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Frequency dependence of average phase shift from human calcaneus in vitro
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10.1121/1.3257550
/content/asa/journal/jasa/126/6/10.1121/1.3257550
http://aip.metastore.ingenta.com/content/asa/journal/jasa/126/6/10.1121/1.3257550

Figures

Image of FIG. 1.
FIG. 1.

Measurements of phase difference, , vs frequency for the polycarbonate plate. Linear and quadratic fits to the data are also shown. Error bars (standard errors) are plotted but may be too small to discern.

Image of FIG. 2.
FIG. 2.

The effect of subtracting the -intercept from a least-squares quadratic fit to the phase-velocity vs frequency data in order to suppress boundary effects in the polycarbonate plate. Previously published measurements by Droin et al. (1998) are also shown.

Image of FIG. 3.
FIG. 3.

Measurements of phase difference, , vs frequency for the parallel-nylon-wire cancellous-bone-mimicking phantom with and . Linear and quadratic least-squares fits to the data are also shown. Error bars are standard errors.

Image of FIG. 4.
FIG. 4.

Estimates of phase velocity at 500 kHz with and without adjustment for -intercept in seven parallel-nylon-wire cancellous-bone-mimicking phantoms.

Image of FIG. 5.
FIG. 5.

Estimates of dispersion with and without adjustment for -intercept in seven parallel-nylon-wire cancellous-bone-mimicking phantoms. Parabolic fits to the data are also shown.

Image of FIG. 6.
FIG. 6.

Experimental measurements of complex transfer function, , and single-wave linearly dispersive transfer function fits [Eq. (1)] for a single bone specimen with attenuation coefficient slope of 19.6 dB/cm MHz and a phase velocity at 500 kHz of 1525 m/s.

Image of FIG. 7.
FIG. 7.

Experimental measurements of complex transfer function, , and single-wave linearly dispersive transfer function fits [Eq. (1)] for a single bone specimen with attenuation coefficient slope of 8.0 dB/cm MHz and a phase velocity at 500 kHz of 1497 m/s.

Image of FIG. 8.
FIG. 8.

Measurements of phase difference, , vs frequency for 30 bone samples. Linear and quadratic least-squares fits to the data are also shown. Error bars are standard errors.

Image of FIG. 9.
FIG. 9.

Phase velocity computed from phase-difference data with no adjustment for boundary effects. Error bars are standard errors.

Image of FIG. 10.
FIG. 10.

Phase velocity computed from phase-difference data with an adjustment for boundary effects based on a linear model for phase difference, , vs frequency . Error bars are standard errors.

Image of FIG. 11.
FIG. 11.

Phase velocity computed from phase-difference data with an adjustment for boundary effects based on a quadratic model for phase difference, , vs frequency . Error bars are standard errors.

Image of FIG. 12.
FIG. 12.

Real and imaginary parts (continuous curves) of the two-wave transfer function, , for a set of parameters that Anderson et al. (2008) showed to result in an attenuation coefficient that appears to vary approximately linearly with frequency: , , , , , , and . Also shown are real and imaginary parts (asterisks and circles) of a single-wave linearly dispersive model (with frequency-independent form for ) fit to , which conform very closely to the two-wave model over the experimental frequency band.

Tables

Generic image for table
TABLE I.

Phantom properties. Trabecular thickness (Tb.Th) corresponds to nylon-wire thickness. The variable is the inter-wire spacing, which is equal to the sum of Tb.Th and Tb.Sp (trabecular separation). The VF is the fraction of volume occupied by nylon wire. .

Generic image for table
TABLE II.

The effect of boundary effects adjustment on estimates phase velocity at 500 kHz and dispersion in human calcaneus samples in vitro. Values are expressed as error of estimate of the mean. The weak dispersion assumption is valid if .

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/content/asa/journal/jasa/126/6/10.1121/1.3257550
2009-12-14
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Frequency dependence of average phase shift from human calcaneus in vitro
http://aip.metastore.ingenta.com/content/asa/journal/jasa/126/6/10.1121/1.3257550
10.1121/1.3257550
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