Necessary and sufficient conditions for global stability and uniqueness in finite element simulations of adaptive bone remodeling
Using a finite element method, the authors studied the necessary and sufficient conditions for global stability and uniqueness of adaptive bone remodeling. For that, they modeled the bone tissue as isotropic with a constant Poisson ratio and with the elastic modulus proportional to volumetric density of calcified tissue raised to the power \(n\). Their remodeling rate equation took the rate of change of volumetric hard tissue density as proportional to the difference between a stimulus and a set point. In one of their previous studies they defined state variables which are conjugate to the remodeling stimulus, and the function which acts as a variational indicator for the remodeling stimulus. Using this variational indicator properties, they studied the stability and uniqueness of the solution to the remodeling rate equations for all possible density distributions. They showed that the solution is the global minimum of a weighted sum of the total strain energy and the integral of density to the power \(m\) over the remodeling elements. In the reviewer's opinion this work is quite interesting and may find readers working in the field of biomechanics.
scientific article; zbMATH DE number 612085