人 類 誌,J.Anthrop. Soc. 90(Suppl.)：105-118(1982)
Mechanical Lower
Properties
of Cross Section
Limb Long Bones in Jomon Tasuku
KIMURA1)
Nippon
of
Man*
and
Hideo
TAKAHASHI2)
1) Department of Legal Medicine, Teikyo University School of Medicine, Itabashi, Tokyo 173, Japan 2) Department of Anthropology, Faculty of Science, The University of Tokyo, Bunkyo, Tokyo 113, Japan Abstract that
The
is,
the
geometric
and
moment the
of
of
bones
tion
of the
ment
was
The
and
strongly
the
measured
such
inside
against
bones
the
bone.
were
The
were
section
cross
moment
importance
in
of the
discussed
from
of the
the
inside
KIMURA,by measuring mechanical
proved
in the forming
bone
function
of the bone was
to be one of the important and remodeling
Conversely,
the
observed
The
function
partly
ancient
function.
Their
be
from
form
were not many
rements
of the
the viewpoint ies.
probably
fessor
the
mechanical properties
long bone
Hisashi
the SUZUKI
70th
can bone. measu-
bones
from
propertof the cross
were
first by one of the present
commemorate
by their
function of
human
of their
of the fossil
the form
quantitative
ancient
The mechanical
section
* To
the
of a
can not be
tested
mechanical
There
from
bones
or experimentally
learned
factors
of the bone.
mechanical
can be estimated
of the bone.
antero-
substance.
in regard
and
of
of the
the
bone
the
those
to the distribumeasure-
out.
INTRODUCTION
The
their and
The
outside
bones,
area with
the volume the
limb
to obtain
compared
bending
bone from
lower
cross-sectional
already.
greatly
of the
the
as the
reported
measurements
substance pointed
Jomon
were
changing
robusticity the
of the
fibula,
Jomon
were
without
between
mid-length the
properties,
area.
resisted
flatness
and
which
direction
difference
at the
tibia
mechanical
Japanese
posterior The
sections the
inertia
recent
Jomon
cross femur,
birthday
studied authors, of Pro-
the geometric
erties
of the broken
tibiae
(ENDO and KIMURA,1970).
The
of the fossil
long bones of the Jomon man have
many
peculiarities
of the
recent
contour limb
sections
prop-
compared
Japanese.
of the cross
bones
has
section
the for in-
femur, the platycne-
mia and the megaperonia, in connection
ence of the Jomon
those
of the lower
been of interest,
stance, the pilastered explained
with
Especially
man,
and they were with the subsistthe
hunter-food
gatherer. The discussion, however, was based only on the observations and measurements from the outside or, at best, from the thickness of the bone substance. The quantitative distribution The present
measurements of the bone have not been done yet fully. study
deals
with
the
cross
106
T.KIMURA
section
of
lower of the sults
the
limb
mid-length
long bones
strength were
recent
with
of the
the
Jomon
H.TAKAHASHI
(1970).
They
twenty-two
the viewpoint
of materials
compared
bones
of
from
and
and
the
re-
dying
that
of
the
All recent
around
dissecting MATERIALS
The skeletons stored
of the
in the
The University of Tokyo. vated
Museum,
the
the
nearly
the coordinates
males of
left bones.
of earth
and
of the bone which
in the medullary
of the
The
old
from the
anatomical
details
de-
of the
bones
in the appendix.
MECHANICAL OF
and
fifteen lower
to determine
later, and to avoid
district.
they were obtained
are reported
The bones
upper
in order
Kanto
were of relatively
rooms
of
partments. All bones, so far as it is known, appear
They
consisting
ends were selected explained
district.
complete
bones
females
1969 in the
to be normal.
University
left twenty
were exca-
of eighteen
females,
right and seventeen with
The
femora
Kanto
bones
fourteen
were
of Anthropology,
Thirty-two
from
were
Jomon man
Section
the
and
samples
age because
Japanese.
were
males
will be
the presence
the mechanical
properties of the cross section of the lower limb bones, we measured the geometric properties area (A),
as follows: the cross-sectional the moment of inertia of the
cross-sectional
area with respect
later, the polar
Jomon period. Seventeen pairs of male tibia and fibula were reported partly by
moment
inertia
one of the authors, KIMURA (1970).
cross-sectional
consisted
left bones.
Island.
of
Late
or
Nearly
complete
lected.
Relatively
in the collection The recent dying
around
were reported
twenty-two Pairs reported
of
and
seven in the
Almost
all bones
Latest
Jomon
pairs of bones
were period.
were se-
flat tibiae were selected of the Museum.
femora
of
the
1979 in the
individuals
Kanto
district
by one of the authors,
KAHASHI (1982), one males
right
They were excavated
Honshu the
of ten
Those
They were from twenty-
and ten females, right recent
TA-
consisting
and
nine
left
lower
leg
bones
by one of the
authors,
of
bones. were
axis (Ix) and
area and
of
the
to the x-
(Iy,) of the xy-
bones
Almost
about
y-axis
to the
or Late
to learn
to be described
belong
Middle
In order
SECTION
coordinates
all bones
cavity.
PROPERTIES
CROSS
(Ip), the the
of
area
y-axis
diameters
of the
radii
cross-sectional gyration
for the
(ky), and
of the
x-axis the
contour
from
properties
the
of
viewpoint (ENDO and
The
shows
area
the normal The
the
moment.
When
is applied bending
KIMURA furthest
on
the
removed
strength
of
force.
shows
resis-
against beam,
against
or tensile)
the bending
stress *max
material
resistivity
of inertia
tivity of the material
the
TAKAHASHI, 1982).
(compressive
moment
x-axis
mean the
of the
materials
(kx)
projected
to the
(dx) and the y-axis (dy). The geometric measurements mechanical
of the
the
appears
the
the bending moment
M
maximum in the
from the neutral
part axis x
Mechanical
of the cross section. tance
Properties
Denoting
to the furthest
of Bone Cross Section
the
dis-
part by h, we obtain
max=Mh/Ix=M/Z where Z=Ix/h ulus.
is called
with
respect
to the
and the section in
the
If a cross section
the
form
moduli
then
of the circular,
elliptic
a is the constant.
the tubular also
proved
if the
again
brief-
ly.
section
of inertia
against
the torque
shows
from
the
is
outer
of
centroid
in all
section
of the
the cases. The y-axis
of the
was
antero-
diameter (dy) (Fig. la). diameter of the section
measured
diameter
cross
to the maximum
after
projecting
coordinates.
The
cord
approximately
resistivity
axes
of the
section.
xy-coordinates
was the
The polar
in the circular
index of cross section
calculated
section
posterior transverse
of the the
the cross
of the
by
In the case of
contour
The center
tibia was parallel
(2)
are similar.
moment
contour.
the methods will be explained
section, the above equation
and inner figures
The
mod-
or rectan-
gular section can be calculated Zx=2Ix/dy= adxdy2 where
(1971) on the lower leg bones and by TAHere
h=dy/2
The
by KIMURA femora.
can be expressed
Zx=2Ix/dy.
described
KAHASHI(1982) on the recent
section
x-axis,
were
107
(1) * is symmetrical
moduli
ric properties
in Jo mon Man
xy-coordinates
The (dx)
HASEBE (1939), to the
x-axis
of the
are
in ac-
coordinates
section of the
with
the
principal
(KIMURA,1971). fibula
the
were
The deter-
of the bone is
diameters
of
the
In this paper we call this index
the index of cross section 1 or the outside index of cross section. section
2 or the mechanical
section
in this
the radii
paper
of gyration
HASHI (1982). the ratio bending
The
of the moment
or rectangular
from
as shown by TAKAsecond
index
shows
against
In the circular, the
case
of
elliptic
second
ratio
to the first ratio:
kx/ky=*Ix/Iy=Zx/Zy=dy/dx In the
the
in the two directions section,
equal
index of cross
is calculated
resistivity
the cross section. becomes
The index of cross
of the
above formula
(3)
tubular
section,
is also proved
tours of the outer
and inner
the
if the configures
are
similar. MEASURING
The
measuring
METHODS
methods
of the
geomet-
Fig.1. The xy-coordinates of the lower bones. a) lower leg bones; b) femur.
limb
108
T.KIMURA
mined
to be the
principal
axes.
respect
to which
the minimum
of inertia
was
axis, with moment denoted
to be the y-axis.
on the average
of the
Accordingly,
in this study
by
spectively
was
The y-axis
was
diameters
the fibula mately
MARTIN (1928) were
the
was
frontal
determined
average of the
approxi-
femur
ends of the greater
was
and lateral
parallel
section
the
to the shaft
The lower
of the
at the mid-length
fibula.
ties
were
plate
with
by
the
Only the compact
tograph
on
the
substance
M 100 ACE)
the
bone was about
sensor
the
the
x-ray
were equal
density
x-rayed
60 kVp,
of 2 m.
under
photograph
num thickness
The contour separately
was regarded
and
the
and
of the bone
The program method
was
devised
micro-computer
with the trapezoidal
as
(Sord method.
errors
of inertia
the measuring cutting
not always
the
was calculat(Sord M 100 based on the by one of the
the
were
reported
measuring
of area
of the
and 3.6 % in
of the cross-sectional method
compared
method
area
with
(ENDO and
the
KIMU-
method could
show the true cross-sectional
area of the bone. method
density,
TAKAHASHI.
RA,1982). The direct cutting
us-
between
Then from this relationship
It was measured One)
the cast was
direct
Pad
(Rhesca
from
were cut and a pho(Bit
alumi-
of the bone
The relationship
The mean square moment
bone density
density
trapezoidal authors,
of with
steps was
by a densitometer
geometric bone distribution ed by a micro-computer ACE).
The
and at a distance
The
to be 10.5 % in the
method.
material
by the unit of the
the bone thickness
proper-
of the
with the bone as
standard.
measured
at the section.
of
supposing
of aluminum
simultaneously
a density
film,
the condition
screens
A block
the was
from 30 to 40 Ams,
FS intensifying x-rayed
x-ray
material
in all parts of the bone.
by the x-ray
femora
well as an on-line
that
on
and
and a pho
rectangular
was taken.
ing a position
measured
measured
as the bone material. The recent
bone
of
was
a 1mm
The geometric
calculated
manually
By this method,
distribution
plane
length
using
method by ENDO
and KIMURA (1982).
°of the
above
compact
The Jomon femora were measured
the distribution
was a little
position
the
as the bone material.
the x-ray non-destructive
250 HS).
Then,
of the Only
bone was calculated
PPA
at
interval
was 0.1mm.
of the biarticular
mesh was placed on the section was taken.
The
minimum
sensor
decided.
of the maximum
A glass
The
were cut horizon-
(MARTIN,1928).
the site of this section the mid-length
femur
H.TAKAHASHI
was
axis (Fig. lb).
leg bones
length of the tibia
condyles.
mid-length
length
angle
tograph
was
trochanter
to the frontal
at
maximum
the
of
to the y-axis of the tibia.
right tally
to be measured The y-axis
the
plane
and the medial in the
in
to be the plane passing through
the posterior x-axis
used re-
diameters
outside. on
parallel
The
diameter. of the cross
as dy and dx
from
to
the maximum
this study were determined easily
parallel
maximum
and the minimum
The
calculated,
approximately
the direction
section
and
spongy
By the direct bone
was
cutting separated
Mechanical
arbitrarily there
Properties
of Bone Cross Section
from the compact bone, though
is no
bone at
large
the
amount
mid-length
of the of the
spongy femur
have a large
influence on the result.
hollow
of the bone
parts
were included The
x-ray
The
identical recent
between The
the
spongy
of the compact
The
bone is not equal
two techniques
the fact that
many
developed
a more
between
the
adding the sum
results
had
are
the differences
and Jomon femora
variance.
included
The results
techniques
of errors
the hollow parts.
109
when we consider
of the measuring
such as canals
method
Man
in the male bones.
in the area by this method.
bone and excluded density
to
clear
in Jomon
into the
corresponded
Jomon
male
linea
to
femora
aspera,
or
in all parts of the bone, but the difference
pilaster, than the recent male bones. The area of the Jomon femora was not signi-
within a bone is not large (SCHMITT,1968).
ficantly
On the other hand, the bone strength
ones, though
relates
with
the
SCHMITT,1968). study
density
cor-
(AMTMANN and
As the aim of the present
is to learn
about
the
mechanical
between
in cutting
bones
destructive
method
was
the non-
introduced
in
this study. Five the
femora
mid-length
of the
They were measured without
The
damage
were
at
measurements and the
antero-posterior of inertia The
that
ficantly
RESULTS
The results
of the
ments of the Jomon Table
bones are
1 comparing
with
measureshown
in
one.
those of the re-
and
cent bones. The recent
Jomon
femur
one in regard
is larger
direction
of inertia
the
diameter
in the antero-posterior
tion, that is, it is longer direction.
and
direction
stronger than
This tendency
recent tional
were
maxi-
larger
of cross
antero-posteriorly The outside
in
male. section
inthe
than length
maximum
male
than the
index of cross
that the Jomon tibia was
The biarticular the
in the
(Ix), the
antero-posteriorly
assumed
(dy), the
length
Jomon
in this
the
recent
of the
tibia
of the
fibula
male than
in the
study.
Even
if we
that the cross section was proporto the length, the measurements
of
the Jomon fibula were larger than those of
(Ix) and the indices of cross sec-
the antero-posterior transverse
than
to the measurements
of the antero-posterior moment
index
larger
was longer
of both
of inertia
the Jomon bones were signi-
bones.
longer
fibula
than in the recent
section indicated
geometric
the area
fibula
mechanical
recent
mass
(dy) and the polar moment
in the
the Jomon male showed
and the
direction
length.
from the mid-length.
of
moment
section of 10
The
with those of the femur.
maximum a distance
larger.
recent
was not so different
of the tibia
basically
at the other
within
mm at the maximum
damaged
of the
them.
mum diameter
Jomon
that
relatively
The results agreed
samples,
than
of the bone material
properties, the x-ray method will be sufficiently useful. Because of the difficulty the ancient
larger
in
in the was
the recent of the
bone.
Jomon
minimum
The standard
fibula,
diameter,
of the recent one.
except
deviation that
was larger
in the
than that
Of the male fibulae
of
110
T. KIMURA Table
1, Measurements
of lower
*: Jomon bone is significantly ( the
) : Including Jomon
ly large called
the estimated
man and
there
thick
were
bones,
limb
and
H. TAKAHASHI
bones.
(pr
