Advanced liver fibrosis is associated with decreased gait speed in older patients with chronic liver disease

This study investigated whether the progression of liver fibrosis affects the prevalence of sarcopenia and incidence of decreased gait speed in older patients with chronic liver disease (CLD). Patients with CLD aged ≥ 60 years were classified into low, intermediate, and high fibrosis 4 (FIB-4) index groups according to the degree of liver fibrosis. The prevalence of sarcopenia and incidence of decreased gait speed (< 1.0 m/s) were compared among the three groups. Logistic regression analysis was performed to investigate factors affecting the risk of decreased gait speed. No significant difference was observed in the prevalence of sarcopenia among the three groups, but the incidence of decreased gait speed significantly differed (p = 0.029). When analyzed individually, a significant difference in decreased gait speed incidence was observed between the high and low FIB-4 index groups (p = 0.014). In logistic regression analysis, the progression of liver fibrosis (odds ratio: 1.32, 95% confidence interval: 1.13-1.55) and lower extremity muscle strength (LEMS) (odds ratio: 0.92, 95% confidence interval: 0.88-0.97) were significantly associated with decreased gait speed. As liver fibrosis progresses in older patients with CLD, it becomes important to focus on not only skeletal muscle mass and grip strength, but also gait speed and LEMS.

Intraocular Pressure Fluctuation during Aerobic Exercise at Different Exercise Intensities

Few studies have examined the effects of different aerobic-exercise intensities on intraocular-pressure (IOP) changes. This may be important for eye diseases that are impacted by IOP or its fluctuation, including glaucoma, and diabetes that is complicated by diabetic retinopathy. We investigated the effects of low-, moderate-, and high-intensity exercise on IOP in healthy subjects. A submaximal cardiopulmonary exercise test was performed in 18 healthy male subjects, and the maximal oxygen uptake was calculated. The subjects then exercised for 20 min at 30%, 50%, and 70% ·VO₂ of maximal oxygen uptake, and their IOP was measured at rest and every 5 min during exercise. Oxygen uptake was monitored using an expiratory gas analyzer during exercise to maintain accurate exercise intensity and adjust exercise load. Oxygen uptake during exercise was significantly higher at all intensities from 5 to 20 min than at rest. IOP was significantly lower at 70% exercise intensity from 5 to 20 min than at rest. A negative correlation existed between IOP and ·VO₂. IOP remained unchanged during low- and moderate-intensity exercise but significantly declined during high-intensity exercise compared with that at rest. Although various factors, such as β-blockers, are involved in IOP decline at rest, a different mechanism is involved in IOP decline during exercise.

Case-control study of the correlation between the five times sit to stand and 6-min walk distance in patients with pancreatic cancer

PURPOSE

Cases of pancreatic cancer are increasing, and the risk of developing this disease reportedly increases with age. In recent years, there has been an increasing number of reports on physical function in patients with pancreatic cancer. Methods such as the 6-min walk distance (6 MWD) should be established to evaluate physical function, as a decline in exercise capacity is an important index in these patients. Recently, the 6 MWD has also been used to evaluate physical function in patients with pancreatic cancer. In healthy older adults, a decrease in 6 MWD is reportedly associated with intrinsic capacity and health status. Such factors make assessing 6 MWD important. However, the measurement of 6 MWD requires a sizable measurement environment. The five times sit to stand (FTSTS) test is a simple method that can be performed using a chair. FTSTS is hypothesized to be a useful assessment scale in patients with pancreatic cancer because it is easy to estimate the decline in physical function in clinical practice if the decline in 6 MWD can be estimated by evaluating FTSTS. The study's purpose was to clarify this hypothesis and ascertain the cutoff required to determine the decrease in 6 MWD in clinical practice.

METHODS

Sixty consecutive patients with preoperative pancreatic cancer who were assessed for physical function were studied. 6 MWD (< 400 m) was the objective variable, and binary logistic regression analysis was performed, with age, BMI, sex, FTSTS, and HGS as explanatory variables. Receiver-operating characteristic (ROC) curve analysis was performed for the explanatory variables, which were found to be significant based on logistic regression analysis. The area under the curve (AUC) was also calculated. Sensitivity, specificity, negative predictive value (NPV), and positive predictive value (PPV) were evaluated. This study was approved by Hiroshima University Hospital's ethics committee (approval number: E808-1).

RESULTS

Fifty-seven of the 60 patients were included in the analysis. Logistic regression analysis showed that FTSTS was a significant explanatory variable; ROC curve analysis showed an AUC of 0.872 and a cutoff value of 8.98 s. The sensitivity, specificity, PPV, and NPV were 82.4%, 80.0%, 63.6%, and 91.4%, respectively.

CONCLUSIONS

A decrease in 6 MWD in preoperative pancreatic cancer patients can be identified by performing FTSTS.

Twenty-four-hour ambulatory oximetry monitoring in a patient with idiopathic pulmonary fibrosis for assisting in the discharge instruction on activities of daily living: a case report

[Purpose] Patients with idiopathic pulmonary fibrosis (IPF) often develop remarkable exercise-induced hypoxemia and are hospitalized for management. The pre-discharge management of activities of daily living (ADL) should determine the amount of exercise-induced hypoxemia permitted during daily activities and inform concrete instructions based on these results. This clinical report aimed to promote 24-hour ambulatory oximetry monitoring in a patient with IPF to guide the pre-discharge management of ADL. [Participant and Methods] Our patient was a 67-year-old male with IPF. He was hospitalized and scheduled to be discharged after introduction of home oxygen therapy. Prior to discharge, we conducted a 24-hour ambulatory oximetry monitoring in the patient’s home. We administered instructions on ADL based on these results. Furthermore, 1 day after discharge, we monitored his oxygen saturation level during ADL in his home. [Results] During the pre-discharge monitoring, the patient experienced hypoxemia during bathing, with a minimum oxygen saturation (SpO₂) level of 87% and SpO₂ level of <90% for 14.3% of the time. The patient was instructed on bathing by a physical therapist before discharge; this led to decreased desaturation, as the patient’s SpO₂ was <90% for 7.7% of the time. [Conclusion] Twenty-four-hour ambulatory oximetry monitoring is effective in guiding the pre-discharge management of ADL in the home with home oxygen therapy for patients with IPF.

Changes in motor function and quality of life after surgery in patients with pancreatic cancer

OBJECTIVE

To determine the changes in motor function and health-related quality of life after pancreatectomy and identify factors influencing postoperative physical functioning in health-related quality of life.

METHODS

This single-centre, prospective, observational study measured 6-min walking distance, grip strength, knee extension strength and health-related quality of life variables in patients with pancreatic cancer, before and after surgery. Paired t- and Wilcoxon signed-rank tests were used to compare pre- and postoperative motor function and health-related quality-of-life variables. Factors associated with postoperative physical functioning scores of health-related quality of life were assessed using multiple regression analysis.

RESULTS

Fifty-nine individuals were enrolled. Motor function values decreased significantly postoperatively, including 6-min walking distance (mean ± standard deviation: 402.5 ± 95.4 vs. 497.7 ± 80.4 m, p < 0.001), knee extensor strength (0.42 ± 0.10 vs. 0.47 ± 0.10 kgf/kg, p < 0.001) and grip strength (22.0 ± 8.9 vs. 24.5 ± 9.2 kg, p = 0.001). Multiple regression analysis showed significant association between 6-min walking distance change and postoperative physical functioning scores of health-related quality of life (p = 0.036).

CONCLUSION

The results suggest that motor function decreases postoperatively, and a decrease in 6-min walking distance after surgery is associated with postoperative physical functioning in patients with pancreatic cancer.

Effect of the use of passive body trunk exercise equipment on oxygen consumption and self-efficacy for carrying out exercise in patients with type 2 diabetes

AIMS/INTRODUCTION

Considering the difficulty in inculcating the habit of exercise among patients with type 2 diabetes, devising an easily maintained means of exercise is preferable. Passive body trunk exercise equipment (PBTE) developed for home use might solve several problems related to exercise therapy, both for patients and clinical staff involved in diabetes treatment; however, its efficacy as a therapeutic exercise device for patients with diabetes has not been ascertained. The purpose of this study was to measure the exercise intensity and self-efficacy of PBTE, and to determine whether PBTE is a useful tool for exercise therapy.

MATERIALS AND METHODS

The participants were 20 patients with type 2 diabetes, and the duration of exercise using the PBTE was set to 10 min. Oxygen consumption during exercise was measured, and self-efficacy for continuing to exercise using the PBTE and for walking was evaluated after completion of the study.

RESULTS

The average exercise intensity using the PBTE was 1.7 metabolic equivalents, whereas the maximum exercise intensity was an average of 2.0 metabolic equivalents; the reported self-efficacy for continuing to exercise using the PBTE was significantly higher than for walking.

CONCLUSIONS

Exercise intensity using the PBTE is similar to low-intensity walking, and thus, it might be a useful therapeutic exercise device for patients with type 2 diabetes. Furthermore, it could be an effective exercise device for diabetes patients who do not have regular exercise habits, especially with reduced motor function or lower leg muscle strength.

Loss of lower extremity muscle strength based on diabetic polyneuropathy in older patients with type 2 diabetes: Multicenter Survey of the Isometric Lower Extremity Strength in Type 2 Diabetes: Phase 2 study

Aims/Introduction

Diabetic polyneuropathy (DPN) is a factor that reduces lower extremity muscle strength (LEMS) in older type 2 diabetes patients. This relationship remains unclear in longitudinal studies. Therefore, we longitudinally investigated the apparent effects of DPN on changes in LEMS. Furthermore, we cross‐sectionally examined relationships among DPN, LEMS, mobility and health‐related quality of life.

Materials and Methods

Bodyweight‐normalized (relative) knee extension force (KEF) was examined in 51 DPN and 54 non‐DPN patients (68.9 ± 5.6 and 70.2 ± 5.9 years, respectively) at baseline and follow up at 3.6 ± 0.6 years. At follow up, mobility was measured using a 25‐question geriatric locomotive function scale. Health‐related quality of life was assessed using the five‐dimensions of EuroQol for quality‐adjusted life years calculation.

Results

Relative KEF in the DPN group was significantly lower at follow up (1.22 ± 0.47 Nm/kg) than at baseline (1.31 ± 0.47 Nm/kg; P < 0.05). DPN significantly affected changes in relative KEF. Mobility decreased by 41 and 65% in the non‐DPN and DPN groups, respectively. Quality‐adjusted life years were significantly lower in the DPN group (0.856 ± 0.131) than in the non‐DPN group (0.920 ± 0.105; P < 0.01). Relative KEF was a significant independent variable that explained quality‐adjusted life years.

Conclusions

DPN clearly reduced LEMS in older type 2 diabetes patients within 4 years. Furthermore, DPN resulted in a loss of LEMS and decrease in mobility. Therefore, DPN development should be monitored closely, with glycemic control and LEMS kept at a high level to maintain health‐related quality of life in older patients with type 2 diabetes.

Precise absolute Seebeck coefficient measurement and uncertainty analysis using high-Tc superconductors as a reference

The intrinsic properties of superconductors enable the direct determination of the absolute Seebeck coefficient at low temperature due to the disappearance of the Seebeck effect to obey the Meissner effect. We report a precision absolute Seebeck coefficient measurement for the fine Pt sample determined using the high-Tc YBa₂Cu₃O_7-x (YBCO) superconductor as a reference and an analysis of the measurement uncertainty. To make a precision measurement and aid in the verification of the uncertainty components, we developed a cryostat system that enables temperature control in a stable manner. The expected performance of the reference superconductor yielded a zero value well below Tc, which was validated by a superconductor-superconductor thermocouple experiment. Uncertainty analysis shows that the main limiting factor for this measurement is the accuracy of the temperature difference measurement using the resistance temperature sensors, along with its analog noise. We obtained values of S = 5.6 ± 0.2 µV/K with a relative expanded uncertainty of 3% at 80 K and precisely compared the Pt value with that determined by the high-Tc Bi₂Sr₂Ca₂Cu₃O_8+δ (Bi-2223) superconductor, which has a higher Tc. We found that there was no difference between the Seebeck coefficient values obtained from the YBCO and Bi-2223 references up to its Tc within the expanded measurement uncertainties of 0.3 µV/K (2σ). These results provide accurate validation that the high-Tc superconductor is a useful reference up to the liquid nitrogen temperature.

Whole-body vibration enhances effectiveness of "locomotion training" evaluated in healthy young adult women

[Purpose] Locomotion training is recommended as a countermeasure against locomotive syndrome. Recently, whole-body vibration has been clinically applied in rehabilitation medicine. Therefore, we aimed to investigate the preliminary effectiveness of whole-body vibration on locomotion training. [Participants and Methods] Overall, 28 healthy adult females were randomly assigned to either a locomotion training group using a whole-body vibration device (whole-body vibration group, n=14) or training on the flat floor (non-whole-body vibration group: n=14). Participants conducted two sets of locomotion training twice a day and three times a week for 12 weeks. [Results] A significant difference was observed in the group factor for all outcome measures and in the before and after the training factor for Timed Up and Go test. After the training, knee muscle strength, dynamic balance, and mobility function in the whole-body vibration group were significantly improved compared with the non-whole-body vibration group. In the whole-body vibration group, the Timed Up and Go time after the training was significantly shorter compared with that before training. [Conclusion] The results suggest that locomotion training with whole-body vibration can improve the physical functions in healthy adult females and locomotion training using whole-body vibration might enhance the effectiveness of locomotion training.

Aging, physical activity, and diabetic complications related to loss of muscle strength in patients with type 2 diabetes

Patients with type 2 diabetes may have motor dysfunctions such as loss of muscle strength. Compared with non-diabetic subjects, patients with diabetes show decreased lower extremity muscle strength. The aim of this review was to describe the influence of factors associated with loss of muscle strength in patients with type 2 diabetes. Aging promotes an accelerated loss of muscle strength in patients with diabetes. Physical inactivity may cause a decline in muscle strength in patients with diabetes. Gradual loss of muscle strength is related to the presence and severity of diabetic neuropathy. Diabetic nephropathy may be a factor contributing to loss of muscle strength, because decrease in skeletal muscle mass is a hallmark of end-stage renal disease. Resistance exercise is an essential component of diabetes treatment regimens and also plays a role in the prevention and management of sarcopenia. Intensive physical therapy intervention should be provided to patients with diabetes having decreased muscle strength.

A Mobile Cough Strength Evaluation Device Using Cough Sounds

Although cough peak flow (CPF) is an important measurement for evaluating the risk of cough dysfunction, some patients cannot use conventional measurement instruments, such as spirometers, because of the configurational burden of the instruments. Therefore, we previously developed a cough strength estimation method using cough sounds based on a simple acoustic and aerodynamic model. However, the previous model did not consider age or have a user interface for practical application. This study clarifies the cough strength prediction accuracy using an improved model in young and elderly participants. Additionally, a user interface for mobile devices was developed to record cough sounds and estimate cough strength using the proposed method. We then performed experiments on 33 young participants (21.3 ± 0.4 years) and 25 elderly participants (80.4 ± 6.1 years) to test the effect of age on the CPF estimation accuracy. The percentage error between the measured and estimated CPFs was approximately 6.19%. In addition, among the elderly participants, the current model improved the estimation accuracy of the previous model by a percentage error of approximately 6.5% (p < 0.001). Furthermore, Bland-Altman analysis demonstrated no systematic error between the measured and estimated CPFs. These results suggest that the developed device can be applied for daily CPF measurements in clinical practice.

Exercise loading for cardiopulmonary assessment and evaluation of endurance in amputee football players

[Purpose] It is difficult for amputees to perform conventional cardiopulmonary exercise testing. Values were determined for two-legged, one-legged, and two-armed exercise testing in healthy adult males (Study 1), for comparison with preliminary measurements of endurance in amputee football players (Study 2). [Participants and Methods] In Study 1, cardiopulmonary exercise testing was performed in healthy adult males. Correlations between oxygen uptake in two-legged and one-legged/two-armed exercise were calculated and a comparison was made between one-legged exercise and two-armed exercise for each measured value. In Study 2, cardiopulmonary exercise testing was performed on male amputee football players using a two-arm-driven ergometer. The measured values obtained for healthy adult males and amputee football players were compared. [Results] In Study 1, peak work rate and peak heart rate values of healthy participants were significantly higher in two-armed exercise than in one-legged exercise. The correlation between peak oxygen uptake values for two-legged and one-legged exercise was decreased. In Study 2, peak work rate of two-armed exercise was significantly higher in amputee football players than in healthy participants. [Conclusion] Study 1 suggested that musculoskeletal factors might have greater significance for one-legged exercise than for two-armed exercise. Study 2 suggested that para-sports, including amputee football, may contribute to physical strength and health maintenance in lower leg amputees.

Estimation of Cough Peak Flow Using Cough Sounds

Cough peak flow (CPF) is a measurement for evaluating the risk of cough dysfunction and can be measured using various devices, such as spirometers. However, complex device setup and the face mask required to be firmly attached to the mouth impose burdens on both patients and their caregivers. Therefore, this study develops a novel cough strength evaluation method using cough sounds. This paper presents an exponential model to estimate CPF from the cough peak sound pressure level (CPSL). We investigated the relationship between cough sounds and cough flows and the effects of a measurement condition of cough sound, microphone type and participant's height and gender on CPF estimation accuracy. The results confirmed that the proposed model estimated CPF with a high accuracy. The absolute error between CPFs and estimated CPFs were significantly lower when the microphone distance from the participant's mouth was within 30 cm than when the distance exceeded 30 cm. Analysis of the model parameters showed that the estimation accuracy was not affected by participant's height or gender. These results indicate that the proposed model has the potential to improve the feasibility of measuring and assessing CPF.

Assessment of lower extremity muscle mass, muscle strength, and exercise therapy in elderly patients with diabetes mellitus

The increase in the proportion of elderly people in the population is one of the most remarkable sociodemographic phenomena of the twenty-first century. The number of patients with diabetes is also increasing worldwide with this demographic change. Given these facts, consideration of the problems the general elderly population is facing in the management of diabetes is essential. In this review article, we focus on sarcopenia, which is the decrease in lower extremity muscle mass and muscle strength accompanying aging, describe the relationship between sarcopenia and diabetes, and highlight the specific factors through which diabetes contributes to loss of muscle strength. The quantitative methods for evaluating lower extremity muscle strength will also be described. These methods hold the key to assessing the effectiveness of exercise therapy and optimizing the assessment of the degree of autonomy in the activities of daily living. Exercise is one of the basic treatments for type 2 diabetes and may also prevent and improve sarcopenia. This review discusses the aspects common to the two health conditions and elucidates the effectiveness and necessity of exercise as a preventive measure against diabetes among the elderly.

Anti-gravity treadmill can promote aerobic exercise for lower limb osteoarthritis patients

[Purpose] The anti-gravity treadmill (Alter-G^®) allows the load on the lower limbs to be adjusted, which is considered useful for patients with lower limb osteoarthritis. The aim of the present study was to examine the effects of aerobic exercise using an anti-gravity treadmill in patients with lower limb osteoarthritis by using a cardiopulmonary exercise load monitoring system. [Subjects and Methods] The subjects were 20 patients with lower limb osteoarthritis. These subjects walked naturally for 8 minutes and then walked on the Alter-G for 8 minutes at their fastest speed at a load where lower limb pain was alleviated. [Results] Subjective and objective exercise intensity did not differ significantly between level ground walking and Alter-G walking neither before nor after walking. Pain before walking did not differ significantly between level ground walking and Alter-G walking, but pain after walking was significantly greater with level ground walking than with Alter-G walking. [Conclusion] Exercise therapy using an anti-gravity treadmill was useful for patients with lower limb osteoarthritis in terms of cardiopulmonary function, which suggested that this could become a new form of exercise therapy.

The effect of anti-gravity treadmill training for prosthetic rehabilitation of a case with below-knee amputation

BACKGROUND

The aim of this case study was to verify the efficacy and safety of anti-gravity treadmill training for prosthetic rehabilitation following below-knee amputation.

CASE DESCRIPTION AND METHODS

The patient underwent left below-knee amputation as a result of diabetic foot gangrene. Since his physical strength and vitality had declined during the perioperative period, anti-gravity treadmill training was introduced for his outpatient prosthetic rehabilitation.

FINDINGS AND OUTCOMES

Stable prosthetic gait exercise could be carried out under guidance on the anti-gravity treadmill, quickly resulting in improved gait. Furthermore, the patient's self-efficacy and exercise tolerance were elevated after the period of anti-gravity treadmill training. At the final evaluation following 6 weeks of rehabilitation with the anti-gravity treadmill, he had acquired prosthetic gait with the assistance of a T-cane.

CONCLUSION

The anti-gravity treadmill was found to be a useful instrument for prosthetic rehabilitation following below-knee amputation.

CLINICAL RELEVANCE

Anti-gravity treadmill training has the potential to support the prosthetic rehabilitation of below-knee amputees, especially for patients whose physical strength and vitality are decreased.

Development of pressure cell for specific heat measurement at low temperature and high Magnetic field

We report the performance of Ag-Pd-Cu alloy as the material of a pressure cell to carry out specific heat measurements at low temperatures and high magnetic fields. The Ag-Pd-Cu alloy is advantageous to reduce the background due to the nuclear specific heat in the pressure cell growing at low temperatures and high magnetic fields. We prepared 70-20-10 alloy composed of 70 mass % of Ag, 20 mass % of Pd, and 10 mass % of Cu. The maximum hardness over 100 HRB (Rockwell-B scale) is achieved by the heat treatment. The magnetization and susceptibility results show that the alloy includes a small amount of magnetic ions, whose concentration is smaller than that in the Be-Cu alloy. We confirm that the specific heat of a piston cylinder cell made of the 70-20-10 alloy increases smoothly from 0.2 to 9 K and the nuclear specific heat decreases drastically in magnetic field compared to that expected in the Be-Cu alloy. The pressure value in the cell at low temperature increases almost linearly up to P=0.4 GPa, which is nearly the limit of the inner piston made of the 70-20-10 alloy, with increasing of the load applied at room temperature.

Coexisting ferromagnetic order and disorder in a uniform system of hydroxyhalide Co2(OH)3Cl

Order or disorder often exists in a uniform spin system consisting of one kind of magnetic ion. Nevertheless, they rarely coexist in normal conditions. Our thermodynamic and microscopic magnetic studies of Co2(OH)3Cl, a distorted tetrahedral lattice compound with uniform Co2+ spin, demonstrate that the spins located on one corner of the tetrahedron are periodically ordered, but those on the other three are disordered below a ferromagnetic transition at TC=10.5 K. The partial order resembles that of the field-induced "kagomé-ice" state in spin ice pyrochlore compounds. Evidence suggests that a distortion in the tetrahedron is responsible for this partial ferromagnetic order in a zero field.

Possible observation of the quadrupolar Kondo effect in dilute quadrupolar system Pr(x)La(1-x)Pb3 for x <or= 0.05

We have studied non-Fermi-liquid (NFL) behavior in Pr(x)La(1-x)Pb3 with Gamma3 quadrupolar moments in the crystalline-electric-field ground state. The specific heat C/T shows NFL behavior in the very dilute region for x <or= 0.05, which is scaled by a characteristic temperature T* in each Pr concentration. The application of a magnetic field leads to a sharp increase of C/T , demonstrating the shift of the entropy existing in the lower temperature region at H=0 T . Moreover, Fermi-liquid behavior emerges at higher fields, in contrast with NFL behavior at lower fields. The observed features indicate that NFL behavior is caused by the quadrupolar Kondo effect.

Coexistence of long-range order and spin fluctuation in geometrically frustrated clinoatacamite Cu2Cl(OH)3

Muon spin rotation experiments are carried out on clinoatacamite, Cu2Cl(OH)3, which is a new geometrically frustrated system featuring a three-dimensional network of corner-sharing tetrahedral 3d Cu2+ spins. A long-range antiferromagnetic order occurs below 18.1 K with a surprisingly small entropy release of about 0.05Rln2/Cu. Below 6.5 K, the static long-range order transforms abruptly into a metastable state with nearly complete depolarization of muon spins which suggests strong fluctuation. The system then enters a state in which partial long-range order and spin fluctuation coexist down to the lowest experimentally attainable temperature of 20 mK. This work presents a novel system for studying geometric frustration.

Specific heat study of an S = 1/2 alternating Heisenberg chain system: F5PNN in a magnetic field

We have measured the specific heat of an S = 1/2 antiferromagnetic alternating Heisenberg chain pentafulorophenyl nitronyl nitroxide in magnetic fields up to H > H(C2). This compound has a field-induced magnetic ordered (FIMO) phase between H(C1) and H(C2). Characteristic behaviors are observed depending on the magnetic field up to above H(C2) outside of the H-T boundary for the FIMO. The temperature and field dependence of the specific heat are qualitatively in good agreement with the theoretical calculation on an S = 1/2 two-leg ladder [Wang et al., Phys. Rev. Lett. 84, 5399 (2000)]]. This agreement suggests that the observed behaviors are related with the low-energy excitation in the Tomonaga-Luttinger liquid.