Historia Modelado

Estimation of

Human Body Segment Parameters

|

Historical Background

by

Jrgen Bjrnstrup

LIA 95 { 20 October 1995

ISSN 0906 { 6233

Internal Tech-Report | Not submitted anywhere.

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 eld 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".

This report is also available through WWW at the URL in the

[

Bjrnstrup, 1995a

]

entry in the list of references.

Contents II

Contents

1 Introduction | Motivation 1

2 Denition of Terms Used in This Report 1

3 The History of Human Body Segment Parameter Estimation 3

1680 | Borelli : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3

1836 | The Weber Brothers : : : : : : : : : : : : : : : : : : : : : : : 4

1860 | Harless : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4

1863 | von Meyer : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4

1889 | Braune and Fischer : : : : : : : : : : : : : : : : : : : : : : : : 5

1894 | Meeh : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5

1931 | Bernstein et al. : : : : : : : : : : : : : : : : : : : : : : : : : : 5

1938 | Weinbach : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7

1955 | Cleveland : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7

1955 | Dempster : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7

1957 | Barter : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7

1960 | Simmons and Gardner : : : : : : : : : : : : : : : : : : : : : : 8

1962 | Whitsett : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8

1963 | Santschi et al. : : : : : : : : : : : : : : : : : : : : : : : : : : : 8

1963 | Gray : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9

1964 | Hanavan : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9

1966 | Drillis and Contini : : : : : : : : : : : : : : : : : : : : : : : : 9

1968 | Bouisset and Pertuzon : : : : : : : : : : : : : : : : : : : : : : 10

1969 | Clauser et al. : : : : : : : : : : : : : : : : : : : : : : : : : : : 10

1972 | Contini : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11

1972 | Wooley : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11

1975 | Chandler et al. : : : : : : : : : : : : : : : : : : : : : : : : : : 11

1975 | Hatze : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12

Contents III

1976 | Huang et al. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13

1978 | Jensen : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13

1980 | Hatze : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14

1983 | Zatsiorsky and Seluyanov : : : : : : : : : : : : : : : : : : : : 14

1989 | Martin et al. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14

1990 | Mungiole and Martin : : : : : : : : : : : : : : : : : : : : : : : 15

1995 | Wei and Jensen : : : : : : : : : : : : : : : : : : : : : : : : : : 15

4 The Tabular History of

Human Body Segment Parameter Estimation 16

5 Concluding Remarks 19

References 20

1 Introduction | Motivation 1

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

dene and portray the \anatomically perfect man".

Nowadays the interest in body segment parameters is, apart from purely aca-

demic 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 inuence 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 eect of space-journeys 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 Denition of Terms Used in This Report

This section describes the terms, related to body segment parameters, used in

this report. Most of the denitions 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

).

2 Denition of Terms Used in This Report 2

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

).

Specic gravity: The specic gravity of an object is the density of the object

compared to the density of \standard" water. Specic 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 simplied physical model assumes

that the total mass of each object is located in an innitely 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 innitely 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 (kgm

2

). Notice that from the denition it follows that a given

object have an innite 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 specic

circle. The circle corresponds to the locations where the total mass of the

object, compressed into an innitely 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 \chronolog-

ical" 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 in-

dividual subjects, or from entire populations, are generally of little

use in motion analysis of, or prosthesis design for, individual sub-

jects. 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 pre-

sented and analyzed in another tech-report (

[

Bjrnstrup, 1995b

]

), which pres-

ently is being prepared.

The material presented below is to some extend obtained from

[

Drillis and Con-

tini, 1966

]

,

[

Clauser et al., 1969

]

and

[


]

, 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

[


]]

, 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 \scientic" or experimental work in the eld 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

1

The purpose of my Ph.D.-thesis (\Image Processing Based Estimation of Body Segment

Parameters| with Application to Motion Analysis") is to apply image processing techniques

to the eld of body segment parameter estimation in order to facilitate and improved esti-

mation of body segment parameters, especially for the extremities, for individual humans.

It is hoped, that this in turn will prove useful in the eld of motion analysis by allowing

parameters obtained from other individuals, or populations, to be replaced by parameters

conforming more precisely to the individual subjects of motion analysis studies, calculations

or simulations.


corresponding to the center of mass for the entire body. See

[

Borelli, 1680{1681,

e.g. cited in

[


]]

for further information.

1836 | The Weber Brothers

The Weber brothers improved the method used by Borelli for estimation of

center of mass, by moving the subjects on a platform supported at the center of

mass of the platform itself. This method made the estimations independent of

the supporting platform and in addition each estimation was performed twice,

the second time with the subject reversed on the platform, and the two estimates

were then averaged to get the nal estimate of the center of mass, thereby

making the estimate more resistant to measurement \noise". See

[

Weber and

Weber, 1836, e.g. cited in

[


]]


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 uid 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, seg-

mented 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,

2

the volume and density of each

segment was estimated. The results of these studies led Harless to conclude that

age and sex have signicant inuence on the density of segments of the human

body. See

[

Harless, 1860a, e.g. cited in

[


]]

and

[

Harless,

1860b, e.g. cited in

[


]]


1863 | von Meyer

Von Meyer estimated the mass and center of mass of the body segments in three

dimensions, instead of just along the longitudinal axis. Based on a \reduced

model" of the body, consisting of a set of ellipsoids and spheres, the center of

2

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.


mass of the entire body could be estimated, given the position and orientation of

each of the body segments. See

[

Meyer, 1863, e.g. cited in

[


]]

and

[

Meyer, 1873, e.g. cited in

[


]]


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 uid 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 xed 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 dierences in and between pop-

ulations. 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 Con-

tini, 1966

]]

,

[

Braune and Fischer, 1892, e.g. cited in

[


]]

and

[

Fischer, 1906, e.g. cited in

[


]]


1894 | Meeh

Meeh pointed out, that the results obtained from cadavers should be supple-

mented with data from living subjects. To estimate the volume of body seg-

ments, each segment was immersed in water up to the joint and the amount of

water displaced hereby 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 rst serious attempt to describe the changes in mass of body

segments during growth. See

[

Meeh, 1894, e.g. cited in

[


]]


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 modied

balance plate. The balance plate technique used by Borelli had been modied

and improved several times over the years and a simplied sketch of the version

used by Bernstein is shown in gure 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

[


]

.

The system in gure 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)

d

w

, where W is the mass of the body segment, D is the distance

between the two supporting knife edges, d

w

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 gure 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

[


]]

,

[

Konrad et al.,

1934, e.g. cited in

[


]]

,

[

Bernstein, 1936, e.g. cited in

[


]]

,

[

Bernstein, 1967, e.g. cited in

[


]]

and

[


]



1938 | Weinbach

Weinbach was the rst to estimate a mass moment of inertia of the human body

by photogrammetry. He did this by mathematically constructing curves based

on body surface-area measurements on photographs of eight living subjects and

by assuming a homogeneous body density at unity. See

[

Weinbach, 1938, e.g.

cited in

[


]]


1955 | Cleveland

Cleveland estimated the mass and center of mass of body segments of 11 male

college students by hydrostatic weighing. The subject was placed on a ham-

mock attached to a spring scale above a tank lled with water. The volume of a

segment (or actually the mass of the water displaced by the segment) was then

estimated by rst weighing the subject in air and then with the segment im-

mersed in water, this part of the method resembles the method used by Harless

a century earlier. The dierence in weight corresponds to the volume of the seg-

ment and the average of the two measurements corresponds to the \weight" of

the subject when half of the volume of the segment is immersed in water. This

was utilized by retracting the segment from the water until the weight equaled

the calculated average weight. The surface of the water then corresponded to

the mid-volume plane (the center of volume). The mass and center of mass of

the segment was estimated by assuming a uniform body density. See

[

Cleveland,

1995, e.g. cited in

[


]]


1955 | Dempster

Dempster examined the cadavers of eight elderly men at the University of Michi-

gan, 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

exed 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 dierent 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

[


]]

,

[

Dempster, 1956

]

and

[


]

for further

information.

1957 | Barter

Barter compiled the body segment parameters published in

[

Braune and Fis-

cher, 1889, e.g. cited in

[


]]

,

[

Fischer, 1906, e.g. cited in


[


]]

and

[

Dempster, 1955, e.g. cited in

[


]]

and produced a series of rst order regression equations, with corresponding

standard error gures, for estimating the mass of body segments based on the

mass of the entire body. These equations have, despite the limitations and inac-

curacies, been used extensively, according to

[


]

, by designers

and engineers, because they provide a rapid estimation of the mass of individual

body segments. See

[

Barter, 1957, e.g. cited in

[


]]

for further

information.

1960 | Simmons and Gardner

Simmons and Gardner developed a model of the human body by approximating

the body segments by eight simple geometric shapes (cylinders and spheres).

The regression equations produced by Barter were then used to estimate pa-

rameters for the geometric forms and subsequently to estimate mass moments

of inertia for the entire body. This elementary work on models was, according

to

[


]

, the genesis of much subsequent modeling activity. See

[

Simmons and Gardner, 1960, e.g. cited in

[


]]

for further

information.

1962 | Whitsett

Whitsett rened 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

[


]]

and the regression equations

from

[

Barter, 1957, e.g. cited in

[


]]

. See

[

Whitsett, 1962, e.g.

cited in

[


]]


1963 | Santschi et al.

Santschi, and coworkers, measured 50 body dimensions on each of 66 subjects

and studied the total body mass moments of inertia (around three orthogonal

axes coincident with the intersections of the three anatomically planes of the

body) and centers of mass of each subjects in eight body positions, e.g., stand-

ing and sitting. It was concluded that the mass moments of inertia of the body

in the various positions correlated well with the height and mass of the subject

and thus that the center of mass and mass moments of inertia of an individ-

ual subject eectively can be estimated from easily obtainable anthropometric

dimensions. See

[

Santschi et al., 1963, e.g. cited in

[


]]

for

further information.


1963 | Gray

Gray was encouraged by the high degree of correlation between the height and

mass of a person and the mass moments of inertia, reported by Santschi and

coworkers, to derive and examine three models (modied versions of the model

developed by Whitsett) of diering body size from Santschi's anthropometric

data. Gray used Barter's regression equations for assigning mass to the body

segments of the model and data for the centers of mass were obtained from

Dempster. By comparing the calculated values for mass moments of inertia and

centers of mass with those experimentally estimated for a group of subjects,

Gray found a disappointingly large deviation and concluded that the model

must be rened to represent the mass distribution of man more precisely. See

[

Gray, 1963, e.g. cited in

[


]]


1964 | Hanavan

Hanavan used a model resembling the ones used by Whitsett and Gray, con-

sisting 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

(dened by Santschi and coworkers) were predicted within 10% of the experi-

mental 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

[


]]


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 gure 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


[


]]

,

[

Contini et al., 1963, e.g. cited in

[


]]

and

[


]


1968 | Bouisset and Pertuzon

Bouisset and Pertuzon used a quick release method (see gure 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

]]


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 iner-

tia of the segment around the

proximal joint can be calcu-

lated as I =

F y

1

y

2

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 anthropomet-

ric 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 dened. It was con-

cluded that the anthropometry of the body and regression equations eectively


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 dier signicantly 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 cen-

ter 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

[


]


1972 | Contini

Contini made, partly based on the studies described in

[

Drillis and Contini,

1966

]

and

[

Contini, 1970, e.g. cited in

[

Contini, 1972

]]

, a survey of methods

for estimation of body segment parameters for living subjects. Furthermore, a

number of tables and graphs with results from the two studies, were presented.

The tables and graphs can be used to provide \average" estimates of a number

of body segment parameters and anthropometric measurements (like the length

of segments), based on a selection of measurements. The number and type of

measurements \supported" by the tables and graphs can vary from only the total

mass and height of the subject to the length and circumferences of individual

segments. See

[

Contini, 1972

]


1972 | Wooley

Wooley simplied the model used by Hanavan, by merging each of the outer-

most segments with the adjoining segment, i.e., by combining the head with the

trunk, the hands with the forearms and the feet with the calves, based on the

assumption that the mass of these outermost segments are relatively small and

that they do not move much relative to the segment which they are attached

to. Wooley compared the calculated results from the simplied model with the

anthropometric measurements produced by Santschi and coworkers and with

the calculated results obtained with Hanavan's original model and found that

the two models were similar in terms of error. Wooley also developed a series

of regression equations for predicting the mass moments of inertia of body seg-

ments, based solely on the mass of the entire body. See

[

Wooley, 1972, e.g. cited

in

[


]]


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

[


]

. In order to estimate the principal mass

moments of inertia each segment was xed 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, xed 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-

isfactory 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

[


]

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 mo-

ment 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 coecient 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 xed to the segment a known distance from

the axis of rotation of the segment, see gure 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 coecient can then be obtained through

an analysis of the oscillogram. See

[

Hatze, 1975

]



Figure 3: Sketch of the setup used in the measuring technique 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 dening the boundaries of

the dierent 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

]]


1978 | Jensen

Jensen made a mathematical model for estimation of body segment parameters

based on the assumption that the body (each segment) can be modeled as a set

of elliptical slices.

The model was used on three boys of dierent body types; ectomorph (\thin"),

endomorph (\fat") and mesomorph (\average"), where the principal axes of

the ellipses were obtained using front and side view images of the subjects,

on which the required points were manually digitized. It was found that the

model estimated the total mass of the body within 2% of the value obtained by

weighing and that this model allows a more accurate description of individual

body shapes and hence a more precise and generally applicable estimation of

body segment parameters. See

[

Jensen, 1978

]



1980 | Hatze

Hatze developed an advanced mathematical model consisting of 17 segments

for estimation of body segment parameters for individual subjects based on 242

[sic] anthropometric measurements taken directly from the subject.

This model has, compared to previous models, the advantages of a more de-

tailed modeling of shape and density uctuations, generally no segmental sym-

metry assumptions, dierentiation between male and female subjects (including

children), adjustment of certain densities based on a special subcutaneous-fat

indicator and fully accounting for the specicities of pregnancy and obesity, and

the 242 required anthropometric measurements are claimed to be obtainable in

less than 80 minutes.

The model was tested on four subjects (two young male athletes, one female

tennis player and one 12 years old boy) and the overall accuracy was found

to be better than 3%, with a maximum error of about 5%, when compared to

experimentally estimated values. See

[

Hatze, 1979, e.g. cited in

[

Hatze, 1980

]]

and

[

Hatze, 1980

]


1983 | Zatsiorsky and Seluyanov

Zatsiorsky and Seluyanov made a study of the mass, center of mass and princi-

pal 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 in-

tensity 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.

1989 | Martin et al.

Martin, and coworkers, performed a study to determine whether valid esti-

mations of body segment parameters can be generated from a series of cross-

sectional MRI (Magnetic Resonance Imaging) scans of the tissue.

The study was based on eight baboon cadaver segments (four forearms, two

upper arms and two lower legs), which were MRI scanned and the boundaries


between dierent tissue in each image were manually digitized to divide the

total areas into areas corresponding to muscle, bone and fat. The volume of

each of the tissues and subsequently the mass distribution and body segment

parameters were then calculated based on these areas, the distance between the

scanned images and the densities, obtained experimentally, of the tissues.

These results were compared to results obtained by standard experimental tech-

niques and it was concluded that MRI represents a promising technique for

estimation of body segment parameters, despite the tendency to overestimate

volume (by an average of 6.3%), mass (by an average of 6.7%) and mass mo-

ments of inertia (by an average of 4.4%). See

[

Martin et al., 1989

]

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 rst

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 cancellous bone reported in

[


]

, 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 in-

ertia 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 dif-

ferences 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

]


1995 | Wei and Jensen

Wei and Jensen constructed a set of regression equations for the average seg-

ment density proles 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 proles were compared with the body segment

parameters calculated assuming a constant density, a common assumption in

previous studies.

4 The Tabular History of Human Body Segment Parameter Estimation 16

The comparison showed that the dierences 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 dierences 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 denitely concluded whether constant density or density proles

yields the most accurate estimates of the body segment parameters, but the

obtained density proles clearly challenge the assumption of constant density

throughout the segments. This led to the conclusion that, since the density vari-

ations aect the mass distribution in the segments, it should be recommended

than segment density proles should be incorporated into future mathematical

models of the human body. See

[

Wei and Jensen, 1995

]


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 male cadavers

14 segments from each cadaver

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

Seluyanov

100 living male

subjects

All body segments

1989 | Martin et al. Baboon cadavers 8 extremity segments

1990 | Mungiole and Martin 12 adult male

distance runners

Lower right leg

1995 | Wei and Jensen 50 young adult Chi-

nese females

All body segments

Table 1: Overview of previous studies of human body segment parameters.

The number and type of subjects examined and the body segments

involved.


Study Main Method(s) Estimated Parameters

1680 | Borelli Balance plate Center of mass of entire body

1836 | The Weber Brothers Balance plate Center of mass of entire body

1860 | Harless Balance plate Center of mass of each segment

Hydrostatic weighing Density of segments

1863 | von Meyer Mathematical model Mass and center of mass of

both segments and entire body

1889 | Braune and Fischer Intersection of plumb

lines

Mass, volume and center of

mass of segments

1894 | Meeh Immersion Volume and mass of segments

1931 | Bernstein et al. Reaction change Mass and center of mass

1938 | Weinbach Photogrammetry Mass moment of inertia

1955 | Cleveland Hydrostatic weighing Volume, center of volume,

mass and center of mass of

segments

1955 | Dempster Balance plate, hydro-

static weighing and

period of oscillation

Volume, mass, density, center

of mass and mass moments of

inertia

1957 | Barter Regression equations Mass

1960 | Simmons and Gardner Simple geometric

model of the human

body

Mass moments of inertia of en-

tire body

1962 | Whitsett Mathematical model Mass distribution, center of

mass, mass moments of iner-

tia and mobility of the human

body

1963 | Santschi et al. Mathematical model

and anthropometric

measurements

Centers of mass and mass mo-

ments of inertia of entire body

1963 | Gray Mathematical model Center of mass and mass mo-

ments of inertia

1964 | Hanavan Mathematical model Center of mass and mass mo-

ments of inertia of entire body

1966 | Drillis and Contini (Incremental) hydro-

static weighing and

balance plate

Volume, mass, center of mass

and mass moments of inertia

of the segments.

1968 | Bouisset and Pertuzon Quick release Mass moment of inertia

1969 | Clauser et al. Balance plate, hydro-

static weighing and

immersion

Volume, mass and center of

mass

1972 | Contini Mathematical models

and a survey of

methods

Volume, mass, density, center

of volume (mass), mass mo-

ments of inertia and radius of

gyration.

1972 | Wooley Mathematical model

and regression

equations

Center of mass and mass mo-

ments of inertia

1975 | Chandler et al. Hydrostatic weighing

and period of

oscillation


and principalmass moments of

inertia

1975 | Hatze Oscillogram analysis Center of mass and mass mo-

ment of inertia

1976 | Huang et al. CT scanning Density, volume and other

parameters


The mainmethod(s) used and the estimated body segment parameters.

Continued in table 3.

5 Concluding Remarks 19

Study Main Method(s) Estimated Parameters

1978 | Jensen Photogrammetry and

mathematical model



inertia

1980 | Hatze Mathematical model

and anthropometric

measurements



inertia

1983 | Zatsiorsky and

Seluyanov

Gamma-scanningand

regression equations

Mass, center of mass, 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 equations

Mass, density proles, center

of mass and mass moment of

inertia


The mainmethod(s) used and the estimated body segment parameters.

Continued from table 2.

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 eld 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 eld.

The information about methods developed before 1970 is primarily obtained

from surveys in

[


]

,

[


]

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 eld of body segment param-

eter 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

[

Bjrnstrup, 1995b

]

.

References 20

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,

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[

Barter, 1957

]

J. T. Barter. Estimation of the mass of body segments. Technical

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This reference is (mainly) reproduced from

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]

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[

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]

N. A. Bernstein, O. A. Salzgeber, P. P. Pavlenko, and

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[


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N. A. Bernstein. Die kymocyclographischeMethode der Bewe-

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[


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[

Bernstein, 1967

]

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ments. Pergamon Press, London, 1967.


[


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[

Bjrnstrup, 1995a

]

Jrgen Bjrnstrup. Estimation of human body segment

parameters | historical background. Technical report, Laboratory of Im-

age Analysis, Institute of Electronic Systems, Aalborg University, E-mail:

[email protected], October 1995.

This tech-report is also available through WWW at the URL:

http://www.vision.auc.dk/

jorgen/PhD/EHBSP background/.

[

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]

Jrgen Bjrnstrup. Estimation of human body segment pa-

rameters | statistical analysis of results from prior investigations. Technical

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borg University, E-mail: [email protected], 1995. Under preparation

| Still unpublished.

This tech-report will also be available through WWW at the URL:

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jorgen/PhD/EHBSP analysis/.

[

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[


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References 21

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[


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[


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Reynolds, and J. W. Young. Investigation of inertial properties of the hu-

man body. Technical Report DOT HS-801 430, Aerospace Medical Research

Laboratory, Wright-Patterson Air Force Base, OH, March 1975.

[


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Charles E. Clauser, John T. McConville, and J. W. Young.

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Report AMRL-TR-69-70 (AD-710 622), Aerospace Medical Research Labo-

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[

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