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Plasticity modelling has long been based on phenomenological models based on ad-hoc assuption of constitutive relations, which are then fitted to limited data. Other work is based on the consideration of physical mechanisms which seek to…
The outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A…
The simplest patterns of qualitative changes on the configurations of lines of principal curvature} around umbilic points on surfaces whose immersions into $\mathbb R^3$ depend smoothly on a real parameter (codimension one umbilic…
Medical imaging is crucial in modern clinics to guide the diagnosis and treatment of diseases. Medical image reconstruction is one of the most fundamental and important components of medical imaging, whose major objective is to acquire…
Many biological phenomena are inherently multiscale, i.e. they are characterized by interactions involving different spatial and temporal scales simultaneously. Though several approaches have been proposed to provide "multilayer" models,…
In this paper we develop a lattice-based computational model focused on bone resorption by osteoclasts in a single cortical basic multicellular unit (BMU). Our model takes into account the interaction of osteoclasts with the bone matrix,…
Recurrence plot based methods are highly efficient and widely accepted tools for the investigation of time series or one-dimensional data. We present an extension of the recurrence plots and their quantifications in order to study recurrent…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…
This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period…
Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of…
The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern…
The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the…
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…
In prokaryotic genomes the number of transcriptional regulators is known to quadratically scale with the total number of protein-coding genes. Toolbox model was recently proposed to explain this scaling for metabolic enzymes and their…
Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
Regulatory networks consist of interacting molecules with a high degree of mutual chemical specificity. How can these molecules evolve when their function depends on maintenance of interactions with cognate partners and simultaneous…
Computational models provide crucial insights into complex biological processes such as cancer evolution, but their mechanistic nature often makes them nonlinear and parameter-rich, complicating calibration. We systematically evaluate…
Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…