Generation of Random Textures

Two models are presented for the generation of isotropic textures.The underlying constituents of these textures are cells of nearlyconstant colour. Textures generated by the first model haveinteresting Markov properties. The second model produces patternsin the manner of a natural cell growth process. Both modelsshould prove useful in perception studies.     

A Porous Media Model for the Description of Adaptive Bone Remodelling

Bones are strong and lightweight structures, which mainly consist of extracellular bone matrix. The bone remodelling is a process of resorption followed by replacement of the bone matrix with small changes in shape, which allow the bones to adapt according to the local loading situation. In the context of the Theory of Porous Media (TPM), a consistent model of bone tissue is introduced, which is able to describe the local accretion and reduction of the extracellular bone matrix. To this end, the bone is treated as an aggregate of two immiscible constituents. In this biphasic macroscopic model, the aggregate consists of the extracellular bone matrix and cells summarised to a solid phase and an interstitial fluid phase comprising nutrients, metabolites and bone precursors. The addition and removal of bone matrix is described by a mass exchange between the constituents, which depends upon the local strain of the material. Additionally, the growth energy is introduced as a non-mechanical quantity, which measures the average amount of chemical energy available for cell metabolism [1, 2], and thus, controls the growth process. The presented numerical example illustrates the fundamental effects of bone remodelling under varying boundary conditions. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling hematopoiesis in health and disease

Hematopoiesis is the process responsible for maintaining the number of circulating blood cells that are undergoing continuous turnover. At the root of this process are the hematopoietic stem cells (HSC), that replicate slowly to self-renew and give rise to progeny cells that proceed along the path of differentiation. The process is complex, with the cells responding to a wide variety of cytokines and growth factors. We discuss the mathematics of hematopoiesis based on stochastic cell behavior. Multiple compartments are introduced to keep track of each cell division process and increasing differentiation. The same mathematical model that describes normal hematopoiesis across mammals as a stable steady state of a hierarchical stochastic process is also used to understand the detailed dynamics of various disorders both in humans and in animal models. The microecology of the multitude of cell lineages that constitute what we call troubled hematopoiesis evolves in time under mutation and selection, the paradigmatic components of Darwinian evolution. Thus, the present approach provides a novel perspective for looking at cancer progression and cure.     

A Porous Media Model to Describe the Behaviour of Brain Tissue

The human brain is a very sensitive organ. Even small changes in the cranium cavity can cause life–threatening effects. In case of medical intervention, biomechanics can assist the therapy decisions by simulating the physical behaviour of brain tissue, e.g., the coupled interaction of the fluid motion and the deformation of the brain tissue. In the context of the Theory of Porous Media (TPM), a convenient model of the brain is introduced, which is able to simulate essential mechanical effects in the porous structure of the brain material. The fluid–saturated brain can be treated as an immiscible binary mixture of constituents. In this macroscopic biphasic model, the mixture consists of a solid phase (brain tissue) and a fluid phase (interstitial fluid or blood plasma). Both constituents are assumed to be materially incompressible. The resulting set of coupled partial differential equations is then spatially discretised using mixed finite elements with a backward Euler time integration. Numerical examples are presented illustrating the fundamental effects on the brain tissue under heart–rate dependent pulsative pressure variations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and remodelling of biological tissue in the framework of continuum biomechanics

A biological tissue in general is formed by cells, extracellular matrix (ECM) and fluids. Consequently, its overall material behaviour results from its components and their interaction among each other. Furthermore, in case of living tissues, the material properties do not remain constant but naturally change due to adaptation processes or diseases. In the context of the Theory of Porous Media (TPM), a continuum-mechanical model is introduced to describe the complex fluid-structure interaction in biological tissue on a macroscopic scale. The tissue is treated as an aggregate of two immiscible constituents, where the cells and the ECM are summarised to a solid phase, whereas the fluid phase represents the extracellular and interstitial liquids as well as necrotic debris and cell or matrix precursors in solution. The growth and remodelling processes are described by a distinct mass exchange between the fluid and solid phase, which also results in a change of the constituent material behaviour. To furthermore guarantee the compliance with the entropy principle, the growth energy is introduced as an additional quantity. It measures the average of chemical energy available for cell metabolism, and thus, controls the growth and remodelling processes. To set an example, the presented model is applied for the simulation of the early stages of avascular tumour growth in the framework of the finite element method (FEM). (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of cell populations interaction

Regenerative medicine and cell therapy provide great hopes for the use of adult and stem cells. The latter are far less present in tissue than the former and must be expanded using cell culture. Stem cells culture requires the conservation of their proliferation and self-renewal capabilities. Still, the complex interaction between cell populations, for example in primary cell cultures, are not well-known and may account for part of the variability of such cultures. In order to represent and understand the evolution of cultured stem cells, we present here a mathematical model of cell proliferation and differentiation. Based on the formalism of cellular automata, this model simulates the evolution of several cell classes (which may represent either different levels of differentiation or different cell types) in an environment modeling the growth medium. We model the cell cycle as on the one hand a quiescence phase during which a cell rests, and on the other hand a division phase during which the cell starts the division process. In order to represent cell–cell interaction, the transition probability between those phases depends on the local composition of the growth medium depending itself on neighboring cells. An interaction between cellular populations is represented by a quantitative parameter which has a direct impact on cellular proliferation. Differentiation results in a change of the cell class and depends on the biological model studied : it may result from an asymmetric division or be a consequence of the local composition of the growth medium. This mathematical model aims at a better understanding of the interactions between cell populations in a culture. By defining constraints on the potential or the type of the cells at the end of a culture, it will then be possible to find optimal experimental conditions for cell production.     

Continuum modeling of the swelling behavior of concrete when modified through superabsorbent polymers

The main purpose of our investigation is to model the physical solidification process of a concrete mixture, involving water absorbing constituents, i. e. Superabsorbent Polymers (SAP). In order to model the chemo-mechanical swelling process, the system is described within the framework of the Theory of Porous Media (TPM). The swelling process is accounted for by including mass exchange terms between free and absorbed water. The chemo-mechanical driving forces are deduced from non-equilibrium thermodynamics while constitutive relations are motivated by appropriate micro-models of the swelling process. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational and experimental analysis of wound healing processes

Wound healing in epidermis is a complex physiological process in which new cells are created to repair the damaged tissue. The timing of cell division and growth mechanisms in wound healing are influenced by biological, mechanical and medical factors. In this work we aim to provide a numerical model based on the observations realised in in-vitro experiments for the understanding of wound healing. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some selection criteria for nested binary choice models: a comparative study

This paper deals with the problem of choosing the optimum criterion to select the best of a set of nested binary choice models. Special attention is given to the procedures which are derived in a decision-theoretic framework, called model selection criteria (MSC). We propose a new criterion, which we call C ₂, whose theoretical behaviour is compared with that of the AIC and SBIC criteria. The result of the theoretical study shows that the SBIC is the best criterion whatever the situation we consider, while the AIC and C ₂ are only adequate in some cases. The Monte Carlo experiment that is carried out corroborates the theoretical results and adds others: finite sample behaviour and robustness to changes in some aspects of the data generating process. The classical hypothesis testing procedures LR and LM are included and compared with the three criteria of the MSC category. The authors wish to thank the financial support provided by the Spanish Department of Education under project BEC 2003-01757.     

Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions

A numerical technique based on the spectral method is presented for the solution of nonlinear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions (RBFs) with the differentiation process (DRBF), using zeros of the shifted Legendre polynomial as the collocation points. Different applications of RBFs are used for this purpose. The integral involved in the formulation of the problems are approximated based on Legendre-Gauss-Lobatto integration rule. The results of numerical experiments are compared with the analytical solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme.     

Nonparametric estimators of the survival function with twice censored data

Patilea and Rolin (Ann Stat 34(2):925–938, 2006) proposed a product-limit estimator of the survival function for twice censored data. In this article, based on a modified self-consistent (MSC) approach, we propose an alternative estimator, the MSC estimator. The asymptotic properties of the MSC estimator are derived. A simulation study is conducted to compare the performance between the two estimators. Simulation results indicate that the MSC estimator outperforms the product-limit estimator and its advantage over the product-limit estimator can be very significant when right censoring is heavy.     

Transport of Mass,Momentum and Energy through Periodic Open Cell Metal Foams Applied in Catalysis

An ODE model to predict the temperature field of periodic open cell metal foams applied in catalysis as carrier structures is presented. The catalytic and highly endothermic reaction takes place in a porous layer which surround the struts of the foam and releases gas from a fluid. The one-dimensional model includes dependencies of the foam structure (strut radius, shape of strut), process conditions (surrounding velocity, surrounding fluid: liquid and/or gas), chemical conditions (reaction enthalpy, activation energy) and material parameters (thermal conductivity, density, viscosity). This makes it possible to estimate optimal parameters, that are able to provide sufficient heat to the reaction. The advantage of this model is the substantial time saving in contrary to three dimensional finite volume simulations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gyroscopic forces in automotive design

The resonance frequencies (eigenfrequencies) of a car may dependsignificantly on the gyroscopic forces resulting from the steeringof the rotating wheels. For example, in the investigated carmodel, the first eigenfrequency decreases considerably withincreasing velocity, and only by taking the gyroscopic forcesinto account do the measured and calculated results match. Asa consequence, it is of great importance to have the gyroscopicforces incorporated in the respective car model. In this paper,for a wheel model with six degrees of freedom (6 DOF), the equationsof motion and eigenvalue equation are set up, where the gyroscopicforces are taken into account exactly. Then, it is shown usingadditional concepts how gyroscopic forces can be incorporatedin the MSC/NASTRAN finite-element package (FE package). Moreover,for a large-scale FE vehicle model, frequency-response calculationswith unbalanced excitation are carried out which exhibit gyroscopiceffects. The results for both the 6-DOF wheel model and theFE vehicle model are illustrated graphically. Among other things,this work has caused the MacNeal Schwendler company to extendthe FE program MSC/NASTRAN in cooperation with Mercedes-Benzso that gyroscopic effects can now be put in directly.     

On heat exchange and heat transport in a geothermal plant

In the long term, the only way to address the challenging task of power supply, is to make renewable energy sources economically attractive and to use them efficiently. In particular, geothermal energy is promising to take over the base load of the power supply. Nevertheless, a lot of investigations needs to be made to use the almost inexhaustible source of thermal energy in the interior of the earth effectively. Starting from the initially isothermal state, a cold fluid is injected through a borehole into a rock. By the rising pressure gradient, the fluid flows through the porous rock and escapes through another borehole. While the fluid passes the micro cracks in the hot rock, the water is heated by the rock due to the heat exchange between the constituents. This process is simulated based on the Theory of Porous Media (TPM). The presented modelling approach of the heat transport and the flow processes in a fully saturated subsurface includes two non-isothermal constituents: an elastically deformable, materially incompressible solid skeleton where thermal expansion is neglected, and a viscous, materially incompressible fluid constituent. To solve the initial-boundary-value problem, the governing primary variables of the coupled model are spatially approximated by mixed finite elements, and the time-discretisation is carried out by an implicit Euler time-integration scheme. The aim of the presented numerical simulations is to study the heat transport and to evaluate the efficiency by varying flow rates. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of stem cells using mathematical models of multistage cell lineages

Stem cells dynamics is an important field of research with promising clinical impacts. Due to the revolutionary new technologies of biological data collection, an enormous amount of information on specific factors and genes responsible for cell differentiation is available. However, the mechanisms controlling stem cell self-renewal, maintenance and differentiation are still poorly understood and there exists no general characterization of stem cells based on observable cell properties. We address these problems with the help of mathematical models. Stem cells are described as the cell type that is most responsive to certain environmental signals. This results in a dynamic characterization of stemness that depends on environmental conditions and is not necessarily linked to a unique cell population.     

Continuum-Mechanical Analysis of Human Brain Tissue

The effective treatment of brain diseases, such as malignant brain tumours, is generally constricted by the controlled contribution of therapeutic agents. Novel brain tumour therapy proceeds from a direct infusion of the drug into the extra-vascular space of the nervous brain tissue (convection-enhanced delivery). This is carried out using catheter to bypass the blood-brain barrier, which effectively separates brain tissue from the intra-vascular space and hence hamper drug delivery through the bloodstream. The dilation of the target tissue, as response to the local pressure increase, initiates interstitial fluid flow and, thus, the distribution of the chemical agents. An adequate constitutive model of the complex tissue aggregate in the framework of the Theory of Porous Media is essential in order to assist modern clinical application via numerical simulations. The presented model consists of an elastically deformable solid skeleton, provided by the tissue cells, permeated by two viscous, materially incompressible pore-liquid phases, interstitial fluid and blood plasma. Both liquids are mobile within the solid skeleton and separated from each other. With regard to simulate a drug infusion process in the extra-vascular space, the interstitial fluid is treated as a solution of a liquid solvent and a dissolved therapeutic solute. The constitutive assumptions for the involved constituents are adjusted in order to describe the physical behaviour of human brain tissue. The presented numerical examples illustrate the fundamental effects during an infusion process. Therefore, the resulting set of coupled partial differential equations is spatially discretised using hexahedral mixed finite elements with an implicit (backward) Euler time integration scheme to solve the considered problem in a monolithic manner for the primary variables. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)