A weighted least squares method for inverse dynamic analysis

Figures & data

Figure 1 Marker set and skeleton model. Numbers indicate the number of DOF assigned to each of the body segments.

Figure 2 Three dimensional joint moments at hip and knee during a representative running trial, obtained with each of the three inverse dynamics methods. Frame rate is 240 Hz and frame 1 represents heel strike.

Figure 3 Peak joint moments (in Nm) in all 23 trials, compared between the NOGRF method (no GRF data used) and the FULLGRF method, where full GRF data is available. Maximum moments were used for hip extensor and both internal rotator moments. Minimum moments were used for knee flexor and both adductor moments.

Figure 4 Peak joint moments in all 23 trials, compared between the FzMxy method (partial instrumentation) and the FULLGRF method, where full GRF data is available.

Table 1. Error measures for joint moments obtained with no force measurement (NOGRF) or partial force measurement (FzMxMy). Each result was compared to a “gold standard” where complete GRF data was used (FULLGRF). Mean relative errors (MRE) and correlation coefficients (r) were computed using equations (9) and (10).

	FzMxMy		NOGRF
Joint moment	MRE (%)	r	MRE (%)	r
Hip extensor	13.5	0.379	11.4	0.263
Hip adductor	9.4	0.827	16.9	0.735
Hip rotator	9.4	0.645	12.4	0.653
Knee flexor	4.4	0.942	12.8	0.663
Knee adductor	11.7	0.946	58.4	0.002
Knee rotator	47.3	0.887	49.6	0.526