A multi-region collision probability method for determining neutron spectra and reaction rates

textThe collision probability approach to neutron transport can be used to obtain the energy-dependent neutron spectrum in nuclear reactor systems as well as other quantities of interest. This method makes the approximation that the neutron distribution is constant within homogeneous regions, or cells, in the system. This assumption restricts geometries that can be modeled by the collision probability approach. The geometry modeled is typically an infinite lattice of two homogeneous cells: a fuel pin cylinder and the coolant that surrounds it. The transport of neutrons between the homogeneous cells is done using probabilities describing the chance that a neutron having a collision in one cell has its next collision in another cell. These collision probabilities can be cast in terms of escape and transmission probabilities for each cell. Some methods exist that extend the collision probability approach to systems composed of more than two homogeneous cells. In this work, we present a novel collision probability method, based on previous work by Schneider et al. (2006a), for an arbitrary number of cells. The method operates by averaging the transmission probabilities across cells of the same shape, and thus assumes a certain level of homogeneity across all cells. When using multigroup cross sections, which the collision probability approach requires, it is necessary to consider the effect that a system's geometry and composition has on those multigroup cross sections. The cross sections must be computed in a way that accounts for the resonance self-shielding that may reduce the reaction rates in the resonance region. The process of developing self-shielded cross sections in a heterogeneous system utilizes an escape cross section. We compute this escape cross section using the same collision probabilities used to obtain the energy spectrum. Results are presented for simple two-cell systems, and preliminary results for four-cell simulations are also given. An extension to the method is provided that accounts for the fact that in thermal systems the assumption of homogeneity is not always valid.Mechanical Engineerin

Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies

Physics-based predictive simulations of human movement have the potential to support personalized medicine, but large computational costs and difficulties to model control strategies have limited their use. We have developed a computationally efficient optimal control framework to predict human gaits based on optimization of a performance criterion without relying on experimental data. The framework generates three-dimensional muscle-driven simulations in 36 min on average—more than 20 times faster than existing simulations—by using direct collocation, implicit differential equations and algorithmic differentiation. Using this framework, we identified a multi-objective performance criterion combining energy and effort considerations that produces physiologically realistic walking gaits. The same criterion also predicted the walk-to-run transition and clinical gait deficiencies caused by muscle weakness and prosthesis use, suggesting that diverse healthy and pathological gaits can emerge from the same control strategy. The ability to predict the mechanics and energetics of a broad range of gaits with complex three-dimensional musculoskeletal models will allow testing novel hypotheses about gait control and hasten the development of optimal treatments for neuro-musculoskeletal disorders.Postprint (published version

The formulation of the foot-ground contact model influences the computation time of biomechanical optimal control problems

Postprint (published version

Algorithmic differentiation improves the computational efficiency of OpenSim-based trajectory optimization of human movement

Algorithmic differentiation (AD) is an alternative to finite differences (FD) for evaluating function derivatives. The primary aim of this study was to demonstrate the computational benefits of using AD instead of FD in OpenSim-based trajectory optimization of human movement. The secondary aim was to evaluate computational choices including different AD tools, different linear solvers, and the use of first- or second-order derivatives. First, we enabled the use of AD in OpenSim through a custom source code transformation tool and through the operator overloading tool ADOL-C. Second, we developed an interface between OpenSim and CasADi to solve trajectory optimization problems. Third, we evaluated computational choices through simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We performed all simulations using direct collocation and implicit differential equations. Using AD through our custom tool was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The linear solver efficiency was problem-dependent and no solver was consistently more efficient. Using second-order derivatives was more efficient for balance simulations but less efficient for walking simulations. The walking simulations were physiologically realistic. These results highlight how the use of AD drastically decreases computational time of trajectory optimization problems as compared to more common FD. Overall, combining AD with direct collocation and implicit differential equations decreases the computational burden of trajectory optimization of human movement, which will facilitate their use for biomechanical applications requiring the use of detailed models of the musculoskeletal system.Postprint (published version

Subject-exoskeleton contact model calibration leads to accurate interaction force predictions

Knowledge of human–exoskeleton interaction forces is crucial to assess user comfort and effectiveness of the interaction. The subject-exoskeleton collaborative movement and its interaction forces can be predicted in silico using computational modeling techniques. We developed an optimal control framework that consisted of three phases. First, the foot-ground (Phase A) and the subject-exoskeleton (Phase B) contact models were calibrated using three experimental sit-to-stand trials. Then, the collaborative movement and the subject-exoskeleton interaction forces, of six different sit-to-stand trials were predicted (Phase C). The results show that the contact models were able to reproduce experimental kinematics of calibration trials (mean root mean square differences - RMSD - coordinates = 1.1° and velocities = 6.8°/s), ground reaction forces (mean RMSD= 22.9 N), as well as the interaction forces at the pelvis, thigh, and shank (mean RMSD = 5.4 N). Phase C could predict the collaborative movements of prediction trials (mean RMSD coordinates = 3.5° and velocities = 15.0°/s), and their subject-exoskeleton interaction forces (mean RMSD = 13.1° N). In conclusion, this optimal control framework could be used while designing exoskeletons to have in silico knowledge of new optimal movements and their interaction forces.Postprint (author's final draft

Computationally efficient predictive muscle-driven simulations of 3D walking

Postprint (published version

Effectively Quantifying the Performance of Lower-Limb Exoskeletons Over a Range of Walking Conditions

Exoskeletons and other wearable robotic devices have a wide range of potential applications, including assisting patients with walking pathologies, acting as tools for rehabilitation, and enhancing the capabilities of healthy humans. However, applying these devices effectively in a real-world setting can be challenging, as the optimal design features and control commands for an exoskeleton are highly dependent on the current user, task and environment. Consequently, robust metrics and methods for quantifying exoskeleton performance are required. This work presents an analysis of walking data collected for healthy subjects walking with an active pelvis exoskeleton over three assistance scenarios and five walking contexts. Spatial and temporal, kinematic, kinetic and other novel dynamic gait metrics were compared to identify which metrics exhibit desirable invariance properties, and so are good candidates for use as a stability metric over varying walking conditions. Additionally, using a model-based approach, the average metabolic power consumption was calculated for a subset of muscles crossing the hip, knee and ankle joints, and used to analyse how the energy-reducing properties of an exoskeleton are affected by changes in walking context. The results demonstrated that medio-lateral centre of pressure displacement and medio-lateral margin of stability exhibit strong invariance to changes in walking conditions. This suggests that these dynamic gait metrics are optimised in human gait and are potentially suitable metrics for optimising in an exoskeleton control paradigm. The effectiveness of the exoskeleton at reducing human energy expenditure was observed to increase when walking on an incline, where muscles aiding in hip flexion were assisted, but decrease when walking at a slow speed. These results underline the need for adaptive control algorithms for exoskeletons if they are to be used in varied environments

An object oriented implementation of the Yeadon human inertia model [v2; ref status: indexed, http://f1000r.es/558]

We present an open source software implementation of a popular mathematical method developed by M.R. Yeadon for calculating the body and segment inertia parameters of a human body. The software is written in a high level open source language and provides three interfaces for manipulating the data and the model: a Python API, a command-line user interface, and a graphical user interface. Thus the software can fit into various data processing pipelines and requires only simple geometrical measures as input

An object oriented implementation of the Yeadon human inertia model [v1; ref status: indexed, http://f1000r.es/4cr]

We present an open source software implementation of a popular mathematical method developed by M.R. Yeadon for calculating the body and segment inertia parameters of a human body. The software is written in a high level open source language and provides three interfaces for manipulating the data and the model: a Python API, a command-line user interface, and a graphical user interface. Thus the software can fit into various data processing pipelines and requires only simple geometrical measures as input