Measuring the Density of Bone
Kyle Strodtbeck
Advisor: David Farrell
Department of Physics, CWRU, 10900 Euclid Ave., Cleveland, Ohio 44106
ABSTRACT
Density and magnetic susceptibility are fundamental
properties of condensed matter and some recent work
[1] suggests that there may be a direct relationship
between them in the case of biological materials.
Magnetic susceptibility may therefore provide a useful
tool to image the density of the human body, which
could be of considerable value in medical diagnostics.
However, probing this relationship quantitatively
demands an accurate measurement of the in-vitro
density of biological samples. Because of their porous
structure, inhomogeneity, and loss of fluid after they are
removed from the living organism, this is a challenging
task. The present investigation is focused on bone,
where the problems mentioned are all present but less
severe than in soft tissue.
Bone samples were
collected for several different species and a specially
designed container was utilized to probe their density
when as a function of their time of immersion in water.
We have discovered that very significant changes in
both volume and mass can occur for (dry) bone
following immersion but that these changes are
correlated in a manner that leads to very small changes
in density. Our results encourage the view that in-vitro
density measurements of the sort described here
provides a good approximation to the true in-vivo
density of bone in living organisms.
Source: US National Cancer Institute
INTRODUCTION
Bones form part of the endoskeleton of vertebrates
and are among the most diverse organs in the human
body. Due to different hormone ratios, collagen
disproportion, water content, and other physiological
variability, bone density is expected, and found in
previous studies [2] to vary significantly between different
species. A further experimental difficulty attaches to invitro density measurements which are not present for the
type of samples normally studied in condensed matter
physics, namely, the loss of fluid attendant upon
separating the bone from its parent organism.
Recent work [1] has suggested that a direct
relationship exists between the magnetic susceptibility
and density of soft biological materials. An extended set
of susceptibility and density measurements on bone
samples from different species is needed to test whether
there is a simple relationship between density and
susceptibility for bone.
RESULTS AND DISCUSSION (continued)
The results tabulated above divide naturally into two
groups, namely, bones with relatively large (>15%)
changes in density (mahi and groupie) and those with
fairly small changes (<3%). Although we made no
experiments on human bone, it is probable that the
human case falls into the latter category, so we
performed detailed time dependent studies of the mass
and volume for three of the second group over shorter
time periods, with the results graphed below. It is clear
from these results that the mass and volume changes are
rapid and substantial, and that the small density changes
simply results from the fact that the mass and volume
changes are closely correlated.
Source: Uniformed Services University
METHODS
The traditional “Archimedes” approach to density
measurement, in which the sample is immersed in
water, was adopted for our measurements.
A container was constructed that allow samples with
relatively large volumes (on the order of 50 cm3) to be
measured. Preliminary measurements were made to
explore the difference between what we term the “dry”
and “wet” state of our samples. In the former, samples
were dried for 50 seconds at medium power in a
household microwave oven.
Their mass was
measured, together with the volume of water displaced
immediately following submersion.
In the other
extreme (“wet samples”) the density was measured
after 24 hours of submerging the dry bone in water.
These initial measurements were followed up with
detailed time-dependent studies of the mass and
volume for three of these samples over shorter time
periods, using the same Archimedian technique.
CONCLUSION
FIGURE ONE
Density container with
small, removable
leak-tight top and black
reference line
RESULTS AND DISCUSSION
Measurements for density were taken in both dry
and wet states, following the procedure outlined above.
Results for both states are presented below, including
the respective percent changes.
Species
Density (g/cm3) Dry
Density (g/cm3) Wet
Percent Change in
Density
Clam
Deer
Cow
Fox Mahi Groupie Snapper
Relatively large changes in mass and volume occur
following submersion of dry bone in water, but in most cases
these changes essentially cancel each other out as far as
the density is concerned. In fact, with the exception of
bones obtained from the groupie and mahi fish, the overall
change in density on immersion in water is just one or two
percent. Physically, it appears that water does not flow into
empty spaces in the structure, which would leave the volume
unchanged, but simply expands the structure by an amount
proportional to the volume of water absorbed. Independent
of their detailed physical interpretation, our results
encourage the view than an in-vitro density measurement of
the sort described here provides a reliable approximation for
the true in-vivo density of bone in a variety of living
organisms.
REFERENCES
[1] D.E. Farrell, private communication (2009).
2.58
1.62
1.99
1.29 1.12
0.97
1.31
2.6
1.66
1.97
1.31
1.14
1.35
1.3
0.7% -1.8% -0.5% 1.6% 15.6% 17.5%
3.05%
[2] Blitz, R., Pellegrino, E. The chemical anatomy of bone: I. A comparative study of
bone composition in sixteen vertebrates. J Bone Joint Surg Am. 51, 456-466
(1969).
[3] Hopkins J.J., & Wehrli F.W. Magnetic susceptibility measurements of insoluble solids by NMR:
Magnetic susceptibility of bone. Magn. Reson. Med. 51, 1077-1082 (2004).
[4] Sumanaweera, T.S., Glover, G.H., Binford, T.O. & Adler J.R. MR susceptibility misregistration
correction. IEEE Trans. Med. Imaging. 12, 251-259 (1993).