Biomedical subjects

T A McMahon

Publications and source records attributed to T A McMahon.

At least 19 recordsLinked to original sources

PubMed1995

The force-velocity curve in passive whole muscle is asymmetric about zero velocity.

The force-velocity property of passive muscle was investigated to determine if a discontinuity of slope occurred at zero velocity. Isolated, unstimulated whole frog sartorius muscles were subjected to constant-velocity stretches and releases using a servo-controlled lever. The force due to damping (delta T) was calculated by subtracting the tension measured at a very low speed (1.0 mm s-1) from the tension measured at the same length while the muscle was shortening or lengthening at a particular test speed. The experiments were performed over a range of speeds at each of several lengths and at two temperatures. For comparison, the same experiments were performed using a strip of pure latex rubber and a steel spring. Curves showing the magnitude of delta T vs velocity were nearly symmetric about the zero-velocity axis for the steel spring and the rubber strip, but were markedly asymmetric for passive muscle, showing a positive delta T for lengthening at all speeds that was between four and 11 times the negative delta T for shortening at the same speed, depending on the temperature and initial stretch length. The force due to damping at a given speed increased with extension above the rest length in passive muscle but decreased with increasing length in experiments using the latex strip. Predictions obtained from a mathematical model based on a damping element in series with a lightly damped spring were fitted to the experimental measurements of delta T vs velocity. The damping parameter provisionally representing interfilamentary sliding was between six and 12 times larger for lengthening than for shortening.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed1995

Arms are different from legs: mechanics and energetics of human hand-running.

To determine whether nonlocomotor limbs (arms) differ from locomotor limbs (legs), we trained human subjects to run on their hands while supporting a fraction of their body weight. We wanted to know whether the low cost of force production and the speed-independent limb stiffness of locomotor limbs were characteristics associated with locomotion or were inherent properties of all limbs. We found that the limb stiffness of the human arm increases by 135% over less than a fourfold range in peak vertical force. In contrast, human legs and a variety of other mammalian locomotor limbs maintain a constant stiffness, regardless of speed and loading, for normal running. In addition, we explored the energetics of locomotion in hand-running. The economy of force generation (in J/N) is invariant with speed, as is found in legged locomotion. However, our results show that the metabolic cost of force generation while running on human arms is four to five times greater than the cost of force generation for the locomotor limbs of running quadrupeds.

Arm↗

PubMed1994

Negative developed tension in rapidly shortening whole frog muscles.

High speed isovelocity shortening using a servo-controlled lever was performed on isolated whole frog sartorius muscles at long lengths to ensure substantial passive tension. The tension records of unstimulated control experiments were subtracted from the tension records of fully-tetanized experiments on the same muscles to yield the developed tension exerted by the contractile proteins alone. There are several main results: (1) the positive developed tension had the same relation with shortening speed observed by other researchers in single fibres with no passive tension present; (2) negative developed tension was always measured at velocities of shortening above Vmax, where Vmax (typically 1.5 muscle-lengths s-1 at 2 degrees C) is defined as the velocity of shortening observed to yield zero developed tension; (3) negative developed tension was roughly asymptotic to -0.05 T(o), where T(o) is the developed isometric tetanic tension for the muscle length at which the developed tension was measured during steady shortening; (4) negative developed tension diminished in magnitude at velocities of shortening above approximately 2.5 Vmax; (5) a 10 degrees C increase in temperature from 2 degrees C to 12 degrees C had no significant effect on the shape of the normalized force-velocity curve (%T(o) versus %Vmax), but did increase Vmax by a factor of 2.6 in agreement with the results of previous studies measuring Vmax in the absence of passive tension; (6) addition of curare in the saline bath did not affect the results.

Animals↗

PubMed1994

Compressive creep behavior of bovine trabecular bone.

There are almost no published data that describe the creep behavior of trabecular bone (at the specimen level), even though the creep behavior of cortical bone has been well documented. In an effort to characterize the creep behavior of trabecular bone and to compare it with that of cortical bone, we performed uniaxial compressive creep tests on 24 cylindrical specimens of trabecular bone taken from 19 bovine proximal tibiae. Six different load levels were used, with the applied stress normalized by the specimen modulus measured prior to creep loading. We found that trabecular bone exhibits the three creep regimens (primary, secondary, and tertiary) associated with metals, ceramics, and cortical bone. All specimens eventually fractured at strains less than 3.8%. In addition, the general shape of the creep curve was independent of apparent density. Strong and highly significant power law relationships (r2 > 0.82, p < 0.001) were found between the normalized stress sigma/E0 and both time-to-failure tf and steady-state creep rate d epsilon/dt: tf = 9.66 x 10(-33) (sigma/E0)-16.18; d epsilon/dt = 2.21 x 10(33) (sigma/E0)17.65. These data indicate that the creep behaviors of trabecular and cortical bone are qualitatively similar. In addition, the strength of trabecular bone can be reduced substantially if relatively large stresses (i.e. stresses approximately half the ultimate strength) are applied for 5 h. Such strength reductions may play a role in the etiology of progressive, age-related spine fractures if adaptive bone remodeling does not arrest creep deformations.

Aging↗

PubMed1994

Trabecular bone exhibits fully linear elastic behavior and yields at low strains.

Using a protocol designed to reduce experimental artifacts associated with the conventional compression test for trabecular bone, we performed in vitro mechanical testing on bovine tibial trabecular bone to obtain accurate descriptions of the elastic and yield behaviors. Reduced-section cylindrical specimens were preconditioned for eight tension-compression (+/- 0.5% strain) cycles and then loaded to failure either in tension (n = 15) or compression (n = 14). We found that the pre-yield behavior for every specimen was fully linear, indicating that the initial nonlinear 'toe' is an experimental artifact. Analysis of variance on the moduli indicated that there was no significant difference between the tensile and compressive moduli before preconditioning. However, preconditioning decreased the tensile and compressive moduli on average by 8.8% (p < 0.01) and 5.3% (p < 0.01), respectively, with the decrease in tensile modulus being larger (p < 0.01). These small but significant decreases in modulus suggest that initial yielding involves microstructural damage (as opposed to plastic slip) of individual trabeculae and also indicate that the tensile and/or the compressive yield strain of (bovine tibial) trabecular bone is less than 0.5%. The mean tensile strength was approximately 70% of the mean compressive strength, although this difference in strengths may have been affected by the preconditioning-induced damage. Taken together, these results suggest that there are more similarities between the elastic and yield behaviors of trabecular and cortical bone than had been assumed previously.

Analysis of Variance↗

PubMed1994

Finite element modeling of damage accumulation in trabecular bone under cyclic loading.

A two-dimensional finite element model of an idealized trabecular bone specimen was developed to study trabecular bone damage accumulation during cyclic compressive loading. The specimen was modeled as a two-dimensional honeycomb-like structure made up of an array of hexagonal cells. Each trabecula was modeled as a linearly elastic beam element with the same material properties as cortical bone. Initial microcracks were assumed to exist within the oblique trabeculae and to grow according to the Paris law. Forces and moments were computed in each trabecula and the microcracks were allowed to propagate until fracture occurred. Between cycles, fractured trabeculae were removed from the finite element mesh, and force and moment distributions were calculated for the next cycle. This iterative process was continued until the simulated trabecular bone specimen showed a 10% reduction in modulus. Creep failure was also studied using a single cell analysis, in which a closed-form solution was obtained after prescribing the creep properties of the trabeculae. The results of the crack propagation analysis showed that fractures of only a small number of individual trabeculae can cause a substantial reduction in the modulus of the trabecular bone specimen model. Statistical tests were performed to compare the slopes and intercepts of the S-N curves of our model predictions to those of experimentally derived S-N curves for bovine trabecular bone. There was no significant difference (p > 0.2 for both slope and intercept) between our model predictions and the experimentally derived S-N curves for the low-stress, high-cycle range. For the high-stress, low-cycle range, the crack propagation model overestimated the fatigue life for a given stress level (for slope, p < 0.001), while the creep analysis agreed well with the experimental data (for slope, p > 0.2). These findings suggest that the primary failure mechanism for low-stress, high-cycle fatigue of trabecular bone is crack growth and propagation, while the primary failure mechanism for high-stress, low-cycle fatigue is creep deformation and fracture. Furthermore, our results suggest that the modulus of trabecular bone at the specimen level may be highly sensitive to fractures of individual trabeculae.

Algorithms↗

PubMed1993

Running springs: speed and animal size.

Trotting and hopping animals use muscles, tendons and ligaments to store and return elastic energy as they bounce along the ground. We examine how the musculoskeletal spring system operates at different speeds and in animals of different sizes. We model trotting and hopping as a simple spring-mass system which consists of a leg spring and a mass. We find that the stiffness of the leg spring (k(leg)) is nearly independent of speed in dogs, goats, horses and red kangaroos. As these animals trot or hop faster, the leg spring sweeps a greater angle during the stance phase, and the vertical excursion of the center of mass during the ground contact phase decreases. The combination of these changes to the spring system causes animals to bounce off the ground more quickly at higher speeds. Analysis of a wide size range of animals (0.1-140 kg) at equivalent speeds reveals that larger animals have stiffer leg springs (k(leg) [symbol: see text] M0.67, where M is body mass), but that the angle swept by the leg spring is nearly independent of body mass. As a result, the resonant period of vertical vibration of the spring-mass system is longer in larger animals. The length of time that the feet are in contact with the ground increases with body mass in nearly the same way as the resonant period of vertical vibration.

Animals↗

PubMed1992

Running on an incline.

Seven male subjects ran at 3.0 m/s on a motorized treadmill including a force platform under the tread. The subjects ran at each of five treadmill inclinations: +0.17, +0.077, 0, -0.077, and -0.17 radians. The position of the subjects' legs were read from ciné films (100 frames/s). Results of the film and force plate analysis generally corroborated the "hanging triangle" hypothesis, which postulates that the angle between the leg and the vertical upon foot strike does not change as the treadmill is tipped up or down. A mathematical model of running, in which the leg is represented as a nonlinear spring, made satisfactory predictions of the way many parameters of running change with the treadmill angle, including the length of the leg at touchdown and liftoff and the peak leg force in the middle of a step. The peak leg force reaches a maximum at a treadmill angle near -0.12 radians, close to the downhill angle where other authors have found a minimum in the rate of oxygen consumption.

Acceleration↗

PubMed1992

Energetics of walking and running: insights from simulated reduced-gravity experiments.

On Earth, a person uses about one-half as much energy to walk a mile as to run a mile. On another planet with lower gravity, would walking still be more economical than running? When people carry weights while they walk or run, energetic cost increases in proportion to the added load. It would seem to follow that if gravity were reduced, energetic cost would decrease in proportion to body weight in both gaits. However, we find that under simulated reduced gravity, the rate of energy consumption decreases in proportion to body weight during running but not during walking. When gravity is reduced by 75%, the rate of energy consumption is reduced by 72% during running but only by 33% during walking. Because reducing gravity decreases the energetic cost much more for running than for walking, walking is not the cheapest way to travel a mile at low levels of gravity. These results suggest that the link between the mechanics of locomotion and energetic cost is fundamentally different for walking and for running.

Energy Metabolism↗

PubMed1991

Prediction of femoral impact forces in falls on the hip.

A major determinant of the risk of hip fracture in a fall from standing height is the force applied to the femur at impact. This force is determined by the impact velocity of the hip and the effective mass, stiffness, and damping of the body at the moment of contact. We have developed a simple experiment (the pelvis release experiment) to measure the effective stiffness and damping of the body when a step change in force is applied to the lateral aspect of the hip. Results from pelvis release experiments with 14 human subjects suggest that both increased soft tissue thickness over the hip and impacting the ground in a relaxed state can decrease the effective stiffness of the body, and subsequently reduce peak impact forces. Comparison between our fall impact force predictions and in-vitro measures of femoral fracture strength suggest that any fall from standing height producing direct, lateral impact on the greater trochanter can fracture the elderly hip.

Accidental Falls↗

PubMed1991

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.

Adult↗

PubMed1990

The mechanics of running: how does stiffness couple with speed?

A mathematical model for terrestrial running is presented, based on a leg with the properties of a simple spring. Experimental force-platform evidence is reviewed justifying the formulation of the model. The governing differential equations are given in dimensionless form to make the results representative of animals of all body sizes. The dimensionless input parameters are: U, a horizontal Froude number based on forward speed and leg length; V, a vertical Froude number based on vertical landing velocity and leg length, and KLEG, a dimensionless stiffness for the leg-spring. Results show that at high forward speed, KLEG is a nearly linear function of both U and V, while the effective vertical stiffness is a quadratic function of U. For each U, V pair, the simulation shows that the vertical force at mid-step may be minimized by the choice of a particular step length. A particularly useful specification of the theory occurs when both KLEG and V are assumed fixed. When KLEG = 15 and V = 0.18, the model makes predictions of relative stride length S and initial leg angle theta o that are in good agreement with experimental data obtained from the literature.

Animals↗

PubMed1990

Muscle stiffness measured under conditions simulating natural sound production.

Isolated whole frog gastrocnemius muscles were electrically stimulated to peak twitch tension while held isometrically in a bath at 4 degrees C. A quartz hydrophone detected vibrations of the muscle by measuring the pressure fluctuations caused by muscle movement. A small steel collar was slipped over the belly of the muscle. Transient forces including plucks and steady sinusoidal driving were applied to the collar by causing currents to flow in a coil held near the collar. The instantaneous resonant frequencies measured by the pluck and driving techniques were the same at various times during a twitch contraction cycle. The strain produced by the plucking technique in the outermost fibers was less than 1.6 x 10(-4%), a strain three orders of magnitude less than that required to drop the tension to zero in quick-length-change experiments. Because the pressure transients recorded by the hydrophone during plucks and naturally occurring sounds were of comparable amplitude, strains in the muscle due to naturally occurring sound must also be of the order 10(-3%). A simple model assuming that the muscle is an elastic bar under tension was used to calculate the instantaneous elastic modulus E as a function of time during a twitch, given the tension and resonant frequency. The result for Emax, the peak value of E during a twitch, was typically 2.8 x 10(6) N/m2. The methods used here for measuring muscle stiffness are unusual in that the apparatus used for measuring stiffness is separate from the apparatus controlling and measuring force and length.

Acoustic Stimulation↗

PubMed1990

Cross-bridge cycling theories cannot explain high-speed lengthening behavior in frog muscle.

The Huxley 1957 model of cross-bridge cycling accounts for the shortening force-velocity curve of striated muscle with great precision. For forced lengthening, however, the model diverges from experimental results. This paper examines whether it is possible to bring the model into better agreement with experiments, and if so what must be assumed about the mechanical capabilities of cross-bridges. Of particular interest is how introduction of a maximum allowable cross-bridge strain, as has been suggested by some experiments, affects the predictions of the model. Because some differences in the models are apparent only at high stretch velocities, we acquired new force-velocity data to permit a comparison with experiment. Using whole, isolated frog sartorius muscles at 2 degrees C, we stretched active muscle at speeds up to and exceeding 2 Vmax. Force during stretch was always greater than the peak isometric level, even during the fastest stretches, and was approximately independent of velocity for stretches faster than 0.5 Vmax. Although certain modifications to the model brought it into closer correspondence with the experiments, the accompanying requirements on cross-bridge extensibility were unreasonable. We suggest (both in this paper and the one that follows) that sarcomere inhomogeneities, which have been implicated in such phenomena as "tension creep" and "permanent extra tension," may also play an important role in determining the basic force-velocity characteristics of muscle.

Animals↗

PubMed1989

The mechanism of mucus clearance in cough.

An instability resembling an avalanche is proposed as the mechanism by which mucus is expelled from the respiratory tract during cough. The cough event was simulated in a model airway. In these experiments, air was forced through a channel whose walls were lined with a non-Newtonian material rheologically similar to tracheal mucus. Frames from high-speed cine photographs showed an unstable event which began as an undulation of the free surface and progressed to a catastrophic clearance of the channel. Measurements of the longitudinal pressure gradient support the hypothesis that the clearance event is initiated when the total stress applied to the mucus analog exceeds its finite yield stress. A continuum model predicts that yielding occurs within the bottom layers of the mucus analog. Calculations based upon estimates of tracheal geometry and air flow show that the clearance event studied here would be expected to occur during a cough but not during normal breathing. Experiments also show that a lubricant introduced between the channel walls and the mucus blanket can reduce the air flow rate required to precipitate the clearance.

Cough↗

PubMed1987

The mechanism of low-frequency sound production in muscle.

Frog gastrocnemius muscles stimulated isometrically in a saline bath at 20 degrees C were found to produce a single ringing sound event beginning just before the tension record began to rise. The sound event was substantially over by the time the isometric tension began to fall. Results from studies correlating the spatial pattern of the sound, the amplitude and frequency of the sound as a function of the muscle length, and the response of both the passive and active muscle to a transverse pluck were found to be consistent with the conclusion that the sounds in these muscles are caused primarily by transverse resonant vibrations. As the muscle develops force, its lack of cylindrical symmetry gives rise to lateral motions, which are most likely the initiators of the bending vibrations detected as sound.

Animals↗

PubMed1987

Groucho running.

An important determinant of the mechanics of running is the effective vertical stiffness of the body. This stiffness increases with running speed. At any one speed, the stiffness may be reduced in a controlled fashion by running with the knees bent more than usual. In a series of experiments, subjects ran in both normal and flexed postures on a treadmill. In other experiments, they ran down a runway and over a force platform. Results show that running with the knees bent reduces the effective vertical stiffness and diminishes the transmission of mechanical shock from the foot to the skull but requires an increase of as much as 50% in the rate of O2 consumption. A new dimensionless parameter (u omega 0/g) is introduced to distinguish between hard and soft running modes. Here, omega 0 is the natural frequency of a mass-spring system representing the body, g is gravity, and u is the vertical landing velocity. In normal running, this parameter is near unity, but in deep-flexed running, where the aerial phase of the stride cycle almost disappears, u omega 0/g approaches zero.

Adult↗

PubMed1987

Load-dependent relaxation with late systolic volume steps: servo-pump studies in the intact canine heart.

In isolated heart muscle preparations an abrupt increase in load during the latter portion of contraction (at a time when there is little if any potential to develop additional force) causes a premature and more rapid relaxation; this load-dependent relaxation characterizes relaxation in myocardium with normal sarcoplasmic reticulum. The purpose of our study was to assess whether or not the phenomenon of load-dependent relaxation is present in the intact heart and to describe the left ventricular response to abrupt load increments (volume steps) throughout the cardiac cycle. Using a microcomputer-controlled servo-pump attached to the apex of an intact canine heart, we studied the effects of 6 ml steps on left ventricular pressure transients during relaxation. Each volume step was carried out in a single beat with 20 stabilization beats separating the intervention beats; thus, at a heart rate of 120 beats/min, a sequence of 10 intervention beats could be carried out in less than 2 min. By performing the experiments on a single-beat basis (control vs intervention beat), we were able to minimize reflex and other physiologic feedback mechanisms that might alter the results. Studies were performed in five anesthetized dogs. In ejecting beats, an early step (immediately after aortic valve opening) caused an increase (3%) in the duration of systole (the time from the onset of pressure rise to the instant at which left ventricular pressure had declined to one-half its maximal value); in contrast, a late step (just before aortic value closure) caused a decrease (7%) in the duration of systole.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗