Computational Modeling to Study Disease Development: Applications to Breast Cancer and an in vitro Model of Macular Degeneration (original) (raw)

A mathematical model to study breast cancer growth

2017 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2017

The aim of this paper is (i)to study breast cancer growth by mean of a mathematical model describing cell population dynamics during cancer growth, and (ii)to use this model to reproduce and explain experimental data. We started from a linear model describing cancer subpopulations evolution based on the Cancer Stem Cell (CSC) theory, and we added feedback mechanisms from the cell populations to mimic micro-environment effects in cancer growth. In details, we hypothesized two feedback mechanisms and we studied their effects both separately and combined together. In this way we obtained three new models that we tuned using data derived by TUBO Cancer cell line and describing the evolution of the total cell population and the subpopulations over time. Finally, we exploited these three models to understand which combination of feedback mechanisms better describe the experimental data. Index Terms-Breast cancer growth model, Cancer Stem Cell theory and mathematical models.

On the Foundations of Cancer Modelling: Selected Topics, Speculations, and Perspectives

Mathematical Models and Methods in Applied Sciences, 2008

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution.

Breast Cancer Modeling in the Clinical Context: Parametric Studies

In the present paper, the dynamic behavior of a clinically-oriented simulation model of breast tumor response to chemotherapy is investigated. The model incorporates various biological processes such as cycling of proliferating cells, quiescence, differentiation and cell death. Indicative results drawn from an extensive parametric analysis of the model are presented.

Modelling Tumour Growth and Progression

Progress in Industrial Mathematics at ECMI 2002, 2004

To develop the path that goes from the clinical experience to the laboratories and back to the clinic, research in cancer modelling need the establishment of strong interactions among different branches of science and a genuinely multidisciplinary approach. In fact, starting from very practical situations this path passes through progressive abstractions and simplification steps to gain insight into the complex phenomena occurring during tumour evolution and growth and this involves different research areas (see Fig. 1). So, from the phenomenological observation of a certain phenomenon in real patients, scientists in bio-medicine try to conceive more handy, reproducible, and relatively harmless biological models, which can be in vivo (e.g., mouse, chicken embryo) or in vitro. They then perform a series of experiments on that model. Either directly from the phenomenological observation or from the biological model, mathematicians and physicists can generate mathematical models aimed at describing the phenomenon of interest. The simulations stemming from them are usually called in silico models by the biologists. The acquisition of this knowledge is then tested back through experimental phases of increasing complexity and hopefully applied in the clinical practice. It is common knowledge that this stepwise process also mean different levels of ethical involvement. Including mathematical modelling and computer simulations in the path mentioned above can speed up the process, provide insight into the mechanisms that control tumour evolution and growth, and, hence, suggest directions for new therapies. The theoretical predictions generated from the models and their simulations can help optimising the experimental protocol by identifying the most promising candidates for further clinical investigation. In fact, the ease with which physical parameters can be manipulated in a computer simulation and the speed with which large numbers of simulations can be performed can help reducing the number of animal experiments to be carried out

Mathematical modeling of cancer: the future of prognosis and treatment

Clinica chimica acta; international journal of clinical chemistry, 2005

Background: Cancer research has undergone radical changes in the past few years. Producing information both at the basic and clinical levels is no longer the issue. Rather, how to handle this information has become the major obstacle to progress. Intuitive approaches are no longer feasible. The next big step will be to implement mathematical modeling approaches to interrogate the enormous amount of data being produced and extract useful answers (a btop-downQ approach to biology and medicine). Methods: Quantitative simulation of clinically relevant cancer situations-based on experimentally validated mathematical modeling-provides an opportunity for the researcher, and eventually the clinician, to address data and information in the context of well-formulated questions and bwhat ifQ scenarios. Results and conclusions: At the Vanderbilt Integrative Cancer Biology Center (VICBC), we are integrating cancer researchers, oncologists, chemical and biological engineers, computational biologists, computer modelers, theoretical and applied mathematicians, and imaging scientists, in order to implement a vision for a combined web site and computational server that will be a home for our mathematical modeling of cancer invasion. The web site (www.vanderbilt.edu/VICBC/ ) will serve as a portal to our code, which simulates tumor growth by calculating the dynamics of individual cancer cells (an experimental bbottom-upQ approach to complement the top-down model). Eventually, cancer researchers outside of Vanderbilt will be able to initiate a simulation based on providing individual cell data through a web page. We envision placing the web site and computer cluster directly in the hands of biological researchers involved in data mining and mathematical modeling. Furthermore, the web site will also contain teaching props for a new generation of biomedical researchers fluent in both mathematics and biology. This is unconventional bioinformatics: We will be incorporating biological data and functional information into a unified community-0009-8981/$ -see front matter D (V. Quaranta).

Computational disease modeling – fact or fiction?

BMC Systems Biology, 2009

Background: Biomedical research is changing due to the rapid accumulation of experimental data at an unprecedented scale, revealing increasing degrees of complexity of biological processes. Life Sciences are facing a transition from a descriptive to a mechanistic approach that reveals principles of cells, cellular networks, organs, and their interactions across several spatial and temporal scales. There are two conceptual traditions in biological computational-modeling. The bottom-up approach emphasizes complex intracellular molecular models and is well represented within the systems biology community. On the other hand, the physics-inspired top-down modeling strategy identifies and selects features of (presumably) essential relevance to the phenomena of interest and combines available data in models of modest complexity.

A computer model for the study of breast cancer

Computers in Biology and Medicine, 2003

A computer model was designed as a relational database to assess breast cancer screening in a cohort of women where the growth and development of breast cancer originates with the ÿrst malignant cell. The concepts of thresholds for growth, axillary spread, and distant sites are integrated. With tumor diagnosis, staging was performed that includes clinical and sub-clinical states. The model was parameterized to have staging characteristics similar to data published by the Surveillance, Epidemiology, and End-Results (SEER) Program. Validation was accomplished by comparing simulated staging results with non-SEER sources, and simulated survival with independent clinical survival data. ?

Recent translational research: computational studies of breast cancer

Breast cancer research : BCR, 2005

The combination of mathematics--queen of sciences--and the general utility of computers has been used to make important inroads into insight-providing breast cancer research and clinical aids. These developments are in two broad areas. First, they provide useful prognostic guidelines for individual patients based on historic evidence. Second, by suggesting numeric tumor growth laws that are correlated to clinical parameters, they permit development of biologically relevant theories and comparison with patient data to help us understand complex biologic processes. These latter studies have produced many new ideas that are testable in clinical trials. In this review we discuss these developments from a clinical perspective, and ask whether and how they translate into useful tools for patient treatment.

State of the art in computational modelling of cancer

Mathematical medicine and biology : a journal of the IMA, 2012

Cancer is a complex, multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Hybrid models provide a way to integrate both discrete and continuous variables that are used to represent individual cells and concentration or density fields, respectively. Each discrete cell can also be equipped with submodels that drive cell behavior in response to microenvironmental cues. Moreover, the individual cells can interact with one another to form and act as an integrated tissue. Hybrid models form part of a larger class of individualbased models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically and extrinsically and are therefore perfectly suited to a systems biology approach to tumor growth.