Cancer chemotherapy optimization under evolving drug resistance

Świerniak, Andrzej; Śmieja, Jarosław

doi:10.1016/s0362-546x(01)00184-5

Cited by 29 publications

(17 citation statements)

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“…Proof. Using the Lyapunov direct stability method, positive definite V(e(t),K p (t)) in Equation 23 and negative semidef-initeV(e(t),K p (t)) in Equation 26 yield that the error dynamics is stable and e(t) andK p (t) are bounded function of time, which conclude the boundedness of x p (t) and K p (t), which guarantees the boundedness oḟe(t). Furthermore, V(e(t),K p (t)) = −̇e T (t)Q ad e(t) − e T (t)Q adė (t) is bounded function of time, which implies thatV(e(t),K p (t)) is uniformly continuous.…”

Section: Mrac Design Problem For Lti Systems With Full State Feedbackmentioning

confidence: 99%

“…Different researchers have proposed several optimal control-based methods for the treatment of cancer patients via chemotherapy. 1,[7][8][9][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] Bahrami and Kim 18 and Swan and Vincent 19 utilized optimal control techniques in chemotherapy for cancer treatment. Swan 7 proposed an optimal solution for cancer treatment through chemotherapy by considering the lower limit for normal cells.…”

Section: Introductionmentioning

confidence: 99%

“…In almost all the proposed optimal control approaches, the optimal amount of the drug is determined for the predefined optimal control problem that needs specific mathematical operations to reach the required solution. 9,[18][19][20][23][24][25][26][27] The state-dependent Riccati equation (SDRE) approach is a rather new methodology for the systematic design of nonlinear suboptimal feedback controllers for a class of state-dependent nonlinear dynamics. 10,36 Recently, the SDRE technique has been utilized by several researchers for the eradication of several problems related to cancer treatment.…”

Section: Introductionmentioning

confidence: 99%

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Controller design for personalized drug administration in cancer therapy: Successive approximation approach

Babaei

Salamcı

2017

Optim Control Appl Methods

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Summary A novel controller design approach is developed to determine personalized chemotherapy drug delivery protocols for cancer treatment. The methodology combines successive approximation approach for optimal control and model reference adaptive control to realize the proposed drug administration scenario for patients without prior knowledge of model parameters in the nonlinear cancer dynamics. Although many approaches have been proposed to determine the optimal drug delivery protocol for eradicating tumor in the nonlinear cancer model, the main shortcoming of these approaches is the requirement of nonlinear model dynamics, which is unknown to physicians in reality. To overcome this deficiency, we first determine the optimal drug delivery protocol for a reference patient with known mathematical model and parameters via successive approximation approach technique. Then, using the proposed approach, we adapt the reference patient's drug administration scenario to unknown cancer patients by suggesting a new adaptation mechanism for the unknown nonlinear plant dynamics. An efficient and robust approach is proposed here for the physicians to prescribe a personalized chemotherapy protocol for a cancer patient by regulating the drug delivery protocol of a reference patient. The efficacy of the proposed algorithm in eradicating the tumor lumps with different sizes in several patients is verified using numerical simulations in which the unknown parameters are randomly selected in the Monte Carlo approach.

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Section: Mrac Design Problem For Lti Systems With Full State Feedbackmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Controller design for personalized drug administration in cancer therapy: Successive approximation approach

Babaei

Salamcı

2017

Optim Control Appl Methods

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“…This is in full agreement with maximum tolerated dose (MTD) protocols in medical practice. However, if models for heterogeneous tumors consisting of subpopulations of cancer cells of various chemotherapeutic sensitivities are considered, specific time-varying administration schedules at less than maximum dose (so-called singular controls) become viable options [29,35,58] and in such a case "more is not necessarily better" [19]. Similarly, in models for anti-angiogenic treatment, the interactions of a primary tumor with the vasculature is largely reduced to angiogenic signaling and the interactions with endothelial cells that form the lining of the newly developing vessels and capillaries (e.g., see [13,17,36,42]) while tumor immune system interactions are not considered.…”

Section: Fig 1 the Tumor Microenvironment: A Strongly Interacting Nomentioning

confidence: 99%

Optimal Control of Cancer Treatments: Mathematical Models for the Tumor Microenvironment

Schättler¹,

Ledzewicz²

2015

Springer INdAM Series

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Mathematical models for cancer treatment are analyzed as optimal control problems when selected aspects of the tumor microenvironment are taken into account. The significance of treatment protocols that administer agents at less than maximum tolerated dose rates is analyzed in this context. When angiogenic signaling or tumor immune system interactions are included in the model, singular controls that administer therapeutic agents at less than maximum dose become optimal. Their relations to metronomic dosing are discussed.

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“…Mathematical models, on the other hand, can be freely used to explore such ideas. There exist an abundance of mathematical models for chemotherapy under tumor heterogeneity ranging from rudimentary models that just distinguish a small number of sub-populations (e.g., Hahnfeldt et al [21], Ledzewicz and Schättler [27,29,31]) to models with increasing degrees of resistance (e.g., Swierniak et al [55,56] or Wang and Schättler [58]) and even a continuum of traits (e.g., Lorz et al [34,35], Billy and Clairambault [3], Delitalia and Lorenzi [8,10], Lavi, Green et al [19,24]). Recurrent conclusions that can be drawn from a variety of these models are that, indeed, if conditions are right (i.e., under assumptions on the relative growth rates of the sub-populations and about the effectiveness of the drugs) it is possible to limit cancer growth through a judicious choice of drug administration schedules.…”

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confidence: 99%

On the role of tumor heterogeneity for optimal cancer chemotherapy

Ledzewicz¹,

Schättler²,

Wang³

2019

Networks &Amp; Heterogeneous Media

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We review results about the influence tumor heterogeneity has on optimal chemotherapy protocols (relative to timing, dosing and sequencing of the agents) that can be inferred from mathematical models. If a tumor consists of a homogeneous population of chemotherapeutically sensitive cells, then optimal protocols consist of upfront dosing of cytotoxic agents at maximum tolerated doses (MTD) followed by rest periods. This structure agrees with the MTD paradigm in medical practice where drug holidays limit the overall toxicity. As tumor heterogeneity becomes prevalent and sub-populations with resistant traits emerge, this structure no longer needs to be optimal. Depending on conditions relating to the growth rates of the sub-populations and whether drug resistance is intrinsic or acquired, various mathematical models point to administrations at lower than maximum dose rates as being superior. Such results are mirrored in the medical literature in the emergence of adaptive chemotherapy strategies. If conditions are unfavorable, however, it becomes difficult, if not impossible, to limit a resistant population from eventually becoming dominant. On the other hand, increased heterogeneity of tumor cell populations increases a tumor's immunogenicity and immunotherapies may provide a viable and novel alternative for such cases.2010 Mathematics Subject Classification. Primary: 92C50, 49K15; Secondary: 93C15.

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Cancer chemotherapy optimization under evolving drug resistance

Cited by 29 publications

References 0 publications

Controller design for personalized drug administration in cancer therapy: Successive approximation approach

Controller design for personalized drug administration in cancer therapy: Successive approximation approach

Optimal Control of Cancer Treatments: Mathematical Models for the Tumor Microenvironment

On the role of tumor heterogeneity for optimal cancer chemotherapy

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