Mathematical models of targeted cancer therapy

Abstract

Improved understanding of the molecular underpinnings of cancer initiation and progression has led to the development of targeted cancer therapies. The importance of these new methods of cancer treatment necessitates further research into the dynamic interactions between cancer cells and therapeutic agents, as well as a means of analysing their relationship quantitatively. The present review outlines the application of mathematical modelling to the dynamics of targeted cancer therapy, focusing particular attention on chronic myeloid leukaemia and its treatment with imatinib (Glivec).

Leukaemia stem cells: hit or miss?

“…In contrast, malignant stem cells are not affected and continue to expand exponentially. Abbott and Michor (2006) show that these assumptions are consistent with clinical data on BCR-ABL1 transcript levels during the first year of imatinib treatment as well as after treatment cessation.…”

“…Particularly in comparison to the hypothesis discussed by Abbott and Michor (2006), the proposed role of the cell-cycle status of leukaemic stem cells might point to an important aspect of the imatinib effect and possibly other tyrosine kinase inhibitors. It is a particular strength of mathematical models to provide testable predictions and, therefore, to guide experimental and clinical research.…”

“…In their publication 'Mathematical models of targeted cancer therapy ' Abbott and Michor (2006) emphasise the role of theoretical modelling for the understanding of cancer initiation, progression and treatment. Herein, they draw a number of general conclusions from a model of BCR-ABL1-positive chronic myeloid leukaemia (CML) under imatinib treatment that has recently been published by Michor et al (2005).…”

“…This long-term behaviour cannot be explained within the model of CML dynamics discussed by Abbott and Michor (2006). Owing to the contribution of CML cells from the Abbott and Michor (2006). Parameters are taken from the original publication of this model (Michor et al, 2005).…”

Modeling the effect of chemotaxis on glioblastoma tumor progression

“…[25][26][27][28] It has also been used to simulate the temporal evolution of tumor cell populations and the effect of therapeutic agents. 27,[29][30][31][32][33][34][35] However, solid tumors develop in a highly heterogeneous environment, and a more realistic description of their progression requires a spatially distributed representation leading to partial differential equations (PDEs). Not surprisingly, the new spatial dimension of tumor development captured by the PDEs comes at the expense of higher computational requirements and the need of efficient solution algorithms.…”