Some Dynamic Aspects of Hematopoietic Stem Cells

Dingli, David; Pacheco, Jorge M.

doi:10.1007/s12015-007-9007-8

Cited by 1 publication

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References 58 publications

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“…Stem cells dynamics may be represented by the generic model presented in the previous section, with a very imited proliferative subpopulation number, since at least in the haematopoietic bone marrow, it has been estimated that very few stem are actively committed in proliferation [71]. More generally, stem cells have been studied by probabilistic modelling [68,70,72], by cellular automata [233], by ODEs [192], by difference equations [139] and by PDEs [140] or delay differential equations [183,186], with applications mainly in haematology and haematological diseases (in particular chronic myelogenous leukemia and cyclical neutropenia), where observations of the resulting mature cells populations are easy to perform in the clinic.…”

Section: Models Involving Stem Cell Dynamics; Maturity-structured Modelsmentioning

confidence: 99%

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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Section: Models Involving Stem Cell Dynamics; Maturity-structured Modelsmentioning

confidence: 99%

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

Clairambault

2009

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

Some Dynamic Aspects of Hematopoietic Stem Cells

Cited by 1 publication

References 58 publications

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

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

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