An Open-Source Toolbox for Surrogate Modeling of Joint Contact Mechanics

FDM data driven U-Net as a 2D Laplace PINN solver

Efficient solution of partial differential equations (PDEs) of physical laws is of interest for manifold applications in computer science and image analysis. However, conventional domain discretization techniques for numerical solving PDEs such as Finite Difference (FDM), Finite Element (FEM) methods are unsuitable for real-time applications and are also quite laborious in adaptation to new applications, especially for non-experts in numerical mathematics and computational modeling. More recently, alternative approaches to solving PDEs using the so-called Physically Informed Neural Networks (PINNs) received increasing attention because of their straightforward application to new data and potentially more efficient performance. In this work, we present a novel data-driven approach to solve 2D Laplace PDE with arbitrary boundary conditions using deep learning models trained on a large set of reference FDM solutions. Our experimental results show that both forward and inverse 2D Laplace problems can efficiently be solved using the proposed PINN approach with nearly real-time performance and average accuracy of 94% for different types of boundary value problems compared to FDM. In summary, our deep learning based PINN PDE solver provides an efficient tool with various applications in image analysis and computational simulation of image-based physical boundary value problems.

Simulated Tibiofemoral Joint Reaction Forces for Three Previously Studied Gait Modifications in Healthy Controls

Gait modifications, such as lateral trunk lean (LTL), medial knee thrust (MKT), and toe-in gait (TIG), are frequently investigated interventions used to slow the progression of knee osteoarthritis. The Lerner knee model was developed to estimate the tibiofemoral joint reaction forces (JRF) in the medial and lateral compartments during gait. These models may be useful for estimating the effects on the JRF in the knee as a result of gait modifications. We hypothesized that all gait modifications would decrease the JRF compared to normal gait. Twenty healthy individuals volunteered for this study (26.7 ± 4.7 years, 1.75 ± 0.1 m, 73.4 ± 12.4 kg). Ten trials were collected for normal gait as well as for the three gait modifications: LTL, MKT, and TIG. The data were used to estimate the JRF in the first and second peaks for the medial and lateral compartments of the knee via opensim using the Lerner knee model. No significant difference from baseline was found for the first peak in the medial compartment. There was a decrease in JRF in the medial compartment during the loading phase of gait for TIG (6.6%) and LTL (4.9%) and an increasing JRF for MKT (2.6%). but none was statistically significant. A significant increase from baseline was found for TIG (5.8%) in the medial second peak. We found a large variation in individual responses to gait interventions, which may help explain the lack of statistically significant results. Possible factors influencing these wide ranges of responses to gait modifications include static alignment and the impacts of variation in muscle coordination strategies used, by participants, to implement gait modifications.

Cartilage contact characteristics of the knee during gait in individuals with obesity

Obesity increases the risk of knee osteoarthritis (OA). Knee joint contact characteristics have been thought to provide insights into the pathogenesis of knee OA; however, the cartilage contact characteristics in individuals with obesity have not been fully described. We conducted cartilage-to-cartilage contact analyses through high-precision fluoroscopy imaging with subject-specific magnetic resonance cartilage models. Twenty-five individuals with obesity were recruited for this study, and previously published data consisted of eight nonobese individuals who were used as the comparator group. In both groups, knees were imaged by a dual fluoroscopic imaging system during treadmill walking, and the tibiofemoral cartilage contact locations were analyzed and described on the tibial plateau in the medial-lateral (ML) and anterior-posterior (AP) directions and on femoral condyle surfaces using contact angles in the sagittal plane and deviation angles in a plane perpendicular to the sagittal plane. On the medial tibial plateau, the ML contact locations in the individuals with obesity were located more medially than in the nonobese group throughout the stance phase. The medial plateau AP contact locations in individuals with obesity showed a different pattern compared with the nonobese group. The ML contact excursions on the medial plateau in the individuals with obesity were larger than in the nonobese group. These findings suggest that obesity affects the contact location mainly in the medial compartment, which explains, in part, the high prevalence of medial knee OA in the obese population.

A Conceptual Blueprint for Making Neuromusculoskeletal Models Clinically Useful

The ultimate goal of most neuromusculoskeletal modeling research is to improve the treatment of movement impairments. However, even though neuromusculoskeletal models have become more realistic anatomically, physiologically, and neurologically over the past 25 years, they have yet to make a positive impact on the design of clinical treatments for movement impairments. Such impairments are caused by common conditions such as stroke, osteoarthritis, Parkinson’s disease, spinal cord injury, cerebral palsy, limb amputation, and even cancer. The lack of clinical impact is somewhat surprising given that comparable computational technology has transformed the design of airplanes, automobiles, and other commercial products over the same time period. This paper provides the author’s personal perspective for how neuromusculoskeletal models can become clinically useful. First, the paper motivates the potential value of neuromusculoskeletal models for clinical treatment design. Next, it highlights five challenges to achieving clinical utility and provides suggestions for how to overcome them. After that, it describes clinical, technical, collaboration, and practical needs that must be addressed for neuromusculoskeletal models to fulfill their clinical potential, along with recommendations for meeting them. Finally, it discusses how more complex modeling and experimental methods could enhance neuromusculoskeletal model fidelity, personalization, and utilization. The author hopes that these ideas will provide a conceptual blueprint that will help the neuromusculoskeletal modeling research community work toward clinical utility.

In Silico-Enhanced Treatment and Rehabilitation Planning for Patients with Musculoskeletal Disorders: Can Musculoskeletal Modelling and Dynamic Simulations Really Impact Current Clinical Practice?

Over the past decades, the use of computational physics-based models representative of the musculoskeletal (MSK) system has become increasingly popular in many fields of clinically driven research, locomotor rehabilitation in particular. These models have been applied to various functional impairments given their ability to estimate parameters which cannot be readily measured in vivo but are of interest to clinicians. The use of MSK modelling and simulations allows analysis of relevant MSK biomarkers such as muscle and joint contact loading at a number of different stages in the clinical treatment pathway in order to benefit patient functional outcome. Applications of these methods include optimisation of rehabilitation programs, patient stratification, disease characterisation, surgical pre-planning, and assistive device and exoskeleton design and optimisation. This review provides an overview of current approaches, the components of standard MSK models, applications, limitations, and assumptions of these modelling and simulation methods, and finally proposes a future direction.

Force Closure Mechanism Modeling for Musculoskeletal Multibody Simulation

OBJECTIVE

Neuro-musculoskeletal multibody simulation (NMBS) seeks to optimize decision-making for patients with neuro-musculoskeletal disorders. In clinical practice, however, the inter-subject variability and the inaccessibility for experimental testing impede the reliable model identification. These limitations motivate the novel modeling approach termed as force closure mechanism modeling (FCM²).

METHODS

FCM ² expresses the dynamics between mutually articulating joint partners with respect to instantaneous screw axes (ISA) automatically reconstructed from their relative velocity state. Thereby, FCM² reduces arbitrary open-chain multibody topologies to force closure n-link pendulums. Within a computational validation study on the human knee joint with implemented contact surfaces, we examine FCM² as an underlying inverse dynamic model for computed muscle control. We evaluate predicted tibiofemoral joint quantities, i.e., kinematics and contact forces along with muscle moment arms, during muscle-induced knee motion against the classic hinge joint model and experimental studies.

RESULTS

Our NMBS study provided the proof-of-principle of the novel modeling approach. FCM² freed us from assuming a certain joint formulation while correctly predicting the joint dynamics in agreement with the established methods. Although experimental results were closely predicted, owing to noise in the ISA estimation, muscle moment arms were overestimated (R_ISA = 0.84 < R_HINGE = 0.97, RMSE_ISA = 13.18 mm > RMSE_HINGE = 6.54 mm), identifying the robust ISA estimation as key to FCM².

CONCLUSION

FCM² automatically derives the equations of motion in closed form. Moreover, it captures subject-specific joint function and, thereby, minimizes modeling and parameterization efforts.

SIGNIFICANCE

Model derivation becomes driven by quantitative data available in clinical settings so that FCM² yields a promising framework toward subject-specific NMBS.

Bioinspired Technologies to Connect Musculoskeletal Mechanobiology to the Person for Training and Rehabilitation

Musculoskeletal tissues respond to optimal mechanical signals (e.g., strains) through anabolic adaptations, while mechanical signals above and below optimal levels cause tissue catabolism. If an individual's physical behavior could be altered to generate optimal mechanical signaling to musculoskeletal tissues, then targeted strengthening and/or repair would be possible. We propose new bioinspired technologies to provide real-time biofeedback of relevant mechanical signals to guide training and rehabilitation. In this review we provide a description of how wearable devices may be used in conjunction with computational rigid-body and continuum models of musculoskeletal tissues to produce real-time estimates of localized tissue stresses and strains. It is proposed that these bioinspired technologies will facilitate a new approach to physical training that promotes tissue strengthening and/or repair through optimal tissue loading.

Evaluation of a Surrogate Contact Model in Force-Dependent Kinematic Simulations of Total Knee Replacement

Knowing the forces in the human body is of great clinical interest and musculoskeletal (MS) models are the most commonly used tool to estimate them in vivo. Unfortunately, the process of computing muscle, joint contact, and ligament forces simultaneously is computationally highly demanding. The goal of this study was to develop a fast surrogate model of the tibiofemoral (TF) contact in a total knee replacement (TKR) model and apply it to force-dependent kinematic (FDK) simulations of activities of daily living (ADLs). Multiple domains were populated with sample points from the reference TKR contact model, based on reference simulations and design-of-experiments. Artificial neural networks (ANN) learned the relationship between TF pose and loads from the medial and lateral sides of the TKR implant. Normal and right-turn gait, rising-from-a-chair, and a squat were simulated using both surrogate and reference contact models. Compared to the reference contact model, the surrogate contact model predicted TF forces with a root-mean-square error (RMSE) lower than 10 N and TF moments lower than 0.3 N·m over all simulated activities. Secondary knee kinematics were predicted with RMSE lower than 0.2 mm and 0.2 deg. Simulations that used the surrogate contact model ran on average three times faster than those using the reference model, allowing the simulation of a full gait cycle in 4.5 min. This modeling approach proved fast and accurate enough to perform extensive parametric analyses, such as simulating subject-specific variations and surgical-related factors in TKR.

Neural Data-Driven Musculoskeletal Modeling for Personalized Neurorehabilitation Technologies

OBJECTIVES

The development of neurorehabilitation technologies requires the profound understanding of the mechanisms underlying an individual's motor ability and impairment. A major factor limiting this understanding is the difficulty of bridging between events taking place at the neurophysiologic level (i.e., motor neuron firings) with those emerging at the musculoskeletal level (i.e. joint actuation), in vivo in the intact moving human. This review presents emerging model-based methodologies for filling this gap that are promising for developing clinically viable technologies.

METHODS

We provide a design overview of musculoskeletal modeling formulations driven by recordings of neuromuscular activity with a critical comparison to alternative model-free approaches in the context of neurorehabilitation technologies. We present advanced electromyography-based techniques for interfacing with the human nervous system and model-based techniques for translating the extracted neural information into estimates of motor function.

RESULTS

We introduce representative application areas where modeling is relevant for accessing neuromuscular variables that could not be measured experimentally. We then show how these variables are used for designing personalized rehabilitation interventions, biologically inspired limbs, and human-machine interfaces.

CONCLUSION

The ability of using electrophysiological recordings to inform biomechanical models enables accessing a broader range of neuromechanical variables than analyzing electrophysiological data or movement data individually. This enables understanding the neuromechanical interplay underlying in vivo movement function, pathology, and robot-assisted motor recovery.

SIGNIFICANCE

Filling the gap between our understandings of movement neural and mechanical functions is central for addressing one of the major challenges in neurorehabilitation: personalizing current technologies and interventions to an individual's anatomy and impairment.