The potential influence of the heel counter on internal stress during static standing: a combined finite element and positional MRI investigation.

Confinement of the heel due to the counter of the shoe is believed to influence heel pad biomechanics. Using a two-dimensional finite element model of the heel pad and shoe during a simulation of static standing, the aim of this study was to quantify the potential effect of confinement on internal heel pad stress. Non-weightbearing MRI and weightbearing MRI with plantar pressure and ground reaction force data were recorded for a single subject. The non-weightbearing MRI was used to create two FE models of the heel pad, using either homogeneous or composite material properties. The composite model included a distinction in material properties between fat pad and skin. Vertical and medial-lateral forces, as measured on the subject's heel, were applied to the models and vertical compressive strains for both models were comparable with those observed by weightbearing MRI. However, only for the composite model was the predicted plantar pressure distribution comparable with measured data. The composite model was therefore used in further analyses. In this composite model, the internal stresses were located mainly in the skin and were predominantly tensile in nature, whereas the stress state in the fat pad approached hydrostatic conditions. A representation of a running shoe, including an insole, midsole and heel counter was then added to the composite heel pad to form the shod model. In order to investigate the counter effect, the load was applied to the shod model with and without the heel counter. The effect of the counter on peak stress was to elevate compression (0-50%), reduce tension (22-34%) and reduce shear (22-28%) in the skin. In addition, the counter reduced both compressive (20-40%) and shear (58-80%) stress in the fat pad and tension in the fat pad remained negligible. Taken together the results indicate that a well-fitted counter works in sympathy with the internal structure of the heel pad and could be an effective reducer of heel pad stress. However, further research needs to be undertaken to assess the long-term effects on the soft-tissues, practicalities of achieving good fit and behavior under dynamic events.

The development of fatigue quality in high- and low-stressed tendons of sheep (Ovis aries).

The time taken to rupture in cyclic fatigue tests, to a stress of 45 MPa, was used to compare the fatigue quality of tendons from sheep of varying ages. Muscle and tendon cross-sectional areas were used to calculate the stress-in-life of each tendon. For any given age, high-stressed plantaris tendons were of a higher fatigue quality than low-stressed extensor tendons. Both fatigue quality and stress-in-life increased with age for each tendon type. High-stressed tendons are subjected to large increases in stress-in-life during growth, and fatigue quality increased significantly with this stress. This relationship was not seen, however, in low-stressed tendons, which are not subjected to a comparable range of stresses over time. It is possible that cells modify tendon fatigue quality in response to tendon loading history. Whilst Young's modulus was seen to increase with age, no difference was detected between high- and low-stressed tendons.

Fatigue quality of mammalian tendons.

When excised tendons are subjected to a prolonged load, whether constant or oscillatory, fatigue damage accumulates, leading eventually to rupture. 'Fatigue quality', assessed by the time-to-rupture under a given stress, was found to vary hugely among the tendons of a wallaby hind limb. This material property correlates with the varied stresses to which tendons from different anatomical sites are exposed in life. The correlation was demonstrated by subjecting each excised tendon to a load equal to the maximum isometric force that its muscle could have developed. The time-to-rupture was then approximately the same for each tendon, on average 4.2 h. A model is introduced in which damage is proposed as the trigger for adaptation of fatigue quality. The model aims, in particular, to explain why low-stressed tendons are not made of a 'better' material, although this clearly exists since it is used in high-stressed tendons. The principle of design to a minimum quality is viable in biology because of the availability of self-repair to balance routine damage. Clinical symptoms, to be included under the general heading of 'overuse injuries', will only arise when this balance fails.

The design of soft collagenous load-bearing tissues.

Tendon, articular cartilage and the human heel pad are all soft load-bearing collagenous tissues but are designed according to utterly different micromechanical principles. Tendon is (probably) a fibre-reinforced composite material. The mechanical properties of cartilage depend on osmotic pressure developed within an aqueous proteoglycan gel and resisted by tension in a collagenous network. The micromechanics of the heel pad have not previously been described quantitatively. Order-of-magnitude calculations are introduced to assess a model based on a fluid-filled cushion. The processes of biological design are illustrated by considering tendon. Structural design determines the tendon's cross-sectional area relative to that of its muscle and, hence, the maximum stress to which the tendon may be subjected in life. Stress-in-life varies widely between tendons. Material design includes the development of compressive stiffness in the regions where transverse loads arise. More generally, the fatigue quality of each tendon is adjusted to suit its stress-in-life. The correlation between fatigue quality and stress-in-life means that every tendon is subject, on average, to a comparable rate of fatigue damage. Homeostasis requires that routine repair can keep up with this rate of damage.

Dimensions and moment arms of the hind- and forelimb muscles of common chimpanzees (Pan troglodytes).

This paper supplies quantitative data on the hind- and forelimb musculature of common chimpanzees (Pan troglodytes) and calculates maximum joint moments of force as a contribution to a better understanding of the differences between chimpanzee and human locomotion. We dissected three chimpanzees, and recorded muscle mass, fascicle length, and physiological cross-sectional area (PCSA). We also obtained flexion/extension moment arms of the major muscles about the limb joints. We find that in the hindlimb, chimpanzees possess longer fascicles in most muscles but smaller PCSAs than are predicted for humans of equal body mass, suggesting that the adaptive emphasis in chimpanzees is on joint mobility at the expense of tension production. In common chimpanzee bipedalism, both hips and knees are significantly more flexed than in humans, necessitating muscles capable of exerting larger moments at the joints for the same ground force. However, we find that when subject to the same stresses, chimpanzee hindlimb muscles provide far smaller moments at the joints than humans, particularly the quadriceps and plantar flexors. In contrast, all forelimb muscle masses, fascicle lengths, and PCSAs are smaller in humans than in chimpanzees, reflecting the use of the forelimbs in chimpanzee, but not human, locomotion. When subject to the same stresses, chimpanzee forelimb muscles provide larger moments at the joints than humans, presumably because of the demands on the forelimbs during locomotion. These differences in muscle architecture and function help to explain why chimpanzees are restricted in their ability to walk, and particularly to run bipedally.

The time-dependent mechanical properties of the human heel pad in the context of locomotion.

Previous measurements of the mechanical properties of the heel pad, especially of the energy loss during a cycle of compressive loading and unloading, have given contrasting values according to whether the investigators used isolated single impacts (e.g. pendulum tests; energy loss approximately 48%) or continuous oscillations (energy loss approximately 30%). To investigate this discrepancy, rest periods were inserted between single compressive cycles, giving intermittent loading as in locomotion. The energy loss, measured as the percentage area of the hysteresis loop, was found to change linearly with the logarithm of the rest time. It was approximately 33% when the rest time was 1 s. Each 10-fold increase in the rest time added approximately 3.7% to the energy loss. Thus, with rest times appropriate to locomotion, the pad is far from fully relaxed. The springy heel pad may help to reposition the foot during the transfer of load from the heel to the forefoot. Information is also included on the load-deformation curves for the heel pad and the way in which these change with rest time. This is presented as equations which may be useful in future models relating the mechanical properties of the heel to either its structure or its function.

The effects of isolation on the mechanics of the human heel pad.

In previous studies on the mechanical properties of the human heel pad (Bennett & Ker, 1990; Aerts et al. 1995) the fat pad and part of the calcaneus was removed from amputated test specimens. The present study tested whether this procedure influences the mechanical behaviour of the sample. Intact amputated feet were therefore mounted on steel rods driven through the calcaneus and placed in a mechanical test situation (pendulum or servohydraulic material tester). The mechanical properties of the pad were determined for a series of experiments in which the pad was gradually freed from the foot in the way done by Bennett & Ker (1990) and Aerts et al. (1995). The results showed no observable differences in the mechanics of the pad by isolating it from the rest of the foot. Thus, in relation to human locomotion, the load-deformation relation of heel pads as described by Aerts et al. (1995) is the most appropriate to date.

The mechanical properties of the human heel pad: a paradox resolved.

In vivo and in vitro mechanical testing of the human heel pad gave apparently different properties for this structure: the in vivo stiffness is about six times lower, whereas the percentage of energy dissipation is about three times higher (up to 95% loss). It was postulated that this divergence must be ascribed to the lower leg being involved in in vivo heel pad testing. This hypothesis is presently evaluated by applying the two experimental procedures formerly used in the in vivo (an instrumented pendulum) and in vitro (an Instron servo-hydraulic testing machine) investigations on the same isolated heel pad samples. Instron load-deformation cycles mimicking pendulum impacts (i.e. 'first loop-half cycles') are first evaluated and then compared to real pendulum impacts. When performed properly, the pendulum test procedure reveals the same mechanics for isolated heel pads as the Instron does. The load-deformation loops are basically identical. Thus similar non-linear stiffnesses (about 900 kN m-1 at body weight) and comparable amounts of energy dissipation (46.5-65.5%) are found with both types of test, still being largely different from the former in vivo results (150 kN m-1 and 95%, respectively). Therefore, the present findings support the hypothesis that the presence of the entire lower leg in in vivo tests indeed influences the outcome of the measurements. It must be concluded that the previously published in vivo data, if interpreted for the heel pad alone, implied not only an incorrectly low resilience but also a value far too low for stiffness.

Creep rupture of wallaby tail tendons.

The tail tendons from wallabies (Macropus rufogriseus) suffer creep rupture at stresses of 10 MPa or above, whereas their yield stress in a dynamic test is about 144 MPa. At stresses between 20 and 80 MPa, the time-to-rupture decreases exponentially with stress, but at 10 MPa, the lifetime is well above this exponential. For comparison, the stress on a wallaby tail tendon, when its muscle contracts isometrically, is about 13.5 MPa. Creep lifetime depends sharply on temperature and on specimen length, in contrast to strength and stiffness as observed in dynamic tests. The creep curve (strain versus time) can be considered as a combination of primary creep (decelerating strain) and tertiary creep (accelerating strain). Primary creep is non-damaging, but tertiary creep is accompanied by accumulating damage, with loss of stiffness and strength. 'Damage' is quantitatively defined as the fractional loss of stiffness. A creep theory is developed in which the whole of tertiary creep and, in particular, the creep lifetime are predicted from measurements made at the onset of creep, when the tendon is undamaged. This theory is based on a 'damage hypothesis', which can be stated as: damaged material no longer contributes to stiffness and strength, whereas intact material makes its full contribution to both.

Fatigue rupture of wallaby tail tendons.

Wallaby tail tendons fail after repeated application of stresses much lower than would be needed to break them in a single pull. We show that this a fatigue phenomenon, distinct from the creep rupture that occurs after prolonged application of a constant stress. The two phenomena are disctinguished by experiments in which tensile stress is cycled at different frequencies, ranging from 1 to 50 Hz.

Ratios of cross-sectional areas of muscles and their tendons in a healthy human forearm.

The muscles and tendons in the forearm and hand of a young man, amputated after an accident, have been weighed and measured. The physiological cross-sectional areas of those muscles that had long tendons were 35 +/- 9 (mean and standard deviation) times the cross-sectional areas of the tendons. The mean is very close to the optimum calculated from the theory of Ker, Alexander & Bennett (1988). It implies that the tendons experience stresses of about 11 MPa and strains of about 1.3%, when the muscles exert their maximum isometric forces. Very much larger forces would be needed to break the tendons.

The mechanical properties of the human subcalcaneal fat pad in compression.

The subcalcaneal fat pads of Homo sapiens were subjected to cyclic compressive loading in a materials testing machine. Rates of loading and the absolute loads to which pads were subjected were chosen to simulate the pattern of forces that the pad would be exposed to during the ground contact phase of the running step. Heel pads were found to be resilient, returning approximately 70% of the energy used to deform them. This was modified little by changes in loading frequency. A reduction of temperature from 37 degrees C to 10 degrees C produced a small, but significant, increase in the percentage energy dissipation.

Foot strike and the properties of the human heel pad.

Many force-plate records of human locomotion show an impulse (the foot strike) shortly after ground contact. The authors' hypothesis is that this results from the rapid deceleration of a mass (the 'effective foot') under forces which compress the heel pad. The quantitative implications are investigated through an illustrative calculation. The observations used are (a) the peak force reached in foot strike (b) the vertical velocity of the foot immediately before ground contact and (c) the properties of the heel pad in compression. Data for (a) and (b) are available in the literature; measurements for (c) are presented here. The deductions are: (a) the time taken to reach peak force is about 5.4 ms, which agrees with published measurements; (b) the mass of the effective foot is about 3.6 kg. The effective foot thus includes a substantial portion of the leg: this seems reasonable. The models used for the calculations clarify the relationship between the foot strike and the shock wave, which it generates.

The spring in the arch of the human foot.

Large mammals, including humans, save much of the energy needed for running by means of elastic structures in their legs and feet. Kinetic and potential energy removed from the body in the first half of the stance phase is stored briefly as elastic strain energy and then returned in the second half by elastic recoil. Thus the animal runs in an analogous fashion to a rubber ball bouncing along. Among the elastic structures involved, the tendons of distal leg muscles have been shown to be important. Here we show that the elastic properties of the arch of the human foot are also important.

Dynamic tensile properties of the plantaris tendon of sheep (Ovis aries).

1. The stresses applied during fast locomotion are sufficient to stretch the tendon far into the linear region of the load-extension plot. 2. The tangent modulus in the linear region is about 1.65 GN.m-2 and is independent of frequency for oscillations in the range 0.22 to 11 Hz. 3. Internal damping dissipates about 7% of the mechanical energy applied during oscillations. The load range (0 to about 1 kN) and frequencies (0.22 to 11 Hz) were comparable to those arising during locomotion. 4. The rate of rise of temperature, during the initial period of an oscillation, was consistent with the mechanical measurement of power loss. 5. The dynamic mechanical properties are appropriate for the hypothesis of energy saving by storage in tendons during fast locomotion.