest surgery for two different stimuli (Sutton et al., 2000;Taggart, 2000). While Kodama et al., Penny et al., and Kimura et al. investigated the effects of simulated ischemia in in vitro guinea pig and cat for 10 and 15 min of ischemia (Kimura et al., 1990;Kodama et al., 1984;Penny and Sheridan, 1983). Many more ischemia experimental animal studies exist; however, these three studies present a degree of ischemia and corresponding changes in biomarkers that are similar to the ones investigated in our study.

Comparison to experimental data
When comparing simulation results to Sutton et al. and Taggart  (Vermeulen, 1996)) and f K(ATP) ¼ 0.08 (as in (Mor ena et al., 1980)) was chosen to reproduce 3 min of ischemia. Table 2 summarizes changes in APD, PRR, and CV between control ([K þ ] o ¼ 4 mM and f K(ATP) ¼ 0) and 3 min of ischemia ([K þ ] o ¼ 7 mM and f K(ATP) ¼ 0.08) for all models in single cell and tissue simulations. We notice that the TP06 model displays the closest change in APD to experimental data (60 ms in single cell and 65 ms in tissue), while the GPB and CRLP models show more than double the change in APD observed experimentally. Nonetheless, all models show a much smaller increase in PRR than the one observed experimentally, apart for the TP06 model in tissue that shows a 62 ms increase in PRR. Finally, the TP06, GPB and CRLP models show a change in CV that is in line with experimental data. Therefore, overall the TP06 model shows best agreement with experimental data from human after 3 min of ischemia, although the PRR change in single cell is lower. Experimental results in animal models after 10 and 15 min of ischemia were compared to simulation results with [K þ ] o ¼ 9 mM and f K(ATP) ¼ 0.2 set as the ischemic conditions (see Table 3). The change in APD is greater for all models (above 144 ms) than in the animal studies (90 ms maximum); however, if we take the % decrease in APD both the experimental and the simulation results show approximately a 40e50% decrease in APD (results not shown). The increase in V rest observed experimentally is between 11 and 25 mV, and all the models show changes within that range. The same was observed for AP amplitude, apart from the GPB model, which shows a bigger change of 51 and 44 mV in single cell and tissue, respectively. Finally, a wide range of values are observed experimentally for the change in dV/dt max , ranging from 80 to 210 mV/ms. The GPB, CRLP and ORd (modified I Na ) models show values that are greater (up to 463 mV/ms in single cell for the GPB model). The ORd (TP06 I Na ) model shows a particularly low value for both single cell and tissue of 8 and 35 mV/ms respectively. The rest of the tissue simulations also show a slightly lower change in dV/dt max (like the ORd (modified I Na ), TP06, and GPB models). Therefore, overall, the TP06, CRLP, and ORd (modified I Na ) models show good agreement with guinea-pig and cat experimental data, apart from dV/dt max . Fig. 6. APD and CV restitution curves in tissue for all models (apart from the original ORd*; TP06 in black, GPB in yellow, CRLP in green, ORd (TP06 I Na ) in purple and ORd (modified I Na ) in red) under control (solid line) and ischemic conditions (dashed line) for varying diastolic intervals (DI). The CRLP model displays alternans for shorter DIs under ischemic conditions. *(as in Fig. 2).

Discussion
This study investigates the behavior of recent human models under control and varying ischemic conditions by evaluating various electrophysiological properties related to arrhythmic risk (such as APD, PRR and CV) in single cell and tissue, and comparing them to available experimental data. Furthermore, our study is the first to introduce adaptations of the ORd (with a modified I Na current) and the GPB (with a modified [K þ ] i ) models, which can reproduce expected ischemia-induced changes. With the alternative formulations, all models tested reproduce ischemia-induced changes in APD (decrease), V rest (less negative), PRR (increase), CV (slower), dV/dt max (decrease), V max (decrease), and restitution curves (flattening; apart from the GPB and ORd (TP06 I Na ) that do not show APD restitution curve flattening), in line with experimental data (Carmeliet, 1999;Coronel et al., 2012;Janse and Wit, 1989;Sutton et al., 2000;Taggart, 2000;Vermeulen, 1996;Watanabe et al., 1997;Wilensky et al., 1986). Dispersion of these properties between the ischemic and normal tissue is critical for investigations of arrhythmogenesis during ischemia, as they play an important role in triggering and sustaining arrhythmias (Janse and Wit, 1989;Nademanee et al., 1985;Zaitsev et al., 2003). To the best of our knowledge, this is the first systematic comparison of these human ventricular AP models under ischemic conditions, which extends our previous study (Dutta et al., 2013), also yielding adaptations of the ORd and the GPB models for evaluation of ischemic conditions. Furthermore, we show the importance of assessing various electrophysiological markers (as limitations of the original ORd are not apparent if one only measures APD), as well as performing both single cell and tissue simulations (the original ORd does not show propagation of excitation in tissue with hyperkalemia).

All models reproduce ischemia-induced changes
Both the single cell and tissue results show that all models reproduce the expected ischemic APD behavior (Figs. 2e4). As [K þ ] o and peak I K(ATP) increase, APD becomes shorter, with the shortest APD occurring for the highest values of [K þ ] o and peak I K(ATP) (Fig. 3). The increased peak I K(ATP) current accelerates the repolarization process due to an increased outward flux of K þ ions; therefore, decreasing the APD, as has been shown experimentally (Carmeliet, 1999;Coronel et al., 1988;Furukawa et al., 1991;Pandit et al., 2011;Sutton et al., 2000;Watanabe et al., 1997). Overall, all models show good quantitative agreement to animal studies; even though the GPB and CRLP models show more than double the change in APD observed clinically after 3 min of ischemia (see Section 3.5).
Both the single cell and tissue results show that all models (except for the original ORd) reproduce an increase in PRR as [K þ ] o increases (Fig. 4). The longest PRR occurs for the highest values of [K þ ] o and peak I K(ATP) . Experimental data has shown that PRR increases significantly under ischemic conditions, as is described in the review by Coronel et al. (2012). and in the clinical studies carried out by Sutton et al. (2000); however, the increase observed in all models is smaller than the one observed clinically, apart from the TP06 model in tissue (see Section 3.5). As [K þ ] o increases, the resting potential becomes less negative and this reduces sodium channel availability, thus decreasing the cell's excitability, as has been described by Taggart et al. (Taggart and Slater, 1971). In all models, the PRR is more sensitive to changes in [K þ ] o than changes in peak I K(ATP) conductance, as [K þ ] o has a greater effect on cell excitability.
As shown in Fig. 5, CV is significantly slower for high values of [K þ ] o , reaching values close to 0.03 cm/ms. Our results shows that CV is more sensitive to [K þ ] o than to the repolarizing current I K(ATP) ; this is expected, as CV is not directly affected by repolarization. Such differences in CV between normal and ischemic tissue often lead to conduction block and reentry due to heterogeneities in tissue activation (Carmeliet, 1999;Dutta et al., 2016;Janse et al., 1980;Tice et al., 2007). Our results are in agreement with human data from Taggart et al. that show CV control values ranging from 0.05 to just under 0.07 cm/ms, and ischemic values of 0.027 cm/ms (Taggart, 2000), apart from the two modified ORd models that show a smaller change in CV.
Finally, dV/dt max and V max also decrease as [K þ ] o increases, as shown experimentally (Kleber, 1983), and most models reproduce a flattening of the APD and CV restitution curves during ischemia, as shown experimentally (Kurz et al., 1994), apart from the GPB and ORd (TP06 I Na ) models, which do not display APD restitution flattening.
As described above, the models qualitatively reproduce the expected ischemia-induced changes (a decrease in APD and CV and an increase in PRR), but in some cases they show quantitative differences. For example, the effect of varying peak I K(ATP) conductance on APD (Figs. 2e4) is more pronounced in the GPB and CRLP models compared to the other models ( Fig. 1) and experimental data (Section 3.5), due to the decreased amplitudes of the repolarizing currents I Kr and I Ks . Moreover, the TP06, CRLP, and GPB models show the greatest change in PRR and CV between control and ischemic conditions due to the gating properties of I Na (Figs. 4 and  6). Finally, the TP06 model shows the greatest change in its APD restitution curve between control and ischemic conditions, while with ischemia the GPB model shows the greatest change in its CV restitution curve and the CRLP model shows AP alternans, which has been reported experimentally, but is difficult to detect clinically in human (Kurz et al., 1994(Kurz et al., , 1993Nakashima et al., 1978). These differences may be important for determining the choice of human model for simulations of ischemia.
Interestingly, while the 3 ORd model versions show similar AP morphology, APD, and V rest under varying ischemic conditions ( Figs. 1 and 2), differences exist for PRR (Fig. 4) and dV/dt max (Fig. 5B), where I Na plays a bigger role. The original ORd formulation does not reproduce an increase in PRR and does not propagate excitation in tissue under ischemic conditions. However, both modified versions of the model do reproduce the expected increase Table 3 Summary of ischemia-induced changes in APD, PRR, CV, V rest , APA and dV/dt max between control ([K þ ] o ¼ 4 mM and f K(ATP) ¼ 0) and after 10 min of ischemia ([K þ ] o ¼ 9 mM and f K(ATP) ¼ 0.2) in single cell/tissue simulations for all models (as in Table 2).
After 10 min of ischemia in PRR, although it remains lower than in the TP06, CRLP, and GPB models.

Comparison between experimental and simulation data
To the best of our knowledge, only Sutton et al. and Taggart et al. present electrophysiological recordings of ischemia on human tissue, and report shortening of APD (by 60 ms) and PRR (by 62 ms), and a decrease in CV (by 10e18 cm/s) following 3 min of coronary occlusion (Sutton et al., 2000;Taggart, 2000). This is consistent with the data obtained by Kodama et al., Penny et al., and Kimura et al. in guinea pig and cat experiments (Kimura et al., 1990;Kodama et al., 1984;Penny and Sheridan, 1983). The models tested in the present study show good agreement with the experimental data, particularly the TP06 and ORd (modified I Na ) models.
The experimental/computational data comparison, however, must be interpreted in light of the following considerations. Firstly, acute ischemia is a dynamic process both spatially and temporally, as shown in a variety of studies and animal species (Carmeliet, 1999;Schaapherder et al., 1990;Vermeulen, 1996;Wilde et al., 1990;Wilensky et al., 1986). The time course of the ischemiainduced alterations is affected by the severity of the lack of flow, as well as other possible factors such as the metabolic state of the tissue prior to the onset of ischemia, the specific ion channel densities in each cell (Gemmell et al., 2016), or the level of ischemic preconditioning (Carmeliet, 1999). It is therefore very likely that the course and severity of electrophysiological changes during acute ischemia in the human population would be variable. Therefore, the data available provide a valuable, but limited snapshot of the electrophysiological consequences of ischemia in the human population.
Secondly, reproducing acute ischemic conditions experimentally is challenging and likely to be greatly influenced by the experimental set up itself. Indeed, measurements during open chest surgery or in isolated hearts, for instance, are likely to be influenced by possible changes in temperature, that are known to lead to an increase in APD (Lab and Woollard, 1978). Furthermore, an important component of acute ischemia is the lack of flow, and hence washout, which enables the extracellular accumulation of potassium; this cannot be easily reproduced (even using mini-wells designed for this purpose), so often solutions mimicking the ischemic changes are used (Kimura et al., 1990;Kodama et al., 1984).
Electrophysiological recordings in acute ischemia and their comparison to simulation results need to be interpreted taking into account these factors (i.e. the dynamic nature of ischemia and the limitations of reproducing these changes experimentally), as well as the importance of evaluating the consistency of the modelsimulation-experiment system (Carusi et al., 2012;Quinn and Kohl, 2013). Therefore, in this study, we evaluate and enhance the ability of the human ventricular models to reproduce the wellestablished electrophysiological alterations of acute ischemia including APD shortening, increased post-repolarization refractoriness, and slow conduction, recorded in human as well as in animal studies. The time course and severity of ischemic changes in human is likely to be very variable and only a limited set of recordings is available, which is within range of the changes shown in the simulations.

Conclusions
In this paper, a systematic analysis is performed to investigate the use of recent human AP models for studies of ischemia. The results present the sensitivity of some important arrhythmic electrophysiological parameters (APD, PRR, and CV) to variations in two primary ischemic parameters (an increase in [K þ ] o and peak I K(ATP) ) in recent human ventricular AP models (TP06, GPB with a modified intracellular potassium concentration, CRLP, ORd, and two versions of ORd with modified I Na current) using single cell and tissue simulations. We show that all the models (after changes to the GPB and ORd model) show the expected ischemia-induced changes, in agreement with experimental data.
Previous studies established that the main factors explaining ischemia-induced changes are hyperkalemia, I K(ATP) activation, and inhibition of the I Na and I CaL currents by acidosis. However, both the SERCA and the sodium potassium pump are also compromised in ischemia (Fuller et al., 2003;Terkildsen et al., 2008;Tran et al., 2009). One of the consequences of sodium potassium pump inhibition is the extracellular accumulation of potassium, which is already accounted for in our simulations. However, SERCA is likely to affect calcium dynamics and promote cardiac alternans (Baumeister and Quinn, 2016;Zhou et al., 2016), which should be investigated in future studies.
Overall, results from this study will help in the selection of an appropriate cell model for human-specific simulations of myocardial ischemia, by demonstrating quantitative differences to ischemia-induced changes across the models. This study also highlights the importance of considering multiple measured parameters in both single cell and tissue simulations when assessing the applicability of models for a given simulation. Finally, the authors suggest the ORd (modified I Na ) model may be a suitable initial choice for ischemia simulations, given that the original ORd model is based on the latest knowledge of human ventricular cells and these features are mostly unchanged in the ORd (modified I Na ) model, while enabling simulations of hyperkalemia.