Analytical approach to recovering bone porosity from effective complex shear modulus

Area of Science:

• Biomechanics
• Materials Science
• Medical Imaging

Background:

• Cancellous bone's mechanical properties are closely linked to its porosity.
• Accurate porosity assessment is crucial for diagnosing bone diseases and evaluating fracture risk.
• Existing methods for porosity measurement can be invasive or lack precision.

Purpose of the Study:

• To develop and validate an analytical method for recovering bone porosity from mechanical properties.
• To establish a link between the spectral measure of cancellous bone and its porosity.
• To demonstrate the method's independence from specific microgeometric assumptions.

Main Methods:

• Exploited the Stieltjes representation of the effective shear complex modulus.
• Recovered the spectral measure from frequency-dependent effective measurements.
• Developed a regularized algorithm to address the ill-posed nature of spectral measure reconstruction.
• Validated the method using finite element analysis on micro-computed tomography (micro-CT) images of human cancellous bone.

Main Results:

• The developed numerical algorithm accurately recovered bone porosity.
• Recovered porosity values showed excellent agreement with true porosity derived from micro-CT images.
• The method successfully modeled bone as a heterogeneous medium with specific material properties for trabeculae and bone marrow.

Conclusions:

• The proposed analytical approach provides a stable and accurate method for determining cancellous bone porosity.
• This technique offers a promising non-invasive tool for bone health assessment and research.
• The method's independence from microgeometry assumptions enhances its generalizability across different bone samples.