Modeling tumor regrowth and immunotherapy

Kuznetsov, Vladimir A.; Knott, Gary D.

doi:10.1016/s0895-7177(00)00314-9

Cited by 140 publications

(96 citation statements)

References 9 publications

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“…On the other hand, varying the frecuency for fixed effective doses values, an oscillating behavior for the population of malignant cells is obtained, as in the previous case. In all these cases, regrowth of malignant cells takes place after treatment interruption [9]. This can be easily understood if we take into account that the population of malignant cells with zero value (x = 0) represents, in the mechanical analogue (Eq.14), an unstable point (a potential maximum, as that shown in Fig.…”

Section: Stability Analysis With Treatment and Biological Implicatmentioning

confidence: 96%

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Behavior of tumors under nonstationary therapy

Sotolongo‐Costa

Molina

Pérez

et al. 2003

Physica D: Nonlinear Phenomena

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Section: Stability Analysis With Treatment and Biological Implicatmentioning

confidence: 96%

“…3b). This state is considered by some authors as a dormant state [7][8][9]15,16]. However in both cases, there exist populations of malignant cells that grow towards a state in which immunological activity has been suppressed.…”

Section: Biological Significancementioning

confidence: 99%

Behavior of tumors under nonstationary therapy

Sotolongo‐Costa

Molina

Pérez

et al. 2003

Physica D: Nonlinear Phenomena

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“…Ordinary differential equation models of the interaction between the tumour and anti-idiotypic antibody are presented in [77]. The cellular immune response to the tumour is also known to be important and ordinary differential equation models of the T cell response to the tumour are given in [78], [79].…”

Section: Models Of the Immune Response To Tumoursmentioning

confidence: 99%

Mathematical Modelling of Tumour Dormancy

Page¹

2009

Math. Model. Nat. Phenom.

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Abstract. Many tumours undergo periods in which they apparently do not grow but remain at a roughly constant size for extended periods. This is termed tumour dormancy. The mechanisms responsible for dormancy include failure to develop an internal blood supply, individual tumour cells exiting the cell cycle and a balance between the tumour and the immune response to it. Tumour dormancy is of considerable importance in the natural history of cancer. In many cancers, and in particular in breast cancer, recurrence can occur many years after surgery to remove the primary tumour, following a long period of occult disease. Mathematical modelling suggested that continuous growth of tumours was incompatible with data of the times of recurrence in breast cancer, suggesting that tumour dormancy was a common phenomenon. Modelling has also been applied to understanding the mechanisms responsible for dormancy, how they can be manipulated and the implications for cancer therapy. Here, the literature on mathematical modelling of tumour dormancy is reviewed. In conclusion, promising future directions for research are discussed.

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“…The two terms in the first equation, F N and F L represent the fraction of tumor cells killed in interactions with the two types of immune cells. Traditionally in the literature these competition terms are proportional to the competing populations, (see [2,4,7]). This form is generally justified by considering a cell-kinetic mechanism through which each immune cell has some fixed probability of encountering each tumor cell.…”

Section: Model Equationsmentioning

confidence: 99%

“…Our representation also extends other lower-dimensional models, such as that described in [3] in which different cell populations are represented as interacting species. Other mathematical models that include an immune interaction with a tumor are described in [4][5][6][7][8][9][10][11][12]. …”

Section: Introductionmentioning

confidence: 99%

A mathematical model of immune response to tumor invasion

Pillis

Radunskaya

2003

Computational Fluid and Solid Mechanics 2003

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Recent experimental studies by Diefenbach et al. [1] have brought to light new information about how the immune system of the mouse responds to the presence of a tumor. In the Diefenbach studies, tumor cells are modified to express higher levels of immune stimulating NKG2D ligands. Experimental results show that sufficiently high levels of ligand expression create a significant barrier to tumor establishment in the mouse. Additionally, ligand transduced tumor cells stimulate protective immunity to tumor rechallenge. Based on the results of the Diefenbach experiments, we have developed a mathematical model of tumor growth to address some of the questions that arise regarding the mechanisms involved in the immune response to a tumor challenge. The model focuses on the interaction of the NK and CD8 + T cells with various tumor cell lines using a system of differential equations. We propose new forms for the tumor-immune competition terms, and validate these forms through comparison with the experimental data of [1].

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Modeling tumor regrowth and immunotherapy

Cited by 140 publications

References 9 publications

Behavior of tumors under nonstationary therapy

Behavior of tumors under nonstationary therapy

Mathematical Modelling of Tumour Dormancy

A mathematical model of immune response to tumor invasion

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