Optimal and receding horizon control of tumor growth in myeloma bone disease

Lemos, João M.; Caiado, Daniela V.; Coelho, Rui Moura; Vinga, Susana

doi:10.1016/j.bspc.2015.10.004

Cited by 13 publications

(5 citation statements)

References 10 publications

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“…The first such application was due to Swan & Vincent [33], who found the optimal treatment strategy for multiple myeloma with the objective to minimize the total amount of drugs by using the Pontryagin minimum principle (PMP) [34]. Since then, others have used the PMP in different cancer treatment problems: a chemotherapy optimization under evolving drug resistance [35][36], optimal scheduling of a vessel disruptive agent [38], MAPK inhibitors [39] input in cancer treatment, minimizing the amount of drugs prescribed in tumour-immune model [40], finding a compromise between drug toxicity and tumour repression for the myeloma bone disease [41], and many others.…”

Section: Introductionmentioning

confidence: 99%

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

2020

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BACKGROUND: Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are administered based on the current state of tumor. But the adaptive treatment policies examined so far have been largely ad hoc. In this paper we propose a method for systematically optimizing the rules of adaptive policies based on an Evolutionary Game Theory model of cancer dynamics.METHODS: Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal treatment strategies. In particular, we optimize the total drug usage and time to recovery by solving a Hamilton-Jacobi-Bellman equation based on a mathematical model of tumor evolution.RESULTS: We compare adaptive/optimal treatment strategy with MTD-based treatment policy. We show that optimal treatment strategies can dramatically decrease the total amount of drugs prescribed as well as increase the fraction of initial tumour states from which the recovery is possible. We also examine the optimization tradeoffs between the total administered drugs and recovery time.CONCLUSIONS: The adaptive therapy combined with optimal control theory is a promising concept in the cancer treatment and should be integrated into clinical trial design. * Other tumor regimes (fully angiogenic and glycolyctic) also exist outside of this parameter range. They are less interesting from the point of view of treatment strategies, but we still consider them for the sake of completeness in Section 6.3 of Supplementary Materials.

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Section: Introductionmentioning

confidence: 99%

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

2020

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“…The first application of optimal control theory in cancer was done by Swan and Vincent 27 who found the optimal treatment strategy for multiple myeloma with the objective to minimize the total amount of drugs used applying the Pontryagin Minimum Principle (PMP) 28 . Since then, others have used the PMP to different optimal cancer treatment problems: a chemotherapy optimization under evolving drug resistance [29][30][31] , optimal scheduling of a vessel disruptive agent 32 , MAPK inhibitors 33 input in cancer treatment, minimization amount of drugs prescribed in tumorimmune model 34 , finding compromise between drug toxicity and tumor repression for the myeloma bone disease 35 , and many others.…”

Section: Introductionmentioning

confidence: 99%

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Gluzman

Scott

Vladimirsky

2018

Preprint

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Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are administered based on the current state of tumor. But the adaptive treatment policies examined so far have been largely ad hoc. In this paper we propose a method for systematically optimizing the rules of adaptive policies based on an Evolutionary Game Theory model of cancer dynamics. Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal treatment strategies. In particular, we optimize the total drug usage and time to recovery by solving a Hamilton-Jacobi-Bellman equation based on a mathematical model of tumor evolution. We compare adaptive/optimal treatment strategy with MTD-based treatment policy. We show that optimal treatment strategies can dramatically decrease the total amount of drugs prescribed as well as increase the fraction of initial tumour states from which the recovery is possible. We also examine the optimization trade-offs between the total administered drugs and recovery time. The adaptive therapy combined with optimal control theory is a promising concept in the cancer treatment and should be integrated into clinical trial design.

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“…Because the literature does not offer a concise way to quantify adverse effects on healthy cells caused by a combination of multiple drugs, we apply a mathematical regularization function to the treatment vector as an idealized measure. Prior work has used L1 [ 22 , 23 ] and L2 [ 56 ] regularization for this purpose. In our simulation study we use L1 ( R L 1 ), L2 ( R L 2 ) and sum of logs regularization ( R ln ) defined as and compare differences in resulting treatments.…”

Section: Methodsmentioning

confidence: 99%

“…R �0 to the treatment vector as an idealized measure. Prior work has used L1 [22,23] and L2 [56] regularization for this purpose. In our simulation study we use L1 (R L1 ), L2 (R L2 ) and sum of logs regularization (R ln ) defined as…”

Section: Combination Treatment Optimizationmentioning

confidence: 99%

Combination treatment optimization using a pan-cancer pathway model

et al. 2021

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The design of efficient combination therapies is a difficult key challenge in the treatment of complex diseases such as cancers. The large heterogeneity of cancers and the large number of available drugs renders exhaustive in vivo or even in vitro investigation of possible treatments impractical. In recent years, sophisticated mechanistic, ordinary differential equation-based pathways models that can predict treatment responses at a molecular level have been developed. However, surprisingly little effort has been put into leveraging these models to find novel therapies. In this paper we use for the first time, to our knowledge, a large-scale state-of-the-art pan-cancer signaling pathway model to identify candidates for novel combination therapies to treat individual cancer cell lines from various tissues (e.g., minimizing proliferation while keeping dosage low to avoid adverse side effects) and populations of heterogeneous cancer cell lines (e.g., minimizing the maximum or average proliferation across the cell lines while keeping dosage low). We also show how our method can be used to optimize the drug combinations used in sequential treatment plans—that is, optimized sequences of potentially different drug combinations—providing additional benefits. In order to solve the treatment optimization problems, we combine the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm with a significantly more scalable sampling scheme for truncated Gaussian distributions, based on a Hamiltonian Monte-Carlo method. These optimization techniques are independent of the signaling pathway model, and can thus be adapted to find treatment candidates for other complex diseases than cancers as well, as long as a suitable predictive model is available.

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Optimal and receding horizon control of tumor growth in myeloma bone disease

Cited by 13 publications

References 10 publications

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Combination treatment optimization using a pan-cancer pathway model

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