American Institute of Mathematical Sciences

Advanced
2005, 2(3): 421-436. doi: 10.3934/mbe.2005.2.421

Using Mathematical Modeling as a Resource in Clinical Trials

Evans K. Afenya 1,

1. 

Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, United States

Received  January 2005 Revised  May 2005 Published  August 2005

In light of recent clinical developments, the importance of mathematical modeling in cancer prevention and treatment is discussed. An existing model of cancer chemotherapy is reintroduced and placed within current investigative frameworks regarding approaches to treatment optimization. Areas of commonality between the model predictions and the clinical findings are investigated as a way of further validating the model predictions and also establishing mathematical foundations for the clinical studies. The model predictions are used to propose additional ways that treatment optimization could enhance the clinical processes. Arising out of these, an expanded model of cancer is proposed and a treatment model is subsequently obtained. These models predict that malignant cells in the marrow and peripheral blood exhibit the tendency to evolve toward population levels that enable them to replace normal cells in these compartments in the untreated case. In the case of dose-dense treatment along with recombinant hematopoietic growth factors, the models predict a situation in which normal and abnormal cells in the marrow and peripheral blood are obliterated by drug action, while the normal cells regain their growth capabilities through growth-factor stimulation.
Keywords: clinical trials., leukemia, mathematical modeling, cancer.
Mathematics Subject Classification: 92D3.
Citation: Evans K. Afenya. Using Mathematical Modeling as a Resource in Clinical Trials. Mathematical Biosciences & Engineering, 2005, 2 (3) : 421-436. doi: 10.3934/mbe.2005.2.421
[1]

Tianfa Xie, Zhong-Zhan Zhang. Identifiability of models for clinical trials with noncompliance. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 805-811. doi: 10.3934/dcdsb.2004.4.805
[2]

Natalia L. Komarova. Mathematical modeling of cyclic treatments of chronic myeloid leukemia. Mathematical Biosciences & Engineering, 2011, 8 (2) : 289-306. doi: 10.3934/mbe.2011.8.289
[3]

Alacia M. Voth, John G. Alford, Edward W. Swim. Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer. Mathematical Biosciences & Engineering, 2017, 14 (3) : 777-804. doi: 10.3934/mbe.2017043
[4]

Elena Fimmel, Yury S. Semenov, Alexander S. Bratus. On optimal and suboptimal treatment strategies for a mathematical model of leukemia. Mathematical Biosciences & Engineering, 2013, 10 (1) : 151-165. doi: 10.3934/mbe.2013.10.151
[5]

Silviu-Iulian Niculescu, Peter S. Kim, Keqin Gu, Peter P. Lee, Doron Levy. Stability crossing boundaries of delay systems modeling immune dynamics in leukemia. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 129-156. doi: 10.3934/dcdsb.2010.13.129
[6]

Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 147-159. doi: 10.3934/dcdsb.2004.4.147
[7]

Avner Friedman, Wenrui Hao. Mathematical modeling of liver fibrosis. Mathematical Biosciences & Engineering, 2017, 14 (1) : 143-164. doi: 10.3934/mbe.2017010
[8]

Yangjin Kim, Avner Friedman, Eugene Kashdan, Urszula Ledzewicz, Chae-Ok Yun. Application of ecological and mathematical theory to cancer: New challenges. Mathematical Biosciences & Engineering, 2015, 12 (6) : i-iv. doi: 10.3934/mbe.2015.12.6i
[9]

M.A.J Chaplain, G. Lolas. Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Networks & Heterogeneous Media, 2006, 1 (3) : 399-439. doi: 10.3934/nhm.2006.1.399
[10]

Amina Eladdadi, Noura Yousfi, Abdessamad Tridane. Preface: Special issue on cancer modeling, analysis and control. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : i-iii. doi: 10.3934/dcdsb.2013.18.4i
[11]

Cristian Tomasetti, Doron Levy. An elementary approach to modeling drug resistance in cancer. Mathematical Biosciences & Engineering, 2010, 7 (4) : 905-918. doi: 10.3934/mbe.2010.7.905
[12]

Pep Charusanti, Xiao Hu, Luonan Chen, Daniel Neuhauser, Joseph J. DiStefano III. A mathematical model of BCR-ABL autophosphorylation, signaling through the CRKL pathway, and Gleevec dynamics in chronic myeloid leukemia. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 99-114. doi: 10.3934/dcdsb.2004.4.99
[13]

Hsiu-Chuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1279-1295. doi: 10.3934/dcdsb.2016.21.1279
[14]

Gang Bao. Mathematical modeling of nonlinear diffracvtive optics. Conference Publications, 1998, 1998 (Special) : 89-99. doi: 10.3934/proc.1998.1998.89
[15]

J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263
[16]

Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 891-914. doi: 10.3934/dcdsb.2013.18.891
[17]

Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040
[18]

Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 945-967. doi: 10.3934/dcdsb.2013.18.945
[19]

Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565
[20]

Karly Jacobsen, Jillian Stupiansky, Sergei S. Pilyugin. Mathematical modeling of citrus groves infected by huanglongbing. Mathematical Biosciences & Engineering, 2013, 10 (3) : 705-728. doi: 10.3934/mbe.2013.10.705

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences