Abstract
Background:
Age is a preoperative prognostic factor for radial closing wedge osteotomy (RCWO) in Kienbock disease. Specifically, for cases classified as Lichtman stage III, clear criteria for selecting RCWO have not been established. We believe that age can provide vital information for determining the appropriate surgical procedure for Kienbock disease. The aim of this study was to investigate RCWO outcomes for Lichtman stage III by examining different age groups from clinical and radiological perspectives.
Methods:
Sixteen patients with Lichtman stage III Kienbock disease underwent RCWO. The median age was 59 years, and the median follow-up period was 2.9 years. We determined the age cutoffs for clinical and radiological outcomes using a receiver operating characteristic curve. Subsequently, we conducted intergroup comparisons of postoperative outcomes between the younger and older age groups.
Results:
Age cutoffs were established at 52.5 and 30 years for clinical and radiological outcomes, respectively. In the comparative analysis, the younger age group (≤52 years; n = 7) demonstrated significantly superior clinical results, including improved range of motion and pain relief, higher postoperative Mayo Wrist Score, and lower Disability of the Arm, Shoulder, and Hand scores. From a radiological perspective, the younger age group (≤30 years; n = 3) experienced segmented lunate bone fragments healing, indicating an improved disease stage compared with the older group.
Conclusion:
Based on previous literature and our research findings, it is reasonable to conclude that RCWO results in improved clinical outcomes for patients up to their mid-50s and enhanced radiological outcomes for those up to approximately at the age of 30 years. Further studies on these age cutoffs will contribute to refining the surgical selection criteria for RCWO.
Level of Evidence:
Prognostic Level IV. See Instructions for Authors for a complete description of levels of evidence.
Introduction
Radial closing wedge osteotomy (RCWO) is a surgical technique reported by Nakamura et al. in 19911. Age is a known prognostic factor for RCWO, with younger patients generally showing better postoperative results2. Although the influence of age on postoperative outcomes in Kienbock disease has been acknowledged, a clear age cutoff value is controversial1-4. Studies vary in their age cutoffs for evaluating RCWO outcomes, highlighting the need for re-evaluation, including a literature review.
In Kienbock disease, particularly Lichtman stage III, the appropriate surgical procedure is controversial5. Although some treatment algorithms are based on morphology and hemodynamics6-8, other factors, including age, are crucial in clinical decision making6. Establishing an age threshold that predicts better outcomes could guide treatment selection.
The aim of this study was to determine the age cutoff values for clinical and RCWO radiological outcomes in Kienbock disease, specifically Lichtman stage III. Our goal was to enhance the reliability of previous findings and clarify age-related postoperative outcomes.
Materials and Methods
This literature review adheres to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The PRISMA checklist was used to ensure a transparent and comprehensive reporting of the review process.
Sixteen patients (16 wrists) who underwent RCWO for Kienbock disease (Lichtman stage III) participated in this study. Stage III was defined as the presence of lunate bone collapse, stage IIIa was defined as having a radioscaphoid angle of more than 60°, and stage IIIb as no more than 60°. In this study, we did not use the modified Lichtman classification, including stage IIIc9.
The surgeries were conducted at 2 hospitals between January 2012 and December 2022. The study sample comprised 10 men and 6 women. The median patient age was 59 years (range, 14-77 years). In this study, the minimum follow-up period was at least 1 year. The median postoperative follow-up period was 2.9 years (range, 1.6-6 years).
Surgical Technique
The anterior approach between the flexor carpi radialis and brachioradialis was used. The procedure involved closed-wedge radial osteotomy, which was performed using a microbone saw. The osteotomy angle was set at 15°10. In the presence of negative ulnar variance (UV), concomitant ulnar shortening osteotomy was performed to achieve zero variance. A small AO Locking Compression Plate (LCP) T-plate or 2.4 mm Variable Angle LCP Volar Extra-Articular Distal Radius from DePuy-Synthes was used as the compression plate (Fig. 1).
Fig. 1.
A 47-year-old man underwent a radial closing wedge osteotomy for Lichtman stage IIIA Kienbock disease. Figs. 1-A and 1-B Preoperative plain radiographs. The white lines indicate the osteotomy line, set at an angle of 15°. Figs. 1-C and 1-D Postoperative plain radiographs at 3-year follow-up. The lunate collapse progressed, and further volar flexion of the scaphoid was observed, indicating progression to Lichtman stage IIIB.
Age Cutoff Values for Postoperative RCWO Outcomes
Age cutoff values for postoperative RCWO outcomes were determined separately for clinical and radiological results (see “Statistical Analysis”).
Clinical Outcome Used to Determine Age Cutoff Value
The Mayo Wrist Score (MWS) rates a patient's wrist function according to pain, range of motion (ROM), grip strength, daily activities, and return to work. Ratings are categorized as follows: excellent (90-100), good (80-89), fair (65-79), and poor (less than 65). MWS at the final postoperative follow-up was used as the basis for categorizing patients into 2 groups: “poor to fair” and “good to excellent”11.
Radiological Outcome Used to Determine Age Cutoff Value
Lunate bone healing was considered important in the radiological outcome. Patients were divided into 2 groups according to the presence or absence of healing of the segmental fragment of the lunate on radiographs at the last postoperative follow-up.
Intergroup Comparison of Postoperative Outcomes
Based on the age cutoff values for clinical (MWS) and radiological (the presence or absence of healing of the segmental fragment of the lunate) outcomes, patients were categorized into 4 groups. Patients below or equal to the MWS age cutoff were the Clinical Younger group, whereas those above it were the Clinical Older group. Patients below or equal to the lunate healing age cutoff are the Radiographic Younger group, whereas those above it are the Radiographic Older group.
Clinical Outcomes
We compared clinical outcomes, including improvements in preoperative and postoperative ROM and pain relief rates, postoperative grip strength compared with healthy individuals, MWS11, and Disability of the Arm, Shoulder, and Hand (DASH) scores12, between the Clinical Younger and Older groups.
Radiological Outcomes
Plain radiographs were used to analyze the healing status of the lunate fragment and changes in the Lichtman classification, carpal height ratio (CHR), and Stahl index (SI) before and after surgery. We compared radiological outcomes between Radiographic Younger and Older groups.
Measurement of Baseline Characteristics and Outcomes
For baseline characteristics, we recorded the following: age and sex at the time of surgery, postoperative follow-up duration, amount of radial shortening before and after surgery, and the preoperative Lichtman classification. In addition, we noted whether radial shortening osteotomy (RSO) was added to the procedure. The amount of radial shortening before and after surgery was measured using plain radiographs taken before and after the procedure. Preoperative Lichtman classification was assessed using plain radiographs taken before surgery13.
In addition, to measure clinical outcomes, ROM was recorded as the value of the combined flexion and extension of the wrist joint. Pain was recorded using the Pain Scale (PS), which is the value of postoperative pain when the intensity of preoperative pain in the affected area is 10. Grip strength was measured using a dynamometer and recorded as the affected-to-healthy ratio. MWS11 was calculated based on medical record information. DASH12 was obtained from a self-administered form.
Finally, plain radiography was performed to measure radiological outcomes. The healing status of the lunate was assessed, and cases were categorized into 3 groups: “no healing,” “partial healing,” and “complete healing.” Afterward, when determining the cutoff value for the receiver operating characteristic (ROC) curve, partial healing was included in the healing category to create a binary variable. To assess changes in the Lichtman classification stage, changes in the stage between the preoperative and final assessments were categorized as “improved,” “unchanged,” or “worsened.” The percentage changes in CHR and SI between the preoperative and final assessments were recorded.
Statistical Analysis
We performed a Mann-Whitney U test and χ2 test or the Fisher exact test to compare continuous and categorical variables, respectively. ROC curves were created based on age at the time of surgery, and age cutoff values were calculated using the Youden Index14. We categorized postoperative clinical (MWS) and radiological (presence or absence of lunate healing) outcomes into binary variables (see “Age cutoff values for postoperative RCWO outcomes”) and created ROC curves for each binary variable based on age. The point on the ROC curve with the maximal Youden Index value was determined as the optimal cutoff point. Statistical analyses were performed using IBM SPSS Statistics, version 28.0.0.0 (IBM Japan), and statistical significance was defined as p < 0.05.
Ethical Considerations
The study was conducted in accordance with the Declaration of Helsinki and approved by the institutional data protection officer and ethics committee (approval No. REC2023-179). The ethics committee waived the requirement for informed consent owing to the retrospective nature of the study.
Results
Patient Demographics
The demographic and clinical characteristics of the patients are presented in Table I.
TABLE I.
Patient Demographics*
| Patient Demographics (n = 16) | Range | |
|---|---|---|
| Age (y) | 59.0 [37.75-67.5] | 14-77 |
| Sex | ||
| Female | 8 | |
| Male | 8 | |
| Follow-up period (yr) | 2.9 [2.0-4.6] | 1.6-6.0 |
| Radial shortening osteotomy | ||
| Added | 8 | |
| Not added | 8 | |
| Amount of radial shortening (mm) | 1.0 [0.0-3.0] | 0.0-5.0 |
| Lichtman classification | ||
| Stage IIIA | 5 | |
| Stage IIIB | 11 |
Presented statistics: median [25th percentile, 75th percentile]; number.
Age Cutoff Values
Age Cutoff Values for Clinical Outcomes
An ROC curve was constructed, and the age cutoff value was determined to be 52.5 years (Fig. 2). Therefore, when comparing clinical outcomes, patients aged 52 years and younger were defined as the Clinical Younger group, whereas those aged 53 years and older were categorized as the Clinical Older group. Age and sex were the only significant patient characteristics between groups (Table II).
Fig. 2.

Receiver operating characteristic (ROC) curve for Mayo Wrist Score (MWS) and age. The ROC curve was constructed with MWS as a binary variable and age as the continuous variable. MWS was divided into good (good to excellent) and poor (fair to poor). The age threshold based on the Youden Index was 52.5 years. The area under the ROC curve was 0.859 (p < 0.05), and the discrimination performance was good.
TABLE II.
Patient Characteristics
| Age Cutoff of 52 yrs | p value§ | Age Cutoff of 30 yrs | p value§ | |||
|---|---|---|---|---|---|---|
| Clinical Younger Group*‡ | Clinical Older Group*‡ | Radiographic Younger Group†‡ | Radiographic Older Group†‡ | |||
| n = 7 | n = 9 | n = 3 | n = 13 | |||
| Age (yr) | 37.5 [26.5-43.3] | 67 [62.5-73.0] | <0.001 | 16.0 [15.0-23.0] | 65 [47.0-69.0] | 0.004 |
| Sex, female | 1 | 7 | 0.04 | 1 | 7 | 1.00 |
| F/U# period (y) | 2.8 [1.9-5.0] | 3.0 [2.0-5.0] | 0.61 | 4.5 [3.5-5.3] | 2.8 [2.0-4.0] | 0.30 |
| Radial shortening osteotomy, added | 4 | 4 | 1.00 | 2 | 6 | 1.00 |
| Amount of radial shortening (mm) | 2.0 [0.0-3.5] | 0.0 [0.0-3.0] | 0.76 | 2.0 [1.0-3.5] | 0.0 [0.0-3.0] | 0.52 |
| Lichtman classification, stage IIIA | 3 | 2 | 0.60 | 1 | 4 | 1.00 |
Clinical Younger group, ≤52 years and Clinical Older group, ≥53 years.
Radiographic Younger group, ≤30 years and Radiographic Older group, ≥31 years.
Presented statistics: median [25th percentile, 75th percentile]; number.
Conducted statistical tests: Mann-Whitney U test.
χ2 test. F/U = follow up.
Age Cutoff Value for Radiological Outcomes
An ROC curve was constructed, and the age cutoff value was determined to be 30 years (Fig. 3). Therefore, when comparing radiological outcomes, the Radiological Younger group was defined as 30 years and younger and the Radiological Older group as older than 31 years. Regarding patient characteristics, age was the only significantly different factor (Table II).
Fig. 3.

Receiver operating characteristic (ROC) curve for healing of the segmented bone fragments of the lunate and age. The ROC curve was constructed using the binary variable of lunate bone fragment healing and the continuous variable of age. The age threshold based on the Youden Index was 30 years. The area under the ROC curve was 1.000 (p < 0.05), and the discriminative power was excellent.
Intergroup Comparisons
Intergroup Comparison of Postoperative Clinical Outcomes
Regarding clinical outcomes, the Clinical Younger group (age ≤52 years) exhibited significantly better results than the Clinical Older group (age ≥53 years) in the following aspects: median postoperative final ROM improvement rate (45.5% vs. 2.5%), postoperative final PS improvement rate (100% vs. 75%), postoperative final MWS (85.0 vs. 75.0), and postoperative final DASH score (4.2 vs. 22.1) (all p < 0.05; Table III). No significant difference was observed between the 2 groups in terms of the grip strength ratio between the affected-to-healthy areas.
TABLE III.
Intergroup Comparison of Clinical Outcomes After Radial Wedge Osteotomy
| Clinical Younger Group*† | Clinical Older Group*† | p value‡ | |
|---|---|---|---|
| n = 7 | n = 9 | ||
| ROM improvement (%) | 45.5 [25.0 to 59.1] | 2.5 [−28.1 to 16.3] | 0.004 |
| Affected/healthy grip strength ratio (%) | 79.1 [70.2 to 97.2] | 75.4 [59.8 to 91.9] | 0.351 |
| PS improvement (%) | 100 [100 to 100] | 75.0 [42.5 to 87.5] | 0.014 |
| MWS4 | 85.0 [85.0 to 100] | 75.0 [60.0 to 77.5] | 0.016 |
| DASH | 4.2 [0.0 to 8.3] | 22.1 [15.6 to 36.3] | 0.009 |
Clinical Younger group, ≤52 years and Clinical Older group, ≥53 years.
Presented statistics: median [25th percentile, 75th percentile].
Conducted statistical tests: Mann-Whitney U test. DASH = Disability of the Arm, Shoulder, and Hand, MWS = Mayo Wrist Score, PS = pain scale, and ROM = range of motion.
Intergroup Comparison of Postoperative Radiological Outcomes
Postoperative healing of the lunate fragments and changes in the Lichtman classification were significantly different between the Radiographic Younger and Older groups (Table IV). Postoperatively, the lunate of patients aged 14 and 16 years achieved complete healing, whereas the lunate of patients aged 30 years achieved partial healing (see Appendix eFigs. 1–3). Their Lichtman classification stage also improved. However, none of the patients aged older than 31 years showed lunate fragments healing, and the Lichtman classification stage remained unchanged or worsened. In addition, the changes in CHR and SI were not significantly different.
TABLE IV.
Intergroup Comparison of Radiological Outcomes After Radial Wedge Osteotomy
| Radiological Younger Group*† | Radiological Older Group*† | ||
|---|---|---|---|
| n = 3 | n = 13 | p value‡ | |
| Healing of bone fragments of the lunate | |||
| Complete healing | 2 | 0 | <0.001 |
| Partial healing | 1 | 0 | |
| No healing | 0 | 13 | |
| Change of Lichtman classification | Improved–3 | Improved–0 | <0.001 |
| Unchanged–0 | Unchanged–9 | ||
| Worsened–0 | Worsened–4 | ||
| CHR change (%) | −1.32 [−1.54 to −0.97] | −3.13 [−4.33 to −2.20] | 0.111 |
| SI change (%) | 4.11 [−13.8 to 5.31] | −15.8 [−32.4 to −6.75] | 0.365 |
Radiological Younger group, ≤30 years and Radiological Older group, ≥31 years.
Presented statistics: median [25th percentile, 75th percentile], number.
Conducted statistical tests: Mann-Whitney U test, Fisher exact test. CHR = carpal height ratio, and SI = Stahl index.
Discussion
In this study, the age cutoff values predicting improved postoperative outcomes varied between clinical and radiological findings. The cutoffs were 30 and 52.5 years for radiological and clinical outcomes, respectively (Table V).
TABLE V.
Summary of Past Literature on Age Thresholds for Postoperative Outcomes in RWO*
| Author (yr) | Participants | Age (yr) | Surgical Procedure (Correction Angle) | F/U Period (mo) | Preoperative Lichtman Stages (Person) | Age Threshold (Outcome) | Threshold Determination |
|---|---|---|---|---|---|---|---|
| Current study | 10 men, 6 women | 51.9 (14-77) | RCWO ± RSO (15°) | 40.8 (18-72) | IIIA: 5 IIIB: 11 |
MWS (52.5), lunate bone union (30) | ROC curve |
| Nakamura3 (1991) | 25 men, 2 women | N/A (14-54) | RCWO ± RSO (5-15°) | 33 (24-60) | N/A | NSS (30) | N/A, but expected based on past study |
| Koh2 (2003) | 18 men, 7 women | 33 (11-55) | 10 wrists; RSO 15 wrists; RCWO | 176 (125-260) | I: 1 II: 4 IIIA: 11 IIIB: 6 |
NSS & MWS (30) | Past study |
| Iwasaki5 (2003) | 25 men 16 women | 36 (13-60) | RCWO ± RSO (15°) | 38 (12-147) | II: 10 IIIA: 5 IIIB: 24 IV: 2 |
Modified NSS (54) | N/A |
| Yamamoto4 (2021) | 9 men, 12 women | 37 (14-74) | 4 wrists; RSO, 17 wrists; RCWO ± RSO (to achieve an angle of radial deviation of 15°) | Younger: 48 (12-120); older: 44.4 (12-132) | II: 4 IIIA: 6 IIIB: 11 |
Clinical and radiological assessment (40) | Determined to equally split the population |
F/U = follow up, MWS = Mayo Wrist Score, N/A = not available, NSS = Nakamura Scoring System, RCWO = radial closing wedge osteotomy, ROC curve = receiver operator characteristic curve, RSO = radial shortening osteotomy, and RWO = radial wedge osteotomy. This table presents a compilation of reports concerning age cutoff values for postoperative outcomes of radial wedge osteotomy, including our current study.
Effect of Radial Closing Wedge Osteotomy
For cases with negative UV, RSO helps correct the UV to neutral6. Radial wedge osteotomy (RWO), including RCWO and radial opening wedge osteotomy, changes the radial inclination. RCWO is the predominant method within RWO15 and is used for neutral or positive UV1,6. RSO and RWO aim to relieve the pressure on the radio-lunate joint. In cases of negative UV, RSO is often combined with RCWO1,3,4, a practice we also use.
The biological mechanism underlying RCWO remains unclear. Decreasing radial inclination increases contact between the radius and lunate, leading to a more uniform force distribution within the wrist joint. This reduction in lunate load is believed to mitigate the risk of damage or pain associated with lunate compression16.
Furthermore, RCWO affects the vascular network of the wrist17 by enhancing blood flow at the osteotomy site, promoting revascularization, improving nutrient delivery to the lunate, and fostering bone healing.
Cutoff Value of Postoperative Radiological Outcome
Our findings showed that a threshold age of 30 years or younger improves postoperative radiological outcomes, consistent with previous literature (Table V). Nakamura et al.1 used the Nakamura Scoring System (NSS) and found excellent outcomes in patients aged younger than 30 years, with radiological improvements being a key factor for years. Two patients aged younger than 30 years achieved excellent results, whereas none aged older than 30 years did, suggesting better radiological findings in patients aged younger than 30 years.
Koh et al.2 reported that in radial osteotomies, including RCWO, the NSS of patients younger than 30 years was superior to that of those older than 31 years. This age cutoff value was based on the report by Nakamura et al.1 Koh et al.2 compared MWS and NSS between age groups and found that in both cases, the results were better for patients younger than 30 years, but the difference in postoperative results for NSS was notably greater than that for MWS. This may be because the NSS includes radiological outcome assessments. Thus, the study suggests that lunate revascularization may be more likely in patients aged younger than 30 years.
Yamamoto et al.3 reported that age was associated with postoperative outcomes in patients who underwent radial osteotomy, most of whom underwent RCWO (RCWO ± RSO, 17 hands; RSO, 4 hands). They found significant improvements in clinical and radiological outcomes, including postoperative CHR, in patients aged younger than 40 years. However, this age cutoff value was determined to divide the study population in half.
Meanwhile, there is some evidence for an age threshold of 30 years18,19. Nakamura et al.18 evaluated NSS and found that of 16 hands from patients aged younger than 30 years, 9 achieved an “excellent” score, whereas none of the 7 hands from patients aged older than 30 years achieved this. Viljakka et al.19 also reported the long-term results of RSO in patients aged 20 to 33 years and noted that the inner lunate structure improved in all cases after RSO. These 2 reports indicate that lunate unloading is more favorable in patients approximately younger than 30 years.
Cutoff Value of Postoperative Clinical Outcomes
Iwasaki et al.4 used a cutoff age of 54 years and reported that postoperative outcomes were better in the younger age group. They used a modified NSS to evaluate postoperative outcomes. The modified NSS excludes imaging findings from the NSS and evaluates only clinical outcomes, such as pain, grip strength, and joint ROM. Although there is no specific description of how the cutoff values were determined, the authors reported superior clinical outcomes in patients younger than 54 years using multivariate analysis. It appears that 54 years could be the cutoff age for expecting improvement in postoperative clinical findings. This cutoff value was close to our cutoff value of 52.5 years.
Surgical Options for Kienbock Disease in Lichtman Stage III
In Lichtman stages IIIA, the carpal bones do not exhibit collapse, so a vascularized bone graft (VBG) can prevent the disease progression by healing the fragmentation and lunate bone compression. However, VBG involves wrist joint invasion, which results in postoperative ROM being inferior to that of osteotomy, including RCWO. Our study reconfirmed that the radiological age cutoff for RCWO is 30 years. This finding suggests that RCWO could be the first-line treatment for young patients, even with stage IIIA.
Recent treatment algorithms6-8 emphasize not only the Lichtman classification but also the lunate vascular evaluation status using the Schmitt classification20 and lunate and wrist condition using the Bain classification8 to determine whether reconstruction or salvage of the lunate and wrist is a reasonable approach. In these algorithms6-8, unloading procedures were limited to cases in which the lunate was intact.
There are reports supporting the RCWO efficacy, even in cases of lunate collapse5,21. Traditionally, RCWO has not been expected to improve radiological outcomes. However, a recent finding suggests that RCWO can enhance blood flow to the lunate and improve collapse22. Osteotomy and core decompression procedures, which also improve blood flow to the lunate, may achieve better radiological outcomes in younger patients.
In Lichtman stage IIIB, where carpal bone collapse is evident, lunate reconstruction alone is insufficient, and procedures such as proximal row carpectomy or partial wrist arthrodesis are recommended23. However, RSO remains a clinically common procedure, even for stage IIIB. Considering our study results, osteotomy may still be a viable option to improve clinical outcomes in stage IIIB. Some researchers have incorporated unloading procedures into the treatment algorithm for stages III and beyond24.
Limitations
When interpreting the results of this study, it is important to note that factors other than age, which may influence the outcomes following RCWO, have not been thoroughly evaluated. First, differences in baseline characteristics could affect the results. In the epidemiology of Kienbock disease, there is a higher incidence between the age of 20 and 40 years, with men being twice as likely to be affected as women25. In addition, in individuals aged 50 years and older, the occurrence of Kienbock disease is associated with osteoporosis, and a higher incidence of Kienbock disease and osteoporosis in women has been reported26. In this study, there were more men in the clinically younger group and more women in the clinically older group, which aligns with the epidemiological features of Kienbock disease.
Furthermore, in this study, RCWO combined with RSO was performed on cases with negative UV. Although this is a generally recommended procedure, the inclusion of the RSO group with the RCWO group makes it more difficult to discern the isolated effect of RCWO alone. Although it may be challenging to address in future studies, this is another factor that should be considered when interpreting the results of this study.
There are differences among reports regarding various patient backgrounds (Table V). Particularly, age shows variability across reports, and in recent studies, such as those by Yamamoto et al.3 and our own, the patient cohorts were relatively older. This may reflect the change of RCWO indication in older patients. However, interestingly, despite the different age distributions among the reports, our cutoff values were similar to those of past studies1,2,4.
The small sample size in this study may increase the likelihood of a Type II error, needing cautious interpretations of the results. In addition, we set the minimum follow-up period to 1 year, which may be short. Therefore, larger cohorts with extended follow-up observations are recommended to more accurately assess final outcomes. It should be considered that the disease may progress further in patients without lunate healing when interpreting our study.
Appendix
Supporting material provided by the author is posted with the online version of this article as a data supplement at jbjs.org (http://links.lww.com/JBJSOA/A688). This content has not been copyedited or verified.
Footnotes
Investigation performed at Fukushima Medical University Hospital, Fukushima, Japan and Iwaki City Medical Center, Iwaki, Japan
This study used existing data and had no funding support.
Disclosure: The Disclosure of Potential Conflicts of Interest forms are provided with the online version of the article (http://links.lww.com/JBJSOA/A687).
Contributor Information
Soichi Ejiri, Email: ejiri@po.mmm.ne.jp.
Nobuyuki Sasaki, Email: nobuyukisasaki14@yahoo.co.jp.
Yuto Akiyama, Email: fmuakiyama@yahoo.co.jp.
Narihiro Toshiki, Email: yamanofudosecond@yahoo.co.jp.
Takuya Kameda, Email: sa57384@cd6.so-net.ne.jp.
Yoshihiro Matsumoto, Email: ymatsu@fmu.ac.jp.
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