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Open AccessArticle

The 3D Spatial Autocorrelation of the Branching Fractal Vasculature

1
Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA
2
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
3
Department of Obstetrics and Gynecology, University of Rochester Medical Center, Rochester, NY 14642, USA
*
Author to whom correspondence should be addressed.
Acoustics 2019, 1(2), 369-381; https://doi.org/10.3390/acoustics1020020
Received: 26 February 2019 / Revised: 28 March 2019 / Accepted: 2 April 2019 / Published: 9 April 2019
(This article belongs to the Special Issue Acoustics in Biomedical Engineering)
The fractal branching vasculature within soft tissues and the mathematical properties of the branching system influence a wide range of important phenomena from blood velocity to ultrasound backscatter. Among the mathematical descriptors of branching networks, the spatial autocorrelation function plays an important role in statistical measures of the tissue and of wave propagation through the tissue. However, there are open questions about analytic models of the 3D autocorrelation function for the branching vasculature and few experimental validations for soft vascularized tissue. To address this, high resolution computed tomography scans of a highly vascularized placenta perfused with radiopaque contrast through the umbilical artery were examined. The spatial autocorrelation function was found to be consistent with a power law, which then, in theory, predicts the specific power law behavior of other related functions, including the backscatter of ultrasound. View Full-Text
Keywords: scattering; backscatter; ultrasound; tissue; medical ultrasound; fractal vasculature; tissue characterization scattering; backscatter; ultrasound; tissue; medical ultrasound; fractal vasculature; tissue characterization
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Parker, K.J.; Carroll-Nellenback, J.J.; Wood, R.W. The 3D Spatial Autocorrelation of the Branching Fractal Vasculature. Acoustics 2019, 1, 369-381.

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