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Variable order 3D models of bone remodelling

Valério D., Neto J., Vinga S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 3

501--508

This paper presents simulations of a three-dimensional model of the bone remodelling process. The model consists of a set of variable order partial differential equations, in which the varying order depends on the presence of tumour cells. The simulations are of a two-dimensional bone, to make visualisation simpler. They show that this model corresponds to the known evolution of bone remodelling, and is simpler than integer order models found in the literature.

SM-Algorithms for Approximating the Variable-Order Fractional Derivative of High Order

Moghaddam B. P., Machado J. A. T.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

293--311

In this paper we discuss different definitions of variable-order derivatives of high order and we propose accurate and robust algorithms for their approximate calculation. The proposed algorithms are based on finite difference approximations and B-spline interpolation. We compare the performance of the algorithms by experimental convergence order. Numerical examples are presented demonstrating the efficiency and accuracy of the proposed algorithms.