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Related papers: Growth Laws in Cancer: Implications for Radiothera…

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Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be…

We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…

Populations and Evolution · Quantitative Biology 2007-05-23 José F. Nieves , Marcelo R. Ubriaco

Grade II gliomas are slowly growing primary brain tumors that affect mostly young patients and become fatal after a few years. Current clinical handling includes surgery as first line treatment. Cytotoxic therapies (radiotherapy RT or…

Quantitative Methods · Quantitative Biology 2014-07-09 Victor M. Perez-Garcia

In this article we shall trace the historical development of tumour growth laws, which in a quantitative fashion describe the increase in tumour mass/volume over time. These models are usually formulated in terms of differential equations…

Tissues and Organs · Quantitative Biology 2013-02-11 P. Gerlee

We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…

Numerical Analysis · Mathematics 2016-02-23 Konstantina Trivisa , Franziska Weber

Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells…

Dynamical Systems · Mathematics 2022-12-01 Frank Alvarez , Yannick Viossat

Despite internal complexity, tumor growth kinetics follow relatively simple macroscopic laws that have been quantified by mathematical models. To resolve this further, quantitative and discriminant analyses were performed for the purpose of…

Quantitative Methods · Quantitative Biology 2014-09-02 Sébastien Benzekry , Clare Lamont , Afshin Beheshti , Amanda Tracz , John M. L. Ebos , Lynn Hlatky , Philip Hahnfeldt

We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. In contrast to the assumption of a fixed power…

Quantitative Methods · Quantitative Biology 2007-05-23 Caterina Guiot , Pier Paolo Delsanto , Alberto Carpinteri , Nicola Pugno Yuri Mansury , Thomas S. Deisboeck

We present in silico simulations and mathematical analyses supporting several hypotheses that explain the saturation expressed in the fractional cell kill law that governs the lysis of tumor cells by cytotoxic CD8 + T cells (CTLs). In order…

Tissues and Organs · Quantitative Biology 2016-08-30 Álvaro G. López , Jesús M. Seoane , Miguel A. F. Sanjuán

Radiation therapy is one of the most common cancer treatments, and dose optimization and targeting of radiation are crucial since both cancerous and healthy cells are affected. Different mathematical and computational approaches have been…

Biological Physics · Physics 2025-11-07 Mirko Bagnarol , Gianluca Lattanzi , Jan Åström , Mikko Karttunen

We propose a mathematical model for the growth and treatment dynamics of Undifferentiated Pleomorphic Sarcoma (UPS) based on a system of nonlinear differential equations. The model integrates Gompertz-type tumor growth with surface-area…

Optimization and Control · Mathematics 2026-03-24 Sumit Roy

A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…

Statistical Mechanics · Physics 2011-03-09 S. C. Ferreira Junior , M. L. Martins , M. J. Vilela

The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully…

Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…

Populations and Evolution · Quantitative Biology 2014-08-27 Andrei R. Akhmetzhanov , Michael E. Hochberg

We analyze the effect of tumor repopulation on optimal dose delivery in radiation therapy. We are primarily motivated by accelerated tumor repopulation towards the end of radiation treatment, which is believed to play a role in treatment…

Medical Physics · Physics 2015-04-28 Thomas Bortfeld , Jagdish Ramakrishnan , John N. Tsitsiklis , Jan Unkelbach

Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…

Quantitative Methods · Quantitative Biology 2009-11-13 Carlos Escudero

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies…

Biological Physics · Physics 2021-04-21 Youness Azimzade , Abbas Ali Saberi , Robert A. Gatenby

In nematodes, environmental or physiological perturbations alter death's scaling of time. In human cancer, genetic perturbations alter death's curvature of time. Those changes in scale and curvature follow the constraining contours of…

Populations and Evolution · Quantitative Biology 2016-08-29 Steven A. Frank

Low grade gliomas (LGGs) are infiltrative and incurable primary brain tumours with typically slow evolution. These tumours usually occur in young and otherwise healthy patients, bringing controversies in treatment planning since aggressive…