AMERICAN SOCIETY OF BIOMECHANICS Presented at the Twenty-First Annual Meeting of the American Society of Biomechanics Clemson University, South Carolina September 24-27, 1997

INTRODUCTION

The purpose of the present study was to evaluate the error obtained in estimations of hamstring muscle fiber lengths during sprinting with the use of a two-dimensional (2D) versus three-dimensional (3D) analysis. This was accomplished using a computer simulation of the leg motion and hamstring muscles during sprinting. It was concluded that a 2D analysis is sufficient for determination of hamstring muscle fiber lengths during sprinting.

REVIEW AND THEORY

The kinematics and kinetics of walking with the use of 2D and 3D analysis have been well documented in the literature. For sprinting the kinematics and kinetics are also well documented but are usually obtained with a 2D analysis, with the exception of Novacheck's (1995) study in which a 3D approach was used. The appropriateness of a 2D instead of a 3D analysis for the sprinting motion has not been studied and is of importance for future research in sprinting.

Presently the attention of many biomechanists is focused on the roles of individual muscles during the execution of a motion. Knowledge of individual muscle forces has many applications. For example, it is of interest to predict the maximum force or individual muscle force versus time relationships of the hamstring muscles during sprinting with regard to training, injury prevention and rehabilitation. With the use of a model the force-length-velocity-activation relationship for each muscle of the hamstring group can be estimated. However, to obtain an accurate estimation of the muscle force , the muscle fiber length must be determined as accurately as possible with the use of the current technology. A question that arises is, what is the magnitude of error in hamstring muscle fiber length estimates obtained by neglecting hip adduction (AD) and abduction (AB) and internal (IntR) and external (ExtR) rotations during sprinting when a 2D analysis is used instead of a 3D analysis ? The purpose of this study was to evaluate the influence of these motions during sprinting on the estimation of the muscle fiber lengths of the bi-articular muscles of the hamstring group; the semitendinosus (ST), semimembranosus (SM) and the biceps femoris long head (BFL).

PROCEDURES

A computer simulation of the leg motion of an individual (1.70m, 70 kg) during sprinting was developed. The hip angle versus time and the knee angle versus time relationships reported by Mann et al. (1986) for a skilled sprinter were used to determine the hip, knee and ankle joint centers during one sprint cycle for the 2D condition. The ranges of hip AD/AB and IntR/ExtR superimposed on the 2D motion to obtain a 3D sprinting motion were as follows:

	Angle (deg)	step (deg)
Adduction (AD)	5 - 30	5
Abduction (AB)	5 - 40	5
Internal Rotation (IntR)	5 - 45.	5
External Rotation (ExtR)	5 - 45	5

The definitions for the embedded coordinate systems and the geometrical muscle data reported by Pierrynowski (1995) were used to determine the muscle-tendon lengths for the ST, SM and BFL. Lines of action of the SM and BFL were modeled as straight lines joining origin and insertion. The muscle-tendon length of the ST was modeled as the sum of two line segments to simulate the wrapping of the tendon around the femoral condyle. The muscle fiber lengths were determined according to the formula's given by Herzog (1985) for pennate muscles. It was assumed that the tendon length and the muscle thickness (perpendicular distance between the tendons) were constant during contraction. The % error in estimation of the muscle fiber length obtained due to the use of a 2D analysis (LF2D) versus a 3D analysis (LF3D) relative to the muscle fiber length in anatomical position (LFA) was determined with the following equation:

% Error = [(LF^3D - LF^2D) / LF^A ] *100

The maximum % errors were determined with the use of the % error versus % sprint cycle relationships of each muscle for all the simulated conditions. If the maximum error obtained for a simulation was less than 5% it was concluded that a 2D analysis is sufficient.

RESULTS AND DISCUSSION

From the %error versus % sprint cycle relationships for AD/AB and the IntR/ExtR conditions for each muscle (e.g. Fig. 1) the maximum error was determined.

Figure 1: The % error for BFL by adding AD/AB and IntR/ExtR during the sprint cycle.

An increase in AD and AB angle (no IntR/ExtR) caused an increase in error for all muscles. The maximum AD/AB angles for each muscle for which an error of < 5 % was obtained during the simulated sprint cycle are summarized in Table 1. These data show that the maximum errors were < 5% of LFA if the motion was simulated with AD <15 deg and AB <35 deg.

	ST	SM	BFL
AD (deg)	20	30	15
AB (deg)	40	40	35

Table 1 : Error < 5 % for AD/AB.

An increase in IntR and ExtR (no AD/AB) also caused an increase in error for all the muscles. The maximum IntR/ExtR for each muscle for which an error of < 5 % was obtained during the simulated sprinting cycle are summarized in Table 2. These data show that the maximum errors were < 5% of LFA if the motion was simulated with IntR <25 deg and ExtR <45deg.

	ST	SM	BFL
IntR (deg)	45	45	25
ExtR (deg)	45	45	45

Table 2 : Error < 5 % for IntR/ExtR

Novacheck (1995) reported values < 10 deg for AD and AB, < 15 deg IntR and 0 deg ExtR. These values were obtained for children (5-18 years). Smaller values would be expected for skilled sprinters due to training and improvement in coordination. If, due to the use of a 2D instead of a 3D analysis, the AD/AB and IntR/ExtR motions as reported by Novacheck are ignored the maximum errors shown in Table 3 may develop. These data show that the use of a 2D rather than a 3D analysis for sprinting will produce a maximum error in hamstring muscle fiber length estimates of < 2.2% of LFA.

	ST	SM	BFL
15 IntR + 10 AD	-1.58	-2.13	1.67
15 IntR + 10 AB	0.78	0.31	1.70

Table 3: Maximum %error expected using 2D.

CONCLUSION

The errors obtained in the estimates of the muscle fiber lengths of the bi-articular muscles of the hamstring group using a 2D rather than a 3D analysis are very small. Therefore, a 2D analysis of sprinting is sufficient to obtain estimates of hamstring muscle fiber lengths.

REFERENCES

Herzog, W. Dissertation, University of Iowa, 1985.

Mann, R.A. et al. Am. J. Sports Med., 14, 501-510,1986.

Novacheck, T.F. Instr. Course Lect.,44,497-506, 1995.

Pierrynowski, M.R. Three dimensional analysis of human movement. 215-256, Human Kinetics, 1995.

ACKNOWLEDGMENTS

I thank Dr. W.G. Darling for his assistance in discussion of the data and preparation of this manuscript.