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The title question is investigated by comparing results of a series of bone strength tests of lumbar vertebrae (L1 and L2) and right wrists (distal radii) of nine cadavers. The paper describes the specimen preparation, the testing, and the analysis procedures. The results show that there is a correlation between the strengths of the lumbar and wrist specimens for the individual cadavers, suggesting that bone integrity is indeed systemic.

At an NIH conference in 2000, osteoporosis was defined as: “a skeletal disorder characterized by compromised bone strength predisposing to an increased risk of fracture” [

In a relatively recent report (2011) the US Preventive Services Task Force (USPSTF) [

The excessive cost of this widespread disease includes not only treatment but also the cost of diagnosis. Currently firm diagnosis typically occurs after a bone fracture via X-ray or MRI imaging of the large bones. However, if diagnosis could be made simpler and sooner, the cost of diagnosis could be reduced and preventive measures (e.g. Diet/exercise as discussed by Dimov (2010)) could be taken [

If osteoporosis is systemic, as opposed to being localized in large bones and vertebrae, then using advanced imaging techniques, diagnosis using extremities is feasible. Indeed, Oyen et al. (2010) [

In vivo MRI studies show that micro MRI imaging can detect architectural changes in trabecular bone of the distal radii. These changes are believed to be good biomarkers for osteoporosis. That is, if a systemic nature of osteoporosis can be established, technical advances in imaging can be used for early osteoporosis diagnosis.

To test the systemic hypothesis, we physically measured and compared the bone strengths of lumbar vertebrae and distal radii of nine cadavers with varying degrees of low bone mineral densities. The results suggest a strong correlation between the strengths of the vertebrae and the radii for individual cadavers.

The balance of the paper is divided into five parts with the first part describing the physical testing, which is then followed by listings of measurement and testing results. The next two parts provide an analysis of the data and subsequent computed results. The final part is a discussion with concluding remarks.

Once harvested the lumbar vertebrae (L1 and L2) were cut through the discs so that the specimens then had flat superior and inferior surfaces. Also, the spinous processes were removed resulting in specimens in the form of short cylinders having curved perimeters as depicted in

We used a dial caliper to measure the five dimensions of

After taking these measurements we placed the specimens in shallow plastic flat-dishes containing a liquid cold-curing resin. Upon hardening the specimens were inverted and the other end (superior end) was placed in hardening resin dishes with care taken to keep the superior/inferior dish surfaces parallel.

Next, we placed each of the 18 constructs in an Instron tester and compressed them to failure (large displacement with minimal load increase). During the compression we recorded the load/displacement values up to failure and then the failure load itself.

As with the vertebrae, the distal radii (once harvested) were cut perpendicular to their axes with the proximal and distal cutting planes being parallel. The bone tissue in the cross-sections was found to be near annular ellipses as represented in

Next, we placed the nine radii constructs in the Instron machine and compressed them to failure. As with the vertebrae, we recorded the load/displacement values up to failure and then the failure load itself.

Tables 3 and 4 list the measurements of the parameters of

Finally,

To determine the vertebral strengths we needed to know their cross-section areas. To this end we used the geometry represented in

Using standard handbook mensuration formulas [

Let t be defined as:

Next, let r be defined as:

Then the cross-section area A of a vertebral specimen is approximately:

^{1} (see

^{1}Measurements are in inches (in) with millimeters (mm) in parentheses.

^{1}Loads are in pounds (lb) with kiloNewtons (kN) in parentheses. ^{2}Stiffnesses are in pounds per inch (lb/in) with kiloNewton per meter (kN/m) in parentheses.

where a, b, c, and e are shown in

where E is the elastic modulus (see Beer and Johnston [

The stress and the strain ε are then defined as

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^{*}Subscripts d for distal Measurements are in inches (in) with millimeters (mm) in parentheses.

^{*} (see

^{*}Subscripts p for proximal. Measurements are in inches (in) with millimeters (mm) in parentheses.

^{1}Loads are in pounds (lb) with kiloNewtons (kN) in parentheses. ^{2}Stiffnesses are in pounds per inch (lb/in) with kiloNewtons per meter (kN/m) in parentheses.

and (5)

with the “strength” being the maximum stress value occurring at the failure load, or at the collapse of the specimen member.

The elastic modulus E is a measure of the stiffness of the specimen. It is simply the slope k of the linear portion of a graphical representation between the stress σ and the strain ε, or equivalently, between the load P and the displacement δ. That is, from Eqs.4 and 5 we have

or (6)

Where Δ is a finite difference.

The strength and the stiffness E are thus measures of the structural integrity of the vertebral specimens and thus can be used for comparison evaluations.

As with the vertebrae, we also needed the cross-section areas of the distal radii, to evaluate their strengths. To this end, consider again the sketch of the distal radii bone specimens shown in

The bone content of the radii cross-sections are nearly annular ellipses. Therefore, with an ellipse area being:, with a and b being semi-major and semi-minor axes, the distal and proximal cross-section areas are:

The average bone cross-section is then

Consider again the side view of the radius specimen as in

Beer and Johnston [

By substituting for A from Eq.9 we find δ to be:

In the course of the loading of the specimen (before collapse) we found the loading and the deformation to be linearly related. That is,

where, as with the vertebrae, the stiffness constant k may be identified as the slope of the newly linear load/displacement relation.

We used the failure load data of

The radii strengths and elastic moduli can be computed using the failure loads and stiffness values listed in

In view of Eq.8, it is helpful to compute some area ratios needed for determining the elastic modulus. Also, it is useful to have the product of the construct height h (see

Finally, using failure loads listed in

Observe also in

Values are in square inches (in^{2}) with square centimeters (cm^{2}) in parentheses, and in pounds per square inch (psi) with mega Pascals (mPa) in parentheses.

^{*}Values are in square inches (in^{2}) with square centimeters (cm^{2}) in parentheses; ^{**}Units in reciprocal square inches (in^{–2}); ^{***}Units in pounds.

Values are in pounds per square inch (psi) with megaPascals (mPa) in parentheses.

Values are in pounds per square inch (psi) with megaPascals (mPa) in parentheses.

This is to be expected since the radii bone is cortical whereas the vertebrae have load sharing between cortical and trabecular bone. Eswaran, et al. (2006) [

The authors acknowledge and appreciate the assistance of Richard Banto, Dale Weber, Y. Su, Susan Neuman, and Linda Levin.

To establish a basis for Eqs.1-3, consider the circle segment in

In view of the dimensions a, ···, e of

Also from [

By solving for r we have

Referring again to

or

Eqs.A2, A4, and A6 form the basis for the algorithm of Equations.