Evaluation of the effectiveness of electrical muscle stimulation on human calf muscles via frequency difference electrical impedance tomography

Figure 1 shows the fd-EIT system composed of four units: a wearable sensor consisting of sixteen dry electrodes (Darma et al 2020), a digital multiplexer (made by Takei lab based on Arduino Due), an impedance analyzer (IM3570, HIOKI, Japan), and a PC including image reconstruction algorithm software. The impedance analyzer injects 1 mA sinusoidal current to the electrodes by the adjacent current injection method (Baidillah et al 2019) then measures the impedance Z by way of the digital multiplexer. The impedance analyzer has an impedance measurement accuracy of 0.08% and excitation frequency coverage from 4 Hz to 5 MHz.

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In order to detect the response muscle areas of human calf muscles, the conductivity distribution images σ ^p are reconstructed based on the theory of quasi-static electromagnetic field analysis (Gandhi et al 1993). In the forward problem, the Jacobian matrix is defined as J = [J₁, J₂,..., J_n ,..., J_N ] ^M×N , where J_n = [J₁, J₂,..., J_m ,..., J_M ]^{T M} , m is the measurement number, n is the mesh number, M is the total measurement number, and N is the total pixel number of space resolution. The Jacobian matrix element J_mn of the mth measured voltage pattern at the nth mesh element (Darma et al 2020) is obtained by

$$\begin{eqnarray}&&{J}_{mn}=\displaystyle \frac{\partial {v}_{m}}{\partial {\sigma }_{n}}=\displaystyle {\int }_{\Omega }{\rm{\nabla }}u\left({i}^{e}\right).{\rm{\nabla }}u\left({i}^{m}\right){\rm{d}}{\rm{\Omega }}\end{eqnarray} \tag{ 1 }$$

where u(i^e ) is the potential field produced by injecting current i into the eth electrode, u(i^m ) is the potential field produced by injecting current i into the mth measured voltage pattern, v_m is the measured voltage at the mth measured electrode pattern (1 ≤ m ≤ M), σ_n is the conductivity at the nth mesh (1 ≤ n ≤ N), and Ω is the electrical field area inside the fd-EIT sensor. J depends on the linearization of conductivity distribution in equation (1). In order to improve the accuracy of the reconstructed image, a modeled inhomogeneous conductivity distribution, which consists of bone (σ_bone =  0.020 S m⁻¹), fat (σ_fat =  0.022 S m⁻¹), and muscle (σ_muscle =  0.321 S m⁻¹) (Gabriel 1996), was used in the forward problem to calculate non-linear J.

Meanwhile, the inverse problem to reconstruct σ ^p from Z (Lionheart 2001) uses the Gaussian–Newton method (Darma et al 2020) expressed by

$$\begin{eqnarray}&&{{\boldsymbol{\sigma }}}^{p}={{\bf{J}}}^{T}{\rm{\Delta }}{{\bf{Z}}}^{p}-{({{\bf{J}}}^{T}{\bf{J}}+\mu {\bf{I}})}^{-1}{{\bf{J}}}^{T}{\rm{\Delta }}{{\bf{Z}}}^{p}\end{eqnarray} \tag{ 2 }$$

where μ is the hyperparameter which was chosen based on the error lying in the L-Curve's elbow (Braun et al 2017). ${\rm{\Delta }}{{\bf{Z}}}^{p}=[{\rm{\Delta }}{Z}_{1}^{p},\ldots ,{\rm{\Delta }}{Z}_{m}^{p},\ldots ,{\rm{\Delta }}{Z}_{M}^{p}]$ $\epsilon$ ℜ^M is the impedance difference between one measured impedance Z^p,f2 at high frequency f₂ injection current and another measured impedance Z^p,f1 at low frequency f₁ injection current in fd-EIT (Baidillah et al 2017), which is expressed by

$$\begin{eqnarray}&&{\rm{\Delta }}{Z}_{m}^{p}=\displaystyle \frac{{Z}_{m}^{p,{f}_{2}}-{Z}_{m}^{p,{f}_{1}}}{{Z}_{m}^{p,{f}_{1}}}\end{eqnarray} \tag{ 3 }$$

where p indicates the experimental protocol, which are pre-training (pre), training (tra), post-training (post), and relaxation (relax).

In this study, we focus on the muscle tissue located deeper in the skin and fat layer of the calf. As we all know, the contact impedance of the skin is very large, but for medical equipment, the injection current of EIT equipment cannot be higher than 1 mA. Therefore, we apply gel on the skin to reduce contact resistance. The reason for obtaining the best image from low frequency is that after EMS, the water content of the intercellular substance changes due to the effect of muscle congestion, and the high frequency directly mixes the intracellular information with the information obtained by the cell, so we believe that using a low frequency better reflects the changes in the moisture of the extracellular fluid. Therefore, two frequencies are heuristically selected as f₁  =  700 Hz and f₂  =  1 kHz to obtain the most clear σ ^p .

Twenty-four healthy young men (age: 30.0 ± 3.0 years, height: 173.5 ± 6.5 cm, skeletal muscle mass: 35.6 ± 6.8 kg) volunteered for this study. None of the subjects had any history of any musculoskeletal or neurological disorders. Figure 2 shows the experimental protocol consisting of four parts: pre-training, training, post-training, and relaxation parts (Zainuddin et al 2005). In all experimental protocols, subjects were measured in a sitting position.

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In the pre-training part, firstly, fd-EIT is conducted to reconstruct the conductivity distribution images σ ^pre in the human right calf; secondly, BIA (Inbody S10, InBody Co., Ltd, Korea) measures the extracellular water ratio β^p =  ECW/TBW, which is compared with the conductivity distribution change. Figure 3 shows the 16 electrodes of the fd-EIT sensor location and distribution.

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In the training and post-training parts, firstly, the subject's calf muscles are stimulated by EMS for 15 min using commercial EMS equipment (SIXPAD Leg belt, Nagoya MTG Ltd, Japan); secondly, fd-EIT is conducted to reconstruct the σ ^post in the human right calf; finally, BIA is used to measure β^p . Figure 4 shows the position of the EMS electrode, which contacts the subject's skin directly. The EMS equipment in this study has a different voltage value but uses a constant-controlled current, which is 8 mA. The stimulation cycle rule is a 4 s stimulation with 4 s pause and the stimulation frequency is 20 Hz. After testing the EMS tolerance limit of each experimental subject, level 10 of EMS training intensity was selected from twenty training levels of EMS in situ. Level 10 means that the EMS output voltage is 26.13 V.

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In the relaxation part, the subjects' calf muscles were relaxed for 20 min by three methods of relaxation. The twenty-four subjects were divided into the massage relaxation (MR) group, cold pack relaxation (CR) group, and hot pack relaxation (HR) group with eight subjects per group. A water bag at around 12 °C was used to relax the subjects' calf muscles in the CR group. A towel soaked in hot water (temperature around 40 °C) was used to relax the subjects' calf muscles in the HR group. The temperatures of the water bag and towel were controlled by a temperature gun (the given error was ±5 °C). After relaxing, firstly, fd-EIT was conducted to reconstruct σ ^relax in the human right calf; finally, BIA was used to measure β^p .

Due to the fd-EIT, the sensor needs to be taken off and worn repeatedly during the above-mentioned experimental protocol. Therefore, it was necessary to test the sensitivity of fd-EIT to displacement. Eight healthy young men (age: 29.6 ± 3.0 years, height: 175.0 ± 6.0 cm, skeletal muscle mass: 34.2 ± 6.2 kg) volunteered for this control group. Figure 3 shows the fd-EIT sensor position, which was marked with yellow tape. In the control group, firstly, fd-EIT was conducted to reconstruct the conductivity distribution images σ ^cg–pre in the human right calf; secondly, the subject was asked to wear the EMS for ten minutes, but the EMS was not switched on; then, fd-EIT was performed again to reconstruct the conductivity distribution image σ ^cg–post of the right calf. The above process was repeated twice for each subject.

In order to quantify the response muscle areas of human calf muscles under EMS, the conductivity distribution images reconstructed by fd-EIT were analyzed by a dedicated Python script. Figure 5 shows an example of σ ^p of human calf muscles in the range of 0 <  σ ^p ≤ 1.0 and the mesh structure used in this study. The mesh consists of 3053 trihedral element and 5263 points. In this paper, the view direction of σ ^p is from the top to the bottom of the human leg, which is contrary to the direction of typical CT images. Normally, the σ ^p indicates two response areas affected by EMS, which are denoted as M₁ and M₂ response areas. The conductivity values of M₁ and M₂ were changed in the pre-training, post-training, and relaxation parts. According to a typical MRI image of the calf muscle structure, M₁ and M₂ were calculated based on J by using the dedicated Python script in each subject. The reason why σ ^pre shows high conductivity in M₁ and M₂ before EMS is that the each subject's muscles have their own conductivity under the modeled inhomogeneous conductivity distribution in the forward problem. Therefore, σ ^pre was used as the baseline for each experimental subject in this study. The conductivity difference ratios Δ σ ^{post– pre} between pre- and post-training parts and Δ σ ^{relax– pre} between pre-training and relaxation parts are defined as

$$\begin{eqnarray}&&{\rm{\Delta }}{{\boldsymbol{\sigma }}}^{post-pre}=\left({{\boldsymbol{\sigma }}}^{post}-{{\boldsymbol{\sigma }}}^{pre}\right)\oslash {{\boldsymbol{\sigma }}}^{pre}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}{{\boldsymbol{\sigma }}}^{relax-pre}=\left({{\boldsymbol{\sigma }}}^{relax}-{{\boldsymbol{\sigma }}}^{pre}\right)\oslash {{\boldsymbol{\sigma }}}^{pre}\end{eqnarray} \tag{ 5 }$$

where the ⊘ symbol is the Hadamard division, which is the element-wise division of the column vector, and σ ^pre , σ ^post , and σ ^relax are the conductivity distribution images in the pre-training, post-training and relaxation parts, respectively.

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The post–pre and relax–pre difference ratios of spatial-mean conductivity Δ〈σ^post–pre 〉_M1,M2 and Δ〈σ^{relax– pre} 〉_M1,M2 in M₁ and M₂ are defined as

$$\begin{eqnarray}&&{\rm{\Delta }}{\left\langle {\sigma }^{post-pre}\right\rangle }_{M1,M2}=\displaystyle \frac{{\left\langle {\sigma }^{post}\right\rangle }_{M1,M2}-{\left\langle {\sigma }^{pre}\right\rangle }_{M1,M2}}{{\left\langle {\sigma }^{pre}\right\rangle }_{M1,M2}}\times 100 \% \end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}{\left\langle {\sigma }^{relax-pre}\right\rangle }_{M1,M2}=\displaystyle \frac{{\left\langle {\sigma }^{relax}\right\rangle }_{M1,M2}-{\left\langle {\sigma }^{pre}\right\rangle }_{M1,M2}}{{\left\langle {\sigma }^{pre}\right\rangle }_{M1,M2}}\times 100 \% \end{eqnarray} \tag{ 7 }$$

where 〈σ^pre 〉_M1,M2, 〈σ^post 〉_M1,M2, and 〈σ^relax 〉_M1,M2 are the spatial-mean conductivity in M₁ and M₂ in the pre-training, post-training, and relaxation parts. The conductivity distribution depends on the individual. In order to draw a general conclusion, we use the difference ratios to quantify the change in electrical conductivity distribution caused by the physiological response of post-training and relaxation of human muscles. Therefore, we proposed the application of fd-EIT to measure the effect of EMS on muscle training. In order to evaluate the difference ratios of spatial-mean conductivity, the post–pre and the relax–pre difference ratios of the extracellular water ratio Δβ^post–pre and Δβ^relax–pre are defined as

$$\begin{eqnarray}&&{\rm{\Delta }}{\beta }^{post-pre}=\displaystyle \frac{{\beta }^{post}-{\beta }^{pre}}{{\beta }^{pre}}\times 100 \% \end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}{\beta }^{relax-pre}=\displaystyle \frac{{\beta }^{relax}-{\beta }^{pre}}{{\beta }^{pre}}\times 100 \% \end{eqnarray} \tag{ 9 }$$

where β^pre , β^post , and β^relax are the extracellular water ratios in the pre-training, post-training, and relaxation parts. The difference ratio quantifies the effects of post-training and relaxation of human muscles as references of Δ〈σ^post–pre 〉_M1,M2 and Δ〈σ^relax–pre 〉_M1,M2. The resolution of Inbody S10 is enough to calculate the percentage value, which can retain one digit after the decimal point (Masuda et al 2016).

In order to use the paired samples t-test on the experimental data, it was necessary to perform a normal distribution test. The descriptive statistics function of SPSS software (version 25.0) was used to test the normal distribution of three parts of experimental data. Table 1 shows the results of the Shapiro–Wilk test and the Kolmogorov–Smirnov test. Under the test level of α  =  0.05, p > 0.05, the null hypothesis is not rejected. Therefore, it can be considered that the experimental data obey a normal distribution.

A paired samples t-test was conducted between the spatial-mean conductivities 〈σ^p 〉_M1,M2 in the M₁ and M₂ response areas in order to elucidate the response muscle areas of human calf muscles under EMS and after relaxation. Also, the t-test is conducted in the extracellular water ratio β^p for the evaluation. The test statistic t-values of the paired samples t-test are calculated by

$$\begin{eqnarray}&&t=\displaystyle \frac{{\bar{x}}_{diff}\sqrt{n}}{{S}_{diff}}\end{eqnarray} \tag{ 10 }$$

where ${\bar{x}}_{diff}$ is the mean difference of the experimental subject number n, and S_diff is the standard deviation of the differences. The level of significance was set as 0.05. The paired samples t-test was performed using SPSS software (version 25.0).

Table 2 shows the conductivity distribution images σ ^cg–pre and σ ^cg–post of eight subjects' calves before and ten minutes after wearing the EMS sensor obtained by equation (2). From σ ^cg–pre and σ ^cg–post , the M₁ and M₂ areas have no significant difference in two-times measurements. Also, figure 6 shows the spatial-mean conductivity 〈σ^cg–pre 〉_M1,M2 and 〈σ^cg–post 〉_M1,M2. The spatial-mean conductivity in M₁ remains unchanged from 〈σ^cg–pre 〉_M1  =  0.159 to 〈σ^cg–post 〉_M1  =  0.160 in the first measurement; also, in the second measurement, the spatial-mean conductivity in M₁ remains unchanged from 〈σ^cg–pre 〉_M1  =  0.158 to 〈σ^cg–post 〉_M1  =  0.157. The spatial-mean conductivity in M₂ holds stable between 〈σ^cg–pre 〉_M2  =  0.052 and 〈σ^cg–post 〉_M2  =  0.055 in the first measurement; similarly, the spatial-mean conductivity in M₂ holds stable between 〈σ^cg–pre 〉_M2  =  0.054 and 〈σ^cg–post 〉_M2  =  0.054 in the second measurement. Therefore, we conclude that only wearing the fd-EIT sensor repeatedly has no significant effect on the conductivity distribution measurement results.

Table 2. Conductivity distribution images σ ^cg–pre and σ ^cg–post before and ten minutes after wearing EMS sensor reconstructed by fd-EIT.

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Table 3 shows the conductivity distribution images σ ^pre and σ ^post of twenty-four subjects' calves in pre- and post-training parts obtained by equation (2), and the conductivity difference ratios Δ σ ^{post– pre} between pre- and post-training parts obtained by equation (4). From the σ ^pre and σ ^post , the response muscle areas are clearly detected in the M₁ and M₂ response areas. Also, from the images Δ σ ^post–pre , the conductivity difference ratios between pre- and post-training parts in the response muscle areas are clearly detected.

Table 3. Conductivity distribution images σ ^pre and σ ^post in pre- and post-training parts reconstructed by fd-EIT and the conductivity difference ratios Δ σ ^{post– pre.}

Solid color bar charts in figure 7 show the spatial-mean conductivity 〈σ^pre 〉_M1,M2 and 〈σ^post 〉_M1,M2 in M₁ and M₂ and extracellular water ratio β^pre and β^post in the pre- and post-training parts. Dot color bar charts in figure 7 show the difference ratio of spatial-mean conductivity Δ〈σ^post–pre 〉_M1,M2 in M₁ and M₂ response areas between pre- and post-training parts. The spatial-mean conductivity in M₁ is increased from 〈σ^pre 〉_M1  =  0.194 to 〈σ^post 〉_M1  =  0.504 by Δ〈σ^post–pre 〉_M1  =  173.0%; also, the spatial-mean conductivity in M₂ is increased from 〈σ^pre 〉_M2  =  0.071 to 〈σ^post 〉_M2  =  0.182 by Δ〈σ^post–pre 〉_M2  =  174.6%. These increase tendencies are similar to the extracellular water ratio from β^pre =  0.369 to β^post =  0.378 by the difference ratio between pre- and post-training parts Δβ^post–pre =  2.3%.

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Table 4 shows the statics of paired samples t-test in the pre- and post-training parts. The null hypotheses in 〈σ^p 〉_{M1, M2} areas are rejected because t-values t_M1  =  −10.452 and t_M2  =  −9.987 are smaller than -t_0.025 (23)  =  −2.069. We conclude that 〈σ^post 〉_{M1, M2} are significantly increased from 〈σ^pre 〉_{M1, M2} in both response areas. Moreover, the null hypothesis in the extracellular water ratio β^p is rejected because t_β =  −9.529 is smaller than t_0.025(23)  =  −2.069. We conclude that β^post is significantly increased from β^pre . The mean difference ${\bar{x}}_{diff}$ of β^post is −0.0085 (n  =  24, p < 0.001) in the post-training part. The bottom row in table 4 and above-mentioned figure 7 show the p-value of 〈σ^p 〉_M1,M2 in the paired samples t-test results between the pre- and post-training parts, which have the same tendency as the p-value of β^p .

Table 4. Statics of paired samples t-test of 〈σ^p 〉_M1,M2 and β^p (p = pre or post) between pre- and post-training parts.

Items	〈σp〉M1	〈σp〉M2	βp
Mean difference ${\bar{x}}_{diff}$	−0.3106	−0.1109	−0.0085
Standard deviation Sdiff	0.1456	0.0544	0.0044
t0.025(23)	−2.069
t-value	−10.452	−9.987	−9.529
p-value	<0.001	<0.001	<0.001

Table 5 shows the conductivity distribution images ${{\boldsymbol{\sigma }}}_{{\rm{{\rm M}}}R}^{relax},$ ${{\boldsymbol{\sigma }}}_{{\rm{CR}}}^{relax}$, and ${{\boldsymbol{\sigma }}}_{{\rm{HR}}}^{relax}$ of the experimental subjects' calves under the three relaxation conditions (MR, CR, and HR) obtained by equation (2). Also, table 5 shows the conductivity difference ratios ${\rm{\Delta }}{{\boldsymbol{\sigma }}}_{{\rm{MR}}}^{relax-pre},$ ${\rm{\Delta }}{{\boldsymbol{\sigma }}}_{{\rm{CR}}}^{relax-pre}$, and ${\rm{\Delta }}{{\boldsymbol{\sigma }}}_{{\rm{HR}}}^{relax-pre}$ between the pre-training and relaxation parts obtained by equation (5). From ${{\boldsymbol{\sigma }}}_{{\rm{{\rm M}}}R}^{relax},$ ${{\boldsymbol{\sigma }}}_{{\rm{CR}}}^{relax}$, and ${{\boldsymbol{\sigma }}}_{{\rm{HR}}}^{relax},$ the response muscle areas are also clearly detected in M₁ and M₂. From ${\rm{\Delta }}{{\boldsymbol{\sigma }}}_{{\rm{MR}}}^{relax-pre},$ ${\rm{\Delta }}{{\boldsymbol{\sigma }}}_{{\rm{CR}}}^{relax-pre}$, and ${\rm{\Delta }}{{\boldsymbol{\sigma }}}_{{\rm{HR}}}^{relax-pre},$ the conductivity difference ratios between the pre-training and relaxation parts in the response muscle areas are clearly detected.

Table 5. Conductivity distribution images σ ^relax in relaxation part reconstructed by fd-EIT and the conductivity difference ratios Δ σ ^relax–pre .

Solid color bar charts in figure 8 show the spatial-mean conductivity 〈σ^relax 〉_{M1,M2(MR,CR,HR)} in M₁ and M₂ in the relaxation part as well as 〈σ^post 〉_M1,M2 in the post-training part for the below-mentioned discussion. The dot color bar charts in figure 8 show the difference ratio of spatial-mean conductivity Δ〈σ^relax–pre 〉_{M1,M2(MR,CR,HR)} in M₁ and M₂ between the pre-training and relaxation parts.

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In MR, the spatial-mean conductivity in M₁ is decreased from 〈σ^post 〉_M1  =  0.504 to 〈σ^relax 〉_M1(MR)  =  0.261 by Δ〈σ^relax–pre 〉_M1(MR)  =  29.5%; also, the spatial-mean conductivity in M₂ is decreased from 〈σ^post 〉_M2  =  0.182 to 〈σ^relax 〉_M2(MR)  =  0.115 by Δ〈σ^relax–pre 〉_M2(MR)  =  40.4%. This decrease tendency is similar to the extracellular water ratio from β^post =  0.378 to ${\beta }_{{\rm{MR}}}^{relax}$  =  0.372 by the difference ratio between pre-training and relaxation parts ${\rm{\Delta }}{\beta }_{{\rm{MR}}}^{relax \mbox{-} pre}$  =  0.5%.

In CR, the spatial-mean conductivity in M₁ is decreased from 〈σ^post 〉_M1  =  0.504 to 〈σ^relax 〉_M1(CR)  =  0.241 by relax–pre ratio Δ〈σ^relax–pre 〉_M1(CR)  =  23.9%; also, the spatial-mean conductivity in M₂ is decreased from 〈σ^post 〉_M2  =  0.182 to 〈σ^relax 〉_M2(CR)  =  0.088 by relax–pre ratio Δ〈σ^relax–pre 〉_M2(CR)  =  26.5%. This decrease tendency is similar to the β^post =  0.378 to ${\beta }_{{\rm{CR}}}^{relax}$  =  0.371 by the difference ratio between pre-training and relaxation parts ${\rm{\Delta }}{\beta }_{{\rm{CR}}}^{relax \mbox{-} pre}$  =  0.4%.

However, in HR, the spatial-mean conductivity in M₁ is increased from 〈σ^post 〉_M1  =  0.504 to 〈σ^relax 〉_M1(HR)  =  0.621 by Δ〈σ^relax–pre 〉_M1(HR)  =  258.6%; also, the spatial-mean conductivity in M₂ is increased from 〈σ^post 〉_M2  =  0.182 to 〈σ^relax 〉_M2(HR)  =  0.207 by Δ〈σ^relax–pre 〉_M2(HR)  =  268.1%. This decrease tendency is similar to the β^post =  0.378 to ${\beta }_{{\rm{HR}}}^{relax}$  =  0.379 by the difference ratio between pre-training and relaxation parts ${\rm{\Delta }}{\beta }_{{\rm{HR}}}^{relax \mbox{-} pre}$  =  3.0%.

Table 6 shows the statics of the paired samples t-test under three relaxation conditions. In MR, the null hypotheses in 〈σ^relax 〉_M1,M2(MR) areas are rejected because t- values t_M1(MR)  =  7.216 and t_M2(MR)  =  7.385 are larger than t_0.025(7)  =  2.365. We conclude that 〈σ^relax 〉_M1,M2(MR) is significantly decreased from 〈σ^post 〉_M1,M2 in both response areas. Moreover, the null hypothesis in the ${\beta }_{{\rm{MR}}}^{relax}$ is rejected because t_β(MR)  =  4.492 is larger than t_0.025(7)  =  2.365. We conclude that ${\beta }_{{\rm{MR}}}^{relax}$ is significantly decreased from β^post . The mean difference ${\bar{x}}_{diff}$ of ${\beta }_{{\rm{MR}}}^{relax}$ is 0.0070 (n  =  8, p < 0.05) in MR. In CR, the null hypotheses in 〈σ^relax 〉_M1,M2(CR) areas are rejected because t- values t_M1(CR)  =  5.269 and t_M2(CR)  =  5.960 are larger than t_0.025(7)  =  2.365. We conclude that 〈σ^relax 〉_M1,M2(CR) is also significantly decreased from 〈σ^post 〉_M1,M2 in both response areas. Moreover, the null hypothesis in the ${\beta }_{{\rm{CR}}}^{relax}$ is rejected because t_β(CR)  =  5.314 is larger than t_0.025(7)  =  2.365. We conclude that ${\beta }_{{\rm{CR}}}^{relax}$ is significantly decreased from β^post . The mean difference ${\bar{x}}_{diff}$ of ${\beta }_{{\rm{CR}}}^{relax}$ is 0.0073 (n  =  8, p < 0.05) in CR.

Table 6. Paired samples t-test results of the 〈σ^p 〉_M1,M2 and β^p between post-training and relaxation parts.

Items	〈σp〉M1			〈σp〉M2			βp
	MR	CR	HR	MR	CR	HR	MR	CR	HR
Mean difference ${\bar{x}}_{diff}$	0.2602	0.3117	−0.1816	0.1013	0.0980	−0.0626	0.0070	0.0073	−0.0028
Standard deviation Sdiff	0.1020	0.1673	0.1230	0.0388	0.0465	0.0382	0.0044	0.0039	0.0033
t0.025(7)	2.365
t-value	7.216	5.269	−4.177	7.385	5.960	−4.635	4.492	5.314	−2.392
p-value	<0.001	0.001	0.004	<0.001	<0.001	<0.05	0.003	0.001	0.048

However, in HR, the null hypotheses in 〈σ^relax 〉_M1,M2(HR) areas are rejected because t-values t_M1(HR)  =  −4.177 and t_M2(HR)  =  −4.635 are smaller than -t_0.025(7)  =  −2.365. We conclude that 〈σ^relax 〉_M1,M2(HR) is significantly increased from 〈σ^post 〉_M1,M2 in both response areas. Moreover, the null hypothesis in the ${\beta }_{{\rm{HR}}}^{relax}$ is rejected because t_β(HR)  =  −2.392 is smaller than -t_0.025(7)  =  −2.365. We conclude that ${\beta }_{{\rm{HR}}}^{relax}$ is significantly increased from β^post . The mean difference ${\bar{x}}_{diff}$ of ${\beta }_{{\rm{HR}}}^{relax}$ is −0.0028 (n  =  8, p < 0.05) in HR. The bottom row in table 5 and above-mentioned figure 8 show the p-value of 〈σ^p 〉_M1,M2 in the paired samples t-test results between the post-training and relaxation parts, which have the same tendency of the p-value of β^p . Therefore, the conductivity change of human calf muscles under different relaxation conditions is related to the muscle tissue fluid.

Firstly, the reason why the conductivities of human calf muscles under EMS in the M₁ and M₂ response areas are increased in the post-training part is discussed. Generally, two types of skeletal muscle fibers exist in human muscles, which are white muscle fibers (type II fast-twitch) and red muscle fibers (type I slow-twitch). When EMS is applied to human muscles, stimulation current induces an eccentric contraction of muscles (Lepley et al 2015). EMS quickly recruits white muscle fibers for contraction (Sinacore et al 1990), which generates high explosive power. The red muscle fibers are mainly used for long-term aerobic exercises (Stuart et al 2013).

Figure 9 shows the human calf muscle structure and cross-sectional image. From this figure, M₁ is recognized as the position of the gastrocnemius muscle. From a previous electromyography study, the gastrocnemius muscle is recognized to be primarily involved in the fast movements of the leg as it is dominated by white muscle fibers (Mademli and Arampatzis 2005). Therefore, the conductivity 〈σ^post 〉_M1 in M₁ is increased in the post-training by gastrocnemius muscle contraction.

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Moreover, M₂ is recognized as the position of the tibialis anterior muscle, extensor digitorum longus muscle, and peroneus longus muscle. From the viewpoint of muscle structure, these muscles in M₂ on the front calf side are stretched while the gastrocnemius muscle is contracted because those muscles of M₁ and M₂ work together to make the tiptoe movement. The muscles in M₂ are also trained simultaneously even though M₂ is not covered by EMS while the gastrocnemius muscle is repeatedly contracted under EMS. Therefore, the spatial-mean conductivity 〈σ^post 〉_M2 in M₂ is also increased in the post-training part.

Secondly, why soleus muscles are not responded by EMS is discussed even though the posterior calf muscles are mainly composed of gastrocnemius muscles and soleus muscles. From figure 9, the soleus muscles located behind the gastrocnemius (farther from the skin) have more red muscle fibers, and are the primary active muscles in a standing posture. While EMS is applied to human calf muscles, the stimulation current does not cause soleus muscle contraction in a short time. In addition, a more recent study has shown that EMS only indiscriminately stimulates the most superficial muscle fibers under the electrodes (Gregory and Bickel 2005). The soleus muscles is located behind the gastrocnemius (farther from the skin). In short, the deep soleus muscle cannot be stimulated by EMS. Therefore, the conductivity in the soleus muscle position is not changed in the post-training part.

Thirdly, the reason why conductivities are increased in M₁ and M₂ is discussed from the viewpoint of the change in muscle tissue extracellular volumes. Fleckenstein et al first reported that T2-weighted active skeletal muscle spin-echo MRI images showed increased signal intensity immediately after EMS training (Fleckenstein et al 1988). This phenomenon has also been studied in other research (Fisher et al 1990). It was proposed that this contrast enhancement of the exercised muscle was caused by increased vascular and extracellular volumes (Fleckenstein et al 1988). Therefore, the change in muscle tissue extracellular volumes is used to determine whether the target muscles are trained effectively. Compared with the pre-training part, the greater β^p recorded in the post-training part is reasonable, since much water is transported to the muscle, causing muscle tissue fluid to increase. Therefore, the spatial-mean conductivity 〈σ^p 〉_M1,M2 of human calf muscles increase.

The reason why the conductivities of human calf muscles in M₁ and M₂ response areas have different changes under the three relaxation conditions is discussed.

In MR, 〈σ^relax 〉_M1,M2(MR) is decreased from 〈σ^post 〉_M1,M2 while ${\beta }_{{\rm{MR}}}^{relax}$ decreases from β^post because MR promotes the removal of metabolites such as lactic acid and H⁺ from the muscle tissues. Massage increases the movement of lymphatic fluid and blood, facilitating their transfer to gluconeogenic organs such as the liver (Stamford et al 1981). Therefore, MR effectively reduces the concentration of muscle cell metabolites, thereby alleviating muscle extracellular volumes in the post-training part.

In CR, 〈σ^relax 〉_M1,M2(CR) is decreased from 〈σ^post 〉_M1,M2 while ${\beta }_{{\rm{CR}}}^{relax}$ decreases from β^post because CR decreases muscle temperature (Enwemeka et al 2002). The decrease in muscle tissue temperature is thought to stimulate the cutaneous receptors, causing the sympathetic fibers to vasoconstrict, which decreases the muscle extracellular volumes (Pugh et al 1955).

In HR, the 〈σ^relax 〉_M1,M2(HR) are increased from 〈σ^post 〉_M1,M2 while ${\beta }_{{\rm{HR}}}^{relax}$ increases from β^post because HR increases muscle tissue temperature, local blood flow, and muscle elasticity and causes local vasodilation (Pugh et al 1955). Therefore, the conductivity distribution change of human calf muscles under EMS is related to muscle extracellular volumes, which has been detected by frequency difference electrical impedance tomography (fd-EIT).