Adaptive Surrogate Modeling for Efficient Coupling of Musculoskeletal Control and Tissue Deformation Models

Background Finite element (FE) modeling and multibody dynamics have traditionally been applied separately to the domains of tissue mechanics and musculoskeletal movements, respectively. Simultaneous simulation of both domains is needed when interactions between tissue and movement are of interest, but this has remained largely impractical due to high computational cost. Method of Approach Here we present a method for concurrent simulation of tissue and movement, in which state of the art methods are used in each domain, and communication occurs via a surrogate modeling system based on locally weighted regression. The surrogate model only performs FE simulations when regression from previous results is not within a user-specified tolerance. For proof of concept and to illustrate feasibility, the methods were demonstrated on an optimization of jumping movement using a planar musculoskeletal model coupled to a FE model of the foot. To test the relative accuracy of the surrogate model outputs against those of the FE model, a single forward dynamics simulation was performed with FE calls at every integration step and compared with a corresponding simulation with the surrogate model included. Neural excitations obtained from the jump height optimization were used for this purpose and root mean square (RMS) difference between surrogate and FE model outputs (ankle force and moment, peak contact pressure and peak von Mises stress) were calculated. Results Optimization of jump height required 1800 iterations of the movement simulation, each requiring thousands of time steps. The surrogate modeling system only used the FE model in 5% of time steps, i.e. a 95% reduction of computation time. Errors introduced by the surrogate model were less than 1 mm in jump height and RMS errors of less than 2 N in ground reaction force, 0.25 Nm in ankle moment, and 10 kPa in peak tissue stress. Conclusion Adaptive surrogate modeling based on local regression allows efficient concurrent simulations of tissue mechanics and musculoskeletal movement

Adaptive Surrogate Modeling for Efficient Coupling of Musculoskeletal Control and Tissue Deformation Models

Background Finite element (FE) modeling and multibody dynamics have traditionally been applied separately to the domains of tissue mechanics and musculoskeletal movements, respectively. Simultaneous simulation of both domains is needed when interactions between tissue and movement are of interest, but this has remained largely impractical due to high computational cost. Method of Approach Here we present a method for concurrent simulation of tissue and movement, in which state of the art methods are used in each domain, and communication occurs via a surrogate modeling system based on locally weighted regression. The surrogate model only performs FE simulations when regression from previous results is not within a user-specified tolerance. For proof of concept and to illustrate feasibility, the methods were demonstrated on an optimization of jumping movement using a planar musculoskeletal model coupled to a FE model of the foot. To test the relative accuracy of the surrogate model outputs against those of the FE model, a single forward dynamics simulation was performed with FE calls at every integration step and compared with a corresponding simulation with the surrogate model included. Neural excitations obtained from the jump height optimization were used for this purpose and root mean square (RMS) difference between surrogate and FE model outputs (ankle force and moment, peak contact pressure and peak von Mises stress) were calculated. Results Optimization of jump height required 1800 iterations of the movement simulation, each requiring thousands of time steps. The surrogate modeling system only used the FE model in 5% of time steps, i.e. a 95% reduction of computation time. Errors introduced by the surrogate model were less than 1 mm in jump height and RMS errors of less than 2 N in ground reaction force, 0.25 Nm in ankle moment, and 10 kPa in peak tissue stress. Conclusion Adaptive surrogate modeling based on local regression allows efficient concurrent simulations of tissue mechanics and musculoskeletal movement

Model-Based Estimation of Muscle Forces Exerted During Movements

Estimation of individual muscle forces during human movement can provide insight into neural control and tissue loading and can thus contribute to improved diagnosis and management of both neurological and orthopaedic conditions. Direct measurement of muscle forces is generally not feasible in a clinical setting, and non-invasive methods based on musculoskeletal modeling should therefore be considered. The current state of the art in clinical movement analysis is that resultant joint torques can be reliably estimated from motion data and external forces (inverse dynamic analysis). Static optimization methods to transform joint torques into estimates of individual muscle forces using musculoskeletal models, have been known for several decades. To date however, none of these methods have been successfully translated into clinical practice. The main obstacles are the lack of studies reporting successful validation of muscle force estimates, and the lack of user-friendly and efficient computer software. Recent advances in forward dynamics methods have opened up new opportunities. Forward dynamic optimization can be performed such that solutions are less dependent on measured kinematics and ground reaction forces, and are consistent with additional knowledge, such as the force–length–velocity–activation relationships of the muscles, and with observed electromyography signals during movement. We conclude that clinical applications of current research should be encouraged, supported by further development of computational tools and research into new algorithms for muscle force estimation and their validation

Robust feature space separation for deep convolutional neural network training

This paper introduces two deep convolutional neural network training techniques that lead to more robust feature subspace separation in comparison to traditional training. Assume that dataset has M labels. The first method creates M deep convolutional neural networks called {DCNNi}M i=1 . Each of the networks DCNNi is composed of a convolutional neural network ( CNNi ) and a fully connected neural network ( FCNNi ). In training, a set of projection matrices are created and adaptively updated as representations for feature subspaces {S i}M i=1 . A rejection value is computed for each training based on its projections on feature subspaces. Each FCNNi acts as a binary classifier with a cost function whose main parameter is rejection values. A threshold value ti is determined for ith network DCNNi . A testing strategy utilizing {ti}M i=1 is also introduced. The second method creates a single DCNN and it computes a cost function whose parameters depend on subspace separations using the geodesic distance on the Grasmannian manifold of subspaces S i and the sum of all remaining subspaces {S j}M j=1,j≠i . The proposed methods are tested using multiple network topologies. It is shown that while the first method works better for smaller networks, the second method performs better for complex architectures

A Three-Dimensional Inverse Finite Element Analysis of the Heel Pad

Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir (“An Elaborate Data Set Characterizing the Mechanical Response of the Foot,” ASME J. Biomech. Eng., 131 (9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson’s ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization