Hyperthermia cancer therapy by domain decomposition methods using strongly continuous semigroups

Abbasi, Ghasem; Malek, Alaeddin

doi:10.1016/j.matcom.2019.02.015

Cited by 7 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As an optimal control problem Mehrali-Varjani et al 18 solved a class of Hamilton Jacobi-bellman equations using pseudospectral methods in the year 2018. Abbasi and Malek 19 presented hyperthermia cancer therapy by domain decomposition methods using strongly continuous semigroups in the year 2019. A pointwise optimal control solution for hyperthermia with thermal wave bioheat transfer was used by Abbasi and Malek 20 in the year 2020.…”

Section: Introductionmentioning

confidence: 99%

Optimal controlling of anti-TGF-$$\beta$$ and anti-PDGF medicines for preventing pulmonary fibrosis

Bahram Yazdroudi,

Malek

2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

In the repair of injury, some transforming growth factor-$$\beta$$ β s (TGF-$$\beta$$ β s) and platelet-derived growth factors (PDGFs) bind to fibroblast receptors as ligands and cause the differentiation of fibroblasts into myofibroblasts. When the injury repair is repeated, the myofibroblasts proliferate excessively, forming fibrotic tissue. We goal to control myofibroblasts proliferation and apoptosis with anti-transforming growth factor-$$\beta$$ β (anti-TGF-$$\beta$$ β ) and anti-platelet-derived growth factor (anti-PDGF) medicines. The novel optimal regulator control problem with two controls (medicines) is proposed to simulate how to the preventing pulmonary fibrosis. Idiopathic pulmonary fibrosis (IPF) consists of restoring a system of cells, protein, and tissue networks with injury and scar. Myofibroblasts proliferation back to its equilibrium position after it has been disturbed by abnormal repair. Thus, the optimal regulator control problem with a parabolic partial differential equation as a constraint, zero flux boundary, and given specific initial conditions, is considered. The myofibroblast diffusion equation stands as a governing dynamic system while the objective function is the summation of myofibroblast, anti-TGF-$$\beta$$ β and anti-PDGF medicines for the fixed final time. Here, myofibroblast is a nonlinear state of time while anti-TGF-$$\beta$$ β and anti-PDGF are two unknown control functions. In order to solve the corresponding problem a weighted Galerkin method is used. Firstly, we convert the myofibroblast diffusion equation to a system of ordinary differential equations using the Lagrangian interpolation polynomials defined at Gauss-Lobatto integration points. Secondly, by the calculus of variations, the optimal control problem is solved successfully using canonical Hamiltonian and extended Riccati equations. Numerical results are given, and the plots are depicted. Moreover, solutions to the problem in which there is no control are compared. Numerical results show that, over time, the myofibroblast increases and then remains constant when there is no control. In contrast, the current solution decreases and vanishes after 300 days by prescribing controller medicines for anti-TGF-$$\beta$$ β and anti-PDGF. The optimal strategy proposed in this paper helps practitioners to reduce myofibroblasts by controlling both anti-TGF-$$\beta$$ β and anti-PDGF medicines.

show abstract

Section: Introductionmentioning

confidence: 99%

Optimal controlling of anti-TGF-$$\beta$$ and anti-PDGF medicines for preventing pulmonary fibrosis

Bahram Yazdroudi,

Malek

2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…According to World Health Organization reports for the year 2019, cancer diseases are considered the main cause of death and the most important cause of life expectancy reduction [1]. Malek and Abbasi [2][3][4][5] in years 2016, 2019, 2020, and 2022 introduced some mathematical models to simulate and solve optimal control problems for cancer therapy. Cancer cells form and reproduce abnormal cells irregularly, while the proliferation of adult normal cells is based on the division and replacement of dying cells.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver

Alimirzaei,

Malek

2023

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Cao and Lesnic reconstructed the perfusion coefficient and initial temperature simultaneously by optimization methods (Cao and Lesnic, 2019). In the year 2019, Abbasi and Malek solved a hyperthermia cancer therapy problem by domain decomposition technique (Abbasi and Malek, 2019). None of the above-mentioned articles consider specific domains for blood flow in large vessels.…”

Section: Introductionmentioning

confidence: 99%

Solving two-dimensional bioheat optimal control problem in solid and vessel domain by pseudospectral discretization

Dastyar

Malek

Yousefi

2022

Transactions of the Institute of Measurement and Control

Self Cite

View full text Add to dashboard Cite

In this paper, an optimal control problem subject to an energy transfer equation in thermally significant blood vessel coupled with the Pennes governing equation is solved. The proposed dynamical system is modeled by a system of conduction-reaction and convection-conduction equations. Chebyshev–Gauss–Lobatto (CGL) and Legendre–Gauss–Lobatto (LGL) points are applied to discretize optimal control problem. Then, the problem transferred into a quadratic programming problem using domain decomposition and matching the solution and its first derivative across the related interfaces. The Tikhonov regularization method is used to compute the optimal regularization parameter for the objective function. Some theories have been discussed to prove that the discrete problem has a solution and it is also consistent with the continuous problem. Numerical results are compared and numerical convergent is shown. Optimal and non-optimal external heat source is compared and it is shown that the mathematical modeling is effective in saving the external heat energy. Numerical results show that by this process of heating at the final time, the temperature is very close to the desired temperature without damaging the vessel domain. Numerical results and corresponding graphs are depicted.

show abstract

Hyperthermia cancer therapy by domain decomposition methods using strongly continuous semigroups

Cited by 7 publications

References 16 publications

Optimal controlling of anti-TGF-$$\beta$$ and anti-PDGF medicines for preventing pulmonary fibrosis

Optimal controlling of anti-TGF-$$\beta$$ and anti-PDGF medicines for preventing pulmonary fibrosis

Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver

Solving two-dimensional bioheat optimal control problem in solid and vessel domain by pseudospectral discretization

Contact Info

Product

Resources

About