The dynamics of drug resistance: A mathematical perspective
Drug Resistance UpdatesPublished 1 February 2012
Orit Lavi, Michael M. Gottesman, Doron Levy
Citations101
SJR quartileQ1
SJR score5.28
SNIP3.63
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
This review covers aspects of MDR that have been mathematically studied, and explains how mathematics can be used to study drug resistance, and discusses quantitative approaches of mathematical analysis.
Abstract
Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance, induced resistance and acquired resistance. In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intracellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance.
Keywords
MathematicsMedicineBiochemistry, Genetics and Molecular Biology
Nature reviews. CancerDrug penetration in solid tumours
2,761 Citations2006Andrew I. Minchinton, Ian F. Tannock
The evidence that indicates that the distribution of many anticancer drugs in tumours is incomplete is summarized, and strategies that might be used either to improve drug penetration through tumour tissue or to select compounds based on their abilities to penetrate tissue are suggested, thereby increasing the therapeutic index.
JNCI Journal of the National Cancer InstituteDrug Resistance and the Solid Tumor Microenvironment
2,107 Citations2007Olivier Trédan, Carlos M. Galmarini +2 more
How the tumor microenvironment may be involved in the resistance of solid tumors to chemotherapy and potential strategies to improve the effectiveness of drug treatment by modifying factors relating to the tumormicroenvironment are described.
Journal of Clinical OncologyRandomized Trial of Dose-Dense Versus Conventionally Scheduled and Sequential Versus Concurrent Combination Chemotherapy as Postoperative Adjuvant Treatment of Node-Positive Primary Breast Cancer: First Report of Intergroup Trial C9741/Cancer and Leukemia Group B Trial 9741
1,564 Citations2003Marc L. Citron, Donald A. Berry +19 more
Dose density improves clinical outcomes significantly, despite the lower than expected number of events at this time, and Sequential chemotherapy is as effective as concurrent chemotherapy.
PubMedA mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate.
1,340 Citations1980Goldie Jh, Coldman Aj
Analysis of the model indicates that the probability of the appearance of a resistant phenotype increases with the mutation rate, and for any population of tumors with a non-zero mutation rate the likelihood of there being at least one resistant cell will go from a condition of low to high probability over a very short interval in the tumor's biologic history.
LeukemiaSix-year follow-up of patients receiving imatinib for the first-line treatment of chronic myeloid leukemia
845 Citations2009Andreas Hochhaus, S G O'Brien +13 more
During the sixth year of study treatment, there were no reports of disease progression to accelerated phase (AP) or blast crisis (BC), and the toxicity profile was unchanged.
Methods in molecular biologyMechanisms of Multidrug Resistance in Cancer
687 Citations2009Jean‐Pierre Gillet, Michael M. Gottesman
Identifying genes and mechanisms critical to the development of MDR in vivo and establishing a reliable method for analyzing clinical samples could help to predict theDevelopment of resistance and lead to treatments designed to circumvent it.
SIAM ReviewMathematical Models of Avascular Tumor Growth
565 Citations2007Tiina Roose, S. Jonathan Chapman +1 more
The aim of the review is to provide a relatively comprehensive list of existing models and discuss several representative models in greater detail and some possible future avenues of mathematical modeling of avascular tumor development are outlined.
Nature reviews. CancerDynamics of cancer progression
498 Citations2004Franziska Michor, Yoh Iwasa +1 more
The fundamental principles that govern the dynamics of activating oncogenes and inactivating tumour-suppressor genes in populations of reproducing cells are revealed.
Proceedings of the National Academy of SciencesDrug resistance in cancer: Principles of emergence and prevention
430 Citations2005Natalia L. Komarova, Dominik Wodarz
It is found that resistance arises mainly before the start of treatment and, for cancers with high turnover rates, combination therapy is less likely to yield an advantage over single-drug therapy.
NaturePredicting the course of Gompertzian growth
320 Citations1976Larry Norton, Richard Simon +2 more
The development of a generalised approach to the analysis of “Gompertzian” growth which enables accurate predictions of future growth for two model tumour systems is reported.
JAMASequential or alternating doxorubicin and CMF regimens in breast cancer with more than three positive nodes. Ten-year results
315 Citations1995Gianni Bonadonna
Mathematical BiosciencesRole of optimal control theory in cancer chemotherapy
313 Citations1990George W. Swan
This paper presents a review of the ways in which optimal control theory interacts with cancer chemotherapy, and suggests for designing better chemotherapy strategies are presented.
Springer texts in electrical engineeringA Mathematical Model
289 Citations1987Charles L. Weber
This chapter shall examine the general reception problem as a statistical-decision problem and hence shall assume certain statistics of the messages and channel disturbances depending on the criterion for system evaluation prescribed and the set of decisions permitted by the receiver.
Journal of Theoretical BiologyDoes tumor growth follow a “universal law”?
240 Citations2003Caterina Guiot, Piero Giorgio Degiorgis +3 more
The results support the notion that tumor growth follows such a universal law, and several important implications are discussed, including its relevance for tumor metastasis and recurrence, cell turnover rates, angiogenesis and invasion.
JAMASequential or Alternating Doxorubicin and CMF Regimens in Breast Cancer With More Than Three Positive Nodes
239 Citations1995Gianni Bonadonna
Findings indicate that in women with extensive nodal involvement, sequential chemotherapy with doxorubicin followed by CMF yields superior results compared with the alternating administration of the same regimens or with classical CMF.
Nature Clinical Practice OncologyThe Norton–Simon hypothesis: designing more effective and less toxic chemotherapeutic regimens
202 Citations2006Richard Simon, Larry Norton
Simon and Norton discuss how they used guiding principles to derive the Norton–Simon hypothesis, and describe how this has improved clinical trial design and helped to achieve the goal of more effective and less toxic chemotherapeutic regimens.
CancerDecelerating growth and human breast cancer
199 Citations1993John A. Spratt, John S. Spratt +4 more
This report uses a large number of patients and assumes an exponential growth rate to improve understanding of human breast cancer growth rates and may have many clinical applications.
British Journal of CancerThe growth law of primary breast cancer as inferred from mammography screening trials data
178 Citations1998Deborah R. Hart, Eliezer Shochat +1 more
This study used large-scale mammography screening trial data to deduce the growth law of primary breast cancer, and showed that the data are inconsistent with the exponential, logistic and Gompertz laws, but support power law growth.
SIAM Journal on Applied MathematicsOptimal Control Applied to Cell-Cycle-Specific Cancer Chemotherapy
159 Citations2000John C. Panetta, K. Renee Fister
This work designs the control functional to maximize both the bone marrow mass and the dose over the treatment interval, and describes the optimal control in terms of the solutions to the optimality system, which is the state system coupled with the adjoint system.
Annals of OncologyProposal for a new model of breast cancer metastatic development
142 Citations1997Romano Demicheli, Michael Retsky +2 more
The proposed model suggests new views concerning scheduling of current chemotherapy, new treatment approaches aimed at keeping micrometastases in a dormant state for the patient's entire life, and the careful reappraisal of the timing of surgery within the multimodal treatment of operable breast cancer.
PubMedTreatment sequencing, asymmetry, and uncertainty: protocol strategies for combination chemotherapy.
137 Citations1986Roger Day
This paper summarizes a large number of simulations which relax the "symmetry" assumptions in the Goldie-Coldman treatment model, which was symmetrical with respect to two drugs considered for use together.
Nature Clinical Practice OncologyIn silico cancer modeling: is it ready for prime time?
131 Citations2008Thomas S. Deisboeck, Le Zhang +2 more
The field of computational or in silico modeling and the simulation of disease processes is becoming increasingly important for hypothesis generation and data integration in both experiments and clinics alike.
Bulletin of Mathematical BiologyOptimal control analysis in the chemotherapy of IgG multiple myeloma
121 Citations1977G SWAN, T. Vincent
The Gompertzian model for the growth of a cancer cell population subject to losses due to the action of cycle nonspecific therapy is used for the determination of a chemotherapy program obtained from optimal control theory for bone cancer IgG multiple myeloma.
European Journal of PharmacologyMathematical modeling as a tool for planning anticancer therapy
119 Citations2009Andrzej Świerniak, Marek Kimmel +1 more
The review covers such major areas of therapy optimization as phase-specific chemotherapy, antiangiogenic therapy and therapy under drug resistance, as well as two more recent areas: angiogenesis of tumors and molecular signaling within and among cells.
Molecular PharmaceuticsComputational Models for Identifying Potential P-Glycoprotein Substrates and Inhibitors
115 Citations2005Patrizia Crivori, Benedetta Reinach +2 more
A method for discriminating P-gp substrates and nonsubstrates has been set up based on calculated molecular descriptors and multivariate analysis using a training set of 53 diverse drugs, which allowed the identification of some key molecular features that differentiate a substrate from an inhibitor.
Current Drug Metabolism(Section A: Molecular, Structural, and Cellular Biology of Drug Transporters) The Role of MDR1 Genetic Polymorphisms in Interindividual Variability in P-glycoprotein Expression and Function
111 Citations2004Erica L. Woodahl, Rodney J. Y. Ho
Haplotype identification may prove to be vital in identifying the functional significance of MDR1 polymorphisms on disease susceptibility and drug disposition, and molecular haplotyping techniques, analysis of linkages on the same chromosome directly by biophysical and biochemical means, may be needed to characterize haplotypes in individuals with a highly polymorphic and large gene like MDR 1.
Current Pharmaceutical DesignEvolution of Resistance to Cancer Therapy
106 Citations2005Franziska Michor, Martin A. Nowak +1 more
A general mathematical framework based on multi-type branching processes designed to study the dynamics of escape of replicating organisms from selection pressures is reviewed and the theory shows how to estimate the probability of success for any treatment regimen.
Proceedings of the National Academy of SciencesRole of symmetric and asymmetric division of stem cells in developing drug resistance
106 Citations2010Cristian Tomasetti, Doron Levy
It is concluded that leukemia stem cells must tend to renew symmetrically as opposed to their healthy counterparts that predominantly divide asymmetrically.
European Journal of BiochemistryKinetics of daunorubicin transport by P‐glycoprotein of intact cancer cells
105 Citations1992Ellen C. Spoelstra, Hans V. Westerhoff +2 more
A method to characterize kinetically the pump in intact cells is demonstrated, which provides evidence that at least two binding sites for daunorubicin are present on the active transport system of daun orubic in their multidrug resistant counterparts.
Mathematical BiosciencesA mathematical model of drug resistance: Heterogeneous tumors
101 Citations1998John C. Panetta
A mathematical model is developed to describe the growth and control of a heterogeneous tumor that takes into account induced drug resistance and how this model may help to develop more effective cancer chemotherapeutic treatments.
Breast Cancer Research and TreatmentComputer simulation of a breast cancer metastasis model
100 Citations1997Michael Retsky, Romano Demicheli +6 more
Analysis of relapse data from untreated early stage breast cancer patients with 16–20 yearfollow-up shows that the frequency of relapse has a double peaked distribution, and model simulations predict that patients who relapse inthe second peak would have micrometastases in states of relatively low chemosensitivity when adjuvant therapy isnormally administered.
BiosystemsA mathematical model of combination therapy using the EGFR signaling network
96 Citations2004Robyn P. Araujo, Emanuel F. Petricoin +1 more
This paper uses mathematical modeling to investigate a novel type of combination therapy in which multiple nodes in a signaling cascade are targeted simultaneously with selective inhibitors, pursuing the hypothesis that such an approach may induce the desired signal attenuation with lower doses of the necessary agents than when one node is targeted in isolation.
Mathematical BiosciencesA mathematical model of breast and ovarian cancer treated with paclitaxel
95 Citations1997John C. Panetta
A mathematical model that describes the effects of cell-cycle-specific drugs on cancer and normal tissue is developed and some acceptable treatment strategies are discussed in terms of treatment period, drug-infusion time, and proliferative fraction of cancer mass.
Journal of Theoretical BiologyEvolution of resistance to anti-cancer therapy during general dosing schedules
93 Citations2009Jasmine Foo, Franziska Michor
Estimates for the probability of developing resistance and moments of the size of the resistant cell population are developed and treatment schedules are optimized to minimize the risk of disease progression due to resistance as well as locate ideal schedules for controlling the population size of resistant clones in situations where resistance is inevitable.
Journal of Clinical OncologyClinical Relevance of Different Sequencing of Doxorubicin and Cyclophosphamide, Methotrexate, and Fluorouracil in Operable Breast Cancer
92 Citations2004Gianni Bonadonna, Milvia Zambetti +3 more
The findings observed in these trials emphasize that the relative merits of anthracycline adjuvant programs also can depend on the modality of administration and must be assessed in properly designed trials in which the magnitude of the benefits can be weighed against potential risks.
PubMedSequential or alternating doxorubicin and CMF regimens in breast cancer with more than three positive nodes. Ten-year results.
89 Citations1995Gianni Bonadonna, Milvia Zambetti +1 more
Mathematical BiosciencesSome optimal control problems in cancer chemotherapy with a toxicity limit
85 Citations1990John M. Murray
This work investigates some models of a cancer chemotherapy problem where the normal cell population must be maintained above a lower limit and a measure of the total drug use is bounded as a limit of toxicity.
Medical HypothesesIs Gompertzian or exponential kinetics a valid description of individual human cancer growth?
79 Citations1990Michael Retsky, Douglas E. Swartzendruber +2 more
The literature contains clinical evidence from individual patients of this growth pattern in primary breast, large intestine and rectum, and pulmonary cancers and metastatic pulmonary cancer, and much data is not consistent with exponential or Gompertzian kinetics but are explainable by irregular growth kinetics.
Biochimica et Biophysica Acta (BBA) - BiomembranesTransepithelial transport of vinblastine by kidney-derived cell lines. Application of a new kinetic model to estimate in situ Km of the pump
77 Citations1990Masaru Horio, Ira Pastan +2 more
The transepithelial transport of the chemotherapeutic drug, vinblastine, in epithelia formed by the kidney cell lines MDCK, LLC-PK1, and OK is studied and the transport pattern observed is that predicted to result from the function of the multidrug transporter in the apical plasma membrane.
Drug resistance in cancer mechanisms and models
72 Citations1998James H. Goldie
Breast Cancer ResearchMolecular biology of breast metastasis The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer
66 Citations2000Susan E. Clare, Faina Nakhlis +1 more
Several mathematical models are discussed, with a focus on how they have been used to predict the initiation time of metastatic growth, the effect of operative therapy on the growth of metastases, and the optimal administration strategy for chemotherapy.
Biochimica et Biophysica Acta (BBA) - Molecular Cell ResearchA model for computer simulation of P-glycoprotein and transmembrane ΔpH-mediated anthracycline transport in multidrug-resistant tumor cells
57 Citations1990Erland J.F. Demant, Maxwell Sehested +1 more
An efflux mechanism which relies solely on pH-dependent drug trapping in a pH 5 endosomal compartment by a simple diffusion process followed by exocytosis, appears inadequate to account for the high rate of DNR efflux in EHR2/DNR+ cells.
Breast CareDose-Dense Chemotherapy: Principles, Clinical Results and Future Perspectives
57 Citations2008Marc L. Citron
Dosedense adjuvant chemotherapy improves clinical outcomes without increasing toxicity, and supporting studies indicate an improved disease-free and overall survival.
Journal of Clinical OncologyShortening Infusion Time for High-Dose Methotrexate Alters Antileukemic Effects: A Randomized Prospective Clinical Trial
52 Citations2011Torben Stamm Mikkelsen, Alex Sparreboom +10 more
Shortening the infusion time of HDMTX reduces accumulation of active methotrexate in leukemia cells and decreases antileukemic effects, with differing consequences among major ALL subtypes.
Journal of Theoretical BiologyModelling chemotherapy resistance in palliation and failed cure
51 Citations2008Helen C. Monro, Eamonn A. Gaffney
Chemotherapy protocol design is considered using a simple, robust, model of advanced tumour growth with Gompertzian dynamics, taking into account the effects of drug resistance, predicted that reduced chemotherapy protocols can readily lead to improved survival times.
PLoS Computational BiologyModeling Mechanisms of In Vivo Variability in Methotrexate Accumulation and Folate Pathway Inhibition in Acute Lymphoblastic Leukemia Cells
49 Citations2010John C. Panetta, Alex Sparreboom +3 more
This study has provided new insights into the intracellular disposition of MTX in leukemia cells and how it affects treatment efficacy and the folate pathway model showed differential inhibition of DNPS relative to MTXPG accumulation, MTX dose, and schedule.
Chemistry & BiodiversityPredicting Ligand Interactions with ABC Transporters in ADME
45 Citations2009Michael Demel, Oliver H. Krämer +3 more
Journal of Theoretical BiologyModeling Multi-drug Chemotherapy: Tailoring Treatment to Individuals
44 Citations2002Shea N. Gardner
The KITT model suggests that including cytostatic drugs like tamoxifen and herceptin during treatment with cytotoxic drugs substantially increases the probability of cure and prolongs patient life, and suggests that altering drug scheduling may be more effective but not more toxic than dose escalation.
Journal of Clinical OncologyMathematics and Oncology: A Match for Life?
44 Citations2003Martine Piccart
Journal of Theoretical BiologyIntegrating cell-cycle progression, drug penetration and energy metabolism to identify improved cancer therapeutic strategies
43 Citations2008Raja Venkatasubramanian, Michael A. Henson +1 more
The therapeutic implications of the simulation results are that monolayer cultures are inadequate for accurately determining therapeutic effects in vitro, decreasing the diffusivity of paclitaxel could increase its efficacy, and measuring the proliferation fraction in tumors could enhance the prediction of therapeutic efficacy.
Cancer Chemotherapy and PharmacologyA mathematical model of in vivo methotrexate accumulation in acute lymphoblastic leukemia
42 Citations2002John C. Panetta, Yuri Yanishevski +7 more
Simulations based on the model-estimated parameters indicated greater accumulation of MTX, MTXPGs and total MTX (MTXPG1–7) with longer MTX infusions and with higher MTX doses, with the highest concentrations in hyperdiploid B-lineage, intermediate in non-hyperdiploids B- lineage, and lowest in T-cell ALL.
Mathematical Models and Methods in Applied SciencesUSING COMPUTER SIMULATIONS FOR EVALUATING THE EFFICACY OF BREAST CANCER CHEMOTHERAPY PROTOCOLS
42 Citations1999Eliezer Shochat, DVORA HART +1 more
Although high dose chemotherapy (HDT) cannot eradicate overt metastatic disease, it may lead to cure if applied early in the natural history of breast cancer, and the simulations suggest that a well tolerable continuous protocol is no less efficient.
Mathematical BiosciencesA mathematical model of the effects of drug resistance in cancer chemotherapy
33 Citations1984B. G. Birkhead, Walter M. Gregory
A mathematical model relating tumor responce under repeated doses of a single cytotoxic agent to the presence and accumulation of phenotypic drug resistance is proposed and it is shown how competing treatment strategies can be simulated and compared.
Cancer ResearchTumor Growth Instability and Its Implications for Chemotherapy
32 Citations2009P. Castorina, Daniela Carcò +2 more
The chemotherapy late intensity schedule is revised to account for tumor growth instability, where a small tumor cell fraction emerges that exhibits a higher proliferation rate than the parent strain.
Cell CycleCell Cycle Phase-Specific CHemotherapy: Computation Methods for Guiding Treatment
30 Citations2002Shea N. Gardner
This review summarizes mathematical models developed to improve the design of treatment regimens using cell-cycle phase-specific chemotherapy, which starts with simple models of dose response, then moves to more complex models of scheduling cell- cycle phase- specific drugs, and finally discusses mechanistic models that incorporate both genetic drug resistance and cell cycle-mediated drug resistance.
Control and CyberneticsQualitative analysis of controlled drug resistance model - inverse Laplace and and semigroup approach
29 Citations1999Andrzej Świerniak, Andrzej Polatiski +3 more
Bulletin of Mathematical BiologyA Mathematical Model of Breast Cancer Treatment with CMF and Doxorubicin
25 Citations2010Rachel Roe-Dale, David Isaacson +1 more
A mathematical model is presented to investigate the ordering phenomenon observed in the comparison of alternating to sequential regimens of CMF and suggests that drug resistance might be a key mechanism in the sequential regimen’s superiority.
Seminars in Cancer BiologyEmergence and prevention of resistance against small molecule inhibitors
25 Citations2005Dominik Wodarz, Natalia L. Komarova
This article applies a mathematical framework to the treatment of CML with Gleevec, in order to demonstrate how this mathematical framework can be applied to thetreatment of a specific cancer with small molecule inhibitors.
Future OncologyFrom the Evolution of Toxin Resistance to Virtual Clinical Trials: The Role of Mathematical Models in Oncology
23 Citations2010Zvia Agur
The use of virtual patients in clinical research will dramatically shorten the period of development of new drugs, and such models can also be used to personalize treatment regimens, substantially reducing the risk of clinical failure.
PubMedNew tools for cancer chemotherapy: computational assistance for tailoring treatments.
20 Citations2003Shea N. Gardner, Michael Fernandes
This review summarizes mechanistic mathematical models developed to improve the design of chemotherapy regimens and addresses the contrasts between mechanistic computational models and microarray technology, and how these two approaches may complement one another.
European Biophysics JournalOn a biophysical and mathematical model of Pgp-mediated multidrug resistance: understanding the “space–time” dimension of MDR
19 Citations2009Vasiliki C. Panagiotopoulou, Giles Richardson +2 more
It is demonstrated that the likelihood of drug-transporter meeting and thus interaction are also driven by the mechanical interaction between drug molecular weight (MW) and the membrane mechanical properties, which should allow us to mechanically control drug delivery.
Computational and Mathematical Methods in MedicineGradient Method for Finding Optimal Scheduling in Infinite Dimensional Models of Chemotherapy
19 Citations2000Jarosław Śmieja, Andrzej Świerniak +1 more
A population of neoplastic cells stratified into subpopulations of cells of different types is considered, in the form of an infinite dimensional system of ordinary differential state equations discussed in previous publications, into the integro-differential form.
JNCI Journal of the National Cancer InstituteEmergence of the Drug-Resistant Phenotype in Tumor Subpopulations: A Hybrid Model
18 Citations1989S. Michelson, Doris L. Slate
A mathematical model is proposed that describes the emergence of drug resistance in a tumor cell population by a stochastic birth-death-migration model with transition probabilities dependent on the deterministic distribution of drug within the average cell.
Cell ProliferationA mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection, design and delivery
18 Citations2002Lawrence M. Wein, Joseph T. Wu +2 more
The results suggest that high specificity is necessary but not sufficient to cure malignant gliomas; a nondispersed spatial profile of pretreatment tumour cells and/or good drug penetration are also required.
JNCI Journal of the National Cancer InstituteDrug Resistance-Reversal Strategies: Comparison of Experimental Data With Model Predictions
17 Citations1991Doris L. Slate, Seth Michelson
The model showed that, for resistant cells with high levels of glutathione, short-term cell survival was dose dependent and that even high doses of drug did not eliminate all of these cells, and may be useful in determining resistance mechanisms, their levels of effectiveness, and concentrations of compounds required at target sites to overcome them.
Mathematical Biosciences & EngineeringAnalysis and Optimization of Drug Resistant an Phase-Specific Cancer
16 Citations2005Andrzej Świerniak, Jarosław Śmieja
This paper presents analysis and biomedical implications of a certain class of bilinear systems that can be applied in modeling of cancer chemotherapy, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy in their different aspects.
Bulletin of Mathematical BiologyA mathematical model of the P-glycoprotein pump as a mediator of multidrug resistance
15 Citations1992S Michelson, Doris L. Slate
A mathematical model of this drug efflux pump has been developed which includes a dynamic calculation for efflux rate which considers Michaelis-Menten kinetics for both the substrate agent and ATP.
Bulletin of Mathematical BiologyA mathematical model for the inhibition of the multidrug resistance-associated p-glycoprotein pump
10 Citations1994S Michelson, Doris L. Slate
An extension of an earlier model of the p170 glycoprotein pump is presented, adding an inhibitor to the model and new equations are derived which represent either competitive or non-competitive inhibition in the pumping action of the glycop protein.
Bulletin of Mathematical BiologyA mathematical model for the inhibition of the multidrug resistance-associated P-glycoprotein pump
8 Citations1994Seth Michelson, Doris L. Slate
An extension of an earlier model of the p170 glycoprotein pump is presented, adding an inhibitor to the model and new equations are derived which represent either competitive or non-competitive inhibition in the pumping action of the glycop protein.
Blood Cancer JournalA new hypothesis: imatinib affects leukemic stem cells in the same way it affects all other leukemic cells
8 Citations2011Cristian Tomasetti
The hypothesis proposed here is that imatinib may be able to affect the LSCs in the same way it affects all other leukemic cells, that is, by inhibiting their proliferation and consequently causing them to reach their life span and die out.
Computational and Mathematical Methods in MedicineScheduling Chemotherapy: Catch 22 between Cell Kill and Resistance Evolution
8 Citations1999Shea N. Gardner
The model suggests that administering each fraction by continuous infusion may be more effective than giving the drug as a bolus, whether the drug is CS or CNS, and tumors with a low growth fraction or slow rate of cell division are predicted to be controlled more easily with CNS drugs.
Breast Cancer ResearchRecent translational research: computational studies of breast cancer
6 Citations2004Michael Retsky, Romano Demicheli +4 more
This review discusses developments in mathematics and computers in breast cancer research and clinical aids from a clinical perspective, and asks whether and how they translate into useful tools for patient treatment.
CytotechnologyMathematical models for multidrug resistance and its reversal
5 Citations1993Seth Michelson
A model which describes the molecular function of the P-glycoprotein pump in multidrug resistant (MDR) cell lines has been developed and is presented in detail and is aimed at a scientifically sophisticated but mathematically innocent audience.
Bulletin of Mathematical BiologyA Mathematical Model of Cell Cycle Effects in Gastric Cancer Chemotherapy
4 Citations2011Rachel Roe-Dale, David Isaacson +1 more
A mathematical model is presented to investigate the relationship between drug order and treatment response in gastric cancer chemotherapy involving a taxane coupled with flavopiridol, and results indicate that for an enhanced synergistic effect, flavopIRidol must be administered following taxane therapy.
…