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Host Mesh Fitting of a Generic Musculoskeletal Model of the Lower Limbs to Subject-Specific Body Surface Data: A Validation Study

Host Mesh Fitting of a Generic Musculoskeletal Model of the Lower Limbs to Subject-Specific Body... Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 8381351, 8 pages https://doi.org/10.1155/2019/8381351 Research Article Host Mesh Fitting of a Generic Musculoskeletal Model of the Lower Limbs to Subject-Specific Body Surface Data: A Validation Study 1 1,2 3 Katja Oberhofer , Silvio Lorenzetti , and Kumar Mithraratne Institute for Biomechanics, Department of Health Sciences and Technology, ETH Zurich, Leopold-Ruzicka-Weg 4, 8093 Zürich, Switzerland Swiss Federal Institute of Sport, Magglingen, Switzerland The Bioengineering Institute, University of Auckland, Auckland, New Zealand Correspondence should be addressed to Katja Oberhofer; katja.oberhofer@hest.ethz.ch Received 31 August 2018; Revised 26 November 2018; Accepted 10 January 2019; Published 17 February 2019 Guest Editor: Ozan Erol Copyright © 2019 Katja Oberhofer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Challenges remain in accurately capturing the musculoskeletal geometry of individual subjects for clinical and biomechanical gait analysis. The aim of this study was to use and validate the Host Mesh Fitting (HMF) technique for fitting a generic anatomically based musculoskeletal model to 3D body surface data of individual subjects. The HMF technique is based on the free-form idea of deforming geometrically complex structures according to the deformation of a surrounding volumetric mesh. Using the HMF technique, an anatomically based model of the lower limbs of an adult female subject (29 years) was customized to subject-specific skin surface data of five typically developing children (mean age 10.2 years) and six children with Cerebral Palsy (CP) (mean age 9.6 years). The fitted lengths and volumes of six muscle-tendon structures were compared against measures from Magnetic Resonance (MR) images for validation purposes. The HMF technique resulted in accurate approximations of the lower limb shapes of all subjects in both study groups. The average error between the MR data and the fitted muscle-tendon lengths from HMF was 4±4% in children without CP and 7± 5% in children with CP, respectively. The average error between the MR data and the fitted muscle volumes from HMF was 28 ± 19% in children without CP and 27 ± 28% in children with CP, respectively. This study presents a crucial step towards personalized musculoskeletal modelling for gait analysis by demonstrating the feasibility of fitting a generic anatomically based lower limb model to 3D body surface data of children with and without CP using the HMF technique. Additional improvements in the quality of fit are expected to be gained by developing age-matched generic models for different study groups, accounting for subject-specific variations in subcutaneous body fat, as well as considering supplementary data from ultrasound imaging to better capture physiological muscle tissue properties. 1. Introduction optical motion capture with computational models of the musculoskeletal system, crucial insights have been gained Computer models of the musculoskeletal system have widely into, e.g., muscle-tendon length changes during walking in been applied to biomechanical and clinical gait analysis. patients with Cerebral Palsy (CP) to help in the targeted Musculoskeletal modelling has provided means to quantify treatment intervention [1], as well as served as intermediate muscle and joint function during walking that cannot be step for calculating muscle-tendon forces and joint loading to assist with rehabilitation intervention and monitoring [2]. measured otherwise. In particular, muscular weaknesses or bilateral asymmetries can result in altered and potentially Generic musculoskeletal models of the lower limbs have harmful internal tissue loading which cannot be investigated traditionally been adopted and crudely scaled to subject- based on external observation alone. By combining data from specific dimensions in order to analyze biomechanical 2 Applied Bionics and Biomechanics musculoskeletal model of the lower limbs of an adult female parameters such as joint forces, muscle-tendon lengths, or lengthening velocities during gait for individual subjects [1, subject to 3D body surface data of children with and without 3, 4]. Thereby, the term “generic” refers to a reference model CP and compare the fitted lengths and volumes of six muscle-tendon structures with the subject-specific muscle- or data set, commonly resembling the anatomy of an adult male or female subject without musculoskeletal injury or dis- tendon lengths and volumes derived from MR data. The ease. In recent years, more advanced optimization algorithms use of 3D body surface data and HMF for fitting musculo- have been introduced in an effort to improve the accuracy of skeletal models to individual subjects is expected to be partic- musculoskeletal modelling results for personalized gait anal- ularly suited for gait analysis in population groups where bony anatomical landmarks are not sufficiently accurate ysis [5–8]. Yet, the most widely used fitting algorithms remain based on the positions of bony anatomical land- and MR scanning not applicable due to time, cost, or ethical constraints. marks, assuming that the skeletal system sufficiently reflects the subject-specific architecture of the entire mus- culoskeletal system. 2. Materials and Methods There is growing evidence that the fitting of musculoskel- 2.1. Volumetric Host Mesh Fitting. In the following, the theo- etal models based on bony anatomical landmarks may lead to retical principles of the HMF technique are summarized. incorrect conclusions, especially for clinical gait analysis in Given a generic 3D model of the musculoskeletal system with patients with severe musculoskeletal impairments due to embedded tissue structures (e.g., muscles-tendon structures conditions such as CP. Muscle architecture has been found and bones of the lower limbs) and subject-specific skin sur- to be significantly altered due to CP [9–11], and bone defor- face data, the HMF process is divided into four steps mities, commonly observed in children with CP, have been (Figure 1). shown to significantly affect joint kinematics, muscle- In Step I “Model registration,” the generic lower body tendon lengths, and muscle moment arms during walking mesh is aligned and homogenously scaled to subject- [12, 13]. Furthermore, bone deformities in the distal seg- specific dimensions by calculating an overall affine transfor- ments have been related to altered joint kinematics in the mation matrix using the conventional positions of bony ana- proximal joints and vice versa [14], and changes in the path tomical landmarks. The affine transformation matrix of one muscle-tendon structure may affect the paths of comprises rotation, scaling, shearing, and translation and is neighboring muscles and hence the dynamics of the entire obtained by minimizing the distances between bony anatom- multibody musculoskeletal system. Such local differences in ical landmarks of the generic model and manually annotated musculoskeletal architecture cannot be captured using subject-specific bony landmarks. In Step II “Recording local generic musculoskeletal models that are simply scaled based muscle position,” the material positions of the muscle- on the positions of bony anatomical landmarks. tendon structures of the generic model are calculated with Magnetic Resonance (MR) and ultrasound imaging pro- respect to the surrounding 3D lower body mesh in prepara- vide additional insights into the musculoskeletal architecture tion for skin mesh fitting. In Step III “Data fitting of skin of individual subjects and have been considered for applica- mesh,” the registered lower body mesh is customized to tion to clinical gait analysis. Novel algorithms have been subject-specific 3D body surface data to find the optimum developed to automatically segment MR images based on mesh nodal degrees of freedom (i.e., mesh nodal parameters, previous knowledge from generic image data sets [15, 16]; including nodal positions as well as nodal derivatives in the and fitting techniques have been introduced to morph case of bicubic-linear interpolation functions). In brief, the generic models of individual organs to a limited number of HMF objective function F u is set up to find the optimum subject-specific MR images [17–19]. Yet, the implementation mesh nodal parameters u that minimize the Euclidean of image-based fitting algorithms to widespread clinical prac- n distances between the subject-specific data points and their tice has often been a challenge due to long acquisition times projections onto the lower body mesh in a least-square of MR imaging as well as high imaging and computational sense as follows: costs. The integration of ultrasound imaging to gait analysis is considered more feasible; yet, ultrasound imaging is con- D N fined to a small imaging field of view, e.g., calf muscles, and F u = 〠 〠 φ p u − s + δ u , γ , 1 thus requires additional means of fitting the entire multibody n d n d n n i d=1 n=1 musculoskeletal system to individual subjects [20]. The aim of this study was to use a free-form deformation whereby p denotes the coordinates of the projection technique known as Host Mesh Fitting (HMF) for fitting points d =1,… , D with respect to the lower body mesh, generic musculoskeletal models to 3D body surface data of and s is the corresponding global coordinates of the individual subjects and assess its accuracy in an effort to subject-specific target points, and δ u , γ is a 3D address the persisting limitations in musculoskeletal model- n i ling for personalized gait analysis. The HMF technique was smoothing constraint called Sobolev function with user- initially introduced to develop subject-specific 3D models of defined penalty parameters γ ∈ 0, 1 for controlling arc individual organs [18] and was later applied and validated lengths, curvatures in element coordinate directions, for predicting the deformation of muscle-tendon structures surfaces area terms, and volume of the lower body mesh. in the lower limbs during walking [21]. The present work Further details to the HMF objective function and 3D extends on these previous efforts by aiming to fit a generic smoothing constraints can be found in [18, 21]. Finally, Applied Bionics and Biomechanics 3 Generic model Model (i) registration Recording local Bony landmarks (ii) muscle position Data fitting (iii) Skin boundary of skin mesh Subject-specific model Updating new (iv) muscle position Customized model Figure 1: The HMF technique is divided into four steps: (I) model registration based on bony landmarks; (II) recording of muscle-tendon nodal parameters with respect to generic lower body mesh; (III) customization of lower body mesh to subject-specific body shape data; and (IV) updating muscle-tendon nodal parameters according to customized skin mesh. Previously acquired MR images of children with and without CP [11] were used for validation purposes in the present work. in Step IV “Updating new muscle position,” the spatial specific data of children with and without CP and comparing positions of the muscle-tendon structures are calculated the predicted muscle-tendon lengths and volumes of the according to the customized position of the lower body fitted model with subject-specific MR data. A generic lower mesh. This is carried out under the assumption that the limb model of an adult female subject, which was previously material positions of the muscle-tendon structures with manually developed based on subject-specific MR data [21], respect to the surrounding 3D lower body mesh do not was used (age 29 y, height 165 cm, and weight 63 kg) for this change during customization. purpose. The lower limb model comprised all lower limb The HMF algorithm is implemented in the modelling bones, 20 muscles-tendon structures, and a volumetric environment CMISS (http://www.cmiss.org). CMISS is an representation of the skin boundary surface of each leg. All interactive computational modelling environment for Con- geometries of the musculoskeletal lower limb model were tinuum Mechanics, Image analysis, Signal processing, and represented using high-order finite element meshes with System identification, which has extensively been used for bicubic-linear interpolation functions. Cubic interpolation high-order subject-specific modelling of the musculoskeletal functions preserve the continuity of the first derivatives of system [11, 18, 21, 22]. CMISS has been developed as part the geometric coordinates with respect to the element coordi- of the International Union of Physiological Sciences (IUPS) nates, which makes them ideal for smoothly approximating Physiome Project [17, 19] and is currently being redeveloped the curved surfaces of biological tissue with a minimum into the open source package Open-CMISS to make it more number of elements [21]. modular, extendable, easier to understand, and able to run MR images of the lower limbs of six children with CP on modern distributed-memory high-performance com- (mean age 9.6 years) and five typically developing children puters (http://www.opencmiss.org). (mean age 10.2 years) were acquired on a Siemens 1.5T MAGENTOM Avanto System. Ethical approval was given 2.2. Validation. The accuracy of the HMF technique was by the NZ Northern Y Regional Ethics Committee, reference assessed by fitting a generic lower limb model to subject- number NTY/06/07/064. Written consent was obtained from 4 Applied Bionics and Biomechanics boundary of each subject were used for the fitting process. all children and their parents or guardians. Subject character- istics and scan protocol have previously been outlined in The HMF technique resulted in smooth approximations of detail [11]. The image processing tools within CMISS were the lower body shapes of all subjects in both study groups employed to automatically segment the skin boundary sur- (Figure 2). The average Root Mean Square (RMS) error faces of the lower limbs. The positions of the following bony between the fitted lower body mesh and the subject-specific landmarks on the skin surface were manually identified surface data from MR imaging was 3 7±1 08 mm. according to standard protocols [23]: right/left asis, sacrum, The average normalized muscle-tendon lengths derived medial/lateral epicondyles, and medial/lateral malleoli. The from HMF compared to the subject-specific values from bony landmarks were used to register the generic model to MR images are given in Table 1. Statistical analysis revealed the subject-specific surface data (Step I, Figure 1). The lower that HMF led to accurate predictions of muscle-tendon body mesh was then customized to subject-specific skin sur- lengths in the children without CP for all muscles except rec- face data and the new configuration of each muscle-tendon tus femoris. In the children with CP, HMF led to accurate structure was calculated according to the customized lower predictions of muscle-tendon lengths for soleus, biceps body mesh (Steps II-IV, Figure 1). femoris, and the vasti group, while significant differences Muscle-tendon lengths and volumes of the fitted models were obtained between the fitted and the MR-based values were numerically derived and compared with subject-specific for gastrocnemius, semimembranosus-semitendinosus, and measures from MR images for validation purposes. The rectus femoris. The average fitting error (equation (2)) in following six muscles were included in the analysis: soleus, muscle-tendon lengths from HMF was 4±4% in the group gastrocnemius, semimembranosus and semitendinosus (rep- of children without CP and 7± 5% in the children with resented as one muscle), biceps femoris, and the vasti group. CP, respectively. Muscle-tendon lengths were defined as the average arc The average normalized muscle volumes derived from lengths between the most distal and most proximal ends of HMF compared to the subject-specific values from MR the muscle-tendon meshes, normalized with respect to images are given in Table 2. Overall, the prediction of muscle segmental lengths. Muscle volumes were derived by perform- volumes was poor, with an average fitting error (equation ing numerical quadrature over the parameterized meshes (2)) of 28 ± 19% in children without CP and 27 ± 28% in chil- (Fernandez et al., 2005), divided by body mass. The fitting dren with CP, respectively. Statistical analysis revealed signif- error E was defined as the relative difference in muscle- icant differences in the predicted muscle volumes from HMF HMF tendon length l, i.e., muscle volume V, between the fitted compared to MR imaging for four muscles in the children values from HMF and the subject-specific values derived without CP (soleus, biceps femoris, rectus femoris, and vasti from the MR images: group) and for two muscles in the children with CP (biceps femoris, semimembranosus-semitendinosus). l − l l C MRI E = , HMF 4. Discussion MRI V − V V C MRI The aim of this study was to address current limitations in E = HMF subject-specific musculoskeletal modelling for personalized MRI gait analysis by applying and validating the HMF technique to fit a generic model to subject-specific 3D body surface 2.3. Statistical Analysis. Statistical analysis was performed to data. The HMF technique extends scaling of generic muscu- assess the significance of the differences in muscle-tendon loskeletal models based on bony anatomical landmarks in lengths and volumes between the fitted and the subject- that it comprises an affine transformation (rotation, transla- specific values from MR imaging. All parameters were tested tion, and scaling) followed by model customization to for a normal distribution prior to data comparison using the account for subject-specific variations in lower limb shape. Kolmogorov and Smirnov method [24]. A repeated measure High accuracies were obtained in the fitted lower limb shapes analysis of variance (ANOVA) with Tukey-Kramer multiple in both study groups with the RMS error between the post hoc test [25] was performed to analyze the pairwise dif- subject-specific 3D body surface data and the fitted lower ferences in muscle-tendon lengths and volumes between the limb mesh being less than 5 mm for all data points. The fitted and the subject-specific measures from MR imaging. accuracies in muscle-tendon lengths are also considered The data of the children with CP and without CP were promising for having the potential to improve gait analysis analyzed independently as two different groups. Statistical results, with an average RMS error of 4±4% in the children analysis was performed using the statistical software Graph- without CP and 7±5% in the children with CP, respectively Pad IntStat. The level of significance was set at p <0 05 for (Table 1). The average RMS errors in muscle-tendon lengths all statistical test. in both study groups are below, or around the lower range, of previously reported errors in muscle-tendon length predic- 3. Results tions using generic musculoskeletal models for clinical gait analysis, e.g., 6% to 50% [26]. However, the accuracies in A generic lower limb model of an adult female subject was fitted to skin surface data of children with and without CP muscle volumes were limited with large variations in both using the HMF technique. Eleven bony landmarks and an study groups compared to the subject-specific MR data average number of 1,858,218 (±845) data points on the skin (Table 2). Applied Bionics and Biomechanics 5 88 cm 64 cm 60 cm (a) (b) (c) Figure 2: (a) The generic lower limb model based on the anatomy of an adult female (Oberhofer et al. 2009). (b) A fitted lower limb model of a child without CP. (c) A fitted lower limb model of a child with CP. Leg lengths of each model, ranging from the hip joint center to the ankle joint center, are given as reference. Table 1: Average normalized muscle-tendon lengths (%) derived from the subject-specific MR images (MRI) compared to the predicted values from HMF for the children without CP and the children with CP. Children without CP Children with CP MRI HMF p value MRI HMF p value Soleus 71 (5.1) 71 (2.2) >0.05 66 (4.7) 69 (2.3) >0.05 <0.05 Gastrocnemius 60 (5.8) 56 (3.6) >0.05 51 (3.7) 55 (1.5) Biceps femoris 58 (4.6) 60 (1.7) >0.05 54 (3.7) 56 (4.8) >0.05 <0.01 Semi group 82 (3.3) 84 (3.7) >0.05 76 (7.2) 81 (3.7) ∗ ∗ <0.05 <0.01 Rectus femoris 76 (1.3) 79 (1.6) 68 (3.1) 75 (2.9) Vasti group 91 (4.1) 91 (5.0) >0.05 85 (2.1) 86 (2.7) >0.05 Difference between MRI and HMF statistically significant (repeated measures ANOVA with Tukey-Kramer multiple Comparison post hoc test, p <0 05). Table 2: Average muscle volumes cm /kg derived from the subject-specific MR images (MRI) compared to the predicted values from HMF for the children without CP and the children with CP. Children without CP Children with CP MRI HMF p value MRI HMF p value <0.01 Soleus 5.5 (0.84) 3.9 (0.30) 4.5 (1.56) 3.7 (0.51) >0.05 Gastrocnemius 4.4 (1.01) 3.6 (0.23) >0.05 3.1 (1.26) 3.6 (0.56) >0.05 ∗ ∗ <0.001 <0.001 Biceps femoris 2.3 (0.44) 3.5 (0.32) 1.6 (0.41) 3.5 (0.33) Semi group 5.1 (0.91) 5.0 (0.30) >0.05 3.9 (0.88) 5.5 (0.51) <0.01 <0.01 Rectus femoris 3.6 (0.69) 2.2 (0.22) 2.6 (0.63) 2.3 (0.63) >0.05 <0.05 Vasti group 20.3 (2.80) 16.7 (1.16) 15.9 (3.20) 16.5 (2.58) >0.05 Difference between MRI and HMF statistically significant (repeated measures ANOVA with Tukey-Kramer multiple comparison post hoc test, p <0 05). The HMF technique is established under the assump- had less subcutaneous fat compared to the adult female sub- tion that the lower limb shape reflects the internal ject, which could partly explain the unsatisfying prediction of musculoskeletal architecture, which is a limitation of the muscle volumes compared to muscle-tendon lengths. Inter- proposed technique. It means that the relative positions of estingly, the average RMS error for muscle volumes was muscle-tendon structures with respect to the skin mesh slightly lower for the children with CP than the children remain constant during model fitting. If, for example, a without CP, which is an unexpected result (Table 2). Based thick subcutaneous fat layer between muscles and skin is on the MR images (Figure 3), it appears as if the percentage present in the generic model, the relative thickness of the of muscle tissue versus fat tissue in children with CP more closely resembled the adult female anatomy, e.g., thicker fat fat layer remains the same throughout HMF. Looking more closely at the MR images (Figure 3), it becomes apparent layer with less muscle tissue, which may explain the unex- that significant differences existed in muscle volumes pected outcome. Thereby, the volumetric tissue distribution between individual subjects. In particular, children subjects critically affects the inertia properties of the multibody 6 Applied Bionics and Biomechanics Adult female subject Child without CP Child with CP (a) (b) (c) Figure 3: Representative MR image of the shank of (a) adult female subject, (b) child without CP, and (c) child with CP. dynamic system and hence gait analysis results. These on several 3D body surface scans that minimizes the defor- mation energy, corresponding to the elasticity of biological insights suggest that additional skin fold measurements may help to improve model fit by allowing to adjust the rel- soft tissue. The consideration of a so-called elastic potential ative thickness of the fat layer, and thus segmental inertia to find the optimum fit solution (equation (1)) while comply- properties, for individual subjects. ing to Newton’s laws of motion for soft tissue is promising The time needed to develop musculoskeletal models by and may offer the potential to improve the accuracy of the HMF fit for subjects with various degrees of subcutaneous manually segmenting MR images is lengthy and can take sev- eral months. Currently, the modelling software CMISS con- body fat versus muscle tissue. Additionally, data from ultrasound imaging may allow tains a library of MR-based lower limb models of one female subject, six children with CP, and five typically devel- further insights into mechanical tissue properties to oping children, which were adopted in the present work. The advance the HMF technique based on anatomically aware principles [20]. Capturing subject-specific mechanical prop- present goal to accurately fit a generic model of an adult female subject to the anatomy of children with severe gait erties of soft tissue is particularly important when aiming to impairments due to CP was ambitious. It is likely that more analyze kinetic variables, e.g., muscle forces, in patients accurate results can be obtained when fitting the generic with musculoskeletal disorders such as CP. Yet, taking model to subjects of similar age and without significant mus- subject-specific tissue samples in vivo for refining musculo- skeletal models remains highly invasive and very compro- culoskeletal impairments. Nevertheless, the present results are promising and considered the first step towards an mised. Ultrasound data would allow to better capture advanced modelling framework for subject-specific simula- mechanical properties of muscles at the tissue level, e.g., tion and analysis of human movement. In addition to the physiological cross-sectional area and fiber pennation angle, MR-based lower limb models within CMISS, data from gait which in turn affect muscle mechanics. Ultrasound imaging is relatively inexpensive, does not involve ionizing radia- analysis was acquired in the same subjects. This unique data- set will allow the comparison of muscle-tendon length calcu- tion, and requires much shorter scan times compared with lation during walking between generic and HMF-fitted other imaging modalities such as MR imaging. Thereby, an musculoskeletal models as a next step. Furthermore, an anatomically aware deformation method was recently intro- extension of the model library based on the Visible Human duced by Saito et al. [29] to predict the growth and size of muscles by discretizing the anisotropic stretch in the direc- Dataset from the U.S. National Library of Medicine, which includes Computed Tomography and MR images of one tion of muscle fibers. The integration of muscle fiber struc- male and one female cadaver, is planned. The Visible Human tures into the present musculoskeletal modelling approach Dataset has been applied to musculoskeletal research, edu- is highly feasible. In particular, a muscle fascicle description cational, virtual reality, industry, and diagnostic purposes has already successfully been integrated into the muscle organ models in CMISS and fitted to subject-specific ultra- and thus will provide widely accepted reference models for future use. sound data with good qualitative agreement to diffusion- The solution of the HMF objective function (equation weighted MR images [30]. (1)) is, in the present form, dependent on the geometry of In this study, the skin boundary surfaces of individual the lower body mesh (i.e., mesh nodal degrees of freedom) subjects were segmented based on MR data, though body surface scanning could be used to capture the outer skin sur- and the magnitudes of the Sobolev smoothing constraints. Both, the geometry of the lower body mesh and the Sobolev face of individual subjects in future work. Body surface scan- smoothing constraints, have not been linked to physiological ning, frequently used in anthropometric body shape analysis and obesity research, offers inexpensive, rapid, and noninva- or anatomically based principles but were defined according to previously established kinematic criteria [18]. Kinematic sive means to characterize the skin boundary in vivo [31] surface-based deformation methods have extensively been and would make the application of the HMF technique fea- used in computer graphics research [27]. Yet, they are tradi- sible in clinical settings. Thereby, the numerical algorithms tionally not considering biological soft tissue as elastic solids associated with HMF, as well as the library of MR-based subject to Newton’s laws of motion. In recent work, Kadleček musculoskeletal models, are currently transferred into the et al. [28] introduced a physics-based model fitting technique open source modelling environment Open-CMISS (http:// to find the optimum shape of a musculoskeletal model based www.opencmiss.org/) to provide the most advanced and Applied Bionics and Biomechanics 7 accessible numerical tools for physiologically based modelling Computational and Mathematical Methods in Medicine, vol. 2015, Article ID 483921, 12 pages, 2015. of deformable organs, e.g., muscle tissue across multiple scales, including multibody dynamic analysis [19, 21, 22, 30]. [3] M. D. Klein Horsman, H. F. J. M. Koopman, F. C. T. van der Helm, L. P. Prosé, and H. E. J. Veeger, “Morphological muscle and joint parameters for musculoskeletal modelling of the 5. Conclusions lower extremity,” Clinical Biomechanics, vol. 22, no. 2, pp. 239–247, 2007. The current study presents a crucial step towards personal- [4] I. Jonkers, C. Stewart, K. Desloovere, G. Molenaers, and ized human movement analysis by demonstrating the feasi- A. Spaepen, “Musculo-tendon length and lengthening velocity bility of fitting a generic musculoskeletal model of the lower of rectus femoris in stiff knee gait,” Gait & Posture, vol. 23, limbs to skin surface data of children with and without CP. no. 2, pp. 222–229, 2006. The musculoskeletal models of the lower limbs and fitting [5] U. Trinler and R. Baker, “Estimated landmark calibration of algorithms are planned to be further developed and shared biomechanical models for inverse kinematics,” Medical Engi- between research centers through the IUPS Physiome Project neering & Physics, vol. 51, pp. 79–83, 2018. [19] and coupled with experimentally measured gait data for [6] J. A. Reinbolt, J. F. Schutte, B. J. Fregly et al., “Determination of dynamic simulations of walking. Additional improvements patient-specific multi-joint kinematic models through in the quality of fit are expected to be gained by developing two-level optimization,” Journal of Biomechanics, vol. 38, age-matched generic models for different study groups, as no. 3, pp. 621–626, 2005. well as taking into account subject-specific skin fold mea- [7] M. E. Lund, M. S. Andersen, M. de Zee, and J. Rasmussen, sures and mechanical properties of muscle tissue based on “Scaling of musculoskeletal models from static and dynamic ultrasound imaging. It is anticipated that the application of trials,” International Biomechanics, vol. 2, no. 1, pp. 1–11, personalized musculoskeletal models to movement analysis will lead to crucial new insights into the complex relationship [8] P. Rymaszewski, C. Stewart, D. Blana, E. Chadwick, S. Sardar, between musculoskeletal architecture and function during and S. Jarvis, “Musculoskeletal modelling simulation with dynamic activities and thus assist in the assessment and optimisation to predict the morphological parameters of the management of movement pathologies due to conditions calf muscle,” Gait & Posture, vol. 57, pp. 87-88, 2017. such as CP. [9] R. Lampe, S. Grassl, J. Mitternacht, L. Gerdesmeyer, and R. Gradinger, “MRT-measurements of muscle volumes of the lower extremities of youths with spastic hemiplegia caused Data Availability by cerebral palsy,” Brain and Development, vol. 28, no. 8, pp. 500–506, 2006. The MR image data used for this study are restricted by the New Zealand Northern Y Regional Ethics Committee [10] A. A. Mohagheghi, T. Khan, T. H. Meadows, K. Giannikas, V. Baltzopoulos, and C. N. Maganaris, “Differences in gas- in order to protect patient privacy. The data is only avail- trocnemius muscle architecture between the paretic and able to researchers who meet the criteria for accessing the non-paretic legs in children with hemiplegic cerebral confidential data. Further information can be obtained palsy,” Clinical biomechanics, vol. 22, no. 6, pp. 718–724, from the corresponding author Dr. Katja Oberhofer (katja.oberhofer@hest.ethz.ch). [11] K. Oberhofer, N. S. Stott, K. Mithraratne, and I. A. Anderson, “Subject-specific modelling of lower limb muscles in children Conflicts of Interest with cerebral palsy,” Clinical Biomechanics, vol. 25, no. 1, pp. 88–94, 2010. All authors declare that they have no proprietary, financial, [12] T. A. Correa, R. Baker, H. Kerr Graham, and M. G. Pandy, professional, or other personal relationships or obligations “Accuracy of generic musculoskeletal models in predicting of any kind with other people or organisations that could the functional roles of muscles in human gait,” Journal of Bio- inappropriately influence their work. mechanics, vol. 44, no. 11, pp. 2096–2105, 2011. [13] L. Scheys, K. Desloovere, P. Suetens, and I. Jonkers, “Level of subject-specific detail in musculoskeletal models affects hip Acknowledgments moment arm length calculation during gait in pediatric sub- Funding for this study was provided by the New Zealand jects with increased femoral anteversion,” Journal of Biome- chanics, vol. 44, no. 7, pp. 1346–1353, 2011. Foundation for Research, Science and Technology. [14] A. Carriero, A. Zavatsky, J. Stebbins, T. Theologis, and S. J. Shefelbine, “Correlation between lower limb bone morphology References and gait characteristics in children with spastic diplegic cere- bral palsy,” Journal of Pediatric Orthopaedics, vol. 29, no. 1, [1] A. S. Arnold, M. Q. Liu, M. H. Schwartz, S. Õunpuu, and S. L. pp. 73–79, 2009. Delp, “The role of estimating muscle-tendon lengths and [15] B. Gilles and N. Magnenat-Thalmann, “Musculoskeletal MRI velocities of the hamstrings in the evaluation and treatment segmentation using multi-resolution simplex meshes with of crouch gait,” Gait & Posture, vol. 23, no. 3, pp. 273–281, medial representations,” Medical Image Analysis, vol. 14, no. 3, pp. 291–302, 2010. [2] F. Schellenberg, K. Oberhofer, W. R. Taylor, and S. Lorenzetti, “Review of modelling techniques for in vivo muscle force esti- [16] L. Scheys, K. Desloovere, A. Spaepen, P. Suetens, and mation in the lower extremities during strength training,” I. Jonkers, “Calculating gait kinematics using MR-based 8 Applied Bionics and Biomechanics kinematic models,” Gait & Posture, vol. 33, no. 2, pp. 158–164, [17] J. Fernandez, P. Hunter, V. Shim, and K. Mithraratne, “A subject-specific framework to inform musculoskeletal model- ing: outcomes from the IUPS physiome project,” in Patient- Specific Computational Modeling, pp. 39–60, Springer, 2012. [18] J. W. Fernandez, P. Mithraratne, S. F. Thrupp, M. H. Tawhai, and P. J. Hunter, “Anatomically based geometric modelling of the musculo-skeletal system and other organs,” Biomechanics and Modeling in Mechanobiology, vol.2,no. 3, pp.139–155, 2004. [19] J. Fernandez, J. Zhang, V. Shim et al., “Musculoskeletal model- ling and the Physiome Project,” in Multiscale Mechanobiology of Bone Remodeling and Adaptation, P. Pivonka, Ed., pp. 123– 174, Springer International Publishing, Cham, 2018. [20] E. Passmore, A. Lai, M. Sangeux, A. G. Schache, and M. G. Pandy, “Application of ultrasound imaging to subject-specific modelling of the human musculoskeletal system,” Meccanica, vol. 52, no. 3, pp. 665–676, 2017. [21] K. Oberhofer, K. Mithraratne, N. S. Stott, and I. A. Anderson, “Anatomically-based musculoskeletal modeling: prediction and validation of muscle deformation during walking,” The Visual Computer, vol. 25, no. 9, pp. 843–851, 2009. [22] N. S. Stott and I. A. Anderson, “A novel approach to compute muscle length during walking using subject-specific musculo- skeletal models,” in The 16th IASTED International Confer- ence on Applied Simulation and Modelling, pp. 451–456, ACTA Press, Palma de Mallorca, Spain, 2007. [23] A. Cappozzo, U. Della Croce, A. Leardini, and L. Chiari, “Human movement analysis using stereophotogrammetry: part 1: theoretical background,” Gait & Posture, vol. 21, no. 2, pp. 186–196, 2005. [24] F. J. Massey Jr, “The Kolmogorov-Smirnov test for goodness of fit,” Journal of the American Statistical Association, vol. 46, no. 253, pp. 68–78, 1951. [25] G. Keppel and T. Wickens, Simultaneous Comparisons and the Control of Type I Errors. Design and Analysis: A Researcher’s Handbook, Pearson Prentice Hall, Upper Saddle River (NJ), 4th ed edition, 2004. [26] K. Oberhofer, K. Mithraratne, N. S. Stott, and I. A. Anderson, “Error propagation from kinematic data to modeled muscle-tendon lengths during walking,” Journal of Biome- chanics, vol. 42, no. 1, pp. 77–81, 2009. [27] D. Lee, M. Glueck, A. Khan, E. Fiume, and K. Jackson, “A sur- vey of modeling and simulation of skeletal muscle,” ACM Transactions on Graphics, vol. 28, no. 4, pp. 1–13, 2010. [28] P. Kadleček, A. E. Ichim, T. Liu, J. Křivánek, and L. Kavan, “Reconstructing personalized anatomical models for physics- based body animation,” ACM Transactions on Graphics, vol. 35, no. 6, pp. 1–13, 2016. [29] S. Saito, Z. Y. Zhou, and L. Kavan, “Computational body- building: anatomically-based modeling of human bodies,” ACM Transactions on Graphics, vol. 34, no. 4, pp. 41:1– 41:12, 2015. [30] M. Alipour, K. Mithraratne, R. D. Herbert, and J. Fernandez, “A 3D ultrasound informed model of the human gastrocnemius muscle,” in Imaging for Patient-Customized Simulations and Systems for Point-of-Care Ultrasound,pp.27–34, Springer, 2017. [31] J. C. K. Wells, A. Ruto, and P. Treleaven, “Whole-body three- dimensional photonic scanning: a new technique for obesity research and clinical practice,” International Journal of Obe- sity, vol. 32, no. 2, pp. 232–238, 2008. 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Host Mesh Fitting of a Generic Musculoskeletal Model of the Lower Limbs to Subject-Specific Body Surface Data: A Validation Study

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Copyright © 2019 Katja Oberhofer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 8381351, 8 pages https://doi.org/10.1155/2019/8381351 Research Article Host Mesh Fitting of a Generic Musculoskeletal Model of the Lower Limbs to Subject-Specific Body Surface Data: A Validation Study 1 1,2 3 Katja Oberhofer , Silvio Lorenzetti , and Kumar Mithraratne Institute for Biomechanics, Department of Health Sciences and Technology, ETH Zurich, Leopold-Ruzicka-Weg 4, 8093 Zürich, Switzerland Swiss Federal Institute of Sport, Magglingen, Switzerland The Bioengineering Institute, University of Auckland, Auckland, New Zealand Correspondence should be addressed to Katja Oberhofer; katja.oberhofer@hest.ethz.ch Received 31 August 2018; Revised 26 November 2018; Accepted 10 January 2019; Published 17 February 2019 Guest Editor: Ozan Erol Copyright © 2019 Katja Oberhofer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Challenges remain in accurately capturing the musculoskeletal geometry of individual subjects for clinical and biomechanical gait analysis. The aim of this study was to use and validate the Host Mesh Fitting (HMF) technique for fitting a generic anatomically based musculoskeletal model to 3D body surface data of individual subjects. The HMF technique is based on the free-form idea of deforming geometrically complex structures according to the deformation of a surrounding volumetric mesh. Using the HMF technique, an anatomically based model of the lower limbs of an adult female subject (29 years) was customized to subject-specific skin surface data of five typically developing children (mean age 10.2 years) and six children with Cerebral Palsy (CP) (mean age 9.6 years). The fitted lengths and volumes of six muscle-tendon structures were compared against measures from Magnetic Resonance (MR) images for validation purposes. The HMF technique resulted in accurate approximations of the lower limb shapes of all subjects in both study groups. The average error between the MR data and the fitted muscle-tendon lengths from HMF was 4±4% in children without CP and 7± 5% in children with CP, respectively. The average error between the MR data and the fitted muscle volumes from HMF was 28 ± 19% in children without CP and 27 ± 28% in children with CP, respectively. This study presents a crucial step towards personalized musculoskeletal modelling for gait analysis by demonstrating the feasibility of fitting a generic anatomically based lower limb model to 3D body surface data of children with and without CP using the HMF technique. Additional improvements in the quality of fit are expected to be gained by developing age-matched generic models for different study groups, accounting for subject-specific variations in subcutaneous body fat, as well as considering supplementary data from ultrasound imaging to better capture physiological muscle tissue properties. 1. Introduction optical motion capture with computational models of the musculoskeletal system, crucial insights have been gained Computer models of the musculoskeletal system have widely into, e.g., muscle-tendon length changes during walking in been applied to biomechanical and clinical gait analysis. patients with Cerebral Palsy (CP) to help in the targeted Musculoskeletal modelling has provided means to quantify treatment intervention [1], as well as served as intermediate muscle and joint function during walking that cannot be step for calculating muscle-tendon forces and joint loading to assist with rehabilitation intervention and monitoring [2]. measured otherwise. In particular, muscular weaknesses or bilateral asymmetries can result in altered and potentially Generic musculoskeletal models of the lower limbs have harmful internal tissue loading which cannot be investigated traditionally been adopted and crudely scaled to subject- based on external observation alone. By combining data from specific dimensions in order to analyze biomechanical 2 Applied Bionics and Biomechanics musculoskeletal model of the lower limbs of an adult female parameters such as joint forces, muscle-tendon lengths, or lengthening velocities during gait for individual subjects [1, subject to 3D body surface data of children with and without 3, 4]. Thereby, the term “generic” refers to a reference model CP and compare the fitted lengths and volumes of six muscle-tendon structures with the subject-specific muscle- or data set, commonly resembling the anatomy of an adult male or female subject without musculoskeletal injury or dis- tendon lengths and volumes derived from MR data. The ease. In recent years, more advanced optimization algorithms use of 3D body surface data and HMF for fitting musculo- have been introduced in an effort to improve the accuracy of skeletal models to individual subjects is expected to be partic- musculoskeletal modelling results for personalized gait anal- ularly suited for gait analysis in population groups where bony anatomical landmarks are not sufficiently accurate ysis [5–8]. Yet, the most widely used fitting algorithms remain based on the positions of bony anatomical land- and MR scanning not applicable due to time, cost, or ethical constraints. marks, assuming that the skeletal system sufficiently reflects the subject-specific architecture of the entire mus- culoskeletal system. 2. Materials and Methods There is growing evidence that the fitting of musculoskel- 2.1. Volumetric Host Mesh Fitting. In the following, the theo- etal models based on bony anatomical landmarks may lead to retical principles of the HMF technique are summarized. incorrect conclusions, especially for clinical gait analysis in Given a generic 3D model of the musculoskeletal system with patients with severe musculoskeletal impairments due to embedded tissue structures (e.g., muscles-tendon structures conditions such as CP. Muscle architecture has been found and bones of the lower limbs) and subject-specific skin sur- to be significantly altered due to CP [9–11], and bone defor- face data, the HMF process is divided into four steps mities, commonly observed in children with CP, have been (Figure 1). shown to significantly affect joint kinematics, muscle- In Step I “Model registration,” the generic lower body tendon lengths, and muscle moment arms during walking mesh is aligned and homogenously scaled to subject- [12, 13]. Furthermore, bone deformities in the distal seg- specific dimensions by calculating an overall affine transfor- ments have been related to altered joint kinematics in the mation matrix using the conventional positions of bony ana- proximal joints and vice versa [14], and changes in the path tomical landmarks. The affine transformation matrix of one muscle-tendon structure may affect the paths of comprises rotation, scaling, shearing, and translation and is neighboring muscles and hence the dynamics of the entire obtained by minimizing the distances between bony anatom- multibody musculoskeletal system. Such local differences in ical landmarks of the generic model and manually annotated musculoskeletal architecture cannot be captured using subject-specific bony landmarks. In Step II “Recording local generic musculoskeletal models that are simply scaled based muscle position,” the material positions of the muscle- on the positions of bony anatomical landmarks. tendon structures of the generic model are calculated with Magnetic Resonance (MR) and ultrasound imaging pro- respect to the surrounding 3D lower body mesh in prepara- vide additional insights into the musculoskeletal architecture tion for skin mesh fitting. In Step III “Data fitting of skin of individual subjects and have been considered for applica- mesh,” the registered lower body mesh is customized to tion to clinical gait analysis. Novel algorithms have been subject-specific 3D body surface data to find the optimum developed to automatically segment MR images based on mesh nodal degrees of freedom (i.e., mesh nodal parameters, previous knowledge from generic image data sets [15, 16]; including nodal positions as well as nodal derivatives in the and fitting techniques have been introduced to morph case of bicubic-linear interpolation functions). In brief, the generic models of individual organs to a limited number of HMF objective function F u is set up to find the optimum subject-specific MR images [17–19]. Yet, the implementation mesh nodal parameters u that minimize the Euclidean of image-based fitting algorithms to widespread clinical prac- n distances between the subject-specific data points and their tice has often been a challenge due to long acquisition times projections onto the lower body mesh in a least-square of MR imaging as well as high imaging and computational sense as follows: costs. The integration of ultrasound imaging to gait analysis is considered more feasible; yet, ultrasound imaging is con- D N fined to a small imaging field of view, e.g., calf muscles, and F u = 〠 〠 φ p u − s + δ u , γ , 1 thus requires additional means of fitting the entire multibody n d n d n n i d=1 n=1 musculoskeletal system to individual subjects [20]. The aim of this study was to use a free-form deformation whereby p denotes the coordinates of the projection technique known as Host Mesh Fitting (HMF) for fitting points d =1,… , D with respect to the lower body mesh, generic musculoskeletal models to 3D body surface data of and s is the corresponding global coordinates of the individual subjects and assess its accuracy in an effort to subject-specific target points, and δ u , γ is a 3D address the persisting limitations in musculoskeletal model- n i ling for personalized gait analysis. The HMF technique was smoothing constraint called Sobolev function with user- initially introduced to develop subject-specific 3D models of defined penalty parameters γ ∈ 0, 1 for controlling arc individual organs [18] and was later applied and validated lengths, curvatures in element coordinate directions, for predicting the deformation of muscle-tendon structures surfaces area terms, and volume of the lower body mesh. in the lower limbs during walking [21]. The present work Further details to the HMF objective function and 3D extends on these previous efforts by aiming to fit a generic smoothing constraints can be found in [18, 21]. Finally, Applied Bionics and Biomechanics 3 Generic model Model (i) registration Recording local Bony landmarks (ii) muscle position Data fitting (iii) Skin boundary of skin mesh Subject-specific model Updating new (iv) muscle position Customized model Figure 1: The HMF technique is divided into four steps: (I) model registration based on bony landmarks; (II) recording of muscle-tendon nodal parameters with respect to generic lower body mesh; (III) customization of lower body mesh to subject-specific body shape data; and (IV) updating muscle-tendon nodal parameters according to customized skin mesh. Previously acquired MR images of children with and without CP [11] were used for validation purposes in the present work. in Step IV “Updating new muscle position,” the spatial specific data of children with and without CP and comparing positions of the muscle-tendon structures are calculated the predicted muscle-tendon lengths and volumes of the according to the customized position of the lower body fitted model with subject-specific MR data. A generic lower mesh. This is carried out under the assumption that the limb model of an adult female subject, which was previously material positions of the muscle-tendon structures with manually developed based on subject-specific MR data [21], respect to the surrounding 3D lower body mesh do not was used (age 29 y, height 165 cm, and weight 63 kg) for this change during customization. purpose. The lower limb model comprised all lower limb The HMF algorithm is implemented in the modelling bones, 20 muscles-tendon structures, and a volumetric environment CMISS (http://www.cmiss.org). CMISS is an representation of the skin boundary surface of each leg. All interactive computational modelling environment for Con- geometries of the musculoskeletal lower limb model were tinuum Mechanics, Image analysis, Signal processing, and represented using high-order finite element meshes with System identification, which has extensively been used for bicubic-linear interpolation functions. Cubic interpolation high-order subject-specific modelling of the musculoskeletal functions preserve the continuity of the first derivatives of system [11, 18, 21, 22]. CMISS has been developed as part the geometric coordinates with respect to the element coordi- of the International Union of Physiological Sciences (IUPS) nates, which makes them ideal for smoothly approximating Physiome Project [17, 19] and is currently being redeveloped the curved surfaces of biological tissue with a minimum into the open source package Open-CMISS to make it more number of elements [21]. modular, extendable, easier to understand, and able to run MR images of the lower limbs of six children with CP on modern distributed-memory high-performance com- (mean age 9.6 years) and five typically developing children puters (http://www.opencmiss.org). (mean age 10.2 years) were acquired on a Siemens 1.5T MAGENTOM Avanto System. Ethical approval was given 2.2. Validation. The accuracy of the HMF technique was by the NZ Northern Y Regional Ethics Committee, reference assessed by fitting a generic lower limb model to subject- number NTY/06/07/064. Written consent was obtained from 4 Applied Bionics and Biomechanics boundary of each subject were used for the fitting process. all children and their parents or guardians. Subject character- istics and scan protocol have previously been outlined in The HMF technique resulted in smooth approximations of detail [11]. The image processing tools within CMISS were the lower body shapes of all subjects in both study groups employed to automatically segment the skin boundary sur- (Figure 2). The average Root Mean Square (RMS) error faces of the lower limbs. The positions of the following bony between the fitted lower body mesh and the subject-specific landmarks on the skin surface were manually identified surface data from MR imaging was 3 7±1 08 mm. according to standard protocols [23]: right/left asis, sacrum, The average normalized muscle-tendon lengths derived medial/lateral epicondyles, and medial/lateral malleoli. The from HMF compared to the subject-specific values from bony landmarks were used to register the generic model to MR images are given in Table 1. Statistical analysis revealed the subject-specific surface data (Step I, Figure 1). The lower that HMF led to accurate predictions of muscle-tendon body mesh was then customized to subject-specific skin sur- lengths in the children without CP for all muscles except rec- face data and the new configuration of each muscle-tendon tus femoris. In the children with CP, HMF led to accurate structure was calculated according to the customized lower predictions of muscle-tendon lengths for soleus, biceps body mesh (Steps II-IV, Figure 1). femoris, and the vasti group, while significant differences Muscle-tendon lengths and volumes of the fitted models were obtained between the fitted and the MR-based values were numerically derived and compared with subject-specific for gastrocnemius, semimembranosus-semitendinosus, and measures from MR images for validation purposes. The rectus femoris. The average fitting error (equation (2)) in following six muscles were included in the analysis: soleus, muscle-tendon lengths from HMF was 4±4% in the group gastrocnemius, semimembranosus and semitendinosus (rep- of children without CP and 7± 5% in the children with resented as one muscle), biceps femoris, and the vasti group. CP, respectively. Muscle-tendon lengths were defined as the average arc The average normalized muscle volumes derived from lengths between the most distal and most proximal ends of HMF compared to the subject-specific values from MR the muscle-tendon meshes, normalized with respect to images are given in Table 2. Overall, the prediction of muscle segmental lengths. Muscle volumes were derived by perform- volumes was poor, with an average fitting error (equation ing numerical quadrature over the parameterized meshes (2)) of 28 ± 19% in children without CP and 27 ± 28% in chil- (Fernandez et al., 2005), divided by body mass. The fitting dren with CP, respectively. Statistical analysis revealed signif- error E was defined as the relative difference in muscle- icant differences in the predicted muscle volumes from HMF HMF tendon length l, i.e., muscle volume V, between the fitted compared to MR imaging for four muscles in the children values from HMF and the subject-specific values derived without CP (soleus, biceps femoris, rectus femoris, and vasti from the MR images: group) and for two muscles in the children with CP (biceps femoris, semimembranosus-semitendinosus). l − l l C MRI E = , HMF 4. Discussion MRI V − V V C MRI The aim of this study was to address current limitations in E = HMF subject-specific musculoskeletal modelling for personalized MRI gait analysis by applying and validating the HMF technique to fit a generic model to subject-specific 3D body surface 2.3. Statistical Analysis. Statistical analysis was performed to data. The HMF technique extends scaling of generic muscu- assess the significance of the differences in muscle-tendon loskeletal models based on bony anatomical landmarks in lengths and volumes between the fitted and the subject- that it comprises an affine transformation (rotation, transla- specific values from MR imaging. All parameters were tested tion, and scaling) followed by model customization to for a normal distribution prior to data comparison using the account for subject-specific variations in lower limb shape. Kolmogorov and Smirnov method [24]. A repeated measure High accuracies were obtained in the fitted lower limb shapes analysis of variance (ANOVA) with Tukey-Kramer multiple in both study groups with the RMS error between the post hoc test [25] was performed to analyze the pairwise dif- subject-specific 3D body surface data and the fitted lower ferences in muscle-tendon lengths and volumes between the limb mesh being less than 5 mm for all data points. The fitted and the subject-specific measures from MR imaging. accuracies in muscle-tendon lengths are also considered The data of the children with CP and without CP were promising for having the potential to improve gait analysis analyzed independently as two different groups. Statistical results, with an average RMS error of 4±4% in the children analysis was performed using the statistical software Graph- without CP and 7±5% in the children with CP, respectively Pad IntStat. The level of significance was set at p <0 05 for (Table 1). The average RMS errors in muscle-tendon lengths all statistical test. in both study groups are below, or around the lower range, of previously reported errors in muscle-tendon length predic- 3. Results tions using generic musculoskeletal models for clinical gait analysis, e.g., 6% to 50% [26]. However, the accuracies in A generic lower limb model of an adult female subject was fitted to skin surface data of children with and without CP muscle volumes were limited with large variations in both using the HMF technique. Eleven bony landmarks and an study groups compared to the subject-specific MR data average number of 1,858,218 (±845) data points on the skin (Table 2). Applied Bionics and Biomechanics 5 88 cm 64 cm 60 cm (a) (b) (c) Figure 2: (a) The generic lower limb model based on the anatomy of an adult female (Oberhofer et al. 2009). (b) A fitted lower limb model of a child without CP. (c) A fitted lower limb model of a child with CP. Leg lengths of each model, ranging from the hip joint center to the ankle joint center, are given as reference. Table 1: Average normalized muscle-tendon lengths (%) derived from the subject-specific MR images (MRI) compared to the predicted values from HMF for the children without CP and the children with CP. Children without CP Children with CP MRI HMF p value MRI HMF p value Soleus 71 (5.1) 71 (2.2) >0.05 66 (4.7) 69 (2.3) >0.05 <0.05 Gastrocnemius 60 (5.8) 56 (3.6) >0.05 51 (3.7) 55 (1.5) Biceps femoris 58 (4.6) 60 (1.7) >0.05 54 (3.7) 56 (4.8) >0.05 <0.01 Semi group 82 (3.3) 84 (3.7) >0.05 76 (7.2) 81 (3.7) ∗ ∗ <0.05 <0.01 Rectus femoris 76 (1.3) 79 (1.6) 68 (3.1) 75 (2.9) Vasti group 91 (4.1) 91 (5.0) >0.05 85 (2.1) 86 (2.7) >0.05 Difference between MRI and HMF statistically significant (repeated measures ANOVA with Tukey-Kramer multiple Comparison post hoc test, p <0 05). Table 2: Average muscle volumes cm /kg derived from the subject-specific MR images (MRI) compared to the predicted values from HMF for the children without CP and the children with CP. Children without CP Children with CP MRI HMF p value MRI HMF p value <0.01 Soleus 5.5 (0.84) 3.9 (0.30) 4.5 (1.56) 3.7 (0.51) >0.05 Gastrocnemius 4.4 (1.01) 3.6 (0.23) >0.05 3.1 (1.26) 3.6 (0.56) >0.05 ∗ ∗ <0.001 <0.001 Biceps femoris 2.3 (0.44) 3.5 (0.32) 1.6 (0.41) 3.5 (0.33) Semi group 5.1 (0.91) 5.0 (0.30) >0.05 3.9 (0.88) 5.5 (0.51) <0.01 <0.01 Rectus femoris 3.6 (0.69) 2.2 (0.22) 2.6 (0.63) 2.3 (0.63) >0.05 <0.05 Vasti group 20.3 (2.80) 16.7 (1.16) 15.9 (3.20) 16.5 (2.58) >0.05 Difference between MRI and HMF statistically significant (repeated measures ANOVA with Tukey-Kramer multiple comparison post hoc test, p <0 05). The HMF technique is established under the assump- had less subcutaneous fat compared to the adult female sub- tion that the lower limb shape reflects the internal ject, which could partly explain the unsatisfying prediction of musculoskeletal architecture, which is a limitation of the muscle volumes compared to muscle-tendon lengths. Inter- proposed technique. It means that the relative positions of estingly, the average RMS error for muscle volumes was muscle-tendon structures with respect to the skin mesh slightly lower for the children with CP than the children remain constant during model fitting. If, for example, a without CP, which is an unexpected result (Table 2). Based thick subcutaneous fat layer between muscles and skin is on the MR images (Figure 3), it appears as if the percentage present in the generic model, the relative thickness of the of muscle tissue versus fat tissue in children with CP more closely resembled the adult female anatomy, e.g., thicker fat fat layer remains the same throughout HMF. Looking more closely at the MR images (Figure 3), it becomes apparent layer with less muscle tissue, which may explain the unex- that significant differences existed in muscle volumes pected outcome. Thereby, the volumetric tissue distribution between individual subjects. In particular, children subjects critically affects the inertia properties of the multibody 6 Applied Bionics and Biomechanics Adult female subject Child without CP Child with CP (a) (b) (c) Figure 3: Representative MR image of the shank of (a) adult female subject, (b) child without CP, and (c) child with CP. dynamic system and hence gait analysis results. These on several 3D body surface scans that minimizes the defor- mation energy, corresponding to the elasticity of biological insights suggest that additional skin fold measurements may help to improve model fit by allowing to adjust the rel- soft tissue. The consideration of a so-called elastic potential ative thickness of the fat layer, and thus segmental inertia to find the optimum fit solution (equation (1)) while comply- properties, for individual subjects. ing to Newton’s laws of motion for soft tissue is promising The time needed to develop musculoskeletal models by and may offer the potential to improve the accuracy of the HMF fit for subjects with various degrees of subcutaneous manually segmenting MR images is lengthy and can take sev- eral months. Currently, the modelling software CMISS con- body fat versus muscle tissue. Additionally, data from ultrasound imaging may allow tains a library of MR-based lower limb models of one female subject, six children with CP, and five typically devel- further insights into mechanical tissue properties to oping children, which were adopted in the present work. The advance the HMF technique based on anatomically aware principles [20]. Capturing subject-specific mechanical prop- present goal to accurately fit a generic model of an adult female subject to the anatomy of children with severe gait erties of soft tissue is particularly important when aiming to impairments due to CP was ambitious. It is likely that more analyze kinetic variables, e.g., muscle forces, in patients accurate results can be obtained when fitting the generic with musculoskeletal disorders such as CP. Yet, taking model to subjects of similar age and without significant mus- subject-specific tissue samples in vivo for refining musculo- skeletal models remains highly invasive and very compro- culoskeletal impairments. Nevertheless, the present results are promising and considered the first step towards an mised. Ultrasound data would allow to better capture advanced modelling framework for subject-specific simula- mechanical properties of muscles at the tissue level, e.g., tion and analysis of human movement. In addition to the physiological cross-sectional area and fiber pennation angle, MR-based lower limb models within CMISS, data from gait which in turn affect muscle mechanics. Ultrasound imaging is relatively inexpensive, does not involve ionizing radia- analysis was acquired in the same subjects. This unique data- set will allow the comparison of muscle-tendon length calcu- tion, and requires much shorter scan times compared with lation during walking between generic and HMF-fitted other imaging modalities such as MR imaging. Thereby, an musculoskeletal models as a next step. Furthermore, an anatomically aware deformation method was recently intro- extension of the model library based on the Visible Human duced by Saito et al. [29] to predict the growth and size of muscles by discretizing the anisotropic stretch in the direc- Dataset from the U.S. National Library of Medicine, which includes Computed Tomography and MR images of one tion of muscle fibers. The integration of muscle fiber struc- male and one female cadaver, is planned. The Visible Human tures into the present musculoskeletal modelling approach Dataset has been applied to musculoskeletal research, edu- is highly feasible. In particular, a muscle fascicle description cational, virtual reality, industry, and diagnostic purposes has already successfully been integrated into the muscle organ models in CMISS and fitted to subject-specific ultra- and thus will provide widely accepted reference models for future use. sound data with good qualitative agreement to diffusion- The solution of the HMF objective function (equation weighted MR images [30]. (1)) is, in the present form, dependent on the geometry of In this study, the skin boundary surfaces of individual the lower body mesh (i.e., mesh nodal degrees of freedom) subjects were segmented based on MR data, though body surface scanning could be used to capture the outer skin sur- and the magnitudes of the Sobolev smoothing constraints. Both, the geometry of the lower body mesh and the Sobolev face of individual subjects in future work. Body surface scan- smoothing constraints, have not been linked to physiological ning, frequently used in anthropometric body shape analysis and obesity research, offers inexpensive, rapid, and noninva- or anatomically based principles but were defined according to previously established kinematic criteria [18]. Kinematic sive means to characterize the skin boundary in vivo [31] surface-based deformation methods have extensively been and would make the application of the HMF technique fea- used in computer graphics research [27]. Yet, they are tradi- sible in clinical settings. Thereby, the numerical algorithms tionally not considering biological soft tissue as elastic solids associated with HMF, as well as the library of MR-based subject to Newton’s laws of motion. In recent work, Kadleček musculoskeletal models, are currently transferred into the et al. [28] introduced a physics-based model fitting technique open source modelling environment Open-CMISS (http:// to find the optimum shape of a musculoskeletal model based www.opencmiss.org/) to provide the most advanced and Applied Bionics and Biomechanics 7 accessible numerical tools for physiologically based modelling Computational and Mathematical Methods in Medicine, vol. 2015, Article ID 483921, 12 pages, 2015. of deformable organs, e.g., muscle tissue across multiple scales, including multibody dynamic analysis [19, 21, 22, 30]. [3] M. D. Klein Horsman, H. F. J. M. Koopman, F. C. T. van der Helm, L. P. Prosé, and H. E. J. Veeger, “Morphological muscle and joint parameters for musculoskeletal modelling of the 5. Conclusions lower extremity,” Clinical Biomechanics, vol. 22, no. 2, pp. 239–247, 2007. The current study presents a crucial step towards personal- [4] I. Jonkers, C. Stewart, K. Desloovere, G. Molenaers, and ized human movement analysis by demonstrating the feasi- A. Spaepen, “Musculo-tendon length and lengthening velocity bility of fitting a generic musculoskeletal model of the lower of rectus femoris in stiff knee gait,” Gait & Posture, vol. 23, limbs to skin surface data of children with and without CP. no. 2, pp. 222–229, 2006. The musculoskeletal models of the lower limbs and fitting [5] U. Trinler and R. Baker, “Estimated landmark calibration of algorithms are planned to be further developed and shared biomechanical models for inverse kinematics,” Medical Engi- between research centers through the IUPS Physiome Project neering & Physics, vol. 51, pp. 79–83, 2018. [19] and coupled with experimentally measured gait data for [6] J. A. Reinbolt, J. F. Schutte, B. J. Fregly et al., “Determination of dynamic simulations of walking. Additional improvements patient-specific multi-joint kinematic models through in the quality of fit are expected to be gained by developing two-level optimization,” Journal of Biomechanics, vol. 38, age-matched generic models for different study groups, as no. 3, pp. 621–626, 2005. well as taking into account subject-specific skin fold mea- [7] M. E. Lund, M. S. Andersen, M. de Zee, and J. Rasmussen, sures and mechanical properties of muscle tissue based on “Scaling of musculoskeletal models from static and dynamic ultrasound imaging. It is anticipated that the application of trials,” International Biomechanics, vol. 2, no. 1, pp. 1–11, personalized musculoskeletal models to movement analysis will lead to crucial new insights into the complex relationship [8] P. Rymaszewski, C. Stewart, D. Blana, E. Chadwick, S. Sardar, between musculoskeletal architecture and function during and S. Jarvis, “Musculoskeletal modelling simulation with dynamic activities and thus assist in the assessment and optimisation to predict the morphological parameters of the management of movement pathologies due to conditions calf muscle,” Gait & Posture, vol. 57, pp. 87-88, 2017. such as CP. [9] R. Lampe, S. Grassl, J. Mitternacht, L. Gerdesmeyer, and R. Gradinger, “MRT-measurements of muscle volumes of the lower extremities of youths with spastic hemiplegia caused Data Availability by cerebral palsy,” Brain and Development, vol. 28, no. 8, pp. 500–506, 2006. The MR image data used for this study are restricted by the New Zealand Northern Y Regional Ethics Committee [10] A. A. Mohagheghi, T. Khan, T. H. Meadows, K. Giannikas, V. Baltzopoulos, and C. N. Maganaris, “Differences in gas- in order to protect patient privacy. The data is only avail- trocnemius muscle architecture between the paretic and able to researchers who meet the criteria for accessing the non-paretic legs in children with hemiplegic cerebral confidential data. Further information can be obtained palsy,” Clinical biomechanics, vol. 22, no. 6, pp. 718–724, from the corresponding author Dr. Katja Oberhofer (katja.oberhofer@hest.ethz.ch). [11] K. Oberhofer, N. S. Stott, K. Mithraratne, and I. A. Anderson, “Subject-specific modelling of lower limb muscles in children Conflicts of Interest with cerebral palsy,” Clinical Biomechanics, vol. 25, no. 1, pp. 88–94, 2010. All authors declare that they have no proprietary, financial, [12] T. A. Correa, R. Baker, H. Kerr Graham, and M. G. Pandy, professional, or other personal relationships or obligations “Accuracy of generic musculoskeletal models in predicting of any kind with other people or organisations that could the functional roles of muscles in human gait,” Journal of Bio- inappropriately influence their work. mechanics, vol. 44, no. 11, pp. 2096–2105, 2011. [13] L. Scheys, K. Desloovere, P. Suetens, and I. Jonkers, “Level of subject-specific detail in musculoskeletal models affects hip Acknowledgments moment arm length calculation during gait in pediatric sub- Funding for this study was provided by the New Zealand jects with increased femoral anteversion,” Journal of Biome- chanics, vol. 44, no. 7, pp. 1346–1353, 2011. Foundation for Research, Science and Technology. [14] A. Carriero, A. Zavatsky, J. Stebbins, T. Theologis, and S. J. Shefelbine, “Correlation between lower limb bone morphology References and gait characteristics in children with spastic diplegic cere- bral palsy,” Journal of Pediatric Orthopaedics, vol. 29, no. 1, [1] A. S. Arnold, M. Q. Liu, M. H. Schwartz, S. Õunpuu, and S. L. pp. 73–79, 2009. Delp, “The role of estimating muscle-tendon lengths and [15] B. Gilles and N. Magnenat-Thalmann, “Musculoskeletal MRI velocities of the hamstrings in the evaluation and treatment segmentation using multi-resolution simplex meshes with of crouch gait,” Gait & Posture, vol. 23, no. 3, pp. 273–281, medial representations,” Medical Image Analysis, vol. 14, no. 3, pp. 291–302, 2010. [2] F. Schellenberg, K. Oberhofer, W. R. Taylor, and S. Lorenzetti, “Review of modelling techniques for in vivo muscle force esti- [16] L. Scheys, K. Desloovere, A. Spaepen, P. Suetens, and mation in the lower extremities during strength training,” I. Jonkers, “Calculating gait kinematics using MR-based 8 Applied Bionics and Biomechanics kinematic models,” Gait & Posture, vol. 33, no. 2, pp. 158–164, [17] J. Fernandez, P. Hunter, V. Shim, and K. Mithraratne, “A subject-specific framework to inform musculoskeletal model- ing: outcomes from the IUPS physiome project,” in Patient- Specific Computational Modeling, pp. 39–60, Springer, 2012. [18] J. W. Fernandez, P. Mithraratne, S. F. Thrupp, M. H. Tawhai, and P. J. Hunter, “Anatomically based geometric modelling of the musculo-skeletal system and other organs,” Biomechanics and Modeling in Mechanobiology, vol.2,no. 3, pp.139–155, 2004. [19] J. Fernandez, J. Zhang, V. Shim et al., “Musculoskeletal model- ling and the Physiome Project,” in Multiscale Mechanobiology of Bone Remodeling and Adaptation, P. Pivonka, Ed., pp. 123– 174, Springer International Publishing, Cham, 2018. [20] E. Passmore, A. Lai, M. Sangeux, A. G. Schache, and M. G. Pandy, “Application of ultrasound imaging to subject-specific modelling of the human musculoskeletal system,” Meccanica, vol. 52, no. 3, pp. 665–676, 2017. [21] K. Oberhofer, K. Mithraratne, N. S. Stott, and I. A. Anderson, “Anatomically-based musculoskeletal modeling: prediction and validation of muscle deformation during walking,” The Visual Computer, vol. 25, no. 9, pp. 843–851, 2009. [22] N. S. Stott and I. A. Anderson, “A novel approach to compute muscle length during walking using subject-specific musculo- skeletal models,” in The 16th IASTED International Confer- ence on Applied Simulation and Modelling, pp. 451–456, ACTA Press, Palma de Mallorca, Spain, 2007. [23] A. Cappozzo, U. Della Croce, A. Leardini, and L. Chiari, “Human movement analysis using stereophotogrammetry: part 1: theoretical background,” Gait & Posture, vol. 21, no. 2, pp. 186–196, 2005. [24] F. J. Massey Jr, “The Kolmogorov-Smirnov test for goodness of fit,” Journal of the American Statistical Association, vol. 46, no. 253, pp. 68–78, 1951. [25] G. Keppel and T. Wickens, Simultaneous Comparisons and the Control of Type I Errors. Design and Analysis: A Researcher’s Handbook, Pearson Prentice Hall, Upper Saddle River (NJ), 4th ed edition, 2004. [26] K. Oberhofer, K. Mithraratne, N. S. Stott, and I. A. Anderson, “Error propagation from kinematic data to modeled muscle-tendon lengths during walking,” Journal of Biome- chanics, vol. 42, no. 1, pp. 77–81, 2009. [27] D. Lee, M. Glueck, A. Khan, E. Fiume, and K. Jackson, “A sur- vey of modeling and simulation of skeletal muscle,” ACM Transactions on Graphics, vol. 28, no. 4, pp. 1–13, 2010. [28] P. Kadleček, A. E. Ichim, T. Liu, J. Křivánek, and L. Kavan, “Reconstructing personalized anatomical models for physics- based body animation,” ACM Transactions on Graphics, vol. 35, no. 6, pp. 1–13, 2016. [29] S. Saito, Z. Y. Zhou, and L. Kavan, “Computational body- building: anatomically-based modeling of human bodies,” ACM Transactions on Graphics, vol. 34, no. 4, pp. 41:1– 41:12, 2015. [30] M. Alipour, K. Mithraratne, R. D. Herbert, and J. Fernandez, “A 3D ultrasound informed model of the human gastrocnemius muscle,” in Imaging for Patient-Customized Simulations and Systems for Point-of-Care Ultrasound,pp.27–34, Springer, 2017. [31] J. C. K. Wells, A. Ruto, and P. Treleaven, “Whole-body three- dimensional photonic scanning: a new technique for obesity research and clinical practice,” International Journal of Obe- sity, vol. 32, no. 2, pp. 232–238, 2008. 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