TECHNICAL NOTES

JOURNAL OF APPLIED BIOMECHANICS, 1993,9,306-314 O 1993 by Human Kinetics Publishers, Inc.

Use of Ground Reaction Force Parameters in Predicting

Peak Tibia! Accelerations in Running

Ewald M. Hennig, Thomas L. Milani, and Mario A. Lafortune

Ground reaction force data and tibial accelerations from a skin-mounted transducer were collected during rearfoot running at 3.3 m/s across a force platform. Five repetitive trials from 27 subjects in each of 19 different footwear conditions were evaluated. Ground reaction force as well as tibial acceleration parameters were found to be useful for the evaluation of the cushioning properties of different athletic footwear. The good prediction of tibial accelerations by the maximum vertical force rate toward the initial force peak (9 = .95) suggests that the use of a force platform is sufficient for the estimation of shock-absorbing properties of sport shoes. If an even higher prediction accuracy is required a regression equation with two vari- ables (maximum force rate, median power frequency) may be used (3 = .97). To evaluate the influence of footwear on the shock traveling through the body, a good prediction of peak tibial accelerations can be achieved from force platform measurements.

In animal experiments repetitive impulse loading of joints has been found to be a contributing factor for the development of degenerative osteoarthritis (Dekel & Weissman, 1978; Radin, Paul, & Rose, 1972). A reduction of skeletal shock waves by shock-absorbing shoe sole materials has been found to result in clinical improvements of patients (Voloshin & Wosk, 198 1). Accelerometers can quantify the shock waves that travel through the body during various sport activities. Although only the acceleration-time curve can give a complete descrip- tion of the transmission phenomena inside the human body, single-peak accelera- tion values are often used to characterize the shock-absorbing properties of materials. Intracortical bone acceleration measurements at the tibia of 6 subjects, running across a force platform, have revealed high correlations for multiple- regression comparisons between the peak tibial accelerations and ground reaction force (GRF) parameters (Hennig & Lafortune, 1991). A regression equation,

Ewald M. Hennig and Thomas L. Milani are with Sportbiomechanik, Universitat GH Essen, Postfach 103 764, 45141 Essen, Germany. Mario A. Lafortune is with the School of Human Biology, University of Guelph, Guelph, ON, Canada NlG 2W1.

Predicting Peak Tibial Accelerations 307

including force rate and peak horizontal braking force, resulted in correlation values of r = .99 for the comparison to the measured peak tibial bone accelerations.

From these experiments it was concluded that ground reaction force mea- surements may be adequate for the prediction of bone accelerations in individuals. A theoretical "effective mass" model (Nigg, Denoth, & Neukomm, 1981) pro- posed a direct relationship between tibial acceleration and ground reaction forces. However, in another study peak tibial acceleration of the bone was found to occur significantly earlier than the first peak of the vertical ground reaction force, and it showed only a moderate correlation to the passive impact force peak (Hennig & Lafortune, 1991).

Therefore, no simple relationship can be assumed between ground reaction forces and the accelerations of lower extremity skeletal structures. Different anthropometric features of subjects and individual running styles result in large differences of ground reaction forces and tibial accelerations between subjects. In many applications, however, it is more important to judge the influence of different shock-absorbing materials on the magnitude of transmission waves through the body. Therefore, the purpose of the present study was to compare the influence of different footwear on the interaction of the foot with the ground. Of special interest was whether a close statistical relationship exists between ground reaction force and tibial acceleration parameters.

Methods

Twenty-seven experienced runners with a mean age of 28 years (SD = 5.6) and a mean body mass of 72.0 kg (SD = 7.2) participated in this study. All subjects performed five trials of rearfoot strike running (3.3 m/s) across a Kistler force platform in each of 19 different commercially available sport shoe constructions. All shoes were top-model running footwear in the highest price category from internationally renowned manufacturers. Three shoe sizes were available from each shoe type. All shoes were tested in randomized order for each subject on a single day. Running speed was controlled by two photocells at equal distance in front of and behind the force platform location. All trials within a range of 3% of the target speed were accepted. After averaging all trials across subjects we determined a mean velocity of 3.30 m/s (SD = 0.01) for the 19 shoe construc- tions. The velocity range between shoes was 3.29 to 3.31 m/s.

Simultaneously with the recording of the ground reaction forces, skin acceleration measurements at the tibia were performed with a low-weight Entran accelerometer (Type EGAX-F-25). The accelerometer was embedded in a small piece of balsa wood. It was fastened to the skin above the medial aspect of the tibia at half the distance between the medial malleolus and the medial tibial condyle. To achieve a good mechanical coupling with the underlying bone, the transducer assembly was glued to the skin and additionally held in place by an elastic bandage that was wrapped around the shank. The mass of the transducer arrangement was less than 1.5 g, including the mass of the balsa wood.

Using a mechanical model, Valiant, McMahon, and Frederick (1987) pro- posed low-weight accelerometers with an additional strap tension for a good estimation of bone accelerations by skin-mounted transducers. The benefit of an additional strap tension was also found for the comparison of tibial bone accelera- tion results with measurements using skin-mounted transducers with and without

308 Hennig, Milani, andLLafortune

strap fastening (Hennig & Lafortune, 1988). The measured peak accelerations on the skin were higher in both skin conditions. However, in comparison to the bone peak acceleration values the additional strap tension reduced the over- estimation of the freely mounted skin accelerometer results by almost 50%.

An impacter assembly (Exeter Research Inc.), similar to the one described by Frederick, Clarke, and Hamill (1984), was employed to characterize the material properties of the rearfoot sole constructions. In the present study, impact tests at the rearfoot construction of the different shoes were performed with a mass of 8.5 kg with a flat circular missile head (diameter 45 mm) at a falling height of 5 cm. At an impact velocity of 96 cmls the peak accelerations were recorded for each shoe from five repetitive trials (Figure 1).

Data Collection and Processing

The vertical and the antero-posterior horizontal ground reaction forces and the axial acceleration signal were sampled simultaneously by a computer-based data acquisition system (12 bit; 1 kHzIchanne1) in a pretrigger mode. A cinemato- graphic evaluation of the stance phase of the running cycle (Lafortune & Hennig, 1991) has shown that centrifugal forces due to angular motion of the tibia have a major influence on the magnitude and shape of tibial acceleration signals. In this comparison of force and acceleration parameters, the acceleration signals were not corrected for gravity and angular motions, since most studies do not simultaneously record accelerations and angular motions of the lower extremities. A threshold of 5 N of the vertical ground reaction force component was chosen to determine the time onset of foot strike. The parameters used to describe the force and axial tibial accelerations are given in Table 1 (see Figure 2). The maximum force rate (DPVF) was determined as the highest differential quotient of adjoining vertical GRF values divided by the time resolution of 1 rns. The

Shoe Code

Figure 1 - Impacter peak acceleration scores (g) from 19 different shoe construc- tions.

Predicting Peak Tibial Accelerations

Table 1

Force and Acceleration Variables

Parameter Code Unit

Peak vertical force 1 PVFl bw Time to first vertical force peak TPVF1 ms Force rate to peak force 1 (PVFliTPVFl) FRPl bw/s Maximum force rate DPVF bw/s Median power frequency of the vertical force MPFZ Hz Peak vertical force 2 PVF2 bw Peak positive axial acceleration PPAC 9

Figure 2 - Typical vertical ground reaction force and axial tibia1 acceleration during the stance phase at a running speed of 3.3 m/s (PVFl, PVF2, TPVF1, and PPAC are defined in Table 1).

310 Hennig, Milan;, and Lafortune

median power frequency of the vertical force (MPFZ) signal was calculated from a 1,024-point Fl;T power spectrum analysis. A low frequency cutoff of 10 HZ was chosen, since only the initial ground reaction force peak was of interest.

The force and acceleration values were calculated as multiples of body weight (bw) and gravitational acceleration (g), respectively. For each subject the measurement parameters of the five repetitive trials were averaged before further statistical treatment. A repeated measures ANOVA as well as linear and stepwise regression analyses were applied to analyze shoe effects and relationships between GRF and acceleration parameters.

Results and Discussion

The ANOVA showed highly significant (p < .01) differences between shoes for PVF1, TPVFI, FRPI, DPVF, MPFZ, and PPAC. For PVF2 with a calculated mean value of 2.64 body weights (bw), no significant differences were found. Table 2 summarizes the mean values, standard deviations, and minima and maxima of the various parameters for the 19 different shoe conditions.

In a comparison of the peak tibial accelerations during running in different shoes with the acceleration scores from the mechanical impacter (Figure 3), only a low, nonsignificant correlation was found (r = .26). Although the impacter scores suggest large differences in shoe midsole stiffness and elasticity between shoes, the material properties have only a small influence on the shock attenuation behavior of shoes. The mechanical impacter seems to produce an unrealistic impact simulation of the initial foot-to-ground contact during running. As it was shown by Nigg and Morlock (1987), the shape of the midsole in the heel region may have a major influence on the amount of pronation as well as on GRF parameters. Therefore, shock attenuation is substantially influenced by construc- tion features of the shoe and is probably also influenced by locomotor adaptation of the subjects to footwear.

Large differences, between 4.5 and almost 8 g, were found for the peak tibial accelerations during running in different footwear. The surprisingly low acceleration value of 4.5 g for one of the shoe constructions is likely the result of its construction characteristic on the lateral side of the rearfoot. For this

Table 2

Acceleration and Force Parameter Values for 19 Different Running Shoes

PPAC (g) PVFl (bw) TPVF1 (rns) MPFZ (Hz) FRPI (bwls) DPVF (bwls) PVF2 (bw)

Range

Predicting Peak Tibial Accelerations

'c 5 5 x E 0J - a3 u 5 U m - m 4.5 X .- e

4 9 10 11 12 13 14 15 16

Impacter scores in g Figure 3 - Comparison of impacter accelerations with peak tibia1 accelerations during running in 19 different footwear conditions.

shoe a high degree of material deformation occurs at the lateral heel during the initial impact of the shoe with the ground. This shoe exhibits also the lowest median power frequency of the initial vertical GRF impact and the lowest maximum force rate. For PPAC and MPFZ single statistical comparisons (Fish- er's PLSD) revealed highly significant ( p < .01) reduced values of this specific shoe toward all other shoes. For DPVF all comparisons but one gave highly significant results.

In spite of lower running speeds the peak accelerations in this study were on average higher than those reported from bone-mounted accelerations (Hennig & Lafortune, 1991). For a running speed of 4.5 m/s a peak acceleration of 5.3 g is contrasted with an acceleration of 6.4 g (across all subjects and shoes) in this study. However, skin-mounted accelerometers overestimate the acceleration of the underlying bone (Hennig & Lafortune, 1988).

A correlation matrix between PPAC and the force-related variables revealed close relationships between most of the chosen parameters. Only TPVFl and PVF2 demonstrated small to very small correlation values (Table 3). A simple regression analysis was performed for the comparison of peak acceleration (PPAC) and the maximum force rate (DPVF) (Figure 4).

With a stepwise regression analysis (F to enter = 4.0) an even better correlation could be found using the two variables DPVF and MPFZ. The regres- sion equation, resulting in a correlation value of r = .99 (1-2 = .97), is as follows:

PPAC (g) = -4.55 + 0.05 . DPVF (bw/s) + 0.45 . MPFZ (HZ).

312 Hennig, Milan;, and Lafortune

Table 3

Correlation Matrix for Acceleration and GRF Parameters

PPAC DPVF MPFZ FRP1 TPVFl PVF2

PPAC 1 DPVF .98 1 MPFZ .94 .9 1 FRPl .82 .84 .71 1 TPVFl -.37 -.38 -.4 -.65 1 PFV2 .I4 .25 .14 .04 .ll 1

Figure 4 - Linear regression curve between maximum force rate (DPVF) and peak acceleration for 19 different running shoe constructions.

To allow an estimation for the accuracy of peak acceleration prediction, the following procedure was introduced. From 15 of the 19 shoe conditions a regression equation was determined to predict the peak acceleration from the remaining 4 shoes. For this purpose the shoes were listed in an ascending order from the smallest to the largest peak acceleration results and grouped into five units of 3 shoes with 4 single shoes in between (3, 1, 3, 1, 3, 1, 3, 1, 3). The 15 shoes were then used to calculate the following prediction equations from linear and stepwise regression analyses.

Predicting Peak Tibial Accelerations

PPAC (g) = 0.16 + 0.07 - DPVF (bwls) PPAC (g) = -5.08 + 0.05 . DPVF (~w/s) + 0.49 . MPFZ (HZ)

Table 4 compares the results from the measured PPAC to those predicted from both regression formulas.

The largest deviation from the predicted to the measured values occurred for the stepwise regression for Shoe 56 with a relative difference of less than 2.5%. The averaged absolute deviations across the 4 shoes between predicted and measured values were for both prediction methods less than 1%.

High positive correlations of r = .87 were found between intracortical peak tibial acceleration and the force rate FRPl from 6 subjects during running at 4.5 m/s (Hennig & Lafortune, 1991). This study found for the effect of footwear again a very close relationship between peak acceleration and force rate (DPVF, r = .98). The results from both studies suggest a strong relationship between ground reaction forces and tibial accelerations.

Table 4

Measured and Predicted Peak Accelerations for Four Different Shoe Types

Shoe code 07 11 56 OB

PPACmeasured 5.94 6.26 6.6 6.99 PPAClinear prediction (DPVF) 5.95 6.25 6.49 7.1 1 PPAC-stepwise prediction (DPVF + MPFZ) 5.86 6.13 6.45 6.99

Summary

Ground reaction forces and tibial acceleration parameters for the impact during running (3.3 m/s) were analyzed for 27 subjects, running in each of 19 different footwear conditions. The present study demonstrates that ground reaction force as well as tibial acceleration measurements can be used to evaluate the cushioning properties of athletic footwear. The good prediction of tibial accelerations by the maximum vertical force rate (3 = .95) suggests that for most applications the use of a force platform is sufficient for the estimation of shock-absorbing properties of sport shoes. If an even higher prediction accuracy is required a regression equation with two variables (DPVF, MPFZ) may be used (1-2 = .97). Acceleration measure- ments are time-consuming, require mounting of sensors at the human body, and may interfere with the movement of subjects. To evaluate the influence of foot- wear on the shock traveling through the body, a good prediction of peak tibial accelerations can be achieved from force platform measurements.

References

Dekel, S., & Weissman, S.L. (1978). Joint changes after overuse and peak overloading of rabbit knees in vivo. Acta Orthopaedica Scandinavica, 49, 519-528.

314 Hennig, Milan;, and Lafortune

Frederick, E.C., Clarke, T.E., & Hamill, C.L. (1984). The effect of running shoe design on shock attenuation. In E.C. Frederick (Ed.), Sport shoes and playing surfaces (pp. 190-198). Champaign, IL: Human Kinetics.

Hennig, E.M., & Lafortune, M.A. (1988). Tibia1 bone and skin accelerations during running. In C.E. Cotton, M. Larnontagne, D.G.E. Robertson, & J.P. Stothart (Eds.), Proceedings of the Vth Biennial Conference of the Canadian Society for Bio- mechanics (pp. 74-75). Ottawa: Spodym.

Hennig, E.M., & Lafortune, M.A. (1991). Relationships between ground reaction force and tibial bone acceleration parameters. International Journal of Sport Biomechanics, 7 , 303-309.

Lafortune, M.A., & Hennig, E.M. (1991). Contribution of angular motion and gravitation to tibial acceleration. Medicine and Science in Sports and Exercise, 23, 360-363.

Nigg, B.M., Denoth, J., & Neukomm, P.A. (1981). Quantifying the load on the human body: Problems and some possible solutions. In A. Morecki, K. Fidelus, K. Kedzior, & A. Wit (Eds.), Biomechanics VII-B (pp. 88-99). Warszawa, Poland: PWN-Polish Scientific.

Nigg, B.M., & Morlock, M. (1987). The influence of lateral heel flare of running shoes on pronation and impact force. Medicine and Science in Sports and Exercise, 19, 294-301.

Radin, E.L., Paul, I.L., & Rose, R.M. (1972). Role of mechanical factors in pathogenesis of primary osteoarthritis. Lancet, 4, 519-522.

Valiant, G.A., McMahon, T.A., & Frederick, E.C. (1987). A new test to evaluate the cushioning properties of athletic shoes. In B. Jonsson (Ed.), Biomechanics X-B (pp. 937-941). Champaign, IL: Human Kinetics.

Voloshin, A., & Wosk, J. (1981). Influence of artificial shock absorbers on human gait. Clinical Orthopaedics, 160, 52-56.