Numerical Simulation of Conduction Delay in Blocked Purkinje Tissue

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Abstract
The model used for passive conduction in muscle fibers consisted of a region of nonpropagating fiber of variable length, bounded proximally and distally by normal active tissue. The voltage variation on this fiber was governed by the passive wave equation. This system was analyzed by Fourier series techniques on the digital computer, using a cardiac action potential as the input. With a fixed distal threshold, delays up to 45 msec were simulated by varying the length of nonconducting fiber. Delay time was very sensitive to the extent of the inactive region. Inactive tissue lengths of 1.6 mm and 2.0 mm caused delays of 6.1 msec and 11.7 msec, respectively, but lengths of 2.35 mm and 2.36 mm caused delays of 31.7 msec and 40.0 msec, respectively. Inactive areas longer than 2.37 mm caused complete block. With inactive regions 2.35 mm long, a 5% reduction in distal threshold reduced the delay time 35% and a 5% increase caused complete block. Delay time was also sensitive to variations in the membrane parameters. A 10% reduction in membrane capacitance produced approximately a 10% decrease in delay, but such a reduction in membrane resistance caused approximately a 10% increase in delay. Curves recorded in blocked regions of canine Purkinje fibers were simulated by superimposing nonpropagating potentials from proximal and distal sites. The familiar two-component wave forms and other contour variations were quite realistic in the simulation, demonstrating its effectiveness in predicting voltage variations in nonpropagating Purkinje tissue.