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A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments…

Tissues and Organs · Quantitative Biology 2013-06-21 Sebastien Benzekry , Dominique Barbolosi , Assia Benabdallah , Florence Hubert , Philip Hahnfeldt

The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…

Data Analysis, Statistics and Probability · Physics 2015-06-15 Paolo Rossi

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to…

Dynamical Systems · Mathematics 2024-05-31 Erik Blom , Stefan Engblom

The morphology and time-evolution of tumors are expected to depend heavily on the detailed balance of the overall physics of the cell assembly (e.g., the kinetic pressure, the cell-cell interaction, and the external trapping by the tissue)…

Soft Condensed Matter · Physics 2007-05-23 P. K. Biswas , M. T. T. Pacheco

In a previous paper we have introduced a phenomenological model of cell metabolism and of the cell cycle to simulate the behavior of large tumor cell populations (Chignola R and Milotti E, Phys. Biol. 2 (2005) 8-22). Here we describe a…

Biological Physics · Physics 2009-11-13 Roberto Chignola , Alessio Del Fabbro , Chiara Dalla Pellegrina , Edoardo Milotti

In this paper, we describe a dataset relating to cellular and physical conditions of patients who are operated upon to remove colorectal tumours. This data provides a unique insight into immunological status at the point of tumour removal,…

Machine Learning · Computer Science 2013-07-08 Chris Roadknight , Uwe Aickelin , Alex Ladas , Daniele Soria , John Scholefield , Lindy Durrant

Resistance to therapy remains a significant challenge in cancer treatment, often due to the presence of a stem-like cell population that drives tumor recurrence post-treatment. Moreover, many anticancer therapies induce plasticity,…

Populations and Evolution · Quantitative Biology 2024-12-25 Chenyu Wu , Einar Bjarki Gunnarsson , Jasmine Foo , Kevin Leder

Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…

Numerical Analysis · Mathematics 2015-04-24 Konstantina Trivisa , Franziska Weber

In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…

Probability · Mathematics 2025-10-02 Kevin Leder , Zicheng Wang , Xuanming Zhang

Genetic mutations are footprints of tumour growth. While mutation data in bulk samples has been used to infer evolutionary parameters hard to measure in vivo, the advent of single-cell data has led to strong interest in the mutational…

Populations and Evolution · Quantitative Biology 2025-07-11 Christo Morison , Dudley Stark , Weini Huang

We present a fast and reliable algorithm that gives precise location of breast tumours for a partial mastectomy. Our algorithm is fully implemented in the Surface Evolver, which is a general-purpose simulator of physical experiments. By…

Image and Video Processing · Electrical Eng. & Systems 2019-12-02 Marcelo Zanchetta do Nascimento , Valério Ramos Batista

The nervous system is today recognized to play an important role in the development of cancer. Indeed, neurons extend long processes (axons) that grow and infiltrate tumors in order to regulate the progression of the disease in a positive…

Dynamical Systems · Mathematics 2022-05-25 Sophie Chauvet , Florence Hubert , Fanny Mann , Mathieu Mezache

Extracting genetic information from a full range of sequencing data is important for understanding diseases. We propose a novel method to effectively explore the landscape of genetic mutations and aggregate them to predict cancer type. We…

Genomics · Quantitative Biology 2018-10-10 Zexian Zeng , Andy Vo , Chengsheng Mao , Susan E Clare , Seema A Khan , Yuan Luo

The pathogenesis of cancer in human is still poorly understood. With the rapid development of high-throughput sequencing technologies, huge volumes of cancer genomics data have been generated. Deciphering those data poses great…

Genomics · Quantitative Biology 2016-04-06 Junhua Zhang , Shihua Zhang

Recent works have stressed the important role that random mutations have in the development of cancer phenotype. We challenge this current view by means of bioinformatic data analysis and computational modelling approaches. Not all the…

Cell Behavior · Quantitative Biology 2017-06-28 Gianluca Ascolani , Pietro Lió

The inverse geometric approach to the modeling of the growth of circular objects revealing required features, such as the velocity of the growth and fractal behavior of their contours, is presented. It enables to reproduce some of the…

Medical Physics · Physics 2007-05-23 Branislav Brutovsky , Denis Horvath , Vladimir Lisy

In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical…

Analysis of PDEs · Mathematics 2015-03-17 Joachim Escher , Anca-Voichita Matioc , Bogdan-Vasile Matioc

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue.…

Computational Engineering, Finance, and Science · Computer Science 2022-09-27 Baoshan Liang , Jingye Tan , Luke Lozenski , David A. Hormuth , Thomas E. Yankeelov , Umberto Villa , Danial Faghihi

We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the…

Analysis of PDEs · Mathematics 2019-02-06 Anderson L. A. de Araujo , Artur C. Fassoni , Luís F. Salvino

Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…

Machine Learning · Computer Science 2020-03-26 Hrushikesh Loya , Pranav Poduval , Deepak Anand , Neeraj Kumar , Amit Sethi