Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment

Pillis, Lisette de; Caldwell, T M; Sarapata, Elizabeth; Williams, Heather

doi:10.3934/dcdsb.2013.18.915

Cited by 29 publications

(42 citation statements)

References 60 publications

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“…It resembles some of the dynamic behaviors of the model developed by De Pillis et al. (, ). The model considers a system of five ordinary differential equations, three representing the interactions between tumor and immune cells and the other two representing immunotherapy and chemotherapy agent dynamic effects.…”

Section: Introductionmentioning

confidence: 56%

“…We now point out the differences between our reduced model and the model presented in Isaeva and Osipov (). In the absence of an immune response, the well‐accepted tumor growth logistic term is used

a_{l} false(1 - b_{l}^{- 1} T false) T

(De Pillis and Radunskaya, ; De Pillis et al., , , ; Mamat et al., ; Sharma and Samanta, ), where

a_{l}

is the growth rate of tumor cells and

b_{l}

is the carrying capacity of tumor cells. This logistic growth model is sufficiently flexible to fit a variety of tumor‐type data.…”

Section: Tumor–immune Mathematical Modelmentioning

confidence: 99%

“…The fraction of destroyed cells for the amount of drug

C (t)

(at time t ) for tumor and CTL cells may be represented by

- M_{X} false(1 - prefixexp (- C false(t false)) false) X false(t false),

where X is T or L . We note that the parameters

M_{X}

, for

X = T

or L , may depend on the concentration of IL‐2 and give the tumor cell (or CTL) killing by chemotherapy (De Pillis et al., , , ; Isaeva and Osipov, ).…”

Section: Tumor–immune Mathematical Modelmentioning

confidence: 99%

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On a multiobjective optimal control of a tumor growth model with immune response and drug therapies

Rocha

Costa

Fernandes

2016

Int Trans Operational Res

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In this paper, we consider a tumor growth mathematical model that includes an immune system and drug therapies. Immuno-and chemodrug administration as well as periodic administration of radiation are integrated in the model. We have set an optimal control (OC) problem relative to the model so that the average number of tumor cells and immuno-and chemotherapeutic drug administration are simultaneously minimized in a multiobjective context. The external injection of two immunostimulators and a chemotherapeutic drug has been considered as control, and the objective functionals aim to reflect the severity of both types of drug administration. The multiobjective approach to the OC of the tumor growth model provides good-quality approximate solutions and has shown to be a valuable procedure to identify good trade-offs between conflicting objectives.

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Section: Introductionmentioning

confidence: 56%

a_{l} false(1 - b_{l}^{- 1} T false) T

(De Pillis and Radunskaya, ; De Pillis et al., , , ; Mamat et al., ; Sharma and Samanta, ), where

a_{l}

is the growth rate of tumor cells and

b_{l}

is the carrying capacity of tumor cells. This logistic growth model is sufficiently flexible to fit a variety of tumor‐type data.…”

Section: Tumor–immune Mathematical Modelmentioning

confidence: 99%

“…The fraction of destroyed cells for the amount of drug

C (t)

(at time t ) for tumor and CTL cells may be represented by

- M_{X} false(1 - prefixexp (- C false(t false)) false) X false(t false),

where X is T or L . We note that the parameters

M_{X}

, for

X = T

or L , may depend on the concentration of IL‐2 and give the tumor cell (or CTL) killing by chemotherapy (De Pillis et al., , , ; Isaeva and Osipov, ).…”

Section: Tumor–immune Mathematical Modelmentioning

confidence: 99%

See 1 more Smart Citation

On a multiobjective optimal control of a tumor growth model with immune response and drug therapies

Rocha

Costa

Fernandes

2016

Int Trans Operational Res

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“…While all these models are neat, they did not include the essential effects of vitamin-D [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Chemical Dynamic Approach to Correlate Autoimmunity and Optimal Vitamin-D Range

2014

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Motivated by several recent experimental observations that vitamin-D could interact with antigen presenting cells (APCs) and T-lymphocyte cells (T-cells) to promote and to regulate different stages of immune response, we developed a coarse grained but general kinetic model in an attempt to capture the role of vitamin-D in immunomodulatory responses. Our kinetic model, developed using the ideas of chemical network theory, leads to a system of nine coupled equations that we solve both by direct and by stochastic (Gillespie) methods. Both the analyses consistently provide detail information on the dependence of immune response to the variation of critical rate parameters. We find that although vitamin-D plays a negligible role in the initial immune response, it exerts a profound influence in the long term, especially in helping the system to achieve a new, stable steady state. The study explores the role of vitamin-D in preserving an observed bistability in the phase diagram (spanned by system parameters) of immune regulation, thus allowing the response to tolerate a wide range of pathogenic stimulation which could help in resisting autoimmune diseases. We also study how vitamin-D affects the time dependent population of dendritic cells that connect between innate and adaptive immune responses. Variations in dose dependent response of anti-inflammatory and pro-inflammatory T-cell populations to vitamin-D correlate well with recent experimental results. Our kinetic model allows for an estimation of the range of optimum level of vitamin-D required for smooth functioning of the immune system and for control of both hyper-regulation and inflammation. Most importantly, the present study reveals that an overdose or toxic level of vitamin-D or any steroid analogue could give rise to too large a tolerant response, leading to an inefficacy in adaptive immune function.

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“…The "tumor killing by NK" term depends on a multiplicative function of Treg (R 2 ) and MDSC cells (M) 55 . Following the approach of De Pillis et al 56 , this inhibition has been modeled by a sum of two negative exponential terms, which becomes close to zero when the amount of Treg or MDSC increases. The mature dendritic cells are described in the Eq.…”

mentioning

confidence: 99%

A QSP model of prostate cancer immunotherapy to identify effective combination therapies

Coletti

Leonardelli

Parolo

et al. 2020

Sci Rep

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dependent on androgen signaling, androgen deprivation therapy, either by chemical or surgical castration, is the first-line treatment for advanced PCa 40. Although this therapy is initially highly effective in most of the patients, in some cases the tumor evolves into an androgen independent form that currently lacks efficacious therapeutic options 41. The transition from the androgen dependent to the androgen independent state may occur through several mechanisms that are not yet completely understood 42. In this context, immunotherapy represents a highly promising new treatment approach. Over the last few years, numerous pre-clinical and clinical studies have been performed to develop and test different PCa immunotherapies 43. A main achievement has been the US Food and Drug Administration (FDA) approval of sipuleucel-T, so far the only approved immunotherapy for PCa treatment 40. Compared with other types of cancer, PCa is relatively insensitive to the most popular immunotherapies and additional studies are needed to understand the mechanisms underlying this lack of immune responsiveness 44. Thus, evaluating combination therapies is another important step to improve therapeutic benefits 45. We herein propose a QSP model of prostate cancer that extends a previous one published by Peng et al. 46 based on data from a murine Pten prostate cancer model 47,48. Although Peng and coworkers already described the action of CTLs, dendritic cells, Tregs, androgens and interleukin-2 (IL-2) in the tumor microenvironment, we extended the characterization of the immune system by including MDSCs and Natural Killer (NK) cells as potential targets for new prostate cancer therapies. The main goal of this contribution is, indeed, to provide a mathematical model able to test the efficacy of several immunotherapies and their combinations. We incorporate a wide range of experimental data from literature 31,46,49-51 to implement seven treatments. The efficacy of therapies is assessed considering the model-predicted tumor inhibitory effect and the synergy of combination therapies. Synergy between treatments plays a crucial role to reduce the dosage of each drug maintaining a satisfactory overall treatment efficacy, improving patients' quality of life 52. The paper is organized as follows. In the result section we provide a description of the model diagram and a detailed explanation of the Ordinary Differential Equations (ODEs) constituting the mathematical model. We provide the model simulations to verify the reproducibility of the experimental data and to compare the predicted outcomes with known biological mechanisms. We identify the most effective treatment combinations for prostate cancer through the model-predicted tumor size and the treatment synergy. Moreover, we emphasize the androgen deprivation therapy as leading treatment in a decision tree to choose the best protocol to treat androgen independent prostate cancer. Finally, a discussion of the results and a description of the study limitations is provided. Results The mathema...

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Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment

Cited by 29 publications

References 60 publications

On a multiobjective optimal control of a tumor growth model with immune response and drug therapies

On a multiobjective optimal control of a tumor growth model with immune response and drug therapies

A Stochastic Chemical Dynamic Approach to Correlate Autoimmunity and Optimal Vitamin-D Range

A QSP model of prostate cancer immunotherapy to identify effective combination therapies

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