Note on the anisotropy of extracellular resistivity in cardiac muscle.

In their recent paper, Roberts et aL (1979) report the following values of intracellular (i), extracellular (o), longitudinal (<f), and transverse (t) resistivity for canine ventricular muscle: r^ = 450 ohms-cm, rot = 750 ohm-cm, ru = 360 ohm-cm, and rit = 3800 ohm-cm. The ratio W r ^ is 1.67. In an earlier paper, Clerc (1976) reported the following resistivity ratios for trabecular bundles from the right ventricle of calf heart: TH/T^ = 9.4 ± 1.0 (mean ± SE) and rot/ro/= 2.69 ± 0.26. Clerc gives his resistivity data in terms of the specific resistivity of the intracellular and extracellular fluids. On the other hand, Roberts et al. use an effective resistivity, where the intracellular and extracellular compartments are each taken to occupy the entire tissue space (see also Miller and Geselowitz, 1978). Clerc's data can be converted to this form using his value of 30% for the volume fraction of extracellular space with the result: r<̂ = 160 ohm-cm, r^ = 423 ohmcm, r,/ = 574 ohm-cm, and r^ = 5170 ohm-cm. In his paper, Clerc presents a model for the anisotropy of intracellular resistivity. With regard to extracellular anisotropy, he simply states that the ratio "being 2.7 may be explained by the tortuous pathway around tightly packed fibres encountered by transverse current." The purpose of this note is to provide a theoretical basis for the ratio nately, this problem was solved by Lord Rayleigh (1892). His result is