Initial/boundary-value problems of tumor growth within a host tissue

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori nonnegativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case.Comment: 30 pages, 5 figure

Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

A multiphase multiscale model for nutrient limited tissue growth

In this work, an effective macroscale description is derived for the growth of tissue on a porous scaffold. A multiphase model is employed to describe the tissue dynamics; linearisation to facilitate a multiple-scale homogenisation provides an effective macroscale description, which incorporates dependence on the microscale structure and dynamics. In particular, the resulting description admits both interstitial growth and active cell motion. This model comprises Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. These are coupled to underlying Stokes-type cell problems that provide permeability tensors, with multiscale dependence incorporating active cell motion, with which to parameterise the macroscale flow. A subset of solutions are illustrated by numerical simulations

Severe plastic deformation for producing superfunctional ultrafine-grained and heterostructured materials: An interdisciplinary review

Ultrafine-grained and heterostructured materials are currently of high interest due to their superior mechanical and functional properties. Severe plastic deformation (SPD) is one of the most effective methods to produce such materials with unique microstructure-property relationships. In this review paper, after summarizing the recent progress in developing various SPD methods for processing bulk, surface and powder of materials, the main structural and microstructural features of SPD-processed materials are explained including lattice defects, grain boundaries and phase transformations. The properties and potential applications of SPD-processed materials are then reviewed in detail including tensile properties, creep, superplasticity, hydrogen embrittlement resistance, electrical conductivity, magnetic properties, optical properties, solar energy harvesting, photocatalysis, electrocatalysis, hydrolysis, hydrogen storage, hydrogen production, CO2 conversion, corrosion resistance and biocompatibility. It is shown that achieving such properties is not limited to pure metals and conventional metallic alloys, and a wide range of materials are currently processed by SPD, including high-entropy alloys, glasses, semiconductors, ceramics and polymers. It is particularly emphasized that SPD has moved from a simple metal processing tool to a powerful means for the discovery and synthesis of new superfunctional metallic and nonmetallic materials. The article ends by declaring that the borders of SPD have been extended from materials science and it has become an interdisciplinary tool to address scientific questions such as the mechanisms of geological and astronomical phenomena and the origin of life

Multiphase models of tumour growth

Mixture theory has been applied to describe the mechanics of biological tis-sues since the sixties. Most of the work was focused on the behaviour of articular cartilages [HHLM89, KLM90, LHM90, MHL84, MKLA80, ML79, MRS90], but applications can be found to many soft tissues, e.g., brai

Analysis of stress-strain state of plates under impact loading

The problem concerning the stress-strain state of a plate under impact load with various intensity levels of collision momentum applying finite-element method was considered. The problem concerning transversal impact of a body in form of a mass point or a finite body to the sheet-formed structures of following type: a plate, a plate strengthened by ribs, a plate with damages was considered. Problem design diagram, design diagram of plate, fields of deflection intensities distribution w for plate central surface, stress distribution fields of the plate based layer, stress distribution fields of the plate based layer equivalent stresses sigma eq =f(m), relations for sigma eq = f(m) and w = f(m) at variation of impact initial velocity, impulse form of view, deflection and equivalent stress sigma eq intensity distribution diagrams in cross-section Kn depending on view form of impulse, the diagram of plate's deflections, the stress field sigma eq of the plate caused by impact body of finite dimensions, the field of deflection intensity distributions w for damage plate, the field of equivalent stress intensity distributions sigma eq for damage plate, the structure diagram of plate with stringers, the deflection field of plate with stringers, diagrams of equivalent stresses sigma eq of plate with stringers in central cross-section along axis x at damage deeps are presented in the paper

Modeling the influence of the Chelyabinsk meteorite's bow shock wave on the Earth's surface

The influence of the Chelyabinsk meteorite’s bow shock wave on the Earth’s surface is modeled. For solving the problem, a 3D statement is considered for its gas-dynamic and seismic parts. The determining equations of a gas-dynamic model and a seismic model are Euler equations with respect to the radiation heat exchange and the equations of linear elasticity theory, respectively. Two parts of the problem are matched by the direct mechanism of the disturbance transmission. A model seismic signal is compared with the real data. Modeling a seismic effect makes it possible to specify the estimate of the typical parameters of the phenomenon (height of the explosion, and the density and characteristic sizes of the meteorite)