from BIOMCH-L 1/6/94

Practically all anthropomorphic models assume that human body segments are rigid, have clearly defined intersegmental boundaries, and possess an invariant endo-structure. All of these assumptions are convenient for modeling purposes but are basically incorrect: First, body segments change their exo- and endomorphologies under the influence of external (inertial) and internal (muscular and passive viscoelastic) forces substantially, sometimes even dramatically (such as the thorax during extensive breathing, and the "wobbling" of soft tissue structures during running). Secondly, segment boundaries are by no means fixed but vary as a segment moves through its range of motion. In this process, mass particles are transferred from one segment to the adjacent one and vice versa. Other contributors to changing segment boundaries are non-stationary joint axes of rotation. Thirdly, the constantly changing volume of body fluids (mainly blood) within a segment also substantially alters the segment's mass distribution. In a 1980-publication, one of us (H. Hatze, Journal of Bio- mechanics 13, pp. 833-843) described all of these phenomena and estimated their influence on the accuracy of the computed parameter values to be no more than 6%. This estimate may, however, be completely wrong. To our knowledge, there exists no reliable study at present which would allow us to give a more accurate estimate. However, we may not be aware of pertinent studies that appeared recently, such as the apparently important MS thesis of Ori Sarfati on which, according to Zvi Ladin, the recent publication by Ori Sarfati and Zvi Ladin of the video- based system for the inertial parameter determination (J. of Biomechanics 26(8), 1011-1016, 1993) is based. (Strangely enough, however, Sarfati and Ladin did not find it worth quoting Sarfati's MS thesis in the reference list of their own publication, although this MS thesis is allegedly fundamental to this publication. Under these circumstances, it is obviously difficult for others to discover such hidden references). Considering the above arguments, one wonders to what extent precision in determining segmental parameter values ( masses, principal moments of inertia, mass centroid coordinates, etc.) is really of relevance. At present, this question is difficult to answer. It is certainly not of much use to the biomechanics researcher or to the clinician when error bounds of 2% are quoted for parameter determinations of artificial uniform test bodies, as is the case with a recently announced system. The user is not interested in errors that pertain to unrealistic uniform test bodies. He wants to know what accuracy he can expect in determining inertial parameter values of real (and much more complex) body segments, the densities and shapes of which are by no means uniform but vary across the cross-section of the segments as well as along their longitudinal axes, facts, which all have to be taken into account in an appropriate anthropomorphic model for inertial parameter determination. Reasonable estimates of error bounds relating to realistic techniques for the determination of inertial segment parameter values exist. The question remains what relevance the stipulation of such error bounds might have in view of the fuzziness of intersegmental boundaries and the inaccuracies introduced by the apparent non-rigidity of real body segments. This is the topic on which we would like to initiate a discussion on this forum. Sincerely Herbert Hatze and Arnold Baca ________________________ In a recent posting, H. Hatze and A.Baca suggested a "discussion forum on the accuracy required in determining human body segment parameters" (BSP's). I would like to address this issue in the context of using the Inverse Dynamic Approach (IDA) to calculate joint moments. (In this approach, kinematic, Ground Reaction Forces (GRF's) and BSP data are all utilized.) The question that has interested me (and others) for some time is, "How important are uncertainties in each type of data set--e.g., does an error of 1% in GRF data degrade the accuracy of hip moments as much as say a 10% error in BSP data? If one uses an approach described by Cappozzo, Leo and Pedotti (Equation 17 in their article in J. Biomechanics, v.8, 307-320, 1975), one can assess the contribution of different errors on the overall uncertainty of a calculated value for a joint moment. I have used the sagittal plane data described in Winter's 1979 book on gait and, as a starting point, assumed the following uncertainties; 1. BSP and acceleration data: 10% of nominal values 2. GRF data: 1% of nominal value (based on forceplate specifications) 3. Position of resultant GRF vector: 6.3 mm (based on Bobbert and Schamhardt's article in J. Biomechanics, v23, 7, 705-710, 1990) 4. Coordinates of joints: 10mm The results of this exercise showed that uncertainties in BSP and acceleration data had little effect on the overall uncertainty of the hip moment during the stance phase of gait, accounting for less than 2% of the total uncertainty. Errors in Center of Pressure (CoP) location, and joint axes had much greater ramifications, accounting for over 64% of the uncertainty. Percentage-wise, the contributions of BSP and accelaration errors became greater during swing (accounting for up to 50% of the average uncertainty), but this must be seen in light of the fact that moments during swing are extremely small. (The only people who placed great importance on the moments during the swing phase were Braune and Fischer who at the turn of the century were testing the theory of the Weber brothers that the leg acted as a pendulum!) The above statements are directly in line with the findings of Capozzo, Leo and Pedotti who stated "Errors in determining the position of the structure, with respect to the vector of ground reactions, are major determinants of the errors on the muscular moments". In summary, one could make a 50% error in one's estimates of BSP parameters and hardly effect the accuracy of calculated values for joint moments. So, in the context of human gait, it makes little sense in striving to get perfect BSP data. It makes more sense to obtain reliable, accurate data for joint centers of rotation and GRF data. Regards, Brian L. Davis, Ph.D. Dept. Biomedical Engineering (Wb3) Cleveland Clinic Foundation 9500 Euclid Avenue Cleveland, Ohio 44195, U.S.A E-Mail: davis@bme.ri.ccf.org Ph: (216) 444-1055 (Work) Fax:(216) 444-9198 (Work) ____________________________ In recent postings Brian Davis and Paul Devita discussed the role of the inertial parameters in the determination of joint moments, suggesting that even large errors in the inertial parameters will lead to relatively small errors in the calculated moments. I would like to address two issues that are related to this discussion - the overall magnitude of the inertial loads (i.e. forces and moments that arise from the motion of the body segments), and the role of the inertial parameters in the determination of the inertial loads. In a study that Ge Wu (who is now at Penn State) and I conducted a few years ago, we used the kinematometers (devices that combine position markers, linear accelerometers and angular velocity sensors) to monitor the kinematics of the lower limb during physical activities ranging from slow walking to jumping. We then compared the magnitudes of inertial and static components of the joint loads (forces and moments). The results were presented last year, during the Second International Symposium on 3-D Analysis of Human Movement (Poitiers, France), and in summary we found that the inertial effects are largest in the transverse plane and that they increase in magnitude in the proximal direction and with an increase in the speed of the activity. We compared the ratios of the maximum inertial forces to the maximum static forces (i.e. the forces needed to maintain equilibrium). In SLOW WALKING the maximum inertial forces for the ankle were on the order of 3-6% (of the maximum static forces) in the vertical direction, 16% in A-P direction and 60-80% in the M-L direction. The corresponding values for the hip were 20% in the vertical direction, 100-110% in the A-P direction and 200-300% in the M-L direction. As the speed of the activity increased, we saw the expected increase in the inertial effects, leading to inertial forces that were either HIGHER than or similar to the static components in the A-P and M-L directions, and are on the order of 10-20% in the vertical direction. These results would be linearly affected by errors in the segmental masses. The corresponding values for the moments were generally smaller, however even there we saw values that were on the order of 20-40% in the medial direction for running. As both Devita and Davis suggest, the results of the moments will be very sensitive to errors in the locations of the joints, however, since the accepted practice of the inverse dynamic solution of the moment equations invovles conducting the calculations in a Body Coordinate System centered at the segmental center of mass, any errors in the location of the COM would have just as grave consequences as errors in the locations of the joint centers (since the equations contain terms that are the radii vectors from the segmental COM to the joint centers). References: Ge Wu and Zvi Ladin. The effect of inertial load pm human joint force and moment during locomotion. Proceedings of the Second International Symposium on Three-Dimensional Analysis of Human Movement, 6/30-7/3/1993, Poitiets, France, pp 106-107. Zvi Ladin Biomedical Engineering Department Boston University e-mail: ZL@buenga.bu.edu ________________________ I enjoyed reading Zvi Ladin's posting on the network, since I think this makes for an interesting discussion. He raised some points that I would like to address below. One such issue concerns the statement he made in his last paragraph "any errors in the location of the COM would have just as grave consequences as errors in the locations of the joint centers". At first glance this statement appears to be correct, since the equations of equilibrium do indeed contain terms that are the radii vectors from the segmental COM to the joint centers. However, after spending the morning thinking about it, I am still of the opinion that errors in the locations of joint axes are MUCH MORE damaging than errors in the location of the segment's COM. I will give my reasons in two ways; (i) a "logical" approach, and (ii) an "analytical" approach. (i). If one regards the foot, and for the moment assumes the GRF acts at the 2nd metatarsal head (MTH), and the COM is midway between the 2nd MTH and the ankle joint, then one can take moments about the COM and solve for the (unknown) joint moment. This equation will involve the distance between the 2nd MTH and COM (call this distance "A") as well as the distance between the COM and the ankle (call this distance "B"). If one makes a mistake in locating the COM, then either (a) A will be bigger and B smaller, or (b) A will be smaller and B will be bigger. The point is that in the equation, these errors will to some extent CANCEL each other. However, if there is an error in the location of the GRF (say A is bigger), then there is nothing in the equation that will cancel this. This is my first argument to support my opinion that errors in either joint axis location or location of GRF are more detrimental than errors in BSP parameters. (The second argument is much longer!) (ii) Analytical approach. Here I am going to try an do a complete error analysis of a somewhat simplified case--a foot in contact with the ground. (The foot does have an angular acceleration (alpha) and a vertical acceleration (Vacc).) F is the magnitude of the GRF, H is the reaction force at the ankle, mg is the weight of the foot (mass, m = 1.16kg, g = 9.81m/s/s) and the moment at the ankle = M. "O" represents the COM and "A" represnts the ankle joint. Fx, Ox and Ax are the x-coordinates of F, O and A respectively. "I" is the moment of inertia of the foot (about the COM). Some of these quantities are indicated in the sketch below. | | | | | | J \ _______ / A @ ) @ represents a clockwise moment ----^ o /|\ / of magnitude M at the ankle joint (____T_______|____|___/ /|\ \|/ |H |F mg | One can sum the vertical forces and take moments at O to obtain the following equation; M = -F*(Ox - Fx) + (m*Vacc + m*g - F)*(Ax - Ox) + I*alpha In performing an uncertainty analysis, one needs to know the partial derivatives of M with repect do each variable in the above equation: dM/dF = -(Ox - Fx) dM/dOx = -m*(Vacc + g) dM/dFx = F dM/dm = (Vacc + g)*(Ax - Ox) dM/dVacc = m*(Ax - Ox) dM/dg = m*(Ax - Ox) dM/dAx = m*(Vacc + g) - F dM/dI = alpha dM/dalpha = I One then needs to substitute actual values into the above equations and multiply by the errors associated with each variable. Then square the results, add up and then take the square root to find the overall uncertainty. i.e., overall uncertainty equals; square root of {([dM/dF]*error in F)^2 + ([dM/dOx]*error in Ox)^2 +.....} I did this for typical data used in gait analysis (using SI units); F = 830 N, Ox = 0.58 m, Fx = 0.5 m, m = 1.16 kg, Vacc = 5.54 m/s/s, g = 9.81 m/s/s, Ax = 0.66 m, I = 0.0099 kg/m2, alpha = 36 r/s/s. By substituting these values into the partial derivatives above, one can get the following values: (next to each is an assumed error for each variable) error dM/dF = -0.08 8.3 N (i.e., 1% of F) dM/dOx = -17.81 0.01 m (i.e., 1 cm) dM/dFx = 830 0.01 m " dM/dm = 1.228 0.116 kg (i.e., 10% of mass) dM/dVacc = 0.093 0.554 m/s/s (i.e., 10% of Vacc) dM/dg = 0.093 0 m/s/s dM/dAx = -812.2 0.01 m (i.e., 1 cm) dM/dI = 37 0.00099 kg/m/m (i.e., 10% of I) dM/dalpha = 0.0099 3.7 m/s/s (i.e., 10% of alpha) The calculated moment at the ankle is 131 Nm with an overall uncertainty of 11.634 Nm. Now for the "bottom line". If the error associated with Fx is reduced to zero, then the overall uncertainty becomes 8.15 Nm. If the error associated with Ax is reduced to zero, the overall uncertainty becomes 8.33Nm. (Both 8.15 and 8.33 are better than 11.6.) However, if the error associated with Ox is reduced to zero (perfect BSP data), the overall uncertainty is 11.632 Nm. (Hardly different to 11.634Nm) So, this tedious exercise has suggested that, for the data given above, COM location is not nearly as important as the location of the external force or the ankle joint center. Another issue that I would like to mention concerns the inclusion or exclusion of inertial components in the Inverse Dynamics Approach. I do not want to give readers the impression that I think inertial components should be excluded. Although I believe errors in either acceleration data or BSP parameters are not that serious (compared to errors in location of GRF and/or joint axes), I do not recommend that the dynamic terms should be neglected. That would be like saying "I am going to CONSISTENTLY overestimate (or underestimate) BSP and acceleration terms by 100%". This scenario is different to the situation where one might have large uncertainties in different variables--which results in some terms being overestimated, and some underestimated. Thus, errors in joint moments will only be linearly affected by errors in BSP parameters (e.g. limb masses) if the estimates are consistently too large or consistently too small. I hope this has added to what I consider an interesting question. Regards, Brian L. Davis, Ph.D. Dept. Biomedical Engineering (Wb3) Cleveland Clinic Foundation 9500 Euclid Avenue Cleveland, Ohio 44195, U.S.A E-Mail: davis@bme.ri.ccf.org Ph: (216) 444-1055 (Work) Fax:(216) 444-9198 (Work)

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