Steinhausen et al. (37) analyzed the propagation of vasomotor responses, induced by local electrical stimulation, in split hydronephrotic rat kidneys. Their results indicate that the responses decay with increasing distance from the stimulation site and that the decay is significantly faster upstream than downstream. An explanation for the asymmetric decay rates, which was elusive, is a motivation for the present study.In a previous study (5), we developed a detailed mathematical model of the myogenic response of a small segment of the afferent arteriole (AA) wall, including the endothelium and the surrounding smooth muscle cells. That model was used to examine the response of the AA segment to changes in mean and pulsatile pressure. Simulation results of that model are consistent with the hypothesis that the AA myogenic response plays an important role in protecting the glomerular capillaries against elevated systolic pressures. The goal of this study is to develop a multicell model of the AA by connecting a series of AA smooth muscle cells and endothelial cells via gap junction coupling and to use the model to study the myogenic response of the AA and its response to local electrical stimulation. The AA model is intended to be used as an essential component in models of integrated renal hemodynamic regulation.
MATHEMATICAL MODELMulticell AA model. The model is an extension of our previous AA cell model (5) and represents a segment of an AA of length L (L ϳ300 m), consisting of a series of N cell ϭ 101 smooth muscle cell models (5), coupled via their gap junctions and via an endothelial cell layer. (An odd number of smooth muscle cell models were represented so that there is a middle cell that can be stimulated to study any asymmetry in the conduction of vasoconstrictive response.) The model AA segment is connected in series to a fixed resistor, denoted R end. The inflow pressure [P 0(t) at x ϭ 0] and the pressure at the end of the fixed resistor P end (at x ϭ 2L) are assumed to be known a priori. A schematic diagram is shown in Fig. 1. When the inflow pressure P 0 is varied or when a vasoconstrictive or vasodilative response is induced, the pressure at the end of the AA segment, which is denoted P(L, t) and which we refer to as the "outflow pressure," may also vary. We set P end to 0 mmHg and R end to equal the time-averaged value of the total resistance of the unstimulated AA with P 0 ϭ 100 mmHg, so that when the inflow pressure P 0 ϭ 100 mmHg, the outflow pressure P(L) Ϸ 50 mmHg.Each AA smooth muscle cell model incorporates the ionic transports, cell membrane potential, muscle contraction of the AA smooth muscle cells, and the mechanics of a thick-walled cylinder. The model represents the interaction of Ca 2ϩ and K ϩ fluxes mediated by voltagegated and voltage-calcium-gated channels, respectively, which gives rise to the periodicity of those transports. This results in a timeperiodic cytoplasmic calcium concentration, myosin light chains phosphorylation, and crossbridge formation with the attending muscle s...