Related papers: Biological remodelling: Stationary energy, configu…
Remodelling of biological tissue, due to changes in microstructure, is treated in the continuum mechanical setting. Microstructural change is expressed as an evolution of the reference configuration. This evolution is expressed as a…
We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or…
Bone remodeling involves the coordinated removal of bone by osteoclasts and addition of bone by osteoblasts, a process that is modulated by the prevailing mechanical environment. In this paper a fully coupled model of bone remodeling is…
In this paper we present a large-deformation formulation of the mechanics of remodeling. Remodeling is anelasticity with an internal constraint -- material evolutions that are mass and volume preserving. In this special class of material…
Bone remodeling is a complex process involving cell-cell interactions, biochemical signaling and mechanical stimuli. Early models of the biological aspects of remodeling were non-spatial and focused on the local dynamics at a fixed location…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly…
In this review, we discuss modularity and hierarchy in biological systems. We review examples from protein structure, genetics, and biological networks of modular partitioning of the geometry of biological space. We review theories to…
Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the…
A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole.…
The concept of evolutionary development of structures constituted a \emph{real} revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system. The investigation of…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…
The multifarious internal workings of organisms are difficult to reconcile with a single feature defining a state of being alive. Indeed, definitions of life rely on emergent properties (growth, capacity to evolve, agency) only symptomatic…
We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modelling to systematically analyse a large class of models of bone remodeling. Our analysis…
This paper introduces a physically-intuitive notion of inter-area dynamics in systems comprising multiple interconnected energy conversion modules. The idea builds on an earlier general approach of setting their structural properties by…