Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver
This paper proposes a real-life volume reduction for cancer cells using optimal doses of radiation and an anti-angiogenic drug. A generalized dynamical system based on the diffusion-consumption equation along with stimulation and inhibition factors is proposed. To achieve continuous and low-dose the...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/5554420 |
| _version_ | 1797670374977044480 |
|---|---|
| author | Iman Alimirzaei Alaeddin Malek |
| author_facet | Iman Alimirzaei Alaeddin Malek |
| author_sort | Iman Alimirzaei |
| collection | DOAJ |
| description | This paper proposes a real-life volume reduction for cancer cells using optimal doses of radiation and an anti-angiogenic drug. A generalized dynamical system based on the diffusion-consumption equation along with stimulation and inhibition factors is proposed. To achieve continuous and low-dose therapy, the related problem is simulated by an optimal regulator problem mathematically. By combining steepest descent, conjugate gradient, and Armijo techniques, a novel hybrid indirect iterative solver is designed. For accuracy and execution speed, the current solver is compared with an interior-point optimizer and sequential quadratic Hamiltonian methods. Cancer therapy under two different treatment strategies and 24 various versions of the general dynamical system is considered numerically. A comprehensive analysis of the corresponding outcomes is presented. Numerical results and related diagrams are provided. |
| first_indexed | 2024-03-11T20:58:49Z |
| format | Article |
| id | doaj.art-8291ce8d4ca745baa08d698689c05360 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-03-11T20:58:49Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-8291ce8d4ca745baa08d698689c053602023-09-30T00:00:02ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/5554420Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect SolverIman Alimirzaei0Alaeddin Malek1Tarbiat Modares UniversityTarbiat Modares UniversityThis paper proposes a real-life volume reduction for cancer cells using optimal doses of radiation and an anti-angiogenic drug. A generalized dynamical system based on the diffusion-consumption equation along with stimulation and inhibition factors is proposed. To achieve continuous and low-dose therapy, the related problem is simulated by an optimal regulator problem mathematically. By combining steepest descent, conjugate gradient, and Armijo techniques, a novel hybrid indirect iterative solver is designed. For accuracy and execution speed, the current solver is compared with an interior-point optimizer and sequential quadratic Hamiltonian methods. Cancer therapy under two different treatment strategies and 24 various versions of the general dynamical system is considered numerically. A comprehensive analysis of the corresponding outcomes is presented. Numerical results and related diagrams are provided.http://dx.doi.org/10.1155/2023/5554420 |
| spellingShingle | Iman Alimirzaei Alaeddin Malek Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver Journal of Mathematics |
| title | Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver |
| title_full | Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver |
| title_fullStr | Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver |
| title_full_unstemmed | Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver |
| title_short | Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver |
| title_sort | optimal control of anti angiogenesis and radiation treatments for cancerous tumor hybrid indirect solver |
| url | http://dx.doi.org/10.1155/2023/5554420 |
| work_keys_str_mv | AT imanalimirzaei optimalcontrolofantiangiogenesisandradiationtreatmentsforcanceroustumorhybridindirectsolver AT alaeddinmalek optimalcontrolofantiangiogenesisandradiationtreatmentsforcanceroustumorhybridindirectsolver |