A mathematical model to study the effects of drugs administration on tumor growth dynamics

Magni, Paolo; Simeoni, Monica; Poggesi, Italo; Rocchetti, Maurizio; Nicolao, Giuseppe De

doi:10.1016/j.mbs.2005.12.028

Cited by 75 publications

(71 citation statements)

References 17 publications

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“…Ordinate represents magnitude of effect (arbitrary units). a Behavior of the cell distribution model; b behavior of the signal distribution model probability density function (10). It is likely that both the cellkill signal and the proportion of cells committed to cell death are defined by such distribution functions.…”

Section: Discussionmentioning

confidence: 99%

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Comparison of Two Pharmacodynamic Transduction Models for the Analysis of Tumor Therapeutic Responses in Model Systems

Yang

Mager

Straubinger

2009

AAPS J

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Abstract. Semi-mechanistic pharmacodynamic (PD) models that capture tumor responses to anticancer agents with fidelity can provide valuable insights that could aid in the optimization of dosing regimens and the development of drug delivery strategies. This study evaluated the utility and potential interchangeability of two transduction-type PD models: a cell distribution model (CDM) and a signal distribution model (SDM). The evaluation was performed by simulating dense and sparse tumor response data with one model and analyzing it using the other. Performance was scored by visual inspection and precision of parameter estimation. Capture of tumor response data was also evaluated for a liposomal formulation of paclitaxel in the paclitaxel-resistant murine Colon-26 model. A suitable PK model was developed by simultaneous fitting of literature data for paclitaxel formulations in mice. Analysis of the simulated tumor response data revealed that the SDM was more flexible in describing delayed drug effects upon tumor volume progression. Dense and sparse data simulated using the CDM were fit very well by the SDM, but under some conditions, data simulated using the SDM were fitted poorly by the CDM. Although both models described the dose-dependent therapeutic responses of Colon-26 tumors, the fit by the SDM contained less bias. The CDM and SDM are both useful transduction models that recapitulate, with fidelity, delayed drug effects upon tumor growth. However, they are mechanistically distinct and not interchangeable. Both fit some types of tumor growth data well, but the SDM appeared more robust, particularly where experimental data are sparse.

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Section: Discussionmentioning

confidence: 99%

“…The cell distribution model (CDM) (8,10) is based on a system of simple transit compartments that link dosing regime (PK) to tumor growth response (PD). The mass of the untreated tumor increases as cells traverse the cell cycle according to a growth model.…”

Section: Theorymentioning

confidence: 99%

Comparison of Two Pharmacodynamic Transduction Models for the Analysis of Tumor Therapeutic Responses in Model Systems

Yang

Mager

Straubinger

2009

AAPS J

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“…The profile simulated with the interval M3 method appears to be the closest to the true profile and especially for high dose for which we observe the lowest tumor volumes. The C T defined by Simeoni et al (8,17) was also impacted. For the Btrue model^C T = 890 ng ml −1 , with the set of parameters estimated with method (a) C T = 974 ng ml −1 and with method (l) C T = 886 ng ml −1 .…”

Section: Visual Predictive Checkmentioning

confidence: 97%

Improvement of Parameter Estimations in Tumor Growth Inhibition Models on Xenografted Animals: a Novel Method to Handle the Interval Censoring Caused by Measurement of Smaller Tumors

Pierrillas

Tod

Amiel

et al. 2016

AAPS J

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Abstract. The purpose of this study was to explore the interval censoring induced by caliper measurements on smaller tumors during tumor growth experiments in preclinical studies and to show its impact on parameter estimations. A new approach, the so-called interval-M3 method, is proposed to specifically handle this type of data. Thereby, the interval-M3 method was challenged with different methods (including classical methods for handling below quantification limit values) using Stochastic Simulation and Estimation process to take into account the censoring. In this way, 1000 datasets were simulated under the design of a typical of tumor growth study in xenografted mice, and then, each method was used for parameter estimation on the simulated datasets. Relative bias and relative root mean square error (relative RMSE) were consequently computed for comparison purpose. By not considering the censoring, parameter estimations appeared to be biased and particularly the cytotoxic effect parameter, k 2 , which is the parameter of interest to characterize the efficacy of a compound in oncology. The best performance was noted with the interval-M3 method which properly takes into account the interval censoring induced by caliper measurement, giving overall unbiased estimations for all parameters and especially for the antitumor effect parameter (relative bias = 0.49%, and relative RMSE = 4.06%). KEY WORDS: below quantification limit; interval censoring; interval-M3 method; simultaneous modeling continuous and categorical data; xenograft model.

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Section: Simple Growth Models With Ordinary Differential Equations (Omentioning

confidence: 99%

“…All these simple models [206] are clearly analytically integrable and are usually too coarse to account for observations of real tumour growth curves, but can be compared with data on tumour growth curves as a reference scale. Another model of the same type [190,245] has tried to give account of what is often observed with tumours growing in laboratory mice: initial exponential growth followed by linear growth, i.e., its eventual solutions are lines with constant slope p. This "ad hoc" model writes:with a high value of ψ, e.g., ψ = 20, which yields the expected behaviour in a smooth manner. The same idea could be followed to combine Gompertz growth followed by linear behaviour, another feature observed at times with tumour growth curves in mice, possibly attributable to an "angiogenic switch" transition, when the tumour succeeds in diverting an important part of the blood flow to its own benefit:…”

mentioning

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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A mathematical model to study the effects of drugs administration on tumor growth dynamics

Cited by 75 publications

References 17 publications

Comparison of Two Pharmacodynamic Transduction Models for the Analysis of Tumor Therapeutic Responses in Model Systems

Comparison of Two Pharmacodynamic Transduction Models for the Analysis of Tumor Therapeutic Responses in Model Systems

Improvement of Parameter Estimations in Tumor Growth Inhibition Models on Xenografted Animals: a Novel Method to Handle the Interval Censoring Caused by Measurement of Smaller Tumors

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

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