From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells

Bellomo, Nicola; Delitala, Marcello Edoardo

doi:10.1016/j.plrev.2008.07.001

Cited by 161 publications

(105 citation statements)

References 97 publications

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“…mainly addressed to a singular antigen, the early BMLF1), respectively. 6 Summarizing, a significant presence of antigen BCRF1 can determine a delay in the immune response. As a result, the immune activity may take a long time for the clearance of the infection; during this time, the concentration of T K cells remains high and polarizes against BMLF1 antigen as if an internal self-reinforcement has occurred.…”

Section: The Epstein-bar Virusmentioning

confidence: 99%

Can persistent Epstein–Barr virus infection induce chronic fatigue syndrome as a Pavlov reflex of the immune response?

Agliari

Barra

Vidal

et al. 2012

Journal of Biological Dynamics

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Chronic Fatigue Syndrome is a protracted illness condition (lasting even years) appearing with strong flu symptoms and systemic defiances by the immune system. Here, by means of statistical mechanics techniques, we study the most widely accepted picture for its genesis, namely a persistent acute mononucleosis infection, and we show how such infection may drive the immune system toward an out-of-equilibrium metastable state displaying chronic activation of both humoral and cellular responses (a state of full inflammation without a direct "causes-effect" reason). By exploiting a bridge with a neural scenario, we mirror killer lymphocytes TK and B cells to neurons and helper lymphocytes TH 1 , TH 2 to synapses, hence showing that the immune system may experience the Pavlov conditional reflex phenomenon: if the exposition to a stimulus (EBV antigens) lasts for too long, strong internal correlations among B, TK , TH may develop ultimately resulting in a persistent activation even though the stimulus itself is removed. These outcomes are corroborated by several experimental findings.

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Section: The Epstein-bar Virusmentioning

confidence: 99%

Can persistent Epstein–Barr virus infection induce chronic fatigue syndrome as a Pavlov reflex of the immune response?

Agliari

Barra

Vidal

et al. 2012

Journal of Biological Dynamics

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“…Regarding the mathematical modelling of the above interactions, many papers have appeared using either a finite dimensional approach (De Lisi and Rescigno 1977, Kirschner and Panetta 1998, Stepanova 1980, Kuznetzov et al 1994, Kuznetzov and Knott 2001, Galach 2003, Szymanska 2003, De Vladar and Gonzalez 2004, De Pillis et al 2005, d'Onofrio 2005, d'Onofrio 2007, Cappuccio et al 2006, Kronik et al 2008, Kirschner and Tsygvintsev 2009 or the theory of kinetic active particles Delitala 2008, Bellomo et al 2008).…”

Section: Introductionmentioning

confidence: 99%

Tumour suppression by immune system through stochastic oscillations

Caravagna

d’Onofrio

Milazzo

et al. 2010

Journal of Theoretical Biology

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The well-known Kirschner-Panetta model for Tumour-Immune System interplay [Kirschner and Panetta, J. Math. Biol 37 (3), 1998] reproduces a number of features of this essential interaction, but it excludes the possibility of tumour suppression by the immune system in the absence of therapy. Here we present a hybrid-stochastic version of that model. In this new framework, we show that in reality the model is also able to reproduce the suppression, through stochastic extinction after the first spike of an oscillation.

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“…Can these opposed views be reconciled? It should be to no avail, advocate Soto and Sonnenschein [248]; yet from a modelling point of view, it could be quite consistent with recent unifying mathematical theories that merge individual stochastic processes into physiologically structured partial differential equation models [25,45,104,105,218], thus authorising a natural multiscale point of view on carcinogenesis (gene, molecule, cell and tissue). In short, a unifying view may consist in seeing cancer more as a tissue disease rather than a single cell disease: the "renegade cell", if it exists, may develop into a robust cell clone only if favourable microenvironmental conditions are present.…”

Section: Disputes On the Origin Of Cancer: Clonal Or Not Clonal?mentioning

confidence: 80%

Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments

Clairambault

2009

Math. Model. Nat. Phenom.

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Abstract. This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the focus will be set here. To this purpose, mathematical modelling should represent proliferating cell population dynamics with natural built-in control targets (which implies modelling the cell division cycle), together with the distribution of drugs in the organism and their molecular actions on different targets at the cell level on proliferation, i.e., molecular pharmacokinetics-pharmacodynamics of antiproliferative drugs. This should make possible optimal control of drug delivery with constraints to be determined according to the main pharmacological issues encountered in the clinic: unwanted toxic side-effects, occurrence of drug resistance. Mathematical modelling should also take into account physiological determinants of cell and tissue proliferation, such as intervention of the immune system, circadian control on cell cycle checkpoint proteins, and activity of intracellular drug processing enzymes together with individual variations in the activities of these proteins (genetic polymorphism). Taking these points into account will add to the rich scenery of normal or disrupted cell and tissue regulations, and their corrections by drugs, a natural environmental, whole body physiological, frame. It is necessary indeed to consider such a framework if one wants to eventually be actually helpful to clinicians who routinely treat by combinations of drugs living Humans with their complex whole body regulations, often dependent on genotypic variations, and not isolated cells or tissues.Key words: cell proliferation, population dynamics, physiologically structured partial differential equations, pharmacological control, pharmacokinetics-pharmacodynamics, physiological modelling, cancer treatments, therapeutic optimisation, individualised medicine AMS subject classification: 92-02, 92B05 Biological common knowledge on cancerThis section shortly presents the general scenery of cancer evolution and features that must be included in models designed to describe and control it, bearing in mind a more descriptive (physicist's) than a therapeutic (physician's) point of view, only to reverse this perspective in the following sections, in which will be stressed the interest of modelling from the point of view of control, at least if one wants to design models for therapeutic applications. This biological section will be only a short sketch, if one considers that on this subject many books have already been written, e.g. [24,78,96,97,223]. Cancer: a challenging public health problemCardiovascular diseases and cancer are by fa...

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From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells

Cited by 161 publications

References 97 publications

Can persistent Epstein–Barr virus infection induce chronic fatigue syndrome as a Pavlov reflex of the immune response?

Can persistent Epstein–Barr virus infection induce chronic fatigue syndrome as a Pavlov reflex of the immune response?

Tumour suppression by immune system through stochastic oscillations

Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments

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