A Dynamic Programming Approach for Approximate Optimal Control for Cancer Therapy

Nowakowski, Andrzej; Popa, Arkadiusz

doi:10.1007/s10957-012-0137-z

Cited by 4 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the HJB equations guarantee that the resulting treatment feedback strategies are globally optimal. Despite these advantages of the HJB, there are only a few treatment optimization studies [43,44] which use this feedback control paradigm.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

2020

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Moreover, the HJB equations guarantees that the resulting treatment feedback strategies are globally optimal. Despite these advantages of the HJB over PMP method, there are few works 38,39 which use the feedback control paradigm to find an optimal treatment strategy.…”

Section: Introductionmentioning

confidence: 99%

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

2020

View full text Add to dashboard Cite

show abstract

“…The fact that these policies are recovered in feedback form makes this approach particularly suitable for optimization of adaptive therapies. But even though the use of general optimal control in cancer treatment is by now common [ 1 ], the same is not true for the more robust HJB-based methods, which so far have been used in only a handful of cancer-related applications [ 4 , 8 , 23 , 29 , 56 – 58 ]. This is partly due to the HJBs’ well-known curse of dimensionality : the rapid increase in computational costs when the system state becomes higher-dimensional.…”

Section: Discussionmentioning

confidence: 99%

Threshold-awareness in adaptive cancer therapy

Wang,

Scott,

Vladimirsky

2024

PLoS Comput Biol

View full text Add to dashboard Cite

Although adaptive cancer therapy shows promise in integrating evolutionary dynamics into treatment scheduling, the stochastic nature of cancer evolution has seldom been taken into account. Various sources of random perturbations can impact the evolution of heterogeneous tumors, making performance metrics of any treatment policy random as well. In this paper, we propose an efficient method for selecting optimal adaptive treatment policies under randomly evolving tumor dynamics. The goal is to improve the cumulative “cost” of treatment, a combination of the total amount of drugs used and the total treatment time. As this cost also becomes random in any stochastic setting, we maximize the probability of reaching the treatment goals (tumor stabilization or eradication) without exceeding a pre-specified cost threshold (or a “budget”). We use a novel Stochastic Optimal Control formulation and Dynamic Programming to find such “threshold-aware” optimal treatment policies. Our approach enables an efficient algorithm to compute these policies for a range of threshold values simultaneously. Compared to treatment plans shown to be optimal in a deterministic setting, the new “threshold-aware” policies significantly improve the chances of the therapy succeeding under the budget, which is correlated with a lower general drug usage. We illustrate this method using two specific examples, but our approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.

show abstract

“…The fact that these policies are recovered in feedback form makes this approach particularly suitable for optimization of adaptive therapies. But even though the use of general optimal control in cancer treatment is by now common [55], the same is not true for the more robust HJB-based methods, which so far have been used in only a handful of cancer-related applications [1, 7, 19, 25, 36, 42, 53]. This is partly due to the HJBs’ well-known curse of dimensionality : the rapid increase in computational costs when the system state becomes higher-dimensional.…”

Section: Discussionmentioning

confidence: 99%

Threshold-awareness in adaptive cancer therapy

Wang

Scott

Vladimirsky

2022

Preprint

View full text Add to dashboard Cite

While adaptive cancer therapy is beginning to prove a promising approach of building evolutionary dynamics into therapeutic scheduling, the stochastic nature of cancer evolution has rarely been incorporated. Various sources of random perturbations can impact the evolution of heterogeneous tumors. In this paper, we propose a method that can effectively select optimal adaptive treatment policies under randomly evolving tumor dynamics based on Stochastic Optimal Control theory. We first construct a stochastic model of cancer dynamics under drug therapy based on Evolutionary Game theory. That model is then used to improve the cumulative ''cost'', a combination of the total amount of drugs used and the time to recovery. As this cost becomes random in a stochastic setting, we maximize the probability of recovery under a pre-specified cost threshold (or a ''budget''). We can achieve our goal for a range of threshold values simultaneously using the tools of dynamic programming. We then compare our threshold-aware policies with the policies previously shown to be optimal in the deterministic setting. We show that this threshold-awareness yields a significant improvement in the probability of under-the-budget recovery, which is correlated with a lower general drug usage. The particular model underlying our discussion has originated in [Kaznatcheev et al. 2017], but the presented approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.

show abstract

A Dynamic Programming Approach for Approximate Optimal Control for Cancer Therapy

Cited by 4 publications

References 15 publications

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

Threshold-awareness in adaptive cancer therapy

Threshold-awareness in adaptive cancer therapy

Contact Info

Product

Resources

About