Abstract

A lumbar spine statistical shape model (SSM) was developed to explain morphological differences in a population with adolescent idiopathic scoliosis (AIS). Computed tomography (CT) was used to collect data on the lumbar spine vertebrae and curvature of 49 subjects. The CT data were processed by segmentation, landmark identification, and template mesh mapping, and then SSMs of the individual vertebrae and entire lumbar spine were established using generalized Procrustes analysis and principal component analysis (PCA). Scaling was the most prevalent variation pattern. The weight coefficient was optimized using the Levenberg–Marquardt (LM) algorithm, and multiple regression analysis was used to establish a prediction model for age, sex, height, and body mass index (BMI). The effectiveness of the SSM and prediction model was quantified based on the root-mean-square error (RMSE). An automatic measurement method was developed to measure the anatomical parameters of the geometric model. The lumbar vertebrae size was significantly affected by height, sex, BMI, and age, with men having lower vertebral height than women. The trends in anatomical parameters were consistent with previous studies. The vertebral SSMs characterized the shape changes in the processes, while the lumbar spine SSM described alignment changes associated with translatory shifts, kyphosis, and scoliosis. Quantifying anatomical variation with SSMs can inform implant design and assist clinicians in diagnosing pathology and screening patients. Lumbar spine SSMs can also support biomechanical simulations of populations with AIS.

References

1.
Kikanloo
,
S. R.
,
Tarpada
,
S. P.
, and
Cho
,
W.
,
2019
, “
Etiology of Adolescent Idiopathic Scoliosis: A Literature Review
,”
Asian Spine J.
,
13
(
3
), pp.
519
526
.10.31616/asj.2018.0096
2.
Konieczny
,
M. R.
,
Senyurt
,
H.
, and
Krauspe
,
R.
,
2013
, “
Epidemiology of Adolescent Idiopathic Scoliosis
,”
J. Child. Orthop.
,
7
(
1
), pp.
3
9
.10.1007/s11832-012-0457-4
3.
Weinstein
,
S. L.
,
2019
, “
The Natural History of Adolescent Idiopathic Scoliosis
,”
J. Pediatr. Orthop.
,
39
(
Suppl. 1
), pp.
S44
S46
.10.1097/BPO.0000000000001350
4.
Marion
,
T. E.
, and
Street
,
J. T.
,
2018
, “
Adolescent Idiopathic Scoliosis: A New Classification to Determine Extent of Spinal Arthrodesis
,” 50 Landmark Papers, A,
R.
Vaccaro
,
C. G.
Fisher
, and
J. R.
Wilson
, eds.,
CRC Press
, Boca Raton, FL, pp.
173
176
.10.1201/9781315154053-33
5.
Pasha
,
S.
,
Cahill
,
P. J.
,
Dormans
,
J. P.
, and
Flynn
,
J. M.
,
2016
, “
Characterizing the Differences Between the 2D and 3D Measurements of Spine in Adolescent Idiopathic Scoliosis
,”
Eur. Spine J.
,
25
(
10
), pp.
3137
3145
.10.1007/s00586-016-4582-5
6.
Ilharreborde
,
B.
,
Steffen
,
J. S.
,
Nectoux
,
E.
,
Vital
,
J. M.
,
Mazda
,
K.
,
Skalli
,
W.
, and
Obeid
,
I.
,
2011
, “
Angle Measurement Reproducibility Using EOS Three-Dimensional Reconstructions in Adolescent Idiopathic Scoliosis Treated by Posterior Instrumentation
,”
Spine
,
36
(
20
), pp.
E1306
E1313
.10.1097/BRS.0b013e3182293548
7.
Somoskeöy
,
S.
,
Tunyogi-Csapó
,
M.
,
Bogyó
,
C.
, and
Illés
,
T.
,
2012
, “
Clinical Validation of Coronal and Sagittal Spinal Curve Measurements Based on Three-Dimensional Vertebra Vector Parameters
,”
Spine J.
,
12
(
10
), pp.
960
968
.10.1016/j.spinee.2012.08.175
8.
Kadoury
,
S.
,
Cheriet
,
F.
,
Laporte
,
C.
, and
Labelle
,
H.
,
2007
, “
A Versatile 3D Reconstruction System of the Spine and Pelvis for Clinical Assessment of Spinal Deformities
,”
Med. Biol. Eng. Comput.
,
45
(
6
), pp.
591
602
.10.1007/s11517-007-0182-1
9.
Golland
,
P.
,
Hata
,
N.
,
Barillot
,
C.
,
Hornegger
,
J.
, and
Howe
,
R.
, eds.,
2014
, “
Medical Image Computing and Computer-Assisted Intervention—MICCAI 2014
,”
17th International Conference
, Boston, MA, Sept. 14–18, Proceedings, Part III,
Springer International Publishing
,
Cham, Switzerland
.10.1007/978-3-319-10443-0
10.
Nault
,
M.-L.
,
Mac-Thiong
,
J.-M.
,
Roy-Beaudry
,
M.
,
Turgeon
,
I.
,
deGuise
,
J.
,
Labelle
,
H.
, and
Parent
,
S.
,
2014
, “
Three-Dimensional Spinal Morphology Can Differentiate Between Progressive and Nonprogressive Patients With Adolescent Idiopathic Scoliosis at the Initial Presentation: A Prospective Study
,”
Spine
,
39
(
10
), pp.
E601
E606
.10.1097/BRS.0000000000000284
11.
Rehm
,
J.
,
Germann
,
T.
,
Akbar
,
M.
,
Pepke
,
W.
,
Kauczor
,
H.-U.
,
Weber
,
M.-A.
, and
Spira
,
D.
,
2017
, “
3D-Modeling of the Spine Using EOS Imaging System: Inter-Reader Reproducibility and Reliability
,”
PLoS One
,
12
(
2
), p.
e0171258
.10.1371/journal.pone.0171258
12.
Wai
,
G.
,
Rusli
,
W.
,
Ghouse
,
S.
,
Kieser
,
D. C.
,
Kedgley
,
A.
, and
Newell
,
N.
,
2023
, “
Statistical Shape Modelling of the Thoracic Spine for the Development of Pedicle Screw Insertion Guides
,”
Biomech. Model. Mechanobiol.
,
22
(
1
), pp.
123
132
.10.1007/s10237-022-01636-8
13.
Clogenson
,
M.
,
Duff
,
J. M.
,
Luethi
,
M.
,
Levivier
,
M.
,
Meuli
,
R.
,
Baur
,
C.
, and
Henein
,
S.
,
2015
, “
A Statistical Shape Model of the Human Second Cervical Vertebra
,”
Int. J. CARS
,
10
(
7
), pp.
1097
1107
.10.1007/s11548-014-1121-x
14.
Assi
,
K. C.
,
Labelle
,
H.
, and
Cheriet
,
F.
,
2014
, “
Statistical Model Based 3D Shape Prediction of Postoperative Trunks for Non-Invasive Scoliosis Surgery Planning
,”
Comput. Biol. Med.
,
48
, pp.
85
93
.10.1016/j.compbiomed.2014.02.015
15.
Peters
,
J. R.
,
Campbell
,
R. M.
, and
Balasubramanian
,
S.
,
2017
, “
Characterization of the Age-Dependent Shape of the Pediatric Thoracic Spine and Vertebrae Using Generalized Procrustes Analysis
,”
J. Biomech.
,
63
, pp.
32
40
.10.1016/j.jbiomech.2017.07.030
16.
González-Ruiz
,
J. M.
,
Pérez-Núñez
,
M. I.
,
García-Alfaro
,
M. D.
, and
Bastir
,
M.
,
2021
, “
Geometric Morphometrics of Adolescent Idiopathic Scoliosis: A Prospective Observational Study
,”
Eur. Spine J.
,
30
(
3
), pp.
612
619
.10.1007/s00586-020-06583-5
17.
Ali
,
A. H. A.
,
Cowan
,
A.
,
Gregory
,
J. S.
,
Aspden
,
R. M.
, and
Meakin
,
J. R.
,
2012
, “
The Accuracy of Active Shape Modelling and End-Plate Measurements for Characterising the Shape of the Lumbar Spine in the Sagittal Plane
,”
Comput. Methods Biomech. Biomed. Eng.
,
15
(
2
), pp.
167
172
.10.1080/10255842.2010.518962
18.
Campbell
,
J. Q.
, and
Petrella
,
A. J.
,
2016
, “
Automated Finite Element Modeling of the Lumbar Spine: Using a Statistical Shape Model to Generate a Virtual Population of Models
,”
J. Biomech.
,
49
(
13
), pp.
2593
2599
.10.1016/j.jbiomech.2016.05.013
19.
Sun
,
X.
,
Wang
,
H.
,
Wang
,
W.
,
Li
,
N.
,
Hamalainen
,
T.
,
Ristaniemi
,
T.
, and
Liu
,
C.
,
2021
, “
A Statistical Model of Spine Shape and Material for Population-Oriented Biomechanical Simulation
,”
IEEE Access
,
9
, pp.
155805
155814
.10.1109/ACCESS.2021.3129097
20.
Hollenbeck
,
J. F. M.
,
Cain
,
C. M.
,
Fattor
,
J. A.
,
Rullkoetter
,
P. J.
, and
Laz
,
P. J.
,
2018
, “
Statistical Shape Modeling Characterizes Three-Dimensional Shape and Alignment Variability in the Lumbar Spine
,”
J. Biomech.
,
69
, pp.
146
155
.10.1016/j.jbiomech.2018.01.020
21.
Tang
,
L.
,
Hu
,
Z.
,
Lin
,
Y.-S.
, and
Hu
,
J.
,
2022
, “
A Statistical Lumbar Spine Geometry Model Accounting for Variations by Age, Sex, Stature, and Body Mass Index
,”
J. Biomech.
,
130
, p.
110821
.10.1016/j.jbiomech.2021.110821
22.
Clouthier
,
A. L.
,
Wenghofer
,
J.
,
Wai
,
E. K.
, and
Graham
,
R. B.
,
2023
, “
Morphable Models of the Lumbar Spine to Vary Geometry Based on Pathology, Demographics, and Anatomical Measurements
,”
J. Biomech.
,
146
, p.
111421
.10.1016/j.jbiomech.2022.111421
23.
Yew
,
Z. J.
, and
Lee
,
G. H.
,
2020
, “
RPM-Net: Robust Point Matching Using Learned Features
,” 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (
CVPR
), Seattle, WA, June 13–19, pp.
11821
11830
.10.1109/CVPR42600.2020.01184
24.
Bookstein
,
F. L.
,
1989
, “
Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
11
(
6
), pp.
567
585
.10.1109/34.24792
25.
Dijksterhuis
,
G. B.
, and
Gower
,
J. C.
,
1991
, “
The Interpretation of Generalized Procrustes Analysis and Allied Methods
,”
Food Qual. Preference
,
3
(
2
), pp.
67
87
.10.1016/0950-3293(91)90027-C
26.
Heimann
,
T.
, and
Meinzer
,
H.-P.
,
2009
, “
Statistical Shape Models for 3D Medical Image Segmentation: A Review
,”
Med. Image Anal.
,
13
(
4
), pp.
543
563
.10.1016/j.media.2009.05.004
27.
Sarkalkan
,
N.
,
Weinans
,
H.
, and
Zadpoor
,
A. A.
,
2014
, “
Statistical Shape and Appearance Models of Bones
,”
Bone
,
60
, pp.
129
140
.10.1016/j.bone.2013.12.006
28.
Li
,
X.
,
Gu
,
X.
,
Jiang
,
Z.
,
Duan
,
H.
,
Zhou
,
J.
,
Chang
,
Y.
,
Lu
,
K.
, and
Chen
,
B.
,
2023
, “
Statistical Modeling: Assessing the Anatomic Variability of Knee Joint Space Width
,”
J. Biomech.
,
147
, p.
111420
.10.1016/j.jbiomech.2022.111420
29.
Patil
,
A.
,
Kulkarni
,
K.
,
Xie
,
S.
,
Bull
,
A. M. J.
, and
Jones
,
G. G.
,
2023
, “
The Accuracy of Statistical Shape Models in Predicting Bone Shape: A Systematic Review
,”
Rob. Comput. Surg.
,
19
(
3
), p.
e2503
.10.1002/rcs.2503
30.
Audenaert
,
E. A.
,
Pattyn
,
C.
,
Steenackers
,
G.
,
De Roeck
,
J.
,
Vandermeulen
,
D.
, and
Claes
,
P.
,
2019
, “
Statistical Shape Modeling of Skeletal Anatomy for Sex Discrimination: Their Training Size, Sexual Dimorphism, and Asymmetry
,”
Front. Bioeng. Biotechnol.
,
7
, p.
302
.10.3389/fbioe.2019.00302
31.
Suwarganda
,
E. K.
,
Diamond
,
L. E.
,
Lloyd
,
D. G.
,
Besier
,
T. F.
,
Zhang
,
J.
,
Killen
,
B. A.
,
Savage
,
T. N.
, and
Saxby
,
D. J.
,
2019
, “
Minimal Medical Imaging Can Accurately Reconstruct Geometric Bone Models for Musculoskeletal Models
,”
PLoS One
,
14
(
2
), p.
e0205628
.10.1371/journal.pone.0205628
32.
Nojiri
,
K.
,
Matsumoto
,
M.
,
Chiba
,
K.
, and
Toyama
,
Y.
,
2005
, “
Morphometric Analysis of the Thoracic and Lumbar Spine in Japanese on the Use of Pedicle Screws
,”
Surg. Radiol. Anat.
,
27
(
2
), pp.
123
128
.10.1007/s00276-004-0305-4
33.
Peters
,
J. R.
,
Servaes
,
S. E.
,
Cahill
,
P. J.
, and
Balasubramanian
,
S.
,
2021
, “
Morphology and Growth of the Pediatric Lumbar Vertebrae
,”
Spine J.
,
21
(
4
), pp.
682
697
.10.1016/j.spinee.2020.10.029
34.
Veldhuizen
,
A. G.
,
Baas
,
P.
, and
Webb
,
P. J.
,
1986
, “
Observations on the Growth of the Adolescent Spine
,”
J. Bone Jt. Surg.
,
68-B
(
5
), pp.
724
728
.10.1302/0301-620X.68B5.3782232
35.
Christiansen
,
B. A.
,
Demissie-Banjaw
,
S.
,
Roberts
,
B. J.
,
Valentine
,
M. J.
,
Shah
,
S. R.
,
Iyer
,
S.
,
Samelson
,
E. J.
,
Kiel
,
D. P.
, and
Bouxsein
,
M. L.
,
2009
, “
Age-, Sex- and Spinal Level-Specific Differences in Bone Density, Geometry, and Compressive Strength of Thoracic and Lumbar Vertebrae
,”
Bone
,
44
, p.
S217
.10.1016/j.bone.2009.03.053
36.
Riggs
,
B. L.
,
Melton
,
L. J.
,
Robb
,
R. A.
,
Camp
,
J. J.
,
Atkinson
,
E. J.
,
Peterson
,
J. M.
,
Rouleau
,
P. A.
,
McCollough
,
C. H.
,
Bouxsein
,
M. L.
, and
Khosla
,
S.
,
2004
, “
Population-Based Study of Age and Sex Differences in Bone Volumetric Density, Size, Geometry, and Structure at Different Skeletal Sites
,”
J. Bone Miner. Res.
,
19
(
12
), pp.
1945
1954
.10.1359/jbmr.040916
37.
Masharawi
,
Y.
,
Salame
,
K.
,
Mirovsky
,
Y.
,
Peleg
,
S.
,
Dar
,
G.
,
Steinberg
,
N.
, and
Hershkovitz
,
I.
,
2008
, “
Vertebral Body Shape Variation in the Thoracic and Lumbar Spine: Characterization of Its Asymmetry and Wedging
,”
Clin. Anat.
,
21
(
1
), pp.
46
54
.10.1002/ca.20532
38.
Mughir
,
A. M. A.
,
Yusof
,
M. I.
,
Abdullah
,
S.
, and
Ahmad
,
S.
,
2010
, “
Morphological Comparison Between Adolescent and Adult Lumbar Pedicles Using Computerised Tomography Scanning
,”
Surg. Radiol. Anat.
,
32
(
6
), pp.
587
592
.10.1007/s00276-009-0612-x
39.
Hong
,
J.-Y.
,
Suh
,
S.-W.
,
Tr
,
E.
,
Hong
,
S. J.
,
Yoon
,
Y.-C.
, and
Kang
,
H.-J.
,
2013
, “
Clinical Anatomy of Vertebrae in Scoliosis: Global Analysis in Four Different Diseases by Multiplanar Reconstructive Computed Tomography
,”
Spine J.
,
13
(
11
), pp.
1510
1520
.10.1016/j.spinee.2013.06.047
40.
Kunkel
,
M. E.
,
Schmidt
,
H.
, and
Wilke
,
H.-J.
,
2011
, “
Prediction of the Human Thoracic and Lumbar Articular Facet Joint Morphometry From Radiographic Images: Prediction of the Facet Joint Morphometry
,”
J. Anat.
,
218
(
2
), pp.
191
201
.10.1111/j.1469-7580.2010.01323.x
41.
Lorenz
,
M.
,
Patwardhan
,
A.
, and
Vanderby
,
R.
,
1983
, “
Load-Bearing Characteristics of Lumbar Facets in Normal and Surgically Altered Spinal Segments
,”
Spine
,
8
(
2
), pp.
122
130
.10.1097/00007632-198303000-00002
42.
Kan
,
M. M. P.
,
Negrini
,
S.
,
Di Felice
,
F.
,
Cheung
,
J. P. Y.
,
Donzelli
,
S.
,
Zaina
,
F.
,
Samartzis
,
D.
,
Cheung
,
E. T. C.
, and
Wong
,
A. Y. L.
,
2023
, “
Is Impaired Lung Function Related to Spinal Deformities in Patients With Adolescent Idiopathic Scoliosis? A Systematic Review and Meta-Analysis—SOSORT 2019 Award Paper
,”
Eur. Spine J.
,
32
(
1
), pp.
118
139
.10.1007/s00586-022-07371-z
43.
Weinstein
,
S. L.
,
Dolan
,
L. A.
,
Cheng
,
J. C.
,
Danielsson
,
A.
, and
Morcuende
,
J. A.
,
2008
, “
Adolescent Idiopathic Scoliosis
,”
Lancet
,
371
(
9623
), pp.
1527
1537
.10.1016/S0140-6736(08)60658-3
44.
Merloz
,
P.
,
Tonetti
,
J.
,
Pittet
,
L.
,
Coulomb
,
M.
,
Lavalleé
,
S.
, and
Sautot
,
P.
,
1998
, “
Pedicle Screw Placement Using Image Guided Techniques
,”
Clin. Orthop. Relat. Res.
,
354
, pp.
39
48
.10.1097/00003086-199809000-00006
45.
Şarlak
,
A. Y.
,
Tosun
,
B.
,
Atmaca
,
H.
,
Sarisoy
,
H. T.
, and
Buluç
,
L.
,
2009
, “
Evaluation of Thoracic Pedicle Screw Placement in Adolescent Idiopathic Scoliosis
,”
Eur. Spine J.
,
18
(
12
), pp.
1892
1897
.10.1007/s00586-009-1065-y
46.
Jinshan
,
T.
,
Ziqiang
,
Z.
,
Tao
,
S.
,
Dechao
,
K.
, and
Xiaojian
,
C.
,
2014
, “
Position and Complications of Pedicle Screw Insertion With or Without Image-Navigation Techniques in the Thoracolumbar Spine: A Meta-Analysis of Comparative Studies
,”
J. Biomed. Res.
,
28
(
3
), p.
228
.10.7555/JBR.28.20130159
47.
Gonzalvo
,
A.
,
Fitt
,
G.
,
Liew
,
S.
,
De La Harpe
,
D.
,
Turner
,
P.
,
Ton
,
L.
,
Rogers
,
M. A.
, and
Wilde
,
P. H.
,
2009
, “
The Learning Curve of Pedicle Screw Placement: How Many Screws Are Enough?
,”
Spine
,
34
(
21
), pp.
E761
E765
.10.1097/BRS.0b013e3181b2f928
48.
De Luca
,
G.
,
Choudhury
,
N.
,
Pagiatakis
,
C.
, and
Laroche
,
D.
,
2019
, “
A Multi-Procedural Virtual Reality Simulator for Orthopaedic Training
,”
Virtual, Augmented and Mixed Reality. Applications and Case Studies
,
J. Y. C.
Chen
and
G.
Fragomeni
, eds.,
Springer International Publishing
,
Cham, Switzerland
, pp.
256
271
.10.1007/978-3-030-21565-1_17
49.
Bryan
,
R.
,
Surya Mohan
,
P.
,
Hopkins
,
A.
,
Galloway
,
F.
,
Taylor
,
M.
, and
Nair
,
P. B.
,
2010
, “
Statistical Modelling of the Whole Human Femur Incorporating Geometric and Material Properties
,”
Med. Eng. Phys.
,
32
(
1
), pp.
57
65
.10.1016/j.medengphy.2009.10.008
50.
Hasegawa
,
K.
,
Okamoto
,
M.
,
Hatsushikano
,
S.
,
Caseiro
,
G.
, and
Watanabe
,
K.
,
2018
, “
Difference in Whole Spinal Alignment Between Supine and Standing Positions in Patients With Adult Spinal Deformity Using a New Comparison Method With Slot-Scanning Three-Dimensional X-Ray Imager and Computed Tomography Through Digital Reconstructed Radiography
,”
BMC Musculoskeletal Disord.
,
19
(
1
), p.
437
.10.1186/s12891-018-2355-5
51.
Rao
,
C.
,
Fitzpatrick
,
C. K.
,
Rullkoetter
,
P. J.
,
Maletsky
,
L. P.
,
Kim
,
R. H.
, and
Laz
,
P. J.
,
2013
, “
A Statistical Finite Element Model of the Knee Accounting for Shape and Alignment Variability
,”
Med. Eng. Phys.
,
35
(
10
), pp.
1450
1456
.10.1016/j.medengphy.2013.03.021
You do not currently have access to this content.