# Miguel A HerreroComplutense University of Madrid | UCM · Departamento de Matemática Aplicada

Miguel A Herrero

Ph.D

## About

136

Publications

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## Publications

Publications (136)

The protection induced by vaccines against infectious diseases such as malaria, dengue or hepatitis relies on a the creation of immune memory by T cells, key components of the human immune system. The induction of a strong T cell response leading to long lasting memory can be improved by using prime-boost (PB) vaccines, which consist in successive...

One of the most remarkable aspects of human homoeostasis is bone remodelling. This term denotes the continuous renewal of bone that takes place at a microscopic scale and ensures that our skeleton preserves its full mechanical compliance during our lives. We propose here that a renewal process of this type can be represented at an algorithmic level...

The human skeleton undergoes constant remodeling throughout the lifetime. Processes occurring on microscopic and molecular scales degrade bone and replace it with new, fully functional tissue. Multiple bone remodeling events occur simultaneously, continuously and independently throughout the body, so that the entire skeleton is completely renewed a...

One sample of the simulation (from initial OCY apoptosis to final equilibrium and renewed bone).
(PDF)

Details of computer simulations of the model of BMU operation during bone remodeling.
(PDF)

Human skeleton undergoes constant remodeling during the whole life. By means of such process, which occurs at a microscopic scale, worn out bone is replaced by new, fully functional one. Multiple bone remodeling events occur simultaneously and independently throughout the body, so the whole skeleton is completely renewed about every ten years.
Bone...

Vaccination with radiation-attenuated sporozoites has been shown to induce CD8+ T cell-mediated protection against pre-erythrocytic stages of malaria. Empirical evidence suggests that successive inoculations often improve the efficacy of this type of vaccines. An initial dose (prime) triggers a specific cellular response, and subsequent inoculation...

Brief outline of the main assumptions of the models used in this article and their hybrid automaton representation.
A series of four tables is included with the raw experimental data shown in Fig 6.
(PDF)

Unlike other cell types, T cells do not form spatially arranged tissues, but move independently throughout the body. Accordingly, the number of T cells in the organism does not depend on physical constraints imposed by the shape or size of specific organs. Instead, it is determined by competition for interleukins. From the perspective of classical...

The first obvious sign of bilateral symmetry in mammalian and avian embryos is the appearance of the primitive streak in the future posterior region of a radially symmetric disc. The primitive streak marks the midline of the future embryo. The mechanisms responsible for positioning the primitive streak remain largely unknown. Here we combine experi...

Recently three branching modes were characterized during the formation of the lung in mice. These modes are highly stereotyped and correspond to domain formation, planar bifurcation and three dimensional branching respectively. At the same time it is proved that although genetic control mechanisms are presumably related to the selection of any of t...

Background
The choice of any radiotherapy treatment plan is usually made after the evaluation of a few preliminary isodose distributions obtained from different beam configurations. Despite considerable advances in planning techniques, such final decision remains a challenging task that would greatly benefit from efficient and reliable assessment t...

Author Summary
Controlling tumor growth remains a major medical challenge. Current clinical therapies focus on strategies to reduce tumor cell proliferation. However, during tumor progression, tumor cells may switch between proliferative and migratory behaviors, thereby allowing adaptation to microenvironmental changes that result in variations in...

This chapter presents some speculations focused on the design of a System Sociology approach. A key feature of that approach consists in the modeling of social and economical systems viewed as living complex systems subject to dynamical evolution. At the technical level, the mathematical techniques proposed to the modeling of social and economic sy...

In the following the reader will find a short description of some issues related to the modeling, analysis and simulation of large populations of living systems, a research field which is currently deserving a considerable interest, and that has been explored during the first 10 editions of the BIOMAT Summer School at Granada.

Adaptive immune responses depend on the capacity of T cells to target specific antigens. As similar antigens can be expressed by pathogens and host cells, the question naturally arises of how can T cells discriminate friends from foes. In this work, we suggest that T cells tolerate cells whose proliferation rates remain below a permitted threshold....

In this work we will discuss on the contribution made by Alan Turing (1912-1954) towards a mathematical foundation of Developmental Biology. To do so, we will briefly review the approach he laid out in his only published work on the subject, and then describe the impact of his work on Mathematics on one hand, and on Biology on the other.En este art...

This work is concerned with the sequence of events taking place during the first stages of bone fracture healing, from bone breakup until the formation of early fibrous callus (EFC). The latter provides a scaffold over which subsequent remodeling processes will eventually result in successful bone repair. Specifically, some mathematical models are...

Tumor cells develop different features to adapt to environmental conditions.
A prominent example is the ability of tumor cells to switch between migratory
and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is
however unclear how this particular phenotypic plasticity affects overall tumor
growth. To address this problem, we...

In this work, we first propose a mathematical model to select radiation dose distributions as solutions (minimizers) of suitable variational problems, under the assumption that key radiobiological parameters for tumors and organs at risk involved are known. Second, by analyzing the dependence of such solutions on the parameters involved, we then di...

Tumor heterogeneity is widely considered to be a determinant factor in tumor progression and in particular in its recurrence after therapy. Unfortunately, current medical techniques are unable to deduce clinically relevant information about tumor heterogeneity by means of non-invasive methods. As a consequence, when radiotherapy is used as a treatm...

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–diffu...

Vascular endothelial growth factor (VEGF) is a central regulator of blood vessel morphogenesis, although its role in patterning of endothelial cells into vascular networks is not fully understood. It has been suggested that binding of soluble VEGF to extracellular matrix components causes spatially restricted cues that guide endothelial cells into...

This paper deals with the modeling of social competition, possibly resulting
in the onset of extreme conflicts. More precisely, we discuss models describing
the interplay between individual competition for wealth distribution that, when
coupled with political stances coming from support or opposition to a
government, may give rise to strongly self-...

Radiotherapy is an important clinical tool to fight malignancies. To do so, a key point consists in selecting a suitable radiation dose that could achieve tumour control without inducing significant damage to surrounding healthy tissues. In spite of recent significant advances, any radiotherapy planning in use relies principally on experience-based...

In this work we present a comprehensive account of our current knowledge on vascular morphogenesis, both from a biological and a mathematical point of view. To this end, we first describe the basic steps in the known mechanisms of blood vessel morphogenesis, whose structure, function and unfolding properties are examined. We then provide a wide, al...

To this day, computer models for stromatolite formation have made substantial use of the Kardar-Parisi-Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites...

During embryonic vasculogenesis, endothelial precursor cells of mesodermal origin known as angioblasts assemble into a characteristic network pattern. Although a considerable amount of markers and signals involved in this process have been identified, the mechanisms underlying the coalescence of angioblasts into this reticular pattern remain unclea...

Criminals are common to all societies. To fight against them the community takes different security measures as, for example, to bring about a police. Thus, crime causes a depletion of the common wealth not only by criminal acts but also because the cost of hiring a police force. In this paper, we present a mathematical model of a criminal-prone se...

Human societies are formed by different socio-economical classes which are characterized by their contribution to, and their share of, the common wealth available. Cheaters, defined as those individuals that do not contribute to the common wealth but benefit from it, have always existed, and are likely to be present in all societies in the foreseea...

In this work a mathematical model for the interaction of two key signalling molecules in rat tibia ossification is presented and discussed. The molecules under consideration are Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHrP). These are known to be major agents in the dynamics of the so-called growth plate, where transition fr...

A mathematical model for the formation of microaggregates (microthrombi) of fibrin polymers in blood flow is considered. It
is assumed that the former are induced by an external source (which may be of inflammatory or tumor nature) located in a tissue
near the vessel. In either case, specific agents (e.g. cytokines) are emitted from that pathologic...

A mathematical model to describe the process of formation of bone tissue by replace-ment 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...

In this work a mathematical model for blood coagulation induced by an activator source is presented. Blood coagulation is viewed as a process resulting in fibrin polymerization, which is considered as the first step towards thrombi formation. We derive and study a system for the first moments of the polymer concentrations and the activating variabl...

This work is concerned with a reaction-diffusion system that has been proposed as a model to describe acid-mediated cancer invasion. More precisely, we consider the properties of travelling waves that can be supported by such a system, and show that a rich variety of wave propagation dynamics, both fast and slow, is compatible with the model. In pa...

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 aut...

This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y . Moreover, Z can also be thought of as a predator of X, since this last po...

Tumour growth can be described in terms of mathematical models from different points of view due to its multiscale nature. Dynamic scaling is a heuristic discipline that exploits the geometrical features of growing fronts using different concepts from the theory of stochastic processes and fractal geometry. This work is concerned with some problems...

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...

The effect of the stirring rate on the crystallization of sodium chlorate was studied in more than 200 experiments using a set-up that allows to perform sets of 20 simultaneous experiments. The crystallization conditions were those that according to previous results lead to only one of both L and D enantiomorphic forms under stirring. The probabili...

This paper presents an asymptotic theory for a large class of Boltzmann-type equations suitable to model the evolution of multicellular systems in biology. The mathematical approach described herein shows how various types of diffusion phenomena, linear and nonlinear, can be obtained in suitable asymptotic limits. Time scaling related to cell movem...

This work deals with the linear wave equation considered in the whole plane ℝ 2 except for a rectilinear moving slit, represented by a curve Γ(t)=(x 1 ,0):-∞<x 1 <λ(t) with t≥0· Along Γ(t), either homogeneous Dirichlet or Neumann boundary conditions are imposed. We discuss existence and uniqueness for these problems, and derive explicit representat...

This work is concerned with a model which has been proposed to describe the growth of solid tumors. More precisely, the model under consideration provides a procedure to extract information about the growth dynamics from the analysis of the geometrical properties of the interface tumor-host tissue. In particular, it is suggested that the tumor boun...

This work is concerned with some aspects of the social life of the amoebae Dictyostelium discoideum (Dd). In particular, we 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. Thi...

We shortly review some classical models of aggregate formation from their elementary monomeric components. Particular attention
is paid to the role played by explicit solutions in the overall evolution of the theory, for which some relevant results and
open questions are stressed.

This work deals with the linear wave equation considered in the whole plane R 2 \mathbb {R}^{2} except for a rectilinear moving slit, represented by a curve Γ ( t ) = { ( x 1 , 0 ) : − ∞ > x 1 > λ ( t ) } \Gamma \left ( t\right ) =\left \{ \left ( x_{1},0\right ) :-\infty >x_{1}>\lambda \left ( t\right ) \right \} with t ≥ 0. t\geq 0. Along Γ ( t )...

In this paper we consider some systems of ordinary differential equations which are related to coagulation-fragmentation processes. In particular, we obtain explicit solutions {ck(t)} of such systems which involve certain coefficients obtained by solving a suitable algebraic recurrence relation. The coefficients are derived in two relevant cases: t...

INTRODUCCIÓN Las líneas que siguen presentan una reflexión acerca de la relación entre las Matemáticas y la Biología. Con frecuencia ambas ciencias aparecen como polos opuestos del pensamiento humano: implacablemente rigurosa la primera, interesada en todo tipo de mutación y variabilidad la segunda. Al igual que tantos estudiosos de ayer y de hoy,...

We consider an infinite system of reaction–diffusion equations that models aggregation of particles. Under suitable assumptions on the diffusion coefficients and aggregation rates, we show that this system can be reduced to a scalar equation, for which an explicit self-similar solution is obtained. In addition, pointwise bounds for the solutions of...

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...

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 filame...

Consider a crack propagating in a plane according to a loading that
results in anti-plane shear deformation. We show here that if the crack
path consists of two straight segments making an angle φ = 0 at
their junction, examples can be provided for which the value of the
stress-intensity factor (SIF) actually depends on the previous history
of the...

We consider here the homogeneous Dirichlet problem for the equation
\( u_t = u\Delta u - \gamma |\nabla u|^2 \quad \mathrm{with} \quad
\gamma \in R, u \geq 0 \)
, in a noncylindrical domain in space-time given by
\( |x| \leq R(t) = (T - t)^p, \quad \mathrm{with} \quad p > 0 \). By means of matched asymptotic expansion techniques
we describe the asy...

We shall briefly review some early nucleation models, and then examine some aspects of the subsequent evolution of their solutions. Such situation is characterised by the onset of comparatively large clusters that can diffuse into the medium and interact among themselves. We next discuss some situations where the aggregates being formed, whose actu...

We consider here the radial Stefan problem with Gibbs–Thomson law, which is a classical model describing growth or melting of a spherical crystal in a surrounding liquid. We shall specialize to the cases of two and three space dimensions and discuss the asymptotic behaviour of a melting crystal near its dissolution time t* > 0. We prove here that,...

We consider problem (1.1), (1.2) below. Using formal arguments based on matched asymp- totic expansion techniques, we give a detailed description of radially symmetric, sign-changing solutions, which blow up at x = 0 and t = T < 1, for space dimension N = 3,4,5,6. These solutions exhibit fast blow up, that is, they satisfy: limt"T(T ¡ t) 1 p¡1u(0,t...

This paper deals with the one-phase, undercooled Stefan problem, in space dimension N=2. We show herein that planar, one-dimensional blow-up behaviours corresponding to the undercooling parameter Δ=1 are unstable with respect to small, transversal perturbations. The solutions thus produced are shown to generically generate cusps in finite time, whe...

We consider an infinite system of reaction–diffusion equations which describes the dynamics of cluster growth, and show that there are solutions which exist for all times and exhibit a sol–gel transition in a finite time. The manner in which such transition occurs is discussed, and a gelation profile is derived.

We discuss in the sequel on the aggregation properties of some systems of nonlinear parabolic equations which have been extensively used as models for chemotaxis. In particular, several blow-up mechanisms are described, and the corresponding singularity patterns are discussed.

We study in this paper the asymptotic behaviour of solutions of a nonlinear Fokker–Plank equation. Such an equation describes the evolution of radiation for a gas of photons, which interacts with electrons by means of Compton scattering and Bremsstrahlung radiation.Assuming that a suitable adimensional parameter ε (which measures the strength of th...

We consider the following system:
which has been used as a model for various phenomena, including motion of species by chemotaxis and equilibrium of self-attracting clusters. We show that, in space dimension N = 3, (S) possess radial solutions that blow-up in a finite time. The asymptotic behaviour of such solutions is analysed in detail. In parti...

This work deals with the problem consisting in the equation (1) ∂f/∂t=1/x2 ∂/∂x[x4(∂f/∂x + f + f2)], when x ∈ (0,∞),t > 0 together with no-flux conditions at x = 0 and x = +∞, i.e. (2) x4(∂f/∂x + f + f2)=0 as x → 0 or x → +∞ Such a problem arises as a kinetic approximation to describe the evolution of the radiation distribution f(x, t) in a homogen...

This work is concerned with the following system: (formula presented) which is a model to describe several phenomena in which aggregation plays a crucial role as, for instance, motion of bacteria by chemotaxis and equilibrium of self-attracting clusters. When the space dimension N is equal to three, we show here that (S) has radial solutions with f...

The pair of parabolic equations , , with a>0 and b>0 models the temperature and concentration for an exothermic chemical reaction for which just one species controls the reaction
rate f. Of particular interest is the case where , which appears in the Frank‐Kamenetskii approximation to Arrhenius‐type reactions. We show here that for a large choice o...

This paper is concerned with positive solutions of the semilinear system: which blow up at x = 0 and t = T < ∞. We shall obtain here conditions on p, q and the space dimension N which yield the following bounds on the blow up rates: for some constant C > 0. We then use (1) to derive a complete classification of blow up patterns. This last result is...

We present an asymptotic analysis of the Gunn effect in a drift—diffusion model — including electric-field-dependent generation—recombination processes — for long samples of strongly compensated p-type Ge at low temperature and under d.c. voltage bias. During each Gunn oscillation, there are different stages corresponding to the generation, motion...