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. 2025 Apr 3;45(7):423–430. doi: 10.1097/BPO.0000000000002964

Outcome and Femoral Head Deformity Following Hip Guided Growth in Children With Cerebral Palsy at Skeletal Maturity

Kevin Chun-Kai Chiu *,, Chia-Che Lee ‡,§, Kuan-Wen Wu ‡,§, Kuang-Yu Cheng *,, Ken N Kuo ‡,, Ting-Ming Wang ‡,§,
PMCID: PMC12233175  PMID: 40178803

Abstract

Background:

Guided growth of the proximal femur, a minimally invasive procedure for coxa valga, shows promising short-term outcomes in cerebral palsy (CP). However, as it alters physis growth, existing studies lack comprehensive long-term analysis until skeletal maturity.

Methods:

This retrospective study included children with spastic CP who underwent proximal femur-guided growth surgery between 2012 and 2017, followed until physeal closure. Radiographic measurements included head-shaft angle (HSA), Hilgenreiner-epiphyseal angle (HEA), acetabular index (AI), Reimer’s migration percentage (MP), and α angle. Outcomes were compared between ambulatory/nonambulatory (GMFCS I-III/IV, V) and with/without soft tissue release. Factors associated with earlier physeal closure and femoral head deformity were analyzed.

Results:

Among 29 patients (53 hips) with guided growth studied at skeletal maturity, 4 patients (6 hips, 11.3%) experienced procedure failure and required varus osteotomy due to severe deformities. It was more common in GMFCS IV-V patients (27.3%, 3/11) than in GMFCS I-III (5.6%, 1/18). In the remaining 25 patients (47 hips), 7 hips (14.9%) received concomitant pelvic osteotomy with AI and MP evaluated separately. All radiographic parameters improved significantly (P<0.001). Epiphysis grew off the screw in 25 hips (53.2%), requiring reinsertion in 19 (40.4%), with a higher rate in nonambulatory children (73.3% vs. 25%, P=0.002). Changes of the parameters showed no difference between ambulatory/nonambulatory (GMFCS I-III/IV, V) and with/without soft tissue release. The cumulative duration of screw crossing the physis was a key factor for earlier closure (P<0.001) and correlated with increased α angle (P=0.039).

Conclusion:

Guided growth successfully improved outcomes in both ambulatory and nonambulatory groups, although less effective in severe dysplasia. This minimally invasive procedure has some concerns, including the epiphysis growing off the screw, reinsertion need, earlier physeal closure, and femoral head deformity.

Level of Evidence:

Level IV, therapeutic study.

Key Words: cerebral palsy, coxa valga, hip-guided growth, long-term, physeal plate, femoral head deformity


Cerebral palsy (CP) is a neurological disorder affecting motor function and musculoskeletal system. Children with CP commonly experience coxa valga and excessive femoral neck anteversion.1 If untreated, hip subluxation and dislocation can significantly impact children’s daily function.2 Traditional surgical managements for unstable hips include soft tissue releases, femoral and pelvic osteotomies.3 However, there are increased risks of operative complications in children with complex medical conditions. In addition, hip immobilization and rehabilitation following osteotomy can significantly impact a child’s school life.4

Hence, a less invasive procedure, guided growth, has been developed to gradually correct angular and rotational limb deformities in children with open physis.57 This procedure modifies physeal growth by placing a transphyseal screw at the inferomedial part of the proximal femoral physis, improving coxa valga and acetabular dysplasia. However, most published studies had relatively short follow-up periods, ranging from 3.8 to 5 years without reaching skeletal maturity.57 In addition, the fusion of growth plate, which significantly influences the outcomes of guided growth, has not been considered in previous studies.

This is the first study to comprehensively analyze the long-term effect of proximal femur-guided growth in children with CP. We investigated long-term radiographic outcomes and complications at physeal closure; compared outcomes between ambulatory (GMFCS I-III)/nonambulatory (GMFCS IV-V) groups, and with/without soft tissue release; identified timing and factors associated with early physeal closure and femoral head deformity.

METHODS

Setting and Participants

This single-institutional retrospective study of consecutive proximal femur-guided growth surgery in children with CP between July 2012 and October 2017. The indications for guided growth were progressive hip displacement (MP >30%) and HSA >155 degrees, with at least 2 years of potential growth remaining. When the patient experienced epiphysis growing off the screw, defined as having no thread remaining within the proximal femoral epiphysis, the indication for revision surgery remains the same as that for primary surgery. This research had Institutional Review Board approval.

Throughout the study period, 47 cerebral palsy children who underwent the index procedure were identified (Fig. 1). After excluding 9 patients with primary femoral osteotomy and 9 without radiographic follow-up until physeal closure, 29 patients remained: 4 (6 hips) in the GG+VO group (guided growth with varus osteotomy) and 25 (47 hips) in the GG group (guided growth alone) (Table 1). Of the GG group, 7 hips underwent concomitant pelvic osteotomy, resulting in 13 hips (24.5%, 13/53) requiring either pelvic or femoral osteotomy. Three case examples are presented in Supplemental Figures 1–3 (Supplemental Digital Content 1, http://links.lww.com/BPO/A867, Supplemental Digital Content 2, http://links.lww.com/BPO/A868, Supplemental Digital Content 3, http://links.lww.com/BPO/A869): one case involved screw reinsertion, another demonstrated severe deformity, and the third with concomitant pelvic osteotomy.

FIGURE 1.

FIGURE 1

The patient cohort flow chart. From July 2012 and October 2017, a total of 47 patients with cerebral palsy underwent hip surgery. After excluding 9 patients who received primary femoral osteotomy and 9 without radiographic follow-up until physeal closure, 29 patients remained. These included 25 patients (47 hips) in the GG group (guided growth alone) and 4 patients (6 hips) in the GG+VO group (guided growth with subsequent varus osteotomy).

TABLE 1.

Demographic Data

Number
Characteristic GG GG + VO Total
Patients (boys/girls) 25 (15/10) 4 (3/1) 29 (18/11)
No. hips 47 6 53
Operation age (y) 8.63 (6-12) 7.15 (4.5-11.08) 8.46 (4.5-12)
Follow-up (y) 8.65 (5.9-11.6) 9.51 (7.5-10.6) 8.77 (5.9-11.6)
Mean physeal closure age (y)
 Boys 14.30 (12-15)
 Girls 12.75 (11-14)
Pelvic osteotomy (hips)
 With pelvic osteotomy 7 5 12
 Without pelvic osteotomy 40 1 41
Soft tissue release (hips)
 With soft tissue release 24 6 30
 Without soft tissue release 23 0 23
GMFCS (patients)
 I 3 0 3
 II 5 0 5
 III 9 1 10
 IV 6 1 7
 V 2 2 4
Screw type (hips)
 Fully threaded 20 3 23
 Partially threaded 27 3 30
Outcomes (hips), n (%)
 Epiphysis growing off the screw 25 (53.2)
 Reoperation 19 (40.4)
Complications
 Perioperative 0
 Postoperative 2*

Continuous variables are reported as mean and range.

*

Of 105 surgeries, including initial insertion, revision, and implant removal, one surgical site infection occurred following implant removal (Clavien-Dindo classification grade 2) and a case of leg length discrepancy in a unilateral case.

GG indicates guided growth alone; GG+VO, guided growth with subsequent varus osteotomy; GMFCS, gross motor function classification system.

Operative Technique

The procedure was performed in a supine position under general anesthesia. Soft tissue release of adductor longus and gracilis muscle was performed for abduction <30 degrees, with additional iliopsoas release for nonambulatory children with hip flexion contracture >20 degrees. Distal hamstring release was done for popliteal angle ≥45 degrees after adductor tenotomies. Then, a guidewire was introduced through a lateral incision aimed at the medial one-third of the capital femoral epiphysis in the coronal plane and centered along the femoral neck in the sagittal plane. We used 2 types of screw, a 6.0-mm fully threaded, titanium alloy, tapered self-compressing screw (Acutrak; Acumed, USA) or a 7.0-mm stainless steel, partially-threaded, standard cannulated screw (Synthes Inc., Switzerland) with a minimum of 3 threads through the physis. In cases with concurrent acetabular dysplasia (acetabular index >22 degrees), a concomitant pelvic osteotomy, either Pemberton or Dega osteotomy, depending on anatomic pathology, was carried out.

Radiographic Outcome Measures

Every patient had serial anteroposterior (AP) and frog-leg lateral (FL) radiographs of the pelvis before and every 6 months after surgery until the physeal plate closure. For AP radiographs, ambulatory patients are positioned standing, while nonambulatory patients are supine with both patellae pointing straight forward in full extension. For FL views, the patient is supine with knees flexed 30 to 40 degrees and hips externally rotated by 45 degrees. The author (K.C.-K.C.), who was not directly involved in patients' primary care, conducted measurements of radiographic parameters, including preoperative, 1-year postoperative, and closure of physics. The radiographic parameters included head-shaft angle (HSA), Hilgenreiner-epiphyseal angle (HEA), acetabular index (AI), Reimer’s migration percentage (MP), and α angle of the femoral head.

Instead of selecting the neck-shaft angle (NSA), which was notably sensitive to malposition, especially with higher GMFCS levels, we opted to measure HSA. Both the HEA and HSA were found to be minimally affected by rotation.8,9 HSA was the angle between a line perpendicular to the capital epiphyseal plate and the femoral shaft axis.9 HEA was the angle between Hilgenreiner’s line and the proximal femoral physis. AI was the angle between Hilgenreiner’s line and a line drawn along the acetabular surface. MP was the percentage of the femoral capital epiphysis situated lateral to the acetabular edge (Perkin’s line). The α angle was measured on the frog-leg lateral view.10,11 This angle is between the axis of the femoral neck and a line drawn to the point where the femoral head begins to lose its sphericity (Fig. 2).

FIGURE 2.

FIGURE 2

Measurement of radiographic parameters. The head-shaft angle (HSA), head-epiphysis angle (HEA), acetabular index (AI), and ɑ angle were shown in the diagram. Migration percentage (MP) is calculated as the percentage of the length of segment a divided by segment b. AI indicates acetabular index; HEA, Hilgenreiner-epiphyseal angle; HSA, head shaft angle.

Intra-rater reliability was assessed by one author (K.C.-K.C.), who measured the parameters at 1-week intervals using AGFA-Orthopaedic-Tools Version 2.10 (Agfa HealthCare NV, Mortsel, Belgium). For inter-rater reliability, a different author (C.K.-Y.) independently measured the same parameters using identical methods.

Closure of Growth Plate on Radiography

We assessed physeal closure according to Cameriere et al’s12 3-stage classifications: stage 1, physis not fused (Fig. 3A); stage 2, fully ossified with visible physeal scar (Fig. 3B); stage 3, fully ossified and physeal scar not visible (Fig. 3C). In our study, stage 2 indicates physeal closure. Previous studies suggested that epiphyseal closure typically occurs simultaneously bilaterally.13,14

FIGURE 3.

FIGURE 3

The degree of ossification. Stage 1, the physis is not fused (A); stage 2, the physis is fully ossified with the physeal scar visible (B); stage 3, the physis is fully ossified and the physeal scar is not visible (C).

Statistical Analysis

GG and GG+VO groups were compared using an independent t test. Within the GG group, a paired t test assessed changes in radiographic measurements from preoperative to physeal closure. Simple regression analyzed the relationship between the cumulative screw-crossing time before physeal closure and radiographic changes. χ2 test compared patients who experienced growing off with different screw types. Ambulatory/nonambulatory groups and with/without soft tissue release patients were compared with independent t tests and χ2 tests.

Independent-sample t test was used for different age group comparisons. We also performed simply to identify the factors associated with the closure age. Pearson correlation coefficient (r) assessed factors affecting the change of ɑ angle. All analyses were performed using SPSS version 27.0 (SPSS Inc, Chicago, IL), with P-value <0.05 considered significant.

The intra-rater intraclass correlation coefficients for HSA, HEA, AI, MP, and ɑ angle were 0.918, 0.931, 0.880, 0.859 and 0.935, respectively. Inter-rater reliability for the same parameters was 0.876, 0.892, 0.843, 0.832, and 0.860, respectively.

RESULTS

Comparison of GG and GG+VO Groups

A comparative analysis (Table 2) showed significantly worse preoperative parameters in the GG+VO group, including higher HSA (172.1 vs. 163.8 degrees, P=0.008), MP (63.0% vs. 35.3%, P=0.008), and AI (31.3 vs. 21.1 degrees, P<0.001), along with a lower HEA (5.7 vs. 13.6 degrees, P=0.003).

TABLE 2.

Comparison of the Preoperative Radiographic Measurements Between 2 Groups

GG GG + VO Difference P *
Hips 47 6
Preoperative HSA (deg.) 163.8 (7.1) 172.1 (5.7) 8.3 [2.2 to 14.3] 0.008
Preoperative HEA (deg.) 13.6 (5.9) 5.7 (6.9) −8.0 [−13.2 to −2.7] 0.003
Preoperative MP (%) 35.3 (5.4) 63.0 (16.2) 27.6 [10.6 to 44.6] 0.008
Preoperative AI (deg.) 21.1 (4.3) 31.3 (3.0) 10.19 [6.5 to 13.8] < 0.001

Continuous variables are presented as mean (SD), and differences are presented as mean [95% confidence interval].

*

Independent sample t test.

Significant effect.

AI indicates acetabular index; GG, guided growth alone; GG+VO, guided growth with subsequent varus osteotomy; HEA, Hilgenreiner-epiphyseal angle; HSA, head shaft angle; MP, migration percentage.

GG Group

Of the 25 hips with capital femoral epiphysis grew off the screw, 19 required revision surgery. For perioperative and postoperative complications, out of 105 surgeries, including initial insertions, revisions, and implant removals, only one surgical site infection was observed following implant removal (Clavien-Dindo classification grade 2). We also observed a case of leg length discrepancy in one unilateral case (Fig. 4) because of the early closure of the growth plate in the operated limb. Furthermore, we observed varying degrees of coxa breva (Fig. 5) and/or femoral head deformity (Fig. 6).

FIGURE 4.

FIGURE 4

Pelvis radiograph and scanogram of one case. This patient underwent unilateral proximal femoral guided growth at ten years old, leading to earlier closure of the growth plate in the operated limb compared with the contralateral one.

FIGURE 5.

FIGURE 5

Pelvis radiograph of one case with coxa breva. This patient underwent proximal femoral guided growth at 9 years old. The coxa breva of both femoral was developed, and the age of physeal closure was 13 years old.

FIGURE 6.

FIGURE 6

Frog-leg lateral view of the left hip demonstrating the femoral head deformity. This is a patient who underwent proximal femoral guided growth at 10 years old, and we noted femoral head deformity upon the physeal closure with ɑ angle at 82 degrees.

All radiographic parameters significantly improved (Table 3). HSA and HEA showed the most substantial changes, from 163.8 to 143.5 degrees, and from 13.7 to 31.9 degrees, respectively. To isolate the true impact of the procedure and mitigate the potential influence of pelvic osteotomy on AI and MP, 7 hips receiving pelvic osteotomy were analyzed separately. Both groups showed significant improvement. However, femoral head deformity was indicated by an increase of α angle from 58.6 degrees preoperatively to 70.8 degrees at the final follow-up (P<0.001). There was no significant difference in the outcome between tapered and standard screws (Supplemental Table 1, Supplemental Digital Content 4, http://links.lww.com/BPO/A870).

TABLE 3.

Radiographic Measurements at the Preoperative and Physeal Closure

Mean SD
Variable N (hips) Preoperative Physeal closure Difference P *
HSA (deg.) 47 163.8 (7.1) 143.5 (5.8) −20.3 [−22.6 to −18.0] < 0.001
HEA (deg.) 47 13.7 (5.9) 31.9 (7.6) 18.2 [15.8 to 20.7] < 0.001
MP - without PO (%) 40 33.9 (4.4) 22.9 (7.1) −11.0 [−13.3 to −8.6] < 0.001
MP - with PO (%) 7 43.5 (3.4) 18.2 (8.4) −25.3 [−33.5 to −17.1] < 0.001
AI - without PO (deg.) 40 20.5 (4.4) 15.1 (3.5) −5.4 [−6.4 to −4.4] < 0.001
AI - with PO (deg.) 7 24.3 (1.3) 18.8 (2.8) −5.5 [−7.4 to −3.6] < 0.001
ɑ angle (deg.) 47 58.6 (14.1) 70.8 (15.8) 12.2 [7.3 to 17.1] < 0.001
*

Paired sample t test.

Differences are presented as mean [95% CI].

AI indicates acetabular index; HEA, Hilgenreiner-epiphyseal angle; HSA, head shaft angle; MP, migration percentage; PO, pelvic osteotomy.

In consideration of epiphysis growing off the screw and replacing it with a new screw, we calculated the cumulative duration while the screw remained crossing the growth plate. A simple regression analysis showed a significant positive correlation between this duration and radiographic changes (HSA: P <0.001; HEA: P <0.001; AI: P=0.005; MP: P=0.043) (Supplemental Table 2, Supplemental Digital Content 5, http://links.lww.com/BPO/A871). No significant difference in the percentage of “growing off” was found between tapered and standard screws, with 55% and 51.9%, respectively (P=0.831, Supplemental Table 3, Supplemental Digital Content 6, http://links.lww.com/BPO/A872).

Nonambulatory patients had a younger operation age (7.64 vs. 9.09 y) and a higher rate of screw reinsertion (73.3% vs. 25%) (Supplemental Table 4, Supplemental Digital Content 7, http://links.lww.com/BPO/A873). However, there were no significant distinctions between ambulatory/nonambulatory groups for the radiologic parameters at preoperation, physeal closure, and the differences between these 2 points. For the difference between with/without soft tissue release, only GMFCS level, and preoperative AI were significant (Supplemental Table 5, Supplemental Digital Content 8, http://links.lww.com/BPO/A874).

For physeal closure age, we divided the children into 2 categories based on their operation age. Children aged 6 to 8 had a mean closure age of 13.17 (SD=1.30), while those aged 9 to 12 had a mean of 14.30 (SD=0.92). Simple regression analysis showed both operation age and cumulative physeal screw-crossing time influenced physeal closure age (P<0.001).

As the α angle significantly increased during the follow-up, we evaluated possible factors associated with the change of α angle from preoperation to physeal closure (Supplemental Table 6, Supplemental Digital Content 9, http://links.lww.com/BPO/A875). The cumulative screw-crossing time (P=0.039), and changes in HSA (P=0.045) yielded significant results. For preoperative radiographic measurement, HEA, AI, and α angle also correlated with this change.

DISCUSSION

Children with CP often experience proximal femoral deformity.1 While traditional femoral and pelvic osteotomy can help maintain hip position, they carry significant complications.15 Alternatively, a minimally invasive proximal femoral guided growth procedure was introduced with promising short-term results.57 However, a long-term evaluation is essential to observe the efficacy of gradual correction exemplified by this study with an average follow-up of 8.77 years (ranging from 5.9 to 11.6).

Two factors necessitated the need for subsequent varus osteotomy in the GG+VO group in our series: advanced age at the time of surgery, which had less growth potential to effectively correct the deformity; and more severe preoperative deformities. As a result, guided growth is more suitable for patients with MP between 30% and 50%. In addition, 27.3% (3/11) of patients functioning at GMFCS IV-V required VO, compared with 5.6% (1/18) in GMFCS I-III.

For the GG group, since guided growth primarily influenced proximal femoral physis, HSA and HEA showed more substantial improvements compared with AI and MP in our study. In contrast to varus derotation osteotomy, guided growth resulted in a remarkable 20.31-degree change in HSA while being significantly less invasive.16 Patients who underwent guided growth alone showed a mean improvement of 5.42 degrees for AI and 10.97% for MP, suggesting it also influences acetabular development and femoral head coverage.6,7 Based on the natural history of children with CP reported, MP generally worsens over time.17 In contrast, our data show that guided growth not only halts this deterioration but actually improves MP. Notably, only 2 patients (2 hips) experienced elevated MP, with a mean increase of 5.32%, while the remaining patients showed improvement.

In a systematic review, epiphysis growing off the screw is common after hip-guided growth.18 We observed this in 25 hips, occurring at an average of 25.5 months postsurgery, and 19 received revision surgery. Timely replacement of a screw is crucial for patients experiencing under-correction since the positive correlation between improvement in radiographic parameters and the duration of the screw crossing the growth plate. In addition, no significant difference in the rate of epiphysis growing off was noted between tapered fully-threaded and standard partial-threaded screws. To minimize the risk of growing off, we ensure the screw is centered in the sagittal plane with at least 3 threads crossing the physis, and avoid performing the procedure in children under 6, as femoral epiphysis is too small for adequate purchase.

The radiographic parameters showed no significant difference between the ambulatory and nonambulatory groups, but the latter required an extended duration to reach comparable results. Consequently, a higher proportion of children in this group underwent additional surgery for growing off to increase the cumulative duration of screw crossing physis. This is attributed to the heightened progression of hip displacement and coxa valga over time in patients with lower functional levels.19,20 As a result, nonambulatory patients typically operated at a younger age. Soft tissue release was more common in children with higher GMFCS levels, which might be due to their higher levels of muscle spasticity and contractures, that necessitate soft tissue release. While preoperative measurements theoretically differ between patients with/without soft tissue release, as the procedure is typically performed on patients with higher levels of deformity. However, only AI showed a significant difference in our results, likely due to the small sample size. Changes in radiographic measurements from pre-operation to physeal closure showed no significant differences, possibly because soft tissue release was selectively performed based on the indication provided. Premature physeal closure is a known consequence of injuries to growth plates.21,22 Given that guided growth involves inserting a screw through the physis, earlier physeal closure is a concern. Normally, physeal closure occurs around 16 years in males and 14 years in females.23 However, in our cohort, closure occurred earlier, at 14.3 years for males and 12.75 years for females. Although the earlier physeal closure might cease the progression of hip instability, it might lead to leg length discrepancy in unilaterally operated individuals.24

We evaluated the plain films and found variable degrees of femoral head deformity. In the natural course of CP, femoral head deformity generally affects the cartilage-covering area of femoral head with medial flattening.25,26 However, our study cohort noted deformities primarily located at the growth plate, resulting in deformity at the physeal junction of femoral head (Fig. 6). The α angle increased significantly from preoperation to physeal closure, and longer cumulative physeal screw-crossing duration was associated with greater femoral head deformity, indicating screw placement duration may contribute to the deformity. Despite the deformity, there were no clinical symptoms. However, monitoring for potential symptoms during follow-up is important.

In our experience, guided growth surgery is better indicated for patients with MP between 30% and 50% and HSA over 155 with at least 2 years of potential growth remaining. In cases of severe deformity, guided growth may be considered earlier age. However, we recommend avoiding the procedure in patients under six years of age because of insufficient purchase of epiphysis. Guided growth surgery is a promising minimally invasive procedure that could be used for other conditions in the future. However, clinicians should be aware of potential complications, such as earlier growth plate closure and femoral head deformity. Will it develop femoral acetabular impingement syndrome? It remains to be proved that further investigation is required.

Limitations

This study has limitations. First, being a retrospective study without a control group, there is a risk of overestimating the treatment benefits. However, ethical considerations of a comparison group in children with CP make this challenging. Second, the sample size was relatively small, potentially limiting the statistical validity and generalizability of the findings. Lastly, selection bias may be present, as children with more severe hip dysplasia might have opted for varus osteotomy as the primary surgical approach.

CONCLUSION

This is the first comprehensive, long-term investigation of proximal femoral guided growth until physeal closure. While guided growth may have a limited role in patients with extremely severe hip dysplasia, it has proven effective in both ambulatory (GMFCS I-III) and nonambulatory (GMFCS IV, V) groups. Furthermore, while undertaking this minimally invasive procedure, it is imperative to acknowledge specific concerns, including epiphysis growing off of the screw, the need for reoperation, the femoral head deformity, and the risk of earlier physeal closure.

Supplementary Material

SUPPLEMENTARY MATERIAL
bpo-45-0423-s001.pdf (521.7KB, pdf)
bpo-45-0423-s002.pdf (391.3KB, pdf)
bpo-45-0423-s003.pdf (382.4KB, pdf)
bpo-45-0423-s004.docx (50.5KB, docx)
bpo-45-0423-s005.docx (50.1KB, docx)
bpo-45-0423-s006.docx (49.7KB, docx)
bpo-45-0423-s007.docx (55.4KB, docx)
bpo-45-0423-s008.docx (55.3KB, docx)
bpo-45-0423-s009.docx (69.4KB, docx)

Footnotes

This study was performed at the Department of Orthopaedic Surgery, National Taiwan University Hospital, Taipei, Taiwan.

The study was not funded by any external or internal party.

The authors declare no conflicts of interest.

Supplemental Digital Content is available for this article. Direct URL citations are provided in the HTML and PDF versions of this article on the journal's website, www.pedorthopaedics.com.

Contributor Information

Kevin Chun-Kai Chiu, Email: kevinckchiu222@gmail.com.

Chia-Che Lee, Email: jackamades@gmail.com.

Kuan-Wen Wu, Email: wukuanwen@gmail.com.

Kuang-Yu Cheng, Email: cky310699@gmail.com.

Ken N. Kuo, Email: kennank@aol.com.

Ting-Ming Wang, Email: dtorth76@yahoo.com.tw.

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