Application of statistical shape modeling to the human hip joint: a scoping review

Abstract

Objective: 

The objective of this scoping review was to identify all examples of the application of statistical shape models to the human hip joint, with a focus on applications, population, methodology, and validation.

Introduction: 

Clinical radiographs are the most common imaging tool for management of hip conditions, but it is unclear whether radiographs can adequately diagnose or predict outcomes of 3D deformity. Statistical shape modeling, a method of describing the variation of a population of shapes using a small number of variables, has been identified as a useful tool to associate 2D images with 3D anatomy. This could allow clinicians and researchers to validate clinical radiographic measures of hip deformity, develop new ones, or predict 3D morphology directly from radiographs. In identifying all previous examples of statistical shape modeling applied to the human hip joint, this review determined the prevalence, strengths, and weaknesses, and identified gaps in the literature.

Inclusion criteria: 

Participants included any human population. The concept included development or application of statistical shape models based on discrete landmarks and principal component analysis. The context included sources that exclusively modeled the hip joint. Only peer-reviewed original research journal articles were eligible for inclusion.

Methods: 

We searched MEDLINE, Embase, Cochrane CENTRAL, IEEE Xplore, Web of Science Core Collection, OCLC PapersFirst, OCLC Proceedings, Networked Digital Library of Theses and Dissertations, ProQuest Dissertations and Theses Global, and Google Scholar for sources published in English between 1992 and 2021. Two reviewers screened sources against the inclusion criteria independently and in duplicate. Data were extracted by 2 reviewers using a REDCap form designed to answer the review study questions, and are presented in narrative, tabular, and graphical form.

Results: 

A total of 104 sources were considered eligible based on the inclusion criteria. From these, 122 unique statistical shape models of the human hip were identified based on 86 unique training populations. Models were most often applied as one-off research tools to describe shape in certain populations or to predict outcomes. The demographics of training populations were skewed toward older patients in high-income countries. A mean age between 60 and 79 years was reported in 29 training populations (34%), more than reported in all other age groups combined, and 73 training populations (85%) were reported or inferred to be from Europe and the Americas. Only 4 studies created models in a pediatric population, although 15 articles considered shape variation over time in some way. There were approximately equal numbers of 2D and 3D models. A variety of methods for labeling the training set was observed. Most articles presented some form of validation such as reporting a model’s compactness (n = 71), but in-depth validation was rare.

Conclusions: 

Despite the high volume of literature concerning statistical shape models of the human hip, there remains a need for further research in key areas. We identified the lack of models in pediatric populations and low- and middle-income countries as a notable limitation to be addressed in future research.

Introduction

The radiograph is the workhorse of imaging in the pediatric orthopedic clinic. Radiographs are used for diagnosis, surveillance, and treatment of hip conditions owing to their low cost, high accessibility, and short duration compared with other methodologies. However, using 2-dimensional (2D) imaging to describe the 3-dimensional (3D) anatomy of the hip may result in poorer outcomes for many patients. For example, some studies have shown a high misdiagnosis rate of common conditions, such as developmental dysplasia of the hip (DDH) and femoroacetabular impingement in adults.^1,2 In rarer conditions, such as Legg-Calvé-Perthes disease (LCPD), high rates of osteoarthritis have been observed after long-term follow-up, even in patients where no residual deformity is visible on radiographs,^3–5 although these findings are not replicated in other studies.^6,7

In these examples, patients would benefit from 3D imaging of complex or subtle 3D deformity,^8–10 but current clinical options are limited. For example, computed tomography (CT) and magnetic resonance imaging (MRI) are not suitable for population-level screening of femoroacetabular impingement or longitudinal monitoring of LCPD due to cost and availability, as well as radiation dose with CT. Additionally, navigating and interpreting a 3D image volume requires more time and experience than performing simple 2D measurements on radiographs.

Statistical shape modeling (SSM) has been applied to bridge the gap between 2D images and 3D deformity. Recent orthopedic applications of SSM have included correlating radiographic metrics with objective 3D shape descriptions,^11,12 identifying new metrics that could be more predictive of outcomes,¹³ estimating patient posture from radiographs,¹⁴ and reconstructing 3D shapes from one or more 2D images.¹⁵ SSM has the potential to evaluate, improve, and supplement the current standard of care. However, no attempt has yet been made to systematically identify all examples of SSM applied to the hip joint; therefore, a scoping review is an important first step in describing the current state of this field.

The results of this review are intended to provide a starting point and database for researchers interested in producing their own SSM of the hip. We aimed to record details of model construction and validation, and identify gaps in the literature to help researchers generate new research questions, particularly concerning modeling pediatric hip pathology. For example, we intend to use this review to inform creation of an SSM of the hip in patients with residual LCPD deformity. This will then be used to evaluate common clinical radiographic outcome measures of the deformity.

In the literature, SSM (also called geometric morphometric analysis in some fields) is a broad term for any way of representing the distribution of shape variation across a similar population. It is used in applications ranging from facial recognition¹⁶ and sex estimation¹⁷ to evolutionary biology.¹⁸

In brief, SSM aims to reduce complex geometry described by hundreds or thousands of variables (ie, spatial coordinates) to a small set of independent parameters while keeping most of the population variability. The method was first described by Cootes et al.¹⁹ in 1992, and their research still forms the foundation for most SSM 30 years later.

The process of creating a statistical shape model can be divided into 4 broad steps:^20,21 labeling the training set, aligning the training set, applying principal component analysis, and fitting new data to the model.

Step 1: label the training set

In the labeling step, the researcher first chooses the anatomy of interest to be represented in the shape model. Then, landmarks are placed around this anatomy to create a discrete, point-based representation of the shape (Figure 1A). One of the key requirements in this step is landmark correspondence. That is, every shape must be described by the same number of landmarks, and each landmark must correspond directly to the equivalent location on every shape. There is a significant variation in how different studies establish landmark correspondence, ranging from manual labeling to automatic entropy-based, iterative, particle-splitting algorithms,²² and recording these methods is one focus of this review.

Figure 1: Key principles behind statistical shape modeling illustrated with 2D femur outlines: A) labeling each training shape with corresponding landmarks; B) aligning labeled shapes, including translation, rotation, and (optional) scaling; C) representation of femurs and other shapes as single points in “shape space” and application of principal component analysis to the femur group

Step 2: align the training set

This step aims to remove any variation in the population that originates from differences in pose. This is almost always done on the labeled training set using Procrustes rotation and translation. Sometimes the training set is also aligned prior to labeling, particularly to aid automated labeling algorithms. Researchers may also choose to use Procrustes scaling, such that only shape changes independent of overall size are included in the model (Figure 1B). If not, then the first mode of variation in the final model typically corresponds to overall size.

Step 3: create model with principal component analysis

The underlying principle behind SSM is that in a group of shapes represented by $n$ landmarks in $m$-dimensional space, the shape’s coordinates can be rearranged into 1 vector, describing a single point in $\left(m\times n\right)$-dimensional space. For example, a femoral outline defined by 50 landmarks on a 2D radiograph would occupy a single point in 100-dimensional “shape space.” Similar outlines would occupy the same region of shape space, whereas a very different outline (eg, a circle) would be more distant in shape space (Figure 1C).

To reduce the dimensionality of the shape-space description, principal component analysis is applied. This identifies a set of orthogonal axes that each, in sequence, describe the most possible variance in the data while being orthogonal to all previous axes. A simple 2D example is illustrated in Figure 1C. The final shape model is expressed as the mean shape and a set of weights applied to the first few principal components (ie, modes of variation).

Step 4: fit new data to model

At this stage, the model is already complete and can serve as a compact description of the training set variation in further analyses. However, for many applications, it is necessary to fit unfamiliar data to the model, such as in automated segmentation algorithms. A number of methods, such as active shape models,^20,23 have been developed to fit these data to SSM.²¹

It is common for SSM to incorporate additional information beyond spatial coordinates, for example, combining shape outline with image intensity distribution within the shape.²⁴ These are often referred to as statistical shape and intensity, density, or appearance models.

Prior to the publication of the protocol for this review,²⁵ we performed a database search of JBI Database of Systematic Reviews and Implementation Reports, Cochrane Database of Systematic Reviews, PubMed, PROSPERO, and IEEE Xplore for review articles using the term “statistical shape model.” No existing papers were found with a similar aim to this review, but some reviews overlap with the current work. Cootes and Taylor²⁴ and Heimann and Meinzer²¹ reviewed SSM it’s as applied to medical image analysis and automated segmentation non-systematically. The focus in these papers was on methods used to create and apply SSM and not on any specific anatomy, such as the hip. Taylor et al.²⁶ reviewed finite element analyses of the hip and knee joints, and Reyneke et al.²⁷ reviewed methods of producing 3D patient-specific bone models from 2D radiographs. Part of both of these reviews covered SSM, but each review is limited in scope to a single application. Siebelt et al.²⁸ covered SSM as part of a review of imaging of early hip osteoarthritis (OA). Finally, van Buuren et al.²⁹ performed a systematic review of SSM of hip OA; this article was published after the publication of our protocol but before our final database search. All of the reviews listed here overlap with our objectives but focus on specific methods, applications, or hip conditions, and therefore do not preclude the broad objectives of this scoping review.

Review questions

How have statistical shape models of the hip joint been applied to human populations? The subquestions of the review are as follows:

• What current or suggested application areas are reported for SSM?
• What populations are most commonly studied with SSM?
• What methods are used to create SSM?
• How have researchers validated the shape models created during their research?
• How is shape variation over time (eg, in pediatric populations) accounted for in SSM?

Inclusion criteria

Participants

Following our a priori protocol,²⁵ this review considered studies that included any number of human participants. This included cases where humans comprise only part of the training set, for example, when combined with other primates^30–32 or with synthetic data.¹⁴

Concept

This review considered studies that explored the development and/or application of SSM on the hip joint, following the broadly accepted definition of SSM^33,34 first described by Cootes et al.¹⁹ and outlined above.

Context

In a deviation from the published protocol, this review only considered studies that exclusively modeled the hip joint, regardless of context. Our definition of the hip joint includes the proximal half of the femur and the pelvic bones surrounding the acetabulum: pubis, ischium, and ilium inferior to the anterior inferior iliac spine. Therefore, studies that modeled the hip as one of many anatomical examples, or that modeled the whole femur or whole pelvis, were excluded. This change was made because it was difficult to define suitable thresholds for biomechanical context, novel modeling technique, and hip focus.

Types of sources

In a deviation from the review protocol, only peer-reviewed original research journal articles were considered eligible. This change was made due to the large number of results, a lack of meaningful information in conference abstracts, and duplication of information from journal articles in conference papers, theses, and reviews.

Methods

This scoping review was conducted in accordance with the JBI methodology for scoping reviews.³⁵ The Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR)³⁶ was used for reporting. This review was conducted in accordance with an a priori protocol.²⁵

Search strategy

The search strategy aimed to locate published original research articles, conference papers and abstracts, reviews and theses. The development and implementation of the literature search used a 3-stage process:

• An initial limited search of MEDLINE (Ovid) and IEEE Xplore was undertaken to identify relevant articles on the topic. The text words contained in the titles and abstracts of relevant articles, and the index terms used to describe the articles, were identified with the Yale MeSH Analyzer (Yale University, CT, USA) and used to develop a full search strategy.
• The final search strategy, including all identified keywords and index terms, was developed for MEDLINE (Ovid), first with input from the study team and peer-reviewed by an independent health sciences librarian. This strategy was then adapted for each included information source, and a complete search of all databases was undertaken on June 15, 2020. The search was updated using the full search strategy across all databases on May 17, 2021. The ull search strategies for each database are provided in Appendix I.
• After screening the database search results, the reviewers performed a forward and backward citation search to identify additional studies that referenced or were referenced in the chosen articles. Forward citation tracking was performed using Google Scholar.

The following databases were searched based on literature search recommendations for orthopedics³⁷: MEDLINE (Ovid), Embase (Ovid), and Cochrane CENTRAL (Ovid). Sources of computer vision articles and gray literature searched included IEEE Xplore, Web of Science Core Collection, OCLC PapersFirst (WorldCat), OCLC Proceedings (WorldCat), the Networked Digital Library of Theses and Dissertations, ProQuest Dissertations and Theses Global, and Google Scholar (up to 10 pages).

This review considered studies published online or in print between January 1, 1992 (the year of first publication of SSM by Cootes et al.¹⁹) and May 17, 2021 (the final database search date). Only studies published in English were considered due to financial restrictions for translations.

Study selection

Following the search, all identified records were collated and uploaded into Rayyan (Rayyan Systems Inc, Cambridge, MA, USA) and duplicates were removed. A pilot test was performed with a random selection of 50 sources from the initial literature search results to clarify inclusion criteria. Amendments to the inclusion criteria were introduced after each pilot test if agreed on by both reviewers, which resulted in deviations from the protocol as outlined in the Context section of the inclusion criteria. Titles and abstracts were then screened independently and in duplicate by 2 reviewers (LJ and AC for the first database search, followed by LJ and SC for the updated database search) for assessment against the inclusion criteria for the review.

Potentially relevant papers, those that appeared to meet the inclusion criteria or for which there was uncertainty, were retrieved in full and imported into a separate project in Rayyan. Following another pilot screening of a random selection of 50 records, full-text studies that did not meet the inclusion criteria were excluded. Full-text screening was performed independently and in duplicate by 2 reviewers (LJ and SC). Any disagreements that arose between the reviewers were resolved through discussion or through third-party arbitration if necessary.

Prior to the forward and backward citation search, all records that had been screened were imported into Mendeley Desktop 1.19.8 (Mendeley Ltd., Elsevier, Netherlands). Potential sources from the citation search were checked against this folder to avoid duplicating the database search results. New sources that had not been captured in the database search were stored in a different Mendeley folder before being uploaded to Rayyan for screening as per the steps above.

Data extraction

Two reviewers (LJ and SC) jointly developed a data extraction form using REDCap (Vanderbilt University, Nashville, TN, USA), based on the framework presented in the a priori protocol.²⁵ The same reviewers charted data independently and in duplicate, and disagreements were resolved through discussion. A summary of the REDCap data entry fields is presented in Appendix II. The data extracted included specific details about the population, concept, context, and methods relevant to the review question and subquestions.

To answer the question “What current or suggested application areas are reported for SSM?” we defined 5 categories to describe the overall application of each article: therapeutic, diagnostic, prognostic, descriptive/exploratory, and other. Descriptions of each category and examples are presented in Table 1.^38–44 Articles could be coded as multiple categories; for example, a study could be motivated by an intended therapeutic application even if the results alone would be coded as exploratory/descriptive.

Table 1 - Description of categories used by reviewers to describe the application areas of statistical shape modeling

Category	Definition	Example(s)
Therapeutic	Article describes or proposes the use of SSM to guide an intervention	2D-3D reconstruction of the femur from radiographs for surgical planning38
Diagnostic	SSM is used to identify specific conditions or distinguish between conditions	Bone shape changes as an early indicator of osteoarthritis39
Prognostic	SSM is used to associate an initial condition with outcomes	Association of acetabulum shape with future total hip replacement,40 association of body mass index during adulthood with hip shape at follow-up41
Descriptive/exploratory	Clinical or basic science studies with no direct clinical outcome/application	Correlation of hip shape with genetic markers,42 development of new SSM modeling protocol43
Other	Does not fit into the above categories	Evolutionary biology,30 SSM used to compare against a new non-SSM method44

SSM, statistical shape modeling.

To answer the question “what populations are most commonly studied with SSM?” we collected demographic information including age and sex distribution, geographic location, and hip pathology. We categorized location according to World Health Organization (WHO) region and country of origin, where available (including in an article’s acknowledgments section or mention of research ethics board approval). For populations where this information was not available, the reviewers attempted to infer country of origin from the authors’ affiliations.

We recorded hip pathologies present in populations if this information was stated by study authors. If the presence of hip pathology was not reported in a population, we coded “normal/no reported condition (NRC).” Additionally, populations were coded as “population cohort” if they consisted of a large number of hips with no exclusion criteria based on pathology, aiming to reflect the demographics of the broader population.

To answer the question “What methods are used to create SSM?” we recorded details including the source imaging modality (eg, CT, radiograph) used to construct the model, how the training set was labeled with landmarks, whether the model was 2D or 3D, whether the training set was aligned using scaling as well as translation, and rotation. We categorized labeling methods as “manual” (every landmark needs to be placed by the user), “semi-automatic” (some landmarks are placed by the user, then automatically optimized or extrapolated to the remainder), and “automatic” (every landmark placed/selected automatically), as well as recording the specific method or software used in each case.

To answer the question, “How have researchers validated the shape models created during their research?” we recorded whether they had evaluated the compactness, generalizability, and application accuracy of their models. Compactness is a property of a shape model that describes how few shape modes are needed to describe the population variance. Typically, compactness is reported informally by describing how many modes were needed to describe a certain proportion of shape variance (eg, 90%). Generalization describes how well a shape model can describe a valid shape outside of the training set that has been labeled with corresponding landmarks. This is presented as the size of the error that results when the model tries to match the new data (eg, a root mean square error of 1 mm). Application accuracy is not a property of a shape model itself, but rather of the full application pipeline, including steps before and after applying SSM. A study is considered to evaluate application accuracy if it compares the results from an SSM-based application to a known ground truth metric (eg, using a receiver-operator curve).

An analysis of source quality and level of evidence was not undertaken, as it was deemed inappropriate for the review’s rationale, which was to determine the literature scope regardless of quality or risk of bias.

Finally, the question “How is shape variation over time (eg, in pediatric populations) accounted for in SSM?” was answered by identifying studies with a longitudinal component and recording details in an open-ended field. These responses were then categorized ex post facto during data analysis. We used the same approach to identify and record pediatric studies in a separate analysis. These studies are of interest because population variation due to normal growth is unavoidable, making it more difficult to identify changes resulting from pathology or other variables of interest.

Data analysis and presentation

The data charted in REDCap were exported to a Microsoft Excel (Redmond, WA, USA) spreadsheet, and coding was developed to tabulate results and create figures. Analysis was carried out by LJ. The relationship between articles, models, and training populations is not straightforward. Some articles reuse models described elsewhere for additional analysis, some produce multiple models from one training population, and some apply models to one or more testing populations. To avoid undercounting or overcounting population and model information, results are presented by article, by unique population, or by unique model, where appropriate.

Results

Study inclusion

The search results and inclusion and exclusion process are described in Figure 2.⁴⁵ Through database searching, 3265 records were identified. After removal of duplicates, title and abstract review, citation search, and full-text review, 104 eligible studies were identified. A list of studies excluded after full-text review with primary exclusion reasons is presented in Supplemental Digital Content 1, https://links.lww.com/SRX/A6. A full reference list of included studies is presented in Appendix III.

Figure 2: Search results and study selection and inclusion process.⁴⁵

Characteristics of included studies

A total of 48 journals are represented in this review. Five journals each published 5 or more articles on this subject, collectively publishing 39 (38%) articles: Osteoarthritis and Cartilage (n = 13), Bone (n = 10), Journal of Orthopaedic Research (n = 6), Arthritis and Rheumatology (formerly Arthritis and Rheumatism; n = 5), and Medical Physics (n = 5). A total of 340 authors are listed for the included articles, including 69 different first authors. Two authors are each listed in 22 separate papers.

The distribution of publications over time was coded by year of first publication, including online publication before print. The earliest journal article in this review was first published online in 2003,⁴⁶ and the publication rate increased to a peak of 13 articles published in 2020, as shown in Figure 3. For 2021, 5 articles were published up to May 17, which projected 13.4 articles for the year.

Figure 3: The number of eligible original research journal articles published per year during the database search period.

Review findings

We identified 122 unique models and 86 unique training populations (ie, sets of labeled hip anatomy, from which statistical models are derived) from the articles included in this review. Additionally, models were applied to 33 unique testing populations (ie, sets of unfamiliar hip anatomy, labeled or unlabeled). A summary of the models and populations presented in each article is available in Appendix IV, including references to the original source in cases where an article reused a pre-existing model or population for its analysis.

Applications for statistical shape modeling

A majority of articles were coded as descriptive/exploratory, followed by a notable number coded as prognostic. Only a handful of articles had therapeutic, diagnostic, or other applications. The total numbers of coded applications are shown in Table 2.

Table 2 - Application areas of statistical shape models presented in included articles

Application category	Number of articles (%)
Therapeutic	11 (11)
Diagnostic	4 (4)
Prognostic	39 (38)
Descriptive/exploratory	77 (74)
Other	3 (3)

Note: Articles may be labeled with more than 1 category.

Populations studied with statistical shape modeling

Training populations: A total of 86 unique training populations were identified from the included journal articles. There was a large range in the size of training populations, from 7 to 19,379 hips. The distribution of training population sizes is shown in Table 3. The median training population size was 110.

Table 3 - Distribution of the population sizes (number of hips) for training and testing populations

Population size (hips)	Number of training populations (%)	Number of testing populations (%)
0-9	1 (1)	8 (24)
10-99	37 (43)	16 (48)
100-999	36 (42)	8 (24)
1000-9999	10 (12)	1 (3)
>10,000	1 (1)	0 (0)
Not reported	1 (1)	0 (0)
Total	86	33

Population age characteristics were reported inconsistently across studies. Age characteristics were often reported for population subgroups (eg, case and control groups) but not overall. Mean ages were calculated from subgroups where possible, and were obtained for 52 training populations (60%). Figure 4 shows the distribution of mean ages, demonstrating a skew toward older populations used to create shape models. Age ranges were reported for 26 training populations (30%), and the tendency toward older populations is also present in these data. Categorizing minimum and maximum ages by decade, the modal population age range was from 50s to 90s (n = 4/26; 15%). Age information was unclear, not reported, or reported as unknown by the researchers in 31 populations (36%).

Figure 4: Distribution of the mean ages of training population participants, where reported.

The sex distribution of training populations was skewed toward female participants. More than half (n = 48; 56%) of the training populations consisted of solely or majority women. In contrast, 16 training populations (19%) were solely or majority men. Neither sex had a majority in 3 populations (3%) in which humans made up only part of the training set.^14,30,31 Sex information was not reported for 19 training populations (22%), and no studies considered intersex or transgender participants.

As shown in Figure 5, the majority of populations originated in Europe (both reported and inferred), with most of the remainder based in the Americas. Three populations were drawn from multiple regions: 1 from both Europe and the Americas,⁴⁷ and 2 from the Americas, Eastern Mediterranean, and African regions.^30,31 No populations were drawn exclusively from the African and Eastern Mediterranean regions.

Figure 5: Global distribution of training populations, where reported or as inferred by reviewers. Categorization by WHO health region.

More than half of the training populations in this review were sourced (reported and inferred) from just 3 countries: USA (18 training populations), UK (14), and the Netherlands (12). A further 10 training populations were sourced from more than one country.

Humans made up only part of the training set in 4 training populations. One population consisted of 130 human hips (42% of the population) and 181 hips from extant hominin species, including chimpanzees, gorillas, orangutans, and gibbons.³⁰ Another population combined this population with an additional 19 extinct hominin species.³¹ A third population consisted of 82 human (66%) and 42 extant and extinct hominin hips.³² Finally, 1 training population consisted of 61 clinical and cadaver human hips (11%) and 500 statistically generated “human” hips created with a previous statistical appearance model.¹⁴

Training populations were most commonly made up of hips that were normal or had no reported condition, coded as normal/NRC (n=34; 40%). Most of the remainder were a combination of normal/NRC and pathologic groups (n = 30; 35%). A full list of modeled conditions is shown in Table 4.

Table 4 - Distribution of reported hip conditions or combinations of conditions present in training populations

Hip conditions modeled in training populations	Number of training populations (%)
Population cohort	11 (13)
Normal/no reported condition	34 (40)
Normal and osteoarthritis	12 (15)
Normal and osteoporosis	12 (15)
Normal and femoroacetabular impingement	4 (5)
Normal and mucopolysaccharidosis type I	1 (1)
Normal and Legg-Calvé-Perthes disease and slipped capital femoral epiphysis	1 (1)
Osteoarthritis	3 (3)
Developmental dysplasia of the hip and avascular necrosis	5 (6)
Femoroacetabular impingement and avascular necrosis	1 (1)
Developmental dysplasia of the hip	1 (1)
Preoperative to hip resurfacing—pathology not specified	1 (1)
Total	86

Many articles aimed to predict hip fracture risk, which was not coded as a hip condition (although some of these articles listed diagnoses of osteoporosis and osteopenia). Out of 104 articles, 18 (17%) used SSM to predict hip fractures directly, for example, by creating a risk prediction function evaluated using receiver-operator curves.^eg, ^48,49 An additional 19 (18%) described hip fracture risk as a motivation or future application of the model.^eg,50,51

Testing populations: After creating models, some studies applied them to separate testing populations that were not part of the training set for further evaluation and analysis. In total, 33 unique testing populations were used in 30 studies (Table 3). Where appropriate, data for testing sets have been included in tables alongside corresponding data for training sets.

Testing populations were typically smaller than training populations, ranging from 1 to 1140. The median testing population had 22 participants/specimens. The age mean and range were available for 9 and 7 populations, respectively; due to these small numbers, it is not appropriate to comment on the age distribution of testing sets.

The sex distribution was reported for 17 (52%) testing populations, a much lower reporting rate than for training populations (78% reported). Thirteen (39%) were solely or majority women, 1 (3%) was solely men, and 3 (9%) did not have a majority of either sex.

The location of origin of the participants or specimens was reported for 17 testing populations (52%) and inferred from author affiliations for 15 populations (43%). The origin of 1 population could not be determined. Counting both reported and inferred results, the most common WHO region was Europe (23 populations; 70%), followed by Western Pacific (6; 18%) and Americas (3; 9%). No testing populations originated from the African, South East Asian, or Eastern Mediterranean regions.

Model creation methods

Included studies presented 122 unique shape models of the hip. About half (n = 59; 48%) were 2D models, with the remainder (n = 63; 52%) being 3D. Cumulatively, 110 models (91%) used CT, plain radiographs, or dual x-ray absorptiometry (DXA) as source images, as shown in Figure 6. The remaining models were produced using landmarks manually digitized from dry bones or fossils,^30–32 MRI scans,^52–54 photographs of bones,^55,56 calibrated screenshots of a CT segmentation surface,⁵⁷ or digitally reconstructed radiographs combined with the output of a previous statistical appearance model.¹⁴

Figure 6: Distribution of source imaging modalities used to create statistical shape modeling.

A wide variety of methods for labeling the training set were described, ranging from fully manual to fully automated. These methods are summarized in Table 5.^{11,55,57–66}

Table 5 - Methods for labeling the training set for each model

Landmarking method	# of models (%)	Example article
Manual	13 (11)
Semi-automatic	44 (36)
ASM toolkit (University of Manchester, Manchester, UK)	29 (24)
Shape (University of Aberdeen, Aberdeen, UK)	9 (7)
Manual + equidistant repositioning	2 (2)	Yoshitani (2019)57
Manual + sliding landmarks	2 (2)	San Millán (2015)55
Manual + non-rigid registration	2 (2)	Xie (2014)58
Automatic	60 (49)
Mesh deformation of reference shape	34 (28)
“Matching with shape contexts”59	8 (7)	Huang (2015)60
BoneFinder (University of Manchester, Manchester, UK)	1 (1)	van der Veer (2021)61
Fully automatic shape model matching	3 (2)	Lindner (2013)62
ShapeWorks (Scientific Computing and Imaging Institute, Salt Lake City, UT, USA)	5 (4)	Harris (2013)11
“Minimum Description Length”-based methods63	7 (6)	Pilgram (2008)64
Gradient-based optimization	1 (1)	Keating (2020)65
Closest point algorithm	1 (1)	Jazinizadeh (2021)66
Not reported	5 (4)

Note: Example references are provided for selected methods.

The number of landmarks used in model construction was reported for 90 models (74%), and ranged from 9⁶⁷ to 295,589.⁶⁸ The median number of landmarks in a 2D model was 60, compared with a median of 4098 for 3D models.

The raters determined that scaling information was removed prior to model construction in 91 models (75%), was included in the model variables in 18 models (15%), and was unclear in the remaining 13 (11%).

The hip was divided into 7 anatomical regions to illustrate the distribution of modeling approaches. Raters counted the number of models that included all or part of each region. Table 6 shows that models most commonly included the femoral head, femoral neck, and greater trochanter. One model placed landmarks at the ends of anatomical axes instead of around anatomical contours or surfaces⁴⁶; this has been coded as “other.”

Table 6 - How often each anatomical region was included in a model

Anatomical region	Number of models (%)
Femoral head	111 (91)
Femoral neck	111 (91)
Greater trochanter	109 (89)
Lesser trochanter	74 (61)
Proximal femoral shaft	44 (36)
Acetabulum	27 (22)
Inferior pelvic bone	12 (10)
Other (anatomical axes)	1 (1)

Validation methods

Key methods of model validation were identified and coded into 3 categories: compactness, generalization, and application accuracy. It was not appropriate to collect and analyze validation results due to extreme heterogeneity in reporting, but the validation method used was recorded for each article and is presented in Appendix IV. Overall, 71 articles reported model compactness, 57 evaluated application accuracy, and 8 reported model generalization.

Longitudinal shape variation

Fifteen articles considered longitudinal shape variation (ie, change over time) in some way. There were 4 main ways that shape changed over time. The first approach was to use 1 group of participants to create separate shape models at different time points. The shape modes from these were then separately compared with other variables.^eg,12,74 The second approach was to combine age groups to make 1 model, then compare the shape modes at different ages, either by dividing a population into age groups,⁵⁶ utilizing longitudinal imaging of the same participants,^eg,52,69 or both.⁶¹ The third approach was to fit an existing model from a different population to the groups of interest and compare the shape modes in the same way.^eg,70,71 Finally, the fourth approach utilized linear regression of healthy control hips to identify changes due to normal adolescent growth, and normalized all hips in the dataset to the mean age to isolate changes due to pathology.^72,73

In total, 9 articles focused on modeling pediatric populations,^{12,61,71–77} 5 of which utilized existing models to perform additional analyses. The 4 articles that created new shape models of the pediatric hip are shown in Table 7.

Table 7 - Included articles that created new models of the pediatric hip

Article	Title	Related papersa
Pollet et al. (2021)12	Morphological variants to predict outcome of avascular necrosis in developmental dysplasia of the hip	—
van der Veer et al. (2021)61	Quantifying the effects of hip surgery on the sphericity of the femoral head in patients with mucopolysaccharidosis type I	—
Chan et al. (2013)72	Statistical shape modeling of proximal femoral shape deformities in Legg-Calvé-Perthes disease and slipped capital femoral epiphysis	Chan et al. (2018)73
Frysz et al. (2019)74	Describing the application of statistical shape modelling to DXA images to quantify the shape of the proximal femur at ages 14 and 18 years in the Avon Longitudinal Study of Parents and Children	Baird et al. (2019)47 (source of adult model), Frysz et al. (2020a),71 Frysz et al. (2020b),75 Frysz et al. (2020c),77 Frysz et al. (2021)76

^aRelated papers provided model information for, or applied the models from, the included articles.

Discussion

This scoping review aimed to capture all examples of SSM studies that focused on the human hip joint. Key questions included what the characteristics of training populations were, which methods have been used to prepare hips for modeling, and how models have been validated.

Articles describing the creation and utilization of SSM to the hip have been published at a growing rate since 2003 and in a wide variety of journals. This trend indicates an increased interest in the field. However, the research community remains small and close-knit, as evidenced by 2 authors each appearing on 22 articles.

Applications for statistical shape modeling

Most of the literature in this review describes cohort-specific models (ie, models created ab initio for the sole purpose of describing shape in that study’s cohort). This has been identified as a limitation, as models are unique and cannot be compared directly with each other in a meta-analysis.⁷⁸ More recent studies show growing interest in “reference models.” The premise behind reference models is that one large model should be sourced from a broad population, and then any future studies of shape in similar populations should be reported in terms of the reference model’s shape scores. One example of this is the model published by Baird et al.,⁴⁷ which used DXAs from multiple population cohort studies and has since been used to describe adolescent populations by Frysz et al.⁷⁴ Reference models are already used in software tools such as the 2D-3D bone mineral density reconstruction tool 3D-SHAPER (3D-Shaper Medical SL, Barcelona, Spain),⁴³ and the automatic segmentation software BoneFinder (University of Manchester, Manchester, UK).⁶² Tools and programs such as these allow for standardization of reporting, as studies using the same underlying model can be compared directly with each other.

Populations studied with statistical shape modeling

Training populations for SSM of the hip exhibited a large amount of heterogeneity, but some populations were still under-represented. When deciding on the size of a training population, researchers face a trade-off between multiple factors, including the target population, computational power, availability of images, and preparation time. In general, 2D models have larger training populations due to ease of markup and the ubiquity of radiographs and DXA scans, whereas 3D imaging is less common and needs more computational power for labeling.

Most populations originated from Europe and North America, and the lack of representation from low- and middle-income countries (LMICs) is a significant weakness in this field. No clinical populations were from the WHO regions of Africa and Eastern Mediterranean, with the only hips from this region obtained from museum collections.^30,31 It is reasonable to expect population-level differences between hip shape and appearance models in high-income countries and LMICs due to differences in ethnicity, nutrition, lifestyle, and access to orthopedic care. To illustrate, estimates of historical anthropometric data, such as height, show large differences between regions and correlation with socioeconomic factors.⁷⁹ Saikia et al.⁸⁰ argued that normal values of hip measurements based on research in high-income countries were not representative of the population in northeast India, which would have repercussions for orthopedic care.

Age-related hip conditions, such as OA and osteoporosis, were a focus of many studies and were the most commonly modeled hip pathologies, likely contributing to the skew toward older populations observed in the literature. There was no consensus on whether to include features of OA, such as joint space narrowing or osteophytes, in the models. Barr et al.⁶⁹ included both, arguing that OA is a disease of the whole joint, but no study compared models with and without joint space narrowing or osteophytes. Other more common deformities, such as cam femoroacetabular impingement, estimated to be present in 37% of the asymptomatic population,⁸¹ were relatively under-represented. The existence of models of large population cohorts may provide an opportunity to perform retrospective studies of the impact of rare conditions on hip shape.

Model creation methods

Because all models in this review were based on the work of Cootes et al.,¹⁹ the mathematical foundation did not differ greatly between articles. However, a noticeable degree of heterogeneity was observed in what data were used to construct models, how the training set was labeled, and how models were validated.

Almost all of the models reported in the literature used common medical imaging modalities (CT, plain radiograph, DXA scans) to provide shape information. Surprisingly, ultrasound imaging was not represented, despite being common in the clinic (eg, screening infants for hip dysplasia). However, the authors are aware of at least one ultrasound-based shape model of the acetabulum published after the final database search.⁸²

The approach to training set labeling differed greatly between 2D and 3D models. Semi-automatic markup tools, such as ASM Toolkit (University of Manchester, Manchester, UK) and Shape (University of Aberdeen, Aberdeen, UK), are available and widely used to add landmarks to radiographs. Equivalent software is not as common in 3D applications, likely because manually reviewing and correcting landmark placement on each shape is not feasible when a shape is defined by hundreds of landmarks on a 3D surface. Instead, most 3D models were labeled by using in-house code to select or define a reference mesh from medical image segmentations, then non-rigidly registering this mesh to all other examples using the mesh vertices as landmark coordinates. An alternative approach is used by the software ShapeWorks (Scientific Computing and Imaging Institute, Salt Lake City, UT, USA), based on an iterative point splitting and energy minimization algorithm.²²

One of the primary motivations behind SSM is to provide an objective definition of shape, removing human bias in measurements. However, most models have human input at some point in the labeling process, such as manual landmark placement or manual segmentation. Even a small measurement error in these stages can have a large impact on the resulting model.^74,83,84 For example, Frysz et al.⁷⁴ measured a mean interobserver point-to-point repeatability of 1.78 px, but even this small difference resulted in a mean intraclass correlation coefficient of only 0.7 for the resulting shape modes. This demonstrates that automated labeling is necessary to ensure repeatability.

The decision on whether to incorporate overall size into an SSM depends on the eventual application of the model. For example, voxels in a CT scan represent a specific position in 3D space, so an SSM-based algorithm to generate a finite element mesh benefits from having the population distribution of scale included in the model.^eg,85,86 The same is not true of pixels on a radiograph; perspective projection between the x-ray source and image plane means the size of a feature on a radiograph does not correspond directly to the size of the anatomy. SSM used for automatic segmentation of radiographs in this review therefore remove scaling information before applying principal component analysis.^eg,60,87

Validation methods

SSM can often appear like a black box to an unfamiliar audience, which may discourage their use in research and the clinic. Thus, it is critical that robust validation is used so that users can be confident in the method. Unfortunately, in-depth evaluation of models was rare in this review. Many articles only provided a simple statement of compactness, such as “the first 5 shape modes described 79% of variance,” which, without context, does not effectively communicate the quality of a model.

Longitudinal shape variation

We identified a number of methods for using SSM to describe shape change over time. Most approaches are specific to the training population, but the method used by Frysz et al.⁷⁴ can be generalized to other data. This allows researchers to directly compare results if the same source model is used for analysis, and can be applied to individual shapes where a large sample size is unavailable. It is also robust to outliers: the study validated the use of an adult model to describe adolescent populations, showing minimal loss of independence using matrix spectral decomposition.

We found a small number of studies that focused on pediatric and adolescent populations.^{12,61,71–77} Some common pediatric hip disorders, such as DDH and morphological changes secondary to cerebral palsy, have not been modeled (although severe Crowe type IV DDH in adults has been modeled⁵⁷), representing an opportunity for future research.

Implications for future research

Despite increased interest in recent years, there are still areas that are relatively unexplored in SSM research. Because some populations, such as patients from LMICs, are under-represented, researchers must be careful to ensure that conclusions based on existing models are not overstated. There is a need for more research into shape variation over time (eg, due to disease progression), and how to distinguish this from expected changes in the wider population, especially in common pediatric hip disorders. Another target for future researchers should be to relate differences in how models are made to clinical outcomes (eg, comparing whether the prediction of OA progression or total hip arthroplasty is improved by including osteophytes and joint space in a model).

There also needs to be a greater focus on effective evaluation of shape model performance, what constitutes a “good” SSM, and usage guidelines for modeling in clinical research. Many articles in this review used SSM for hypothesis-free analysis.^{eg,41,47,83,88} Instead of predefined measures of shape, the model itself defines the shape characteristics to be used as exposures or outcomes. This approach has benefits and drawbacks. It allows shape to be considered holistically and objectively, but the output can be difficult to understand. Therefore, there is potential to overdraw conclusions or assign significance where perhaps there is none, or little that is clinically relevant. Better reporting standards for model validation, usage guidelines, and more open-source reference models would help to mitigate this risk.

Limitations

This review has a number of limitations. We limited our inclusion criteria to original research journal articles, as other study types mostly duplicated information that existed in these articles. Despite efforts to avoid double counting of populations and models during data collection, we cannot guarantee that duplicates have been removed completely. It was common to have overlap between populations. For example, 2 studies by Harmon^30,31 used almost identical populations, with the only difference being the presence of extinct hominoid femurs in one but not the other. We only collected data from studies in English, which may explain some of the geographic distribution of training populations.

This review has captured uses of SSM in the research literature but is unable to capture commercial uses. The authors are aware of some examples of applications that utilize proprietary SSM or similar concepts, including SOMA⁸⁹ (Stryker, Kalamazoo, MI, USA) and the EOS imaging system⁹⁰ (ATEC Spine Inc, Carlsbad, CA, USA). The review is also restricted to methods that use both corresponding landmarks and principal component analysis: the point distribution model. Finally, any evaluation of source quality was not within the scope of this review.

Conclusions

This review provides a detailed description of how SSM has been applied to the human hip joint in the research literature. It has informed the next phase of our study by collecting the modeling methods that have been used in pediatric and adolescent populations, and those that have not but are potentially useful. By identifying studies with similar methods, populations, or applications to our proposed model, we have been able to assess the strengths and weaknesses of our approach and refine it accordingly. Articles by Chan et al.,^72,73 as the only existing studies that model LCPD deformity, are of particular interest.

There are broad implications for the research community resulting from this scoping review. This review has identified a need for further research into populations from LMICs, pediatric populations, and further development of SSM from primarily a research tool to a clinical application.

A full systematic review is needed to narrow the scope to specific conditions or populations. One research question with potential is: does statistical shape and appearance modeling improve prediction of hip fracture risk? This question has a clear outcome measure, consistent reporting (typically receiver-operator characteristics), and manageable number of studies. An avenue for future research of interest to our group is large-scale radiographic models of pediatric hip disorders, such as LCPD, in collaboration with researchers from LMICs. This would cover 2 of the main gaps in the literature described here: a lack of pediatric models and a lack of models representing low-income populations globally.

Funding

This review was supported by the Canadian Institutes of Health Research (CIHR; funding reference number 165956). The funder did not have any role in content development.