Standing waves of depolarization, produced at the surface ofrabbitheart in vitro by periodic voltage driving,eliminate propagationactivity in the heart, thusproviding a defibrillating effect (Gray et.al., 2001). The phenomenon cannot be reproduced by cable orbidomain models of cardiac tissue. In such models,voltage appliedthrough an external electrode decayswithin the tissueexponentially with a space constantof ~1 mm.As a result, externalvoltagedriving of such a tissue cannot generate standing waves,asonly regions of the tissue near the electrode are entrained.However,a bidomain model of ventricular tissue, accounting forexistence of a bathing solution to which electrodes are applied,allows simulation of the standing waves in 1 and 2dimensions(Aslanidi et. al., 2002).We consider asteady linear bidomain modelwitha bath, which describes steady distribution of voltage in apassive1-dimensional tissue surrounded by a bathing solution.Themodel comprises three equations describing intracellularvoltageV_i, extracellular cleft voltage V_e, and voltage of the bath V_s.

 

V_m”= (R_e+R_i) R_m-1V_m – R_e R_d-1 Vd;

 

Vd”= (Re+Rs)Rd-1 Vd – Re Rm-1 Vm;

 

Vs”= – R_s R_d-1 V_d.

 

Here Vm = V_i – V_e is the membrane voltage, V_d= V_e – V_s is thedepth voltage, “ sign denotessecond spatial derivative. The onlyparameters of themodel are intracellular, extracellular and bathresistances, R_i, R_eand R_s, the membrane resistance Rm and thedepth resistance Rd,all of which are set to experimentally validatedvalues.Analyticalstudy of the model equations reveals the existenceofthree space constants: the classical space constant λ₁ ≅ 1 mm,an unusually long space constant λ₂ ≅ 20 mm, and a trivial spaceconstant λ₃ = 0 giving rise to alinear component of the bathvoltage. Thus, decay ofthe membrane voltage in the bidomainmodel with a bathis characterized by multiple space constants,λ₁and λ₂, one of which has a usual value of ~1 mm, and anotheris 20-fold longer. The latter constant is robust inrespect tochanging values of the conductancesR_i = 0.4 kΩ cm, R_e = 0.1 kΩcm, R_m = 10 kΩcm2, R_s = 0.02 kΩ cm, R_d= 200 kΩ cm2 by up to20%.We conclude that the existence of such a longspace constantis the reason why the bidomain model with a bath, as well asexperiment,produces standing waves entraining areas in the farfieldzone,20-40 mm away from the electrodes.