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2022 | OriginalPaper | Chapter

9. An Electrochemo-Poromechanical Theory for the Mechanobioelectricity of Cell Clusters

Author : Alessandro Leronni

Published in: Modeling the Electrochemo-poromechanics of Ionic Polymer Metal Composites and Cell Clusters

Publisher: Springer International Publishing

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Abstract

This chapter is adapted from “Leronni [11], Modeling the mechanobioelectricity of cell clusters, Biomechanics and Modeling in Mechanobiology, 20:535–554”.

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previous chapter On the Coupling of Mechanics with Bioelectricity and Its Role in Morphogenesis

next chapter Discussion

In Eq. (9.47b), $D_\mathrm {i}^\mathrm {m}$ is regarded as a constant. Actually, the value of $D_\mathrm {i}^\mathrm {m}$ depends on the gating of ion channels. For certain applications, it may be relevant to explicitly account for this. In general, in the presence of voltage-gated, ligand-gated and mechanosensitive ion channels, $D_\mathrm {i}^\mathrm {m}$ could be written as:

$$\begin{aligned} D_\mathrm {i}^\mathrm {m}=D_\mathrm {i}^\mathrm {m,0} +D_\mathrm {i}^\mathrm {VC}p_\mathrm {open}^\mathrm {VC}(\psi ^\mathrm {m}) +D_\mathrm {i}^\mathrm {LC}p_\mathrm {open}^\mathrm {LC}(C_\mathrm {i},C_\mathrm {i}^\mathrm {e}) +D_\mathrm {i}^\mathrm {MC}p_\mathrm {open}^\mathrm {MC}(p_\mathrm {mec})\,, \end{aligned}$$

(9.48)

where $D_\mathrm {i}^\mathrm {VC}$, $D_\mathrm {i}^\mathrm {LC}$ and $D_\mathrm {i}^\mathrm {MC}$ are the diffusivities across the (open) voltage-gated, ligand-gated and mechanosensitive channels, and $p_\mathrm {open}^\mathrm {VC}$, $p_\mathrm {open}^\mathrm {LC}$ and $p_\mathrm {open}^\mathrm {MC}$ are the respective open probabilities, modulated by the membrane potential $\psi ^\mathrm {m}$, the IC and EC ion concentrations $C_\mathrm {i}$ and $C_\mathrm {i}^\mathrm {e}$, and the mechanical pressure $p_\mathrm {mec}$, respectively; $D_\mathrm {i}^\mathrm {m,0}$ denotes the diffusivity across the lipid bilayer. Equation (9.48) extends Eq. (8.50), where only mechanosensitive channels are considered.

The pull back operation is defined by the relations $\mathbf {J}=J\mathbf {F}^{-1}\mathbf {j}$ and $\mathrm {grad}=\mathbf {F}^\mathrm {-T}\nabla $.

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Title: An Electrochemo-Poromechanical Theory for the Mechanobioelectricity of Cell Clusters
Author: Alessandro Leronni
Publisher: Springer International Publishing
Book: Modeling the Electrochemo-poromechanics of Ionic Polymer Metal Composites and Cell Clusters
Print ISBN: 978-3-030-92275-7

Electronic ISBN: 978-3-030-92276-4

Copyright Year: 2022
DOI: https://doi.org/10.1007/978-3-030-92276-4_9

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