1.

A model for acid-mediated tumour growth with nonlinear acid production term
- Holder, Andrew B.; Rodrigo, Marianito R.; Herrero, Miguel A.
This article considers a mathematical model for tumour growth based on an acid-mediated hypothesis, i.e. the assumption that tumour progression is facilitated by acidification of the region around the tumour-host interface. The resulting destruction of the normal tissue environment promotes tumour growth. We will derive and analyse a reaction–diffusion model for tumour progression that includes different aspects of pathological and healthy cell metabolism to check tumour growth. Our results can provide insights into the governing dynamics of invasive processes that may suggest possible intervention strategies, leading to the design of new and better experiments or treatments.

2.

Comparison of Modal Variables Using Multivariate Analysis
- Doria, Isabel; Sousa, Áurea; Bacelar-Nicolau, Helena; Le Calvé, Georges
Domiciliary palliative care satisfaction and quality were estimated by caregivers via ﬁve perception scales with partly ordered answering modalities. The perception scales were codiﬁed as symbolic modal variables and analyzed using two multivariate approaches based on complex (symbolic) data to compare modal variables. This study compares the outcomes of previous work by Doria (Representações euclidianas de dados: Uma abordagem para variáveis heterogéneas. Tese de doutoramento, Universidade de Lisboa, Lisboa, 2008), Doria et al. (Livro de Resumos da XI Conferencia Española de Biometria e Primer Encuentro Iberoamericano de Biometria (CEIB2007)101–102,2007) and Bacelar-Nicolau et al. (Revista Portuguesa de Filosoﬁa 66(2):427–460,2010). In particular,...

3.

Biometria florestal: modelos de crescimento e produção: anais.
- REUNIÃO TÉCNICA, 2013, Colombo.
Crescimento e produção florestal; Crescimento e produção das variáveis dendrométricas; Variáveis fundamentais nos modelos de produção; Métodos para estimativa da altura por meio da análise de tronco; Métodos para classificação de sítios florestais; Técnicas de predição e projeção do crescimento e produção como suporte para o manejo florestal; Modelos biomatemáticos e modelos implícitos de produção e crescimento; Modelos para povoamentos desbastados; Modelos para árvores individuais; Modelagem em florestas nativas; Taxa de corte sustentada em Floresta Ombrófila Densa.

4.

The mathematics of chemotaxis
- Herrero, Miguel A.
This chapter provides a description of some of the mathematical approaches that have been developed to account for quantitative and qualitative aspects of chemotaxis. This last is an important biological property, consisting in motion of cells induced by chemical substances, which is known to occur in a large number of situations, both homeostatic and pathological. Particular attention will be paid to the limits on a cell's capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slime mold Dictyostelium discoideum on the other.

5.

Reaction-diffusion systems: a mathematical biology approach
- Herrero, Miguel A.
This book is addressed at curricula in applied mathematics, bio-physics, bio-mathematics, and theoretical biology and medicine. It is proposed as an advanced textbook for graduate interdisciplinary courses having as a common point the interest in modelling and simulation of tumoural systems. The aim of this volume is to give both types of readers a common starting block, and complete knowledge of the mathematical and biological aspects of tumor growth. In the chapters contributed by an interdisciplinary team of leading researchers, this book addresses the entire modelling process, from phenomenological observations to simulation and validation, through the development of mathematical models...

6.

Bone formation: biological aspects and modelling problems
- Herrero, Miguel A.; López, J. M.
In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological
experimentation

7.

Lines and nets: models of filamentary structures
- Herrero, Miguel A.
We shall recall some reaction-difussion models which have been used to describe the growth of net-like structures, mainly in a biological context. In particular, a modified activator-inhibitor system proposed by Hans Meinhardt in 1976 will be considered, and some properties of their solutions will be analyzed

8.

A blow-up mechanism for a chemotaxis model
- Herrero, Miguel A.; Velázquez, J.J. L.
We consider the following nonlinear system of parabolic equations: (1) ut =Δu−χ∇(u∇v), Γvt =Δv+u−av for x∈B R, t>0. Here Γ,χ and a are positive constants and BR is a ball of radius R>0 in R2. At the boundary of BR, we impose homogeneous Neumann conditions, namely: (2) ∂u/∂n=∂v/∂n=0 for |x|=R, t>0.
Problem (1),(2) is a classical model to describe chemotaxis, i.e., the motion of organisms induced by high concentrations of a chemical that they secrete. In this paper we prove that there exist radial solutions of (1),(2) that develop a Dirac-delta type singularity in finite time, a feature known in...

9.

Asymptotic properties of reaction-diffusion systems modeling chemotaxis
- Herrero, Miguel A.
This paper examines a system first introduced by Keller and Segel in 1970 to model the tendency of slime molds to move towards higher concentrations of a chemical which they themselves secrete. The paper particularly addresses the question of blow-up or chemotactic collapse, i.e., the formation of single point aggregations of the cells. Results are discussed for 2 and 3 space dimensions. Asymptotic computations yield information on the manner of the blow-up.

10.

A mathematical model for the growth of elongated bones
- Fasano, A.; Herrero, Miguel A.; López, J. M.; Medina Reus, Elena
A mathematical model to describe the process of formation of bone tissue by replacement of cartilage tissue is presented and discussed. This model is based on an absorption-diffusion system which describes the interaction of two key signalling molecules. These molecules characterize the dynamics of the transition zone between the cartilage and the bone tissue. Some experimental data are needed to estimate some model parameters. We discuss
how our results are essentially unaffected by small variations, and in a particular case, not necessarily small variations in the experimental values.

11.

Modelo não isotérmico de um biorreator experimental
- Luvizetto, Débora Jung; Ferreira, Luciane da Silveira; Longhi, Luís Gustavo Soares; Rech, Rosane; Ayub, Marco Antônio Záchia; Secchi, Argimiro Resende
12.

The Role of the Delay Time in the Modeling of Biological Range Expansions
- Ortega-Cejas, Vicente; Fort, Joaquim; Méndez López, Vicenç
The time interval between successive migrations of biological species causes a delay time in the reaction-diffusion equations describing their space-time dynamics. This lowers the predicted speed of the waves of advance, as compared to classical models. It has been shown that this delay-time effect improves the modeling of human range expansions. Here, we demonstrate that it can also be important for other species. We present two new examples where the predictions of the time-delayed and the classical (Fisher) approaches are compared to experimental data. No free or adjustable parameters are used. We show that the importance of the delay effect...

13.

Linear stability analysis and metastable solutions for a phase-field model
- Jiménez Casas, Ángela; Rodríguez Bernal, Aníbal
We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable solutions that evolve very slowly in time.

14.

Models of aggregation in Dictyostelium discoideum: On the track of spiral waves
- Herrero, Miguel A.; Sastre, Leandro
This work is concerned with some aspects of the social life of the amoebae Dictyostelium discoideum (Dd). In particular, we shall focus on the early stages of the starvation-induced aggregation of Dd cells. Under such circumstances, amoebae are known to exchange a chemical messenger (cAMP) which acts as a signal to mediate their individual behaviour. This molecule is released from aggregation centres and advances through aggregation fields, first as circular waves and later on as spiral patterns. We shall recall below some of the basic features of this process, paying attention to the mathematical models that have been derived to...

15.

Biological optimization of tumor radiosurgery
- Cappuccio, Antonio; Herrero, Miguel A.; Nuñez, Luis
In tumor radiosurgery, a high dose of radiation is delivered in a single session. The question then naturally arises of selecting an irradiation strategy of high biological efficiency. In this study, the authors propose a mathematical framework to investigate the biological effects of heterogeneity and rate of dose delivery in radiosurgery. The authors simulate a target composed by proliferating and hypoxic tumor cells as well as by normal tissue. Treatment outcome is evaluated by a functional of the dose distribution that counts the LQ-surviving fractions of each cell type. Prescriptions on intensity, homogeneity, and duration of radiation delivery are incorporated...

16.

Tumour radiotherapy and its mathematical modelling
- Cappuccio, Antonio; Herrero, Miguel A.; Nuñez, Luis
Radiotherapy consists in the delivery of ionizing radiation with curative goals. It represents a major modality for treating solid malignancies in any anatomical site. It requires extremely precise dosimetry and delivery to control the lesion while sparing the surrounding normal tissue. This is currently achieved by means of a combination of techniques. Among these, mathematical modelling may contribute to design improved treatment plans. In the present work, we provide an overview of the basic features of radiotherapy. Thereafter, we describe concrete examples of how mathematical modelling has so far been employed to simulate radiotherapy and to theoretically explore alternative strategies....

17.

Through a glass, darkly: Biology seen from mathematics Comment on "Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives" by N. Bellomo and B. Carbonaro
- Herrero, Miguel A.
18.

On the growth of filamentary structures in planar media
- Andreucci, D.; Herrero, Miguel A.; Velázquez, J.J. L.
We analyse a mathematical model for the growth of thin filaments into a two dimensional medium. More exactly, we focus on a certain reaction/diffusion system, describing the interaction between three chemicals (an activator, an inhibitor and a growth factor), and including a fourth cell variable characterising irreversible incorporation to a filament. Such a model has been shown numerically to generate structures shaped like nets. We perform an asymptotical analysis of the behaviour of solutions, in the case when the system has parameters very large and very small, thereby allowing the onset of different time and space scales. In particular, we...

19.

Singularity patterns in a chemotaxis model
- Herrero, Miguel A.; Velázquez, J.J. L.
The authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time. Such a finite-time blow-up of solutions implies chemotactic collapse, namely, concentration of species to form sporae. The model studied is the limiting case of a basic chemotactic model when diffusion of the chemical approaches infinity, which has the form ut=Δu−χ(uv), 0=Δv+(u−1), on ΩR2, where Ω is an open disc with no-flux (homogeneous Neumann) boundary conditions. The initial conditions are continuous functions u(x,0)=u0(x)≥0, v(x,0)=v0(x)≥0 for xΩ. Under these conditions, the...

20.

Modeling And Analysis Of A Marine Bacteriophage Infection With Latency Period
- Edoardo Beretta; Istituto Di Biomatematica; Yang Kuang
A mathematical model for the marine bacteriophage infection with explicit latency period is proposed as a system of discrete time delay differential equations and its important mathematical features are analyzed. Let i represent the death constant rate in the class of infected bacteria during latency period "T ." Only the fraction "exp(; i T )" of the bacteria infected at "t ;T " will release by lysis at time "t""b" new phages, where b 2 (1# +1)iscalled "virus replication factor." Hence, if i ? 0, the main parameter on whichthe dynamics of the model depends on is "b exp(; i...