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## Publications

Publications (128)

This work considers the propagation of a tumor from the stage of a small avascular sphere in a host tissue and the progressive onset of a tumor neovasculature stimulated by a pro-angiogenic factor secreted by hypoxic cells.
The way new vessels are formed involves cell sprouting from pre-existing vessels and following a trail via a chemotactic mecha...

The present study aims to clarify the role of the fraction of patients under antiretroviral therapy (ART) achieving viral suppression (VS) (i.e. having plasma viral load below the detectability threshold) on the human immunodeficiency virus (HIV) epidemic in Italy. Based on the hypothesis that VS makes the virus untransmittable, we extend a previou...

In the present paper we propose a simple time-varying ODE model to describe the evolution of HIV epidemic in Italy. The model considers a single population of susceptibles, without distinction of high-risk groups within the general population, and accounts for the presence of immigration and emigration, modelling their effects on both the general d...

We consider a model with age and space structure for the epidermis evolution. The model, previously presented and analyzed with respect to the suprabasal epidermis, includes different types of cells (proliferating cells, differentiated cells, corneous cells, and apoptotic cells) moving with the same velocity, under the constraint that the local vol...

In this paper we analyze the impact of the stochastic fluctuation of genes between their ON and OFF states on the pharmacodynamics of a potentially large class of drugs. We focus on basic mechanisms underlying the onset of in vitro experimental dose-response curves, by investigating two elementary molecular circuits. Both circuits consist in the tr...

Author Summary
P53 is an antitumor gene regulating vital cellular functions such as repair of DNA damage, cellular suicide, and cell proliferation: in many tumors p53 is lowly expressed and/or mutated. Drugs targeting the biomolecular network of p53 are becoming important. The network includes the key proteins Mdm2 and PTEN, whose production is reg...

With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how dif...

This paper proposes an approach for building epidemiological models that incorporate the intra-host pathogen-immunity dynamics. The infected population is structured in terms of pathogen load and level of immunity, and the initial infection load may depend on the load of the individual from whom the infection is acquired. In particular, we focus on...

Autopsy studies of adults dying of non-cancer causes have shown that virtually all of us possess occult, cancerous lesions. This suggests that, for most individuals, cancer will become dormant and not progress, while only in some will it become symptomatic disease. Meanwhile, it was recently shown in animal models that a tumor can produce both stim...

In this paper we propose a model for the evolution of a tumor spheroid assuming a structure in which the central necrotic region contains an inner liquid core surrounded by dead cells that keep some mechanical integrity. This partition is a consequence of assuming that a finite delay is required for the degradation of dead cells into liquid. The ph...

We present a mathematical model describing the time development of a
population of tumors subject to mutual angiogenic inhibitory signaling. Based
on biophysical derivations, it describes organism-scale population dynamics
under the influence of three processes: birth (dissemination of secondary
tumors), growth and inhibition (through angiogenesis)...

In this paper, we study a system of nonlinear hyperbolic equations, with nonlocal boundary conditions and a free boundary, arising in the modeling of epidermis growth. The model was introduced in a previous paper (Gandolfi et al. in J Math Biol 62(1):111–141, 2010) where conditions for the existence of a steady state were investigated. The present...

Cells from different tumour cell lines can be grown in vitro to form spheroidal masses, called multicellular tumour spheroids, currently considered valuable experimental models of avascular tumours [35, 37, 50, 51, 58]. Multicellular tumour spheroids have been extensively investigated in that they provide a useful model to assess the effects of oxy...

Recent deterministic models suggest that for solid and nonsolid tumors the delivery of constant continuous infusion therapy may induce multistability in the tumor size. In other words, therapy, when not able to produce tumor eradication, may at least lead to a small equilibrium that coexists with a far larger one. However, bounded stochastic fluctu...

There is an increasing awareness that to properly understand how tumors originate and grow, and then how to develop effective cures, it must be taken into account the dynamics of tumors and its great complexity. Tumors are characterized not only by the coexistence of multiple scales, both temporal and spatial, but also by multiple and quite differe...

By studying a simple but realistic biophysical model of tumor growth in the presence of a constant continuous chemotherapy, we show that if an extended Norton–Simon hypothesis holds, the system may have multiple equilibria. Thus, the stochastic bounded fluctuations that affect both the tumor carrying capacity and/or the drug pharmacodynamics (and/o...

In our paper [ibid. 8, No. 2, 239–252 (2011; Zbl 1259.92039)], equation (45) has been reported incorrectly. Its actual form is as follows: 2γ R=1 ν(1-ν)χR 2 3KR ρ D 1-ρ P R 3 -3 21-ρ P R 2 +4 3η C χR ρ D 3 1-ρ P R 3 +23τ 0 lnρ P ρ D +1 3ln2(R ρ P ) 3 +1+2(R ρ P ) 6 2+3· The comments that followed Eq. (45) then change accordingly. It is immediate to...

Part I Towards a Comprehensive Theory of Cancer Growth.- Combining Game Theory and Graph Theory to Model Interactions between Cells in the Tumor Microenvironment.- Growth as the Root of all Evil in Carcinomas: Synergy between pH Buffering and Anti-Angiogenesis prevents Emergence of Hallmarks of Cancer.- Phase Transitions in Cancer.- Part II Cancer...

The future of oncology seems to lie in Molecular Medicine (MM). MM is a new science based on three pillars. Two of them are evident in its very name and are well known: medical science and molecular biology. However, there is a general unawareness that MM is firmly based on a third, and equally important, pillar: Systems Biomedicine. Currently, thi...

In this paper we examine the steady state of tumour spheroids considering a structure in which the central necrotic region contains an inner liquid core surrounded by dead cells that keep some mechanical integrity. This partition is a consequence of assuming that a finite delay is required for the degradation of dead cells into liquid. The phenomen...

Tumor angiogenesis is a landmark of solid tumor development, but it is also directly relevant to chemotherapy. Indeed, the density and quality of neovessels may influence the effectiveness of therapies based on blood-born agents. In this paper, first we define a deterministic model of antiproliferative chemotherapy in which the drug efficacy is a u...

In this work we propose to model chemotherapy taking into account the mutual interaction between tumour growth and the development of tumour vasculature. By adopting a simple model for this interaction, and assuming that the efficacy of a drug can be modulated by the vessel density, we study the constant continuous therapy, the periodic bolus-based...

The paper addresses the question of how to formulate a mathematical model allowing to predict the size of a multicellular spheroid once it has reached equilibrium. All previous models postulate some law of removal of necrotic material from the spheroid, compensating the new cellular volume produced by proliferation. However, such removal process ha...

We propose a model with age and space structure for the evolution of the supra-basal epidermis. The model includes different types of cells: proliferating cells, differentiated cells, corneous cells, and apoptotic cells. We assume that all cells move with the same velocity and that the local volume fraction, occupied by the cells is constant in spa...

Although commonly related to nutrient deprivation, the cause of the formation of the necrotic core in the multicellular tumour spheroids is still a controversial issue. We propose a simple model for the cell ATP production that assumes glucose and lactate as the only fuel substrates, and describes the main reactions occurring in the glycolytic and...

We propose a spatially distributed continuous model for the spheroid response to radiation, in which the oxygen distribution is represented by means of a diffusion-consumption equation and the radiosensitivity parameters depend on the oxygen concentration. The induction of lethally damaged cells by a pulse of radiation, their death, and the degrada...

The administration schedule appears to be a particularly relevant factor in determining the effectiveness of an antiangiogenic drug. A better quantitative knowledge of the interactions between tumour growth and the development of its vasculature could help to design effective therapies.
Biological and clinical inferences were derived from the analy...

In this paper we propose a class of models that describe the mutual interaction between tumour growth and the development of tumour vasculature and that generalize existing models. The study is mainly focused on the effect of a therapy that induces tumour vessel loss (anti-angiogenic therapy), with the aim of finding conditions that asymptotically...

We present and analyze a model for the dynamics of the interactions between a pathogen and its host's immune response. The model consists of two differential equations, one for pathogen load, the other one for an index of specific immunity. Differently from other simple models in the literature, this model exhibits, according to the hosts' or patho...

After a single dose of radiation, transient changes caused by cell death are likely to occur in the oxygenation of surviving cells. Since cell radiosensitivity increases with oxygen concentration, reoxygenation is expected to increase the sensitivity of the cell population to a successive irradiation. In previous papers we proposed a model of the r...

A model of tumor growth taking into account its vascularization due to angiogenesis and antiangiogenic cancer chemotherapy is proposed and analised. The model is a modified Hahnfeldt model and the analysis has two goals: first of all we check stability of the equilibrium point of the model using Lyapunov first and second methods to find conditions...

In the present paper we propose a continuous cell population model based on Shackney's idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 < or = x < or = 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump tran...

We review some of the models that have been proposed to describe tumour growth and treatment. A first class is that of models
which include the analysis of stresses. Here the question of blood vessel collapse in vascular tumours is treated briefly.
Results on the existence of radially- and of non-radially-symmetric solutions are illustrated togethe...

After a single dose of an anticancer agent, changes due to cell death are expected to occur in the distribution of cells between proliferating and quiescent compartment as well as in the oxygenation and nutritional state of surviving cells. These changes are transient because tumour regrowth tends to restore the pretreatment status. The reoxygenati...

Blood flow in tumour vasculature carries oxygen and nutrients necessary for cell life and proliferation, and allows delivery
of therapeutic agents within the tumour. To reach their target cells, these agents must extravasate and be transported by
diffusion and by the convection associated to the movement of extracellular fluid. Convective transport...

Mathematical models of tumour spheroids, proposed since the early seventies, have been generally formulated in terms of a single diffusive nutrient which is critical for cell replication and cell viability. Only recently, attempts have been made to incorporate in the models the cell energy metabolism, by considering the interplay between glucose, o...

Mathematical models of tumour spheroids, proposed since the early seventies, have been generally formulated in terms of a single diffusive nutrient which is critical for cell replication and cell viability. Only recently, attempts have been made to incorporate in the models the cell energy metabolism, by considering the interplay between glucose, o...

Metabolically healthy skeletal muscle possesses the ability to switch easily between glucose and fat oxidation in response to homeostatic signals. In type 2 diabetes mellitus and obesity, the skeletal muscle shows a great reduction in this metabolic flexibility. A substrate like dodecanedioic acid (C-12), able to increase skeletal muscle glycogen s...

In the first part of this paper we study the properties of a class of linear differential equations with periodic real coefficients and show that the structure of this family of systems guarantees the unstability of the null solution. In the second part, we use this property to demonstrate that antiangiogenic drugs that act only inhibiting the endo...

A model of antiangiogenic cancer chemotherapy is proposed and analyzed. The model is a modified Hahnfeldt model and the analysis has two goals: first of all we check stability of the equilibrium point of the model to find conditions leading to tumour eradication then we propose an optimization problem and give necessary conditions of its solution.

This work extends a previous model that described the evolution of a tumor cord (a cylindrical arrangement of tumor cells, generally surrounded by necrosis, growing around a blood vessel of the tumor) under the activity of cell killing agents. In the present model we include the most relevant aspects of the dynamics of extracellular fluid, by compu...

This work illustrates the behavior of the interstitial pressure and of the interstitial fluid motion in tumor cords (cylindrical arrangements of tumor cells growing around blood vessels of the tumor) by means of numerical simulations on the basis of a mathematical model previously developed. The model describes the steady state of a tumor cord surr...

In this paper, we investigate the formation of tumour cords (cylindrical arrangements of tumour cells around blood vessels) within a tumour tissue. The shrinkage and the expansion of the cord following a stepwise decrease or, respectively, increase of oxygen tension in the blood vessel are also described. The model represents the tumour cell popula...

A continuous cell population model, which represents both the cell cycle phase structure and the kinetic heterogeneity of the population following Shackney's ideas [J. Theor. Biol. 38 (1973) 305–333], is studied. The asynchronous exponential growth property is proved in the framework of the theory of strongly continuous semigroups of bounded linear...

The model proposed by Hahnfeldt et al. (1999) describes the growth of a tumour assuming that tumour growth is strictly controlled by the evolution of the vascular network that supplies oxygen and nutrients to tumour cells. Consequently, it provides a framework to represent the effects of antiangiogenic therapies. In this paper, some possible modifi...

A system of tumor cords is schematized by an array of identical cords, each one having approximately a rotational symmetry around its central blood vessel. A mathematical model for the evolution of the cord is presented, taking into account the influence of a limiting nutrient on the proliferation and death of the cells, the volume reduction of the...

This chapter describes the response of tumor cords to a cell killing agent, representing the cord as a continuum with cylindrical symmetry and accounting for cell motion in a purely kinematic framework. The model takes into account oxygen diffusion, the dependence of cell proliferation and death rates on oxygen concentration, and the dissolution of...

This chapter describes the response of tumor cords to a cell killing agent, representing the cord as a continuum with cylindrical symmetry and accounting for cell motion in a purely kinematic framework. The model takes into account oxygen diffusion, the dependence of cell proliferation and death rates on oxygen concentration, and the dissolution of...

In this paper, the evolution of a tumour cord after treatment is investigated by extensive numerical simulations on the basis of a mathematical model developed by Bertuzzi et al. (submitted). The model is formulated in cylindrical symmetry adopting the continuum approach, and takes into account the influence of oxygen level on the proliferation and...

Tumour cells growing around blood vessels form structures called tumour cords. We review some mathematical models that have been proposed to describe the stationary state of the cord and the cord evolution after single-dose cell killing treatment. Whereas the cell population has been represented with age or maturity structure to describe the cord s...

A mathematical model is developed that describes the proliferative behaviour at the stationary state of the cell population within a tumour cord, i.e. in a cylindrical arrangement of tumour cells growing around a blood vessel and surrounded by necrosis. The model, that represents the tumour cord as a continuum, accounts for the migration of cells f...

In the present paper we propose a method of analysis of the cell kinetic characteristics of in vivo experimental tumours, that uses DNA-BrdUrd flow cytometry data at various times after the bromodeoxyuridine (BrdUrd) injection and mathematical modelling. The model of the cell population takes into account the cell-cell heterogeneity of the progress...

The role of tryptophan (TRY) and its metabolites in the pathogenesis of hepatic encephalopathy is conflicting. The aim of the present study is to investigate in posthepatitis cirrhotic patients with encephalopathy the serum levels of TRY and those of its metabolite indole-3-acetic acid, as well as TRY binding curve to serum albumin and the competit...

In some tumours, the viable cells grow around blood vessels forming cylindrical structures called tumour cords, which are surrounded by regions of necrosis. In the present paper, we propose a mathematical model for the cell kinetics in a tumour cord at the stationary state. Both proliferating cells and quiescent cells are considered, and the prolif...

The disposition of dodecanedioic acid (C12) was investigated in six overnight-fasting healthy male volunteers, who received a 165-min i. v. infusion of 42.45 mmol of C12 added to 150 microCi of [1-12-(14)C]C12. Blood samples were collected up to 360 min after the start of infusion, and concentration of serum labeled C12 was determined. Expired radi...

In the present paper, on the basis of the thermodynamic theory proposed by Bell et al. [1], conditions for adhesion are given and the number of bound receptors on a cell is computed, under the hypothesis that two independent receptor-ligand systems, which differ in their affinity, concur to the formation of the molecular bridges which link the cell...

We analyze the growth of a tumor cord in cylindrical symmetry, when nutrient is supplied by the central vessel and by a distributed peripheral source. The model equations describe the diffusion and consumption of the nutrient, together with the dynamics of growth of the cord and the formation of necrosis in the tumor or in the surrounding normal ti...

The pharmacokinetics of disodium sebacate (Sb) was studied in Wistar rats of both sexes. Sebacate was administered either as intra-peritoneal (i.p.) bolus (six doses ranging from 10 mg to 320 mg) or as oral bolus (two doses: 80 and 160 mg). Plasma and urinary concentrations of Sb and urinary concentrations of Sb and its products of beta-oxidation (...

A mathematical model that describes the time evolution of the DNA-BrdUrd distribution, as measured in experimental tumours after labelling with BrdUrd, is proposed. Cell-to-cell heterogeneity within the tumour and the rate of progression across cell cycle phases is taken into account, and a strict correlation between the durations of S and G2M phas...

For the multiple linear regression model, regions in the parameter space are constructed, in which the ridge estimator with a given value of the biasing parameter is preferred to the OLS estimator and, respectively, the OLS estimator is preferred to the ridge estimator, according to the E.J.G. Pitman’s criterion [Proc. Camb. Philos. Soc. 33, 212-22...

Indole-3-acetic acid (IAA) is a product of tryptophan (Trp) metabolism and is found to be markedly increased in uremic sera. IAA binding to defatted human serum albumin at 37 degrees C and pH 5, 7.4, and 8.5 was studied by equilibrium dialysis, and data were analyzed assuming two independent high affinity binding sites plus a class of low affinity...

The in vivo infusion of Bromodeoxyuridine (BrdUrd), followed by delayed biopsy and bivariate DNA-BrdUrd flow cytometry, allows the potential doubling time (Tpot) of human tumors to be estimated. According to Steel, the mathematical definition of Tpot is Tpot = ln 2/Kp, where Kp is the rate constant of cell production. All the operative formulas whi...

The in vivo infusion of Bromodeoxyuridine (BrdUrd), followed by delayed biopsy and bivariate DNA‐BrdUrd flow cytometry, allows the potential doubling time (Tpot) of human tumors to be estimated. According to Steel, the mathematical definition of Tpot is Tpot = ln 2/Kp, where Kp is the rate constant of cell production. All the operative formulas whi...

Dodecanedioic acid (C12), a saturated aliphatic dicarboxylic acid with twelve C atoms, was given as an intraperitoneal bolus to male Wistar rats, with the aim of evaluating C12 suitability as an energy substrate for parenteral nutrition. The 24 h urinary excretion of C12 was 3.9% of the administered dose. C12 kinetics were investigated by a one-com...

The in vivo infusion of the thymidine analogue bromodeoxyuridine (BrdUrd), followed by delayed biopsy and bivariate DNA-BrdUrd flow cytometry, makes it possible to estimate Steel's potential doubling time (Tpot) of human tumors. In the present paper, the expression of Steel's Tpot for a rather general cell population model, in which the distributio...

The level of free tryptophan (Trp) and its metabolites in serum appears to be related to some pathologic states, such as chronic renal failure and neuropsychiatric disorders, so that a precise characterization of tryptophan binding to serum albumin is of interest. In the present paper, the binding of L-tryptophan to defatted human serum albumin at...

Glucose kinetics in rat was investigated by analysing <sup>14</sup>C-glucose concentration data through a two-compartment model. The two compartments represent the glucose pool and the glucose precursor pool. Since the system was not in the steady state due to adrenergic response, two alternative models were considered, in which either the rate coe...

Excretion and tissue uptake of dodecanedioic acid (C12), a proposed alternative fuel substrate, was investigated in humans by bolus experiments.
Seven overnight-fasting healthy male volunteers received i.v. a bolus (1 g) of C12. Blood samples were collected after C12 administration at intervals of 15 minutes, and C12 serum concentration was measure...

Cell populations pulse-labelled with BrdUrd, and sampled at increasing times after the pulse, yield DNA-BrdUrd distributions from which the relative movement (RM) and the depletion function (DF) of labelled, undivided cells can be calculated. In this paper we present an extension of the equation for the time course of RM, given by White and Meistri...

In order to study the feasibility of using dicarboxylic acids for parenteral nutrition, the authors studied the pharmacokinetics in man of azelaic acid and sebacic acid. The pharmacokinetic analysis presented here shows that there are different modalities in the urinary excretion of the dicarboxylic acids with 9 or 10 carbon atoms. While azelaic ac...

In white noise theory on Hilbert spaces, it is known that maps which are uniformly continuous around the origin in the S-topology constitute an important class of “physical” random variables. We prove that random variables having such a continuity property can be approximated in the Gaussian measure by polynomial random variables. The proof relies...

The paper discusses some mathematical methods, presented in the literature or proposed by the authors, which aim at the estimation of cell kinetic parameters from DNA-BrdUrd distributions obtained by the pulse labelling technique. In particular, we give an expression for the time behaviour of the relative movement of BrdUrd-labelled undivided cells...

In white noise theory on Hilbert spaces, it is known that maps which are uniformly continuous around the origin in the S-topology constitute an important class of "physical" random variables. We prove that random variables having such a continuity property can be approximated in the gaussian measure by polynomial random variables. The proof relies...

In order to study the relationship between plasma level and urinary excretion rate of Tryptophan in man, a mathematical model of the reabsorption-excretion process of Tryptophan is proposed. The model embodies the mass balance between glomerular filtration, carrier-mediated reabsorption and excretion in the urine. Model parameters are estimated by...

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