The International Union of Physiological Sciences Physiome Project was initiated to promote anatomically and biophysically based computational modeling.1 The Physiome project was first discussed in 1993 and a commission started in 2000 (https://physiomeproject.org/). As part of that framework, a database of anatomically based musculoskeletal geometries was developed along with tools to personalize models. These were used to build anatomically based finite element models2,3 to explore structure–function relationships and pathological conditions.4,5
Building on some of the Physiome project’s early ideas, the Musculoskeletal Atlas Project (MAP)6 (https://simtk.org/projects/map) was developed to combine population-based modeling and statistical shape models to create reusable open-source workflows for visualizing, segmenting, and generating personalized models. A client-side application (MAP Client) was designed to enable users to export personalized models to popular packages including OpenSIM (https://simtk.org/projects/opensim/),7 and finite element software FEBio (https://febio.org/).8 The MAP includes tools to explore geometrical variation in a population, perform anatomically informed segmentation, scale musculoskeletal models, and create finite element meshes.
Personalized musculoskeletal models are key for making plausible model-based recommendations and clinical evaluations. Personalized (or subject specific) models have been shown to provide more accurate kinematics, kinetics, and muscle force predictions and these predictions may deviate even more from generic models where there are substantial geometric differences from pathology or between limbs.9,10 Moreover, personalized geometries and muscle forces further influence finite element model predictions where generic models might not highlight subject-specific variations in tissue stress and strain.11,12
In this narrative review, we explore the evolution of these concepts and how they have been applied with illustrative examples to showcase their implementation using the Physiome and MAP tools. Applications include muscle and bone deformation to personalize data, modeling of Achilles tendinopathy, model creation and classification of the trapeziometacarpal (TMC) and tibiofemoral joints, exploring differences in pediatric lower limb bones, and personalizing muscle architecture. This article proposes the future for the MAP client and how we can share tools in the biomechanics community. Finally, a future direction of model personalization is discussed through the use of a novel framework for creating multiscale models or scaffolds.
Personalized Geometrical Modeling Using Free-Form Deformation
Aside from simple linear scaling, one of the earlier approaches toward personalized computational geometrical modeling was the application of free-form deformation (FFD). FFD is a computer graphics technique used to deform an underlying geometry with many degrees of freedom using a coarse mesh with only a few degrees of freedom.13 The coarse mesh is deformed so as to minimize the distance between strategically chosen control points and this deformation is passed to the embedded geometry within. The “host-mesh” technique permits deformation of anatomical geometries given a sparse set of data points. This is most useful where limited information is available, such as magnetic resonance imaging (MRI) from a knee coil but not containing the remaining lower limb, computed tomography (CT) data limited by metal artifacts, or only discrete anatomical landmarks, such as with optical motion capture. This idea was extended to musculoskeletal structures suitable for finite element modeling using a generic template called “host-mesh” fitting,2 developed from the popular Visible Human Male.14
Geometric customization of the femur is a good example of FFD application (Figure 1A), where a generic femur embedded in a host is deformed to a subject-specific geometry through minimizing the difference between anatomical control points. Muscle has also been deformed using this technique (Figure 1B) where the Visible Human Male rectus femoris muscle is customized to a subset of points along the muscle belly taken from a slimmer subject. The slimmer deformed muscle matched the manually segmented subject by less than 2 mm root mean square (RMS). This technique was further evaluated for the complete lower limb by matching MRI segmented geometries at 15° and 45° flexion with host-mesh predicted muscle shapes producing errors less than 3.7 mm RMS,5 and the FFD method has been integrated with finite elastic mechanics to constrain soft tissue volume and interaction with other tissues.4
—Host-mesh customization of the femur (A), rectus femoris muscle (B), and Achilles tendon used for mechanics simulations (C).
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
FFD has been instrumental in analyzing subject-specific tissue stress in the musculoskeletal system to help identify patterns of pathology. An illustrative example is Achilles tendinopathy (Figure 1C), one of the most common lower limb injuries.15 Achilles tendinopathy is thought to be influenced by multiple factors including tendon morphology (size and shape), material properties, load history, and biological sex. Finite element analysis of the Achilles tendon can account for some of these differences; however, the generation of patient-specific finite element models is time-consuming, particularly when manual image segmentation is required. Figure 1C highlights a workflow where cross-sectional areas of a cadaveric tendon measured with high-frequency ultrasound16 provided anatomical target points to capture the shape of the tendon using FFD. Tendon material properties were based on published constitutive law values as a starting point and optimized until model predictions matched experimental creep and cyclic loading profiles, to predict the stress distribution of the tendon under mechanical stimulation. In silico experiments illustrated the influence of morphology on stress concentrations within the tissue, showing that the rupture location was dependent on the shape of the tendon while the rupture (failure) load was more dependent on the material properties.17 Applying these models to patients with and without tendinopathy showed that the magnitude of tendon stress was, on average, 24% lower in tendinopathy patients, which was primarily due to greater tendon cross-sectional area of tendons with tendinopathy. This illustrates the biological adaptation of tendinopathy, which counteracts reduced mechanical strength by tendon thickening.18 Furthermore, the majority of tendon ruptures occur at 2 to 6 cm from the calcaneus insertion, as highlighted by this model.19 In this case, FFD enabled rapid generation of multiple subject models from sparse imaging data to provide insight to observed experimental and clinical information.
Statistical Shape Modeling to Capture Musculoskeletal Morphology
One of the challenges of using FFD to generate personalized models is that nonphysiological deformations can result if care is not taken during the fitting process. This limitation can be addressed by constraining the fitting using known morphological variations from a population. In recent years, the biomechanics community has used statistical shape modeling (SSM) to understand variation in morphology (size and shape) of musculoskeletal tissue across populations and integrated these tools into workflows to improve personalized model creation.20,21 SSM is a technique that allows the characterization of complex 3D morphologies by decomposing shape features into a set of statistically significant modes that describe the main variations in the population.22 Decomposition is commonly performed using principal component analysis (PCA),23 an unsupervised machine learning method that allows any set of shape descriptors (eg, coordinates, deformation fields) in the training set to be approximated as a sum of the mean shape descriptor and the weighted sum of principal components. Because PCA is unsupervised, it does not depend on a priori assumptions, allowing for patterns and relationships to emerge from the data. This technique has resulted in a paradigm shift in the generation of personalized models in biomechanics, particularly in how patient-specific morphology is parameterized across individuals. Specifically, the relationships between the morphology and determinants of health and function can be explored.
The process can be described using a bone example in Figure 2. After obtaining a representative sample (training set) of shapes (Figure 2A), the key steps in SSM are to (1) describe each shape in the training set using correspondent shape descriptors such as XYZ coordinates (Figure 2B–2C); (2) remove translational, rotational, and potentially size variations using a partial or full Procrustes analysis (Figure 2D); and (3) apply statistical analysis such as PCA (Figure 2D–2E).24
—Schematic overview of the workflow employed for statistical shape analysis of the trapeziometacarpal joint. A training set of computed tomography images of healthy and osteoarthritic joints (A) were manually segmented to produce a triangulated mesh (B). Vertices of a representative triangulated mesh were extracted as a point cloud on which a parametric template mesh (C) was created. The template mesh was fitted to all point clouds in an iterative fitting process (D). The principal components of variation were determined (E). Linear discriminant analysis was performed on the principal component weights to classify between healthy and OA joints (F). Linear discriminant analysis reconstructions of healthy and EOA trapeziometacarpal joint bones were generated and overlaid, and absolute pointwise distance maps were calculated and visualized. EOA indicates early osteoarthritic.
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
This process does not have to be constrained to a single bone. In the case of SSM of joints, the shapes of several bones can be described together and coupled changes in bone morphology can be characterized. Recently, statistical shape models have played several key roles in joint biomechanics,20,22,25-28 where its main applications have included classification and image segmentation.24
Classification of Disease Using Statistical Shape Models
As part of personalizing models, we often need to classify different groups using SSM, for example, the differences in morphology between asymptomatic and osteoarthritis joints to characterize the onset and progression of osteoarthritis (OA; Figure 2F).29,30 Methods such as linear discriminant analysis and logistic regression were performed on the principal component weights to find features that best classified the 2 groups. Asymptomatic TMC joints were compared with TMC joints with early OA, and it was found that joints with early OA exhibited lower aspect ratio compared with asymptomatic joints (Figure 2F). Other morphological characteristics of early OA included protrusions at the volar beak of the first metacarpal, osteophyte formation along the concave margin, and widening and deepening of the articular surface. In the knee, we compared asymptomatic tibiofemoral joints to those with later stage OA and found that osteoarthritis knees exhibited subchondral bone expansion or osteophyte formation surrounding the femoral condyles and at the posteromedial part of the tibial plateau. Classification accuracy appeared to be dependent on the severity of OA. For example, the classification accuracy of TMC joints with early OA was much lower (74% accuracy, 85% sensitivity, and 41% specificity)29 than in knee joints with late-stage OA (95% accuracy, 96% sensitivity, and 94% specificity).30
The SSM technique is not restricted to the analysis of shape descriptors, or one type of shape descriptor. Additional data, such as bone mineral density or cortical thickness, can be embedded in the model to explore coupled variations. For example, cartilage thickness and bone shape variations were explored together by embedding cartilage into the statistical shape model as a thickness field (Figure 3).31 When applying PCA to combinations of different data types, normalization is necessary to ensure that the results are unbiased toward any particular feature.
—Overview of random forest regression voting automatic segmentation algorithm.92 3D Haar-like features and corresponding displacements were used to train a RF regressor on the spatial distribution of features around each node of the shape model mesh. During segmentation, the shape model mesh (white dotted line) was initialized, and 3D Haar-like features were randomly sampled from the mesh node. The regressor for each node uses the features to predict the correct location of the node in the CT image. CU indicates computed tomography; CT, computed tomography; RF, random forest; SSM, statistical shape modeling.
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
Multiple linear regression was used to explore the influence of sex, height, body mass, and age on shape, and multiple logistic regression was performed to characterize the coupled morphological differences between male and female knees (Figure 3). We found that in healthy young adult knees, sex and height influenced the morphology, but body mass and age did not. We demonstrated coupled relationships between the bone morphology and cartilage thickness in a healthy young adult population, showing that cartilage is thicker with increased bone size, diaphysis size, and decreased femoral skew.31
Image Segmentation Using Active Shape Modeling
Segmentation of medical imaging data such as clinical CT is required to obtain anatomically accurate 3D models of joints for the purpose of biomechanical modeling or morphological analysis. Traditional manual and semiautomatic approaches are time-consuming and require human input to complete the segmentation of an image volume. Segmented data, such as point clouds or image contours, require meshing in order to be suitable for SSM, musculoskeletal modeling, and finite element analysis. Statistical shape models can be used to automate image segmentation. Active shape modeling32 is a well-established automatic segmentation method that utilizes a statistical shape model to make the segmentation robust to noise in the image. However, active shape modeling alongside other automatic segmentation methods such as region growing are reliant on correct initialization, linear search spaces perpendicular to the model surface, high contrast edges, and high resolution relative to object feature size.
An alternative approach is to use 3D random forest regression voting to train a forest of decision trees on randomly sampled image features (eg, 3D Haar-like features) to predict the most likely image location of the joint (Figure 4). During segmentation, statistical shape models can then be used to constrain the possible shape to produce realistic patient-specific meshes. In the TMC joint, we demonstrated this approach, with an average segmentation time of ∼2 minutes per joint and low segmentation errors of 1.1 mm RMS for the first metacarpal and 0.6 mm RMS for the trapezium.33
—Schematic of workflow to generate cartilage thickness field and bone shape model and classification of sex differences. MRI (n = 51) of the knee were segmented, processed in MAP Client, and resampled (A) to produce bone and cartilage point clouds. Parametric or correspondent bone point clouds were obtained via an iterative fitting process (B). Subchondral bone node numbers on these correspondent point clouds were found by combining node numbers obtained from all subjects using a closest-point algorithm (C). Cartilage thickness maps were calculated (D) by computing the magnitude of the projection of the closest articular cartilage point to the normal vector of each subchondral bone node. Principal component analysis (E) was performed on features consisting of the corresponding nodal coordinates of the bone and the cartilage thickness per subchondral node to produce a statistical model of the cartilage thickness and bone shape. A 3D scatter of principal component 1, 2, and 4 of the training set was plotted by sex (F), showing the decision boundary plane (gray) of the logistic regression model, and a vector (green) that passes through the average male and female knee. MRI indicates magnetic resonance imaging; PC, principal components; 3D, 3-dimensional.
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
Statistical Shape Models to Characterize a Pediatric Population
One of the best examples of model personalization is the understanding that population variation is quite different in the pediatric population. Children and infants are not simply small adults for the purpose of model customization. Furthermore, conditions such as developmental hip dysplasia, cerebral palsy (CP), and slipped capital femoral epiphysis can lead to complex hip and knee deformities in pediatric and adolescent patients.34-37 For example, slipped capital femoral epiphysis is a hip disorder seen predominantly in overweight adolescents that affects the femoral growth plate, creating a 3-dimensional deformity in the proximal femoral neck.34,35 The prevalence of slipped capital femoral epiphysis is unusually high in New Zealand, with 4.2 and 5.6 times higher frequency rates reported in the Māori and Pacific population compared with the New Zealand European population.37,38 CP is another condition that leads to complex joint deformities and is the most common cause of childhood disability affecting 1 in 325 children and growing.39,40 CP leads to a spectrum of impairments, including epilepsy, impaired cognition and deficits in motor planning, balance, and posture, often accompanied by musculoskeletal deformities. Between 50% and 60% of children with CP are ambulatory, but experience limitations in their walking skills and physical activity. Because the effects of CP are heterogeneous, the outcomes of therapy and surgical interventions are variable, which make it difficult to quantify efficacy of an individual treatment, or know which interventions are most effective for which child.
The variability in pediatric conditions necessitate patient-specific assessment to provide personalized treatments. Three-dimensional gait analysis is offered to most ambulatory children with CP to evaluate their lower limb impairments. It often uses optical motion capture to evaluate pelvis, hip, knee, and ankle movement during gait. Three-dimensional gait analysis has transformed the treatment of CP, enabling critical preoperative assessment of the specific pathologies of the patient, and postoperative assessment of outcome. In this manner, 3-dimensional gait analysis has become an essential tool in the treatment of CP.41 Modern approaches to the biomechanical analysis of gait often rely on the use of lower-limb musculoskeletal models, such as those used in OpenSim.7 These computational models have provided new ways to study muscle and joint function during motion and elucidate effects of musculoskeletal deformities on gait dynamics.42,43 However, these models are typically based on a generic bone geometry model, which takes into account the subject’s skeletal dimensions by linear scaling of template models. Alternatively, personalized models can be built based on information from magnetic resonance images. Image-based subject-specific models show much promise for predicting functional or clinical outcomes.44-46 However, creating subject-specific models is time-consuming, costly, and requires a very high level of expertise. Solving this challenge is a significant step toward bringing computational modeling into the clinic. The population-based MAP software platform contains imaging and functional data obtained from hundreds of adults,47,48 and is currently being extended to a pediatric population. The scientific and pediatric clinical community will benefit greatly from a pediatric population-based anatomical and functional atlas that is capable of predicting the form–function relationships of the musculoskeletal system.
Lower Limb Bones Shape Variation in Children Aged 4–18 Years
To build this pediatric population-based model, we have obtained a data set of 333 postmortem CT scans of children aged 4–18 years from the Victorian Institute of Forensic Medicine49 with ethical approval. From this data set, we have segmented the pelvis, femur, and tibia/fibula and performed a generalized Procrustes analysis to understand the variation in bone shape from this population. In the Procrustes analysis, the bones are freely adjusted in space and size to be aligned to their barycenter and uniformly scaled to a template bone shape, one for the pelvis, femur, and tibia/fibula. Then we performed a PCA to compute the different modes of shape variation from our population. The pelvis and femur are shown as examples.
Pelvis
The first mode of variation accounted for 28% of the total variation in shape, which was observed to correspond to the shape variation between the anterior superior iliac spine (ASIS; iliac shape) and pelvis width at the ischial spine (Figure 5A). The second mode of variation accounted for 17% of the total pelvis shape variation which corresponded to the shape variation in the iliac crest and pubic arch which is usually seen in female versus male differences in the adult population. The third mode of variation accounted for 9% of the variation which corresponded to the posterior superior iliac spine and the acetabulum shape.
—Procrustes analysis in the pelvis (A), femur (B), and tibia/fibula (C). In the middle is the mean shape, from top to bottom, the first 3 modes of variation represented by −2 and + 2 SD.
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
Femur
The first mode of variation accounted for 17% of the total variation in the femur, which corresponded to the variation in the lesser and greater tronchater (absent in the youngest participants) and condyles shape variation (which are not yet well defined in the smaller children; Figure 5B). The second mode of variation accounted for 14% of the total variation and was mainly defined by the change in the neck shaft angle and diaphysis width. The third mode of variation accounted for 9% of the variation and correlates with the change in femoral rotation (anteversion).
Tibia/Fibula
The first mode of variation accounted for 25% of the total shape variation and represented the change of tibia/fibula shape with age; definition of the condyles, medial malleolus; and the location of the fibula head with respect to the tibia (Figure 5C). The second mode of variation accounted for 13% of total variation and represented the relationship between the fibula and the tibia and the change in tibial width. The third mode of variation accounted for 11% and represented the change in fibula width and the definition of the head of the fibula and lateral malleolus.
Predicting Pediatric Bone Morphology Using Partial Least Squares Regression
Now that we understand the variation in shape for pediatric bones, we created a statistical shape model based on an unscaled PCA49 to be able to predict bone shape in children outside of our data set. A Partial Least Square Regression is commonly used21,50,51 to incorporate demographic information with principal component weights and modes to build statistical shape models of bones. A multiple comparison analysis previously showed that shape variation is highly correlated with the participant’s age, height, and mass and some key bony landmarks measurement such as the ASIS and posterior superior iliac spine width in the pelvis, epicondylar width and femoral length for the femur and tibial length, malleolar and condyle width in the tibia/fibula.49 By using these discrete variables, our statistical shape model can predict pelvis, femur, and tibia/fibula shape with an average root mean square error, between the segmented bone vertices and statistical shape model predictions, of 2.91 mm, 2.01 mm, and 1.85 mm, respectively (Figure 6, blue violin). This was a significant improvement compared with the root mean square error between the segmented bone vertices and the linearly scaled musculoskeletal models, such as typically performed in the scaling process of OpenSim7 (Figure 6, orange violin).
—The RMSE distances (in millimeters) between the segmented bone vertices from the CT scans (pelvis, femur, and tibia) and the resulting SSM prediction (SSM in blue), and between the segmented bone vertices and the isometric adult scaled model (scaled adult in orange). CIT indicates computed tomography; RMSE, root mean square error; SSM, statistical shape model.
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
Additionally, using the pediatric statistical shape model decreased the error in hip joint center prediction compared with linear scaling and regression analysis.52 Using the same data set, we found that the Euclidian distance error in hip joint center was, on average, 3 mm for the statistical shape model, 5.45 mm using the linear scaling method, and 6.24 mm when using regression equations. Our pediatric statistical shape model had lower error than our adult shape model,53 which was not unexpected given the variance of pediatric bone morphology compared to an adult cohort. Similar errors were found in another study using a combination of motion capture marker data, adult SSM, and sparse MRI information to predict hip joint center in 18 children (aged 6–18 y).54
Combined Shape Model of the Lower Limb for Musculoskeletal Modeling
After understanding shape variation for each individual bone, we combined the pelvis, femur, and tibia/fibula for each participant into a combined shape model of the lower limb. The bones were combined, and the shape model was characterized using a PCA.21 The predictive power of the shape model was assessed with a leave-one-out analysis using height, ASIS width, femur length, and tibial length, which were found to be the best predictive factors. The first 3 principal components (PCs) captured 92.5%, 2.07%, and 0.53% of the variation in the data set. The first mode of variation described combined size and shape variation and the second and third PCs described shape variation and the aspect ratio of the long bones. Despite the first mode of variation describing over 90% of the overall shape variation, it is quite different to a simple scaled model, such as that with OpenSIM. While size is a big factor, other fundamental shape variation exists, such as bony curvature and twist as previously demonstrated in a study of single bones.49 We have demonstrated that by scaling the average shape model of the pediatric population resulted in errors closer to the scaled adult OpenSim model compared to using the predicted bones from the unscaled statistical shape model with PC1 representing over 90% of total shape variation.49
The results from the leave-one-out analysis gave an average root mean square error of 2.94 (0.83) mm. Recent work has demonstrated the application of SSM to skeletal muscle in pediatric populations in both healthy and pathological cases,55 suggesting a vast landscape for continued development and integration of pediatric statistical shape models.
Personalizing 3D Models of Skeletal Muscle
Generation of muscle size, shape, and architecture data is essential for creating high-fidelity musculoskeletal models. Skeletal muscles are the unique drivers of movement in humans as the tissues that generate force for the body. The specific forces and contraction dynamics generated by skeletal muscles can be estimated accurately from their overall size, shape, and fiber arrangement.56 For this reason, accurate determination and recapitulation of muscle architecture is a critical step for generating subject-specific biomechanical models.
Muscle architecture describes the arrangement of muscle fibers within a muscle and involves measurements such as fascicle length, pennation angle, and Physiological Cross-Sectional Area. Full descriptions of each of these measurements have been offered in the past.56 Briefly, fascicle length represents the length of a muscle along the muscle fiber direction, pennation angle describes the angle between the muscle’s line of action and the direction of muscle fibers, and physiological cross-sectional area represents the cross-sectional area of a plane orthogonal to the muscle fiber direction. These measurements are important because they relate to functional metrics of the muscle’s mechanics: fascicle length indicates the muscle’s operating range of motion and its maximum velocity of contraction, pennation angle indicates the degree of fiber packing and the proportion of a muscle’s force which is transmitted to the tendon, and physiological cross-sectional area indicates the total force-generating capacity of a muscle where muscles with larger cross sections can generate larger forces.56
Subject-specific muscle shapes and sizes may be obtained from fully manual or semiautomatic segmentation of medical images.57-63 For skeletal muscle, MRI is a common modality for generating high-signal and high-contrast muscle images. Three-dimensional ultrasound has also shown promising advancements in determining 3D muscle shape and size in high fidelity64-66; however, these approaches are seldom used to generate data sets for multiple muscles and bones within a limb and are limited by deformation of superficial muscles caused by the pressure of the transducer on tissue.67 The process of image segmentation is time-consuming and prone to subjective error. Automatic approaches for determining subject-specific muscle shapes from MRI have included atlas-based methods68,69 and convolutional neural networks.53 Note that each of these methods requires input of previously segmented data for development and training of the tool. Thus, having access to large data sets of medical images and undertaking the challenge of manually or semiautomatically segmenting the muscles in these data sets is essential. Convolutional neural network tools work well at segmenting new data sets accurately based on previously segmented images introduced as training data.53 It remains to be seen how well these tools work with the introduction of data from participants with neuromuscular pathologies or other abnormalities. Continual development of these tools with larger and more diverse data sets will likely lead to fully automatic determination of muscle size and shape profiles. Fully segmented data sets can be used to assess subject-specific muscle volumes,57,58,70 which may indicate heterogeneity of impaired muscle growth57 or nonuniformity of hypertrophy patterns in athletic populations.70 Beyond this, muscle size and shape data derived from segmented images can be used to develop statistical shape models for assessing morphological variations within populations or between controls and pathological groups.55
Several imaging methods may be used to determine muscle fiber directions for use in subject-specific modeling such as 2D ultrasound or Diffusion Tensor Imaging (DTI). 2D ultrasound has been used to visualize fascicle direction and pennation angle in skeletal muscles in vivo. Limitations include the 2D nature of these measurements and deformation of superficial muscles with the transducer.67 Nevertheless, 2D ultrasound has been used successfully in the past to inform muscle architecture.71-73 DTI is an MRI method capable of estimating 3D muscle architecture by imaging fluid diffusion in multiple directions and solving for principal direction of diffusion.74 Tractography algorithms can improve estimates for muscle architecture by discarding regions of voxels containing spurious directions. While DTI can be expensive and time-consuming, it generates in vivo 3D muscle fiber architecture data that can be applied to subject-specific musculoskeletal models. Some limitations of DTI include its cost, deviations between the true fiber direction and direction determined from DTI, noise associated with the method, and regions of muscle that may lack any fiber directions after DTI tractography. The latter 2 limitations can be a challenge for applying DTI-derived fiber architecture directly to 3D musculoskeletal models. Computational methods, on the other hand, exist that can create smooth and continuous fields of muscle fiber architecture for use in biomechanical modeling.75-79
Template mapping is a technique whereby a template shape of muscle architecture is fit to a subject-specific 3D surface of a muscle.75 In this method, the subject-specific 3D shape of a muscle is extracted from segmented MRI data. Generic anatomical knowledge of that muscle would then be used to develop or choose a fiber template consistent with the generic architecture of that muscle. The template would then be mapped onto the subject’s 3D muscle shape data to generate a volumetric mesh that includes subject-specific shape and generic muscle architecture data.
Computational fluid dynamics (CFD) approaches are another technique that takes a generic principle applied to subject-specific muscle geometries obtained from imaging. Choi and Blemker76 introduced this technique in recognition of the apparent similarity between muscle architecture and the streamlines resulting from Laplacian flow. In this technique, the proximal and distal aponeuroses (ie, the muscle fibers’ origin and insertion) act as the inlet and outlet, respectively, for an incompressible fluid where all other muscle surfaces are defined as impenetrable. Subsequent work has demonstrated close similarity between muscle fiber directions observed in vivo with DTI and those predicted from CFD,77–79 and have taken advantage of these methods to generate local fiber directions in mechanical finite element simulations.77,79,80 It should be noted that, thus far, CFD muscle tractography has been demonstrated for 21 muscle architectural arrangements including the soleus, gastrocnemius, iliacus, adductor magnus, adductor brevis, gluteus maximus, vastus lateralis, deltoid, rectus femoris, tibialis anterior, biceps femoris, the palate muscles levator veli palatini and palatopharyngeus, 8 muscles in the tongue, as well as the Achilles tendon.76-78,80 Application to more anatomical shapes with a variety of architectures remains an exciting area of future exploration and development. With its ability to produce smooth, continuous, and dense muscle fiber architecture throughout a 3D muscle volume, this simulation technique is attractive for use in modeling applications. Currently, 3D muscle volumes are determined subject specifically while location of inlet and outlet boundaries are generally estimated from anatomical resources.78 With recent advances in tendon imaging,81 it may be possible to determine all the needed information from in vivo imaging (Figure 7). A combination of high-contrast muscle MRI with dual echo ultrashort echo time sequences tuned to maximize tendon contrast could then produce all of the inputs for CFD tractography, and yielding a fully subject-specific approach to determine muscle architecture for musculoskeletal models. Adding DTI to this workflow would allow for validation of the method or, alternatively, a hybrid approach taking DTI data as a soft constraint while solving the Laplace equation for muscle tractography. To the authors’ knowledge, such a hybrid approach has not yet been fully developed and tested but sufficient imaging data sets and implementation may occur in the coming years.
—Proposed pipeline for high-fidelity modeling of subject-specific muscle architecture. MRI is used to collect high-contrast muscle images, dual-echo UTE images for high connective tissue signal, and DTI images. The muscle of interest can be segmented (medial gastrocnemius segmented in grey) to generate a 3D digital model of the muscle. In parallel, proximal (red) and distal (blue) aponeuroses can be identified from dual-echo UTE images. The 3D model and the aponeuroses’ locations provide all the necessary inputs for a Laplacian flow simulation, which generates 3D muscle fiber architecture data that is smooth, dense, and continuous. DTI muscle tracts can offer validation or used in a hybrid mode to inform the Laplacian simulation. DTI indicates diffusion tensor imaging; MRI, magnetic resonance imaging; UTE, ultrashort echo time; 3D, three dimensional.
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
Subject-specific modeling in biomechanics is a goal that has spanned several decades. The ultimate goal is to be able to create hyperrealistic models of a living individual’s biomechanics, such that the model can be probed and studied to improve body mechanics, prevent injury, promote recovery, and myriad other potential applications. Due to the critical aspects of muscle architecture to the function of the musculoskeletal system, it is essential that muscle architecture is captured and recapitulated in order to generate high-fidelity subject-specific models. Pipelines that involve advanced imaging, particularly those that can capture both muscle and connective tissue, and methods like CFD tractography can generate subject-specific 3D descriptions of muscle architecture and promote high-fidelity biomechanics modeling into the future.
The Future of the MAP
Personalizing computational musculoskeletal models using the MAP has advanced through the use of SSM integrated with MRI, CT, and ultrasound. The initial vision of the MAP was to provide a framework for biomechanics researchers to rapidly generate anatomical models of the musculoskeletal system. Image processing, meshing, and population-based modeling tools have been implemented with some early integration into other computational modeling packages, such as OpenSim and FEBio. As a global, open-source digital database, the MAP also forms as a repository for models and associated data, leaning heavily on the infrastructure provided by the Physiome Project. The full scale and potential of this tool will be realized in the coming years with several ongoing initiatives:
- 1.Inclusion of upper limb scaling tools: Much of our work has focused on building tools to reconstruct the lower limb,21,50 but recent efforts incorporate shape models of the spine,82 and upper limb, with the intention of providing whole-body scaling (in support of our Scaffold-maker, see below Figure 8).
- 2.Include scaling tools for soft tissue structures: We intend to incorporate 3-dimensional representation of muscles and connective tissue into our modeling framework,83 thus addressing limitations of using line-segment representations of muscle-tendon actuators. These data can also be used to estimate body segment parameters, which are particularly important for solving upper limb multibody dynamics problems. Statistical surrogate modeling of complex finite element simulations provide a mechanism to incorporate detailed soft tissue mechanics into musculoskeletal modeling simulation.84
- 3.Harmonize large existing data sets: Comparing experimental data across different research groups remains a major challenge limiting knowledge that could be gained from combining large data sets. Clinical gait analysis data, for example, can be challenging to share simply due to different experimental and modeling approaches, such as marker sets for motion capture, coordinate system definitions, and kinematic representations of joints.85 The use of statistical shape models provides an opportunity to harmonies these data and modeling processes, providing a constraint on feasible anatomical scaling, which can be agnostic to the marker set and prior kinematic modeling. We have already shown how shape model scaling can improve estimates of limb length scaling,86 anatomical joint centres,87 and repeatability of kinematic data.88
- 4.Integrate functional, wearable data using surrogate models: Characterizing the intricate form–function relationship of musculoskeletal tissues requires measurement of function as well as form. Our focus on reconstructing the tissue-level morphology provides sufficient detail to simulate 3-dimensional mechanics of bone, joints, and soft tissue. The inclusion of functional data within the MAP (including multiscale data) will provide a valuable resource for the biomechanics community to improve the accuracy and repeatability of computational models (as achieved by the Grand Knee Challenge data set44 and the KneeHUB reproducibility project.89,90
—(A) Model customization from a muscle scaffold. The scaffold for the brachioradialis muscle is customized to a subject-specific geometry with the pipeline in the Scaffold-Maker software. (B) Generation of the whole-body model by incorporating scaffolds of the musculoskeletal and other systems in the body.
Citation: Journal of Applied Biomechanics 39, 5; 10.1123/jab.2023-0079
The Future of Multiscale Models and Geometric Meshing in the Physiome Project—Scaffolds
“Scaffolds” are high-order (cubic Hermite basis function) finite element descriptions of organs that are designed to provide a reference material coordinate system for any organ across species and across populations. They were developed under the NIH-funded SPARC project (see SPARC Portal) in order to define common coordinate systems for embedding autonomic nervous system data in a way that would allow cross-species comparisons, that is, any aspect of the tissue material properties (such as protein expression levels) could be compared at the same anatomical location across for example mouse, rat, pig, and human. A finite element mesh of any type, appropriate for a particular computational study, can be created from the scaffolds.
The SPARC project was designed to map autonomic innervation for the visceral organs, but a new project called “12 Labors” integrated with the Physiome Project is now underway to establish multiscale computational models linked with clinical workflows for a number of other application areas, including neuromusculoskeletal applications. A scaffold for the whole-body has also been established, into which the organ scaffolds are embedded (Figure 8). Systems that connect organs, such as the vascular system and autonomic nervous system, are also embedded within the whole-body material coordinate system. Fitting the whole-body model to skin surface scan data is being used to personalize the model for clinical applications.
For this purpose, we have developed Computer Aided Design software called Scaffold-Maker (freely available for use at https://github.com/ABI-Software/scaffoldmaker) for creating 3D material coordinate systems for body organs including the musculoskeletal tissues. These coordinates are capable of identifying the position of any material locations within the tissue, independent of its location in 3D space as well as the extent of tissue deformation. It is called a “scaffold” because it is a coordinate framework into which many different features of tissue structures such as fiber orientations can be assembled and incorporated.91
Each scaffold is created with a generic geometry of the organ or tissue and is annotated with distinct regions (eg, muscle attachment points in the bones) as well as key anatomical locations. These are used in customizing the generic shape into subject-specific shapes by computing the optimum correspondence to the annotated coordinate data from the subject (Figure 8A). This feature can be extended to statistical shape models to describe population level variations in shape with 3D solid models.
Moreover, these organ scaffolds for bones and muscles as well as other key organs can be parametrically assembled into a whole-body model (Figure 8B) using the 3D body coordinate system which defines the material coordinates of each organ with respect to the whole body. Moving forward, this novel framework will allow us to build a true digital representation of ourselves that integrates machine learning and multiscale modeling to continuously learn and dynamically update itself as our environment changes in real time.
The Future of Musculoskeletal Modeling Tools
The open-source tools within the Musculoskeletal Atlas and Physiome projects developed over the last 20 years have enabled rapid personalization of musculoskeletal models from population data and have been shared and used by the wider biomechanics’ community. Particular efforts have been made to interface these tools with other popular biomechanics resources including OpenSIM and FEBio. Musculoskeletal models that are personalized have been demonstrated to produce better model-based recommendations. A future modeling challenge for the biomechanics community is linking personalized rigid body and finite element models together consistently. As the community moves forward extending efforts from neurotypical adults to pediatric and pathological populations, it is essential that the community remains open-source and ensures developed tools are integrated with existing resources, are well-documented, and shared with the community to evaluate and consistently improve.
Acknowledgments
The authors acknowledge all members of the Auckland Bioengineering Institute who have contributed many of the tools discussed in this paper. Specific funding acknowledgement includes Aotearoa fellowships for Handsfield and Choisne, Health Research Council for Choisne, Royal Society New Zealand Marsden Fast-Start for Handsfield, Ministry of Business, Innovation, and Employment funding for Besier and Fernandez, and MBIE “12 Labors” funding for Hunter.
References
- 1.↑
Hunter PJ. The IUPS Physiome Project: a framework for computational physiology. Prog Biophys Mol Biol. 2004;85(2–3):551–569. doi:10.1016/j.pbiomolbio.2004.02.006
- 2.↑
Fernandez JW, Mithraratne P, Thrupp SF, Tawhai MH, Hunter PJ. Anatomically based geometric modelling of the musculo-skeletal system and other organs. Biomech Model Mechanobiol. 2004;2(3):139–155. doi:10.1007/s10237-003-0036-1
- 3.↑
Shim VB, Pitto RP, Streicher RM, Hunter PJ, Anderson IA. Development and validation of patient-specific finite element models of the hemipelvis generated from a sparse CT data set. J Biomech Eng. 2008;130(5):51010. doi:10.1115/1.2960368
- 4.↑
Fernandez JW, Ho A, Walt S, Anderson IA, Hunter PJ. A cerebral palsy assessment tool using anatomically based geometries and free-form deformation. Biomech Model Mechanobiol. 2005;4(1):39–56. doi:10.1007/s10237-005-0071-1
- 5.↑
Oberhofer K, Lorenzetti S, Mithraratne K. Host mesh fitting of a generic musculoskeletal model of the lower limbs to subject-specific body surface data: a validation study. Appl Bionics Biomech. 2019;2019:1351. doi:10.1155/2019/8381351
- 6.↑
Zhang J, et al. The MAP client: user-friendly musculoskeletal modelling workflows. Lec Notes Comput Sci. 2014;8789:182–192.
- 7.↑
Seth A, Hicks JL, Uchida TK, et al. OpenSim: simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. PLoS Comput Biol. 2018;14(7):e1006223. doi:10.1371/journal.pcbi.1006223
- 8.↑
Maas SA, Ellis BJ, Ateshian GA, Weiss JA. FEBio: finite elements for biomechanics. J Biomech Eng. 2012;134(1):11005. doi:10.1115/1.4005694
- 9.↑
Akhundov R, Saxby DJ, Diamond LE, et al. Is subject-specific musculoskeletal modelling worth the extra effort or is generic modelling worth the shortcut? PLoS One. 2022;17(1):e0262936. doi:10.1371/journal.pone.0262936
- 10.↑
Kainz H, Wesseling M, Jonkers I. Generic scaled versus subject-specific models for the calculation of musculoskeletal loading in cerebral palsy gait: effect of personalized musculoskeletal geometry outweighs the effect of personalized neural control. Clin Biomech. 2021;87:105402. doi:10.1016/j.clinbiomech.2021.105402
- 11.↑
Fernandez J, Sartori M, Lloyd D, Munro J, Shim V. Bone remodelling in the natural acetabulum is influenced by muscle force-induced bone stress. Int J Numer Method Biomed Eng. 2014;30(1):28–41. doi:10.1002/cnm.2586
- 12.↑
Funaro A, Shim V, Crouzier M, Mylle I, Vanwanseele B. Subject-specific 3D models to investigate the influence of rehabilitation exercises and the twisted structure on achilles tendon strains. Front Bioeng Biotechnol. 2022;10:914137. doi:10.3389/fbioe.2022.914137
- 13.↑
Sederberg TW, Parry SR. Free-form deformation of solid geometric models. ACM SIGGRAPH Comput Graph. 1986;20(4):151–160. doi:10.1145/15886.15903
- 15.↑
Jarvinen TA, Kannus P, Maffulli N, Khan KM. Achilles tendon disorders: etiology and epidemiology. Foot Ankle Clin. 2005;10(2):255–266. doi:10.1016/j.fcl.2005.01.013
- 16.↑
Wren TA, Lindsey DP, Beaupré GS, Carter DR. Effects of creep and cyclic loading on the mechanical properties and failure of human Achilles tendons. Ann Biomed Eng. 2003;31(6):710–717. doi:10.1114/1.1569267
- 17.↑
Shim VB, Fernandez JW, Gamage PB, et al. Subject-specific finite element analysis to characterize the influence of geometry and material properties in Achilles tendon rupture. J Biomech. 2014. 47(15):3598–3604. doi:10.1016/j.jbiomech.2014.10.001
- 18.↑
Shim VB, Hansen W, Newsham-West R, et al. Influence of altered geometry and material properties on tissue stress distribution under load in tendinopathic Achilles tendons—a subject-specific finite element analysis. J Biomech. 2019;82:142–148. doi:10.1016/j.jbiomech.2018.10.027
- 19.↑
Theobald P, Benjamin M, Nokes L, Pugh N, et al. Review of the vascularisation of the human Achilles tendon. Injury. 2005;36(11):1267–1272. doi:10.1016/j.injury.2005.02.012
- 20.↑
van Buuren MMA, Arden NK, Bierma-Zeinstra SMA, et al. Statistical shape modeling of the hip and the association with hip osteoarthritis: a systematic review. Osteoarthritis Cartilage. 2021;29(5):607–618. doi:10.1016/j.joca.2020.12.003
- 21.↑
Zhang J, Fernandez J, Hislop-Jambrich J, Besier TF. Lower limb estimation from sparse landmarks using an articulated shape model. J Biomech. 2016;49(16):3875–3881. doi:10.1016/j.jbiomech.2016.10.021
- 22.↑
Heimann T, Meinzer HP. Statistical shape models for 3D medical image segmentation: a review. Med Image Anal. 2009;13(4):543–563. doi:10.1016/j.media.2009.05.004
- 24.↑
Fernandez J, et al. On the Use of Population-based Statistical Models in Biomechanics. Elsevier; 2019.
- 25.↑
Baldwin MA, Langenderfer JE, Rullkoetter PJ, Laz PJ. Development of subject-specific and statistical shape models of the knee using an efficient segmentation and mesh-morphing approach. Comput Methods Programs Biomed. 2010;97(3):232–240. doi:10.1016/j.cmpb.2009.07.005
- 26.
Bredbenner TL, Eliason TD, Potter RS, Mason RL, Havill LM, Nicolella DP. Statistical shape modeling describes variation in tibia and femur surface geometry between Control and Incidence groups from the osteoarthritis initiative database. J Biomech. 2010;43(9):1780–1786. doi:10.1016/j.jbiomech.2010.02.015
- 27.
Rao C, Fitzpatrick CK, Rullkoetter PJ, Maletsky LP, Kim RH, Laz PJ. A statistical finite element model of the knee accounting for shape and alignment variability. Med Eng Phys. 2013;35(10):1450–1456. doi:10.1016/j.medengphy.2013.03.021
- 28.↑
Smoger LM, Shelburne KB, Cyr AJ, Rullkoetter PJ, Laz PJ. Statistical shape modeling predicts patellar bone geometry to enable stereo-radiographic kinematic tracking. J Biomech. 2017;58:187–194. doi:10.1016/j.jbiomech.2017.05.009
- 29.↑
Schneider M, Zhang J, Walker CG, et al. Early morphologic changes in trapeziometacarpal joint bones with osteoarthritis. Osteoarthritis Cartilage. 2018;26(10):1338–1344. doi:10.1016/j.joca.2018.06.008
- 30.↑
Lynch JT, et al. Statistical Shape Modelling Reveals Large and Distinct Subchondral Bony Differences in Osteoarthritic Knees. Elsevier; 2019:177–184.
- 31.↑
Schneider MTY, Rooks N, Besier T. Cartilage thickness and bone shape variations as a function of sex, height, body mass, and age in young adult knees. Sci Rep. 2022;12(1):707. doi:10.1038/s41598-022-15585-w
- 32.↑
Cootes TF, Taylor CJ, Cooper DH, Graham J. Active shape models-their training and application. Comput Vis Image Underst. 1995;61(1):38–59. doi:10.1006/cviu.1995.1004
- 33.↑
Schneider MTY, Zhang J, Crisco JJ, et al. Automatic segmentation of the thumb trapeziometacarpal joint using parametric statistical shape modelling and random forest regression voting. Comput Methods Biomech Biomed Eng: Imaging Vis. 2019;7(3):297–301. doi:10.1080/21681163.2018.1501765
- 34.↑
Aronsson DD, Loder RT, Breur GJ, Weinstein SL. Slipped capital femoral epiphysis: current concepts. J Am Acad Orthop Surg. 2006;14(12):666–679. doi:10.5435/00124635-200611000-00010
- 35.↑
Ganz R, Horowitz K, Leunig M. Algorithm for femoral and periacetabular osteotomies in complex hip deformities. Clin Orthop Relat Res. 2010;468(12):3168–3180. doi:10.1007/s11999-010-1489-z
- 36.
Pirpiris M, Trivett A, Baker R, Rodda J, Nattrass GR, Graham HK. Femoral derotation osteotomy in spastic diplegia. proximal or distal? J Bone Joint Surg Br. 2003;85(2):265–272. doi:10.1302/0301-620X.85B2.13342
- 38.↑
Loder RT, Skopelja EN. The epidemiology and demographics of slipped capital femoral epiphysis. ISRN Orthop. 2011;2011:486512. doi:10.5402/2011/486512
- 39.↑
Cans C, De-la-Cruz J, Mermet MA. Epidemiology of cerebral palsy. Paediatr Child Health. 2008;18(9):393–398. doi:10.1016/j.paed.2008.05.015
- 40.↑
Odding E, Roebroeck ME, Stam HJ. The epidemiology of cerebral palsy: incidence, impairments and risk factors. Disabil Rehabil. 2006;28(4):183–191. doi:10.1080/09638280500158422
- 41.↑
DeLuca PA, Davis RB 3rd, Ounpuu S, Rose S, Sirkin R. Alterations in surgical decision making in patients with cerebral palsy based on three-dimensional gait analysis. J Pediatr Orthop. 1997;17(5):608–614. doi:10.1097/01241398-199709000-00007
- 42.↑
Abel MF, Juhl GA, Vaughan CL, Damiano DL. Gait assessment of fixed ankle-foot orthoses in children with spastic diplegia. Arch Phys Med Rehabil. 1998;79(2):126–133. doi:10.1016/S0003-9993(98)90288-X
- 43.↑
Rosenberg M, Steele KM. Simulated impacts of ankle foot orthoses on muscle demand and recruitment in typically-developing children and children with cerebral palsy and crouch gait. PLoS One. 2017;12(7):e0180219. doi:10.1371/journal.pone.0180219
- 44.↑
Fregly BJ, Besier TF, Lloyd DG, et al. Grand challenge competition to predict in vivo knee loads. J Orthop Res. 2012;30(4):503–513. doi:10.1002/jor.22023
- 45.
Kinney AL, Besier TF, D'Lima DD, Fregly BJ. Update on grand challenge competition to predict in vivo knee loads. J Biomech Eng. 2013;135(2):021012. doi:10.1115/1.4023255
- 46.↑
Scheys L, Spaepen A, Suetens P, Jonkers I. Calculated moment-arm and muscle-tendon lengths during gait differ substantially using MR based versus rescaled generic lower-limb musculoskeletal models. Gait Posture. 2008;28(4):640–648. doi:10.1016/j.gaitpost.2008.04.010
- 47.↑
Killen BA, Brito da Luz S, Lloyd DG, et al. Automated creation and tuning of personalised muscle paths for OpenSim musculoskeletal models of the knee joint. Biomech Model Mechanobiol. 2021;20(2):521–533. doi:10.1007/s10237-020-01398-1
- 48.↑
Davico G, Lloyd DG, Carty CP, Killen BA, Devaprakash D, Pizzolato C. Multi-level personalization of neuromusculoskeletal models to estimate physiologically plausible knee joint contact forces in children. Biomech Model Mechanobiol. 2022;21(6):1873–1886. doi:10.1007/s10237-022-01626-w
- 49.↑
Carman L, Besier TF, Choisne J. Morphological variation in paediatric lower limb bones. Sci Rep. 2022;12(1):3251. doi:10.1038/s41598-022-07267-4
- 50.↑
Zhang J, Besier TF. Accuracy of femur reconstruction from sparse geometric data using a statistical shape model. Comput Methods Biomech Biomed Eng. 2017;20(5):566–576. doi:10.1080/10255842.2016.1263301
- 51.↑
Zhang J, Hislop-Jambrich J, Besier TF. Predictive statistical models of baseline variations in 3-D femoral cortex morphology. Med Eng Phys. 2016;38(5):450–457. doi:10.1016/j.medengphy.2016.02.003
- 52.↑
Carman L, Besier TF, Choisne J. Predicting the hip joint centre in children: new regression equations, linear scaling, and statistical shape modelling. J Biomech. 2022;142:111265. doi:10.1016/j.jbiomech.2022.111265
- 53.↑
Bahl JS, Zhang J, Killen BA, et al. Statistical shape modelling versus linear scaling: effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis. J Biomech. 2019;85:164–172. doi:10.1016/j.jbiomech.2019.01.031
- 54.↑
Davico G, Pizzolato C, Killen BA, et al. Best methods and data to reconstruct paediatric lower limb bones for musculoskeletal modelling. Biomech Model Mechanobiol. 2020;19(4):1225–1238. doi:10.1007/s10237-019-01245-y
- 55.↑
Bin Ghouth SG, Williams SA, Reid SL, Besier TF, Handsfield GG. A statistical shape model of soleus muscle morphology in spastic cerebral palsy. Sci Rep. 2022;12(1):7711. doi:10.1038/s41598-022-11611-z
- 56.↑
Lieber RL, Friden J. Functional and clinical significance of skeletal muscle architecture. Muscle Nerve. 2000;23(11):1647–1666. doi:10.1002/1097-4598(200011)23:11<1647::AID-MUS1>3.0.CO;2-M
- 57.↑
Handsfield GG, Meyer CH, Abel MF, Blemker SS. Heterogeneity of muscle sizes in the lower limbs of children with cerebral palsy. Muscle Nerve. 2016;53(6):933–945. doi:10.1002/mus.24972
- 58.↑
Handsfield GG, Meyer CH, Hart JM, Abel MF, Blemker SS. Relationships of 35 lower limb muscles to height and body mass quantified using MRI. J Biomech. 2014;47(3):631–638. doi:10.1016/j.jbiomech.2013.12.002
- 59.
Holzbaur KR, Murray WM, Gold GE, Delp SL. Upper limb muscle volumes in adult subjects. J Biomech. 2007;40(4):742–749. doi:10.1016/j.jbiomech.2006.11.011
- 60.
Noble JJ, Fry NR, Lewis AP, Keevil SF, Gough M, Shortland AP. Lower limb muscle volumes in bilateral spastic cerebral palsy. Brain Dev. 2014;36(4):294–300. doi:10.1016/j.braindev.2013.05.008
- 61.
Oberhofer K, Stott NS, Mithraratne K, Anderson IA. Subject-specific modelling of lower limb muscles in children with cerebral palsy. Clin Biomech.2010;25(1):88–94. doi:10.1016/j.clinbiomech.2009.09.007
- 62.
Nordez A, Jolivet E, Südhoff I, Bonneau D, de Guise JA, Skalli W. Comparison of methods to assess quadriceps muscle volume using magnetic resonance imaging. J Magn Reson Imaging. 2009;30(5):1116–1123. doi:10.1002/jmri.21867
- 63.↑
Sudhoff I, de Guise JA, Nordez A, et al. 3D-patient-specific geometry of the muscles involved in knee motion from selected MRI images. Med Biol Eng Comput. 2009;47(6):579–587. doi:10.1007/s11517-009-0466-8
- 64.↑
Barber L, Barrett R, Lichtwark G. Validation of a freehand 3D ultrasound system for morphological measures of the medial gastrocnemius muscle. J Biomech. 2009;42(9):1313–1319. doi:10.1016/j.jbiomech.2009.03.005
- 65.
Delcker A, Walker F, Caress J, Hunt C, Tegeler C. In vitro measurement of muscle volume with 3-dimensional ultrasound. Eur J Ultrasound. 1999;9(2):185–190. doi:10.1016/S0929-8266(99)00023-3
- 66.↑
MacGillivray TJ, Ross E, Simpson HA, Greig CA. 3D freehand ultrasound for in vivo determination of human skeletal muscle volume. Ultrasound Med Biol. 2009;35(6):928–935. doi:10.1016/j.ultrasmedbio.2008.11.013
- 67.↑
Bolsterlee B, Veeger HE, van der Helm FC, Gandevia SC, Herbert RD. Comparison of measurements of medial gastrocnemius architectural parameters from ultrasound and diffusion tensor images. J Biomech. 2015;48(6):1133–1140. doi:10.1016/j.jbiomech.2015.01.012
- 69.↑
Baudin PY, Azzabou N, Carlier PG, Paragios N. Automatic skeletal muscle segmentation through random walks and graph-based seed placement. 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), Barcelona, Spain, 2012, pp. 1036–1039. doi:10.1109/ISBI.2012.6235735
- 70.↑
Handsfield GG, Knaus KR, Fiorentino NM, Meyer CH, Hart JM, Blemker SS. Adding muscle where you need it: non-uniform hypertrophy patterns in elite sprinters. Scand J Med Sci Sports. 2017;27:1050–1060. doi:10.1111/sms.12723
- 71.↑
Ito M, Kawakami Y, Ichinose Y, Fukashiro S, Fukunaga T. Nonisometric behavior of fascicles during isometric contractions of a human muscle. J Appl Physiol. 1998;85(4):1230–1235. doi:10.1152/jappl.1998.85.4.1230
- 72.
Kawakami Y, Ichinose Y, Fukunaga T. Architectural and functional features of human triceps surae muscles during contraction. J Appl Physiol. 1998;85(2):398–404. doi:10.1152/jappl.1998.85.2.398
- 73.↑
Narici MV, Binzoni T, Hiltbrand E, Fasel J, Terrier F, Cerretelli P. In vivo human gastrocnemius architecture with changing joint angle at rest and during graded isometric contraction. J Physiol. 1996;496(1):287–297. doi:10.1113/jphysiol.1996.sp021685
- 74.↑
Heemskerk AM, Damon BM. Diffusion tensor MRI assessment of skeletal muscle architecture. Curr Med Imaging Rev. 2007;3(3):152–160. doi:10.2174/157340507781386988
- 75.↑
Blemker SS, Delp SL. Three-dimensional representation of complex muscle architectures and geometries. Ann Biomed Eng. 2005;33(5):661–673. doi:10.1007/s10439-005-1433-7
- 76.↑
Choi HF, Blemker SS. Skeletal muscle fascicle arrangements can be reconstructed using a laplacian vector field simulation. PLoS One. 2013;8:576. doi:10.1371/journal.pone.0077576
- 77.↑
Gomez AD, Elsaid N, Stone ML, Zhuo J, Prince JL. Laplace-based modeling of fiber orientation in the tongue. Biomech Model Mechanobiol. 2018;17(4):1119–1130. doi:10.1007/s10237-018-1018-7
- 78.↑
Handsfield GG, Bolsterlee B, Inouye JM, Herbert RD, Besier TF, Fernandez JW. Determining skeletal muscle architecture with Laplacian simulations: a comparison with diffusion tensor imaging. Biomech Model Mechanobiol. 2017;16(6):1845–1855. doi:10.1007/s10237-017-0923-5
- 79.↑
Varvik J, Besier TF, Handsfield GG. Computational fluid dynamics simulations for 3D muscle fiber architecture in finite element analysis: comparisons between computational fluid dynamics and diffusion tensor imaging. Int J Numer Method Biomed Eng. 2021;37(12):e3521. doi:10.1002/cnm.3521
- 80.↑
Knaus KR, Handsfield GG, Blemker SS. A 3D model of the soleus reveals effects of aponeuroses morphology and material properties on complex muscle fascicle behavior. J Biomech. 2022. 130:110877. doi:10.1016/j.jbiomech.2021.110877
- 81.↑
Handsfield GG, Greiner J, Madl J, et al. Achilles subtendon structure and behavior as evidenced from tendon imaging and computational modeling. Front Sports Act Living. 2020;2:70. doi:10.3389/fspor.2020.00070
- 82.↑
Yeung S, Toor A, Deib G, Zhang J, Besier T, Fernandez J. Relationship between lower lumbar spine shape and patient bone metabolic activity as characterised by (18)F NaF bio-markers. Comput Biol Med. 2020;116:103529. doi:10.1016/j.compbiomed.2019.103529
- 83.↑
Yeung S, Fernandez JW, Handsfield GG, Walker C, Besier TF, Zhang J. Rapid muscle volume prediction using anthropometric measurements and population-derived statistical models. Biomech Model Mechanobiol. 2020;19(4):1239–1249. doi:10.1007/s10237-019-01243-0
- 84.↑
Pizzolato C, Shim VB, Lloyd DG, et al. Targeted Achilles tendon training and rehabilitation using personalized and real-time multiscale models of the neuromusculoskeletal system. Front Bioeng Biotechnol. 2020;8:878. doi:10.3389/fbioe.2020.00878
- 85.↑
Rooks NB, Besier TF, Schneider MTY. A parameter sensitivity analysis on multiple finite element knee joint models. Front Bioeng Biotechnol. 2022;10:841882. doi:10.3389/fbioe.2022.841882
- 86.↑
Bakke D, Besier T. Shape-model scaled gait models can neglect segment markers without consequential change to inverse kinematics results. J Biomech. 2022;137:111086. doi:10.1016/j.jbiomech.2022.111086
- 87.↑
Bakke D, Zhang J, Hislop-Jambrich J, Besier T. Hip centre regression progression: same equations, better numbers. J Biomech. 2023. 147:111418. doi:10.1016/j.jbiomech.2022.111418
- 88.↑
Bakke D, Besier T. Shape model constrained scaling improves repeatability of gait data. J Biomech. 2020;107:109838. doi:10.1016/j.jbiomech.2020.109838
- 89.↑
Erdemir A, Besier TF, Halloran JP, et al. Deciphering the “art” in modeling and simulation of the knee joint: overall strategy. J Biomech Eng. 2019;141(7):0710021–07100210. doi:10.1115/1.4043346
- 90.↑
Rooks NB, Schneider MTY, Erdemir A, et al. Deciphering the “art” in modeling and simulation of the knee joint: variations in model development. J Biomech Eng. 2021;143(6):28. doi:10.1115/1.4050028
- 91.↑
Osanlouy M, Bandrowski A, de Bono B, et al. The SPARC DRC: building a resource for the autonomic nervous system community. Front Physiol. 2021;12:693735. doi:10.3389/fphys.2021.693735
- 92.↑
Schneider M. Random Forest Regression Voting Automatic Shape Model Segmentation. The University of Auckland; 2022.
