Abstract
Introduction
Fifth lumbar (L5) vertebral morphology contributes to spondylolysis. However, there are no comprehensive examinations of the three-dimensional vertebral shape in early-stage cases. This study aimed to investigate the overall L5 vertebral shape in early-stage spondylolysis.
Methods
Homologous models of the L5 vertebra were constructed using computed tomography data from 72 patients with early-stage spondylolysis (SP group) and 95 patients without spondylolysis (CON group). Principal component analysis was performed on the three-dimensional coordinates of all vertices of the generated homologous models. The groups' principal component scores were compared.
Results
Principal component (PC) 3, which represents the morphology of the cross-sectional area of the vertebral body; length of pedicle, neural arch, and isthmus; shape of the vertebral body; and spinous process orientation were significantly higher in the SP group than in the CON group. Additionally, the SP group showed higher values for PC10, which represents the morphology of the anteroposterior length of the vertebral body and transverse process orientation. Compared to the CON group, the SP group's PC3 had a smaller cross-sectional vertebral body area, longer pedicle and neural arch length, larger dorsal wedge shape of the vertebral body, horizontally oriented spinous process, and a shorter isthmus length. PC10, compared with the CON group, indicated the SP group had a shorter anteroposterior length of the superior and inferior surfaces of the vertebral body and a coronally oriented transverse process.
Conclusions
The overall L5 vertebral shape differed between individuals with and without early-stage spondylolysis. Our findings suggest that a wedge-shaped vertebral body and shorter isthmus length may be associated with spondylolysis development. Our study may be valuable in elucidating spondylolysis pathogenesis and may contribute to early detection and prevention.
Keywords: Lumbar, Spondylolysis, Bone morphology, Homologous model, Adolescent
Introduction
Lumbar spondylolysis is a stress fracture of the pars interarticularis that predominantly occurs in adolescents. It appears more often in athletes1), primarily affecting the fifth lumbar (L5) vertebra2,3). Various factors contribute to its development, including repeated trunk rotation or extension4) and bone morphology of the lumbar vertebrae and sacrum5-17).
Many studies on the L5 vertebra in spondylolysis have examined single aspects of vertebral morphology, such as the facet orientation5-7), inter-facet distance8-11), vertebral body shape12), and cross-sectional area (CSA) of the vertebral body13). A recent study reported that individuals with spondylolysis exhibit different overall three-dimensional (3D) shape features of the L5 vertebra compared to those without spondylolysis18). This study demonstrated that the characteristic bone morphology in spondylolysis does not occur in a single part of the vertebra, but throughout the vertebra as a combination of morphological variations at multiple sites. However, because that study used skeletal specimens, the overall shape might have reflected postonset adaptive bone changes. Therefore, investigations focusing on early-stage cases are necessary to exclude the effects of an extended postonset period. By clarifying the overall L5 vertebral shape in early-stage spondylolysis, new insights into spondylolysis pathogenesis may be gained, and early detection and prevention may become feasible.
This study aimed to investigate the overall L5 vertebral shape characteristics in early-stage spondylolysis. We employed a novel method called homologous modeling, which standardizes 3D shapes and enables statistical comparison of the three-dimensional morphology of a given bone among different populations. It has characterized bone morphology by disease, sex, and age19-21).
Materials and Methods
This cross-sectional study used digital imaging and communications in medicine (DICOM) data from initial computed tomography (CT) images obtained for the clinical evaluation of low back pain between April 2012 and December 2020. The Ethics Committee of the study institution approved this study.
Participants
This study included adolescent patients with low back pain who visited a hospital. Seventy-two patients diagnosed with early-stage L5 spondylolysis (mean age=14.7, standard deviation=1.6) and 95 patients without spondylolysis (mean age=14.7, standard deviation=1.5) were enrolled in the spondylolysis (SP) and control (CON) groups, respectively. Early-stage spondylolysis was defined as a fissure in the pars on CT images22). The inclusion criteria were (1) male sex and (2) 12 to 18 years old. The exclusion criteria were (1) progressive or terminal stage spondylolysis, (2) spondylolysis at levels other than L5, (3) bony abnormalities in lumbar or sacral regions (e.g., past fracture, sacralization of L5, lumbarization of S1, or spina bifida occulta), and (4) low back pain caused by organic abnormalities (e.g., spondylolisthesis, lumbar disk herniation, or scoliosis). Based on these criteria, 195 patients were excluded from the study.
Creation of 3D lumbar bone models
Using medical image-processing software (Mimics Innovation Suite 22, Materialise, Leuven, Belgium), we created 3D bone models of the L5 vertebra for participants from the DICOM data. The CT images had a slice thickness of 0.625 mm and a voxel size of 0.35 mm. Each 3D bone model was optimized with data optimization software (Materialise 3-matic Ver14, Materialise, Leuven, Belgium) to have approximately 60,000 vertices and saved in Standard Triangulated Language file formats.
Creation of homologous models
All 3D bone models were homologized using homologous modeling software (mHBM, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan) and homologous modeling support software (HBM-Rugle, Medic Engineering, Kyoto, Japan). The steps for creating homologous models are described below (Fig. 1).
Figure 1.
Procedure for creating homologous models. A: Template and 41 landmarks. B: Setting the coordinate system. Origin: at the most posterior point sequential with the largest anteroposterior diameter on the undersurface of the vertebral body. Z: Line with the largest anteroposterior diameter on the undersurface of the vertebral body. Y: Vertical line perpendicular to the Z-axis passing through the origin. X: Horizontal line perpendicular to the Z- and Y-axis passing through the origin. C: Landmark placement on each three-dimensional bone model. D: Homologous model of image C.
Template creation and landmark placement (Fig. 1A)
The 3D shape data, referred to as the “template,” was created from ten 3D bone models of the CON group using mHBM and HBM-Rugle with a symmetrical and uniform mesh structure with 4,506 vertices. Forty-one landmarks were placed on the template based on inflection points.
Adjustment of the position and orientation and establishment of the coordinate system
Each 3D bone model's position and orientation were adjusted visually to remain constant and establish a coordinate system (Fig. 1B).
Landmark placement (Fig. 1C)
The 41 landmarks, corresponding anatomically to the template landmarks, were placed for each adjusted model.
Homologation of each 3D bone model (Fig. 1D)
The template size, orientation, and position were adjusted automatically to minimize the distance between the template landmarks and those of the adjusted 3D bone model. The template's adjusted shape and landmark data and those of the 3D bone model, were transmitted to mHBM. Subsequently, mHBM deformed the template to conform to the 3D bone model's shape, creating a homologous model. After this procedure, the L5 vertebrae of all individuals were represented as a mesh structure with 4,506 anatomically corresponding vertices.
Average intersurface distance
The average intersurface distance (AISD) assessed the magnitude of error in the created homologous models. The AISD is the mean distance from each vertex of the created homologous model to the nearest point on the original 3D bone model. It quantifies the extent to which model deviates in shape from the original 3D bone model. Smaller AISD values indicate smaller errors.
Principal component analysis
Principal component analysis (PCA) was performed on the 3D coordinates of all vertices of the generated homologous models using homologous model statistical software (HBS, Medic Engineering, Kyoto, Japan) and HMB-Rugle. The coordinate values (X, Y, Z) of the 4,506 vertices of the homologous model represent variables describing the shape of the L5 vertebra. PCA condensed them into new variables representing morphological variations in the overall shape of the L5 vertebra, known as “Principal components (PCs).” The value of each PC, referred to as the principal component score (PCS), was calculated for each participant and used to compare the overall shape between the two groups statistically. The following steps were implemented automatically to avoid generating PCs due to variations in size, position, and orientation of the vertebra and adjust these factors using HBM-Rugle before PCA:
(1) The average shape of all participants was created based on all vertex coordinates.
(2) The sum of the distance of each vertex from the center of gravity was calculated for all homologous models and the average shape, and the ratio of the average shape to each homologous model was computed.
(3) Each homologous model size was normalized by multiplying it with the ratio obtained in Step 2.
(4) Each vertebra's position and orientation were adjusted to minimize the squared distances between each vertex for the average shape and normalized vertebra.
The vertebral shape remained unchanged after the adjustment. Based on the PCS, virtual shapes were created for each PC, ranging from +3 standard deviations (SD) to −3 SD. These virtual shapes were used to interpret the morphological variations in each PC. The PCs with a contribution ratio of 2.0% or greater were examined.
Statistical analyses
The Shapiro-Wilk test assessed normality before comparing age and each PCS between the two groups. If the data were not normally distributed, the Mann-Whitney U test was used. Levene's test was used to test for homogeneity of variance if the data were normally distributed. If the data were assumed to have homoscedasticity, the unpaired t-test was employed; otherwise, Welch's t-test was used with a significance level of 5%. Statistical analyses were performed using statistical software (SPSS Statistics ver. 26, IBM, Armonk, NY, USA).
Results
Age
There was no significant difference in age between the two groups (P=0.36).
Average intersurface distance
The mean AISD for all participants was 0.18±0.02 mm.
PC analysis
Table 1 lists the PCA results. We investigated PC1 to PC11, and the cumulative contribution ratio up was 64.05%. The virtual shapes from +3 SD to −3 SD for PC1, the component representing the greatest individual variation, are depicted in Fig. 2. Based on these virtual shapes (Fig. 2), PC1 was interpreted as a component that exhibited the following characteristics when the PCS was larger (+3 SD direction): a smaller cross-sectional area of the superior (arrow 1) and inferior (arrow 2) surfaces of the vertebral body; coronally oriented transverse process (arrow 3); a longer neural arch length (arrow 4); coronally oriented facet joints (arrow 5); a lower height of the anterior and posterior vertebral body (arrow 6); a shorter, narrower, and downward-oriented spinous process (arrow 7); a larger left-right distance of the superior and inferior articular processes (arrow 8); and a lower vertical distance between the superior and inferior articular processes (arrow 9). The virtual shapes of PCs other than PC1 are shown in Fig. 3, 4 and Figs. S1-S8. The morphological variation each PC represents is summarized in Table 2, 3. The PCS comparison results are in Table 4. Compared with the CON group, the SP group exhibited significantly higher values for PC3 (SP, 6.80±29.86; CON, −7.86±28.63) and PC10 (SP, 4.17±18.05; CON, −1.88±16.78) (Table 4).
Table 1.
Principal Component Analysis Results.
| Principal Component | Contribution Rate (%) | Cumulative Contribution Rate (%) |
|---|---|---|
| 1 | 21.93 | 21.93 |
| 2 | 9.00 | 30.93 |
| 3 | 7.03 | 37.97 |
| 4 | 6.41 | 44.37 |
| 5 | 4.38 | 48.75 |
| 6 | 3.34 | 52.08 |
| 7 | 2.84 | 54.92 |
| 8 | 2.59 | 57.52 |
| 9 | 2.39 | 59.90 |
| 10 | 2.14 | 62.05 |
| 11 | 2.00 | 64.05 |
Figure 2.
Morphological variation of the first principal component in all participants. SD: Standard deviation. Cross-sectional area of the superior (arrow 1) and inferior (arrow 2) vertebral body surfaces; transverse process orientation (arrow 3); neural arch length (arrow 4); facet joints orientation (arrow 5); height of the anterior and posterior vertebral body (arrow 6); spinous process orientation, length, and width (arrow 7); left-right distance of the superior and inferior articular processes (arrow 8); and vertical distance between the superior and inferior articular processes (arrow 9).
Figure 3.
Morphological variation of the third principal component in all participants. SD: Standard deviation. The cross-sectional area of the superior (arrow 1) and inferior (arrow 2) vertebral body surfaces, pedicle (arrow 3) and neural arch (arrow 4) length, dorsal wedge shape of the vertebral body (arrow 5), spinous process orientation (arrow 6), and isthmus length (arrow 7).
Figure 4.
Morphological variation of the tenth principal component in all participants. SD: Standard deviation. Anteroposterior length of the superior (arrow 1) and inferior (arrow 2) surfaces of the vertebral body and transverse process orientation (arrow 3).
Table 2.
Characteristics of Morphological Variation in the Fifth Lumbar Vertebra Represented by Each Principal Component (PC1 to PC6).
| Principal Component | Characteristics observed with larger principal component scores |
|---|---|
| 1 | Smaller cross-sectional area of the superior and inferior vertebral body surfaces |
| Coronally oriented transverse process | |
| Longer neural arch length | |
| Coronally oriented facet joints | |
| Lower height of the anterior and posterior vertebral body | |
| Shorter, narrower, and downward-oriented spinous process | |
| Larger left-right distance of the superior and inferior articular processes | |
| Lower vertical distance between the superior and inferior articular processes | |
| 2 | Larger cross-sectional area of the superior and inferior vertebral body surfaces |
| Shorter transverse process | |
| Lower height of anterior and posterior vertebral body | |
| Shorter and narrower spinous process | |
| 3 | Smaller cross-sectional area of the superior and inferior vertebral body surfaces |
| Longer pedicle and neural arch length | |
| Larger dorsal wedge shape of the vertebral body | |
| Horizontally oriented spinous process | |
| Shorter isthmus length | |
| 4 | Longer width of the superior vertebral body surface |
| Shorter pedicle length | |
| Narrower and horizontally oriented spinous process | |
| 5 | Coronally oriented transverse process |
| Longer width of the inferior vertebral body surface | |
| Higher height of the posterior vertebral body | |
| Smaller dorsal wedge shape of the vertebral body | |
| Shorter isthmus length | |
| 6 | Shorter left-right distance of the inferior articular processes |
| Greater vertical distance between the superior and inferior articular processes |
Table 3.
Characteristics of Morphological Variation in the Fifth Lumbar Vertebra Represented by Each Principal Component (PC7 to PC11).
| Principal Component | Characteristics observed with larger principal component scores |
|---|---|
| 7 | Longer width of the superior vertebral body surface |
| Horizontally oriented spinous process | |
| Upward-oriented transverse processes | |
| 8 | Shorter anteroposterior length of the superior and inferior vertebral body surfaces |
| Longer pedicle length | |
| Higher height of the posterior vertebral body | |
| Smaller dorsal wedge shape of the vertebral body | |
| Shorter spinous process and isthmus length | |
| Horizontally oriented transverse processes | |
| 9 | Shorter width of the superior and inferior vertebral body surfaces |
| Longer anteroposterior length of the superior and inferior vertebral body surfaces | |
| Lower height of the anterior vertebral body | |
| Smaller dorsal wedge shape of the vertebral body | |
| Greater vertical distance between the superior and inferior articular processes | |
| 10 | Shorter anteroposterior length of the superior and inferior vertebral body surfaces |
| Coronally oriented transverse process | |
| 11 | Shorter anteroposterior length of the superior vertebral body surface |
| Longer width of the inferior vertebral body surface | |
| Sagittally oriented facet joints |
Table 4.
Comparison of Principal Component Scores.
| Principal Component | Principal Component Score | p value | |
|---|---|---|---|
| SP (n=72) | CON (n=95) | ||
| 1 | −3.45±51.45 | −3.68±57.93 | 0.87 |
| 2 | 6.29±30.21 | −2.36±33.54 | 0.18 |
| 3 | 6.80±29.86 | −7.86±28.63 | 0.01* |
| 4 | 5.01±25.41 | 1.20±30.30 | 0.53 |
| 5 | −0.66±20.93 | −0.64±26.99 | 0.86 |
| 6 | −0.12±18.43 | 1.32±20.39 | 0.38 |
| 7 | −0.03±21.24 | −0.52±18.46 | 0.80 |
| 8 | −0.52±19.48 | 2.91±17.38 | 0.31 |
| 9 | −1.71±18.81 | 1.19±17.72 | 0.44 |
| 10 | 4.17±18.05 | −1.88±16.78 | 0.04* |
| 11 | −0.89±16.17 | −1.42±15.47 | 0.52 |
Abbreviations: SP, Spondylolysis group; CON, Control group
Principal Component Scores are presented as mean±standard deviation.
* p<0.05.
Bone morphology characteristics of the spondylolysis group
As previously noted, the PCS of both PC3 and PC10 was significantly higher in the SP group than in the CON group. This result indicated that the bone morphology of the SP had +3 SD characteristics. Regarding PC3 (Fig. 3), compared to the CON group (−3 SD direction), the SP group (+3 SD direction) had the following characteristics: a smaller CSA of the superior (arrow 1) and inferior (arrow 2) surfaces of the vertebral body; longer pedicle (arrow 3) and neural arch (arrow 4) length; a larger dorsal wedge shape of the vertebral body (arrow 5); a horizontally oriented spinous process (arrow 6); and shorter isthmus length (arrow 7). For PC10 (Fig. 4), compared with the CON group (−3 SD direction), the SP group (+3 SD direction) tended to have the following characteristics: a shorter anteroposterior length of the superior (arrow 1) and inferior (arrow 2) surfaces of the vertebral body and a coronally oriented transverse process (arrow 3).
Discussion
This study used a homologous model technique to investigate the overall L5 vertebral shape in early-stage spondylolysis. The AISD, representing the homologous model accuracy, was found to be 0.18 mm. It ranged from 0.12 to 1.0 mm in previous studies19,20). Therefore, the homologous models in this study were sufficiently accurate.
We found that the overall L5 vertebral shape differed depending on the presence of early-stage spondylolysis. The results for PC3, where there were significant differences, indicated that the SP group had a smaller CSA of the superior and inferior vertebral body surfaces and a larger dorsal wedge shape of the vertebral body compared to the CON group (Fig. 3). Previous studies associated a smaller CSA of the vertebral body with a wedge shape13,23). A wedge-shaped vertebral body causes increased lumbar lordosis12), along with the anterior tilt of the sacrum, increases stress on the pars interarticularis during trunk movement24). Therefore, the wedge-shaped vertebral body observed at PC3 may increase lumbar lordosis and stress on the pars interarticularis during movement. Additionally, compared with the CON group, the SP group tended to have a shorter isthmus length (Fig. 3). However, contrasting findings have been reported, with more longer isthmus lengths observed in the case of spondylolysis12). These contradicting results may be attributable to differences in the ages of participants and measurement methods. The shorter isthmus length indicates vulnerability to mechanical stress, which may increase stress on the pars interarticularis during movement. These two characteristics, a wedge-shaped vertebral body and a smaller isthmus length, were considered to increase stress on the pars interarticularis. Similar to PC3, the other PCs (PC5, PC8, and PC9) were also related to vertebral shape in the sagittal plane (Table 2, 3; Fig. S3, S6, and S7, respectively), but no significant differences were observed between the groups. In PC5 and PC8, the isthmus length was longer in conjunction with the larger dorsal wedge shape of the vertebral body (Table 2, 3; Fig. S3 and S6, respectively), showing different morphological variations from PC3. Additionally, PC9 was unrelated to the isthmus length (Table 3; Fig. S7). The absence of significant differences in these PCs suggests that the combination of morphological characteristics―a wedge-shaped vertebral body and a smaller isthmus length―may be associated with spondylolysis development. The results also indicate that, when examining the bony morphology of spondylolysis, it is important to identify the overall shape of the vertebra rather than focusing solely on single aspects of vertebral morphology.
The PC10 results showed that the SP group tended to have a shorter anteroposterior length of the superior and inferior surfaces of the vertebral body and a coronally oriented transverse process (Fig. 4). A previous study indicated that transverse processes in spondylolysis are oriented dorsally18); however, we attribute this conflict to differences in age, time from onset, and other factors. The transverse process is the attachment site for the erector spinae and psoas major muscles associated with lumbar lordosis25). Changes in the orientation of the transverse processes may alter the lever arm lengths of these muscles, potentially affecting the stress exerted on the pars interarticularis during movement. Further studies are needed to determine how the orientation of the transverse processes affects the action of the attached muscles and the stresses on the pars interarticularis.
Several studies involving adults reported that the facet joint is oriented frontally in patients with spondylolysis5,6,18). However, in our study, which focused on early-stage cases, the PCs that differed between the SP and CON groups (PC3 and PC10) were unrelated to facet joint orientation. A previous study reported that facet joint orientation of L4/L5 and L5/S1 tends to be more frontal with age, and this tendency is even more pronounced in the case of spondylolisthesis26). Therefore, the previously reported characteristics of the facet orientation may represent morphological changes after spondylolysis onset and may be unrelated to the onset. Longitudinal studies from the adolescent stage are necessary to clarify the cause of the frontally oriented facet joints.
Our study suggests that a wedge-shaped vertebral body and a smaller isthmus length may be associated with spondylolysis development. Therefore, adolescents with these morphological features may be at a high risk of spondylolysis. As a clinical application of our findings, we could confirm the risk by obtaining vertebral shape data through medical examinations of adolescent athletes. Early detection may be possible through regular check-ups for the athletes identified as high risk. Various studies have suggested an association between lower extremity inflexibility and spondylolysis development27-31). Providing continuous stretching exercises to these athletes could be effective in prevention. Exploring the effectiveness of early detection and prevention is crucial in the future.
This study has several limitations. The effects of the observed shape in the SP group on stress in the pars interarticularis during trunk movements are unclear. Investigations using finite element models are warranted to clarify them. The overall shape of the lumbar vertebrae, excluding L5, and the sacrum in early-stage spondylolysis, must also be clarified to investigate the stress in the pars interarticularis of the L5 vertebra. Although we confirmed the medical records within the verifiable period before grouping, it is possible that individuals classified into the CON group developed spondylolysis afterward or were diagnosed elsewhere.
In summary, we concluded that the overall L5 vertebral shape differed between individuals with and without early-stage spondylolysis. Our findings indicated that specific morphological characteristics, such as a wedge-shaped vertebral body and a shorter isthmus length, may be associated with the development of spondylolysis. Examining these characteristics in adolescent athletes could predict their susceptibility to spondylolysis risk factors.
Conflicts of Interest: The authors declare that there are no relevant conflicts of interest.
Sources of Funding: None.
Author Contributions: Yuji Yamane: conception and design; data acquisition; analysis of data; manuscript drafting.
Hajime Toda: conception and design; critical revision.
Masaki Katayose: conception and design; critical revision; supervision.
Ethical Approval: This study was approved by the Ethics Committee of Sapporo Medical University (Approval code: 2-1-67).
Informed Consent: This study did not require informed consent because it was conducted using an Opt-out approach.
Supplementary Material
Acknowledgement
We would like to thank Kazuhiko Nakano for collecting the subject data, Toyohisa Tanijiri for providing technical advice, and Editage (www.editage.com) for editing the English language.
References
- 1.Tawfik S, Phan K, Mobbs RJ, et al. The incidence of Pars interarticularis defects in athletes. Global Spine J. 2020;10(1):89-101. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.El Rassi G, Takemitsu M, Woratanarat P, et al. Lumbar spondylolysis in pediatric and adolescent soccer players. Am J Sports Med. 2005;33(11):1688-93. [DOI] [PubMed] [Google Scholar]
- 3.Ladenhauf HN, Fabricant PD, Grossman E, et al. Athletic participation in children with symptomatic spondylolysis in the New York area. Med Sci Sports Exerc. 2013;45(10):1971-4. [DOI] [PubMed] [Google Scholar]
- 4.Sairyo K, Katoh S, Komatsubara S, et al. Spondylolysis fracture angle in children and adolescents on CT indicates the fracture producing force vector: A biomechanical rationale. Internet J of Spine Surg. 2005;1(2):2. [Google Scholar]
- 5.Masharawi YM, Alperovitch-Najenson D, Steinberg N, et al. Lumbar facet orientation in spondylolysis: a skeletal study. Spine. 2007;32(6):E176-80. [DOI] [PubMed] [Google Scholar]
- 6.Don AS, Robertson PA. Facet joint orientation in spondylolysis and isthmic spondylolisthesis. J Spinal Disord Tech. 2008;21(2):112-5. [DOI] [PubMed] [Google Scholar]
- 7.Eroğlu A, Sarı E, Cüce F, et al. The investigation of the role of the facet joint angle in the development of L5-S1 spondylolysis in young men. Turkiye Fiziksel Tip ve Rehab Derg. 2017;63(3):253-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8.Zehnder SW, Ward CV, Crow AJ, et al. Radiographic assessment of lumbar facet distance spacing and pediatric spondylolysis. Spine (Phila Pa 1976). 2009;34(3):285-90. [DOI] [PubMed] [Google Scholar]
- 9.Ward CV, Latimer B, Alander DH, et al. Radiographic assessment of lumbar facet distance spacing and spondylolysis. Spine (Phila Pa 1976). 2007;32(2):E85-8. [DOI] [PubMed] [Google Scholar]
- 10.Ward CV, Mays SA, Child S, et al. Lumbar vertebral morphology and isthmic spondylolysis in a British medieval population. Am J Phys Anthropol. 2010;141(2):273-80. [DOI] [PubMed] [Google Scholar]
- 11.Masharawi Y, Dar G, Peleg S, et al. Lumbar facet anatomy changes in spondylolysis: A comparative skeletal study. Eur Spine J. 2007;16(7):993-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 12.Masharawi Y. Lumbar shape characterization of the neural arch and vertebral body in spondylolysis: A comparative skeletal study. Clin Anat. 2012;25(2):224-30. [DOI] [PubMed] [Google Scholar]
- 13.Wren TAL, Ponrartana S, Aggabao PC, et al. Increased lumbar lordosis and smaller vertebral cross-sectional area are associated with spondylolysis. Spine (Phila Pa 1976). 2018;43(12):833-8. [DOI] [PubMed] [Google Scholar]
- 14.Bugg WG, Lewis M, Juette A, et al. Lumbar lordosis and pars interarticularis fractures: A case-control study. Skeletal Radiol. 2012;41(7):817-22. [DOI] [PubMed] [Google Scholar]
- 15.Oh YM, Choi HY, Eun JP. The comparison of sagittal spinopelvic parameters between young adult patients with L5 spondylolysis and age-matched control group. J Korean Neurosurg Soc. 2013;54(3):207-10. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16.Sugawara K, Iesato N, Katayose M. Comparison of the sacral table angles by progression stage of lumbar spondylolysis. Spine Deform. 2020;8(1):123-7. [DOI] [PubMed] [Google Scholar]
- 17.Ergun T, Sahin MS, Lakadamyali H. Evaluation of the relationship between L5-S1 spondylolysis and isthmic spondylolisthesis and lumbosacral-pelvic morphology by imaging via 2- and 3-dimensional reformatted computed tomography. J Comput Assist Tomogr. 2011;35(1):9-15. [DOI] [PubMed] [Google Scholar]
- 18.Plomp KA, Dobney K, Collard M. Spondylolysis and spinal adaptations for bipedalism: The overshoot hypothesis. Evol Med Public Health. 2020;2020(1):35-44. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19.Biwasaka H, Aoki Y, Takahashi Y, et al. A quantitative morphological analysis of three-dimensional CT coxal bone images of contemporary Japanese using homologous models for sex and age estimation. Leg Med (Tokyo). 2019;36:1-8. [DOI] [PubMed] [Google Scholar]
- 20.Yamatsu K, Hayashi M, Takashima H, et al. Comparison of the three-dimensional bone morphology of the first proximal phalanx and first metatarsal between normal and hallux valgus foot using the homologous model technique. Foot (Edinb). 2023;54:101968. [DOI] [PubMed] [Google Scholar]
- 21.Inoue K, Nakano H, Sumida T, et al. A novel measurement method for the morphology of the mandibular ramus using homologous modelling. Dentomaxillofac Radiol. 2015;44(8):20150062. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 22.Fujii K, Katoh S, Sairyo K, et al. Union of defects in the pars interarticularis of the lumbar spine in children and adolescents. The radiological outcome after conservative treatment. J Bone Joint Surg Br. 2004;86(2):225-31. [DOI] [PubMed] [Google Scholar]
- 23.Wren TA, Ponrartana S, Aggabao PC, et al. Association between vertebral cross-sectional area and vertebral wedging in children and adolescents: A cross-sectional analysis. J Bone Miner Res. 2017;32(11):2257-62. [DOI] [PubMed] [Google Scholar]
- 24.Sterba M, Arnoux PJ, Labelle H, et al. Biomechanical analysis of spino-pelvic postural configurations in spondylolysis subjected to various sport-related dynamic loading conditions. Eur Spine J. 2018;27(8):2044-52. [DOI] [PubMed] [Google Scholar]
- 25.Troup JD. Mechanical factors in spondylolisthesis and spondylolysis. Clin Orthop Relat Res. 1976;117:59-67. [PubMed] [Google Scholar]
- 26.Morimoto M, Higashino K, Manabe H, et al. Age-related changes in axial and sagittal orientation of the facet joints: Comparison with changes in degenerative spondylolisthesis. J Orthop Sci. 2019;24(1):50-6. [DOI] [PubMed] [Google Scholar]
- 27.Kemmochi M, Sasaki S, Ichimura S. Association between reduced trunk flexibility in children and lumbar stress fractures. J Orthop. 2018;15(1):122-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 28.Iwaki K, Sakai T, Hatayama D, et al. Physical features of pediatric patients with lumbar spondylolysis and effectiveness of rehabilitation. J Med Invest. 2018;65(3):177-83. [DOI] [PubMed] [Google Scholar]
- 29.Sato M, Mase Y, Sairyo K. Active stretching for lower extremity muscle tightness in pediatric patients with lumbar spondylolysis. J Med Invest. 2017;64(1):136-9. [DOI] [PubMed] [Google Scholar]
- 30.Takei S, Torii S, Taketomi S, et al. Is increased kicking leg iliopsoas muscle tightness a predictive factor for developing spondylolysis in adolescent male soccer players? Clin J of Sport Med. 2022;32(2):e165-71. [DOI] [PubMed] [Google Scholar]
- 31.Nagamoto H, Abe M, Konashi Y, et al. Rotation-related sports players demonstrate rotation-type lumbar spondylolysis fracture angle and decreased hip internal rotation range of motion. J Orthop. 2021;28:101-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.