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Using ultrasonic attenuation in cortical bone to infer distributions on pore size

Journal Article · · Applied Mathematical Modelling
 [1];  [2];  [3];  [2];  [4];  [2];  [2];  [5];  [5];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); North Carolina State University, Raleigh, NC (United States)
  2. North Carolina State University, Raleigh, NC (United States)
  3. Columbia University, New York, NY (United States)
  4. North Carolina State University, Raleigh, NC (United States); Applied Research Associates, Raleigh, NC (United States)
  5. Sorbonne University, Paris (France)
+ Show Author Affiliations
Here, in this work we infer the underlying distribution on pore radius in human cortical bone samples using ultrasonic attenuation data. We first discuss how to formulate polydisperse attenuation models using a probabilistic approach and the Waterman Truell model for scattering attenuation. We then compare the Independent Scattering Approximation and the higher-order Waterman Truell models’ forward predictions for total attenuation in polydisperse samples. Following this, we formulate an inverse problem under the Prohorov Metric Framework coupled with variational regularization to stabilize this inverse problem. We then use experimental attenuation data taken from human cadaver samples and solve inverse problems resulting in nonparametric estimates of the probability density function on pore radius. We compare these estimates to the “true” microstructure of the bone samples determined via microCT imaging. We find that our methodology allows us to reliably estimate the underlying microstructure of the bone from attenuation data.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
National Institutes of Health (NIH); National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
NA0003525
OSTI ID:
1872035
Alternate ID(s):
OSTI ID: 1871270
Report Number(s):
SAND2022-6952J; 706666
Journal Information:
Applied Mathematical Modelling, Journal Name: Applied Mathematical Modelling Vol. 109; ISSN 0307-904X
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

97 MATHEMATICS AND COMPUTING
Waterman truell
cortical bone
inverse problems
polydisperse
ultrasound
variational regularization