22 Citations (Scopus)

Abstract

Introduction to Mathematical Oncology presents biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models. After introducing the general theory of medicine and exploring how mathematics can be essential in its understanding, the text describes well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. It continues the topic of avascular tumor growth in the context of partial differential equation models by incorporating the spatial structure and physiological structure, such as cell size. The book then focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. It also examines more mechanistically formulated models, including cell quota-based population growth models, with applications to real tumors and validation using clinical data. The remainder of the text presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts. Extensively classroom-tested in undergraduate and graduate courses, this self-contained book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment. It can be used in a variety of ways, including a single-semester undergraduate course, a more ambitious graduate course, or a full-year sequence on mathematical oncology.

Original languageEnglish (US)
PublisherCRC Press
Number of pages453
ISBN (Electronic)9781584889915
ISBN (Print)9781482262360
StatePublished - Apr 5 2016

Fingerprint

Oncology
Cancer
Tumor Growth
Neoplasms
neoplasms
Tumors
Biology
Growth
Multiscale Modeling
Prostate Cancer
Cell Size
Population Growth
college students
Spatial Structure
Dynamical Model
Population Model
Growth Model
Remainder
Modeling
Mathematics

ASJC Scopus subject areas

  • Mathematics(all)
  • Medicine(all)
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)

Cite this

Kuang, Y., Nagy, J. D., & Eikenberry, S. E. (2016). Introduction to mathematical oncology. CRC Press.

Introduction to mathematical oncology. / Kuang, Yang; Nagy, John D.; Eikenberry, Steffen E.

CRC Press, 2016. 453 p.

Research output: Book/ReportBook

Kuang, Y, Nagy, JD & Eikenberry, SE 2016, Introduction to mathematical oncology. CRC Press.
Kuang Y, Nagy JD, Eikenberry SE. Introduction to mathematical oncology. CRC Press, 2016. 453 p.
Kuang, Yang ; Nagy, John D. ; Eikenberry, Steffen E. / Introduction to mathematical oncology. CRC Press, 2016. 453 p.
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