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We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…
Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…
Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not…
This work provides a comprehensive overview of the fundamental concepts in continuum mechanics, focusing on the behaviour of materials under mechanical loads. It discusses the distinction between elastic and plastic, highlighting their…
Morphological development into evolutionary patterns under structural instability is ubiquitous in living systems and often of vital importance for engineering structures. Here we propose a data-driven approach to understand and predict…
Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how inter-cellular mechanical interactions may drive…
Generative models hold the promise of significantly expediting the materials design process when compared to traditional human-guided or rule-based methodologies. However, effectively generating high-quality periodic structures of materials…
We study a class of time evolution models that contain dissipation mech- anisms exhibited by geophysical materials during deformation: plasticity, viscous dissipation and fracture. We formally prove that they satisfy a Clausius-Duhem type…
Identifying concentrations of components from an observed mixture is a fundamental problem in signal processing. It has diverse applications in fields ranging from hyperspectral imaging to denoising biomedical sensors. This paper focuses on…
Biological cells are the prototypical example of active matter. Cells sense and respond to mechanical, chemical and electrical environmental stimuli with a range of behaviors, including dynamic changes in morphology and mechanical…
Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is…
We discuss the role coarse-grained models play in the investigation of the structure and thermodynamics of bilayer membranes, and we place them in the context of alternative approaches. Because they reduce the degrees of freedom and employ…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…
Capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects.…
The biomolecules in and around a living cell -- proteins, nucleic acids, lipids, carbohydrates -- continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given…
A fundamental assumption in our understanding of material rheology is that when microscopic deformations are reversible, the material responds elastically to external loads. Plasticity, i.e. dissipative and irreversible macroscopic changes…
This chapter summarizes several approaches combining theory, simulation and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane mediated…
Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically…
The fundamental understanding of how cells physically interact with each other and their environment is key to understanding their organisation in living tissues. Over the past decades several computational methods have been developed to…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…