Relationship between fat thickness and current density magnitude in calf muscles compartments under electrical muscle stimulation (EMS) by coupling of electromagnetic simulation and electrical impedance tomography (ES-EIT)

Abstract

The relationship between fat thickness t_fat and current density magnitude |i_φ| has been clarified by coupling of electromagnetic simulation and electrical impedance tomography (ES-EIT) under electrical muscle stimulation (EMS) in three responsive calf muscle compartments which are called M₁ compartment of gastrocnemius muscle, M₂ compartment of tibialis anterior, extensor digitorum longus, and peroneus longus muscles, and M₃ compartment of soleus muscle. ES-EIT images the current density magnitude |i_φ| from the conductivity distribution σ reconstructed by EIT for the decision of optimum voltage intensity ${\boldsymbol{\varphi }}_{\mathbf{O}\mathbf{V}\mathbf{I}}^{\mathbf{i}}$ of EMS. As a result, the highest sensitivity of |i_φ| to fat thickness t_fat is M₁, the physiological-induced conductive response in M₂ depends not only on the |i_φ|, but also on the muscle mechanical motion. The Pearson correlation coefficient (PCC) r between spatial-mean current density magnitude <|i_φ|> and spatial-mean conductivity difference Δ < σ^φ−pre> in M₁, M₂ and M₃ shows high correlation under EMS. The t_fat and |i_φ| are negatively correlated in muscle compartments of each subject. The individual t_fat and |i_φ| are negatively correlated in muscle compartments of each subject because the fat layer becomes an obstacle against |i_φ| from the skin to the subcutaneous tissue. As a discussion, the optimum voltage intensity ${\boldsymbol{\varphi }}_{\mathbf{O}\mathbf{V}\mathbf{I}}^{\mathbf{i}}$ and ${\boldsymbol{\varphi }}_{\mathbf{O}\mathbf{V}\mathbf{I}}^{{\varvec{\upsigma}}}$ of M₁ are defined as the highest point of second-order difference of spatial-mean current density magnitude $\langle {\left.\frac{{\partial }^{2}\left|{\mathbf{i}}_{\boldsymbol{\varphi }}^{{\varvec{M}}1}\right|}{\partial {\boldsymbol{\varphi }}^{2}}\right|}_{\boldsymbol{\varphi }}\rangle$ and spatial-mean conductivity $\langle {\left.\frac{{\partial }^{2}{{\varvec{\upsigma}}}_{\boldsymbol{\varphi }}^{{\varvec{M}}1}}{\partial {\boldsymbol{\varphi }}^{2}}\right|}_{\boldsymbol{\varphi }}\rangle$ under EMS, which are increased with the increase in t_fat. The absolute difference |Δφ_OVI| between ${\boldsymbol{\varphi }}_{\mathbf{O}\mathbf{V}\mathbf{I}}^{\mathbf{i}}$ and ${\boldsymbol{\varphi }}_{\mathbf{O}\mathbf{V}\mathbf{I}}^{{\varvec{\upsigma}}}$ is decreased with increasing t_fat, which is due to the fact that the effect of EMS loading voltage on muscle diminishes with increasing t_fat, thus reducing the effect of muscle quality on the results of optimum voltage intensity calculations.

Graphical Abstract