Spatial Buffering Mechanism: Mathematical Model and Computer Simulations

Abstract

Abstract. It is generally accepted that the spatial buffering mechanism is important to buffer extracellular-space potassium in the brain-cell microenvironment. In the past, this phenomenon, generally associated with glial cells, has been treated analytically and numerically using a simplified one-dimensional description. The present study extends the previous research by using a novel numerical scheme for the analysis of potassium buffering mechanisms in the extracellular brain-cell microenvironment. In particular, a lattice-cellular automaton was employed to simulate a detailed two-compartment model of a two-dimensional brain-cell system. With this numerical approach, the present study elaborates upon previous theoretical work on spatial buffering (SB) by incorporating a more realistic structure of the brain cell microenvironment, which was not feasible earlier. We use the experimental paradigm consisting of iontophoretic injection of KCl to study the SB mechanism. Our simulations confirmed the results reported in the literature obtained by an averaged model. The results also show that the additional effects captured by a simplified twodimensional geometry do not alter significantly the conclusions obtained from the averaged model. The details of applying such a numerical method to the study of ion movements in cellular environments, as well as its potential for future study, are discussed.2000 Mathematics Subject Classification. 92C05.

Validating a computational framework for ionic electrodiffusion with cortical spreading depression as a case study

“…Therefore, the conductance for the K + inward rectifier current (K ir 4.1, A/m 2 ) is modelled as an expression depending on the extracellular and intracellular ion concentrations for the glial cell. Following Steinberg et al (2005), the K ir 4.1 conductance (,S/m 2 ) is modelled as: where (S/m 2 ) is the resting membrane conductance, and corresponds to the conductance when and . The value of can be found in Table 6.…”

“…Therefore, the conductance for the K + inward rectifier current (K ir 4.1, A/m 2 ) is modelled as an expression depending on the extracellular and intracellular ion concentrations for the glial cell. Following Steinberg et al (2005), the K ir 4.1 conductance (g K ir 4.1 , S/m 2 ) is modelled as:…”

Algorithm-Oriented SIMD Computer Mathematical Model and Its Application

“…Therefore, many computer researchers have conducted in-depth research on the improvement of computer mathematical models. For example, Miura et al (2017) expounded on the importance of the spatial buffer mechanism in the field of brain cell research and proposed a novel spatial buffer computer mathematical model to analyze the buffer characteristics in the brain cell environment. These researchers verified the performance of the model by simulation experiments.…”