Different Strategies for Cancer Treatment: Mathematical Modelling

Isaeva, O. G.; Osipov, V. A.

doi:10.1080/17486700802536054

Cited by 34 publications

(35 citation statements)

References 45 publications

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“…This process can be approached from multiple perspectives, such as clinical trials on humans and animals, but one unique way is through the lens of mathematical biology; mathematical simulations provides numerous benefits such as the non-reliance upon human/animal models as well as predicting future behaviors for a system [10,25]. Although mathematical modeling cannot portray life to complete accuracy, this process can find qualitative and quantitative hidden behaviors not seen in clinical trials.…”

Section: Resultsmentioning

confidence: 99%

“…A Monte-Carlo simulation was necessary to incorporate into the model since it considers a probabilistic input (tumor antigen size) and turns it into a deterministic output (immune response). Multiple simulations can be run and can determine possible outcomes of an individual's immune profile [2,10,11,12].…”

Section: Model Developmentmentioning

confidence: 99%

“…which studied the interactions of cancer and the immune system utilizing mathematical biology [9]. Mathematical Biology is a field of research that draws aspects from both mathematics and the biological sciences to represent, model, and analyze complex biological processes through techniques such as numerical simulations or phase plane analysis [7,[10][11][12][13]. Mathematical modeling provides insight and validity to a complex biological system for clinical research without the utilization of human or animal models, entirely bypassing ethics boards completely [7,10,12].…”

Section: Introductionmentioning

confidence: 99%

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A Mathematical Investigation on Tumor-Immune Dynamics: The Impact of Vaccines on the Immune Response

Quinonez¹,

Dasu²,

Qureshi³

2017

J Cancer Sci Ther

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Mathematical models analyzing tumor-immune interactions provide a framework by which to address specific scenarios in regard to tumor-immune dynamics. Important aspects of tumor-immune surveillance to consider is the elimination of tumor cells from a host's cell-mediated immunity as well as the implications of vaccines derived from synthetic antigen. In present studies, our mathematical model examined the role of synthetic antigen to the strength of the immune system. The constructed model takes into account accepted knowledge of immune function as well as prior work done by de Pillis et al. All equations describing tumor-immune growth, antigen presentation, immune response, and interaction rates were numerically simulated with MATLAB. Here, our work shows that a robust immune response can be generated if the immune system recognizes epitopes that are between 8 to 11 amino acids long. We show through mathematical modeling of how synthetic tumor vaccines can be utilized to mitigate a developing cancer.utilized mice that were inoculated with chemically-induced cancer cells; such cells lacked the capability to metastasize within a host. Over time, this led to the development of cancer-specific immunity in the recipient mice. This discovery provided the evidence needed for Ehrlich's hypothesis. Such experiments demonstrated that it is essential to have the presence of an antigen to elicit an immune response in the host, because if no distinctive structures exist, then no recognition would be established [9]. F. Macfarlane Burnet and Lewis Thomas, well-known immunologists during the 20 th century, hypothesized that for immunosurveillance to exist, lymphocytes would need to act aggressively akin to sentinels to recognize and eliminate a cancer threat. The cancer immunosurveillance theory revolves around three transitions states, denoted as "E's" [9]:• Elimination-The establishment of a strong cancer surveillance network by both the innate and adaptive immune system that seeks to eliminate cancer populations.• Equilibrium-The long-term process of combat between a cancer population and a host's immunosurveillance network.• Escape-The overpowering of cancer surveillance network by strong tumor variants, which results in host death.

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Section: Resultsmentioning

confidence: 99%

Section: Model Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Mathematical Investigation on Tumor-Immune Dynamics: The Impact of Vaccines on the Immune Response

Quinonez¹,

Dasu²,

Qureshi³

2017

J Cancer Sci Ther

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“…According to the study by Isaeva et al for the Gompertzian-based mathematical model, the administration sequence of chemotherapy ahead of immunotherapy can achieve a better therapeutic effectiveness than that of either immunotherapy in advance of chemotherapy or a concurrent chemoimmunotherapy does (Isaeva and Osipov 2009). In our current work, the effect of administration sequence on the therapeutic effectiveness is also observed as well as diversified when the administration sequences with a positive, zero or negative coupling are involved, respectively, as shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The review article by Chou (2006) is worth referring to for a comprehensive understanding of the median-effect model, the dose-effect as well as the synergism and antagonism of administered drugs in combination. Isaeva and Osipov (2009) studied a Gompertzian-based mathematical model of chemotherapy, immunotherapy and vaccine treatments for a tumour treatment under different applied sequences of administration and immune responding levels. They have found that the sequence of chemotherapy with immunotherapy achieves a better therapeutic effectiveness than that of either immunotherapy with chemotherapy or a concurrent chemoimmunotherapy does.…”

Section: Introductionmentioning

confidence: 99%

In Silico Synergism and Antagonism of an Anti-tumour System Intervened by Coupling Immunotherapy and Chemotherapy: A Mathematical Modelling Approach

Zhong

Wang

et al. 2011

Bull Math Biol

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Based on the logistic growth law for a tumour derived from enzymatic dynamics, we address from a physical point of view the phenomena of synergism, additivity and antagonism in an avascular anti-tumour system regulated externally by dual coupling periodic interventions, and propose a theoretical model to simulate the combinational administration of chemotherapy and immunotherapy. The in silico results of our modelling approach reveal that the tumour population density of an anti-tumour system, which is subject to the combinational attack of chemotherapeutical as well as immune intervention, depends on four parameters as below: the therapy intensities D, the coupling intensity I, the coupling coherence R and the phase-shifts Φ between two combinational interventions. In relation to the intensity and nature (synergism, additivity and antagonism) of coupling as well as the phase-shift between two therapeutic interventions, the administration sequence of two periodic interventions makes a difference to the curative efficacy of an anti-tumour system. The isobologram established from our model maintains a considerable consistency with that of the well-established Loewe Additivity model (Tallarida, Pharmacology 319(1):1-7, 2006). Our study discloses the general dynamic feature of an anti-tumour system regulated by two periodic coupling interventions, and the results may serve as a supplement to previous models of drug administration in combination and provide a type of heuristic approach for preclinical pharmacokinetic investigation.

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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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Different Strategies for Cancer Treatment: Mathematical Modelling

Cited by 34 publications

References 45 publications

A Mathematical Investigation on Tumor-Immune Dynamics: The Impact of Vaccines on the Immune Response

A Mathematical Investigation on Tumor-Immune Dynamics: The Impact of Vaccines on the Immune Response

In Silico Synergism and Antagonism of an Anti-tumour System Intervened by Coupling Immunotherapy and Chemotherapy: A Mathematical Modelling Approach

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

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