Mechanobiology of bone remodelling

Bone as most of living tissues is able, during its entire lifetime, to adapt its internal microstructure and subsequently its associated mechanical properties to the specific mechanical and physiological environment in a process commonly known as bone remodelling. Bone is therefore continuously renewed and microdamage removed minimizing the risk of fracture. Bone remodelling is controlled by mechanical and metabolical stimuli. In this paper, we introduce a new model of bone remodelling that takes into account both types of influences. The predicted results show a good correspondence with experimental and clinical data. For example, in disuse, bone porosity increases until an equilibrium situation, while, in overloading, decreases unless the damage rate is so high that causes resorption and "stress fracture". This model has been employed to predict bone adaptation in the proximal femur after total hip replacement proving its consistence and good correspondence with well-known clinical experiences.

Improved bounds for subband-adaptive iterative shrinkage/thresholding algorithms.

This paper presents new methods for computing the step sizes of the subband-adaptive iterative shrinkage-thresholding algorithms proposed by Bayram & Selesnick and Vonesch & Unser. The method yields tighter wavelet-domain bounds of the system matrix, thus leading to improved convergence speeds. It is directly applicable to non-redundant wavelet bases, and we also adapt it for cases of redundant frames. It turns out that the simplest and most intuitive setting for the step sizes that ignores subband aliasing is often satisfactory in practice. We show that our methods can be used to advantage with reweighted least squares penalty functions as well as L1 penalties. We emphasize that the algorithms presented here are suitable for performing inverse filtering on very large datasets, including 3D data, since inversions are applied only to diagonal matrices and fast transforms are used to achieve all matrix-vector products.