# Changes in Cell-to-Cell Electrical Coupling Associated With Left Ventricular Hypertrophy

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## Abstract

*Abstract *The impedance to current flow in the intracellular compartment of guinea pig left ventricular myocardium was measured at 20°C and 37°C using tissue from hypertrophied hearts subjected to aortic constriction. Alternating current of varying frequency was passed longitudinally along myocardial preparations, which revealed two time constants: one attributed to the surface membrane at the ends of the preparation and a second lying in the intracellular pathway. The longitudinal impedance was quantitatively analyzed in terms of a parallel intracellular and extracellular pathway; the former had two series components, one attributable to the sarcoplasm and the other to the low-resistance junctions between adjacent cells. This interpretation was consistent (1) with control experiments using *n*-heptanol, which increased the component attributed to intercellular junctions but not sarcoplasmic resistivity, and (2) with suspensions of isolated myocytes, which yielded a similar value for the sarcoplasmic resistivity. Aortic constriction increased the heart weight–to–body weight ratio of experimental animals from a mean value of 3.10±0.28 to 5.05±0.83 g/kg after 50 days of constriction and 5.60±0.95 g/kg after 150 days of constriction. An increase of heart weight–to–body weight ratio at 150 days of constriction was associated with an increased intracellular resistivity, which could be attributed solely to an increase of the junctional resistance between adjacent cells by ≈44% at 20°C and 140% at 37°C; the sarcoplasmic resistivity was unchanged. The results are discussed in terms of altered conduction in hypertrophied myocardium as a possible basis for arrhythmias in this tissue.

Left ventricular hypertrophy significantly increases the risk of sudden cardiac death^{1} and is associated with a greater prevalence of cardiac arrhythmias,^{2} which could arise from reentrant mechanisms, afterdepolarizations, or other forms of abnormal automaticity.^{3} ^{4} ^{5} Reentrant mechanisms require regions of abnormal action potential conduction, but little attention has been focused on conduction defects or the underlying electrical properties of myocardium that cause this phenomenon in hypertrophied tissue. Cable theory predicts that as cell diameter increases, as occurs in cardiac hypertrophy, conduction velocity will be increased. However, using isolated hypertrophied human myocardium, it has been found that a reduced conduction velocity accompanies cell enlargement, and it was proposed that this was due to an additional increase of *R*_{i}.^{6} The objective of the present study was to examine directly the hypothesis that hypertrophy is associated with increased *R*_{i}.

Several models of ventricular loading that induces left ventricular hypertrophy are available; these include models of renal artery stenosis,^{7} infrarenal aortic banding,^{8} and increased growth hormone secretion.^{9} Interpretation of the data may be difficult when these various models are compared. We have used a guinea pig model of thoracic aortic constriction that also demonstrates reduced action potential conduction in whole-heart preparations^{10} and most closely approximates the human condition associated with aortic stenosis.^{11} Multicellular tissue strands were used, so the resistivity estimations are macroscopic values rather than the properties of individual cells, but they represent the average intracellular pathway through which local circuits flow. The magnitude of the intracellular resistance is the sum of the sarcoplasmic resistance and that offered by intercellular junctions, and data analysis was extended to measure separately these two fractions. It is concluded that an increase of *R*_{i} does accompany the later stages of hypertrophic growth and that the increase can be attributed solely to a raised junctional resistance.

## Materials and Methods

### Animal Model of Left Ventricular Hypertrophy

Left ventricular hypertrophy was induced in Dunkin-Hartley guinea pigs, weighing 600 to 800 g, by placing a high-density plastic disk (internal diameter, 1.99 mm) around the ascending aorta under anesthesia (0.22 mL·kg^{−1} sodium pentobarbitone, followed by inhalation of a 49% N_{2}O/49% O_{2}/2% halothane mixture; the animals were subsequently allowed to recover. Postoperative analgesia was given after wound closure (50 μg·kg^{−1} subcutaneous buprenorphine). A sham operation, without clip placement, was performed as a control. Animals were divided into four groups: 50 days of constriction (n=8), 50 days after sham operation (n=9), 150 days of constriction (n=8), and 150 days after sham operation (n=6). Guinea pigs were killed by cervical dislocation, and the hearts were rapidly removed and placed in gassed Tyrode’s solution at 37°C. No animals showed evidence of heart failure, liver and lung weights were normal, and the liver was free of ascites. Procedures were performed according to Guidance on the Operation of the Animals (Scientific Procedures) Act 1986, Her Majesty’s Stationery Office, London, England.

### Solutions

Experiments were carried out in Tyrode’s solution (mmol/L): NaCl 118, KCl 4.0, NaHCO_{3} 24, NaH_{2}PO_{4} 0.4, MgCl_{2} 1.0, CaCl_{2} 1.8, glucose 6.1, and sodium pyruvate 5.0. The solution was gassed at 37°C with 95% O_{2}/5% CO_{2}, pH 7.35±0.03.

### Longitudinal Impedance

The longitudinal impedance of subendocardial left ventricular preparations (diameter, 0.88±0.02 mm; n=31) was measured by constraining alternating current to flow along the intracellular pathway. A three-chambered bath, separated by rubber membranes, was used, and the preparation was pulled through tight holes in the membranes with at least 1 mm protruding into the outer chambers. The length of muscle in the central chamber was 3.0±0.7 mm. The central chamber contained mineral oil, and the outer chambers contained Tyrode’s solution. A thin layer of Tyrode’s solution was often trapped around the preparation, under the mineral oil, which contributed to the overall extracellular space. The thickness was measured with a binocular microscope (×80) and was variable between being completely absent to 0.3 mm (mean±SD, 0.08±0.07 mm). The bath was placed on a water-heated aluminum block at 37°C. Measurements were also made at 20°C to allow comparison with values of *R*_{c} in myocyte suspensions (see below) and to permit the temperature coefficient of *R*_{c} to be calculated.

It was important to avoid a hypoxic core to the preparation because this would falsely increase *R*_{i}. Several lines of evidence indicated that this was so: (1) the preparation diameter was <1 mm; (2) the preparation never showed histological evidence of damage, as evidenced by gross cellular necrosis or enlarged extracellular space; (3) impedance measurements were stable for at least 30 minutes (below); and (4) aspiration of the adhering Tyrode’s layer in the central chamber had a Po_{2} in excess of 65 kPa, and the Po_{2} in the outer chambers was 86.3±5.7 kPa (n=5).

Alternating current (frequency [f], 20 Hz to 300 kHz) was passed via platinum black electrodes between the outer chambers. The resistance (*r*) and capacitance (*c*) of the system were recorded with a balanced Wien bridge (Wayne-Kerr 6425), assuming a parallel *rc* configuration.^{12} ^{13} Two complete sets of recordings were made at 10-minute intervals; values always agreed within 5%, and the average value was used. In three separate preparations, six sets of recordings were made at 10-minute intervals; only the sixth varied by >5% from the others. At the end of recordings, the preparation was immediately fixed for histological estimation of muscle CSA (below). Platinum black electrode resistance (*r*_{e}) and capacitance (*c*_{e}) were separately measured over the same frequency range in a large volume of Tyrode’s solution before and after the experiment and varied by <5%. The resistivity of Tyrode’s solution was measured at 20°C and 37°C using the same platinum black electrodes in a conductivity cell of known dimensions (length, 1.0 cm; CSA, 0.070 cm^{2}) and had values of 64±2 and 49±1 Ω·cm (n=5) at the two respective temperatures.

Polarization resistance (*r*_{p}) and capacitance (*c*_{p}) of the electrode were calculated from *r*_{e} and *c*_{e}, assuming that *r*_{p} and *c*_{p} lie in series.^{14} (1) Preparation impedance (*z*_{s}) was expressed in resistive (*r*_{s}) and reactive (*x*_{s}) components (*z*_{s}=*r*_{s}+j*x*_{s}, where j is the complex operator √−1. *r*_{s} and *x*_{s} were calculated from the measured *r* and *c* values and corrected for the electrode properties, *r*_{p} and *c*_{p}, and ω is the radial frequency [ω=2πf]): (2) *r*_{s} values were plotted (abscissa) as a function of −*x*_{s} values (ordinate). Circular portions (dispersions) were fitted to the equation of an arbitrary circle, with *a*, *b*, and *r* indicating constants; (*r*_{s}−*a*)^{2}+(*x*_{s}*−b*)^{2}=*r*^{2} and the intersections on the *r*_{s} axis were calculated. Lowercase values of all terms represent dimensionless values (units, Ω and F). Values of specific resistivity quoted in “Results” (uppercase *R*; units, Ω·cm) were calculated from the above values using the length of the preparation in the oil gap and the CSA of muscle in the preparation^{12} : they thus represent a macroscopic value of the specific resistivity of the intracellular compartment.

### Isolated Myocytes

Left ventricular myocytes were prepared by perfusing the coronary circulation with a collagenase-containing solution. The heart was initially perfused for 4 minutes at 40 mm Hg with a nominally Ca^{2+}-free solution (solution A, mmol/L): NaCl 120, KCl 5.4, MgSO_{4} 5.0, sodium pyruvate 5.0, glucose 20, taurine 20, and HEPES 20, pH 6.95, followed by 2.0 minutes of perfusion with solution A plus 200 nmol/mL CaCl_{2} and 0.3 mg/mL protease. A final 5.0- to 7.0-minute perfusion was carried out in solution A plus 200 nmol/mL Ca^{2+}, 0.33 mg/mL collagenase, and 0.6 mg/mL hyaluronidase. After perfusion, the atria and right ventricular free wall were cut away, and the remainder was chopped into small pieces and gently triturated and stored in solution A plus 1.8 mmol/L CaCl_{2}.

### Measurement of *R*_{c}

*R*_{c} was estimated separately at 20°C by measuring the impedance of myocyte suspensions over the range 20 Hz to 30 kHz in a Perspex chamber (CSA, 0.05 cm^{2}) via platinum black electrodes separated by 200 μm. Myocytes were suspended in Tyrode’s solution in which NaCl had been replaced by sucrose to maximize current flow through the suspension; the resistivity of this solution was 349±5 Ω·cm (n=4). Values of *r* and *c* obtained from the Wien bridge were corrected for electrode resistance and capacitance as described above and converted to *r*_{s} and *x*_{s} values, which were finally converted to specific values, *R*_{s} and *X*_{s} (Ω·cm), using the chamber CSA and electrode separation. Resistance-reactance plots (see Fig 1B⇓) showed a single dispersion attributable to the surface membrane as it was completely removed by 10 μmol/L digitonin.^{15} Low-frequency (*R*_{1}) and high-frequency (*R*_{2}) intercepts of the plot with the resistance axis were estimated, and the value of *R*_{2} was used to calculate *R*_{c}. *R*_{c} values were calculated from Equation 3^{16} : (3) where *R*_{T} is the resistivity of Tyrode’s solution, *p* is the percentage volume occupied by myocytes assuming a random orientation of axes in the chamber, and *p**=2/3*p*. *p* was calculated from the following:

### Histology

Muscle samples were fixed in half-strength Karnovsky fixative at 4°C and processed in wax. Sections (3 μm) were cut and fixed in hematoxylin and eosin for measurement of cell diameter and further stained in trichrome MSB for connective tissue to estimate muscle proportion in the cross section. CSA of the individual cells was measured in the narrowest plane across the nucleus to avoid oblique sections^{17} with an image acquisition system (Seescan). At least 75 cells from each section were measured.

### Statistics

Values are quoted as mean±SD. Statistical differences between data sets were calculated by Student’s *t* test. The null hypothesis was rejected when *P*≤.05.

## Results

### Development of Left Ventricular Hypertrophy

Guinea pigs were divided into four experimental groups, those at 50 and 150 days after the operation, with or without aortic constriction. Aortic constriction significantly and progressively increased HBR compared with the sham operation; the data are shown in Table 1⇓. The increase of HBR in the constricted groups was not due to a decrease of body weight (Table 1⇓) and therefore reflects an increase of heart weight. Table 1⇓ also shows that myocardial growth was mirrored by an increase of cell CSA. In the constricted groups at 50 and 150 days after the operation, the HBRs and the CSAs were both significantly increased compared with the age-matched sham-operated control groups. In addition, the mean HBR value after 150 days of constriction was significantly greater than after 50 days of constriction, although this was not so for the CSA.

### Measurement of *R*_{i}

Fig 1A⇑ shows the impedance, *Z*_{s}, of two myocardial preparations in the oil-gap chamber as a function of frequency between 20 Hz and 300 kHz; one preparation was from a 50-day sham-operated animal (closed symbols), and the other was from a 150-day constricted animal (open symbols). In each case, impedance declines with increasing frequency, leveling off toward a constant finite value at higher frequencies. The plot is interpreted as one or more parallel *rc* circuits in series with a resistance. For each *rc* circuit with a different time constant (τ=*rc*), there will be a specific range of frequencies over which the impedance will decline. In Fig 1A⇑, two phases of decline are apparent before attainment of a constant value.

More accurate analysis was obtained by plotting, at each frequency, the resistive (*R*_{s}) and reactive (−*X*_{s}) components of *Z*_{s} as a function of each other. Fig 1B⇑ shows such plots using the data of Fig 1A⇑; points for lowest frequencies are on the right side, and each time constant shows as a separate semicircular locus. Semicircles were fitted to the left (higher frequencies) loci, and the intercepts with the *R*_{s} axis are shown as *R*_{1} and *R*_{2}. The plots were analyzed in terms of circuit elements in the longitudinal pathway of the muscle preparations, in parallel with a resistive shunt, *R*_{ec}, which is present in the extracellular space of the preparation and in the thin layer of Tyrode’s solution adhering to the muscle beneath the oil in the central chamber (see below and Fig 1C⇑).

Such plots do not specifically display frequency information, but the values of some frequencies are shown on the plots. The time constant, τ, of the parallel *rc* circuit generating a particular dispersion is obtained from the relationship 2πf*τ=1, where f* is the frequency generating the maximum value of −*X*_{s} in the locus. The low-frequency dispersion exhibited a maximum reactance at ≈40 Hz, equivalent to a time constant of ≈4 ms and similar to that of the myocardial membrane time constant.^{18} Thus, the low-frequency dispersion was interpreted as resulting from the surface membrane of the preparation in the outer chambers, *R*_{m} and *C*_{m} in Fig 1C⇑.

The high-frequency dispersions (maximum reactance at 10 to 40 kHz) have been interpreted as a junctional impedance between cells in the longitudinal pathway.^{12} ^{13} ^{19} ^{20} The residual resistance at the higher frequencies was considered to result from the resistance of the sarcoplasm. Fig 1C⇑ shows an equivalent circuit that was used to analyze the −*X*_{s}/*R*_{s} plots of Fig 1B⇑. Included in the circuit is a shunt resistance, *R*_{ec}, representing current flow through the extracellular compartment of the preparation in the oil gap. The low-frequency intercept of the left dispersion with the resistance axis, *R*_{2}, is a parallel combination of *R*_{ec} and the total intracellular resistivity, *R*_{i}, where *R*_{i} is the sum of *R*_{c} and *R*_{j}. The high-frequency intercept, *R*_{1}, is a parallel combination of *R*_{ec} and *R*_{c} alone. The difference, *R*_{2}−*R*_{1}, will therefore be a function of *R*_{j} and *R*_{ec}. The values of the intercepts *R*_{1} and *R*_{2} were determined in all preparations, along with the preparation length in the oil gap, total CSA (including the adherent layer of Tyrode’s solution), and the proportion of CSA occupied by muscle for calculation of the specific resistances in units of Ω·cm. There were no significant differences in preparation dimensions between each of the four experimental groups.

Total *R*_{i} in myocardial preparations from sham-operated and constricted guinea pigs was measured at 20°C and 37°C; the values are shown in Table 2⇓. In sham-operated animals, 50- and 150-day postoperation values were not significantly different at either 20°C or 37°C. After 50 days of constriction, the mean value of *R*_{i} was also not significantly different from the age-matched control group at 20°C or 37°C. However, at 150 days after the operation, values of *R*_{i} in the constricted group were significantly greater than in the sham-operated control group at both temperatures.

### Estimation of Junctional and Sarcoplasmic Impedances

Separate values of sarcoplasmic, *R*_{c}, and junctional, *R*_{j}, impedance were calculated to determine which component was responsible for the increase of *R*_{i}; the data are shown in Table 2⇑, and the 37°C results are also shown in Fig 2⇓. Fig 2⇓, top, shows *R*_{c} values, and Fig 2⇓, bottom, shows the corresponding values of *R*_{j}. At each temperature, values of *R*_{c} were the same in control and hypertrophied groups, both at 50 and 150 days after the operation. Combining data from all experimental groups, *R*_{c} was 147±76 Ω·cm at 20°C and 100±52 Ω·cm at 37°C. This represents an average Q10 of ≈1.28 over this range of temperatures. The Q10 of the specific resistivity of a 150 mmol/L KCl solution has an average value of 1.23 over this range, calculated from Onsager’s limiting law for conductivity.^{21} The similarity of Q10 values is consistent with considering the sarcoplasm as a simple ionic solution.

Calculated mean values of *R*_{j} mirrored changes to total *R*_{i} induced by hypertrophy. At 37°C, values of *R*_{j} at 50 days after surgery were not significantly different in the control and hypertrophied groups. However, after 150 days, compared with the control group, there was a significant increase in the hypertrophied group: at 20°C, the same pattern was observed. Therefore, the observed increase of *R*_{i} after 150 days of hypertrophy can be accounted for solely by an increase of junctional resistance.

### Control Experiments

It is important to provide supportive evidence for the interpretation of the longitudinal impedance data in terms of sarcoplasmic and junctional impedances. This was carried out by two experiments: (1) an independent estimate of *R*_{c}, which was determined from suspensions of isolated myocytes, where the junctional impedance would not be expected to contribute to the overall impedance of the preparation, and (2) manipulation of junctional impedance with *n*-heptanol, which has been demonstrated to have a fairly specific effect on junctional impedance.^{22}

### Myocyte Suspensions

In four preparations with a packing fraction of 0.32±0.02, the high-frequency specific impedance, *Z*_{s}, was 420±50 Ω·cm, which from Equations 3, and 4 (see “Materials and Methods”) yielded a value for *R*_{c} of 442±32 Ω·cm in the sucrose-containing Tyrode’s solution (see “Materials and Methods”). An extensive study of the effect of changes in *R*_{ec} on the value of cytoplasmic resistivity, *R*_{c}, has been carried out in suspensions of isolated cells (rods)^{16} : ie, 1/*R*_{c}=0.5/*R*_{ec}+constant. If a similar relationship existed in these isolated myocytes, a value of 123±3 Ω·cm (n=4) was calculated for *R*_{c} at 20°C in normal Tyrode’s solution (*R*_{Tyr}=68 Ω·cm). This value was not significantly different from the above value obtained for *R*_{c} at 20°C in the longitudinal impedance measurements (147±76 Ω·cm).

### Experiments With *n*-Heptanol

Values of *R*_{c} and *R*_{j} were calculated at 20°C in further longitudinal impedance measurements, after 30 minutes of pretreatment in gassed Tyrode’s solution containing 2 mmol/L *n*-heptanol. These values were compared with those from five control experiments made on strips immersed only in Tyrode’s solution for 30 minutes. Fig 3⇓ shows examples of two resistance-reactance plots obtained in control Tyrode’s solution (closed symbols) and 2 mmol/L heptanol Tyrode’s solution (open symbols). The high-frequency intercepts of the left loci, *R*_{1}, are not greatly different; however, the low-frequency intercept, *R*_{2}, of the heptanol-treated preparation is larger than that for the control strip, suggesting a selective increase of *R*_{j}. Values of *R*_{c} in control and *n*-heptanol–treated strips were not significantly different, 113±29 Ω·cm (n=5) and 147±24 Ω·cm (n=6), respectively. However, *R*_{j} was significantly greater in the *n*-heptanol–pretreated group (200±47 versus 308±52 Ω·cm (*P*<.05). Therefore, *n*-heptanol selectively increased the component of *Z*_{s} attributed to *R*_{j}, providing support for the interpretation of the impedance data in terms of the circuit elements of Fig 1C⇑.

## Discussion

### Left Ventricular Hypertrophy

The data show that constriction of the ascending aorta in guinea pigs produces cardiac hypertrophy, demonstrated by an increase of HBR. Such hypertrophy was reflected in an increase of cellular dimensions when expressed as the mean CSA in histological preparations. HBR also increased significantly between 50 and 150 days of constriction, whereas no such progressive increase was seen in the cellular CSA. Therefore, it is likely that part of the increased cardiac growth between 50 and 150 days of constriction results from an increase in the proportion of nonmyocardial tissue, but nevertheless, significant cellular hypertrophy can be demonstrated at both time intervals.

### Control Values of the Intracellular Pathway

The specific value of *R*_{i} from control hearts was 216±64 Ω·cm at 37°C and 373±103 Ω·cm at 20°C, similar to that obtained by DC cable analysis (eg, Reference 18^{18} ; 152 Ω·cm, 37°C). *R*_{i} has been modeled as a series combination of a sarcoplasmic resistance and a junctional impedance. *R*_{c} was 100±52 and 147±76 Ω·cm at 20°C and 37°C, respectively. An independent measurement of *R*_{c} was made in isolated myocyte suspensions to corroborate the above values, with the assumption that the quantitative relationship between changes of *R*_{ec} and *R*_{c} was the same in cardiac myocytes and the rods.^{16} However, the value of 123±3 Ω·cm at 20°C was very close to that obtained in the longitudinal impedance experiments. The contribution that the intercalated disks make to the *R*_{i} was also calculated, assuming that the myocytes are simple cylinders, with intercalated disks occupying the entire end region (116±35 Ω·cm at 37°C and 233±89 Ω·cm at 20°C). Although this does not reflect accurately the distribution of intercellular couplings, it permits comparison with other experimental and theoretical studies that use a similar model. Using the above values for *R*_{j} and a length of guinea pig myocytes of 147±33 μm (n=50; authors’ unpublished data, 1996), we obtained a value for the specific disk resistance of 1.7 Ω·cm^{2} for the control myocardial tissue at 37°C, which compares well with the value of 3 Ω·cm^{2} obtained by Weidmann.^{23}

### The Intracellular Pathway in Myocardial Hypertrophy

After 150 days of aortic constriction in a guinea pig model of myocardial hypertrophy, there is an increase of *R*_{i}. This increase was attributed solely to an increase of the junctional impedance between adjacent cells; *R*_{c} was unchanged. There is no evidence for alteration to cell length in this model of hypertrophy (K. Ryder, personal communication, 1996), so that if the same calculation for specific disk resistance is carried out, the value will increase to ≈4.0 Ω·cm^{2}. The finding of an increased *R*_{i} is at variance with that in a rat model of renal artery stenosis, where no change was measured.^{24} However, in this model there was no increase of HBR, so that comparison with the above data is difficult.

Electrical connections between contiguous myocardial cells are mediated by connexin proteins, which form functional pores. Alteration of connexin electrical conductance can be mediated in two ways: (1) a decrease of the conductance of existing connexins, mediated, for example, by a fall of intracellular pH or pCa,^{25} and (2) alteration of the number, distribution, and type of connexin subtypes. An intracellular acidosis of 0.19 pH units accompanies left ventricular hypertrophy in this model^{26} ; however, using available quantitative data,^{25} this would decrease conductance by only ≈4%. This suggests that the important change in myocardial hypertrophy is in connexin density and maybe in their distribution and subtype. In human hypertrophied myocardium, a reduction of connexin43 (the predominant subtype) density has been reported,^{27} which would support the above electrical data. However, it is important to note that the distribution of connexins on the cell surface is very plastic with a rapid turnover,^{28} so that a raised longitudinal impedance could be achieved equally well by a redistribution of connexins from the longitudinal to transverse axes. The electrophysiological consequences of these possibilities and means of distinguishing between them are discussed below.

### Consequences for the Electrical Properties of Myocardium

A consequence of a raised *R*_{i} will be a reduced velocity of action potential propagation. Data using this guinea pig model,^{10} as well as human hypertrophied myocardium,^{6} show that when the preparation behaves as a one-dimensional cable, conduction velocity is inversely related to cell diameter. One-dimensional cable theory would predict the opposite relationship between the two variables unless there was also a concomitant rise of *R*_{i}, as demonstrated in the present study. The magnitude of the rise of *R*_{i} is important, because theoretical studies have shown that an excessive increase can result in discontinuous propagation. Using baseline variables similar to the experimental values reported here, it has been shown that an increase of *R*_{i} above ≈1000 Ω·cm results in deviation from the behavior of a one-dimensional cable to one permitting discontinuous propagation to occur.^{29} This conclusion is of importance, since it has been suggested that discontinuous propagation is an important precursor of reentrant behavior in myocardium.^{30} Such high values of *R*_{i} were not, on average, observed in the present study; however, the fact that an increase of *R*_{i} can be demonstrated does not preclude much higher local changes or the possibility that it might reinforce other factors that increase *R*_{i}, such as tissue hypoxia.^{31} Thus, a combination of these two conditions could produce the conditions for discontinuous propagation more effectively than either condition alone. Studies are under way to quantify the effects of hypoxia on the electrical properties and action potential propagation in hypertrophied myocardium.

The fact that the increase of *R*_{i} is due solely to a raised *R*_{j} has additional consequences. Myocardial resistivity is a heterogeneous property, which is greater in dimensions transverse to the longitudinal axis because of the asymmetrical connexin distribution. Factors such as heptanol, which increase *R*_{j} and preferentially attenuate transverse conduction,^{22} may increase the propensity for reentrant circuits to develop.^{32} If connexin conductance were to decrease equally in all dimensions during hypertrophy, such a condition may well arise; however, if redistribution were to occur, as discussed above, then the difference between longitudinal and transverse impedances would diminish. Thus, it is vital to differentiate between such possibilities, and this can be achieved by measuring the ratio of transverse to longitudinal conduction velocities and by use of a three-dimensional map of *R*_{i} in hypertrophied myocardium.^{12} Such measurements are also presently under way.

## Selected Abbreviations and Acronyms

CSA | = | cross-sectional area |

HBR | = | heart weight–to–body weight ratio |

Q10 | = | proportional change of variable (R_{c}) for a change of temperature by 10°C |

R
_{c}
| = | sarcoplasmic resistivity |

R
_{ec}
| = | extracellular resistivity |

R
_{i}
| = | intracellular resistivity |

R
_{j}
| = | junctional resistivity |

R
_{s}
| = | resistive component of Z_{s} |

−X_{s} | = | reactive component of Z_{s} |

Z
_{s}
| = | total longitudinal impedance |

## Acknowledgments

We thank the British Heart Foundation for financial assistance and M. Turner for technical help.

- Received October 7, 1996.
- Accepted February 21, 1997.

- © 1997 American Heart Association, Inc.

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- Changes in Cell-to-Cell Electrical Coupling Associated With Left Ventricular HypertrophyM. Cooklin, W. R. J. Wallis, D. J. Sheridan and C. H. FryCirculation Research. 1997;80:765-771, originally published June 19, 1997http://dx.doi.org/10.1161/01.RES.80.6.765
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