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)

Bo Sun, Panji Nursetia Darma, Kaname Ikeda, Tomoyuki Shirai, Kosei Narita, Masahiro Takei

Abstract: The relationship between fat thickness tfat and current density magnitude |iφ| 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 |iφ| 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 |iφ| to fat thickness tfat is M1, the physiological-induced conductive response in M2 depends not only on the |iφ|, but also on the muscle mechanical motion. The Pearson correlation coefficient (PCC) r between spatial-mean current density magnitude <|iφ|> and spatial-mean conductivity difference Δ < σφ−pre> in M1, M2 and M3 shows high correlation under EMS. The tfat and |iφ| are negatively correlated in muscle compartments of each subject. The individual tfat and |iφ| are negatively correlated in muscle compartments of each subject because the fat layer becomes an obstacle against |iφ| 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 tfat. The absolute difference |ΔφOVI| 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 tfat, which is due to the fact that the effect of EMS loading voltage on muscle diminishes with increasing tfat, thus reducing the effect of muscle quality on the results of optimum voltage intensity calculations.