Last edited by Mikasho
Tuesday, May 5, 2020 | History

2 edition of Mathematical models in cancer research found in the catalog.

Mathematical models in cancer research

T. E. Wheldon

# Mathematical models in cancer research

## by T. E. Wheldon

Written in English

Subjects:
• Cancer -- Mathematical models,
• Carcinogenesis -- Mathematical models,
• Tumors -- Growth -- Mathematical models,
• Biological models,
• Tumors

• Edition Notes

The Physical Object ID Numbers Statement T. E. Wheldon. Series Medical science series Pagination xvi, 247 p. ; Number of Pages 247 Open Library OL23749786M

Cancer growth and therapy and the use of mathematical models. Then I will show a variety of mathematical models which have been used a multiscale vision Cancer therapeutics: current regimens and pitfalls Various models of cancer growth and therapy Using mathematical models to optimise therapy. Cancer, a major public health problem in Europe. research on cancer modelling can even further beneﬁt from these methods. Speciﬁcally, PDE models have been used for solid tumors and tumor cords (see Preziosi’ book, ), for a-vascular tumors (Byrne), for angiogenesis (Chaplain, Anderson), for vascular tumors, and tumor invasions (Chaplain), and for File Size: KB.

A mathematical model is developed to describe the growth and. control of a heterogeneous tumor. The main aspect of the model is that it takes into account induced drug resistance. The mathematical model is a system of two ordinary differential equations that describes the growth of the cancer along with the effects of chemotherapy. A periodic mathematical model of cancer treatment by radiotherapy is presented and studied in this paper. Conditions on the coexistence of the healthy and cancer cells are obtained. Furthermore, sufficient conditions on the existence and globally asymptotic stability of the positive periodic solution, the cancer eradication periodic solution, and the cancer win periodic solution are by: 9.

2. MATHEMATICAL MODEL The brain-cancer cells is grow very fast, and at any point in time, only a portion of them are replicating and most cancer treatments only kill cells during this active phase. This means that, when determining the net tumor-cell kill rates, models need take this constraint into account.   As in physics, understanding the complex, non-linear systems in cancer biology will require ongoing interdisciplinary, interactive research in which mathematical models Cited by:

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### Mathematical models in cancer research by T. E. Wheldon Download PDF EPUB FB2

Mathematical models enable quantitative representations of the changes affecting cell state and cell number. This book provides a review of the scope of mathematical modelling in cancer research, bringing together for the first time a group of related mathematical topics including multistage carcinogenesis, tumour growth kinetics, growth control, radiotherapy, chemotherapy and biological targeting in.

Mathematical Models in Cancer Research. International Mathematical models in cancer research book of Radiation Biology: Vol. 57, No. 5, pp. Author: Howard Thames. Additional Physical Format: Online version: Wheldon, T.E. Mathematical models in cancer research. Bristol ; Philadelphia: A.

Hilger, © (OCoLC) This book chapter reviews the scope of mathematical and computational models in cancer research. Mathematical models have substantially improved our ability to predict the response of a. In their original research article, Yamamoto et al 22 used data from a rapid autopsy program for patients with pancreatic cancer to estimate parameters of a stochastic mathematical model of individual cell growth.

Using this model, the authors derived expectation times for primary tumor growth, time to metastasis, and even : Russell C. Rockne, Jacob G. Scott. The cancer cell model is realized by the deregulation in the model of healthy cell.

In addition, potential therapy targets are predicted by using mathematical simulation. This model has been done entirely within an in silico research work.

The theoretical foundations with which we constructed the differential equations for the quantitative model are strongly connected with biochemistry fields for many years, and not only allow one to apply mathematics Cited by: 3. A book about mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells has been recently published: "Mathematically, the book starts with relatively simple ordinary differential equation models, and subsequently explores more complex stochastic and spatial models.

Facing complex biological data in cancer research A mathematical model relates the dependent variables (such as a population growth or a particular molecular concentration growth) by means of a mathematical equation demonstrating the output cell response for a given : Abdallah K Alameddine, Frederick Conlin, Frederick Conlin, Brian Binnall.

Synthesizing many years experience with all the major in vivo models currently available for the study of malignant disease, Tumor Models in Cancer Research 2nd edition, provides preclinical and clinical cancer researchers alike with a comprehensive guide to the selection of these models, their effective use, and the optimal interpretation of.

Chapter 2. Biology of Cancer Tumors 3 Chapter 3. PDE Models of Cancer Tumors 5 1. Background PDEs and Physical Laws 5 2.

The Di usion Equation/Heat Equation 5 3. Continuity Equation 5 4. Darcy’s Law 7 5. Mixed Models M 3 7 6. Mixed Models M 2 11 7. Models with only Proliferating Cells 13 Chapter 4.

Mathematical Results for a Spherically Author: Alicia Marinis. A new mathematical model developed by researchers at the Broad Institute of MIT and Harvard and Massachusetts General Hospital (MGH) could.

Platinum-based chemotherapy constitutes the backbone of clinical care in advanced solid cancers such as high-grade serous ovarian cancer (HGSOC) and has prolonged survival of millions of cancer patients.

Most of these patients, however, become resistant to chemotherapy, which generally leads to a fatal refractory disease. We present a comprehensive stochastic mathematical model and Cited by: 5. Mathematical modeling, analysis and simulation are set to play crucial roles in explaining tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial scales.

This book, the first to integrate state-of-the-art numerical techniques with experimental data, provides an in-depth assessment of tumor cell modeling at multiple by: A good survey of mathematical models of cancer growth and development can be found in the excellent book , and an excellent survey of the range of mathematical and computational modelling techniques used for biological problems on different scales can be found in the book .Cited by: The mathematics of cancer: integrating quantitative models Philipp M.

Altrock 1,2*, Lin L. Liu 1* and Franziska Michor Abstract | Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments.

Indeed, a significant amount of research effort has been devoted to developing mathematical models that identify the most effective chemotherapeutic administration regimens using optimization and control techniques (Coldman and Murray, ; Costa et al.,; Katouli and Komarova, ; Kimmel M., ; Ledzewicz and Schattler, ; Martin et al., ; Martin and Cited by: Mathematical modelling approaches have become increasingly abundant in cancer research.

The complexity of cancer is well suited to quantitative approaches as it provides challenges and. Complex mathematical models are helping researchers understand cancer's evolution and providing clues on how to thwart drug resistance.

Einstein once called pure mathematics “the Cited by: 9. Over the last few decades, there have been significant developments in theoretical, experimental, and clinical approaches to understand the dynamics of cancer cells and their interactions with the immune system. These have led to the development of important methods for cancer therapy including virotherapy, immunotherapy, chemotherapy, targeted drug therapy, and many by: 1.

I study the evolution of cancer and its resistance to treatment through mathematical and computational modeling. My interests lie in both theoretical aspects of these models and their application.

On the theoretical side, I study stochastic processes, especially multi-type branching processes, and their finite time characteristics. Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics.

We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor Cited by:   In this chapter, we review recent literature of mathematical models of tumor growth and response to radiation therapy (RT) and discuss the clinical utility of mathematical models, as well as provide a forward-looking perspective into how mathematical models may enhance patient outcomes through well-designed clinical by: 4.Mathematical models of tumor growth and the efficacy of drugs help clinicians devise treatment regimens.

Skipper’s Laws. The first of Skipper’s laws is that the doubling time of a tumor is constant. A plot of the number of cells in the tumor over time on a semi-log graph forms a straight line.