Optimal therapeutic protocols in cancer immunotherapy

Ghaffari, Ali; Naserifar, Naser

doi:10.1016/j.compbiomed.2009.12.001

Cited by 38 publications

(22 citation statements)

References 13 publications

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“…The equilibrium point in this case is unstable because the value of 1 s is smaller than critical value (540), but optimal solution of equations pushes the system to the area with smaller cancerous cells. In this work in comparison with the works done in [16][17][18] (see Figures 3 and 4).…”

Section: Results Of the Immunotherapy Modelmentioning

confidence: 73%

Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

Ghomanjani¹

2012

ICA

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Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is associated with injecting small doses of tumor-bearing molecules or even using drugs. The problem is that how to schedule these injections effectively and/or how to apply drugs in a way to decrease toxic side effects of drugs such that the tumor growth to be stopped or at least to be limited. Here, the theory of optimal control has been applied to find the optimal schedule of injections of an immunotherapeutic agent against cancer. The numerical method employed works for any dynamic linear system and has almost precise solution. In this work, it was tested for a well known model of the tumor immune system interaction.

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Section: Results Of the Immunotherapy Modelmentioning

confidence: 73%

Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

Ghomanjani¹

2012

ICA

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“…(1) To lessen the treatment burden of patients. This method considers some constraints on the treatment policy [32].…”

Section: Introductionmentioning

confidence: 99%

“…Previous studies have investigated the effects of therapeutic inputs, which are considered to have direct effects on the system states [32][33][34][35][36][37][38][39][40][41][42][43]. However, the behavior of cancer changes as the disease progresses [44].…”

Section: Introductionmentioning

confidence: 99%

A mixed radiotherapy and chemotherapy model for treatment of cancer with metastasis

Ghaffari

Bahmaie

Nazari

2016

Math Methods in App Sciences

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In this paper, a mathematical model of cancer treatment, in the form of a system of ordinary differential equations, by chemotherapy and radiotherapy where there is metastasis from a primary to a secondary site has been proposed and analyzed. The interaction between immune cells and cancer cells has been examined, and the chemotherapy agent has been considered as a predator on both normal and cancer cells. The metastasis may be time delayed. For better investigation of the treatment process and based on physical investigation, the immanent effects of inputs on cancer dynamic have been investigated. It is supposed that the interaction between NK cells and tumor cells changes during the chemotherapy. Thisnovel approach is useful not only to gain a broad understanding of the specific system dynamics but also to guide the development of combination therapies. The analysis is carried out both analytically (where possible) and numerically. By considering such immanent effects, the tumor-free equilibrium point will be stable at the end of treatment, and the tumor can not recur again, and the patient will totally recover. So, the present analysis suggests that a proper treatment method should change the dynamics of the cancer instead of only reducing the population of cancer cells.

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“…A down-side to the model was that at the end of treatment, tumor mass tended to start regrowth. Ghafferi and Naserifar [31] improved upon the model of Burden at al. [7] by including a linear penalty, −ωy(t f ), where ω is constant, y is the quantity of cancer cells and t f is the final time-point of observation, such that their objective functional is J G (u) = −ωy(t f ) + J B (u) (note that −ωy(t f ) is the terminal payoff for J G (u), as defined above).…”

Section: Optimal Control Theorymentioning

confidence: 99%

Addressing current challenges in cancer immunotherapy with mathematical and computational modeling

Konstorum¹,

Vella

Adler

et al. 2017

Preprint

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The goal of cancer immunotherapy is to boost a patient's immune response to a tumor. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumor microenvironment, immune-modulating effects of conventional treatments, and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modeling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumor classification, optimal treatment scheduling, and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modelers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumor-immune biology. We conclude the review with recommendations for modelers both with respect to methodology and biological direction that might help keep modelers at the forefront of cancer immunotherapy development.

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Optimal therapeutic protocols in cancer immunotherapy

Cited by 38 publications

References 13 publications

Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

A mixed radiotherapy and chemotherapy model for treatment of cancer with metastasis

Addressing current challenges in cancer immunotherapy with mathematical and computational modeling

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