【title】
Effectiveness of impedance parameters for muscle quality evaluation in healthy men【Abstract】
We investigated the relationship between impedance parameters and skeletal muscle function in the lower extremities, aswell as the effectiveness of impedance parameters in evaluating muscle quality. Lower extremity impedance of 19 healthymen (aged 23-31 years) measured using the Direct Segmental Multi-Frequency bioelectrical impedance analysis were arcoptimized using the Cole-Cole model, following which phase angle (PA), 𝑅! ⁄𝑅" , and β were estimated. Skeletal muscle
function was assessed by muscle thickness, muscle intensity, and isometric knee extension force (IKEF). IKEF was
positively correlated with PA (r = 0.58, p < 0.01) and β (r = 0.34, p < 0.05) was negatively correlated with 𝑅! ⁄𝑅" (r = －0.43, p < 0.01). Stepwise multiple regression analysis results revealed that PA, β, and 𝑅! ⁄𝑅" were correlated with IKEF
independently of muscle thickness. This study suggests that arc-optimized impedance parameters are effective for
evaluating muscle quality and prediction of muscle strength.
【Keywords】
Phase angle, bioelectrical impedance analysis, Cole–Cole model, muscle quality【Introduction】
Skeletal muscle function has been shown to be influenced by both quantitative factors (e.g., number of muscle fibers andcross-sectional area) and qualitative factors [1]. Qualitative factors include an increase in non-contractile tissue (e.g., fatty
infiltration in skeletal muscle and myofascial degeneration) [2]. These are known to be caused by inactivity even in young
people [3]. In recent years, skeletal muscle dysfunction has attracted attention not only for the decline of physical function,
but also for the risk of developing lifestyle diseases and mortality after their occurence, and for the quality of life. [4-6].
Methods for evaluating muscle quality include physiological tests and diagnostic imaging tests such as computed
tomography (CT), magnetic resonance imaging (MRI), and ultrasonography (US). Of these tests, US is noninvasive anddoes not limit the measurement location or posture. This test can be conducted in various settings such as medical
institutions and sports facilities [7, 8]. Muscle intensity (MI), which quantifies the extent of black and white areas fromcross-sectional images of the skeletal muscle taken with US, reflects noncontractile tissue (e.g., increase in intramyocellularlipids and connective tissue). MI is therefore expected to be an effective index for evaluating muscle quality [9]. However,there have been several problems regarding the reproducibility and sensitivity of evaluation with MI, including 1)
fluctuating numerical values depending on the measurement method and instrument settings, making comparison withother research data difficult, and 2) the rate of change in noncontractile tissue and luminance is not linear [10].
Indirect body composition evaluation, which estimates skeletal muscle mass and body fat mass using differences in tissue
electrical conductivity and transmittance in bioelectrical impedance analysis (BIA) and dual-energy X-ray absorptiometry,has recently become widespread. BIA is a non-invasive measurement technique based on the electrophysiologicalproperties of biological tissues. Muscle mass evaluation using BIA has been shown to be as highly accurate as that byconventional measurement methods [11]. Impedance parameters of the biological tissue can also be qualitative factors inskeletal muscle evaluation because they reflect the mass and uniformity of cells and the condition of cell membranes [12].

Particularly, phase angle (PA), which is the phase difference between current and voltage, is related not only to survivalrate, nutritional status [13], and the occurrence of sarcopenia and frailty [14] but also to muscle strength [15], exercise
tolerance [16], and physical activity level [17] in the field of geriatrics as well as to physical fitness and sports science.
Thus, it has attracted attention as a means of qualitative assessment of muscle cell function, which was previously difficult
to evaluate noninvasively.
Thus, although impedance parameters are attractive for muscle quality evaluation, when used as objective indicators, theyrequire correction to accommodate for changes in frequency characteristics associated with skeletal muscle physiology anddecline in anatomical function due to aging or disease. A decline in skeletal muscle function causes changes in the cell
membrane resistance and an increase in the noncontractile tissue, which changes the central relaxation frequency (𝑓# ) at
which reactance reaches its maximum value [18]. Thus, optimizing the arc using the Cole-Cole model is recommended tocompensate for these changes and measure the maximum PA of the target muscle [19]. Employing the Cole-Cole model,
the PA (PAcole) is calculated using 𝑅! ⁄𝑅" (known as the intracellular fluid resistance-to-extracellular fluid resistance ratio)
and the beta parameter (β) as shown in Equations 1 and 2, respectively. PAcole is an indicator of the structural perfection ofskeletal muscle cells. 𝑅! /𝑅" refers to the balance between the intracellular fluid resistance and extracellular fluid
resistance, and β refers to cell homogeneity [20]. Therefore, PAcole is said to be an indicator of the structural completenessof skeletal muscle cells [21]. Previous studies have shown that intracellular and extracellular water contents estimated using
Ri/Re of the lower extremity are useful for evaluating the skeletal muscle mass [22]. β is one of the performance indicesof the capacitor in the equivalent circuit model, and is an index of the uniformity of the measured structure. It is quantified
on a scale from 0 to 1. 0, indicating non-uniform and perfectly uniform tissue, respectively [23]. It has been shown thatchanges in myofiber type and fatty infiltration could be assessed using this parameter [24].
However, to the best of our knowledge, there has been no study on the relationship between muscle strength and muscle
mass and arc-optimized impedance parameters (PAcole, 𝑅! ⁄𝑅" , β), focusing on the lower extremity skeletal muscle function.
We presumed that PAcole and 𝑅! ⁄𝑅" , β could be effective for the qualitative assessment of skeletal muscle composition
related to muscle strength. This study aimed to verify the effectiveness of impedance parameters by simultaneously
evaluating muscle thickness (MT) and MI with arc-optimized impedance parameters and US using Cole-Cole analysis formuscle quality evaluation to predict muscle strength.

【Methods】
Subjects
Nineteen healthy adult men (aged 23-31 years), with a total of 38 left and right lower extremities, were included. The study
protocol was approved by the ethics review board of the Kawasaki Medical School (approval No.: 2846). Written informed
consent was obtained from all participants. The inclusion criteria were as follows: (a) no history of lower extremity trauma
or surgery, (b) no history of neuromuscular disorders, (c) not using an artificial pacemaker, (d) the ability to provide
informed consent with no serious cognitive impairment, and (e) no regular exercise routine. Height and weight were
measured, with the subjects standing barefoot and wearing light training clothes. Measurements were taken to the nearest
0.1 cm and 0.1 kg, and the body mass index (BMI) was calculated. Table 1 shows the physical characteristics of theparticipants.
Experimental procedure
The impedance parameters were measured using Direct Segmental Multi-Frequency Bioelectrical Impedance Analysis(DSM-BIA), MT, and MI were measured using US, and muscle strength was measured using isometric maximum muscle
strength. The test procedures were uniform among all subjects. All assessments were performed on the same day. The
subjects rested for 15 minutes in the supine position immediately before US and BIA measurements to stabilize body water[25].
Bioelectrical impedance
Lower extremity impedance was measured with DSM-BIA using the InBody S10 (InBody Japan, Tokyo, Japan), which
has a tetrapolar eight-point tactile electrode system and three different frequencies (5 kHz, 50 kHz, 250 kHz). Eightelectrodes were attached to the thumb and middle finger of the hand for the upper limb, and to the back of the endocarpus
and exocarpus for the lower limb. DSM-BIA measurements have been shown to be as accurate as those of the DEXA [11].
Measurements were taken in the supine position after 15 minutes of rest. The subjects were instructed to refrain fromalcohol intake and excessive exercise on the day before the test. Measurements were performed in a controlled clinic roomwith a room temperature of 24-26°C. Contact between trunk and extremities was prevented by placing the upper and lower
extremities in the 30° abduction position [25].
Cole-Cole model
The Cole-Cole model was used to estimate the impedance parameters optimized for the arc [19]. The arc of the Cole-Colemodel is shown in Equation 1 and Figure 1, and the biological equivalent circuit model is shown in Equation 2 and Figure
2.
Z(f) = R + jX = Z$ +Z% − Z$f '1 + 1j f 2
&

1
1
1
=
+
Z(f) R ( R ) + Z* (f)

(1)

(2)

where f is the frequency, Z(f) is the complex-valued impedance as a function of f, R is the resistance, X is thereactance, and j is an imaginary unit, Z% is R when f = 0, Z% is R when f = ∞, R ( is the extracellular fluid

resistance, R ) is the intracellular fluid resistance, and Z* (f) is the cellular membrane impedance as a function of f.
Z$ , Z% , f& , β were estimated using Equation 1. Z(f) and Z* (f) varies with f.
(3)

R ( = Z%R) =Z* (f) =Z% Z$
Z% + Z$(4)(Z% )+f ,'1j 2
Z% − Z$ f&(5)

R & and −X& were determined from the obtained Z% and Z$ and is given by
R& =Z% + Z$
2

(6)

βπ
2
−X& =
βπ
2 11 + cos 2 2(Z% − Z$ ) sin(7)

where R & is R when the f is f& and X& is X when the f is f& .
PA&-.( was measured from the obtained R & and −X& and is given byβπβπ
R ( sin 2
sin 2−X&PA&-.( = arctan 1
2=
=
.
βπ
R
βπ
R&
(R ( + 2R ) ) 11 + cos 2 G1 + 2 ) H 11 + cos 2
2
R(
2

(8)

The 50 kHz PA (PA50) used in previous research was added as a variable to evaluate the effects of the Cole-Cole analysis.
Search of 𝒁𝟎 , 𝒁$ 𝜷,𝒇𝒄
The estimation of the four parameters was explored using an optimization method as shown in Equation 9. Impedance andReactance data measured by DSM-BIA were used for the impedance data.
4++

𝐸 = O PQ𝑅1 (𝑓2 ) − 𝑅3 (𝑓2 )R + Q𝑋1 (𝑓2 ) − 𝑋3 (𝑓2 )R T

(9)

256

where 𝑓6 = 5 kHz, 𝑓+ = 50 kHz, 𝑓4 = 250 kHz, 𝑅1 (𝑓2 ) 𝑎𝑛𝑑 𝑋1 (𝑓2 ) are the measured value of resistance and reactance at
frequency 𝑓2 , 𝑅3 (𝑓2 ) and 𝑋3 (𝑓2 ) are the resistance and reactance in Equation 1 at the frequency 𝑓2 , respectively.
We searched for 𝑍% , 𝑍$ 𝛽,𝑓# so that the evaluated value E was the minimum.
Ultrasonography
Quadriceps femoris MT (QFMT) and MI (QFMI) were measured from cross-sectional images of the skeletal muscle using
diagnostic ultrasound imaging equipment (SonoSite M-turbo, FUJIFILM). Measurements were taken in the brightness
mode using a 6–15 MHz linear probe (56 mm). Hard-type echo gel (Conductor TM Transmission Gel, Chattanooga) wasused to prevent the probe from touching the skin. Each measurement was taken twice. The target muscle group was the QF(rectus femoris, vastus medialis, vastus intermedius, and vastus lateralis). The measurement site for rectus femoris, vastus
intermedius, and vastus lateralis was the midway point between the anterior superior iliac spine and the upper margin ofpatella, while that for vastus medialis was the point located 70% distal to the anterior superior iliac spine and the uppermargin of the patella. Image analysis was performed using Image J-WinJP (LISIT, Tokyo, Japan) and using a partiallymodified method referencing the method proposed by Berger et al. [26]. Muscle luminance was measured using convex
hull. After the upper and lower parts were surrounded to ensure the fascia was excluded, the values were quantified in therange of 0–255 with an 8-bit gray scale using histogram analysis, and the mean value of the area was calculated. QFMT(mm) and QFMI were calculated from the total value of the four muscles using the mean of two measurements taken foreach muscle (Fig. 2). The measurements were taken by one examiner. The reliability of this measurement method has been
demonstrated in previous studies [27].
Muscle strength
Muscle strength was measured from isometric knee extension force (IKEF). The measurement was taken while the subject
was seated in a chair without a backrest with the hip and knee joints at 90°. The equipment used for measurement was a
handheld dynamometer (μ-TAS F-1, Anima, Japan). The sensor position was the distal part of the lower leg, and the arm
length (m) was measured from the knee joint space to the center of the sensor. A 3-second maximum contraction was
performed twice, with a 1-minute break, and the maximum value (N) was used. The measured value was the value obtainedby multiplying the measured value by the arm length (Nm).

Statistical analysis
All data are expressed as mean ± standard deviation. All statistical analyses were performed in EZR (Ver 1.4, Saitama
Medical Center, Jichi Medical University, Saitama, Japan) [28]. Significance level was set as less than 5% (p < 0.05).
Pearson's correlation coefficient was used for calculating the correlation of IKEF with QFMT, QFMI, PA50, PAcole, β, 𝑅! ⁄𝑅" ,𝑓# , and BMI. Stepwise multiple regression analysis was conducted with IKEF as the dependent variable to examine theeffects of PAcole and β, 𝑅! ⁄𝑅" on IKEF. The linear models were as follows: Model 1, with QFMT, QFMI, and BMI as
independent variables; Model 2, with PAcole added; and Model 3, with β and 𝑅! ⁄𝑅" added. Variance inflation factor (VIF)
was calculated to confirm the existence of multicollinearity.
【Results】
The subjects’ physical characteristics and data of IKEF, QFMT, QFMI, and lower extremity impedance parameters are given
in Tables 1 and 2, respectively. Data of the correlation between the subjects’ IKEF and QFMT, QFMI, and lower extremity
impedance parameters are shown in Table 3. IKEF had a significantly positive correlation with MT (r = 0.58, p < 0.01),
PAcole (r = 0.53, p < 0.01), and β (r = 0.55, p = 0.04) and a significantly negative correlation with 𝑅! ⁄𝑅" (r = －0.42, p <0.01). The results of stepwise multiple regression analysis with IKEF as the objective variable are given in Table 4. QFMT
was shown to be significantly related in Model 1. PAcole, and β and 𝑅! ⁄𝑅" were selected as significant variables in Models
2 and 3, respectively. The VIF was within the range of 1.05–1.36 for all variables, indicating no multicollinearity.
【Discussion】
To the best of our knowledge, this is the first study to investigate the relationship between the two components (𝑅! /𝑅" , β)of the phase angle in the central frequency from the Cole-Cole model of site-specific impedances of the lower extremity,using optimization calculations and conventional assessment of skeletal muscle function. Previous studies have reported
the relationship between whole-body PA50 and upper and lower extremity muscle strength and exercise tolerance [15-16].
In this study, we demonstrated the correlation between lower extremity impedance parameters (PAcole, 𝑅! ⁄𝑅" , β, and 𝑓# )and QFMT, QFMI, IKEF, and BMI. Further, when PAcole (Model 2) and 𝑅! ⁄𝑅" and β (Model 3) were added as independent
variables in the stepwise multiple regression analysis where IKEF was set as a dependent variable, it resulted in increased
R2 and decreased QFMT standardized partial regression coefficient (SC). A noteworthy finding is that in Model 3, both
𝑅! ⁄𝑅" and β were shown to be factors that affect IKEF independent of QFMT. These results support our hypothesis thathigh muscle thickness and high PAcole are independently associated with IKEF in healthy men and that impedance
parameters (PAcole, 𝑅! ⁄𝑅" , β) as a muscle quality evaluation parameter enhances the suitability of muscle strength
evaluation. This study suggests that simultaneous evaluation of QFMT and impedance parameters (PAcole, 𝑅! ⁄𝑅" , β) could
enable accurate estimation of muscle strength.
First, this study demonstrated the correlation between lower extremity impedance parameters (PAcole, 𝑅! ⁄𝑅" , β, and 𝑓# )and QFMT, QFMI, IKEF, and BMI (Table 3). Evaluation of skeletal muscle composition is important for predicting skeletal
muscle function and physical function and for evaluating the effects of aging and disease [29]. PA50 has been shown to berelated to muscle strength, exercise tolerance, fall history, and physical activity in the field of geriatrics, physical fitness,and sports science [15-17]. Furthermore, studies investigating changes before and after resistance training and age-relatedchanges show that fluctuations in resistance and reactance associated with changes in skeletal muscle function affect PA50[30]. Thus, although there are an increasing number of studies showing the relationship of skeletal muscle and physicalfunction with impedance parameters, those studies use an impedance parameter with a frequency of only 50 kHz.
Conventionally, the 𝑓# in biological tissues is approximated as 50 kHz, which is the reason for using the 50 kHz impedancevalue usually [31]. However, the change in muscle fiber size, increase in connective tissue, and fatty infiltration in skeletal
muscle change the frequency characteristics of the skeletal muscle; therefore, the impedance parameter in 𝑓# using theCole-Cole model is optimal for evaluating changes in skeletal muscle function [32]. In this study, the 𝑓# (38.1 ± 8.1 kHz)was lower than 50 kHz in all subjects. The results of this study showed a moderately positive correlation between IKEF
and PAcole (r = 0.58 p < 0.01), although PA50 did not show a significant correlation (r = 0.11, p = 0.53). Furthermore, there
was a positive correlation between IKEF and β (r = 0.34, p = 0.04), and a moderately negative correlation with 𝑅! ⁄𝑅" (r= －0.43, p < 0.01). A notable finding is that 𝑓# did not have a significant correlation with muscle strength (r = －0.03,
p = 0.8). Previous studies indicated significant correlations between, 𝑅! ⁄𝑅" and/or 𝑓# , which constitute PAcole. However,there was no correlation with muscle strength and muscle mass [22, 34-36]. Most of these studies focused on age-relatedchanges in the aging process in older adults and aged mice, focusing on changes in the intracellular water to extracellularwater ratio and the decrease in phase angle associated with age-related muscle mass loss [22, 34-36]. Conversely, as shownin Equation 8 and Figure 1, in addition to the intracellular water to extracellular water ratio (𝑅! /𝑅" in the present study),
the β has an effect on the phase angle. Despite the fact that β reflects cell homogeneity and may be affected by qualitativechanges in skeletal muscle [20], no studies have focused on β. In the present study, β demonstrated a moderately positive
correlation with IKEF, indicating that in addition to 𝑅! /𝑅" , β is a factor that reflects the influence of skeletal muscle
function.
Second, when PAcole (Model 2) and 𝑅! ⁄𝑅" and β (Model 3) were added as independent variables in stepwise multiple
regression analysis with IKEF as a dependent variable, it resulted in increased R2 and decreased QFMT SC in both models

(Table 4). It has previously been reported that the prediction accuracy of muscle strength dramatically improves with a
combination of muscle mass and muscle quality, rather than using muscle mass alone [37]. Additionally, the importance ofevaluating muscle quality is increasing because the decline in muscle quality precedes the decline in muscle strength [38].
With the change from Models 1 to 2, the QFMT SC decreased from 0.57 to 0.46, while R2 increased from 0.29 to 0.53. The
PAcole SC was 0.49, which was approximately the same value as that for QFMT, indicating that it had an effect independentof other variables. As expected, the analysis for predicting muscle strength produced results similar to those of the study
conducted by Bourgeois et al. [37], where muscle mass and PA were set as variables. In Model 3, the components of PAcole
were divided into 𝑅! ⁄𝑅" and β, and the effects of those variables were analyzed. New findings in this study indicate thatboth 𝑅! ⁄𝑅" (SC: －0.43, p < 0.01) and β (SC: 0.55, p < 0.01) are factors that affect IKEF independently of QFMT. The
low contribution of QFMI is due to the muscle quality evaluation with MI that tends not to show up as changes in the degreeof whiteness unless there is more than a certain level of fascia degeneration or adipose tissue, which suggests that thesechanges may be underestimated in certain subjects [10]. In addition, as there is a difference in the percentage of fat
infiltration between the distal part and the proximal part in the lower extremity [10], measurement accuracy can be
improved by evaluating not just a single slice using US but evaluating a wide range. These findings suggest that using theimpedance parameter in a wide range of tissues with DSM-BIA may enable more accurate detection of muscle quality
condition than echo intensity (EI). The numerical values of 𝑅! ⁄𝑅" and β in the evaluation of muscle quality may fluctuate
due to various muscle quality disorders such as an increase in the noncontractile tissue, muscle fiber atrophy, and a decline
in fascia function. Thus, further study is needed, analyzing each element separately. Our results show that 𝑅! ⁄𝑅" and β
can be used to evaluate muscle quality, which is difficult to express with EI, and that both are factors that independently
affect muscle strength.
Evaluation of body composition using DSM-BIA is currently used in various fields such as medical care and athletes [39,40]. Unlike CT and MRI, it does not require a special environment, and it is highly reproducible, making it widely used
for training and evaluation of disease-related skeletal muscle mass loss. Evaluating muscle quality using a combination of
PAcole, 𝑅! ⁄𝑅" , and β, rather than measuring skeletal muscle mass alone, may mean that skeletal muscle function can bepredicted with higher accuracy than before. Prediction of skeletal muscle function using a combination of muscle mass and
impedance parameters could be applied to various fields such as medical care, sports, and community-dwelling elderly
once data have been accumulated considering race, gender, and age.
This study has several limitations. First, the subjects in this study were limited to healthy adult men. Given that gender,
age, and nutritional status have an influence on the impedance parameters, the findings may not be applicable to otherpopulations including women, the elderly, and sick patients. Second, it is necessary to consider that lower extremity
impedance parameters in DSM-BIA may be affected by tissue impedance other than skeletal muscle. Furthermore, it has
been shown that the 95% limits of agreement are larger than that of dual-energy X-ray absorptiometry and dilutionmeasured total body water methods [41]. In cases where it is possible to establish a measurement method that minimizes
the effect of the skin and subcutaneous fat using electrical impedance myography applying BIA, it would be possible toimprove the evaluation accuracy methods using skeletal muscle alone. Finally, this study did not perform physiologicaland anatomical evaluations showing evidence that PAcole, 𝑅! ⁄𝑅" , and β reflect the quality of the skeletal muscle.
Based on the results of this study, further research analyzing 𝑅! ⁄𝑅" and β is required to increase the effectiveness ofimpedance parameters for evaluating muscle quality.

【Conclusion】
This study shows that PAcole, 𝑅! ⁄𝑅" , and β calculated using the Cole–Cole model are factors that independently affectmuscle strength, even when muscle mass is added to the variables. Thus far, this is the first study showing an association
between the lower extremity impedance parameters in DSM-BIA and skeletal muscle function. These factors can bemeasured non-invasively in a short period of time, making them effective as muscle quality indicators in a wide range ofsubjects. 𝑅! ⁄𝑅" and β may present with more characteristic changes than the results of this study in the elderly and inpatients with diseases, although these points need further investigation.
Acknowledgements
The authors also thank all individuals who participated in the study. This study was not funded by any institutions, agencies,
or companies.
Author contributions
Conceptualization: NT, KK, KK, HK. Date curation and Formal Analysis: KK, KT. Investigation and Methodology: NT,
KT, KT. Wrote the paper: NT, KT. Critical revision: NT, KT, KK, KK, HK. All authors read and approved the manuscript.
Compliance with ethical standards
Conflict of interest
The authors have no conflicts of interest to disclose.

【Table】
Table 1 Physical Characteristics and Muscle strength, quantity and quality of the participants

Mean±SD
Physical Characteristics
Age (year)

29.6±5.8

Height (cm)172.4±4.3

Weight (kg)68.8±10.7

BMI (kg/m2)

23.1±3.2

Isometric Knee Extension Force (Nm)

180.8±31.8

Quadriceps Femoris muscle thickness (mm)86.0±9.5

Quadriceps Femoris muscle intensity

86.9±19.3

SD standard deviation, BMI body mass index
Table 2 Impedance parameter of the lower extremitymean ± SD
𝑅# (Ω)

226.9±23.5

𝑋# (Ω)

28.7±3.9

𝑍% (Ω)

274.4±28.4

𝑍$ (Ω)

181.6±18.4

𝑓# (kHz)38.1±8.1

𝑅! ⁄𝑅"

1.98±0.23

β0.71±0.03

PAcole (deg)7.17±0.52

PA50 (deg)

6.88±0.65

SD standard deviation, 𝑅# Resistance of 𝑓 = 𝑓# , 𝑋# Reactance of 𝑓 = 𝑓# , 𝑍% Resistance of 𝑓 = 0 ,𝑍$ Resistance of 𝑓 = ∞ , 𝑓# Central relaxation frequency, 𝑅! / 𝑅" Ratio of intracellular fluid resistance toextracellular fluid resistance, 𝛽 Beta parameter, PAcole Phase angle of Cole-Cole model, PA50 Phase angleof 50 kHzTable 3 Correlation coefficients between muscle strength, muscle strength, muscle thickness, muscle

intensity, impedance parameters and physical characteristics of the lower extremities (n = 38)
IKEF
QFMT

IKEF

QFMT

QFMI

PAcolePA50

𝛽

𝑅! /𝑅"

𝑓#

BMI―

0.578**－0.2290.583**

0.105

0.34*

－0.43**－0.027

0.032―－0.272

0.215

0.282

0.187

－0.101－0.094

0.151

―

－0.05

－0.295

0.122

0.124

－0.056－0.305―－0.0530.008－0.852**

－0.29

0.079

―

－0.0150.003－0.0680.187―

0.554**－0.109－0.165―0.238－0.238―－0.343*

QFMI
PAcolePA50
𝛽
𝑅! /𝑅"𝑓#
BMI―

IKEF Isometric knee extension force, QFMT Muscle thickness of quadriceps femoris, QFMI Muscle intensityof quadriceps femoris, PAcole Phase angle of Cole-Cole model, PA50 Phase angle of 50 kHz, 𝛽 Beta
parameter, 𝑅! /𝑅" Ratio of intracellular fluid resistance to extracellular fluid resistance, 𝑓# Central relaxation
frequency, BMI body mass index
Statistical significance: * p ˂ 0.05, ** p ˂ 0.01

Table 4 Predictors of muscle strength in lower extremity (n = 38)

Dependent

Independent

variables

variables

CoefficientStandardized

p value

95% CI

VIF

coefficient

Model 1
𝑅+ = 0.29

QFMT

19.13

0.57

<0.01

[9.26, 28.9]

1.09

QFMI

－0.16

－0.09

0.53

[－0.66, 0.34]

1.18

BMI

－0.89

－0.09

0.55

[－3.92, 2.13]

1.11

QFMT

15.7

0.46

<0.01

[0.22, 0.71]

1.14

QFMI

－0.18

－0.1

0.39

[－0.35, 0.14]

1.18

PAcole

29.8

0.49

<0.01

[0.25, 0.72]

1.05

BMI

－1.16

－0.11

0.34

[－0.35, 0.13]

1.11

QFMT

11.6

0.35

<0.01

[0.13, 0.56]

1.23

QFMI

－0.15

－0.09

0.37

[－0.3, 0.12]

1.21

𝑅! /𝑅"

－79.2

－0.43

<0.01

[－0.64, -0.22]

1.14

β

17.6

0.55

<0.01

[0.34, 0.76]

1.13

BMI

－0.95

－0.09

0.36

[－0.29, 0.11]

1.11

Model 2
𝑅+ = 0.53

Model 3𝑅+ = 0.66

R2 represents the adjusted coefficient of determination
CI confidence intervals, VIF Variance Inflation Factor, QFMT Muscle thickness of quadriceps femoris, QFMI
Muscle intensity of quadriceps femoris, PAcole phase angle of Cole-Cole model, 𝛽 Beta parameter, 𝑅! /𝑅"
Ratio of intracellular fluid resistance to extracellular fluid resistance, BMI body mass index

【Artwork】

Fig.
1 The arc of the Cole-Cole modelFig. 2 Equivalent circuit model of biological tissue

Fig. 3 Measurement of muscle thickness (MT) and muscle intensity (MI)Abbreviations𝛽Beta parameter (cell homogeneity)

BIA

Bioelectrical Impedance Analysis

BMI

Body mass index

CT

Computed tomography

DSM-BIA

Direct Segmental Multi-Frequency Bioelectrical Impedance Analysis𝑓#Central relaxation frequencyMI

Muscle intensity

MRI

Magnetic resonance imaging

MT

Muscle thickness

PA

Phase angle

PAcolePhase angle of Cole-Cole model

PA50

Phase angle of 50 kHz

QFMTMuscle thickness of Quadriceps femoris

QFMI

Muscle intensity of Quadriceps femoris

𝑅! ⁄𝑅"

Ratio of intracellular fluid resistance to extracellular fluid resistanceUS

Ultrasonography

VIF

Variance inflation factor

Declarations
Ethics approval and consent to participate: The study protocol was approved by the ethics review board of Kawasaki

Medical School (Approval No.: 2846). Written informed consent was obtained from all participants.
Consent for publication: Written informed consent for publication was obtained from all participants.
Availability of data and materials: The datasets used and/or analyzed during the current study are available from thecorresponding author on reasonable request.
Competing interests: Not applicable
Funding: Not applicable
Authors' contributions: Study concept and design: NT, KK, KK, HK. Performed the experiments and acquisition of data:
KK, KT. Analysis and interpretation of the data: NT, KT, KT. Drafted the paper: NT, KT. Critical revision: NT, KT, KK,
KK, HK. All authors read and approved the manuscript.
Acknowledgements: Not applicableReferences
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