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of Estimation Human Body Segment Parameters Historical Background by J rgen Bj rnstrup LIA 95 { 20 October 1995 ISSN 0906 - 6233 Internal Tech-Report - Not submitted anywhere. Note: This is a condensed and abbreviated version of the original document whose title is above. The original can be found in postscript form at . http://www.vision.auc.dk/j rgen/PhD/EHBSP background Abstract This tech-report provides a survey of the, mostly invasive, methods used and studies performed, from the 17th century to the present time, in order to determine/estimate human body segment parameters. The purpose of this report is not to provide a complete, all-inclusive and \in-depth examination of prior work, but merely to provide a historical background for, and overview of, the field of and methods for human body segment parameter estimation. This report is furthermore intended as \interim documentation for a part of the initial work on my Ph.D.-thesis on \Image Processing Based Estimation of Body Segment Parameters - with Application to Motion Analysis . 1 Introduction - Motivation Humans have been interested in the proportions of human beings, if not always then, at least since the \Old Greeks . This initial quantitative interest in human proportions was presumably, to a large extend, aimed toward the attempt to define and portray the anatomically perfect man . Nowadays the interest in body segment parameters is, apart from purely academic interests, mainly due to the need for these parameters in two areas; motion analysis and prosthesis design. The motion analysis term here covers both analysis and description of why a person moves the way (s)he does, and computer simulations and visualizations of motion under influence of external forces and/or constraints. A few examples of areas where motion analysis is used is in the design of impact protective systems, e.g., for cars, in simulations of the effect of spacejourneys on humans, in examination and improvement of work-environments and in sport. Prosthesis design is partly a matter of making prostheses that looks right, i.e. natural, but also, and even more importantly, a matter of making prostheses which feel right, i.e. like the limb the prosthesis is replacing. If a prosthesis is to feel right, or at least as little wrong as possible, then it should obviously have the right size, e.g., length, but the prosthesis should also have the right total mass and mass distribution. 2 Definition of Terms Used in This Report This section describes the terms, related to body segment parameters, used in this report. Most of the definitions are adapted from [Drillis and Contini, 1966] and [Alonso and Finn, 1980]. Object: The object is whatever the measurements are being performed on, e.g., a complete body, a body segment (e.g., a leg) or an inherently inanimate object (e.g., a book). Body segment parameters: The rest of the terms on this list covers the terms usually described as the body segment parameters, when used on body segments. The complete set of body segment parameters include these parameters for at least each of the major body segments (head, trunk, upper-arms, forearms, hands, thighs, calfs and feet) as well as for the whole body. Mass: The mass of an object is the quantity of matter in the object. At the surface of the earth, the mass of an object corresponds to the weight of the object. The mass is measured in grams (g) or kilograms (kg). Volume: The volume of an object is the 3D space occupied by the object. Volume is measured in liters (l ) or cubic centimeters (cm 3 ). Density: The (average) density of an object is the mass of the object divided by the volume of the object. Density is measured in grams per cubic centimeter (g/cm 3 ) or kilograms per cubic meter (kg/m 3 ). Specific gravity: The specific gravity of an object is the density of the object compared to the density of \standard water. Specific gravity has thus no unit, and are numerically equal to the density of the object. Center of mass: The center of mass of an object is the location, i.e. point, that represents the mean position of the matter in the body. The center of mass for body segments can be expressed in an external coordinate system, but is usually expressed as a distance and a, possibly implicit, direction with respect to another point on the segment itself, e.g., the proximal end of the segment. Many simplified physical model assumes that the total mass of each object is located in an infinitely small volume at the center of mass of the object. Center of volume: The center of volume of an object is the location, i.e. point, that represents the mean position of the total volume. If the material is homogeneous, i.e. the density is constant throughout the object, then the center of volume coincides with the center of mass. However, most (larger) living \organisms do not have a constant density throughout. Mass moment of inertia: The mass moment of inertia of an object around an axis is the resistance, i.e. inertia, that the body exhibit against being set in rotation, or being stopped while rotating, around the axis. The mass moment of inertia of an object around an axis is proportional to the sum of all the infinitely small masses constituting the object each multiplied with their individual squared distance to the axis of rotation. Mass moment of inertia is thus measured in units of mass times squared distance (kg m2). Notice that from the definition it follows that a given object have an infinite number of mass moments of inertia as the mass moment of inertia depends both on the object and on the axis of rotation. See [Chandler et al., 1975] for further information about the calculation of mass moment of inertia and the mathematically convenient framework of an \ellipsoid of inertia . Radius of gyration: The radius of gyration of an object around an axis of rotation is the distance between the axis and the points on a specific circle. The circle corresponds to the locations where the total mass of the object, compressed into an infinitely small volume, would have the same mass moment of inertia around the axis as the object itself. The radius of gyration is, of course, measured in units of length, e.g., in centimeters (cm) or meters (m). 3 The History of Human Body Segment Parameter Estimation The purpose of this main section of the tech-report is to provide a "chronological overview of the history of body segment parameter estimation from the 17th century to the present time. The emphasis of the overview is placed on the methods used for estimating body segment parameters, and not on the obtained (quantitative) results. The reason for this is a consequence of the assumption underlying my Ph.D.-thesis: 1 \ The estimated body segment parameters obtained from other individual subjects, or from entire populations, are generally of little use in motion analysis of, or prosthesis design for, individual subjects. Accurate motion analysis, and prosthesis design, should, as far as possible, be based directly on measurements, or estimations, performed on the individual subject. However, this assumption clearly needs to be validated and the results of prior investigations and estimations of body segment parameters are thus being presented and analyzed in another techreport ([Bj rnstrup, 1995b]), which presently is being prepared. The material presented below is to some extend obtained from [Drillis and Contini, 1966], [Clauser et al., 1969] and [Chandler et al., 1975], where some further information about the methods, and many results from the studies, can be found. Many of the provided references are also obtained from these reports, and are repeated here for the convenience of the especially interested reader, with reference to the report, where the reference was found. Such references are written as [Borelli, 1680{1681, e.g. cited in [Clauser et al., 1969]], meaning that the original work presumably is called [Borelli, 1680{1681], but that the information about the reference (mainly) is reproduced from [Clauser et al., 1969]. 1680 - Borelli The earliest recorded \scientific or experimental work in the field of body (segment) parameter estimation appears to have been performed in the last part of the 17th century. Borelli estimated the center of mass of nude men by having them stretch out on a rigid platform supported on a knife edge. The platform was then repositioned until is balanced, thereby indicating a location corresponding to the center of mass for the entire body. See[Borelli, 1680{1681, e.g. cited in [Clauser et al., 1969]] for further information. | 1860 - Harless Harless used the same method as the Weber brothers, but extended the studies to include estimates of absolute and relative location of the center of mass, along the longitudinal axis, of the largest possible number of movable body segments. Initially, the cadavers of, two executed criminals were segmented into 18 segments. The two cadavers were segmented along planes passing through the axis of rotation of each of the primary joints. The tissue near the planes of segmentation was then sutured together over the stumps to reduce tissue and fluid losses. The mass and center of mass of the body segments were then measured/estimated using sensitive scales and a balance plate and the volume of each body segment was estimated/calculated from the mass, using a density of 1.066 g/cm 3 for the entire body. Subsequently Harless examined 44 extremity segments from seven cadavers, segmented as described above, to verify and extend the results of the just described study. Each disarticulated body segment was weighed both in air and under water. Based on the principle of Archimedes,* the volume and density of each segment was estimated. The results of these studies led Harless to conclude that age and sex have significant influence on the density of segments of the human body. See[Harless, 1860a, e.g. cited in [Drillis and Contini, 1966]] and [Harless, 1860b, e.g. cited in [Clauser et al., 1969]] for further information. * The principle of Archimedes states, that when an object is submerged in liquid then the weight of the object is reduced by the weight of the displaced liquid. Given the weight reduction and the density of the liquid, then the calculation of the volume of the object is straightforward. 1889 - Braune and Fischer Braune and Fischer made a very careful study of mass, volume and center of mass of three adult male cadavers and their body segments. The cadavers were close to the average build of German soldiers of that period and they were all dead from suicides. To avoid fluid loss etc. the cadavers were kept frozen throughout the study. The center of mass of each body segment were not estimated by the use of balance plates, as in the previously described studies, but by driving thin rods into the tissue and hanging the body segment from three axes. The intersection of three externally fixed planes, e.g. vertically through each of the axes, formed on the segment, corresponds to the center of mass. This study was so thorough that it uncritically was used as a standard for more than half a century, despite the pronounced differences in and between populations. Braune and Fischer also introduced the use of regression equations for estimation of body segment parameters, based on the length and mass of body segments. See [Braune and Fischer, 1889, e.g. cited in [Drillis and Contini, 1966]], [Braune and Fischer, 1892, e.g. cited in [Clauser et al., 1969]] and [Fischer, 1906, e.g. cited in [Clauser et al., 1969]] for further information. 1894 - Meeh Meeh pointed out, that the results obtained from cadavers should be supplemented with data from living subjects. To estimate the volume of body segments, each segment was immersed in water up to the joint and the amount of water displaced thereby was measured. This method was found to be inexact and each measurement was therefore repeated several times and averaged. Using the densities found by Harless, Meeh was able to estimate the absolute and relative mass of each body segment from its volume and to make a series of graphs to illustrate the growth of the body and its segments as a function of age. This was the first serious attempt to describe the changes in mass of body segments during growth. See [Meeh, 1894, e.g. cited in [Clauser et al., 1969]] for further information. 1931 - Bernstein et al. Bernstein, and his coworkers at the Russian All-Union Institute of Experimental Medicine in Moscow, conducted an extensive investigation of body segment parameters of living subjects. A total of 152 subjects of both sexes, ranging in age from 10 to 75 years were examined and the mass and center of mass of all limb, excluding the center of mass of hands and feet, were estimated. The estimations of the mass of body segments were performed using a modified balance plate. The balance plate technique used by Borelli had been modified and improved several times over the years and a simplified sketch of the version used by Bernstein is shown in Figure 1. Figure 1: Estimation of the mass of a body segment by the method of reaction change, assuming that the location of the center of mass of the segment is known. Reproduced from [Clauser et al., 1969]. The system in Figure 1, can be used to establish a relation between the mass and the displacement of the center of mass of a body segment. The relation is given by W =D( R) dw , where W is the mass of the body segment, D is the distance between the two supporting knife edges, dw is the displacement of the center of mass of the body segment and R is the change in pressure exerted on the scale due to this displacement (see Figure 1). The problem that remains is that neither the center of mass nor the mass of the segment easily and accurately can be estimated by other methods. Bernstein concluded, however, by examining frozen cadaver segments, that the center of mass of a segment, for most practical purposes, coincides with the center of volume. Assuming this coincidence and since the volume and center of volume of a segment can be estimated in vivo, then the center of mass and subsequently the mass of the body segments of living subjects can be estimated. Bernstein concluded, that the individual variations was so great that either complex measuring techniques, as the ones described above, should be used on every individual subject that is dealt with, or anthropometric and structural correspondences (correlations), which allow estimations to be performed based on general habits and anthropometric data, should be established. See [Bernstein et al., 1931, e.g. cited in [Clauser et al., 1969]], [Konrad et al., 1934, e.g. cited in [Drillis and Contini, 1966]], [Bernstein, 1936, e.g. cited in [Clauser et al., 1969]], [Bernstein, 1967, e.g. cited in [Clauser et al., 1969]] and [Clauser et al., 1969] for further information. 1955 - Dempster Dempster examined the cadavers of eight elderly men at the University of Michigan, and estimated the volume, mass, density, center of mass and mass moments of inertia for the body segments. The limb segments were separated at each of the primary joints (after being exe to mid-range and frozen) and the trunk divided into units corresponding to the neck, shoulders, thorax and abdominopelvis. Each segment was then weighed, the center of mass was estimated with a specially designed balance plate, two different mass moments of inertia (around a transverse axis through the center of mass and around a parallel axis through the center of the proximal joint) was estimated from the period of oscillation and the volume was estimated by the principle of Archimedes (see footnote 2). See [Dempster, 1955, e.g. cited in [Clauser et al., 1969]], [Dempster, 1956] and [Chandler et al., 1975] for further information. 1962 - Whitsett Whitsett refined the mathematical model developed by Simmons and Gardner by increasing the number of modeled segments to 14 and by using additional geometric shapes in order to obtain a better approximation to the shape of the body segments. Whitsett s model consisted of spheres, ellipsoids, cylinders, frustums of cones and rectangular parallelepipeds and allowed estimation of the mass distribution, center of mass, mass moments of inertia and mobility of the human body. The model was primarily based on the body segment data from [Dempster, 1955, e.g. cited in [Clauser et al., 1969]] and the regression equations from [Barter, 1957, e.g. cited in [Clauser et al., 1969]]. See[Whitsett, 1962, e.g. cited in [Chandler et al., 1975]] for further information. 1964 - Hanavan Hanavan used a model resembling the ones used by Whitsett and Gray, consisting of 15 segments as the torso was modeled as two segments. To validate the model, Hanavan compared the calculated results with the anthropometric measurements produced by Santschi and coworkers. He found that in half the cases the total body mass moments of inertia around the two horizontal axes (defined by Santschi and coworkers) were predicted within 10% of the experimental data and that the mass moment of inertia around the vertical axis was predicted within 20% of the experimental data. The prediction of the vertical location (the horizontal location could not be compared) of the center of mass was found to be within 7 10 of an inch of the experimental data in half the cases. See [Hanavan, 1964, e.g. cited in [Chandler et al., 1975]] for further information. 1966 - Drillis and Contini The initial interest of Drillis and Contini was the design of improved prosthetic devices, but since this require good estimates of the mass, center of mass and mass moments of inertia of the segments, 20 young living male subjects were carefully examined. Body segment volumes were determined both with a method similar to the one used by, e.g., Cleveland and Dempster (hydrostatic weighing) and by a segment zone method (incremental hydrostatic weighing). The segment zone method is like hydrostatic weighing, but the measurements are performed repeatedly as the segment is lowered into the water in small equidistant steps. This method makes it possible to estimate the volume of each of the slices formed by the stepwise immersion. The center of mass was assumed to be coincident with the mid-volume, which made an estimation of the center of mass possible. The mass of the segments were estimated with a highly sensitive balance plate resembling the one in Figure 1. The study resembles the one performed by Bernstein, but are concentrated on the body segment parameters of young men and are considered to be well thought out and carefully executed. See [Duggar, 1962, e.g. cited in [Clauser et al., 1969]], [Contini et al., 1963, e.g. cited in [Clauser et al., 1969]] and [Drillis and Contini, 1966] for further information. 1968 - Bouisset and Pertuzon Bouisset and Pertuzon used a quick release method (see Figure 2) developed for legs to measure the mass moment of inertia of the combined forearm and hand around the elbow for 11 living subjects. They concluded that the quick release method is reliable for estimation of mass moments of inertia. The method can, however, only be used on the outermost segments, e.g., forearms/hand and calf/foot segments, due to errors introduced by segments joined distally to the segment for which the mass moment of inertia around the proximal joint is being estimated. See [Bouisset and Pertuzon, 1968, e.g. cited in [Chandler et al., 1975]] for further information. If the force F is measured be- fore the segment is released, the acceleration a is measured just after the release and y 1 and y 2 are the indicated distances then the mass moment of inertia of the segment around the proximal joint can be calculated as I = (F y1 y2)/a . Figure 2: Sketch of the setup used for estimation of the mass moment of inertia of distal segments by the quick release method. Reproduced from [Winter, 1979]. 1969 - Clauser et al. Clauser, and coworkers, performed a study designed to supplement the existing knowledge of the mass, volume and center of mass of body segments and to permit a more accurate estimation of these measurements from anthropometric dimensions. The study was based on 13 preserved male cadavers, which each were dissected into 14 body segments. The mass, volume and center of mass were measured for each segment with methods resembling the ones used by both Braune and Fisher and by Dempster. Anthropometric measurements like the length, circumference and breadth or depth of each body segment were also measured and a series of regression equations estimating the body segment parameters based on anthropometric measurements were defined. It was concluded that the anthropometry of the body and regression equations effectively can be used to estimate the mass and center of mass of body segments, under the assumption that all individuals essentially have the same body proportions. This can, however, not be assumed in general and will thus lead to major errors in estimates for those individuals, or groups, that differ significantly from the average of the group of subjects from which the regression equations are derived. The assumption, used in many earlier studies, that the center of mass and center of volume of body segments are nearly coincident was also investigated. It was concluded, that the two centers not are coincident, but that the center of volume of a segment generally are less that two to three centimeters proximal to the center of mass. See [Clauser et al., 1969] for further information. 1975 - Chandler et al. Chandler, and coworkers, performed a study to investigate, and supplement the existing knowledge about, the mass distribution characteristics of the human body as described by the principal mass moments of inertia. The mass, volume, center of mass and principal mass moments of inertia were estimated for the 14 segments from each of six frozen preserved adult male cadavers and, excluding the volume, for each of the entire cadavers. Anthropometric measurements were also obtained both for the entire cadavers and for each of the segments. The methods and procedures used in this study for obtaining a total of 116 anthropometric measurements of each cadaver, segmentation of the cadavers and estimation of mass, volume and center of mass to a large extend resemble the ones used in [Clauser et al., 1969]. In order to estimate the principal mass moments of inertia each segment was fixed in a segment holder of Styrofoam of minimal size in order to minimize the potential errors introduced by the holder. Each segment holder was then used to establish an external Cartesian coordinate system, fixed with respect to the otherwise geometrically irregular body segment. Each segment, in its segment holder, was then swung around six axes as a pendulum and the period of oscillation around each axis was measured at least twice, each for a period of 50 swing cycles of the \pendulum . Based on these measurements, corrected with similar measurements performed on the empty segment holder, and a precise measurement of the local gravitational constant, the mass moment of inertia of the segment around each of the six axes were calculated. Based on these calculations the three principal mass moments of inertia of each body segment were estimated. Some of the results of this study of cadavers were compared to those obtained, by Santschi and coworkers, on living subjects and it was concluded that a sat- is factory level of agreement exists. It was also concluded that the principal mass moments of inertia of body segments correlates well with total body mass and (especially) with segment volume. See [Chandler et al., 1975] for further information. 1975 - Hatze Hatze developed a method which, based on a single measurement on a living subject, allows a highly reproducible experimental estimation of the mass moment of inertia of a segment around the axis of rotation of the proximal joint, the center of mass of the segment and the angular damping coefficient of the joint for a given joint position. Estimates obtained with this method also appear to correspond well with estimates obtained by other, more laborious, methods. The distal end of the segment, or rigid \group of segments, e.g. an entire leg, is suspended horizontally by a spring fixed to the segment a known distance from the axis of rotation of the segment, see Figure 3. The distal end of the segment is raised until the spring force equals zero and is then released. When this happens, the distal end of the segment will perform a damped passive oscillation about its horizontal equilibrium and the estimates of the mass moment of inertia, center of mass and angular damping coefficient can then be obtained through an analysis of the oscillogram. See [Hatze, 1975] for further information. Figure 3: Sketch of the setup used in the technique measuring developed by Hatze. Adapted from [Hatze, 1975]. 1976 - Huang et al. Huang and Wu developed a technique for estimation of tissue density of living subjects based on CT (Computerized Tomography) scanning. The estimations, based on cross-sectional CT scans of the head and chest, showed good agreement with bone, muscle and fat densities obtained in previous studies. The work was later extended, by Huang and other coworkers, to estimations of body segment parameters. This was done by defining the boundaries of the different tissues in the CT images and subsequently estimating the body segment parameters based on tissue densities and volume data. See [Huang and Wu, 1976, e.g. cited in [Martin et al., 1989]], [Huang et al., 1979, e.g. cited in [Martin et al., 1989]] and [Huang and Suarez, 1983, e.g. cited in [Martin et al., 1989]] for further information. 1983 - Zatsiorsky and Seluyanov Zatsiorsky and Seluyanov made a study of the mass, center of mass and principal mass moments of inertia of the body segments of 100 living male subjects (primarily students). The study was performed by scanning the subjects with a gamma-radiation beam. When gamma-radiation passes through material, e.g., a human body, the intensity is attenuated. If the intensity of the radiation is measured both before and after it passes through the material, then it is possible to calculate the surface density of the material. The surface density is the amount of mass \be- low a surface area of unit size, i.e. the mass of the material in a \cylinder , with a cross-section area of one area unit, between the two positions where the radiation is measured. Based on the scannings, average values and second order regression equations for the mass, the center of mass and principal mass moments of inertia of the body segments were derived. See [Zatsiorsky and Seluyanov, 1983] for further information. 1990 - Mungiole and Martin Mungiole and Martin next made a study of the applicability of MRI as a basis for estimation of body segment parameters of living human subjects. To archive this, the lower right leg of 12 adult male distance runners were MRI scanned in transverse slices 2.5 cm apart along the longitudinal axis. The MRI images were subsequently manually segmented into areas corresponding to bone, muscle and fat and the areas were converted into volumes by a first order extrapolation between the adjacent MRI images in the image-stack. The volumes were then converted into masses using the densities of muscle, fat, cortical bone and cancerous bone reported in [Clauser et al., 1969], and the total mass, center of mass and mass moment of inertia of each leg around a transverse axis through the estimated center of mass was calculated. The MRI-based estimates were compared to estimates obtained with other methods and it was shown that the MRI-based estimates all fell within the range of values obtained with other methods. All the estimation methods resulted in approximately the same center of mass, but the mass and mass moments of inertia showed considerable variability among the estimation methods, generally with the MRI-based estimates among the highest values. This tendency towards high values was, however, assumed to be related to the age and structural differences between the living young runners of this study and the cadavers used in the other studies and was thus taken to provide further support for MRI as a valid foundation for estimation of body segment parameters. See [Mungiole and Martin, 1990] for further information. 1995 - Wei and Jensen Wei and Jensen constructed a set of regression equations for the average segment density profiles of 50 young adult Chinese females based on axial densities obtained from CT images of the body segments. The body segment parameters calculated using these density profiles were compared with the body segment parameters calculated assuming a constant density, a common assumption in previous studies. The comparison showed that the differences between two methods of calculation, on the average, only caused the mass of the total body to vary by less than 0.85%, the mass of segments by less than 2.7%, the center of mass by less 0.54% and the principal mass moments of inertia by less than 3.8%. The average deviations are thus rather small, but for individual segments from individual subjects the differences in results were found to range as high as 22.5% for the mass moment of inertia around the longitudinal axis of a foot of an infant. It was not definitely concluded whether constant density or density profiles yields the most accurate estimates of the body segment parameters, but the obtained density profiles clearly challenge the assumption of constant density throughout the segments. This led to the conclusion that, since the density variations affect the mass distribution in the segments, it should be recommended than segment density profiles should be incorporated into future mathematical models of the human body. See[Wei and Jensen, 1995] for further information. 4 The Tabular History of Human Body Segment Parameter Estimation Some of the key information about the studies described in the preceding section is summarized and repeated in the following three tables. Table 1 provides a tabular overview of the type and number of subjects involved in each study and of the body segments that the individual studies were concerned with. Table 2 and 3 provide a summary of the main method(s) used (and possibly developed) in each study and of the parameters estimated by these methods during the study. Study Subjects Segments 1680 - Borelli Living men Entire body 1836 - The Weber Brothers N/A Entire body 1860 - Harless 2 cadavers 18 segments from each cadaver 7 cadavers 44 extremity segments 1863 - von Meyer N/A The major segments 1889 - Braune and Fischer 3 adult male cadavers All body segments 1894 - Meeh Living and cadavers N/A 1931 - Bernstein et al. 152 living men and women All limbs 1938 - Weinbach 8 living subjects Entire body 1955 - Cleveland 11 male college students All body segments 1955 - Dempster 8 elderly male cadavers All body segments 1957 - Barter Literature study All body segments 1960 - Simmons and Gardner Literature study Body divided into 8 segments 1962 - Whitsett Literature study Body divided into 14 segments 1963 - Santschi et al. 66 living subjects Entire body 1963 - Gray Literature study All body segments 1964 - Hanavan Literature study 15 segments 1966 - Drillis and Contini 20 young living men All body segments 1968 - Bouisset and Pertuzon 11 living subjects Combined forearm and hand 1969 - Clauser et al. 13 preserved male cadavers 14 segments from each cadaver 1972 - Contini Living subjects All body segments 1972 - Wooley Literature study 9 segments 1975 - Chandler et al. 6 frozen preserved adult 14 segments from each cadaver male cadavers 1975 - Hatze Living subjects Extremity segments 1976 - Huang et al. Living subjects Any body segment 1978 - Jensen 3 living boys All body segments 1980 - Hatze 4 living subjects 17 segments 1983 - Zatsiorsky and 100 living male subjects All body segments Seluyanov 1989 - Martin et al. Baboon cadavers 8 extremity segments 1990 - Mungiole and Martin 12 adult male distance Lower right leg runners 1995 - Wei and Jensen 50 young adult Chinese All body segments females Table 1: Overview of previous studies of human body segment parameters. The number and type of subjects examined and the body segments involved. Study 1680 - Borelli 1836 - The Weber Brothers 1860 - Harless Main Method(s) Balance plate Balance plate Balance plate Hydrostatic weighing Mathematical model Estimated Parameters Center of mass of entire body Center of mass of entire body Center of mass of each segment Density of segments Mass and center of mass of both segments and entire body Mass, volume and center of mass of segments Volume and mass of segments Mass and center of mass Mass moment of inertia Volume, center of volume, mass and center of mass of segments Volume, mass, density, center of mass and mass moments of inertia Mass Mass moments of inertia of entire body Mass distribution, center of mass, mass moments of inertia and mobility of the human body Centers of mass and mass moments of inertia of entire body Center of mass and mass moments of inertia Center of mass and mass moments of inertia of entire body Volume, mass, center of mass and mass moments of inertia of the segments. Mass moment of inertia 1863 - von Meyer 1889 - Braune and Fischer 1894 - Meeh 1931 - Bernstein et al. 1938 - Weinbach 1955 - Cleveland Intersection of plumb lines Immersion Reaction change Photogrammetry Hydrostatic weighing 1955 - Dempster 1957 - Barter 1960 - Simmons and Gardner 1962 - Whitsett Balance plate, hydrostatic weighing and period of oscillation Regression equations Simple geometric model of the human body Mathematical model 1963 - Santschi et al. 1963 - Gray 1964 - Hanavan Mathematical model and anthropometric measurements Mathematical model Mathematical model 1966 - Drillis and Contini (Incremental) hydrostatic weighing and balance plate Quick release 1968 - Bouisset and Pertuzon 1969 - Clauser et al. 1972 - Contini Balance plate, hydrostatic weighing and immersion Mathematical models and a survey of methods 1972 - Wooley 1975 - Chandler et al. Mathematical model and regression equations Hydrostatic weighing and period of oscillation Oscillogram analysis CT scanning 1975 - Hatze 1976 - Huang et al. Volume, mass and center of mass Volume, mass, density, center of volume (mass), mass moments of inertia and radius of gyration. Center of mass and mass moments of inertia Volume, mass, center of mass and principal mass moments of inertia Center of mass and mass moment of inertia Density, volume and other parameters Table 2: Overview of previous studies of human body segment parameters. The main method(s) used and the estimated body segment parameters. Continued in table 3. Study Main 1978 - Jensen Estimated Parameters Volume, mass, center of mass and principal mass moments of inertia 1980 - Hatze Mathematical model and Volume, mass, center of anthropometric mass and principal mass measurements moments of inertia 1983 - Zatsiorsky and Gamma-scanning and Mass, center of mass, Seluyanov regression equations principal mass moments of inertia and radius of gyration 1989 - Martin et al. MRI scanning Volume, mass, density, center of mass and mass moment of inertia 1990 - Mungiole and Martin MRI scanning Volume, mass, center of mass and mass moment of inertia 1995 - Wei and Jensen CT scanning and regression Mass, density profiles, equations center of mass and mass moment of inertia Table 3: Overview of previous studies of human body segment parameters. The main method(s) used and the estimated body segment parameters. Continued from table 2. Method(s) Photogrammetry and mathematical model 5 Concluding Remarks The purpose of this report is, as stated earlier, to provide a \chronological overview of the methods used for estimation of body segment parameter from the 17th century to the present time. The purpose has not been to provide a complete, all-inclusive and \in-depth examination of prior work, but merely to provide a historical background for, and overview of, the field of and methods for human body segment parameter estimation. It is therefore natural at this point to provide (and restate) some references to other surveys of the field. The information about methods developed before 1970 is primarily obtained from surveys in [Drillis and Contini, 1966], [Clauser et al., 1969] and [Chandler et al., 1975]. These surveys can be read for further information, especially quantitative results, which are omitted from this survey. A more recent survey can be found in [Reid and Jensen, 1990]. This report has focused on the methods used in the field of body segment parameter estimation and only qualitative or summarized results have been presented. Some of the quantitative results are, however, presently being analyzed and a survey of these results will soon be available in [Bj rnstrup, 1995b]. References [Alonso and Finn, 1980] Marcelo Alonso and Edward J. Finn. Mechanics and Thermodynamics, volume I of Fundamental University Physics. Addison- Wesley Publishing Company, Inc., Reading, Massachusetts, second edition, 1980. [Barter, 1957] J. T. Barter. Estimation of the mass of body segments. Technical Report TR-57-260 (AD 118 222), Wright Air Development Center, Wright- Patterson Air Force Base, Ohio, 1957. This reference is (mainly) reproduced from [Clauser et al., 1969]. [Bernstein et al., 1931] N. A. Bernstein, O. A. Salzgeber, P. P. Pavlenko, and N. A. Gurvich. 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Investigation of inertial properties of the human body. Technical Report DOT HS-801 430, Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, OH, March 1975. [Clauser et al., 1969] Charles E. Clauser, John T. McConville, and J. W. Young. Weight, volume, and center of mass of segments of the human body. Technical Report AMRL-TR-69-70 (AD-710 622), Aerospace Medical Research Laboratory, Aerospace Medical Division, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, August 1969. [Cleveland, 1995] H. G. Cleveland. The Determination of the Center of Gravity of Segments of the Human Body. Dissertation, University of California, Los Angeles, 1995. This reference is (mainly) reproduced from [Clauser et al., 1969]. [Contini et al., 1963] Renato Contini, Rudolfs Drillis, and Morris Bluestein. Determination of body segment parameters. Hum. Factors, 5(5):493{504, 1963. This reference is (mainly) reproduced from [Clauser et al., 1969]. [Contini, 1970] Renato Contini. Body segment parameters (pathological). Technical Report 1584.03, New York University, School of Engineering and Science, June 1970. This reference is (mainly) reproduced from [Contini, 1972]. [Contini, 1972] Renato Contini. Body segment parameters, part II. Artificial Limbs, 16(1):1{19, Spring 1972. [Dempster, 1955] Wilfrid Taylor Dempster. Space requirements of the seated operator. Technical Report USAF, WADC TR-55-159 (AD 87 892), Wright Air Development Center, Wright-Patterson Air Force Base, Ohio, 1955. This reference is (mainly) reproduced from [Clauser et al., 1969]. [Dempster, 1956] Wilfrid Taylor Dempster. The anthropometry of body action. Annals New York Academy of Sciences, 63:559{585, 1956. [Drillis and Contini, 1966] Rudolfs Drillis and Renato Contini. Body segment parameters. 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[Hatze, 1979] Herbert Hatze. A model for the computational determination of parameter values of anthropometric segments. Technical Report TWISK 79, National Research Institute for Mathematical Sciences, CSIR, Pretoria, South Africa, 1979. This CSIR Tech. Report, which contains all technical details of the model presented in [Hatze, 1980], is obtainable from the author free of charge. This reference is (mainly) reproduced from [Hatze, 1980]. [Hatze, 1980] Herbert Hatze. A mathematical model for the computational determination of parameter values of anthropometric segments. J. Biomechanics, 13:833{843, 1980. [Huang and Suarez, 1983] H. K. Huang and F. R. Suarez. Evaluation of cross- sectional geometry and mass distribution of humans and laboratory animals using computerized tomography. J. Biomechanics, 16:821{832, 1983. This reference is (mainly) reproduced from [Martin et al., 1989]. [Huang and Wu, 1976] H. K. Huang and S. C. Wu. 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