Modelling bistable tumour population dynamics to design effective treatment strategies

Akhmetzhanov, Andrei R.; Kim, Jong Wook; Sullivan, Ryan J.; Beckman, Robert A.; Tamayo, Pablo; Yeang, Chen‐Hsiang

doi:10.1016/j.jtbi.2019.05.005

Cited by 20 publications

(6 citation statements)

References 70 publications

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“…Careful experiments need to be set up to discriminate between the two possible mechanisms, as they may have different implications for how a more optimal treatment would be designed. Positive clinical results for evolutionary-guided therapies remain confounded by other potential mechanisms driving them, including the effect of intermittent scheduling on the intratumoral vasculature, 79,80 reversible gene expression profiles affecting drug resistance of a single subclone, 81 or the immune system. 82 -85 The uncertainty about correct model assumptions is termed uncertainty about “model topology.” FQM attempts to do a sensitivity analysis across multiple model topologies.…”

Section: Coping With Uncertaintymentioning

confidence: 99%

How Should Cancer Models Be Constructed?

2020

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Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

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Section: Coping With Uncertaintymentioning

confidence: 99%

How Should Cancer Models Be Constructed?

2020

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“…A promising engineering approach is to use a mathematical model describing the effect of the drug on tumor growth and use this model to generate an optimal therapy. There are numerous models in the literature (see [10], [13], [14], [15] and several therapy generation algorithms [10], [16], [17], [18]). A specific characteristic of this physiological problem is that the input is the injection, which is positive, and the system is impulsive.…”

Section: Introductionmentioning

confidence: 99%

Positive Impulsive Control of Tumor Therapy—A Cyber-Medical Approach

Kovács,

Ferenci,

Gombos

et al. 2024

IEEE Trans. Syst. Man Cybern, Syst.

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Chemotherapy optimization based on mathematical models is a promising direction of personalized medicine. Personalizing, thus optimizing treatments, may have multiple advantages, from fewer side effects to lower costs. However, personalization is a complicated process in practice. We discuss a mathematical model of tumor growth and therapy optimization algorithms that can be used to personalize therapies. The therapy generation is based on the concept of keeping the drug level over a specified value. A mixed-effect model is used for parametric identification, and the doses are calculated using a two-compartment model for drug pharmacokinetics, and a nonlinear pharmacodynamics and tumor dynamics model. We propose personalized therapy generation algorithms for having a maximal effect and minimal effective doses. We handle inter-and intra-patient variability for the minimal effective dose therapy. Results from mouse experiments for the personalized therapy are discussed and the algorithms are compared to a generic protocol based on overall survival. The experimental results show that the introduced

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“…There is a hope that mathematical models of the dynamics and treatment of melanoma will help to choose the optimal treatment protocol. Mathematical models of cancer are commonly developed on the basis of ordinary differential equations or partial differential equations [9,10,[13][14][15][16][17]. There are several articles that use optimal control theory to control drug dosage in various models of melanoma [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Optimal Melanoma Treatment Protocols for a Bilinear Control Model

Хайлов

Grigorieva

2023

Mathematics

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In this research, for a given time interval, which is the general period of melanoma treatment, a bilinear control model is considered, given by a system of differential equations, which describes the interaction between drug-sensitive and drug-resistant cancer cells both during drug therapy and in the absence of it. This model also contains a control function responsible for the transition from the stage of such therapy to the stage of its absence and vice versa. To find the optimal moments of switching between these stages, the problem of minimizing the cancer cells load both during the entire period of melanoma treatment and at its final moment is stated. Such a minimization problem has a nonconvex control set, which can lead to the absence of an optimal solution to the stated minimization problem in the classes of admissible modes traditional for applications. To avoid this problem, the control set is imposed to be convex. As a result, a relaxed minimization problem arises, in which the optimal solution exists. An analytical study of this minimization problem is carried out using the Pontryagin maximum principle. The corresponding optimal solution is found in the form of synthesis and may contain a singular arc. It shows that there are values of the parameters of the bilinear control model, its initial conditions, and the time interval for which the original minimization problem does not have an optimal solution, because it has a sliding mode. Then for such values it is possible to find an approximate optimal solution to the original minimization problem in the class of piecewise constant controls with a predetermined number of switchings. This research presents the results of the analysis of the connection between such an approximate solution of the original minimization problem and the optimal solution of the relaxed minimization problem based on numerical calculations performed in the Maple environment for the specific values of the parameters of the bilinear control model, its initial conditions, and the time interval.

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Modelling bistable tumour population dynamics to design effective treatment strategies

Cited by 20 publications

References 70 publications

How Should Cancer Models Be Constructed?

How Should Cancer Models Be Constructed?

Positive Impulsive Control of Tumor Therapy—A Cyber-Medical Approach

Optimal Melanoma Treatment Protocols for a Bilinear Control Model

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