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Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography
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10.1121/1.4739455
/content/asa/journal/jasa/132/3/10.1121/1.4739455
http://aip.metastore.ingenta.com/content/asa/journal/jasa/132/3/10.1121/1.4739455

Figures

Image of FIG. 1.
FIG. 1.

Ultrasonic rf signals having propagated through a water path (gray circles) and the same path with a cancellous bone sample inserted (black circles).

Image of FIG. 2.
FIG. 2.

Experimental data from human calcaneus, Bayesian model, and residual. The top panel shows the experimental data that are input into the algorithm. The Bayesian model is generated as described in Sec. II D. The bottom plot shows the residual, defined as the difference between the experimental data and the Bayesian model, on a substantially expanded vertical scale.

Image of FIG. 3.
FIG. 3.

A representative model waveform (same waveform as in Fig. 2) and the fast and slow waves that comprise it.

Image of FIG. 4.
FIG. 4.

Fast wave speed (left panel) and slow wave speed (right panel) plotted against sample porosity. Porosity was determined by . Each value shown is the mean of six runs. The vertical bar on each point represents the standard deviation of these six runs.

Image of FIG. 5.
FIG. 5.

Slope of attenuation for the fast wave (left panel) and slow wave (right panel) plotted against sample porosity. Porosity was determined by . Each value shown is the mean of six runs. The vertical bar on each point represents the standard deviation of these six runs. The solid lines are linear best fit lines. The R-squared value for the fit is shown in each panel.

Image of FIG. 6.
FIG. 6.

Fast wave amplitude (left panel) and slow wave amplitude (right panel) plotted against sample porosity. Porosity was determined by . Each value shown is the mean of six runs. The vertical bar on each point represents the standard deviation of these six runs. The solid lines are linear best fit lines. The R-squared value for the fit is shown in each panel.

Image of FIG. 7.
FIG. 7.

The ratio of the fast wave amplitude to the slow wave amplitude plotted against porosity. Porosity was determined by . Each value shown is the mean of six runs. The vertical bar on each point represents the standard deviation of these six runs. The solid line is a linear best fit line. The R-squared value for the fit is shown.

Tables

Generic image for table
TABLE I.

Physical characteristics of defatted calcaneus samples. Direct thickness measurements are reported as mean plus or minus the standard deviation of five independent manual measurements.

Generic image for table
TABLE II.

Derived parameters of defatted calcaneus bone samples. Apparent density was determined by dividing the mass of the dehydrated samples (mass column of Table I) by the product of the mean linear dimensions (direct thickness measurement columns in Table I). The micro-computed tomography system provides a bone volume per total volume measurement. Porosity is .

Generic image for table
TABLE III.

Prior probability distributions used for Bayesian calculations. Each prior distribution is a bounded Gaussian described by the four parameters in this table. For each parameter, the upper and lower bounds were chosen to be wide enough so as to affect the final result only minimally. The mean was chosen to be the midpoint between the upper and lower bounds, and the standard deviation was chosen to be one half of the difference between the upper and lower bound.

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/content/asa/journal/jasa/132/3/10.1121/1.4739455
2012-09-12
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography
http://aip.metastore.ingenta.com/content/asa/journal/jasa/132/3/10.1121/1.4739455
10.1121/1.4739455
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