Multiscale Model for Ion Transport in Cellular Media and Applications in Smooth Muscle Cells

Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like the smooth muscles on vessel walls, can be treated as periodic bi-domain structures consisting of the intracellular space (ICS) and extracellular space (ECS) with semipermeable membranes in between. In this work, we first use a multi-scale asymptotic method to derive a macroscopic homogenized bidomain model from the microscopic electro-neutral (EN) model with different diffusion coefficients and nonlinear interface conditions. Then, the obtained homogenized model is applied to study ion transportation and micro-circulation in multi-celluar tissues under the impact of agonists, an internal calcium source, and extracellular potassium. Our model serves as a useful bridge between existing ordinary differential equation models and partial differential models that take into consideration spatial variation. On the one hand, numerical results show that ECS variables are almost invariant in the first two scenarios and confirm the validity of existing single-domain models, which treat variables in the ECS as constants. On the other hand, only the bidomain model is applicable to consider the effect of local extracellular potassium. Finally, the membrane potential of syncytia formed by connected cells is found to play an important role in the propagation of oscillation from the stimulus region to the non-stimulus region. Author summarySmooth muscle cells (SMCs) play a vital role in neurovascular coupling, which is the mechanism by which changes in neural activity are linked to alterations in blood flow. Dysfunctional SMCs can have significant implications for human health. The activation of SMCs is primarily regulated by the intracellular concentration of calcium ions (Ca2+). A multi-scale model for ion transport in multicellular tissue with varying connectivity has been proposed to investigate SMC activation under different stimuli. The simulation results confirm the critical role of gap junctions in wave propagation and vasoconstriction in the vessel wall. The blockage of gap junctions prevents the spread of the wave. Furthermore, the propagation of membrane potential is the primary cause of wave propagation.