Non-uniqueness of the bicompartmental contact force solution in a lumped-parameter mathematical model of the knee.
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Biomedical subjects
Publications and source records attributed to J G Andrews.
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Many anatomic structures around the hip contribute either actively (i.e., muscle contractile elements) or passively (i.e., capsule, ligaments, non-contractile portions of muscles) to the intersegmental resultant forces and moments. Investigators have often assumed that the passive elements contribute negligibly to those moments, but without substantial supporting data. We explored this assumption by measuring the 'passive moments' in 15 normal subjects from near full extension to 60 degrees of hip flexion at speeds used in slow and normal walking. The data suggest that throughout most of the gait cycle and normal stair climbing, the passive structures contribute a small portion of the total moment, usually well less than 10%. Thus, for this limited range of activities, the assumption of negligible contribution of passive structures is reasonable.
The single joint distribution problem with two or more unknown bony contact forces is considered, and an optimal solution procedure free of ad hoc assumptions is described. If two bony contact forces are present, a strictly muscle force dependent equality constraint exists that allows for initial independent estimation of muscle forces, followed by unique estimation of all bony contact force components perpendicular to the straight line connecting their known points of application. However, if three or more bony contact forces are present, no strictly muscle force dependent equality constraint exists, solution separability is lost, and optimal muscle and bony contact forces are obtained simultaneously.
This paper describes an experimental investigation to determine the biomechanical efficacy of the extensor carpi radialis longus (ECRL) to extensor carpi ulnaris (ECU) tendon transfer procedure used in rheumatoid hand reconstruction. Six normal cadaver specimens were tested in an apparatus that measured (a) the forces acting on the hand to restrain it in seven characteristic wrist configurations, and (b) the amount of hand pronation/supination that occurred as a result of loads applied to the tendons of the six major wrist muscles. Each specimen was tested with the ECRL tendon intact, surgically released, and transferred to the insertion point of ECU. In the intact and transferred states, the ECRL tendon was loaded sequentially while the remaining five wrist tendons were subjected to equal constant loads. In all three experimental ECRL test states, forces were also applied to all intact wrist tendons in a manner designed to represent physiologic load sharing. When the ECRL tendon was loaded sequentially, the transfer resulted in the predictable increase in the radially directed restraining force and the predictable supination of the hand relative to the forearm. When all intact tendons were loaded physiologically, the transfer also resulted in an increase in the radially directed restraining force. Significant differences between test states occurred generally only between the intact and release states of the ECRL tendon and not between release and transferred states.(ABSTRACT TRUNCATED AT 250 WORDS)
The purposes of this study were to describe the functional roles of the hamstrings and quadriceps at the hip and knee during cycling as determined both by the standard kinetic (SK) classification method and by the Andrews kinematic (AK) classification method (Andrews, J. biomech Engng 107, 348-353, 1985), and to examine the effect of using these two different methods on the existence of paradoxical muscle behavior (Lombard's Paradox). The results of this study indicated that the functional roles determined by the SK and AK methods differed considerably, and these differences led to the existence of paradoxical behavior in the hamstrings and quadriceps at different regions of the crank cycle. Both classification methods led to the existence of considerable paradoxical muscle behavior, with the SK method predicting somewhat more non-paradoxical activity and somewhat less paradoxical activity than the AK method at both the hip and the knee.
The purpose of this investigation was to obtain a comprehensive description of the kinematic behavior of the combined talocalcaneal/talocrural joint during the support phase of running. Considerable variation in kinematic data was exhibited by a heterogeneous subject sample (N = 5). The results indicated that: eversion/inversion may not be the only rotational component that should be considered when examining total talocalcaneal/talocrural joint motion; the common definitions for pronation and supination do not always accurately describe the relative motion of the shank relative to the calcaneus; and a combined talocalcaneal/talocrural joint behaving as an oblique hinge was not an adequate model for describing the relative motion of the shank with respect to the calcaneus. It was concluded that further investigation is needed to categorize subjects according to common kinematic characteristics. This categorization may be necessary to better understand characteristic variations in normal joint behavior, to diagnose joint pathology, and to prescribe effective injury prevention and rehabilitation modalities.
The objectives of this study were to describe the three-dimensional in vivo kinematic behavior of wrists affected by rheumatoid arthritis, to correlate kinematic parameters and two radiographic indices of carpal disease, and to describe the in vivo kinematic behavior of the Swanson Silastic wrist implant. Fifteen normal wrists, 17 rheumatoid wrists, and 7 wrists with Silastic wrist implants were tested using a three-dimensional sonic digitizing system. The motion of the hand segment relative to the forearm segment, corresponding to the positions exhibited during flexion-extension motion (FEM) and radial-ulnar deviation (RUD), was described using the equivalent screw displacement (ESD) concept. The mean magnitudes of ESD rotation for both FEM and RUD were statistically different (p less than 0.05) among the normal, rheumatoid, and implant groups. The remaining ESD parameters (i.e., mean values for the translation, the direction angles of the ESD axis, and the intercepts of this axis with the planes of motion), the minimum separation between the FEM and RUD axes, and the coordinates of the midpoint of this separation were not statistically different (p greater than 0.05) among the normal, rheumatoid, and implant groups. The two radiographic indices (carpal collapse and carpal translation) did not correlate with the magnitude of rotation or with any other ESD parameter.
This article describes and explains the moment arm vector (MAV) concept, uses the concept for the quantitative classification of hip muscles according to action, and applies the findings to selected clinical problems. A three-dimensional, straight-line model of hip musculature was used. Measurements made on a matched, dry bone specimen provided muscle attachment point location data for the model. Straight lines of muscle action between attachment sites were simulated for a variety of hip configurations during simple hip motions in three principal anatomical planes. We used the MAV concept to identify the three contributions of a muscle (flexion-extension, abduction-adduction, and internal-external rotation) tending to rotate the thigh segment relative to the pelvis. Muscles were classified according to their action or turning effect at 0, 40, and 90 degrees of hip flexion. Certain muscles exhibited significant changes in their action during these simple motions. Model results were verified using an articulated, dry bone specimen with elastic strings stretched between muscle attachment sites. Based on this geometrical model, a "pathological posture" of hip flexion, adduction, and internal rotation was identified, which is a posture prevalent in spastic, brain damaged patients.
The purposes of this study were (1) to describe normal wrist kinetics, and (2) to investigate the in-vitro kinetics of four currently available wrist prostheses (Swanson, Meuli, Volz, Hamas). The effective tendon moment arms of the six major wrist muscles were determined through the use of load cells and applied weights. Testing was conducted in a neutral wrist configuration with hand pronation-supination both constrained and unconstrained. The results indicate that each of the muscles studied has a unique set of effective tendon moment arms about the normal wrist as well as about wrists with the implanted prostheses, and that none of the prosthetic wrists studied duplicated normal wrist kinetics.
This paper presents a general classification method for determining the functional role of any muscle, and a procedure for determining the sensitivity of that role to small changes in system parameters. The classification method is based on the premise that the system model, when acted upon solely by the muscle of interest, will depart from any initial rest configuration in such a way as to decrease the muscle's length. This method is particularly useful for multiple-joint muscles, and is illustrated by examining a slider-crank mechanism and straight line muscle model to determine the functional role of the hamstrings during a constrained leg flexion motion.
This paper briefly reviews the concept of the center of percussion of a rigid body, with special emphasis on the requirements for its existence, the two complementary methods used to determine its location, and the system parameters on which its location depends. A consistent generalization of this concept is then proposed for the case when the rigid body is initially moving arbitrarily in three-dimensional inertial space and is restrained in such a way that no impulsive reaction torque can be applied to the body at the point of restraint. The basic requirement for the existence of a center of percussion in this generalized case is identified, and the location of the center of percussion is obtained using one of the two complementary solution methodologies. Six special cases are considered when the existence requirement is satisfied, and these cases are illustrated using examples from common sport situations.
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This paper identifies those particular force and torque quantities that arise most frequently in biomechanical investigations, and which, when appropriately combined with the system's kinematic behavior, appear to be related most directly to muscular effort, i.e., the metabolic cost associated with producing muscle tension, in a joint neighborhood. Depending upon whether the joint distribution problem has been solved, muscular effort is best determined either by the individual variable muscle force magnitudes or by the magnitude of the variable muscle force-dependent component of the resultant joint torque. Discrete biomechanical measures that can be used to represent these continuously-varying scalar functions are identified and examined critically. These include instantaneous measures (e.g., the extremes and other characteristic force, torque, and power values) and interval measures (e.g., average force, torque, and power values, work performed, change in mechanical energy, and linear and angular impulses). If the variation of the effort function is negligible, instantaneous measures may suffice provided there exists a reliable scaling factor relating these quantities to metabolic cost. If the variation of the effort function is appreciable, then properly weighted impulse measures may be the most appropriate because they appear to reflect muscular effort over the widest range of human activities, including those that involve isometric contractions.
An analytical method is presented for determining the post-impact motion of a rough elastic ball which collides with and rebounds from an arbitrarily oriented rough inertial surface. Pre-impact ball motion is completely general, and the contact interface is assumed to be sufficiently rough to provide a no-slip condition during the restitution phase of the short impact interval. A solution to the impulse-momentum equations is obtained by using Newton's linear coefficient of restitution, and by introducing a torsional coefficient of restitution to account for changes in the magnitude and direction of the component of the ball's angular velocity vector perpendicular to the inertial surface. This method is used to analyze the hop or hook-serve used in advanced-level handball play. An expression for the hop angle gamma is derived, which depends on the components of the mass center velocity and angular velocity vectors imparted to the ball by the server. These results are consistent with the natural tendency for right- and left-handed servers to generate characteristic hops to the left and right, respectively. These same results also indicate, however, that many handball authorities are not giving proper instructions when teaching hop servers how the ball should be spinning after hand impact.
The instantaneous functional role of a voluntary muscle in the neighborhood of a joint is often described in clinical terms (e.g. flexor; abductor; external rotator; agonist; contracting concentrically and isokinetically) that seen sufficiently explicit and clear in certain simple situations, but have not yet been carefully defined in precise biomechanical terminology for the general case. In order to describe the functional role of a voluntary muscle as its acts to change and/or maintain the configuration of a joint, it is necessary to make certain modeling assumptions. These include modeling the joint, modeling the muscle force line of action in the joint neighborhood, and establishing the location and orientation of the three joint axes for all possible joint configurations. Modeling the joint as a point leads to simple and sensible definitions which are consistent with clinical practice. The straight line model is most conveniently used to establish the muscle force line of action. A RHO coordinate system embedded in the distal joint segment with origin at the joint center point, and with intersecting axes coincident with the F/E, A/A and I/XR axes when the joint is in the anatomical position, is the joint coordinate system of choice to describe the turning effects of the muscle about the joint. Sensible and simple biomechanical definitions for clinical terms describing muscular contractions (i.e. concentric; eccentric; isometric; isokinetic; isotonic) were presented and appear to be relatively uncontroversial. Alternative biomechanical definitions for agonistic and antagonistic muscular activity were also presented, as were arguments for choosing a simple definition based on using the joint resultant moment as the criterion measure relative to which the individual muscle's moment about J should be compared. Biomechanical definitions for determining when a muscle functions as a joint flexor or extensor, abductor or adductor, and internal or external rotator were also presented. These definitions were based on the classical concept where the muscle's instantaneous turning effect is determined by its moment about the joint center. The algebraic signs and relative magnitudes of the components of the muscle's moment about J were used to determine not only the functional behavior of the muscle (e.g. flexor vs. extensor), but also the relative contributions of the muscle to producing rotations about the three joint axes through J. A detailed critique of the restricted functional classification scheme proposed by Molbech and Carlsöö was also presented.(ABSTRACT TRUNCATED AT 400 WORDS)
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Biomechanics researchers have relied heavily on the inverse dynamics approach for calculating the forces and torques at human joints. However, implicit in this approach is the assumption that there are sufficient independent equations of motion to uniquely determine these unknown kinetics. There exists a class of problems, commonly referred to as closed loop problems, when there are insufficient equations and indeterminacy arises. The purposes of the present paper are (1) to develop a general classification system of closed loop problems for whole body movements; and (2) to identify the minimum number of force transducing devices necessary to uniquely determine joint kinetics for these problems. The classification system is based on the human subject's interaction with his environment and with himself. Two criteria are considered: first, the number of the subject's extremities in contact with fixed external reference systems, and second, the number of closed loops formed by those extremities not in contact with fixed external systems. Different combinations of these two criteria are examined and grouped into five cases according to the degree to which the equations of motion are over-determined, determined, or under-determined. Examples are given to illustrate the concepts. It is felt that the use of this system should aid in the understanding of joint force and torque calculations, especially with regard to the under-determined cases.