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\begin{document}

\title{Formation of a border ischemic zone depends on plasma potassium
concentration.}



\author[1]{Olesya Bernikova}%
\author[1]{Aleksandra Durkina}%
\author[1]{Mikhail Gonotkov}%
\author[1]{Elena Minnebaeva}%
\author[1]{Natalia Arteyeva}%
\author[1]{Jan Azarov}%
\affil[1]{Russian Academy of Sciences}%


\vspace{-1em}



  
  \date{May 27, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
In the border zone of ischemic myocardium, extracellular potassium
concentration ({[}K+{]}) gradually decreases from the ischemic to normal
area. Since blood {[}K+{]} is equilibrated with the normal tissue
{[}K+{]}, it might affect the {[}K+{]} and modify electrophysiological
properties in the border zone. The study aimed at evaluation of
distribution of depolarization and repolarization characteristics across
the ischemic-normal border under blood {[}K+{]} variation. 64-lead
epicardial mapping was performed in 26 anesthetized rats with {[}K+{]}
ranged from 2.3 to 6.4 mM in an in vivo model of acute
ischemia/reperfusion. The animals with {[}K+{]}\textless{}4.7 mM
(low-normal potassium) had a typical ischemic zone with ST-segment
elevation and activation delay, a border zone with ST-segment elevation
and no activation delay, and a normal zone without electrophysiological
abnormalities. The animals with {[}K+{]} \textgreater{}4.7 mM
(normal-high potassium) had only the typical ischemic and normal zones
and no transitional area. Activation-repolarization intervals and local
conduction velocities were inversely associated with {[}K+{]} in linear
regression analysis with the adjustment for a zone of myocardium. The
reperfusion extrasystolic burden (ESB) was greater in the low-normal as
compared to normal-high potassium animals. Ventricular
tachycardia/fibrillation incidence did not differ between the groups. In
patch-clamp experiments, hypoxia shortened action potential duration at
5.4 mM but not at 1.3 mM of {[}K+{]}. The IK(ATP) current was lower at
1.3 mM than at 5.4 mM of {[}K+{]}. The formation of the border zone was
associated with attenuation of IK(ATP) response to hypoxia in low-normal
{[}K+{]} and increased ESB at reperfusion.%
\end{abstract}%



\sloppy


\textbf{Formation of a border ischemic zone depends on plasma potassium
concentration.}

Olesya Bernikova\textsuperscript{1,2}*, Aleksandra
Durkina\textsuperscript{1}, Mikhail Gonotkov\textsuperscript{1}, Elena
Minnebaeva \textsuperscript{1,3}, Natalia Arteyeva\textsuperscript{1},
Jan~Azarov. \textsuperscript{1,2,3,4}

\textsuperscript{1} Department of Cardiac Physiology, Institute of
Physiology, Komi Science Center, Ural Branch, Russian Academy of
Sciences, Syktyvkar, Russia;

\textsuperscript{2} Department of Mathematical Physiology, Institute of
Immunology and Physiology, Ural Branch, Russian Academy of Sciences,
Ekaterinburg, Russia;

\textsuperscript{3} Institute of Medicine, Pitirim Sorokin Syktyvkar
State University, Syktyvkar, Russia;

\textsuperscript{4} Department of Biomedical Technology, Faculty of
Biomedical Engineering, Czech Technical University in Prague, Kladno,
Czech Republic

Short title: Border zone and potassium concentration.

\textbf{* Correspondence:}

Olesya G. Bernikova\textbf{,} Department of Cardiac Physiology,
Institute of Physiology, Komi Science Center, Ural Branch, Russian
Academy of Sciences, 50 Pervomayskaya Street, 167982, Syktyvkar, Russia.
Tel:+79042716438

Email:

\emph{bernikovaog@gmail.com}\textbf{}

Funding information: The study was supported by Russian Science
Foundation (RSF 21-14-00226).

\textbf{Abstract}

In the border zone of ischemic myocardium, extracellular potassium
concentration ({[}K+{]}) gradually decreases from the ischemic to normal
area. Since blood {[}K+{]} is equilibrated with the normal tissue
{[}K+{]}, it might affect the {[}K+{]} and modify electrophysiological
properties in the border zone. The study aimed at evaluation of
distribution of depolarization and repolarization characteristics across
the ischemic-normal border under blood {[}K+{]} variation. 64-lead
epicardial mapping was performed in 26 anesthetized rats with {[}K+{]}
ranged from 2.3 to 6.4 mM in an in vivo model of acute
ischemia/reperfusion. The animals with {[}K+{]}\textless{}4.7 mM
(low-normal potassium) had a typical ischemic zone with ST-segment
elevation and activation delay, a border zone with ST-segment elevation
and no activation delay, and a normal zone without electrophysiological
abnormalities. The animals with {[}K+{]} \textgreater{}4.7 mM
(normal-high potassium) had only the typical ischemic and normal zones
and no transitional area. Activation-repolarization intervals and local
conduction velocities were inversely associated with {[}K+{]} in linear
regression analysis with the adjustment for a zone of myocardium. The
reperfusion extrasystolic burden (ESB) was greater in the low-normal as
compared to normal-high potassium animals. Ventricular
tachycardia/fibrillation incidence did not differ between the groups. In
patch-clamp experiments, hypoxia shortened action potential duration at
5.4 mM but not at 1.3 mM of {[}K+{]}. The IK(ATP) current was lower at
1.3 mM than at 5.4 mM of {[}K+{]}. The formation of the border zone was
associated with attenuation of IK(ATP) response to hypoxia in low-normal
{[}K+{]} and increased ESB at reperfusion.

\textbf{KEYWORDS}

border zone, myocardial ischemia, potassium, epicardial mapping, action
potential duration, potassium ionic currents

\textbf{INTRODUCTION}

Acute regional myocardial ischemia leads to the development of
myocardial regions with different properties: an ischemic zone in the
nonperfused myocardium with metabolic and electrolytic disturbances, a
normal zone in the perfused area with unchanged properties, and a border
zone with mild transitional changes located in the perfused area between
the normal and ischemic zones. The border zone is thought to play an
important role as a substrate and a source of triggers for
arrhythmias\textsuperscript{1-3}.

The ischemic zone characterized by a local increase in extracellular
potassium concentration ({[}K+{]}) (``local hyperkalemia''). The
excessive K+ leak from the affected cells and its accumulation in the
extracellular space \textsuperscript{4} are caused by the opening of the
ATP-dependent potassium channels \textsuperscript{5, 6} and inhibition
of Na,K-ATPase \textsuperscript{7} in conditions of the depletion of
ATP. The increased extracellular {[}K+{]} gradually declines in the
direction from the ischemic to normal myocardium \textsuperscript{8-11}.
In such a case, {[}K+{]} in the transition zone depends on the K+ efflux
from the ischemic zone and the {[}K+{]} in the normal zone, which is
equilibrated with a plasma {[}K+{]} level.

Extracellular {[}K+{]} influences the major parameters of the action
potential such as its duration, resting membrane potential (RMP), and
dV/dt max \textsuperscript{12}. Hypokalemia and hyperkalemia lead to the
decrease or increase in K+ channel conductance, lengthening or
shortening of action potential duration (APD), hyperpolarization or
depolarization of RMP, respectively. Both disturb myocardial conduction
and repolarization and promote ventricular arrhythmias. The low
(\textless{}3.5 mM) and high ([?]4.5 mM) serum {[}K+{]} levels are known
to increase the risk of ventricular fibrillation (VF) and mortality of
patients with myocardial infarction \textsuperscript{13}.

Inhomogeneity of electrophysiological properties of myocardium is one of
the major prerequisites of arrhythmogenesis, and the ischemia-related
spatial differences of the extracellular {[}K+{]} promote action
potential heterogeneity and electrical instability in the heart.

Since blood {[}K+{]} affects {[}K+{]} in the myocardial tissue, the
ischemia-related myocardial electrical heterogeneities might be modified
in hypo- or hyperkalemic conditions. The aim of the present study was to
evaluate the effect of the variation of blood {[}K+{]} level on the
distribution of depolarization and repolarization characteristics across
the ischemic, border and normal zones and to test them for the
association with arrhythmic outcomes.

\textbf{RESULTS}

\textbf{2.1 Electrophysiological mapping in vivo}

The achieved range of blood {[}K+{]} was from 2.33 to 6.42 mM. On the
axis from the ischemic zone to the normal zone, two variants of the
distribution of ATs and ARIs were observed at different levels of
{[}K+{]}. In the animals with blood {[}K+{]} \textless{}4.7 mM
(low-normal potassium), the affected area with ST-segment elevation was
heterogeneous, and as a result three electrophysiological zones were
discerned in the mapped area: an ischemic zone with ST-segment elevation
and activation delay, a border zone with ST-segment elevation and no
activation delay, and a normal zone without electrophysiological
abnormalities. The animals with blood {[}K+{]} \textgreater{}4.7 mM
(normal-high potassium) had only the ischemic and normal zones and did
not have any transitional area (Fig.1). CV gradually decreased from the
normal to ischemic zone in all animals (Fig.2).

The normal-high potassium animals had more pronounced activation delay
(greater ATs) in the ischemic zone as compared to low-normal potassium
animals (Fig.1), while ARIs were longer in the low-normal potassium rats
in the normal, border, and ischemic zones (Fig.1, 3A). CV at lower
{[}\selectlanguage{russian}К+{]} was greater in all zones of myocardium as compared to CV at
higher {[}К+{]} (Fig.2, 3B). It was found that the ARIs and CV were
inversely associated with blood {[}K+{]} in linear regression analysis
with adjustment for a zone of myocardium (B = -2.34 95\%~CI
\selectlanguage{english}-3.448~--~\selectlanguage{english}-1.284), p\textless{}0.001; and B = -0.024 95\% CI -0.039 --
-0.009, p=0.002, respectively) (Fig.3).

The extrasystolic burden at the 1\textsuperscript{st} min of reperfusion
was greater in animals with low-normal potassium (7.5\selectlanguage{ngerman}±2.0 bpm) as
compared to animals with normal-high potassium (1.2±0.4 bpm, p=0.006).
Reperfusion ventricular tachycardia (VT) and fibrillation (VF) incidence
did not differ between the groups (\selectlanguage{greek}χ\selectlanguage{english}2 = 0.079, p=0.779).

\textbf{2.2 Transmembrane potentials and potassium currents in vitro}

Hypoxia led to shortening of action potential duration (APD) of isolated
cardiomyocytes at 5.4 mM of {[}K+{]} and did not change APD at 1.3 mM of
{[}K+{]} o (Fig. 4). The current density of IK1 and IK(ATP) current was
lower at 1.3 mM than at 5.4 mM of {[}K+{]} (Fig. 5).

\textbf{DISCUSSION}

\textbf{3.1 Potassium-dependent development of a border zone}

In this study, we investigated experimentally the effect of variation in
{[}K+{]} from hypokalemic (2.33 mM) to hyperkalemic (6.42 mM)
concentration on electrophysiological parameters of myocardial zones
developed at local ischemia. Of particular interest was the border zone
as a possible source of triggered activity and a substrate for reentrant
arrhythmias.

Extracellular {[}K+{]} greatly affects cardiac susceptibility to
arrhythmias. Regional heterogeneities in {[}K+{]}, I(KATP), and pH
arising at coronary occlusion result in the increased dispersion of
conduction velocity, action potential duration and effective refractory
periods \textsuperscript{14}. Moreover, since extracellular potassium
flows from the ischemic zone into the normal zone \textsuperscript{8,
9}, the greatest inhomogeneity of {[}K+{]} is observed in the border
zone \textsuperscript{10}. The spatial heterogeneity of the action
potential properties, gradient in I(KATP) activation and the presence of
ischemic border zone per se provide the substrate for re-entrant
arrhythmias \textsuperscript{15, 16}.

The major question addressed in the present study was how the background
{[}K+{]} (i.e., {[}K+{]} before local ischemia) influences the formation
of electrophysiological zones of myocardium and arrhythmogenicity in
general. We found that the myocardium of the low-normal potassium
animals was electrophysiologically more heterogeneous. Besides the
normal and typical ischemic zones, there was a border zone demonstrating
ST-segment elevation, normal activation, and ARIs of intermediate
duration. At the same time, the normal-high potassium animals
(\textgreater{}4.7 mM) had only the typical ischemic and normal zones
with abrupt but still monotonic transition between each other.

The development of the border zone at low-normal potassium conditions
warrants explanation. We assume that the area between the typical
ischemic and normal zones experienced relatively mild ischemia.
Therefore, the formation of the electrophysiological border zone was due
to the combined effect on the electrophysiological parameters resulting
from {[}K+{]} decrease and the mild ischemia.

First, we should provide an explanation for the ST-segment elevation in
the border zone. After coronary occlusion onset, the RMP becomes
depolarized in the ischemic zone. It produces the electromotive force
responsible for the elevation of the ST-segment \textsuperscript{17}.
The decrease in extracellular {[}K+{]} leads to the opposite changes. It
means that the mildly ischemic area in the hypokalemic conditions should
experience counterbalanced effects on the RMP. However, the RMP in the
normal zone in hypokalemia gets also hyperpolarized and therefore the
potential difference between the zones persisted and the ST-segment
elevation in the border zone develops. At a higher level of
extracellular {[}K+{]}, the RMP gets depolarized in the normal
zone\textsuperscript{18}, as well as in the ischemic zone, though to a
lesser extent, therefore the mildly ischemic transitional zone
demonstrated the less, if any, ST-segment elevation.

The other distinction of the border zone observed in the present study
is preserved activation. We suggest that the low-normal potassium
animals had not only lower blood {[}K+{]}, but also lower local
extracellular {[}K+{]} in the affected area. According to this
assumption, the absence of the activation delay in the border zone of
low-normal potassium animals was due to preserved sodium channel
availability. The basis for such considerations is given below.

It is generally acknowledged that ischemia leads to impulse conduction
slowing manifesting as an AT delay or electrocardiographic QRS complex
prolongation. One of the causes of this effect is a decrease in sodium
channel availability caused by RMP depolarization due to local
accumulation of extracellular potassium in the affected
region\textsuperscript{19}. As expected, we observed the significant AT
delay in the ischemic zone (Fig.1) and a gradual decrease in CV from the
normal to ischemic zone (Fig. 2) with occasional development of a
conduction block.

It might be also expected that the conduction disturbances in the
affected myocardium, (whose perfusion is compromised or completely
ceased) would be determined by the severity of the ischemic injury and
local rise of extracellular {[}K+{]}, which should not strongly depend
on the background level of blood {[}K+{]}. However, the low-normal
potassium animals had a less pronounced AT delay in the ischemic zone
and higher CV in all zones of myocardium as compared to the normal-high
potassium rats. It also means that although the low-normal potassium
rats demonstrated the progressive decrease in CV from the normal to
ischemic areas, the CV observed in the border zone in these animals was
still higher than CV in a spatially corresponding area, which might have
been the border zone in the normal-high potassium animals.

The explanation for these observations can be provided by the data of
IK(ATP) current measurements in the patch-clamp experiments. IK(ATP)
activation is considered as one of the major mechanisms of the
extracellular {[}K+{]} rise in the ischemic
conditions\textsuperscript{20}. Here, we demonstrated that the decrease
in the extracellular {[}K+{]} dramatically reduced the density of
IK(ATP). The lower IK(ATP) might underlie a less accumulation of
extracellular potassium in the affected regions, which should be
associated with lesser depolarization of the RMP and higher availability
of the sodium channels.

The above considerations suggest that the transitional area in the
low-normal potassium animals experienced several influences, which could
modify the conduction. (i) Since this area could preserve some
interaction with the normal tissue via diffusion of interstitial fluid
or partial perfusion with blood flow, the decreased blood {[}K+{]} would
decrease the local extracellular {[}K+{]}, which led to
hyperpolarization of the RMP. (ii) Mild ischemia in this area would
contribute to the accumulation of extracellular potassium resulting in
the depolarization of the RMP and sodium channel inactivation. (iii) The
background low extracellular {[}K+{]} would attenuate these ischemic
consequences due to the inhibition of IK(ATP). Collectively, all these
factors would likely result in the preservation of activation in the
border zone observed in the present study.

\textbf{3.2 Hypokalemia-ischemia-induced changes of repolarization and
arrhythmogenesis}

In addition to having the specific border zone, the low-normal potassium
rats demonstrated prolonged repolarization in all zones and attenuated
shortening of repolarization in ischemia. Moreover, the inverse
association between the blood {[}K+{]} and ARI duration was observed. It
can be explained by the suppression of K+ channels conductance at
lowering the extracellular {[}K+{]}, specifically IK1
inhibition\textsuperscript{21} and reduced Na+/K+-ATPase
currents\textsuperscript{22} resulting in the prolongation of the
repolarization phase. As it has been already mentioned above, the ARI
shortening in the ischemic zone might be expected to be determined not
by the blood {[}K+{]} level but by the local rise of extracellular
{[}K+{]}. However, the ARIs in the ischemic zone at lower blood {[}K+{]}
were longer than at higher blood {[}K+{]}. This observation is in line
with the previously discussed one that the low-normal potassium animals
had less affected conduction characteristics in the ischemic zone and
preserved activation in the border zone. The in vivo observations were
supported by the in vitro patch-clamp experiments, where APD shortened
at high-normal extracellular {[}K+{]} and did not change at low {[}K+{]}
under hypoxic conditions. As expected, IK1 current decreased at low
extracellular {[}K+{]} due to the hypokalemic reduction of the
conductance for K+ channels \textsuperscript{21}. The less pronounced
APD shortening in hypoxia could be explained by the found decreased
IK(ATP) at low extracellular {[}K+{]}.

In the present study, we observed the increased ESB in the low-normal
potassium rats as compared to the normal-high rats. The prolongation of
APD caused by the reduction of outward potassium currents, Na,K-ATPase
inhibition, Na+ and Ca2+ intracellular overload at hypokalemic
conditions promotes the occurrence of early
afterdepolarization\textsuperscript{12, 23}. This fact could explain the
greater extrasystolic burden in low-normal potassium animals, with the
possible origin of triggers from the border zone, where the ischemic
changes overlapped the relatively prolonged APD. It is of note that
IK(ATP) activation has been reported to abolish triggered
activity\textsuperscript{24}. We found that IK(ATP) was significantly
suppressed in the low-potassium animals, which could further facilitate
ectopic activity. Interestingly, the incidence of life-threatening
arrhythmias (VT/VF) did not differ between the low-normal and
normal-high potassium animals despite the difference in ESB, which
usually serves as triggers for reentrant arrhythmias. The high ESB did
not realize in an appropriately high incidence of lethal arrhythmias in
this group possibly due to the preserved activation characteristics in
the border zone of myocardium.

Hypokalemia has long been recognized as a proarrhythmic condition as it
prolongs APD, promotes abnormal automaticity and afterdepolarizations,
affects excitation thresholds and refractoriness \textsuperscript{25}.
These effects are well documented in individual cardiomyocytes, and the
present study extends this consideration into ``spatial dimension''. Our
findings demonstrated that the decrease in extracellular {[}K+{]}
resulted in the formation of the border zone adjacent to the typical
ischemic zone. It is noteworthy that the cut-off {[}K+{]} level (4.7 mM)
is far above true hypokalemia, which implies that such a phenomenon may
be quite common. Furthermore, this relatively high cut-off {[}K+{]}
level implies that the observed increased ESB was due to the presence of
the border zone itself rather than the hypokalemia-induced changes in
individual cells.

Broadly speaking, the border zone can be considered as a mildly ischemic
myocardial region with preserved activation characteristics and abnormal
repolarization. Most likely, the role of the border zone in
arrhythmogenesis could not be ascribed to the changes in dispersion of
repolarization, but its critical arrhythmogenic property appears to be
the prolonged APD \textsuperscript{26-28}, which may be caused not only
by {[}K+{]} changes studied here, but also by early ischemic APD
prolongation \textsuperscript{29}. The findings obtained in the present
and previous studies cited above suggest that the border zone can
present a source of ectopic activity, which might trigger VT/VF.
Prolonged APD prone to early afterdepolarizations in combination with
preserved excitability may underlie this activity. The chances of
inducing the reentrant arrhythmias by these extrasystoles would probably
depend on other myocardial properties, for example, characteristics of
the ischemic region.

\textbf{Limitations}

There are some limitations of the present study, which warrant cautious
interpretation of the findings obtained. The experimental model is far
from clinical conditions concerning mostly the species (rats), which
demonstrate specific electrophysiological myocardial properties, and the
short duration of the ischemic episode. In vitro experiments could not
technically reproduce the situation in the in vivo experiments. The
mapping technique did not allow us to characterize the entire
ventricular surface, and therefore the exact configuration of the
ischemic/border/normal zones remained unknown.

\textbf{CONCLUSIONS}

The present study demonstrated that the formation of the border zone
depends on the extracellular potassium concentration likely due to the
attenuation of IK(ATP) response to hypoxia in low-normal {[}K+{]}. The
border zone was characterized by the preserved excitation and altered
repolarization processes and was associated with the increased
extrasystolic burden.

\textbf{METHODS}

Effects of extracellular {[}K+{]} on electrophysiological parameters
were investigated \emph{in vivo} in a rat model of heart
ischemia/reperfusion as well as \emph{in vitro} in isolated
cardiomyocytes. Experiments were performed in a total of 26 Wistar male
rats (4-month-old, 323\selectlanguage{ngerman}±8 g) obtained from the Scientific Collection of
Experimental Animals of the Institute of Biology, Federal Research
Center, Komi Scientific Center, Ural Branch of the Russian Academy of
Sciences. The study conformed to the Guide for the Care and Use of
Laboratory Animals, 8th Edition published by the National Academies
Press (US), 2011, the guidelines from Directive 2010/63/EU of the
European Parliament on the protection of animals used for scientific
purposes, and was approved by the ethical committee of the Institute of
Physiology of the Komi Science Centre, Ural Branch of Russian Academy of
Sciences (approval 08 December 2022).

\textbf{2.1 In vivo experiments}

The rats were anesthetized with zoletil (Virbac S.A., Carros, France, 15
mg/kg, i.m.) and xylazine (Interchemie, Castenray, Netherlands, 0.1
mg/kg, i.m.) and ventilated mechanically. The chest was opened via a
midsternal thoracotomy and the heart was exposed. Blood {[}K+{]} was
decreased by hypokalemi\selectlanguage{russian}с diet contained only cereal and furosemide
administration (2 mg/kg dose i.m. daily, 3 days before experiment). To
increase blood {[}K+{]}, i.v. infusion of 10\% KCl solution was
performed during the acute experiment.

Acute local ischemia was induced by a ligation of a proximal third of
the left anterior descending coronary artery (LAD) by a coated braided
polyester ligature (\selectlanguage{english} 5-0, Ti-Cron, Cardiopoint, Covidien, Dominican
Republic). After 5-min of coronary occlusion ligature was loosened to
provide reperfusion. This technique of short ischemia followed by
reperfusion was used in a number of our previous studies and was
verified to produce a sufficient number of ventricular
arrhythmias\textsuperscript{27, 30}. The measurements of blood {[}K+{]}
were done immediately before the onset of ischemia (EasyStat, Medica
Corp, USA) in blood samples withdrawn from the femoral vein. Ventricular
tachycardia and fibrillation were assessed at first min of reperfusion.
Extrasystolic burden (ESB) was calculated as a sum of ESs during the
first min of reperfusion divided by 60 sec excluding periods of VF or
VT, if any.

Epicardial mapping was performed from the epicardium of the left
ventricle (LV) using a square multielectrode array (8\selectlanguage{ngerman}×8 leads, 0.5 mm
interelectrode spacing) by a custom-designed 128-channel recording
system (16 bits; bandwidth 0.05 to 1000 Hz; sampling rate of 4000 Hz).
The mapping array was located on the anterior surface of LV in a way to
cover equally (at approximately 1:1 ratio spatially) the normal and
affected areas. The latter was recognized by cyanotic coloration (Fig. 6
A, B) at the time of electrode application. At subsequent analysis, the
affected zone was defined as lead sites demonstrating ST-segment
elevation during the period of ischemia. In each lead, activation time
(AT) and repolarization time (RT) were determined as the instants of
dV/dt min during QRS complex and dV/dt max during T-wave respectively.
ARI, a surrogate for action potential duration (APD), was calculated as
ARI = RT -- AT (Fig.6 C).

Conduction velocity (CV) was measured using isochrone activation mapping
under electrical stimulation (400 bpm, 2 mA, 2 ms) in the middle of the
LV. Pacing stimuli were delivered to the unaffected area (Fig.1D). In
order to calculate local CVs, local gradients of activation (AG) were
computed using finite difference method \textsuperscript{31, 32} well
suited for the regularly spaced electrode array (Fig. 6E). The
horizontal and vertical components of AG were computed for the sites of
the electrode array using standard first-order finite-difference stencil
(Fig. 6F) as AGx=(ti+1,j -- ti--1,j)/2d, AGy=(ti,j+1 -- ti,j--1)/2d.

Along with AG, which is an averaged parameter, we also considered the
minimal activation velocity between the given point and its eight
nearest neighbors located top, bottom, right, left and diagonally (Fig.
6F). The magnitudes of the minimal activation velocity were used to
detect the boundary between the normal and ischemic zones and the
direction of activation wavefront, which was not known a priori. The
boundary electrodes located on the edge of the multielectrode array
(Fig. 6E) were excluded from the analysis, since they did not have
enough neighboring electrodes for accurate determination of activation
velocity. In some neighboring electrodes, activation times could
coincide; such points were also excluded from the analysis.

\textbf{2.2 In vitro patch-clamp experiments}

Cardiomyocytes were enzymatically isolated from the excised hearts of 26
rats after in vivo electrophysiological study. The isolated heart was
retrogradely perfused for 10 minutes through the aorta in the
Langendorff system with a modified Tyrode calcium free solution of the
following composition (mM): 120 NaCl, 5.4 KCl, 5 MgSO4 · 7H2O, 5 sodium
pyruvate, 20 glucose, 20 taurine, and 10 HEPES; pH 7.2, at 37\selectlanguage{english}@C
saturated with carbogen gas mixture (95\% O2, 5\% CO2). Then, perfusion
was turned on the same solution supplemented with collagenase type II
(0.5 mg/ml, Sigma Aldrich, USA), protease (0.01 mg/ml, Sigma Aldrich,
USA) and 20 \selectlanguage{greek}μ\selectlanguage{english}M CaCl2 for 35 min. At the end of enzymatic perfusion, the
ventricles were minced with fine scissors and triturated with the
transfer pipettes. After that the cardiomyocytes were isolated from the
chunks by filtering through a 200 \selectlanguage{greek}μ\selectlanguage{english}m mesh net in Kraft-Br\selectlanguage{ngerman}ühe solution
containing (mM): 30 KCl, 50 glutamic acid, 30 K2HPO4 · 2H2O, 3 MgSO4 ·
7H2O, 0.5 EGTA, 10 glucose, 20 taurine, and 10 HEPES; pH 7.2.

Whole-cell patch-clamp experiments were performed at room temperature
(22-24\selectlanguage{english}@ C) with the Axopatch 200B (Axon instrument, Burlingham, CA,
USA). Ventricular cardiomyocytes were placed into an RC26 experimental
chamber (Warner Instrument Corp, Brunswick, CT, United States). Patch
pipettes were made of borosilicate glass (Sutter In-struments, United
States) and pulled on a HEKA pipette puller type PIP 6 (HEKA
Electronics, Germany).

To record the IK1 current (in a voltage-clamp mode) and action
potentials (in a current-clamp mode), the pipettes were filled with a
solution containing (mM) 140 KCl, 25 HEPES, 5 MgATP, 0.4 NaGTP, 0.5
EGTA; pH 7.2. To record IK(ATP), the pipette solution was modified so
that MgATP and NaGTP were replaced by 5 MgCl2. A bath chamber was
perfused with the solution containing (mM): 150 NaCl, 5.4 (or 1.3, to
mimic hypokalemic conditions) KCl, 1.8 CaCl2, 1.2 MgCl2, 10 glucose, 10
HEPES, pH 7.4.

The IK1 current was evoked by a ramp voltage protocol (voltage range +60
to -120 mV) in the presence of 10 \selectlanguage{greek}μ\selectlanguage{english}M nifedipine and 2 mM 4-aminopyridine
in solution. IK(ATP) was evoked by the same voltage ramp in the presence
of 10 \selectlanguage{greek}µ\selectlanguage{english}M pinacidil. To determine the magnitude of the leakage current, 3
mM BaCl2 was added to the bath solution at the end of measurements.

Acute hypoxia was produced by bubbling the extracellular perfusate
(normal extracellular solution for current recording, without glucose)
with 100\% N2 gas for 30 min with pH being continuously controlled. The
bath solution PO2 was reduced thereby to 10 mm Hg and controlled by a
multimeter Mettler Toledo Seven Duo Pro with the oxygen probe InLab
605-ISM-5m. The recorded traces were analyzed using Clampfit 9.2
(Molecular Devices, San Jose, CA, United States).

\textbf{Statistical Analysis}

Statistical analysis was performed with SPSS package (IBM SPSS
Statistics 23, Armonk, North Castle, NY, USA). Parametric and
nonparametric tests were used according to the Kolmogorov-Smirnov
normality test. Parametric Student's t-test and nonparametric
Mann-Whitney test were used for comparison the groups of animals. The
incidence of arrhythmia was compared by Chi-square test. Linear
regression analysis was used to test associations between
electrophysiological parameters and potassium concentration. All data
are presented as mean \selectlanguage{ngerman}± SEM, the di\selectlanguage{english}fferences were considered signi\selectlanguage{english}ficant
at p \textless{} 0.05.

\textbf{AUTHOR CONTRIBUTIONS}

Conceptualization: Olesya Bernikova, Jan Azarov; Methodology: Olesya
Bernikova, Natalia Arteyeva; Formal analysis and investigation: Olesya
Bernikova, Aleksandra Durkina, Mikhail Gonotkov, Elena Minnebaeva;
Writing-original draft preparation: Olesya Bernikova; Writing-review and
editing: Jan Azarov. All authors read and approved the final manuscript.

\textbf{FUNDING INFORMATION}

The study was supported by Russian Science Foundation (RSF 21-14-00226).

\textbf{CONFLICT OF INTEREST}

The authors declare that they have no conflict of interest.

\textbf{DATA AVAILABILITY STATEMENT}

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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\textbf{FIGURE LEGENDS}

\textbf{Figure 1.}

\selectlanguage{russian}А. Representative epicardial maps of ATs and ARIs distribution in three
rats across ischemic, border and normal zones at the low and high levels
of {[}K+{]}.

Numbers indicate the values of ATs and ARIs in individual leads. The
filling color in the maps corresponds to a time scale (red for short and
blue for long time values). The red, blue, and black numbers refer to
the ischemic area with ST--segment elevation and activation delay; the
border zone with ST--segment elevation without activation delay; and the
normal area without AT and ARI abnormalities, respectively.

B. The representative profiles of ATs and ARIs on the ischemia-to-normal
axes indicated by dotted arrows in the corresponding epicardial maps of
ATs and ARIs. Red, blue, and black sections of the diagrams correspond
to the ischemic zone, border zone, and normal zone, respectively. See
the absence of the border zone at {[}К+{]}=6.28 mM.

C. Representative electrograms recorded in the ischemic (1), border (2)
and normal (3) zones.

\textbf{Figure 2.}

А. Representative isochrone AT maps during electrical pacing across the
normal-(border)-ischemic zones at the low and high levels of {[}К+{]}.
Electrical step symbols indicate a site of pacing.

B. Representative maps of CV distribution in the normal (site of pacing)
and ischemic zones. The border zone was determined as an area with
transitional values of CV. The red numbers refer to ischemic area zone,
the blue -border zone, the black - normal area.

C. The representative profiles of CV on the ischemia-to-normal axes
indicated by dotted arrows in the corresponding epicardial maps of CV
(panel B). Note the higher CV at low {[}К+{]} as compared to high
{[}К+{]}.

\textbf{Figure 3.}

Relationships between ARI and CV in different zones and potassium
concentration. Note prolonged ARIs and greater CV at lower {[}К+{]}.

\textbf{Figure 4.}

Effects of different levels of extracellular potassium concertation on
hypoxia-induced changes of transmembrane potentials. Panels A and B:
Action potential durations at the level of 20\%, 50\% and 90\% of
repolarization (APD20, APD50, and APD90, respectively) at {[}K+{]} of
1.3 mM and 5.4 mM, respectively. *-p\textless{}0.05. Panels C and D:
Representative recordings of action potentials at extracellular {[}К+{]}
of 1.3 mM and 5.4 mM, respectively. See a shortening of APD at 5.4 mM of
{[}К+{]} in hypoxia and the absence of hypoxia-induced APD shortening at
1.3 mM {[}К+{]}.

\textbf{Figure 5.}

Current-voltage relationships of IK1 and I(KATP) currents. See a
decrease of density of IK1 and IK(ATP) at 1.3 mM {[}K+{]}. **-p=0.03 for
IK(ATP) current from -80 mV to positive voltage values.

\textbf{Figure 6.}

\begin{enumerate}
\tightlist
\item
  Multielectrode array covering the affected (noncolored) and
  nonaffected (blue) zones (postmortem staining by Evans blue dye);
\item
  Photo of multielectrode array;
\item
  Unipolar electrograms with AT, RT, and ARI measurements;
\item
  Conduction velocity measurements across the normal and ischemic zones
  with representative electrograms recorded at sites a, b, and c
  corresponding to the normal, border and ischemic zones, respectively.
  ``St'' indicates a pacing artifact. Electrical step symbol indicates a
  pacing site. Arrow shows the direction of impulse propagation from
  normal to ischemic zone;
\item
  Regularly spaced multielectrode array with interelectrode distance d.
  The boundary electrodes located on the edge of the array (white);
\item
  Gradients of activation were computed using the finite difference
  technique along the dotted lines, in the horizontal and vertical
  directions, using the times at the four highlighted electrodes to
  calculate the conduction velocity vector for the center point.
\end{enumerate}\selectlanguage{english}
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