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Forys U.,University of Warsaw | Bodnar M.,University of Warsaw | Kogan Y.,Institute for Medical BioMathematics
Journal of Mathematical Biology | Year: 2016

In the case of some specific cancers, immunotherapy is one of the possible treatments that can be considered. Our study is based on a mathematical model of patient-specific immunotherapy proposed in Kronik et al. (PLoS One 5(12):e15,482, 2010). This model was validated for clinical trials presented in Michael et al. (Clin Cancer Res 11(12):4469–4478, 2005). It consists of seven ordinary differential equations and its asymptotic dynamics can be described by some t-periodic one-dimensional dynamical system. In this paper we propose a generalised version of this t-periodic system and study the dynamics of the proposed model. We show that there are three possible types of the model behaviour: the solution either converges to zero, or diverges to infinity, or it is periodic. Moreover, the periodic solution is unique, and it divides the phase space into two sub-regions. The general results are applied to the PC specific case, which allow to derive conditions guaranteeing successful as well as unsuccessful treatment. The results indicate that a single vaccination is not sufficient to cure the cancer. © 2016 The Author(s)


Kronik N.,Holon Institute of Technology | Kogan Y.,Institute for Medical BioMathematics | Schlegel P.G.,University of Wurzburg | Wolfl M.,University of Wurzburg
Journal of Immunotherapy | Year: 2012

T-cell mediated immunotherapy for malignant diseases has become an effective treatment option, especially in malignant melanoma. Recent advances have enabled the transfer of high T-cell numbers with high functionality. However, with more T cells becoming technically available for transfer, questions about dose, treatment schedule, and safety become most relevant. Mathematical oncology can simulate tumor characteristics in silico and predict the tumor response to novel therapeutics. Using similar methods to classical pharmacokinetics/pharmacodynamics-type models, mathematical oncology translates the findings into a multiparameter model system and simulates T-cell therapy for malignant diseases. The tumor and immune system dynamics model can provide minimal requirements (in terms of T-cell dose and T-cell functionality) depending on the tumor characteristics (growth rate, residual tumor size) for a clinical study, and help select the best treatment schedule (repetitive doses, minimally required duration, etc.). Here, we present a new mathematical model developed for modeling cellular immunotherapy for melanoma. Computer simulations based on the new model offer an explanation for the observed finding from clinical trials that the patients with the smallest tumor load respond better. We simulate different parameters critical for improvement of cellular therapy for patients with high tumor load of fast-growing tumors. We show that tumor growth rate and tumor load are crucial in predicting the outcome of T-cell therapy. Rather than intuitively extrapolating from experimental data, we demonstrate how mathematical oncology can assist in rational planning of clinical trials. Copyright © 2012 by Lippincott Williams & Wilkins.


Jager E.,Institute for Medical BioMathematics | van der Velden V.H.J.,Rotterdam University | te Marvelde J.G.,Rotterdam University | Walter R.B.,Fred Hutchinson Cancer Research Center | And 4 more authors.
PLoS ONE | Year: 2011

Gemtuzumab ozogamicin (GO) is a chemotherapy-conjugated anti-CD33 monoclonal antibody effective in some patients with acute myeloid leukemia (AML). The optimal treatment schedule and optimal timing of GO administration relative to other agents remains unknown. Conventional pharmacokinetic analysis has been of limited insight for the schedule optimization. We developed a mechanism-based mathematical model and employed it to analyze the time-course of free and GO-bound CD33 molecules on the lekemic blasts in individual AML patients treated with GO. We calculated expected intravascular drug exposure (I-AUC) as a surrogate marker for the response to the drug. A high CD33 production rate and low drug efflux were the most important determinants of high I-AUC, characterizing patients with favorable pharmacokinetic profile and, hence, improved response. I-AUC was insensitive to other studied parameters within biologically relevant ranges, including internalization rate and dissociation constant. Our computations suggested that even moderate blast burden reduction prior to drug administration enables lowering of GO doses without significantly compromising intracellular drug exposure. These findings indicate that GO may optimally be used after cyto-reductive chemotherapy, rather than before, or concomitantly with it, and that GO efficacy can be maintained by dose reduction to 6 mg/m 2 and a dosing interval of 7 days. Model predictions are validated by comparison with the results of EORTC-GIMEMA AML19 clinical trial, where two different GO schedules were administered. We suggest that incorporation of our results in clinical practice can serve identification of the subpopulation of elderly patients who can benefit most of the GO treatment and enable return of the currently suspended drug to clinic. © 2011 Jager et al.


Kronik N.,Institute for Medical BioMathematics | Kronik N.,Holon Institute of Technology | Kogan Y.,Institute for Medical BioMathematics | Elishmereni M.,Institute for Medical BioMathematics | And 3 more authors.
PLoS ONE | Year: 2010

Background: Therapeutic vaccination against disseminated prostate cancer (PCa) is partially effective in some PCa patients. We hypothesized that the efficacy of treatment will be enhanced by individualized vaccination regimens tailored by simple mathematical models. Methodology/Principal Findings: We developed a general mathematical model encompassing the basic interactions of a vaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole-cell vaccine. For model validation in the absence of any other pertinent marker, we used the clinically measured changes in prostate-specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were divided into each patient's training set and his validation set. The training set, used for model personalization, contained the patient's initial sequence of PSA levels; the validation set contained his subsequent PSA data points. Personalized models were simulated to predict changes in tumor burden and PSA levels and predictions were compared to the validation set. The model accurately predicted PSA levels over the entire measured period in 12 of the 15 vaccination-responsive patients (the coefficient of determination between the predicted and observed PSA values was R2 = 0.972). The model could not account for the inconsistent changes in PSA levels in 3 of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. Personalized regimens predicted to enhance the effects of therapy differed among the patients. Conclusions/Significance: Using a few initial measurements, we constructed robust patient-specific models of PCa immunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value and feasibility of individualized model-suggested immunotherapy protocols. © 2010 Kronik et al.


Agur Z.,Institute for Medical BioMathematics | Agur Z.,Optimata | Elishmereni M.,Institute for Medical BioMathematics | Elishmereni M.,Optimata | And 2 more authors.
Wiley Interdisciplinary Reviews: Systems Biology and Medicine | Year: 2014

Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology. For further resources related to this article, please visit the WIREs website. Conflict of interest: The authors have declared no conflicts of interest for this article. © 2014 Wiley Periodicals, Inc.

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