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Introduction
Our CT
based structural analysis for predicting fracture through a skeletal
metastasis is based on the hypothesis that all bone (normal or
pathologic) follows the same constitutive relationships established for
rigid porous foams, i.e. the strength (sY)
and modulus of elasticity (E) of bone depend on both the bone tissue
density (rtiss)
and the bone volume fraction (Vvb) squared:
sY,
E = aŚrtissŚ(Vvb)2+b
The rtiss
accounts for changes in tissue mineralization, and the Vvb
accounts for changes in trabecular morphology. To the best of our
knowledge, this hypothesis has never been validated for metastatic
cancer bone tissue. Therefore, it was our objective to establish that
the mechanical properties of metastatic cancer bone tissue were governed
by the power law functions expressed in the equation above. We also
hypothesized that the mechanical behavior of the entire bone specimen
was governed by the least rigid transaxial cross-section of bone
throughout the specimen and that the cross-section with the minimum Vvb
predicted the mechanical properties of the specimen better than the
average Vvb for the entire specimen.
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Methods
After obtaining IRB approval, 15 patients underwent excisional biopsy of
metastatic prostate, breast, lung, ovarian or colon cancer at surgery or
necropsy. Lytic or osteoblastic metastases were identified from biplaner
radiographs. Of these specimens, 11
(7 male, 4 female, 70 ±15 years) were of adequate size to undergo
specimen preparation for mechanical testing. In addition, 18 cadaveric
femurs (13 male, 5 female, 58 ± 21 years) were obtained. After freezing,
specimens were cored collinear with the predominant trabecular
orientation to form 57 (31 cancer, 26 non-cancer) cylindrical rods with
a 2:1 aspect ratio (diameter = 4.57 ±0.15 mm, h = 9.85 ±0.80 mm). A
pathologist confirmed the presence of metastatic cancer in each cancer
specimen histologically. The rtiss
of each specimen was measured using a pycnometer (Quantachrome). The
average Vvb for the entire specimen and the Vvb
for each of 10 equally divided transaxial sub-regions were determined
from thresholded μCT images (Scanco Medical AG, Bassersdorf,
Switzerland). Uniaxial compressive strains were applied to the
specimens using a custom-made micro-mechanical testing device.
Progressive step-wise compressive strains of 0%, 2%, 4%, 8% and 12% were
applied to each specimen at a strain rate of 0.01s-1. Each
sample was μCT imaged initially and after the application of each strain
step to visualize the location of progressive deformation of trabeculae
throughout the specimen. To eliminate artifacts related to crushing of
the unsupported ends of the specimens, brass caps were attached to each
end using cyanoacrylate. Each specimen was preconditioned to 0.3% strain
for 10 cycles at a strain rate of 0.005 s-1 to eliminate
settling artifact. The modulus was determined from the slope fit to
the linear portion of the composite step-wise stress-strain data. The
yield stress was determined at the point where the stress-strain data
became non-linear using 0.2% strain offset. Regression models were fit
(Levenberg-Marquardt method) to the function: sY,
E = aŚrtissŚ(Vvb)2
+ b.
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Results
The average bone tissue densities for cancer and non-cancer specimens
were 1.66 ±0.32 and 1.82 ± 0.31 g/cc respectively (statistically not
significant, p=0.40). For all specimens, serial μCT images demonstrated
that failure occurred predominantly at the transaxial subregion that
exhibited the minimum-Vvb (Figure C.1.3.1). For both the
cancer (CA) and non-cancer (NC) specimens the sub-region with the
minimum-Vvb accounted for more of the variability in the
measured mechanical properties than the average Vvb for the
entire specimen (Table C.1.3.1). |
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Discussion
The
results of this study validate the application of power law functions of
bone tissue density and bone volume fraction to derive the strength and
modulus of pathologic bone tissue. The constitutive relationships for
metastatic cancer bone tissue and non-cancer bone are similar and can be
approximated statistically by a single power law function with Vvb
and rtiss
as independent explanatory variables that model trabecular bone as a
rigid porous foam. Similar to pathologic bone in-situ, the
trabecular morphology was inhomogeneous for both the cancer and
non-cancer specimens. The weakest transaxial sub-region (with the
minimum-Vvb) accounted for more of the variability in the
measured mechanical properties than the average Vvb for the
entire specimen. Therefore the weakest portion of the specimen not
the average properties of the specimen governed the mechanical behavior
of these pathologic bone specimens. Bone tissue densities were in
the normal range for the non-cancer specimens. Although not
statistically significant, the bone tissue densities of the metastatic
cancer specimens were somewhat under mineralized possibly reflecting the
effects on bone of malnourishment and anti-cancer therapy.
Our
results support the view that bone itself is a substrate that undergoes
remodeling by osteoblasts and osteoclasts in response to local (e.g.
PTHrP expressed by tumors) and/or systemic (e.g. estrogen deprivation)
modulators of their activity. Since bone material properties can be
described analytically using a bivariate model consisting of bone tissue
density and bone volume fraction, then monitoring the structural
properties of bone using CT-based image analysis may provide a
non-invasive assay for monitoring the response of skeletal metastases to
treatment. |
