Biomechanical analysis of primate bipedal walking by computer simulation

A computer simulation technique was applied to make clear the mechanical characteristics of primate bipedal walking. A primate body and the walking mechanism were modeled mathematically with a set of dynamic equations. Using a digital computer, the following were calculated from these equations by substituting measured displacements and morphological data of each segment of the primate: the acceleration, joint angle, center of gravity, foot force, joint moment, muscular force, transmitted force at the joint, electric activity of the muscle, generated power by the leg and energy expenditure in walking.The model was evaluated by comparing some of the calculated results with the experimental results such as foot force and electromyographic data, and improved in order to obtain the agreement between them.The level bipedal walking of man, chimpanzee and Japanese monkey and several types of synthesized walking were analyzed from the viewpoint of biomechanics.It is concluded that the bipedal walking of chimpanzee is nearer to that of man than to that of the Japanese monkey because of its propulsive mechanism, but it requires large muscular force for supporting the body weight.     

Mechanics of running under simulated low gravity.

Using a linear mass-spring model of the body and leg (T. A. McMahon and G. C. Cheng. J. Biomech. 23: 65-78, 1990), we present experimental observations of human running under simulated low gravity and an analysis of these experiments. The purpose of the study was to investigate how the spring properties of the leg are adjusted to different levels of gravity. We hypothesized that leg spring stiffness would not change under simulated low-gravity conditions. To simulate low gravity, a nearly constant vertical force was applied to human subjects via a bicycle seat. The force was obtained by stretching long steel springs via a hand-operated winch. Subjects ran on a motorized treadmill that had been modified to include a force platform under the tread. Four subjects ran at one speed (3.0 m/s) under conditions of normal gravity and six simulated fractions of normal gravity from 0.2 to 0.7 G. For comparison, subjects also ran under normal gravity at five speeds from 2.0 to 6.0 m/s. Two basic principles emerged from all comparisons: both the stiffness of the leg, considered as a linear spring, and the vertical excursion of the center of mass during the flight phase did not change with forward speed or gravity. With these results as inputs, the mathematical model is able to account correctly for many of the changes in dynamic parameters that do take place, including the increasing vertical stiffness with speed at normal gravity and the decreasing peak force observed under conditions simulating low gravity.     

Contribution of the support limb in control of angular momentum after tripping

Tripping over an obstacle can result in a fall when the forward angular momentum, obtained from impact with the obstacle, is not arrested. Angular momentum can be restrained by proper placement of the recovery limb, anteriorly of the body, but possibly also by a reaction in the contralateral support limb during push-off. The purpose of this study was to quantify the extent to which the support limb contributes to recovery after tripping by providing time and clearance for proper positioning of the recovery limb, and by restraining the angular momentum of the body during push-off. Twelve young adults were repeatedly tripped over an obstacle during mid-swing, while walking over a platform. Kinematics and ground reaction forces at the support limb were measured. Quantification of the angular momentum was based on calculation of the external moment, which equals the rate of change in the angular momentum of the body. Results showed that all subjects acquired a similar increase in angular momentum during foot–obstacle contact, on average 11.4 kg m² s⁻¹. In all subjects, the support limb played a role in recovery after tripping by providing time and clearance for proper positioning of the recovery limb, as indicated by body elevation (6%) and the increased forward pelvis displacement over recovery stride (43%). Almost all subjects were also able to restrain the forward angular momentum of the body during push-off by the support limb. Less angular momentum remained to be further accomplished by the recovery limb. Reductions in the quality of the support limb responses may be among the factors that increase the risk of falling in the elderly.     

Modelling of the biomechanics of posture and balance

A technique for studying the relationship of posture to balance has been developed. To investigate this relationship quantitatively, the human body was treated as consisting of 11 rigid body segments, each with six degrees of freedom. A bilateral Selspot II/TRACK data acquisition system provides position and orientation kinematic data for estimation of the trajectories of the individual body segment centers of gravity. From these, the whole body center of gravity is estimated and compared to concurrent force plate center of force data. Center of gravity and center of force excursions agree where dynamics are not significant. The technique may be employed to study quiet stance, response to postural disturbances, or the initiation and coordination of complex movements such as gait.     

Dynamics of the in-run in ski jumping: a simulation study

A ski jumper tries to maintain an aerodynamic position in the in-run during changing environmental forces. The purpose of this study was to analyze the mechanical demands on a ski jumper taking the in-run in a static position. We simulated the in-run in ski jumping with a 4-segment forward dynamic model (foot, leg, thigh, and upper body). The curved path of the in-run was used as kinematic constraint, and drag, lift, and snow friction were incorporated. Drag and snow friction created a forward rotating moment that had to be counteracted by a plantar flexion moment and caused the line of action of the normal force to pass anteriorly to the center of mass continuously. The normal force increased from 0.88 G on the first straight to 1.65 G in the curve. The required knee joint moment increased more because of an altered center of pressure. During the transition from the straight to the curve there was a rapid forward shift of the center of pressure under the foot, reflecting a short but high angular acceleration. Because unrealistically high rates of change of moment are required, an athlete cannot do this without changing body configuration which reduces the required rate of moment changes.     

How do non-muscular torques contribute to the kinetics of postural recovery following a support surface translation?

The common platform translation paradigm used in balance control studies employs a disturbance event that applies non-muscular forces to the body for the duration of the disturbance. Previous research has explored the process of constructing the balance recovery by considering these perturbations to be trigger events, not events with an ongoing force application timeline. The purpose of this study was to quantify the effect of muscular and non-muscular torques on post-perturbation balance with particular interest in the role of the external perturbation in balance recovery. Five young adult males experienced backward translations of the support surface at three different speeds. Integration intervals were defined for each segment and angular impulses were calculated for a period of increasing angular momentum (destabilization), and a period of decreasing angular momentum (restabilization). Destabilization of distal segments was primarily due to impulse generated by the motion of the support surface. For the trunk, however, muscle and motion-dependent sources contributed most to increasing momentum. Restabilization of distal segments was achieved by muscle and platform impulses while trunk restabilization was achieved by muscle and motion-dependent terms in opposition to gravity. Increased platform speed resulted in increased muscular contribution only in the control of the trunk, while demand on distal musculature decreased with change in platform speed as the platform contribution to restabilization increased in these segments. Therefore, impulses from non-muscular sources, including the perturbation itself, are significant modifiers of the response to balance disturbances and must be accounted for in balance research.     

重力对锥形血管中血流压力的影响——基于考虑体位改变的三维流固耦合数学模型

重力是体位改变过程中最基本的生物力学刺激因素．血流压力是表征心血管功能状态的一个基本指标．目前,体位改变影响心血管系统的确切内部机制尚不清楚．为此,采用在流体和固体方程中分别引入体力项的方法,建立一个基于血流动力学概念的三维流固耦合数学模型,用以研究体位改变,确切量化重力对血流压力的影响．通过数值计算,得到以下结果．水平卧位条件下：a．单一血管中血流压力由无重力影响的轴对称二维分布变为重力影响下的三维不对称分布;b．随着进出口压差由小变大,重力对压力分布和极值的影响由大变小,当压差值分别达到10 665.6 Pa(80 mmHg)和2 666.4 Pa(20 mmHg)时,重力的影响就不再随进出口压差增大而变化;对三维单一流体,重力影响的总体趋势类似．对正、倒直立位,压力均为二维轴对称分布,其重力影响强度约为水平卧位的2倍以上．结果表明：基于血流动力学概念,引入体力项,建立三维流固耦合模型为研究体位改变提供了一种新思路,重力对单一血管中血流压力分布和大小的影响因体位不同而不同,并与进出口压差密切相关,提示,若血管进出口压差较小,忽略重力影响,不考虑体位改变,以二维轴对称模型来研究血管中血流状态,须谨慎解释所得结果．     

Geotaxis in protozoa I. A propulsion-gravity model for Tetrahymena (Ciliata)

A propulsion-based model for negative geotaxis of ciliated protozoa is presented which views geotaxic reorientation as the unbalancing of gyrational torque by a sedimentation torque. The balanced gyrational torque results from the location of the propulsive center of effort forward of the body center of mass. When gravity is ignored, the propulsive forces generating the gyrational moments may be confined to an envelope surrounding the cell. The effect of gravity is to induce sedimentation of the body-plus-envelope system. Viscous resistance to this sedimentation at the envelope “surface” is transmitted to the beating cilia whose net constant energy output must now deal with a new source of dissipation (not “present” when gravity was ignored) which is maximal in the downswing portion of the gyration cycle. In such a manner sedimentation resistance acts as a counter torque to the downswing gyrational moment of force and an enhancing torque to the upswing moment thereby generating a net upward reorientation of the gyrational axis. Upon addition of the translational component of propulsion, the negative geotaxis behavior pattern is completed. The forward location of the center of effort which provides the basic validity indicator for the model is verified by observations from the ciliate Tetrahymena.     

A planar model of the knee joint to characterize the knee extensor mechanism

A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.     

Standing sway: iterative estimation of the kinematics and dynamics of the lower extremities from force-plate measurements

In this study, a model for the estimation of the dynamics of the lower extremities in standing sway from force plate data only is presented. A three-dimensional, five-segment, four-joint model of the human body was used to describe postural standing sway dynamics. Force-plate data of the reactive forces and centers of pressure were measured bilaterally. By applying the equations of motion to these data, the transversal trajectory of the center of gravity (CG) of the body was resolved in the sagittal and coronal planes. An inverse kinematics algorithm was used to evaluate the kinematics of the body segments. The dynamics of the segments was then resolved by using the Newton-Euler equations, and the model's estimated dynamic quantities of the distal segments were compared with those actually measured. Differences between model and measured dynamics were calculated and minimized, using an iterative algorithm to re-estimate joint positioning and anthropometric properties. The above method was tested with a group of 11 able-bodied subjects, and the results indicated that the relative errors obtained in the final iteration were of the same order of magnitude as those reported for closed loop problems involved in direct kinematics measurements of human gait. Received: 22 July 1997 / Accepted in revised form: 29 January 1998     

A biomechanical model of the foot: the role of muscles,tendons, and ligaments

A biomechanical model of the foot is developed and analyzed to determine the distribution of support under the metatarsal heads, the tension in the plantar aponeurosis, and the bending moment at each of the joints of the foot. This model is an extension of our earlier work to include the role of muscles, tendons, and ligaments. Two cases are presented: in the first the center of gravity of the body is over the mid foot, and in the second, the center of gravity is anterior, over the metatarsals, and no support is provided by the heel. The model shows the extent to which the muscles reduce the force in the supporting ligaments at each of the joints and decrease the tension in the plantar aponeurosis, and that this effect is more pronounced when the center of gravity of the body is moved forward.     

The measurement and lateral comparison of the peak torque caused by the fast abduction exercise of stretched upper extremities in normal and trained adults

The maximal torque effect of the middle portion of action of the deltoid muscle while raising an outstretched upper limb was measured from left and right sides of normal untrained young adults and of the same age elite athletes. Seventeen strongly right-handed untrained males and females and 10 elite tennis players were tested. All participants were required to raise (abduct) one arm (right and then left, or vice versa) as fast as possible with maximal amplitude while standing on an electronic platform scale which measured to 0.001 kg. An assumed force at the centre of mass of the entire upper limb was considered. The force consisted of two components, namely static weight force of the upper limb and a dynamic force component created by upward acceleration of the limb. Using regression equations and scaling methods the static weight of the upper limb was derived and combined with the dynamic component to produce the total force, applied to the centre of mass of the limb. The total force multiplied by the distance from the centre of mass to point of rotation of the limb equated to the torque produced by deltoid muscle. Using video system analyses the angle of abduction was measured for each individual exercise. The additional anthropometrical tests identified proportionality and body mass indices for each participant.

There was no significant difference in dynamic force and torque between left and right limb from the three groups. Sportsmen demonstrated greater lateral abduction when performing the exercise from the dominant side of the body. Sportsmen also demonstrated greater range of abduction, bigger dynamic force and torque on both sides in comparison to untrained adults. Remarkably, the absolute and relative length of arms of athletes were shorter in comparison to untrained males, but the radius of gyration from the stretched upper limb (from its centre of gravity to the shoulder joint) were greater. This phenomenon may be due to distal shifting of the gravity center of the entire upper limb in elite athletes, perhaps, because greater investment of the distal portion of the limb with skeletal muscle tissue.     

Mechanics of a constrained chair-rise

A sit-to-stand task is analyzed by a method which estimates the segmental and whole body center of mass (CoM) kinematics and kinetics using bilateral whole body kinematic data from nine healthy young female subjects. The sit-to-stand, or chair-rise, task is constrained with regard to chair height, pace, initial lower limb position and arm use. The chair-rise maneuver is divided into four phases; (1) the flexion momentum phase; (2) the momentum transfer phase; (3) the vertical extension phase; and (4) the stabilization phase; the first three are examined in detail here. The momentum transfer phase, which immediately follows lift-off from the seat of the chair, is the most dynamic portion of the event, demanding a high degree of coordination. This maneuver is analyzed in order to determine if trunk movement is used only to position the body center of gravity or if the trunk motion generates momentum which is important during the brief but critical period of dynamic equilibrium immediately following lift-off from the chair. Our evidence points to the latter case and indicates that inter-segmental momentum transfer is possible during this period.     

A gravitational impulse model predicts collision impulse and mechanical work during a step-to-step transition

The simplest walking model, which assumes an instantaneous collision with negligible gravity effect, is limited in its representation of the collision mechanics of human gaits because the actual step-to-step transition occurs over a finite duration of time with finite impulsive ground reaction forces (GRFs) that have the same order of magnitude as the gravitational force. In this study, we propose a new collision model that includes the contribution of the gravitational impulse to the momentum change of the center of mass (COM) during a step-to-step transition. To validate the model, we measured the GRFs of six subjects' over-ground walking at five different gait speeds and calculated the collision impulses and mechanical work. The data showed a significant contribution of the gravitational impulse to the momentum change during collision. To compensate for the gravity, the magnitudes of collision impulse and COM work were estimated to be much greater than in previous predictions. Consistent with the model prediction, push-off propulsion fully compensated for the collision loss, implying the step-to-step transition occurred in an energetically optimal manner. The new model predicted a moderate change in the collision mechanics with gait speed, which seems to be physiologically achievable. The gravitational collision model enables us to better understand collision dynamics during a step-to-step transition.     

Estimating net lumbar sagittal plane moments from EMG data. The validity of calibration procedures.

In the present study the validity of EMG based methods to estimate the net moment working at the lumbar spine was investigated. Eight subjects performed a series of static and dynamic tasks. EMG was recorded from 8 locations over the back muscles. At the same time force platform and kinematic data for a linked segment analysis were collected. The net moment at the lumbar spine was calculated from the latter data and compared to EMG based estimates of the same moment. These estimates were derived from a linear regression between the EMG amplitudes and the net moments obtained during static ramp calibrations. It appeared that calibration in several postures, covering the range occurring in the tasks studied, and in a posture in the middle of this range, yielded estimates of the group averaged 10th, 50th, and 90th percentile of the net moments which were within 10% of the real value. The explained variance obtained in the calibration procedure proved not to be a good indicator of the validity of the procedure.     

Bend propagation in flagella. I. Derivation of equations of motion and their simulation.

A set of nonlinear differential equations describing flagellar motion in an external viscous medium is derived. Because of the local nature of these equations and the use of a Crank-Nicolson-type forward time step, which is stable for large deltat, numerical solution of these equations on a digital computer is relatively fast. Stable bend initiation and propagation, without internal viscous resistance, is demonstrated for a flagellum containing a linear elastic bending resistance and an elastic shear resistance that depends on sliding. The elastic shear resistance is derived from a plausible structural model of the radial link system. The active shear force for the dynein system is specified by a history-dependent functional of curvature characterized by the parameters m0, a proportionality constant between the maximum active shear moment and curvature, and tau, a relaxation time which essentially determines the delay between curvature and active moment.     

Kinetic analysis of the center of gravity of the human body in normal and pathological gaits

The kinetics of the body's center of gravity during level walking were analyzed in 50 normal subjects and 47 patients. The three-dimensional displacements of the center of gravity were computed by the integration of force plate data. The energy levels and the power requirements of the center of gravity were also calculated, and the average and standard deviation of these variables were determined for normal and pathological gaits. The sex-related variation in normal gait, as suggested by previous force plate studies, was clearly demonstrated in our study. The parameters obtained from the displacements and the energy variations of the center of gravity are considered useful in the evaluation of stability and efficiency for pathological gaits.     

A continuous dynamic beam model for swimming fish

When a fish swims in water, muscle contraction, controlled by the nervous system, interacts with the body tissues and the surrounding fluid to yield the observed movement pattern of the body. A continuous dynamic beam model describing the bending moment balance on the body for such an interaction during swimming has been established. In the model a linear visco-elastic assumption is made for the passive behaviour of internal tissues, skin and backbone, and the unsteady fluid force acting on the swimming body is calculated by the 3D waving plate theory. The body bending moment distribution due to the various components, in isolation and acting together, is analysed. The analysis is based on the saithe (Pollachius virens), a carangiform swimmer. The fluid reaction needs a bending moment of increasing amplitude towards the tail and near-standing wave behaviour on the rear-half of the body. The inertial movement of the fish results from a wave of bending moment with increasing amplitude along the body and a higher propagation speed than that of body bending. In particular, the fluid reaction, mainly designed for propulsion, can provide a considerable force to balance the local momentum change of the body and thereby reduce the power required from the muscle. The wave of passive visco-elastic bending moment, with an amplitude distribution peaking a little before the mid-point of the fish, travels with a speed close to that of body bending. The calculated muscle bending moment from the whole dynamic system has a wave speed almost the same as that observed for EMG-onset and a starting instant close to that of muscle activation, suggesting a consistent matching between the muscle activation pattern and the dynamic response of the system in steady swimming. A faster wave of muscle activation, with a variable phase relation between the strain and activation cycle, appears to be designed to fit the fluid reaction and, to a lesser extent, the body inertia, and is limited by the passive internal tissues. Higher active stress is required from caudal muscle, as predicted from experimental studies on fish muscle. In general, the active force development by muscle does not coincide with the propulsive force generation on the tail. The stiffer backbone may play a role in transmitting force and deformation to maintain and adjust the movement of the body and tail in water.     

A double-inverted pendulum model for studying the adaptability of postural control to frequency during human stepping in place

In order to analyze the influence of gravity and body characteristics on the control of center of mass (CM) oscillations in stepping in place, equations of motion in oscillating systems were developed using a double-inverted pendulum model which accounts for both the head-arms-trunk (HAT) segment and the two-legged system. The principal goal of this work is to propose an equivalent model which makes use of the usual anthropometric data for the human body, in order to study the ability of postural control to adapt to the step frequency in this particular paradigm of human gait. This model allows the computation of CM-to-CP amplitude ratios, when the center of foot pressure (CP) oscillates, as a parametric function of the stepping in place frequency, whose parameters are gravity and major body characteristics. Motion analysis from a force plate was used to test the model by comparing experimental and simulated values of variations of the CM-to-CP amplitude ratio in the frontal plane versus the frequency. With data from the literature, the model is used to calculate the intersegmental torque which stabilizes the HAT when the Leg segment is subjected to a harmonic torque with an imposed frequency. Received: 24 February 1997 / Accepted in revised form: 30 June 1998     

Evaluation of peak power prediction equations in male basketball players

This study compared peak power estimated using 4 commonly used regression equations with actual peak power derived from force platform data in a group of adolescent basketball players. Twenty-five elite junior male basketball players (age, 16.5 +/- 0.5 years; mass, 74.2 +/- 11.8 kg; height, 181.8 +/- 8.1 cm) volunteered to participate in the study. Actual peak power was determined using a countermovement vertical jump on a force platform. Estimated peak power was determined using countermovement jump height and body mass. All 4 prediction equations were significantly related to actual peak power (all p < 0.01). Repeated-measures analysis of variance indicated significant differences between actual peak power and estimate peak power from all 4 prediction equations (p < 0.001). Bonferroni post hoc tests indicated that estimated peak power was significantly lower than actual peak power for all 4 prediction equations. Ratio limits of agreement for actual peak power and estimated peak power were 8% for the Harman et al. and Sayers squat jump prediction equations, 12% for the Canavan and Vescovi equation, and 6% for the Sayers countermovement jump equation. In all cases peak power was underestimated.