| |
Introduction
Failure of a bone structure does not depend on its average properties
but instead depends on its weakest section. From mechanics of
structures, the load carrying capacity of a bone is governed by the
cross-section through the bone with the weakest structural rigidity,
since bone fails at a constant strain independent of the bone densit1.
Structural rigidity is the product of the modulus of elasticity of the
bone tissue, (material property), and a measure of the bone
cross-sectional geometry that defines an attribute of the distribution
of bone tissue in space (i.e. area, moment of inertia or polar moment of
inertia). Changes in bone material properties, cross-sectional geometric
properties or both are reflected by changes in the cross-sectional
structural rigidity. Current methods of fracture risk prediction based
on the size and location of the defect alone fail to account for the
“quality” of the underlying bone substrate. It is our hypothesis that
structural rigidity as assessed by algorithms based on transaxial
computed tomography measurements predicts the load carrying capacity
(i.e. failure load) of a bone containing a defect better than current
radiographic techniques. We previously demonstrated that structural
rigidity analysis of transaxial quantitative computed tomography (QCT)
images accurately predicted failure load of vertebrae with simulated
osteolytic defects ex-vivo. Since the spine is the most frequent site of
skeletal metastases in breast cancer patients, the aim of this work was
to prove that structural rigidity analysis of transaxial QCT image data
in-vivo predicts fracture of breast cancer patients with spinal
metastases better than current clinical and radiographic guidelines. The
risk that a bone will fracture depends on the load carrying capacity of
the bone and the magnitude of the loads applied to it. We prospectively
evaluated the fracture risk of 106 women with metastatic breast cancer
to the spine. The in-vivo load carrying capacity of vertebrae with
metastatic breast cancer was estimated non-invasively using our QCT
based algorithm. The loads applied to affected thoracic and lumbar
vertebrae during typical activities of daily living such as bending over
to lift a 10 kg mass or arising from a chair were estimated using our
optimization based model for spinal loading that takes into account the
load bearing capacity of the thoracic cage. The quotient of the load
applied to the affected vertebra divided by the load carrying capacity
of the vertebra provides an index for assessing fracture risk during
this specific activity. This fracture risk index (FRI), given by the
ratio of the applied load to the failure load of the affected vertebra,
was calculated for each vertebrae between T8-L5 using two different load
scenarios for each patient: a) lifting a 10 kg mass and b) arising from
a chair. FRI>1 implies that fracture would occur during the applied load
condition. To test the hypothesis that structural rigidity assessed by
algorithms based on CT measurements predicted the failure load of a
vertebra containing a defect better than current radiographic methods we
compared the accuracy of FRI to the best available clinical and
radiographic criteria for predicting metastatic spine fracture.
QCT Rigidity Analysis
An analytical method for assessing fracture risk using QCT rigidity
analysis was developed to estimate the load carrying capacity of the
vertebra. QCT scans were performed on all patients to provide the data
to calculate the load capacity (failure load) of the vertebrae. A Ca10(PO4)6(OH)2
phantom was imaged with each patient to convert Hounsfield units to
equivalent bone density (ρ). Axial and bending rigidities were
calculated relative to the modulus-weighted centroid:
Axial rigidity, EA=∫E(ρ)da
Bending rigidity, EI=∫E(ρ)x2da - EAX2,
where E(ρ)=0.82*ρ2+0.07 for trabecular bone, E(ρ)=21.91* ρ
-23.5 for cortical bone, x=distance to neutral axis, da=pixel area, and
X is the coordinate of the modulus weighted centroid. The load carrying
capacity of each vertebra was calculated using a two-dimensional plane
strain model for the vertebra loaded in combined axial compression and
forward bending. The yield load for this scenario was calculated from
the cross-sectional geometric and material properties of the vertebra:
e = Fz / EA + My c / EI,
where e, the strain at failure = 1% (since at the material level bone
fails in compression at a constant strain of 1% independent of density),
c=distance from neutral axis to the outermost point in the AP direction,
and My= Fz x, where x = distance from the neutral
axis to the point of load application at the center of the vertebral
body.
Estimation of Applied
Spine Loads
The applied load at each vertebra for simple
lifting tasks was calculated using an optimization-based model that
accounted for the subject’s height and weight. For this model it was
necessary to have accurate muscle cross-sectional areas and the location
of muscle groups at all thoracic and lumbar levels. Transaxial CT scans
of the torso for a population of 27 men and 29 women over 60 years of
age was analyzed. Muscle boundaries for the erector spinae, rectus
abdominus, external oblique, internal oblique, latissimus dorsi, psoas,
quadratus lumborum, and transversus abdominus were digitized on
transaxial CT images of the torso from T8 to L5. The rib cage and the
vertebral body at each level were also digitized. The rib cage was
segmented into three parts: the left rib cage (including ribs and
intercostal muscles), the right rib cage, and the sternum and costal
cartilage. The distance from the centroid of the vertebral body to the
centroid of each muscle group and the centroid of the rib cage elements
was calculated.
The analytic model
was constructed in two parts. First, the moments and forces for each
cross-section through the torso were calculated from a static force
balance of the upper body. Average anthropometrical parameters for the
torso were obtained from literature sources. The subjects were modeled
doing straight and bent knee lifts in which the weight of the upper body
and added weight in the hands were balanced over the feet. For bent
knee lifts, initially the knees were assumed to be flexed at 90 degrees
when the hips were flexed at 90 degrees. A second analysis was done to
calculate the segmental compressive force on each vertebra from the
cross-sectional forces and moments calculated for the torso. To
calculate axial compressive vertebral loads for cross-sections through
the lumbar region (L2 to L5), a linear optimization technique was used
to distribute muscle forces that minimized the maximum muscle force per
unit area of muscle (i.e. the maximum muscle intensity). Using the
maximum muscle intensity as a constraint, the minimum axial compressive
spine load was calculated. For cross-sections in the thoracic and
thoraco-lumbar regions (T8 to L1), it was necessary to account for the
contribution of the rib cage to axial load support. Four forces
represented the contribution of the rib cage: a longitudinal sternum
force, two tensile rib cage forces and a trans-thoracic horizontal force
centered at the sternum. Maximum muscle intensity was minimized at the
L2 level. This maximum muscle intensity was assumed to remain constant
throughout the thoracic region. Using this maximum muscle intensity as a
constraint, linear optimization of the muscle forces was used to
minimize the unsupported moment, which was then distributed to the four
rib cage forces. The axial compressive force at each vertebra was
calculated from the remaining axial compressive spine load.
The model was validated by comparing predicted muscle intensity (stress
level) to literature data on EMG activity of the erector spinae muscles
at levels in the thoracic and lumbar spine as a function of torso
flexion angle. Correlation coefficients of 0.93 at the eighth thoracic
level and 0.95 at the third lumbar level were found.
Radiographic
Assessment of Fracture Risk
There are few radiographic guidelines for predicting vertebral
fracture. Most guidelines based on plain radiographs of the spine in
the frontal and sagittal projections are used to predict spinal
instability and risk for neurologic injury after the fracture has
already occurred. The CT based method described by Taneichi et al. to
predict vertebral fracture risk as a function of the size and location
of the defect alone was the best radiographic method reported in the
literature. Four factors were combined to assess fracture risk:
percentage of tumor occupancy in the vertebral body, destruction of the
pedicle, destruction of the posterior elements except the pedicle, and
destruction of the costovertebral joint. Probability of fracture was
calculated for all spine levels.
For T8-T10: p(T)=exp(lT)/{1+exp(lT)},
where lT=0.089x1+0.546x2+0.161x3+2.319x4-4.597
for T11-L5, p(L)= exp(lL)/{1+exp(lL)}, where lL=0.147x1+5.694x2-3.609x3-5.492
x1=percentage of tumor occupancy in the vertebral body, x2=destruction
of the pedicle (0=intact, 1=involved),
x3=destruction of the posterior elements except the pedicle
(0=intact, 1=involved), and x4=destruction of the
costovertebral joint (0=intact, 1=involved). Fracture risk was defined
as predicted probability>0.5
Clinical Vertebral Fracture Assessment
To assess the accuracy of the two methods for predicting vertebral
fracture, it was necessary to determine if a vertebral fracture occurred
in the study subjects. Metastatic lesions are constantly changing in
size, shape and the bone tissue forming the lesion. Therefore any
method that predicts fracture risk for skeletal metastases is valid for
only a finite period of time. Vertebral fracture occurrence was
determined over a four-month surveillance period. We were blinded to the
patients’ clinical course or treatment regimen. Patients with previous
spine fractures were eliminated from the analysis so as not to
positively bias our results.
Vertebral fracture occurrence was defined by
commonly used criteria for osteoporotic vertebral fracture. Vertebral
heights were measured on all subjects from plain radiographs and/or MRI
scans that included part or all of the spinal column. Wedge fractures
were diagnosed if there was a 15% loss of height from one side of the
vertebrae compared to the other in either the frontal or sagittal
planes. Axial compression fractures were diagnosed if there was a 15%
loss of vertebral height compared to adjacent vertebrae. An independent
observer, unaware of the fracture risk predictions of the subjects,
reviewed all plain radiographs and MRI scans.
Results
The CT based
structural rigidity analysis and CT based analysis of lesion size and
location using Taneichi guidelines for assessing fracture risk were
compared using clinical data from breast cancer patients with spinal
metastases. After IRB approval, the medical records from 1024 breast
cancer patients were reviewed. One hundred six patients (average age=55
years, range=36-88 years) with radiographically documented spinal
metastases were analyzed prospectively over a four-month interval to
check the accuracy of the fracture risk predictions based on CT scans of
the spine and torso using the algorithms described above.
Ten patients suffered a new vertebral fracture over the 4-month
observation period. Both the CT based structural rigidity analysis and
the Taneichi CT criteria predicted that these 10 patients were at
increased fracture risk (sensitivity = 100% for either method).
However, the CT rigidity analysis was better at predicting which
patients would not fracture an affected vertebra (specificity=49% when
FRI>1 for lifting a 10 kg mass) compared to the Taneichi CT criteria
(specificity=20%). Instead of calculating the FRI for lifting a 10 kg
mass, if the load carrying capacity of the vertebra was normalized by
the patient’s body mass index and the threshold for predicting vertebral
fracture set to achieve 100% sensitivity, the specificity for predicting
no vertebral fracture was improved to 69%.
Discussion
We have developed a
non-invasive method using transaxial CT images of the torso which are
attained routinely in breast cancer patients for surveillance of liver
metastases and demonstrated that these same images can be used
successfully to predict the risk of vertebral fracture in those patients
with metastases to the spine. Structural analysis based on composite
beam theory was used to determine the load carrying capacity of each
vertebra with a metastatic lesion. A fracture risk index (FRI), formed
by the ratio of the applied load to the load carrying capacity was
calculated for each affected vertebra. The vertebral fracture risk
predictions based on CT based structural rigidity analysis were compared
to the only other CT based fracture probability model reported in the
literature for metastatic cancer to the spine. Over a four-month
surveillance period, both models were 100% sensitive for predicting
vertebral fracture. However, fracture risk predictions based on
structural analysis were significantly more specific, (49% for FRI>1 for
lifting 10 Kg package; 69% for vertebral load capacity normalized by
body mass index) than criteria based on the size and location of the
lesion on transaxial CT images alone (20% for Taneichi probability
model). In conclusion, CT based structural rigidity analysis was as
sensitive but more specific than the best radiographic guidelines for
estimating metastatic cancer vertebral fracture risk.
The Taneichi criteria only take into account the size and location of
the metastatic lesion in the vertebra. The CT based structural rigidity
analysis accounts for both changes in bone material behavior and changes
in bone structural geometry. This is crucial in evaluating the strength
of a vertebra with a metastatic lesion since many of these patients are
post-menopausal women with pre-existing osteoporosis. Therefore the
density of the trabecular bone comprising the vertebra may be lower at
baseline placing these patients at increased risk for vertebral fracture
independent of the presence of a metastatic lesion. A smaller lytic
lesion in the vertebra of an osteoporotic female may have greater
potential for vertebral fracture compared to the same size lesion in
denser bone. All these patients were being treated with bisphosphonates
in addition to various chemotherapy regimes. Both CT based methods for
predicting metastatic spine fracture were 100% sensitive, but the CT
based structural rigidity analysis was more specific. This suggests that
compensatory remodeling of the bone in response to anticancer treatment
in the form of sclerotic margination around the periphery of the lesion,
periosteal expansion of the vertebral body or densification of the
remaining trabecular bone in the vertebral body are not accounted for by
the size and location of the lesion alone. Improved specificity means
that fewer patients would be recommended for additional therapies such
as radiation or surgery.
The analytic model estimates the load
applied to each vertebra for specific loading cases. A patient may be
at increased fracture risk when applying large loads to the spine,
during heavy lifting, but at low fracture risk when performing less
strenuous activities, such as getting up from the seated position. Many
of the patients enrolled in our study were instructed by their
oncologists to refrain from strenuous activities that might put them at
increased risk for vertebral fracture. Patients abstaining from
activities such as heavy lifting negatively bias our analysis and
decrease the number of vertebral fractures since fewer patients engaged
in the index activity that we simulated. In fact in another study we
conducted predicting fracture risk in children with benign tumors of the
appendicular skeleton using CT based structural analysis, our fracture
risk predictions were 100% sensitive and 94% specific since none of
these children were aware of the presence of the tumor and did nothing
to alter their physical activities. In the future it may be useful to
patients and their physicians to provide a list of activities that
result in FRI>1 and FRI < 1. Other structural parameters were tested to
predict vertebral fracture from metastatic cancer independent of patient
activity level. These parameters were developed retrospectively, by
determining a threshold that maximized specificity while maintaining100%
sensitivity. By normalizing the load carrying capacity of the vertebra
by the patient’s body mass index, the specificity improved significantly
to 69% compared to the 49% specificity for FRI>1 when lifting a 10 kg
mass.
|
