Biomedical subjects

F C Anderson

Publications and source records attributed to F C Anderson.

10 recordsLinked to original sources

PubMed2001

Static and dynamic optimization solutions for gait are practically equivalent.

The proposition that dynamic optimization provides better estimates of muscle forces during gait than static optimization is examined by comparing a dynamic solution with two static solutions. A 23-degree-of-freedom musculoskeletal model actuated by 54 Hill-type musculotendon units was used to simulate one cycle of normal gait. The dynamic problem was to find the muscle excitations which minimized metabolic energy per unit distance traveled, and which produced a repeatable gait cycle. In the dynamic problem, activation dynamics was described by a first-order differential equation. The joint moments predicted by the dynamic solution were used as input to the static problems. In each static problem, the problem was to find the muscle activations which minimized the sum of muscle activations squared, and which generated the joint moments input from the dynamic solution. In the first static problem, muscles were treated as ideal force generators; in the second, they were constrained by their force-length-velocity properties; and in both, activation dynamics was neglected. In terms of predicted muscle forces and joint contact forces, the dynamic and static solutions were remarkably similar. Also, activation dynamics and the force-length-velocity properties of muscle had little influence on the static solutions. Thus, for normal gait, if one can accurately solve the inverse dynamics problem and if one seeks only to estimate muscle forces, the use of dynamic optimization rather than static optimization is currently not justified. Scenarios in which the use of dynamic optimization is justified are suggested.

Computer Simulation↗

PubMed2001

Dynamic optimization of human walking.

A three-dimensional, neuromusculoskeletal model of the body was combined with dynamic optimization theory to simulate normal walking on level ground. The body was modeled as a 23 degree-of-freedom mechanical linkage, actuated by 54 muscles. The dynamic optimization problem was to calculate the muscle excitation histories, muscle forces, and limb motions subject to minimum metabolic energy expenditure per unit distance traveled. Muscle metabolic energy was calculated by slimming five terms: the basal or resting heat, activation heat, maintenance heat, shortening heat, and the mechanical work done by all the muscles in the model. The gait cycle was assumed to be symmetric; that is, the muscle excitations for the right and left legs and the initial and terminal states in the model were assumed to be equal. Importantly, a tracking problem was not solved. Rather only a set of terminal constraints was placed on the states of the model to enforce repeatability of the gait cycle. Quantitative comparisons of the model predictions with patterns of body-segmental displacements, ground-reaction forces, and muscle activations obtained from experiment show that the simulation reproduces the salient features of normal gait. The simulation results suggest that minimum metabolic energy per unit distance traveled is a valid measure of walking performance.

Adult↗

PubMed2000

A governing relationship for repetitive muscular contraction.

During repetitive contractions, muscular work has been shown to exhibit complex relationships with muscle strain length, cycle frequency, and muscle shortening velocity. Those complex relationships make it difficult to predict muscular performance for any specific set of movement parameters. We hypothesized that the relationship of impulse with cyclic velocity (the product of shortening velocity and cycle frequency) would be independent of strain length and that impulse-cyclic velocity relationships for maximal cycling would be similar to those of in situ muscle performing repetitive contraction. Impulse and power were measured during maximal cycle ergometry with five cycle-crank lengths (120-220mm). Kinematic data were recorded to determine the relationship of pedal speed with joint angular velocity. Previously reported in situ data for rat plantaris were used to calculate values for impulse and cyclic velocity. Kinematic data indicated that pedal speed was highly correlated with joint angular velocity at the hip, knee, and ankle and was, therefore, considered a valid indicator of muscle shortening velocity. Cycling impulse-cyclic velocity relationships for each crank length were closely approximated by a rectangular hyperbola. Data for all crank lengths were also closely approximated by a single hyperbola, however, impulse produced on the 120mm cranks differed significantly from that on all other cranks. In situ impulse-cyclic velocity relationships exhibited similar characteristics to those of cycling. The convergence of the impulse-cyclic velocity relationships from most crank and strain lengths suggests that impulse-cyclic velocity represents a governing relationship for repetitive muscular contraction and thus a single equation can predict muscle performance for a wide range of functional activities. The similarity of characteristics exhibited by cycling and in situ muscle suggests that cycling can serve as a window though which to observe basic muscle function and that investigators can examine similar questions with in vivo and in situ models.

Adult↗

PubMed1995

Application of high-performance computing to numerical simulation of human movement.

We have examined the feasibility of using massively-parallel and vector-processing supercomputers to solve large-scale optimization problems for human movement. Specifically, we compared the computational expense of determining the optimal controls for the single support phase of gait using a conventional serial machine (SGI Iris 4D25), a MIMD parallel machine (Intel iPSC/860), and a parallel-vector-processing machine (Cray Y-MP 8/864). With the human body modeled as a 14 degree-of-freedom linkage actuated by 46 musculotendinous units, computation of the optimal controls for gait could take up to 3 months of CPU time on the Iris. Both the Cray and the Intel are able to reduce this time to practical levels. The optimal solution for gait can be found with about 77 hours of CPU on the Cray and with about 88 hours of CPU on the Intel. Although the overall speeds of the Cray and the Intel were found to be similar, the unique capabilities of each machine are better suited to different portions of the computational algorithm used. The Intel was best suited to computing the derivatives of the performance criterion and the constraints whereas the Cray was best suited to parameter optimization of the controls. These results suggest that the ideal computer architecture for solving very large-scale optimal control problems is a hybrid system in which a vector-processing machine is integrated into the communication network of a MIMD parallel machine.

Computer Systems↗

PubMed1995

Optimal control of non-ballistic muscular movements: a constraint-based performance criterion for rising from a chair.

To understand how humans perform non-ballistic movements, we have developed an optimal control model to simulate rising from a chair. The human body was modeled as a three-segment, articulated, planar linkage, with adjacent links joined together by frictionless revolutes. The skeleton was actuated by eight musculotendinous units with each muscle modeled as a three-element entity in series with tendon. Because rising from a chair presents a relatively ambiguous performance criterion, we chose to evaluate a number of different performance criteria, each based upon a fundamental dynamical property of movement; muscle force. Through a quantitative comparison of model and experiment, we found that neither a minimum-impulse nor a minimum-energy criterion is able to reproduce the major features of standing up. Instead, we introduce a performance criterion based upon an important and previously overlooked dynamical property of muscle: the time derivative of force. Our motivation for incorporating such a quantity into a mathematical description of the goal of a motor task is founded upon the belief that non-ballistic movements are controlled by gradual increases in muscle force rather than by rapid changes in force over time. By computing the optimal control solution for rising from a static squatting position, we show that minimizing the integral of a quantity which depends upon the time derivative of muscle force meets an important physiological requirement: it minimizes the peak forces developed by muscles throughout the movement. Furthermore, by computing the optimal control solution for rising from a chair, we demonstrate that multi-joint coordination is dictated not only by the choice of a performance criterion but by the presence of a motion constraint as well.

Adult↗

PubMed1993

Storage and utilization of elastic strain energy during jumping.

Based upon the optimal control solutions to a maximum-height countermovement jump (CMJ) and a maximum-height squat jump (SJ), this paper provides a quantitative description of how tendons and the elastic elements of muscle store and deliver energy during vertical jumping. After confirming the ability of the model to replicate the major features of each jump (i.e. muscle activation patterns, body-segmental motions, ground reaction forces, jump height, and total ground contact time), the time histories of the forces and shortening velocities of all the musculotendon actuators in the model were used to calculate the work done on the skeleton by tendons as well as the series-elastic elements, the parallel-elastic elements, and the contractile elements of muscle. We found that all the elastic tissues delivered nearly the same amount of energy to the skeleton during a CMJ and an SJ. The reason is twofold: first, nearly as much elastic strain energy was stored during the SJ as the CMJ; second, more stored elastic strain energy was lost as heat during the CMJ. There was also a difference in the way energy was stored during each jump. During the CMJ, strain energy stored in the elastic tissues came primarily from the gravitational potential energy of the skeleton as the more proximal extensor muscles were stretched during the downward phase of the jump. During the SJ, on the other hand, energy stored in the elastic tissues came primarily from the contractile elements as they did work to stretch the tendons and the series-elastic elements of the muscles. Increasing tendon compliance in the model led to an increase in elastic energy storage and utilization, but it also decreased the amount of energy delivered by the contractile elements to the skeleton. Jump height therefore remained almost the same for both jumps. These results suggest that elastic energy storage and utilization enhance jumping efficiency much more than overall jumping performance.

Adult↗

PubMed1992

A parameter optimization approach for the optimal control of large-scale musculoskeletal systems.

This paper describes a computational method for solving optimal control problems involving large-scale, nonlinear, dynamical systems. Central to the approach is the idea that any optimal control problem can be converted into a standard nonlinear programming problem by parameterizing each control history using a set of nodal points, which then become the variables in the resulting parameter optimization problem. A key feature of the method is that it dispenses with the need to solve the two-point, boundary-value problem derived from the necessary conditions of optimal control theory. Gradient-based methods for solving such problems do not always converge due to computational errors introduced by the highly nonlinear characteristics of the costate variables. Instead, by converting the optimal control problem into a parameter optimization problem, any number of well-developed and proven nonlinear programming algorithms can be used to compute the near-optimal control trajectories. The utility of the parameter optimization approach for solving general optimal control problems for human movement is demonstrated by applying it to a detailed optimal control model for maximum-height human jumping. The validity of the near-optimal control solution is established by comparing it to a solution of the two-point, boundary-value problem derived on the basis of a bang-bang optimal control algorithm. Quantitative comparisons between model and experiment further show that the parameter optimization solution reproduces the major features of a maximum-height, countermovement jump (i.e., trajectories of body-segmental displacements, vertical and fore-aft ground reaction forces, displacement, velocity, and acceleration of the whole-body center of mass, pattern of lower-extremity muscular activity, jump height, and total ground contact time).

Adult↗

PubMed1990

Interlaboratory quality assurance program.

The Coulter Interlaboratory Quality Assurance Program (IQAP) analyses data from several thousand haematology laboratories which use Coulter haematology controls (4C). Such peer group analyses are done at monthly intervals. These analyses compare the individual laboratory's performance with other laboratories using the same lot(s) of control cells on the same instruments. The data receipt and peer analysis methods are outlined using flow charts which describe the process.

Clinical Laboratory Techniques↗

PubMed1969

Oxygen flow rates.

Explore the source record for details and available documents.

Blood Chemical Analysis↗

PubMedDate not supplied

Dynamic simulation of human movement using large-scale models of the body.

A three-dimensional model of the body was used to simulate two different motor tasks: vertical jumping and normal walking on level ground. The pattern of muscle excitations, body motions, and ground-reaction forces for each task were calculated using dynamic optimization theory. For jumping, the performance criterion was to maximize the height reached by the center of mass of the body; for walking, the measure of performance was metabolic energy consumed per meter walked. Quantitative comparisons of the simulation results with experimental data obtained from people indicate that the model reproduces the salient features of maximum-height jumping and normal walking on the level. Analyses of the model solutions will allow detailed explanations to be given about the actions of specific muscles during each of these tasks.

Biomechanical Phenomena↗