Simulations of passive properties and action potential conduction in an idealized bullfrog atrial trabeculum

This study investigates the properties of a distributed parameter model of an idealized trabeculum of cardiac muscle surrounded by a resistive-capacitive trabecular sheath. A mathematical approach is developed that permits the direct solution for the absolute potential in each medium [i.e., the intracellular (Vi), interstitial (Ve), and external (Vo) potentials), as opposed to obtaining solutions for the transmembrane potential V (where V identical to Vi-Ve). The mathematical description of the underlying individual cell is based upon quantitative whole-cell voltage-clamp measurements in bullfrog atrial myocytes. "Reduced" or "simplified" cell membrane models that lack the complete complement of transmembrane currents are compared with regard to their accuracy in representing the root, upstroke, and plateau regions of the propagated action potential in the complete model. The results show that a reduced cell membrane model must contain the sodium current INa, calcium current ICa, and background-rectifying K+ current IK1. A cell membrane model that contains a linear background K+ current IL instead of IK1 results in much poorer approximation to the upstroke, plateau, and conduction velocities of an action potential. The effects of varying the resistive-capacitive parameters of the trabecular sheath on both the passive properties (the time and space constants and the input resistance) and conduction parameters (time and space constants of the foot and conduction velocity of the action potential) of the trabeculum are also investigated. These simulations show that electrical activity within the trabeculum is much more sensitive to variations in the resistive component than in the capacitive component of the sheath. The trabecular sheath reduces the extracellular resistance seen by the cell by shunting current away from highly resistive interstitial medium into the volume conductor medium, which is of low resistance, and thereby increases conduction velocity. Finally, the addition of the cholinergic neurotransmitter acetylcholine to the extracellular medium reduces both the space constant of the trabeculum and the conduction velocity of propagated electrical activity.