Competition between cancer cells and T cells under immunotherapy: a structured population approach

Delitala, Marcello Edoardo; Lorenzi, Tommaso; Melensi, Matteo

doi:10.1051/itmconf/20150500005

Cited by 4 publications

(2 citation statements)

References 9 publications

(7 reference statements)

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“…According to the World Health Organization (WHO), in 2020, the last year of available data, around 1.93 × 10 7 new cases were registered, having an estimated mortality of almost 1 × 10 7 , constituting approximately 1∕6 of total human deaths in the world [1]. Among the treatments used to fight cancer, there are those based on purely medical (surgery [2]), physical (radiotherapy [3][4][5][6][7]), chemical (chemotherapy [8][9][10][11]), biological (immunotherapy [12,13], targeted gene therapy [14], oncolytic [15] and hormonal) aspects, and combinations of the above mentioned. Cancer has acquired singular importance in recent decades due to its impact on society and the efforts dedicated to combating it.…”

Section: Introductionmentioning

confidence: 99%

Exploring chronomodulated radiotherapy strategies in a chaotic population model

Ramírez-Ávila

Kurths

Gonze

et al. 2023

Chaos, Solitons & Fractals

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Section: Introductionmentioning

confidence: 99%

Exploring chronomodulated radiotherapy strategies in a chaotic population model

Ramírez-Ávila

Kurths

Gonze

et al. 2023

Chaos, Solitons & Fractals

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“…Despite this, only a small reduction in either the probability of a cytotoxic effector cell killing or deactivating a tumor cell, or the rate of influx of these lymphocytes into the tumor vicinity, has been found sufficient to provoke tumor regrowth [86]. It is clear that overcoming lapses in immune response which can lead to the tendency for regrowth is crucial: immune memory boosting in combination with other treatment protocols has demonstrated the potential to help to establish stable dormancy [88].…”

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confidence: 99%

From concept to clinic: mathematically informed immunotherapy

Walker

Enderling

2015

Preprint

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IntroductionMathematical modeling has become a valuable tool in the continued effort to understand, predict and ultimately treat a wide range of cancers in recent years [1,2]. By describing biological phenomena in the concise and formal language of mathematics, it is possible to elucidate key components of complex systems and ultimately develop tools capable of quantifying and predicting system behavior under given conditions. When these tools are applied as a complement to the detailed understanding of cancer biology provided by biological scientists and clinicians, new insights can be gained into the mechanisms and first-order principles of cancer development and control [3].To date, although mathematical tools have been applied extensively in understanding tumor growth and dynamic interactions between cancer and host, studies involving the theoretical modeling of patient response to treatment and the contribution of such findings to the development of clinically-actionable therapeutic protocols remain strikingly limited. In particular, despite the rising emergence of immunotherapy as a promising cancer treatment, knowledge gained from mathematical modeling of tumorimmune interactions often still eludes application to the clinic. The currently underutilized potential of such techniques to forecast response to treatment, aid the development of immunotherapeutic regimes and ultimately streamline the transition from innovative concept to clinical practice is hence the focus of this review. Mathematical oncologyDue to the simplifications inherent in the development of a mathematical model of a complex biological system, early attempts at combining mathematics with biology were often met with skepticism from experimentalists and clinicians. The misconception that simplifications render mathematical models meaningless is still found in some more conservative areas of medical research. Thankfully, the great potential for theoretical models to help unravel highly complex and multifaceted processes without the need for . CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/027979 doi: bioRxiv preprint first posted online 2 time-consuming experimentation is becoming more widely appreciated [4]. Insights can be gained into mechanisms or relationships that may not be obvious or intuitive, allowing the generation of novel hypotheses on which to base future experimentation.Formalized descriptions of dynamic processes that have achieved a balance of both simplicity and applicability have contributed greatly to biological research to date. For example, in the field of oncology, tumor growth has been modeled extensively using methods ranging from simple one-equation models featuring logistic, Gompertz or exponential growth functions to detailed 3-dimensional spatio-temporal systems [5][6][7][8][9][10][11][12][13][14][15]. Detailed reviews of tumor growth modeling over the last few decades are...

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Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

et al. 2018

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Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.

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Competition between cancer cells and T cells under immunotherapy: a structured population approach

Cited by 4 publications

References 9 publications

Exploring chronomodulated radiotherapy strategies in a chaotic population model

Exploring chronomodulated radiotherapy strategies in a chaotic population model

From concept to clinic: mathematically informed immunotherapy

Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

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