An information-theoretic approach to motor action decoding with a reconfigurable parallel architecture.

Methods for decoding movements from neural spike counts using adaptive filters often rely on minimizing the mean-squared error. However, for non-Gaussian distribution of errors, this approach is not optimal for performance. Therefore, rather than using probabilistic modeling, we propose an alternate non-parametric approach. In order to extract more structure from the input signal (neuronal spike counts) we propose using minimum error entropy (MEE), an information-theoretic approach that minimizes the error entropy as part of an iterative cost function. However, the disadvantage of using MEE as the cost function for adaptive filters is the increase in computational complexity. In this paper we present a comparison between the decoding performance of the analytic Wiener filter and a linear filter trained with MEE, which is then mapped to a parallel architecture in reconfigurable hardware tailored to the computational needs of the MEE filter. We observe considerable speedup from the hardware design. The adaptation of filter weights for the multiple-input, multiple-output linear filters, necessary in motor decoding, is a highly parallelizable algorithm. It can be decomposed into many independent computational blocks with a parallel architecture readily mapped to a field-programmable gate array (FPGA) and scales to large numbers of neurons. By pipelining and parallelizing independent computations in the algorithm, the proposed parallel architecture has sublinear increases in execution time with respect to both window size and filter order.

Limitations of parallel global optimization for large-scale human movement problems.

Global optimization algorithms (e.g., simulated annealing, genetic, and particle swarm) have been gaining popularity in biomechanics research, in part due to advances in parallel computing. To date, such algorithms have only been applied to small- or medium-scale optimization problems (<100 design variables). This study evaluates the applicability of a parallel particle swarm global optimization algorithm to large-scale human movement problems. The evaluation was performed using two large-scale (660 design variables) optimization problems that utilized a dynamic, 27 degree-of-freedom, full-body gait model to predict new gait motions from a nominal gait motion. Both cost functions minimized a quantity that reduced the external knee adduction torque. The first one minimized footpath errors corresponding to an increased toe out angle of 15 degrees, while the second one minimized the knee adduction torque directly without changing the footpath. Constraints on allowable changes in trunk orientation, joint angles, joint torques, centers of pressure, and ground reactions were handled using a penalty method. For both problems, a single run with a gradient-based nonlinear least squares algorithm found a significantly better solution than did 10 runs with the global particle swarm algorithm. Due to the penalty terms, the physically realistic gradient-based solutions were located within a narrow "channel" in design space that was difficult to enter without gradient information. Researchers should exercise caution when extrapolating the performance of parallel global optimizers to human movement problems with hundreds of design variables, especially when penalty terms are included in the cost function.

Parallel asynchronous particle swarm optimization.

The high computational cost of complex engineering optimization problems has motivated the development of parallel optimization algorithms. A recent example is the parallel particle swarm optimization (PSO) algorithm, which is valuable due to its global search capabilities. Unfortunately, because existing parallel implementations are synchronous (PSPSO), they do not make efficient use of computational resources when a load imbalance exists. In this study, we introduce a parallel asynchronous PSO (PAPSO) algorithm to enhance computational efficiency. The performance of the PAPSO algorithm was compared to that of a PSPSO algorithm in homogeneous and heterogeneous computing environments for small- to medium-scale analytical test problems and a medium-scale biomechanical test problem. For all problems, the robustness and convergence rate of PAPSO were comparable to those of PSPSO. However, the parallel performance of PAPSO was significantly better than that of PSPSO for heterogeneous computing environments or heterogeneous computational tasks. For example, PAPSO was 3.5 times faster than was PSPSO for the biomechanical test problem executed on a heterogeneous cluster with 20 processors. Overall, PAPSO exhibits excellent parallel performance when a large number of processors (more than about 15) is utilized and either (1) heterogeneity exists in the computational task or environment, or (2) the computation-to-communication time ratio is relatively small.

Evaluation of a particle swarm algorithm for biomechanical optimization.

Optimization is frequently employed in biomechanics research to solve system identification problems, predict human movement, or estimate muscle or other internal forces that cannot be measured directly. Unfortunately, biomechanical optimization problems often possess multiple local minima, making it difficult to find the best solution. Furthermore, convergence in gradient-based algorithms can be affected by scaling to account for design variables with different length scales or units. In this study we evaluate a recently-developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithm's global search capabilities were investigated using a suite of difficult analytical test problems, while its scale-independent nature was proven mathematically and verified using a biomechanical test problem. For comparison, all test problems were also solved with three off-the-shelf optimization algorithms--a global genetic algorithm (GA) and multistart gradient-based sequential quadratic programming (SQP) and quasi-Newton (BFGS) algorithms. For the analytical test problems, only the PSO algorithm was successful on the majority of the problems. When compared to previously published results for the same problems, PSO was more robust than a global simulated annealing algorithm but less robust than a different, more complex genetic algorithm. For the biomechanical test problem, only the PSO algorithm was insensitive to design variable scaling, with the GA algorithm being mildly sensitive and the SQP and BFGS algorithms being highly sensitive. The proposed PSO algorithm provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units.

Determination of patient-specific multi-joint kinematic models through two-level optimization.

Dynamic patient-specific musculoskeletal models have great potential for addressing clinical problems in orthopedics and rehabilitation. However, their predictive capability is limited by how well the underlying kinematic model matches the patient's structure. This study presents a general two-level optimization procedure for tuning any multi-joint kinematic model to a patient's experimental movement data. An outer level optimization modifies the model's parameters (joint position and orientations) while repeated inner level optimizations modify the model's degrees of freedom given the current parameters, with the goal of minimizing errors between model and experimental marker trajectories. The approach is demonstrated by fitting a 27 parameter, three-dimensional, 12 degree-of-freedom lower-extremity kinematic model to synthetic and experimental movement data for isolated joint (hip, knee, and ankle) and gait (full leg) motions. For noiseless synthetic data, the approach successfully recovered the known joint parameters to within an arbitrarily tight tolerance. When noise was added to the synthetic data, root-mean-square (RMS) errors between known and recovered joint parameters were within 10.4 degrees and 10 mm. For experimental data, RMS marker distance errors were reduced by up to 62% compared to methods that estimate joint parameters from anatomical landmarks. Optimized joint parameters found using a loaded full-leg gait motion differed significantly from those found using unloaded individual joint motions. In the future, this approach may facilitate the creation of dynamic patient-specific musculoskeletal models for predictive clinical applications.

Evaluation of parallel decomposition methods for biomechanical optimizations.

As the complexity of musculoskeletal models continues to increase, so will the computational demands of biomechanical optimizations. For this reason, parallel biomechanical optimizations are becoming more common. Most implementations parallelize the optimizer. In this study, an alternate approach is investigated that parallelizes the analysis function (i.e., a kinematic or dynamic simulation) called repeatedly by the optimizer to calculate the cost function and constraints. To evaluate this approach, a system identification problem involving a kinematic ankle joint model was solved using a gradient-based optimizer and three parallel decomposition methods: gradient calculation decomposition, analysis function decomposition, or both methods combined. For a given number of processors, analysis function decomposition exhibited the best performance despite the highest communication and synchronization overhead, while gradient calculation decomposition demonstrated the worst performance due to the fact that the necessary line searches were not performed in parallel. These findings suggest that the method of parallelization most commonly used for biomechanical optimizations may not be the most efficient, depending on the optimization algorithm used. In many applications, the best computational strategy may be to focus on parallelizing the analysis function.