Transmembrane Action Potential Duration Research Articles

Cardioprotective effects of simvastatin on reversing electrical remodeling induced by myocardial ischemia-reperfusion in normocholesterolemic rabbits

Recent studies have revealed that pretreatment with statin is effective in preventing arrhythmia, but its electrophysiological mechanism is unclear. This study was conducted to investigate the cardioprotective effects of simvastatin on reversing electrical remodeling in left ventricular myocytes of rabbit heart undergoing ischemia-reperfusion, so as to explore the ionic mechanism responsible for the anti-arrhythmic effect of statin. Forty-five rabbits were randomly divided into three groups: ischemic-reperfusion group (I-R), simvastatin intervention group (Statin) and sham-operated control group (CON). Anesthetized rabbits were subjected to 30-minute ischemia by ligation of the left anterior descending coronary artery and a 60-minute reperfusion after a 3-day administration of oral simvastatin of 5 mg x kg(-1) x d(-1) in the Statin group or a placebo in the I-R group. Single ventricular myocytes were isolated enzymatically from the epicardial zone of the infracted region derived from the hearts in the I-R and Statin group and the same anatomical region in the CON animals. The whole cell patch-clamp technique was used to record membrane ionic currents, including sodium current (I(Na)), L-type calcium current (I(Ca-L)) and transient outward potassium current (I(to)). Simultaneously, the level of serum cholesterol was examined. There was no significant difference in the serum cholesterol concentration among the three groups. The peak I(Na) current density (at -30 mV) was significantly decreased in I-R ((-22.46+/-5.32) pA/pF, n=12) compared with CON ((-42.78+/-5.48) pA/pF, n=16, P<0.01) and Statin ((-40.66+/-5.89) pA/pF, n=15, P<0.01), while the peak I(Na) current density in the Statin group was not different from CON (P>0.05). The peak I(Ca-L) current density (at 0 mV) was significantly increased in I-R ((-4.34+/-0.92) pA/pF, n=15) compared with CON ((-3.13+/-1.22) pA/pF, n=13, P<0.05) and Statin ((-3.46+/-0.85) pA/pF, n=16, P<0.05), while the Peak I(Ca-L) current density in Statin was not different from CON (P>0.05). The I(to) current density (at +60 mV) was significantly decreased in I-R ((9.49+/-1.91) pA/pF, n=11) compared with CON ((17.41+/-3.13) pA/pF, n=15, P<0.01) and Statin ((14.54+/-2.41) pA/pF, n=11, P<0.01), although there was a slight reduction in the Statin group compared with CON (P<0.05). It is implied that ischemia-reperfusion induces significant down-regulation of I(Na) and I(to) and up-regulation of I(Ca-L), which may underlie the altered electrical activity and long abnormal transmembrane action potential duration of the surviving ventricular myocytes, thus contributing to ventricular arrhythmias during acute ischemia-reperfusion period. Pretreatment with simvastatin could attenuate these changes and reverse this electrical remodeling without lowering the serum cholesterol level, contributing to the ionic mechanism of statin in treatment of arrhythmia independent of a decrease in cholesterol.

Cardioprotective effects of KATP channel activation during hypoxia in goldfish Carassius auratus

The activation of ATP-sensitive potassium (K ATP) ion channels in the heart is thought to exert a cardioprotective effect under low oxygen conditions, possibly enhancing tolerance of environmental hypoxia in aquatic vertebrates. The purpose of this study was to examine the possibility that hypoxia-induced activation of cardiac K ATP channels, whether in the sarcolemma (sarcK ATP) or mitochondria (mitoK ATP), enhances viability in cardiac muscle cells from a species highly tolerant of low oxygen environments, the goldfish Carassius auratus. During moderate hypoxia (6-7 kPa), the activation of sarcK ATP channels was indicated by a reduction in transmembrane action potential duration (APD). This response to hypoxia was mimicked by the NO-donor SNAP (100 micromol l(-1)) and the stable cGMP analog 8-Br-cGMP, but abolished by glibenclamide or l-NAME, an inhibitor of NO synthesis. The mitoK ATP channel opener diazoxide did not affect APD. Isolated ventricular muscle cells were then incubated under normoxic and hypoxic conditions. Cell viability was decreased in hypoxia; however, the negative effects of low oxygen were reduced during simultaneous exposure to SNAP, 8-Br-cGMP, and diazoxide. The cardioprotective effect of diazoxide, but not 8-Br-cGMP, was reduced by the mitoK ATP channel blocker 5-HD. These data suggest that hypoxia-induced activation of sarcK ATP or mitoK ATP channels could enhance tolerance of low-oxygen environments in this species, and that sarcK ATP activity is increased through a NO and cGMP-dependent pathway.

β-adrenergic stimulation is highly arrhythmogenic following ischemic/reperfusion injury in the isolated canine right atrium

We studied arrhythmic effects of acute ischemia (IS) and reperfusion (REP) as well as β-adrenergic stimulation (isoproterenol, ISO, 0.2 μM) before and after IS/REP injury in the canine isolated coronary-perfused right atrium (RA). Transmembrane action potential duration (APD70), refractoriness, conduction velocity (CV, measured with unipolar electrograms), and pseudo-ECG were recorded. Spontaneous and programmed electrical stimulation-induced atrial fibrillation (AF) and flutter (AFl) were evaluated.

Molecular Design and Development of Potassium Channel Blockers

AbstractFor Abstract see ChemInform Abstract in Full Text.

Molecular Design and Development of Potassium Channel Blockers

During the past decade, much attention has been directed toward the development of potassium channel blockers, which were expected to be a novel type of antiarrhythmic agent. Pharmacological screening for new cardiovascular agents led us to discover the potassium channel blocking activity of MS-3579 which we originally prepared as a β-blocking agent. Since MS-3579 lacks potency as a class III agent and its (aryloxy) propanolamine moiety was thought to be the typical β-blocking pharmacophore, we decided to manipulate this moiety to diminish β-blocking activity and potentiate class III activity. In this paper we introduce the development of Nifekalant Hydrochloride, which selectively modulates potassium channel and homogeneously prolongs the transmembrane action potential duration (APD) and consequently, refractoriness, without slowing intercardiac condition, and can terminate reentry. Nifekalant Hydrochloride was approved and launched as the first class III antiarrhythmic agent, developed in Japan.

New p-methylsulfonamido phenylethylamine analogues as class III antiarrhythmic agents: design, synthesis, biological assay, and 3D-QSAR analysis.

Class III antiarrhythmic agents selectively delay the effective refractory period (ERP) and increase the transmembrane action potential duration (APD). Using dofetilide (2) as a template of class III antiarrhythmic agents, we designed and synthesized 16 methylsulfonamido phenylethylamine analogues (4a-d and 5a-l). Pharmacological assay indicated that all of these compounds showed activity for increasing the ERP in isolated animal atrium; among them, the effective concentration of compound 4a is 1.6 x 10(-8) mol/L in increasing ERP by 10 ms, slightly less potent than that of 2, 1.1 x 10(-8) mol/L. Compound 4a also produced a slightly lower change in ERP at 10(-5) M, DeltaERP% = 17.5% (DeltaERP% = 24.0% for dofetilide). On the basis of this bioassay result, these 16 compounds together with dofetilide were investigated by the three-dimensional quantitative structure-activity relationship (3D-QSAR) techniques of comparative molecular field analysis (CoMFA), comparative molecular similarity index analysis (CoMSIA), and the hologram QSAR (HQSAR). The 3D-QSAR models were tested with another 11 compounds (4e-h and 5m-s) that we synthesized later. Results revealed that the CoMFA, CoMSIA, and HQSAR predicted activities for the 11 newly synthesized compounds that have a good correlation with their experimental value, r(2) = 0.943, 0.891, and 0.809 for the three QSAR models, respectively. This indicates that the 3D-QSAR models proved a good predictive ability and could describe the steric, electrostatic, and hydrophobic requirements for recognition forces of the receptor site. On the basis of these results, we designed and synthesized another eight new analogues of methanesulfonamido phenylethyamine (6a-h) according to the clues provided by the 3D-QSAR analyses. Pharmacological assay indicated that the effective concentrations of delaying the ERP by 10 ms of these newly designed compounds correlated well with the 3D-QSAR predicted values. It is remarkable that the percent change of delaying ERP at 10(-5) M compound 6c is much higher than that of dofetilide; the effective concentration of compound 6c is 5.0 x 10(-8)mol/L in increasing the ERP by 10 ms, which is slightly lower than that of 2. The results showed that the 3D-QSAR models are reliable and can be extended to design new antiarrhythmic agents.

ATP-sensitive K+ Channels in Cardiac Muscle from Cold-Acclimated Goldfish: Characterization and Altered Response to ATP

ATP-sensitive potassium channels (K ATP) play an important, if incompletely defined, role in myocardial function in mammals. With the discovery that K ATP channels are also present at high densities in the hearts of vertebrate ectotherms, speculation arises as to their function during periods of cold-acclimation and depressed ATP synthesis. We used single-channel and intracellular recording techniques to examine the possibility that channel activity would be altered in cardiac muscle from goldfish ( Carassius auratus) acclimated at 7 ± 1°C relative to control (21 ± 1°C). As previously observed in mammals, K ATP channels in isolated ventricular myocytes were inwardly rectified with slope conductances of 63 pS. However, channel mean open-time and overall open-state probability (P o) were significantly increased in cells from the cold-acclimated animals. In addition, K ATP channels in cells from fish acclimated at 7° were nearly insensitive to the inhibitory effects of 2 mM ATP, whether studied at 7 or at 21°C. Transmembrane action potential duration (APD) in hearts of cold-acclimated fish studied at 21° was significantly shorter than that observed in hearts of warm-acclimated fish at the same temperature; this difference was eliminated by the K ATP channel antagonist glibenclamide (5 μM). These data suggest that K ATP channels in the hearts of cold-acclimated animals are more active and less sensitive to ATP-inhibition than those in warm-acclimated fish, possibly reflecting a functional adaptation to promote tolerance of low temperatures in this species.

Rate-independent effects of the new class III antiarrhythmic agent ambasilide on transmembrane action potentials in human ventricular endomyocardium.

The electrophysiologic effects of ambasilide, a new class III antiarrhythmic drug reported to be a nonselective blocker of both components (I(Kr) and I(Ks)) of the delayed-rectifier potassium current (I(K)) and other repolarizing potassium currents (I(tol), I(so)), were studied in specimens of left ventricular endomyocardium of human hearts obtained from 10 patients undergoing either heart transplantation (n = 4) or mitral valve replacement (n = 6). We recorded transmembrane action potential (TAP) characteristics at different stimulation frequencies (0.5, 1, 1.5, and 2 Hz) and with different dosages of ambasilide (1, 10, and 50 microM) by using conventional microelectrode techniques. Beginning at a concentration of 10 microM ambasilide, the TAP duration at 90% repolarization (TAPD90) was significantly prolonged and independent of stimulation frequency with a mean percentage prolongation of 18% at 10 microM and 30% at 50 microM ambasilide. TAP duration at 50% repolarization was not significantly prolonged except for 10 microM ambasilide at 0.5 Hz (17%; p < 0.05). The frequency-independent action potential (AP) prolongation by ambasilide in human ventricular endomyocardium indicates that a nonselective block of repolarizing potassium currents seems to be more favorable than a selective block of I(Kr).

Temperature acclimation of the perch Perc fluviatilis L.): Changes in duration of cardiac action potential

1. 1. Temperature acclimation for the duration of transmembrane action potential (AP) of heart ventricle was studied in vitro in the perch in winter, spring and autumn when the animals were acclimated to 2–6°C, but acclimated in the laboratory to 5 and 16°C up to 5 weeks. 2. 2. Warm acclimation caused shortening of the AP at high temperatures. Acclimation was of Prosser's type III, rotation with an intersecting point at about 7°C. In warm acclimated fish the temperature dependency was greater than in cold acclimated fish. 3. 3. Warm acclimation shown in the duration of the AP was more pronounced in winter and spring than in autumn. 4. 4. It is concluded that the annual rhythm of the physiological state of eurythermic fish is an important factor for temperature acclimation.

Inhibitory effect of 9-amino- 1,2,3,4-tetrahydroacridine (THA) on the potassium current of rabbit sinoatrial node

STUDY OBJECTIVE - To examine the effect of 9-amino-1,2,3,4-tetrahydroacridine (THA), a compound similar to the K+ blocker 4-aminopyridine, on potassium channels in the sinoatrial node. DESIGN - The pacemaking portion of rabbit sinoatrial nodes was studied using the double microelectrode voltage clamp method in the presence of THA at various concentrations. MEASUREMENTS AND RESULTS - Above 1 mumol.litre-1, THA prolonged the spontaneous cycle length and the transmembrane action potential duration at 50% repolarisation. Above 10 mumol.litre-1, the compound also decreased the maximum rate of rise, the action potential amplitude, and the rate of diastolic depolarisation. Under voltage clamp conditions, THA reduced the time dependent K+ current (IK) in a dose dependent manner. Neither the decay process of IK nor its activation process were altered by THA. CONCLUSIONS - THA depresses sinoatrial node IK without changing its kinetics. Thus it may inhibit the open state of the potassium channels.

Correlation between in vivo transmembrane action potential durations and activation-recovery intervals from electrograms. Effects of interventions that alter repolarization time.

Classic cable theory was used to analyze the relation between the activation-recovery interval measured from unipolar electrograms and transmembrane action potential duration. Theoretic analysis demonstrated that the temporal derivative of the extracellular potential is proportional to a spatial weighting of the third temporal derivative of the transmembrane action potentials along a cable with uniform propagation in a homogeneous medium. Thus, the activation-recovery interval, measured as the interval between times of minimum derivative (Vmin) of the QRS and maximum derivative (Vmax) of the T wave, should be related to action potential duration, measured as the interval between times of Vmax of the upstroke and Vmin of the downstroke of the transmembrane action potential. This relation was examined experimentally in 12 anesthetized dogs. Unipolar electrograms and transmembrane action potentials were recorded simultaneously from sites within 2 mm of each other during control states, cardiac sympathetic nerve stimulation, localized epicardial warming, and graded reductions in myocardial perfusion. The heart was paced from several sites. There was close correlation between activation-recovery interval and action potential duration measurements taken during cardiac sympathetic nerve stimulation and local epicardial warming (r = 0.96 and 0.99 for cardiac sympathetic nerve stimulation and warming, respectively). In five animals in which coronary perfusion pressure was gradually lowered, the variables correlated closely over a range of values from 62 to 212 msec (r = 0.98). However, although the overall correlation was good and mean differences between activation-recovery interval and action potential duration were small, in individual cases there were differences up to 24 msec.(ABSTRACT TRUNCATED AT 250 WORDS)

Modulation of the effects of sotalol on Purkinje strand electromechanical characteristics

The modulation of the effects of sotalol (30 microM) by two sodium channel blockers, tetrodotoxin (0.07 microM) and lidocaine (50 microM), and by a potassium channel activator, nicorandil (30 microM), were examined. Sotalol alone greatly increased Purkinje fiber transmembrane action potential duration and, in some preparations, induced early after depolarizations. Concurrent with the changes in action potential duration, sotalol also increased isolated Purkinje strand developed force paced at slow rates (0.33 Hz). These sotalol-induced alterations of Purkinje strand electromechanical characteristics were similar to those produced by either veratrine (0.6 or 1.0 micrograms/mL) or by tetraethylammonium (10 mM). The effects of sotalol on action potential duration and force development were reversed by exposure to either tetrodotoxin or nicorandil. Lidocaine also reversed the effects of sotalol on action potential duration and developed force. The sotalol-induced increase in action potential duration and development of early after depolarizations may, therefore, be abated by combination with drugs that either block cardiac sodium channels or that increase membrane potassium conductance. Combination with such drugs may help prevent the adverse arrhythmogenic effects of sotalol.

Monophasic Action Potentials During Reentrant Atrial Flutter in the Dog: Effects of Clofilium and Acetylcholine

Monophasic action potentials (MAP) were recorded from canine atrium during reentrant flutter resulting from circus movement in atrial tissue above the tricuspid ring. A catheter and plaque contact electrodes were developed to record MAP from the epicardium or endocardium during sinus rhythm, paced rhythms, and flutter. The transmembrane action potential duration of tricuspid ring tissue also was studied in vitro. During flutter at cycle lengths of 140-160 ms, MAP showed incomplete repolarization. Pacing at comparable cycle lengths had a similar effect. Acetylcholine (10 micrograms/kg, i.v.) shortened MAP duration during pacing and, during flutter, decreased cycle length and increased MAP amplitude. Clofilium (500 micrograms/kg, i.v.) prolonged flutter cycle length by 18% and terminated the flutter within 30-120 s. During pacing at a cycle length of 300 ms, clofilium increased MAP duration and effective refractory period (ERP) by 30%. Transmembrane action potentials showed that clofilium (0.2 mg/L) modified only action potential duration. Conduction velocity was significantly decreased by clofilium during flutter but not during pacing at a cycle length of 300 ms. These data support the conclusion that in this model of flutter, the circus movement occurs in partially repolarized tissue. The circus movement can be accelerated by agents (acetylcholine) that reduce ADP, and slowed and terminated by agents (clofilium) that increase it.

Basic and Clinical Pharmacology of Amiodarone: Relationship of Antiarrhythmic Effects, Dose and Drug Concentrations to Intracellular Inclusion Bodies

Amiodarone is a unique class III antiarrhythmic drug with several unusual pharmacokinetic, pharmacodynamic, and toxicological actions which are quite distinct from those of the standard antiarrhythmic drugs. Extensive animal and clinical studies have demonstrated that amiodarone and its major metabolite, desethylamiodarone, both produce a marked increase in the duration of transmembrane action potential, which may be related to their antiarrhythmic as well as clinical electrophysiological activity. Unlike most other cardiovascular drugs, it has been recognized for more than 20 years that optimal antiarrhythmic effects may take several days to weeks after onset of oral therapy. Amiodarone is highly lipid soluble and exhibits at least three separate compartments of drug distribution, with a long elimination half-life of 14-120 days after chronic therapy. The pharmacokinetic profile of desethylamiodarone is qualitatively similar to that of amiodarone, but its elimination half-life is even longer and its tissue distribution may be slightly different. Although there may not be any correlation between serum drug levels and clinical toxicity of amiodarone during long-term therapy, recent animal as well as clinical data suggest that multilamellar intracellular inclusions can be dissociated from cell death or clinical toxicity. Thus, it is possible that amiodarone toxicity can be minimized with low doses or low serum drug concentrations. The metabolite(s) of amiodarone may play a major role in its pharmacological and toxicological actions.

In Vitro Investigations on a New Positive Inotropic and Vasodilating Agent (BM 14.478) That Increases Myocardial Cyclic AMP Content and Myofibrillar Calcium Sensitivity

BM 14.478 (7,7-dimethyl-2-(4-pyridyl)-6,7-dihydro-3H,5H pyrrolo[2,3-f]benz-imidazol-6-one) was investigated in several in vitro experiments to elucidate its positive inotropic and vasodilating efficacy and its mode of action. A direct positive inotropic action was achieved in papillary muscles (10(-6) to 5 X 10(-4) M) and electrically driven atria (10(-8) to 5 X 10(-4) M) from guinea pig hearts. The effect was not affected by propranolol, cimetidine, or tetrodotoxin, but diminished by carbachol. The effect of isoprenaline was amplified by threshold concentrations of BM 14.478 (10(-6) M). There was only a slight intrinsic chronotropic activity in spontaneously beating guinea pig atria. Atrial cyclic AMP (cAMP) was increased from 1.46 +/- 0.06 to 1.97 +/- 0.03 pmol/mg wet wt, at 3 X 10(-6) M. This might be due to an inhibition of cardiac phosphodiesterase(s) (PDE). IC50 of bovine PDE was 7.2 X 10(-5) M (5.4 X 10(-5) M to 9.7 X 10(-5) M). BM 14.478 shortened the duration of transmembrane action potential (90% repol.) by 8% and increased the Vmax of slow action potentials by 32% at 3 X 10(-4) M. In skinned porcine heart muscle fibers an increase in calcium-activated force up to 43 +/- 7% was observed (10(-7) to 10(-4) M). Rat aortas were relaxed by about 75% maximally (10(-7) to 10(-4) M). It is concluded that BM 14.478 is a potent inotropic drug which acts via an increase in myocardial cAMP content and in calcium sensitivity of contractile proteins.

Comparative electrophysiological response of young and old rat myocardium to pharmacological agents

1. Age-related changes in electrophysiological and pharmacological properties of rat ventricular cells have been investigated. 2. As compared to adults, transmembrane action potential (TAP) of aged rat myocardium exhibits a prolonged phase of repolarization. 3. For both young and aged groups tetrodotoxin reduces TAP duration. 4. Nifedipine and isoproterenol induce more pronounced modifications of the TAP in aged subjects. 5. Amiloride and tetraethylammonium ions prolong, for both groups, phase 2 of repolarization. This effect is more marked in the aged group. 6. Our results suggest that the prolonged TAP in aged myocardium could result from an age-related increase in calcium current.

Actions of lofepramine, a new tricyclic antidepressant, and desipramine on electrophysiological and mechanical parameters of guinea pig atrial and papillary muscles.

The effects of lofepramine on the isolated guinea pig atrial trabeculae were compared with those of desipramine. The preparations were taken from the same animal and mounted in the same tissue bath. All parameters were recorded in parallel. Lofepramine 10 microM was shown to exhibit minor changes in the transmembrane action potential duration only. The action potentials of the atrial trabeculae were prolonged, whereas they were shortened in the papillary muscles. Desipramine was about ten times more potent than lofepramine, but produced similar qualitative changes. Desipramine 10 microM and lofepramine 100 microM showed local anaesthetic properties: a decreased overshoot without a decreased resting potential, a decreased and rate-dependent Vmax, and a decrease in propagation velocity. After the addition of either drug in a lower concentration, a transient increase in force development and a concomitant increase in repolarization phase height (atrial trabeculum) or plateau length (papillary muscle) were recorded. The steady state effect on the force development was a decrease accompanied by a shortening of the action potential duration (papillary muscle). It is suggested that the action of lofepramine 100 microM and desipramine 10 microM on phase 0 of the action potential are produced by blockage of the fast sodium channel. The transient increase in developed force and the increase in repolarization phase height (atrial trabeculum) or plateau length (papillary muscle) could be caused by inhibition of the membrane re-uptake system for released noradrenaline. The steady state shortening and flattening of the plateau (papillary muscle) and the decrease in force development could be the cause of a block in the slow channel system.

Enhancement of ouabain arrhythmias by fatty acids.

Possible enhancement by free fatty acids (FFA) of the arrhythmogenic actions of ouabain was studied in rabbits. The mean dose of ouabain required for inducing ventricular tachycardia or fibrillation in conscious animals was significantly lowered by intravenous injection of 5 ml of a 20% fat emulsion (Lipofundin), which significantly elevated circulating FFA. Lipofundin alone did not initiate arrhythmias in another group of animals. The transmembrane action potential duration (APD) and the maximum rate of depolarization (Vmax)recorded from rabbit papillary muscles were markedly reduced under the influence of 2 mM octanoate, a short-chain FFA. Ouabain, 10(-7M), reduced significantly only the APD measured at zero level of repolarization. In papillary muscles exposed to both octanoate and ouabain, resting potential, overshoot, APD, and Vmax were all significantly decreased below control values. The synergistic arrhythmogenic actions of FFA and ouabain might be explained by the inhibiting effect of both agents on membrane (Na+ + K+)ATPase.

Electrophysiologic properties of a new antiarrhythmic drug—Tocainide

Tocainide (Astra W36095) is an orally active antiarrhythmic drug that is structurally related to lidocaine. This paper describes in vivo and in vitro studies undertaken to assay the electrophysiologic properties of this compound. Ouabain-induced ventricular ectopic activity was abolished by this drug in both isolated canine Purkinje fibers and in intact dogs. Similarly, the ventricular ectopic activity that occurs 24 hours after the two stage Harris coronary arterial ligation procedure also was abolished by tocainide. The amount of current necessary to evoke an action potential by intracell stimulation during diastole was Increased in direct relation to drug concentration. Similarly, in dogs anesthetized with pentobarbital sodium, tocainide increased the ventricular fibrillation threshold up to 150 percent above control values during normal supraventricular rhythm and up to 285 percent after premature ventricular beats. The transmembrane action potential duration and effective refractory period of isolated canine Purkinje fibers were shortened by tocainide. Tocainide depressed atrioventricular nodal conduction in anesthetized dogs, an effect that was magnified in the presence of premature atrial beats but had no effect on His, Purkinje or ventricular muscle conduction. These results Indicate that tocainide is a potentially effective antiarrhythmic agent and deserves further investigation in patients.

Theoretical analysis of T-wave polarity based on a model of cardiac electrical activity

The effect of the gradient of transmembrane action potential duration through the ventricular wall on T-wave polarity and QRS-T angle was investigated using a mathematical model of the electrical activity of the heart which incorporates the characteristic electrophysiological properties of the left ventricular wall. Two models, a rectangular solid model and a concave model, were constructed to simulate a part of the left ventricular wall. The ventricular gradient was defined as a linear decrease (beta msec/cm) of the action potential duration from the endocardium to epicardium. The theoretically-obtained relationship between the QRS-T angle and the ventricular gradient revealed that the transmural gradient (beta) was 10--40 msec/cm when the QRS-T angle was within the normal range. The positive T wave was obtained at the observation point which would correspond to the precordial lead when the transmural gradient was more than 30 msec/cm. The amplitude of the simulated T-wave increased with the ventricular gradient. Thus, our mathematical models can provide the quantitative relationship between the transmural ventricular gradient and T-wave polarity and are compatible with further simulation study for various pathological conditions.