In running the instant that the heel contacts the ground a very rapid deceleration occurs, resulting in a shock wave that is transmitted throughout the skeletal system. Factors such as the velocity of progression and stride length affect the level of shock seen in the lower extremity. As velocity of progression increases the impact shock in the tibia also increases(4). Another factor that can influence impact shock is alterations in the stride length. Researchers have found that lower stride frequencies (greater stride lengths) are associated with higher impact peaks at the tibia while running on a treadmill (9). Several studies have shown that by the time the shock wave reaches the head the magnitude is greatly attenuated (9,13,18). Further, the body appears to increase shock attenuation in response to increased impact magnitude (9,18). The mechanism and location of this increased shock attenuation is largely unknown.
Passive structures such as the ground, the shoe midsole, the heel pad, bone, and cartilage all play a role in the attenuation of shock that results from heel impact during running (15). However, muscle has the greatest potential to attenuate shock, both in terms of its ability to actively adjust the amount of shock attenuation and its large capacity to deform when stressed. Elftman (6) stated that the dissipation of energy by muscles is “indispensable when the body must lose energy, as in deceleration.” This dissipation of energy can be achieved by eccentric contractions of the muscles crossing the hip, knee, and ankle joints.
Energy absorption has been measured using several different protocols in which the subjects must stop downward motion. Both the knee extensors and the ankle plantar flexors are involved in significant energy absorption during stair descent (12). Increasing the impact velocity increases the energy absorption while dropping from various heights(14). Downhill running increases impacts(7) as well as increases negative work done on the extensor muscles of the knee and ankle (3).
While running a substantial amount of mechanical energy must be absorbed during the impact phase to bring the vertical velocity of the body segments to zero. Winter (23) showed, in a sagittal plane analysis, that energy is absorbed during the initial portion of stance and generated during the latter portion. During the absorption phase, muscles in the lower extremity contract eccentrically to slow the descent of the body mass. He points out that during the stance phase of jogging, energy is absorbed primarily at the knee joint and generated primarily at the ankle joint. Winter(24) has also investigated the response of the body to increase cadence. Greater energy absorption at the knee joint was associated with increasing running velocity. This information suggests that increasing impact loads experienced by the body may be countered by increased energy absorption at some lower extremity joints.
A failure of the lower extremity muscles to adequately absorb the energy of impact may lead to over-reliance on passive structures that attenuate shock. During an unexpected step down a person can overextend the knee such that it becomes locked. Knee extensor muscles cannot absorb energy in this position and the shock wave initiated by the heel impact is left underattenuated by the muscles. As a result, passive structures in the hip or back may experience an overload (22).
The purpose of this study was to investigate the locus of energy absorption during the impact phase of the running cycle. It was hypothesized that the body would attenuate the increased impact shock as it does in treadmill running (9). Further, it was thought that increased shock attenuation would manifest in increased energy absorption at the ankle, knee, and hip joints. These hypotheses were tested by calculating a transfer function that shows the transmission of shock from the tibia to the head and by an examination of the muscular energy absorption at each of these joints during running at various stride lengths.
Subjects. Ten healthy, male university students participated in the study. The mean age of the subjects was 27 ± 5 yr, mean height was 1.79 ± 0.05 m, and mean body mass was 75.5 ± 12.2 kg. No lower extremity abnormalities were apparent in the gait of any of the subjects.
Instrumentation. Two quartz shear piezoelectric accelerometers(model 353B17, PCB Piezotronics, Inc., Depew, NY) were used to measure accelerations of the distal anteromedial aspect of the right tibia(20) and of the frontal bone of the head (forehead)(25). These sites were selected to minimize soft tissue oscillations during the impact. The accelerometers were secured with elastic straps tightened to the threshold of subject tolerance. The ± 3dB frequency range of the accelerometers was 0.35 to 30,000 Hz, the resonant frequency was greater than 70 kHz, and the resolution was 0.01 g. Each accelerometer and mounting bracket had a mass of 3.8 g. The accelerometers were powered by a battery driven power unit (model 480E06, PCB Piezotronics) which had a selectable gain of 1, 10, or 100. The gains for each subject were set to take advantage of the full range of the analog to digital converter.
The amplified signals were recorded by a battery powered data logger(Tattletale model 7, Onset Computer Corp., Pocasset, MA) that digitized the signal at 1000 Hz with 12-bit resolution. Data were temporarily stored on the data logger and then downloaded to the hard disk of a micro computer after each stride length condition. Sampling was initiated with an infrared device that the investigator used to trigger the data logger before heel contact on the force platform. The entire accelerometer data collection system weighed 2.5 kg and was carried by the subject in a waist pack.
To calculate the energy absorbed at each joint, ground reaction forces and kinematics were collected and synchronized both spatially and temporally. Ground reaction forces were measured with an AMTI strain gauge force platform and digitized using a 12-bit analog to digital converter at a rate of 1000 Hz. An NAC camera (model MOS V-14) interfaced to a 200 Hz high speed recorder was placed perpendicular to the plane of movement so that the right sagittal view of the subject could be recorded. Joint markers were digitized using a Motion Analysis VP-110 digitizing system. The data were then low-pass filtered using an optimal cut-off frequency based on an analysis of residuals(10). The 200 Hz video data were reconstructed at 1000 Hz using the Shannon reconstruction formula (8).
The force platform data were synchronized with the kinematic data via an electronic circuit that sensed a threshold voltage from the vertical force channel. Upon heel-strike the circuit generated a positive square wave that activated a light emitting diode placed in the field of view of the camera. A simultaneous signal was sent to the analog to digital converter so that heel strike could be identified in both the force platform data and the kinematic data.
Protocol. Upon entering the laboratory, all subjects read and signed a university approved Informed Consent Document and successfully completed a Physical Activity Readiness Questionnaire before being allowed to participate in the study. The study was conducted in accordance with the policy statements of the American College of Sports Medicine. Eight anthropometric measurements were obtained from each subject to estimate the parameters necessary to construct a rigid body model(21). To define the segments, light-weight reflective markers were placed over the lateral head of the 5th metatarsal, lateral aspect of the calcaneus, lateral malleolus, femoral condyle, greater trochanter, and humeral head. Preferred stride length (PSL) was defined as the freely chosen stride length at a running velocity of 3.83 m·s-1(7:00 min·mile-1 pace). Each subject ran in five stride length conditions: PSL, +20% of PSL, -20% of PSL, +10% of PSL, and -10% of PSL. In all conditions the nominal progression velocity was 3.83 m·s-1. Markers were placed on the runway to assist the subjects in maintaining the correct stride length. Subjects practiced each stride length condition until they felt comfortable meeting the conditions of an acceptable trial. Trials were accepted if the velocity was within ±5% of 3.83 m·s-1, if there was no visible alteration of the stride length, and if the right foot of the subject fell entirely on the force platform. A minimum of six acceptable trials per stride length condition were required of each subject.
Accelerometry. The accelerometers attached to the head and tibia output acceleration magnitudes in multiples of gravity (9.81 m·s-2 = 1g). To isolate the impact frequencies(9,18), these time based signals were converted to the frequency domain using a Fast Fourier Transform (FFT)(16). The stance phase of each time-based accelerometry curve was identified and extracted for calculation of the power spectral density (PSD). The mean value and the trend between the first and last data points were removed before using the FFT algorithm. Because the FFT requires the number of data points to be a multiple of a power of two, zero values were padded to the end of the data until the total number of points was 2048. This translated into 0.488 Hz per frequency bin of the resulting PSD curve. The PSD curves were then adjusted so that each bin was equal to 1.0 Hz. This resulted in PSD units of g2·Hz-1.
A transfer function (TF) was calculated for each 1.0 Hz frequency bin using the following formula(18): where PSDhead and PSDleg were the power spectral density functions of the head and leg, respectively. This transfer function results in positive values for frequencies that show a gain in signal strength and negative values for frequencies that show an attenuation of signal strength.
Joint power. Joint moments were calculated from the kinetic, anthropometric, and kinematic information collected from each subject(2). Joint muscle powers were then calculated by multiplying the joint moments by the angular velocity of the joint. The joint muscle power curves were integrated to give the net energy being absorbed(negative work) or generated (positive work) at each joint(17).
Statistical analysis. Mean values were calculated across trials for each stride length of each subject. One-way repeated measures ANOVA(condition by subjects) were performed on the subject means. In tests that resulted in a significant F-ratio (P < 0.05), a Tukey multiple comparison test was performed to identify the location of the significant differences. In addition, the impact data and energy absorption values were analyzed for significant first- and second-order polynomial contrasts to identify trends in the data. Impact attenuation values were converted from log to linear scaling before statistically statistical tests were performed.
The accelerometry data allowed the calculation of transfer functions, which were used to determine the gain or attenuation of the shock wave as it traveled from the leg to the head. Figure 1 shows typical time domain and frequency domain profiles for both the leg and the head accelerometer. In the time domain there is a rapid increase in the leg acceleration profile that occurs immediately after heel strike. This shock wave traverses the skeletal system and is seen in the head profile about 10 ms after it is seen in the leg profile. By the time it reaches the head, the shock wave has been substantially reduced in magnitude and is no longer the dominant feature in the curve.
In the frequency domain the leg acceleration spectrum typically has two peaks. The high frequency peak (10-20 Hz) represents the impact. The low frequency peak (3-8 Hz) indicates the general up and down movement of the leg that occurs during the running cycle. The head acceleration spectrum indicates that the impact frequencies had very little power. Most of the power in the head spectrum resided in the 3-8 Hz range, with the peak power occurring at a slightly lower frequency than the low frequency peak in the leg spectrum.
Figure 2 shows the grand ensemble transfer function for each of the stride length conditions. Low frequencies (0-5 Hz) actually showed an increase in the acceleration as the shock wave moved from the leg to the head. However, frequencies associated with impact (10-20 Hz) showed a progressive increase in impact shock attenuation (IA) as the stride length increased.
Table 1 shows the mean peak tibial acceleration (TA), mean peak head acceleration (HA), and the mean impact attenuation (IA) for each stride length. Both TA and HA showed statistically significant linear trends with stride length (both with P < 0.05). However, the HA values decreased by 0.8g from the +20% condition to the -20% condition, while the TA values decreased by 5.6g. There was also a statistically significant second-order trend to the TA data (P < 0.05). This was because of a greater effect of stride length during the conditions greater than PSL compared with those less than PSL. Polynomial contrasts indicated that there was a statistically significant linear trend(P < 0.05) to the IA data but no second-order trend (P= 0.72). Impact attenuation decreased from -36.1 to -28.4 dB as stride length decreased from +20% of PSL to -20% of PSL. Statistically significant differences are indicated in Table 1.
Because of the stride length alterations, mean stance times varied across conditions (243, 240, 238, 235, and 228 ms for the +20% to the -20% conditions, respectively). For visual comparisons, the joint angle, moment, and power curves were normalized to stance time. This provided the advantage of enabling comparisons of timing, but it also led to some distortion because of the unequal stance times. All quantitative values discussed below were from analyses of variables on the absolute time scale.
The impact phase was defined as the time between heel contact and the time at which the support leg center of mass stops decelerating. The deceleration profile of the support leg is symmetrical with a peak value occurring at approximately the same time as the peak impact value of the vertical ground reaction force (1). Thus the impact phase was estimated to be twice the time to the peak impact (T1) of the vertical ground reaction force (Fig. 3). The average time of the impact phase ranged from 0.58 ms (23.7% of stance) in the +20% condition to 68 ms (30.0% of stance) in the -20% conditions.
The ensemble joint angle curves in Figure 4 depict joint flexion with a positive slope and joint extension with a negative slope. Joint angles of zero represent the sagittal view of the lower extremity in the anatomical position. The hip joint was relatively stable at approximately 25° during the first 10-20% of stance and then tended to flex(Fig. 4a). This flexion occurred earlier and with a greater velocity during the longer stride length conditions.
The knee was the only joint that was flexing during the entire impact phase(Fig. 4b). At contact the knee angle was 15-19°. Average maximum knee flexion occurred at approximately midstance and was greatest in the +20% condition (50.5°) and least in the -20% condition(43.9°).
During the first half of the impact phase, the ankle joint plantarflexed to enable the foot to be placed flat on the ground (Fig. 4c). The joint then dorsiflexed as the leg pivoted about the ankle and the center of mass of the body passed from behind the ankle joint to in front of it. The least amount of ankle plantarflexion occurred during the -20% condition. The ankle plantarflexion velocities were greatest during the long stride length conditions.
Figure 5 shows the ensemble hip, knee, and ankle moment curves normalized to body mass. Positive values represent net extensor moments and negative values represent net flexor moments. The hip moment reached a peak extensor value during the first half of the impact phase(Fig. 5a). The greatest peak extensor moment occurred during the +20% condition and the largest differences between the stride length conditions occurred at contact. At this point the -20% condition had the greatest extensor moment and the +20% had a slight flexor moment.
During the first half of the impact phase the knee joint had a slight flexor moment (Fig. 5b) and the ankle joint moment values were near zero (Fig. 5c). The moments for both of these joints switched to extensor and increased in magnitude throughout the second half of the impact phase. The longer stride length conditions produced larger extensor moments at both the knee and the ankle joints.
Figure 6 shows the ensemble hip, knee, and ankle power curves normalized to body mass. The area below the zero line represents the amount of energy that is absorbed by eccentric activity at the joint. Concentric activity, and thus energy generation, is represented by positive values. Recall that there was an increase in impact shock at the leg (TA inTable 1) and an increase in impact attenuation (IA inTable 1 and Fig. 7) with longer stride lengths. There was a corresponding trend in joint energy absorption, with a progressive increase in the amount of energy absorbed at each joint as stride length increased. The least amount of energy was absorbed during the impact phase of the -20% condition and the most in the +20% condition. Statistically significant differences between stride length conditions are given inTable 1. There was a statistically significant linear trend in the energy absorbed at all three lower extremity joints, but second-order trends were not significant.
During the PSL condition the hip absorbed the least amount of energy during the impact phase (0.8 J·kg-1), while the knee absorbed slightly more energy than the ankle (2.2 J·kg-1 vs 2.0 J·kg-1). Relative to the PSL condition, the +20% stride length condition had absorption values of 150%, 141%, and 120% at the hip, knee, and ankle, respectively. For the -20% condition hip absorption decreased to 13% of the PSL values while the reductions in the knee and ankle absorption values were less (59% and 75%, respectively). In absolute terms the range of energy absorption values for the hip, knee, and ankle (1.1, 1.8, and 0.9 J·kg-1) indicate that the knee is most responsive to alterations in stride length.
In this study the impact load on the body increased with stride length despite a constant running velocity. The subjects responded to the greater impacts by increasing the attenuation of the shock wave before it reached the head. This increased attenuation was most probably accomplished by using active muscles to absorb the impact energy at the hip, knee and ankle joints.
Mean transfer functions at the impact frequencies were slightly greater than comparable values shown in the literature(9,18). This could be a result of different progression velocities. The average velocity of progression was 2.44 m·s-1 in Hamill et al. (9) compared to 3.81 m·s-1 in the current study. This greater velocity produced greater impacts with the ground and thus allowed for greater attenuation. Another reason for the difference may be the method of accelerometer attachment. Shorten and Winslow (18) used an accelerometer attached to a bar clenched between the teeth rather than one strapped over the frontal bone of the head. This more direct attachment may have caused a difference in peak impacts to be measured at the level of the head. In addition, in both of these studies the subjects ran on a treadmill. The treadmill bed may have added some degree of compliance to the system and thus reduced the amount of attenuation required by the body compared with the overground trials in this study.
Joint moment curves were similar in shape and magnitude to those calculated by Simpson and Bates (19) after adjustments for normalization. These researchers found predominately extensor moments at the hip, knee, and ankle joints during the support phase of running. The notable exceptions were during the initial portion of knee joint moment and during the final stage of the hip joint moment. During these times there were slight flexor moments. These findings are consistent with the current study.
Stride length is not the only variable that can influence the magnitude of the impact. Clarke et al. (4) found that running speed could influence the impact peak of a tibial mounted accelerometer by 34% for each 1.0 m·s-1 increase in running speed. Because of the relatively complex task of maintaining an abnormal stride length, it was necessary to allow the subjects in the present experiment to vary their speed by ± 5% (0.383 m·s-1) to obtain an adequate number of acceptable trials. This range of velocities had the potential to alter the impacts independent of stride length. As a check, center of mass velocity was estimated by the average horizontal velocity of the hip marker during the stance phase. The velocities measured in this manner ranged from 3.77 m·s-1 in the -20% condition to 3.56 m·s-1 in the+20% condition. Therefore, the greatest velocities were found in the conditions that exhibited the lowest impacts. This indicates that the estimations of the influence of stride length on impacts derived in this paper may be conservative.
Ideally the accelerometers mounted on the body would be exactly parallel to each other for all of the stride length conditions. This would ensure that shock attenuation is not confused with a changing orientation between the accelerometers. This factor was a concern in this study because of the possible changing kinematics between conditions. If the leg orientation changed as stride length was altered, the results could be confounded. Leg angle at contact was measured during each trial of the experiment. During the+20% condition the average value of the leg angle was 8.1° from vertical at contact. This compares to 7.9° from vertical during the -20% condition. The greatest deviation from vertical was found during the PSL condition(10.1°). These small differences between stride length conditions had a maximal effect between conditions of less than 0.1 g.
Another concern was the possibility that the angular velocity of the leg would change between stride length conditions. This would alter the magnitude of the centripetal acceleration experienced by the accelerometer mounted to the distal leg. The angular velocity of the leg was averaged from contact to the time of the impact peak of the vertical ground reaction force. Assuming a radius of 0.12 m between the accelerometer and the ankle joint, the effect of the centripetal acceleration ranged from 0.31g during the -20% condition to 0.41g during the PSL condition. This 0.1g difference is low and would probably only affect the low frequency portion of the spectrums. Thus, the attenuation of the impact was not affected by differences between stride length conditions associated with centripetal acceleration.
Greater vertical impulses were associated with longer stride lengths (4.41, 4.03, 3.74, 3.44, and 3.18 N·s·kg-1 for the +20% to -20% conditions, respectively). These greater impulses indicated that the subjects left the ground and subsequently landed with greater vertical center of mass velocity during the longer stride lengths. Vertical heel marker velocities at contact confirmed that the foot also had greater vertical velocities with longer strides (-0.79, -0.61, -0.47, -0.39, and -0.37 m·s-1 for the +20% to -20% conditions, respectively). These velocities were brought to zero as ground contact was made; therefore, larger velocities required larger decelerations of the tibia. Average peak impact values at the leg(Table 1) show that the average tibial accelerations ranged from 11.3g during the +20% stride length condition to 5.7g during the -20% condition, a difference of 5.6g. The head accelerations changed by 0.8 g's across stride length conditions(Table 1).
Greater impact loads were countered by greater shock attenuation. During greater stride lengths, the greater impacts seen at the tibia were matched by increased energy absorption by the muscles that cross the hip, knee, and ankle joints. This resulted in greater attenuation of the shock wave in response to greater impacts. Head accelerations remained relatively constant across all stride length conditions. The body seems to strive for stability at the head in response to this increased impact load on the lower extremity(9).
The adaptation to increased shock was not the same at each joint. During the stride lengths less than PSL, most of the energy absorption was shared equally between the knee and the ankle. As the impact shock increased during the stride lengths longer than PSL, the knee joint became the dominant shock attenuator with an increase in energy absorbed of 0.9 J·kg-1. The hip and ankle joints showed less than half the increase in energy absorption experienced by the knee from PSL to +20% (0.4 J·kg-1 for each).
The direction of the line of action of the resultant ground reaction force(GRF) can alter the amount of energy that is absorbed at a joint. At the moment of ground contact, the center of mass of the body had a vertical velocity of slightly less than -1.0 m·s-1 during the PSL condition. This velocity must be reversed during the stance phase to keep the body from collapsing. The vertical GRF is responsible for the impulse that decreases the velocity of the center of mass, but this impulse does not act in isolation. The anterioposterior GRF causes a braking impulse during the first half of stance and a propelling impulse during the second half. This anterioposterior GRF can change the direction of the line of action of the resultant GRF. An increasing braking impulse causes the line of action to move posteriorly during the impact phase of the running cycle.
Lafortune et al. (11) have shown that knee angle at contact plays an important role in body stiffness and thus shock transmission during lower extremity impacts with a solid object. At least part of the adaptation to long stride lengths seen in this study can be explained by examining the distance (dk) between the line of action of the ground reaction force and the knee joint center of rotation. If the line of action travels through the knee joint (dk = 0), it will tend not to rotate the segments about the joint and the muscles that cross this joint will be unable to absorb energy. On the other hand, if the distance dk is increased, an equivalent force will produce a greater torque about the joint and will tend to cause greater changes in angular velocity. This mechanism may allow the muscles that cross the knee joint to increase the amount of energy that they absorb during the eccentric contraction phase and thus attenuate more shock. During the peak deceleration of the support leg the average line of action distances for the knee joint (dk) were -4.08, -3.74, -3.46,-2.84, and -2.83 cm for the +20% to -20% conditions, respectively. The negative values indicate that the line of action passed behind the knee at this point and thus tended to flex the joint. To counteract this moment, the knee extensor muscles must contract to produce an extensor moment.
The ankle joint was unable to contribute as much energy absorption as the knee in the longer stride length conditions. This may be partly a result of the more restricted line of action to ankle joint center distance (da). For any given joint, the resultant force vector will act at a distance that is related to the height of the joint and the angle of the force vector. Thus, changes in the force vector angle will change dk more than da. Another factor contributing to the lower ankle energy values during the impact phase was the two-dimensional nature of the energy analysis in this study. Such an analysis will tend to underestimate the contribution of the ankle because this joint has substantial frontal plane motion occurring during the impact phase that cannot be detected in a 2-D analysis. Ankle eversion during the impact phase is a likely mechanism of energy absorption and thus shock attenuation (5).
It has been suggested in this paper that the distance between the line of action of the force vector and the joint center can be altered to adjust the amount of shock attenuated by some joints. This mechanism may be useful to attenuate shock, but it is also metabolically costly. Increases in the line of action distance will require greater muscular effort to counteract. Hamill et al. (9) showed that stride lengths greater than preferred were associated with increases in the volume of oxygen consumed while running on a treadmill. Part of this increase in metabolic expenditure may be caused by adjustments that the body is making in response to increased impact loads. During the fatigued state the body may reduce shock attenuation provided by the muscles in favor of metabolic savings. This mechanism would suggest greater impact forces transmitted to the head and a greater injury potential while in a fatigued state.
Address for correspondence: Timothy R. Derrick, 235 Physical Education Building, Department of Health and Human Performance, Iowa State University, Ames, IA, 50011. E-mail: [email protected].
1. Bobbert, M. F., H. C. Schamhardt, and B. M. Nigg. Calculation of vertical ground reaction force estimates during running from positional data. J. Biomech.
2. Bresler, B. and J. P. Frankel. The forces and moments in the leg during level walking. Trans. Am. Soc. Mech. Eng.
3. Buczek, F. L. and P. R. Cavanagh. Stance phase knee and ankle kinematics and kinetics during level and downhill running. Med. Sci. Sports Exerc.
4. Clarke, T. E., L. B. Cooper, D. E. Clark, and C. L. Hamill. The effect of increased running speed upon peak shank deceleration during ground contact. In: Biomechanics IX-B,
D. Winter, R. Norman, R. Wells, K. Hayes, and A. Patla (Eds.). Champaign, IL: Human Kinetics, 1985, pp. 101-105.
5. Denoth, J. Load on the locomotor system and modeling. In:Biomechanics of Running Shoes,
B. M. Nigg (Ed.). Champaign, IL: Human Kinetics, 1983, pp. 63-116.
6. Elftman, H. The function of muscles in locomotion.Am. J. Physiol.
7. Hamill, C. L., T. E. Clarke, E. C. Frederick, L. J. Goodyear, and E. T. Howley. Effects of grade running on kinematics and impact force. Med. Sci. Sports Exerc.
8. Hamill, J., G. E. Caldwell, and T. R. Derrick. Reconstructing digital signals using Shannon's sampling theorem. J. Appl. Biomech.
9. Hamill, J., T. R. Derrick, and K. G. Holt. Shock attenuation and stride frequency during running. Hum. Mov. Sci.
10. Jackson, K. M. Fitting of mathematical functions to biomechanical data. IEEE Trans. Biomed. Eng.
11. Lafortune, M. A., M. J. Lake, and E. M. Hennig. Differential shock transmission response of the human body to impact severity and lower limb posture. J. Biomech.
12. McFadyen, B. J. and D. A. Winter. An integrated biomechanical analysis of normal stair ascent and descent. J. Biomech.
13. McMahon, T. A., G. Valiant, and E. C. Frederick. Groucho running. J. Appl. Physiol.
14. McNitt-Gray, J. L. Kinetics of the lower extremities during drop landings from three heights. J. Biomech.
15. Nigg, B. M., G. K. Cole, and G. P. Brüggemann. Impact forces during heel-toe running. J. Appl. Biomech.
16. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in Pascal
. New York: Cambridge University Press, 1989, pp. 422-497.
17. Robertson, D. G. E. and D. A. Winter. Mechanical energy generation, absorption and transfer amongst segments during walking. J. Biomech.
18. Shorten, M. R. and D. S. Winslow. Spectral analysis of impact shock during running. Int. J. Sport Biomech.
19. Simpson, K. J. and B. T. Bates. The effects of running speed on lower extremity joint moments generated during the support phase.Int. J. Sport Biomech.
20. Valiant, G. A., T. A. McMahon, and E. C. Frederick. A new test to evaluate the cushioning properties of athletic shoes. In:Biomechanics X-B,
B. Jonsson (Ed.). Champaign, IL: Human Kinetics, 1987, pp. 937-941.
21. Vaughan, C. L., B. L. Davis, and J. C. O'Connor.Dynamics of Human Gait
. Champaign, IL: Human Kinetics, 1992, pp. 17-22.
22. Voloshin, A. and J. Wosk. An in vivo
study of low back pain and shock absorption in the human locomotor system. J. Biomech.
23. Winter, D. Moments of force and mechanical power
in jogging. J. Biomech.
24. Winter, D. The Biomechanics and Motor Control of Human Gait
. Waterloo, Canada: University of Waterloo Press, 1987, pp. 38-43.
25. Wosk, J. and A. Voloshin. Wave attenuation in skeletons of young healthy persons. J. Biomech.