| Abstract: |
| Most patients diagnosed with prostate cancer (PC) are cured with surgery or radiation therapy. Those with metastases or relapse require additional systemic hormonal therapy. Unfortunately, over time, cancer cells develop resistance, which is usually first clinically observed as a rise in PSA levels followed by disease progression. Drug resistance varies from patient to patient, ranging from a few months to two years.
The role of intermittent (adaptive) therapy~(IAS), as opposed to continuous hormonal therapy~(CAS), is currently being actively studied to prolong quality of life and investigate the sensitivity of PC to pharmacological intervention.
IAS stops hormonal therapy when a clinical goal is reached or PSA levels fall. Then, after a certain period of time, when the cancer returns or the PSA threshold~ rerises, this process continues in a cyclical manner until resistance develops and the disease treatment requires other medical interventions. During IAS, patients are switched between on and off therapy according to the PSA threshold or alternately at regular intervals until treatment becomes ineffective.
In this study, we constructed a bilinear control model that describes the relationship between a population of androgen-dependent cancer cells and two populations of androgen-independent cancer cells, both during and without hormonal therapy. Using the properties of the reachable set and Pontryagin maximum principle, we solve an optimal control problem of minimization of the total cancer load at the end of the treatment period and answer the following important questions:
1) will a certain treatment (such as CAS or IAS) be effective?
2) how long will it take for the treatment to become effective?
3) what is the optimal schedule for the on`` and off`` periods? |
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