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M G Pandy

Publications and source records attributed to M G Pandy.

At least 19 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

Musculoskeletal model of the upper limb based on the visible human male dataset.

A mathematical model of the human upper limb was developed based on high-resolution medical images of the muscles and bones obtained from the Visible Human Male (VHM) project. Three-dimensional surfaces of the muscles and bones were reconstructed from Computed Tomography (CT) images and Color Cryosection images obtained from the VHM cadaver. Thirteen degrees of freedom were used to describe the orientations of seven bones in the model: clavicle, scapula, humerus, radius, ulna, carpal bones, and hand. All of the major articulations from the shoulder girdle down to the wrist were included in the model. The model was actuated by 42 muscle bundles, which represented the actions of 26 muscle groups in the upper limb. The paths of the muscles were modeled using a new approach called the Obstacle-set Method [33]. The calculated paths of the muscles were verified by comparing the muscle moment arms computed in the model with the results of anatomical studies reported in the literature. In-vivo measurements of maximum isometric muscle torques developed at the shoulder, elbow, and wrist were also used to estimate the architectural properties of each musculotendon actuator in the model. The entire musculoskeletal model can be reconstructed using the data given in this paper, along with information presented in a companion paper which defines the kinematic structure of the model [26].

Adult↗
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↗
PubMed2001

Computer modeling and simulation of human movement.

Recent interest in using modeling and simulation to study movement is driven by the belief that this approach can provide insight into how the nervous system and muscles interact to produce coordinated motion of the body parts. With the computational resources available today, large-scale models of the body can be used to produce realistic simulations of movement that are an order of magnitude more complex than those produced just 10 years ago. This chapter reviews how the structure of the neuromusculoskeletal system is commonly represented in a multijoint model of movement, how modeling may be combined with optimization theory to simulate the dynamics of a motor task, and how model output can be analyzed to describe and explain muscle function. Some results obtained from simulations of jumping, pedaling, and walking are also reviewed to illustrate the approach.

Bone and Bones↗
PubMed1997

A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions.

A model of the knee in the sagittal plane was developed to study the forces in the ligaments induced by isometric contractions of the extensor and flexor muscles. The geometry of the distal femur was obtained from cadaver data. The tibial plateau and patellar facet were modeled as flat surfaces. Eleven elastic elements were used to describe the mechanical behavior of the anterior and posterior cruciate ligaments (ACL and PCL), the medial and lateral collateral ligaments (MCL and LCL), and the posterior capsule. The model knee was actuated by 11 musculotendinous units, each muscle represented by a Hill-type contractile element, a series-elastic element, and a parallel-elastic element. Tendon was assumed to be elastic. The response of the model to anterior-posterior drawer suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Calculations for a simulated quadriceps leg raise indicate further that the two-dimensional model reproduces the response of the three-dimensional knee under similar conditions of loading and constraint. During maximum isometric contractions of the quadriceps, the model ACL is loaded from full extension to 80 degrees C of flexion; the model PCL is loaded at 70 degrees of flexion and greater. For maximum isometric extension, ACL forces in the range 0-20 degrees of flexion depend most heavily upon the force-length properties of the quadriceps. At flexion angles greater than 20 degrees, cruciate ligament forces are determined by the geometry of the articulating surfaces of the bones. During isolated contractions of the hamstrings and gastrocnemius muscles, the model ACL is loaded from full extension to 10 degrees of flexion; the model PCL is loaded at all flexion angles greater than 10 degrees. Isolated contractions of the flexor muscles cannot unload the ACL near full extension, as the behavior of the ACL in this region is governed by the shapes of the bones. At 10 degrees of flexion or greater, the overall pattern of PCL force is explained by the force length properties of the hamstrings and by the geometrical arrangement of the flexor muscles about the knee.

Adult↗
PubMed1997

Dependence of cruciate-ligament loading on muscle forces and external load.

A sagittal-plane model of the knee is used to predict and explain the relationships between the forces developed by the muscles, the external loads applied to the leg, and the forces induced in the cruciate ligaments during isometric exercises. The geometry of the model bones is adapted from cadaver data. Eleven elastic elements describe the geometric and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by 11 musculotendinous units, each unit represented as a three-element muscle in series with tendon. For isolated contractions of the quadriceps, ACL force increases as quadriceps force increases for all flexion angles between 0 and 80 degrees; the ACL is unloaded at flexion angles greater than 80 degrees. When quadriceps force is held constant, ACL force decreases monotonically as knee-flexion angle increases. The relationship between ACL force, quadriceps force, and knee-flexion angle is explained by the geometry of the knee-extensor mechanism and by the changing orientation of the ACL in the sagittal plane. For isolated contractions of the hamstrings, PCL force increases as hamstrings force increases for all flexion angles greater than 10 degrees; the PCL is unloaded at flexion angles less than 10 degrees. When hamstrings force is held constant, PCL force increases monotonically with increasing knee flexion. The relationship between PCL force, hamstrings force, and knee-flexion angle is explained by the geometry of the hamstrings and by the changing orientation of the PCL in the sagittal plane. At nearly all knee-flexion angles, hamstrings co-contraction is an effective means of reducing ACL force. Hamstrings co-contraction cannot protect the ACL near full extension of the knee because these muscles meet the tibia at small angles near full extension, and so cannot apply a sufficiently large posterior shear force to the leg. Moving the restraining force closer to the knee-flexion axis decreases ACL force; varying the orientation of the restraining force has only a small effect on cruciate-ligament loading.

Anterior Cruciate Ligament↗
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↗
PubMed1993

A two-dimensional dynamic model of the human knee joint.

A two-dimensional dynamic model of the knee joint was incorporated into a four-segment, eight-muscle model of the human body to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans stand up from a static squatting position. Our optimal control model predicted peak tibiofemoral contact forces as high as 8 times body weight. Furthermore, ligament forces, especially those in the anterior-cruciate, were nearly body weight as knee flexion approached 90 degrees. Ligament and tibiofemoral contact loads were dominated by the forces exerted by muscles during the movement.

Biomechanical Phenomena↗
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↗
PubMed1991

Optimal muscular coordination strategies for jumping.

This paper presents a detailed analysis of an optimal control solution to a maximum height squat jump, based upon how muscles accelerate and contribute power to the body segments during the ground contact phase of jumping. Quantitative comparisons of model and experimental results expose a proximal-to-distal sequence of muscle activation (i.e. from hip to knee to ankle). We found that the contribution of muscles dominates both the angular acceleration and the instantaneous power of the segments. However, the contributions of gravity and segmental motion are insignificant, except the latter become important during the final 10% of the jump. Vasti and gluteus maximus muscles are the major energy producers of the lower extremity. These muscles are the prime movers of the lower extremity because they dominate the angular acceleration of the hip toward extension and the instantaneous power of the trunk. In contrast, the ankle plantarflexors (soleus, gastrocnemius, and the other plantarflexors) dominate the total energy of the thigh, though these muscles also contribute appreciably to trunk power during the final 20% of the jump. Therefore, the contribution of these muscles to overall jumping performance cannot be neglected. We found that the biarticular gastrocnemius increases jump height (i.e. the net vertical displacement of the center of mass of the body from standing) by as much as 25%. However, this increase is not due to any unique biarticular action (e.g. proximal-to-distal power transfer from the knee to the ankle), since jumping performance is similar when gastrocnemius is replaced with a uniarticular ankle plantarflexor.

Adult↗
PubMed1990

An optimal control model for maximum-height human jumping.

To understand how intermuscular control, inertial interactions among body segments, and musculotendon dynamics coordinate human movement, we have chosen to study maximum-height jumping. Because this activity presents a relatively unambiguous performance criterion, it fits well into the framework of optimal control theory. The human body is modeled as a four-segment, planar, articulated linkage, with adjacent links joined together by frictionless revolutes. Driving the skeletal system are eight musculotendon actuators, each muscle modeled as a three-element, lumped-parameter entity, in series with tendon. Tendon is assumed to be elastic, and its properties are defined by a stress-strain curve. The mechanical behavior of muscle is described by a Hill-type contractile element, including both series and parallel elasticity. Driving the musculotendon model is a first-order representation of excitation-contraction (activation) dynamics. The optimal control problem is to maximize the height reached by the center of mass of the body subject to body-segmental, musculotendon, and activation dynamics, a zero vertical ground reaction force at lift-off, and constraints which limit the magnitude of the incoming neural control signals to lie between zero (no excitation) and one (full excitation). A computational solution to this problem was found on the basis of a Mayne-Polak dynamic optimization algorithm. Qualitative comparisons between the predictions of the model and previously reported experimental findings indicate that the model reproduces the major features of a maximum-height squat jump (i.e. limb-segmental angular displacements, vertical and horizontal ground reaction forces, sequence of muscular activity, overall jump height, and final lift-off time).

Biomechanical Phenomena↗
PubMed1989

Quantitative assessment of gait determinants during single stance via a three-dimensional model--Part 1. Normal gait.

In this two-part paper, a variety of three-dimensional, dynamical models are constructed for simulating the single support phases of normal and pathological human gait. A major objective of this work is to quantify the influence of individual gait determinants on the ground reaction forces generated during normal, level walking. To this end, Part 1 presents a three-dimensional, seven degree-of-freedom model incorporating five of the six fundamental determinants of gait. On the basis of crude muscle-force and/or joint-moment trajectories, body-segmental motions and ground reaction forces are synthesized open loop. Through a quantitative comparison with experimental gait data, the model's predictions are evaluated. Our simulation results suggest that pelvic list is not as dominant a dynamical determinant as either stance knee flexion-extension or foot and knee interaction. Transverse pelvic rotation, however, makes an important contribution by limiting the magnitude of the horizontal ground reaction prior to opposite heel-strike.

Adult↗
PubMed1989

Quantitative assessment of gait determinants during single stance via a three-dimensional model--Part 2. Pathological gait.

A three-dimensional model for normal gait formulated in Part 1 is now altered to simulate the dynamics of pathological walking. Mechanisms fundamental to the production of a normal gait pattern are systematically removed, in order to assess contributions from individual gait determinants. Four separate pathological cases are studied: a model neglecting ankle plantarflexor activity; absence of stance knee flexion-extension and foot and knee interaction; both pelvic list and transverse pelvic rotation removed; and finally, a model with all major gait determinants missing. These are used collectively to show that stance knee flexion-extension and foot and knee interaction successively dominate lower-extremity dynamical response during the single support phase of normal gait. The hip abductor muscles, while effecting pelvic list, serve to stabilize this limb, rather than actively determine whole-body vertical acceleration. Mechanisms compensating for a loss in joint motion are also explored. Complete ankle loss may be successfully compensated with increased hip abductor muscle activity; the loss of both ankle and knee, however, demand unacceptable levels of vertical pelvic displacement.

Adult↗
PubMed1988

A numerical method for simulating the dynamics of human walking.

This paper presents a general method for simulating the movement of the lower extremity during human walking. It is based upon two separate algorithms: one for single support (an open kinematic chain), and the other for the double support phase (a closed-loop linkage). Central to each of these is the recursive Newton-Euler inverse dynamics algorithm, applicable, as given, to any serial, spatial linkage. For the unconstrained single support model, the Newton-Euler scheme is applied directly to numerically generate the equations of motion. In the case of double support, however, the kinematic constraint equations are used to first eliminate the redundant degrees of freedom, and then solve for the unknown ground reactions under the constrained limb. The attractiveness of the method is that it offers a compact alternative to manually deriving the equations defining a mathematical model for human gait.

Algorithms↗
PubMed1988

Synthesis of human walking: a planar model for single support.

A mathematical model for the single support phase of normal, level, human walking is formulated. The motion of the lower extremity is synthesized using a preprogrammed set of inputs, recognized by the model as a simple collection of applied joint moments. Two mechanisms are forwarded as candidates for producing the observed peaks in the vertical ground reaction. The first, stance knee flexion-extension, generates the necessary level of whole-body vertical acceleration during the initial region of single support (opposite toe-off to heel-off). A model accounting for the determinants of foot and knee interaction then predicts the second peak to be the result of an increasing ankle moment in the region from heel-off to opposite heel-strike.

Acceleration↗