Ionic Mechanisms of Variability in Electrophysiological Properties in Ischemia:A Population-based Study

A Minchole S Dutta, J Walmsley, B Rodrıguez

Computational Biology Group, University of Oxford, Oxford, UK

Abstract

Electrophysiological heterogeneities in ischemia pro-vide a pro-arrhythmic substrate that can lead to ventricu-lar arrhythmias. However, the mechanisms underlying in-tersubject variability in the pro-arrhythmic response of thehuman ventricles to acute ischaemia are unknown. In thisinitial study, we investigated the ionic basis of variabilityin cellular electrophysiological properties in normal andacutely ischemic human ventricular cardiomyocytes us-ing a population-based simulation study. Additionally, weanalysed the importance of hyperkalemia, IK(ATP ) activa-tion and acidosis-induced ICaL and INa inhibition in mod-ulating these electrophysiological properties within the hu-man cell population. Results show that in the occurrenceof APD alternans, the conductance gCaL plays the mostimportant role followed by the Na/K pump whereas underischemic conditions, other mechanisms also become im-portant such as Na/Ca exchanger and the IKr and IKs cur-rents. On the maximum restitution slope, under ischemicconditions, gNa and gNaCa become important while gKr

reduce its influence on it.

1. Introduction

Ventricular arrhythmias caused by myocardial ischemiaare a main cause of mortality. Ischemia due to cessation ofblood supply in the cardiac tissue results in profound dy-namic spatio-temporal electrophysiological changes whichpromote arrhythmogenesis [1]. Animal studies haveshown that ischemia-related pro-arrhythmia is caused bya combination of ionic changes including hyperkalemia(i.e. elevated extracellular potassium concentration [K]o),hypoxia-induced activation of the ATP-dependent potas-sium current IK(ATP ), and a decrease in the conductancesof the fast sodium (INa) and L-type calcium (ICaL) cur-rents caused by acidosis [1]. The effect and severity ofischemia-induced changes in human ventricular electro-physiology is likely to exhibit high inter-subject variability,but its characterisation is challenging due to difficulties inperforming appropriate measurements. Hence, the mech-

anisms underlying inter-subject variability in determiningthe response to ischemic changes in human are currentlyunknown.

In the present study, we investigate variability in thehuman ventricular cardiomyocyte response to ischaemia-induced ionic alterations using a population-based compu-tational approach. Variability underlying the physiolog-ical and pathological responses of human cardiomyocytesis investigated using a calibrated population of human ven-tricular cell models [2, 3]. The human model population isthen used to quantify the relative importance of ionic con-ductances and ischemic changes in determining intersub-ject variability in each electrophysiological property foreach pacing frequency.

2. Methods

2.1. Construction of the population

We constructed a population of human ventricular actionpotential (AP) models based on the endocardial ten Tuss-cher model TP06 [4] using the cardiac simulation softwareChaste [5]. The model population consisted of an ensem-ble of cellular models, sharing the same equations as theTP06, but with varying ionic conductances values.

We generated an initial population of 5000 models bysampling the ionic conductances to ±50% of TP06 origi-nal values using Latin hypercube sampling (as in [2]). Theconductances of the main ionic currents during repolariza-tion and depolarization were varied: the fast sodium (gNa),L-type calcium (gCaL), rapid delayed rectifier potassium(gKr), slow delayed rectifier potassium (gKs), inward rec-tifier potassium (gK1), transient outward (gto) and theNa+/Ca2+ exchanger (gNaCa) currents, and the Na+/K+pump current permeability (gNaK).

2.2. Calibration of the population

The initial population was calibrated to determine themodels that were in agreement with the experimentallyobserved ranges of APD90 and APD50 at different cyclelengths (CL) in human. Experimental data used in the

ISSN 2325-8861 Computing in Cardiology 2013; 40:691-694.691

calibration included those obtained by [6–8] in nonfailinghearts and also in vivo [9] in acute ischaemia. Each modelwas paced for 300 beats at different CLs from 1500 to 300ms. Models with APD90 between 250 to 400ms for the CLof 1000ms and between 225 to 340ms for CL of 500ms,and with APD50 between 200 to 350ms for CL of 1000ms,and between 175 to 300ms for CL of 500ms were includedin the population (see Figure 1). In addition, the popula-tion was calibrated by ensuring the restitution curve wasmonotonic. The experimentally-calibrated population ofmodels retained 2133 models.

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Figure 1. Action potentials (left) and restitution curves(right) simulated using the 2133 human ventricular mod-els in the experimentally calibrated model population. Thesolid black line corresponds to the original TP06 APmodel.

Four different ischemic conditions were applied to thecalibrated control population:

• Mild hyperkalemia and hypoxia with [K]o = 8mM andfK(ATP ) = 10%• Severe hyperkalemia and hypoxia with [K]o =10.8mM and fK(ATP ) = 10%• Hyperkalemia with [K]o = 10.8mM• Simulated ischemia (hyperkalemia, hypoxia and acido-sis) with [K]o = 10.8mM , fK(ATP ) = 10% and a reduc-tion of 30% in the gCaL and gNa.

These ischemic changes are in line with experimentalrecordings [1].

2.3. Electrophysiological properties

In order to determine ischemia-induced electrophysio-logical effects, we quantified the following properties inthe simulations: APD at 90% repolarization, the restingpotential, the maximum AP upstroke velocity (dV/dtmax),the maximum APD restitution slope and the occurrence ofAPD alternans. Alternans were defined as >10 ms dif-ference in APD between consecutive beatsin steady-stateconditions. All these electrophysiological properties areknown to be modified during the process of ischemia.

2.4. Statistical methods

In order to quantify the relative importance of each ionicconductance on changes of a specific biomarker, a linearregression analysis was performed [3]. Each biomarkercomputed for each of the models of our calibrated popula-tion can be approximated by a linear expression in termsof the eight ionic conductances. The importance of theseionic conductances is given by the regression coefficients.

We further investigated the relative importance of thethree pathological components of ischemia: hyperkalemia,activation of IK(ATP ) and simulation of acidosis in de-termining the changes of the different electrophysiologi-cal properties. We performed a linear regression with re-spect to [K]o, fK(ATP ) and a categorical variable set to onewhen representing that the acidosis is present in the modelor to zero when it is not.

3. Results and discussion

3.1. Population variability in electrophysi-ological properties

Figure 2 illustrates the variability in each of the electro-physiological properties obtained in the simulated humanventricular cell population under control and ischaemia-related conditions by showing probability density func-tions for each biomarker. Figure 2A and 2B shows thatfirstly the width and height of each distribution is similarin all conditions, indicating that the variability in physi-ological conditions (control) determines variability underischaemia-related conditions for APD at both CLs. Sec-ondly, IK(ATP ) activation results in significant APD short-ening, which is further increased by acidosis-induced inhi-bition of ICaL and INa and to a smaller extent by hyper-kalemia. This is in agreement with previous results ob-tained in experimental and theoretical studies [1, 10]. Fig-ures 2C and 2D highlight the importance of hyperkalemiain raising resting potential towards less negative potentialsand decreasing dV/dtmax, an effect which is reduced byIK(ATP ) activation. Figure 2E shows that all ischaemia-related conditions result in a flattening of the APD resti-tution, reflected by the decrease in the maximum resti-tution slope. A narrower distribution than in control isobserved in simulated ischemia and severe hyperkalemiawith IK(ATP ) activation.3.2. Occurrence of APD alternans

We also quantified the occurrence of alternans in thehuman ventricular model population under control andischemia-related conditions for a range of cycle lengths(Figure 3). Simulation results show that all ischemia-related alterations facilitate the occurrence of alternans atlonger CLs. Cells which failed to activate not shown.

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Figure 2. Probability density functions representing pop-ulation variability in APD (A) at CL of 500 ms and (B)at CL of 1000ms, resting potential (C), dV/dtmax (D) andmaximum restitution slope (E) in control (solid black line)and in hyperkalemia (green), mild and severe combinedhyperkalemia and hypoxia (magenta and blue lines) andsimulated ischaemia (red) for CL=1000ms.

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Figure 3. Number of human models in the populationexhibiting APD alternans in control (solid black line) andin hyperkalemia (green), mild and severe combined hyper-kalemia and hypoxia (magenta and blue lines) and sim-ulated ischaemia (red) for each CL tested from 350 to1500ms.

3.3. Ionic basis of variability

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gCaL gKr gKs gK1 gNaCa gto gNaK gNa

Figure 4. Relative importance of ionic conductances indetermining APD values for CL= 500ms (top) and 1000ms(bottom) for the human ventricular cell population in con-trol, and in the four ischemic conditions. Each bar plotshows regression coefficients obtained for each conduc-tance.

Linear regression analysis was conducted on the simu-lated population results to quantify the relative importanceof ionic conductances and ischemia-related changes in de-termining human electrophysiological variability. Figure 4indicates that 1) gKr, gto and gNaCa are the main determi-nants of APD variability in most simulated conditions; 2)The importance of gKr in APD increases under conditionsof combined hyperkalemia and hypoxia. Finally, for CL of500 ms, we observe a higher importance of gKs, gCaL andthe NaK pump during hyperkalemia.

In the occurrence of APD alternans, gCaL is the con-ductance that plays the most important role followed bythe NaK pump. Under ischemic conditions, other mecha-

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Figure 5. Relative importance of ischaemia-induced al-terations in determining electrophysiological properties:APDs at CLs of 500 and 1000 ms, resting potential,dV/dtmax, APD restitution slope and the APD alternans.Y axis corresponds to normalised regression coefficient foreach condition (control, hyperkalemia and acidosis).

nisms also become important such as NaCa exchanger andthe IKr and IKs currents.

The main mechanism that modifies the resting potentialis the NaK pump permeability followed by gK1 in control.Under ischemic conditions, gK1 reduces its relative impor-tance whereas gCaL increases in importance.

Regression shows that under ischemic conditions, gNa

and gNaCa become important while gKr reduces its influ-ence on the maximum restitution slope. Acidosis, an earlyischemia response, inhibits INa dynamically, affecting therestitution slope in turn. All the regression coefficients in-crease under hyperkalemia resulting in a wider distributionas shown in Figure 2E and, therefore in a higher variability.On the other hand, the regression coefficients in the otherischemic conditions decrease, reducing the variability ofmaximum APD restitution slopes.

We also analysed the importance of hyperkalemia,IK(ATP ) activation and acidosis-induced ICaL and INa

inhibition in determining electrophysiological propertieswithin the human cell population. Results shown in Fig-ure 5 indicate that IK(ATP ) activation is the strongest de-terminant of APD for both CLs, hyperkalemia determinesresting potential and dV/dtmax and both factors play a crit-ical role in determining the APD restitution slope and theoccurrence of alternans. Our quantitative results are inagreement with results obtained in previous studies [11].

4. ConclusionsIn this study, we investigated the ionic basis of vari-

ability in the response of the human ventricles to acute is-chaemia using a population-based computation approach.Results suggest that some electrophysiological propertiessuch as APD or resting potential do not increase in vari-ability relative to control whereas maximum upstroke ve-locity or maximum restitution slope have reduced in vari-ability during different ischemia-related conditions. Fur-ther studies should be done to investigate the potential im-

plications of variability in electrophysiological propertiesduring acute ischemia.

AcknowledgmentsAM holds a Marie Curie Intra-European fellowship

(FP7-PEOPLE-2011-IEF and acknowledges support ofgrant TEC2010-19410 from MINECO, Spain. BR holdsMedical Research Council Career Development, IndustrialPartnership and MRC Centenary Awards. SD acknowl-edges EPSRC. JW acknowledges MRC Centenary Awards.

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