MMB Framework for ageing bone based on CT images

Osteoporosis compromises skeletal structural integrity and constitutes a
growing public health burden, in part because current diagnostic methods
focus primarily on mineral density and may underestimate fracture risk.
A fundamental limitation of many density-based approaches is that they
neglect the coupled effects of tissue composition, trabecular architecture,
and mechanical competence. This work presents a biologically informed
micromechanical homogenisation framework that translates \ct-derived
apparent density ($\rho_{\mathrm{app}}$) and bone volume fraction
($\mathrm{BV/TV}$) into spatially resolved effective elastic properties
while simultaneously estimating apparent trabecular microarchitectural
descriptors. The model incorporates age-dependent compositional changes
through the mineral, organic, and water phase relationships reported by
Bonicelli et al.~\cite{Bonicelli2022}. Trabecular thickness
($\mathrm{Tb.Th}$), trabecular number ($\mathrm{Tb.N}$), and trabecular
separation ($\mathrm{Tb.Sp}$) were derived separately from
$\mathrm{BV/TV}$ and a polynomial approximation of $\mathrm{BS/TV}$
fitted to the morphometric data of Adams et al.~\cite{Adams2018}.

The model produced a non-monotonic, boomerang-like relationship between
material and apparent density, comparable in form to those reported by
Zioupos et al.~\cite{Zioupos2008} and Adams et al.~\cite{Adams2018}.
This shape depends partly on the chosen density and $\mathrm{BV/TV}$
mappings. Unpaired comparisons with experimental data showed partial
consistency in density trends within the overlapping range, but did not
establish agreement across the full experimental distributions. The
apparent trabecular descriptors and elastic properties were not validated
against matched human measurements. This pilot study demonstrates the
feasibility of integrating clinical CT, age-informed composition, and
hierarchical micromechanics to generate patient-specific property estimates
for further evaluation.