A 3D multiscale model of cancer stem cell in tumor development

BackgroundRecent reports indicate that a subgroup of tumor cells named cancer stem cells (CSCs) or tumor initiating cells (TICs) are responsible for tumor initiation, growth and drug resistance. This subgroup of tumor cells has self-renewal capacity and could differentiate into heterogeneous tumor cell populations through asymmetric proliferation. The idea of CSC provides informative insights into tumor initiation, metastasis and treatment. However, the underlying mechanisms of CSCs regulating tumor behaviors are unclear due to the complex cancer system. To study the functions of CSCs in the complex tumor system, a few mathematical modeling studies have been proposed. Whereas, the effect of microenvironment (mE) factors, the behaviors of CSCs, progenitor tumor cells (PCs) and differentiated tumor cells (TCs), and the impact of CSC fraction and signaling heterogeneity, are not adequately explored yet.MethodsIn this study, a novel 3D multi-scale mathematical modeling is proposed to investigate the behaviors of CSCsin tumor progressions. The model integrates CSCs, PCs, and TCs together with a few essential mE factors. With this model, we simulated and investigated the tumor development and drug response under different CSC content and heterogeneity.ResultsThe simulation results shown that the fraction of CSCs plays a critical role in driving the tumor progression and drug resistance. It is also showed that the pure chemo-drug treatment was not a successful treatment, as it resulted in a significant increase of the CSC fraction. It further shown that the self-renew heterogeneity of the initial CSC population is a cause of the heterogeneity of the derived tumors in terms of the CSC fraction and response to drug treatments.ConclusionsThe proposed 3D multi-scale model provides a new tool for investigating the behaviors of CSC in CSC-initiated tumors, which enables scientists to investigate and generate testable hypotheses about CSCs in tumor development and drug response under different microenvironments and drug perturbations.

[1]  S Saito,et al.  Increased tumor tissue pressure in association with the growth of rat tumors. , 1986, Japanese journal of cancer research : Gann.

[2]  Mark S. Gockenbach,et al.  Understanding and implementing the finite element method , 1987 .

[3]  L. Norton.  A Gompertzian model of human breast cancer growth. , 1988, Cancer research.

[4]  J. Dick,et al.  Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell , 1997, Nature Medicine.

[5]  Chi-Wang Shu,et al.  Total variation diminishing Runge-Kutta schemes , 1998, Math. Comput..

[6]  I. Weissman,et al.  Stem Cells Units of Development, Units of Regeneration, and Units in Evolution , 2000, Cell.

[7]  S Torquato,et al.  Simulated brain tumor growth dynamics using a three-dimensional cellular automaton. , 2000, Journal of theoretical biology.

[8]  Michael F. Clarke,et al.  Applying the principles of stem-cell biology to cancer , 2003, Nature Reviews Cancer.

[9]  S. Morrison,et al.  Prospective identification of tumorigenic breast cancer cells , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[10]  G. Truskey,et al.  Transport phenomena in biological systems , 2004 .

[11]  V. Cristini,et al.  Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method , 2005, Bulletin of mathematical biology.

[12]  D. Gary Gilliland,et al.  Cancer biology: Summing up cancer stem cells , 2005, Nature.

[13]  A. Anderson,et al.  A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. , 2005, Mathematical medicine and biology : a journal of the IMA.

[14]  H. Frieboes,et al.  An integrated computational/experimental model of tumor invasion. , 2006, Cancer research.

[15]  R. Ganguly,et al.  Mathematical model for the cancer stem cell hypothesis , 2006, Cell proliferation.

[16]  Sean J. Morrison,et al.  Asymmetric and symmetric stem-cell divisions in development and cancer , 2006, Nature.

[17]  J. Rich,et al.  Cancer stem cells in radiation resistance. , 2007, Cancer research.

[18]  J. Dick,et al.  A human colon cancer cell capable of initiating tumour growth in immunodeficient mice , 2007, Nature.

[19]  Arne Traulsen,et al.  Correction: (A)Symmetric Stem Cell Replication and Cancer , 2007, PLoS Comput. Biol..

[20]  Yi Jiang,et al.  A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. , 2007, Biophysical journal.

[21]  Arne Traulsen,et al.  (A)Symmetric Stem Cell Replication and Cancer , 2007, PLoS Comput. Biol..

[22]  H. Frieboes,et al.  Computer simulation of glioma growth and morphology , 2007, NeuroImage.

[23]  Franziska Michor,et al.  Mathematical models of cancer stem cells. , 2008, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[24]  R. Weinberg,et al.  Cancer stem cells: mirage or reality? , 2009, Nature Medicine.

[25]  John M L Ebos,et al.  Accelerated metastasis after short-term treatment with a potent inhibitor of tumor angiogenesis. , 2009, Cancer cell.

[26]  Masahiro Inoue,et al.  Antiangiogenic therapy elicits malignant progression of tumors to increased local invasion and distant metastasis. , 2009, Cancer cell.

[27]  S. McDougall,et al.  Multiscale modelling and nonlinear simulation of vascular tumour growth , 2009, Journal of mathematical biology.

[28]  Louis Vermeulen,et al.  Wnt activity defines colon cancer stem cells and is regulated by the microenvironment , 2010, Nature Cell Biology.

[29]  S. McWeeney,et al.  Cancer stem cell tumor model reveals invasive morphology and increased phenotypical heterogeneity. , 2010, Cancer research.

[30]  Mei Zhang,et al.  Selective targeting of radiation-resistant tumor-initiating cells , 2010, Proceedings of the National Academy of Sciences.

[31]  Ling Xia,et al.  Cancer stem cell, niche and EGFR decide tumor development and treatment response: A bio-computational simulation study. , 2011, Journal of theoretical biology.

[32]  Jian Yang,et al.  A 3-dimentional multiscale model to simulate tumor progression in response to interactions between cancer stem cells and tumor microenvironmental factors , 2012, 2012 IEEE 6th International Conference on Systems Biology (ISB).

[33]  Peter Dirks,et al.  Cancer stem cells: an evolving concept , 2012, Nature Reviews Cancer.

[34]  Shuji Ogino,et al.  Differential WNT activity in colorectal cancer confers limited tumorigenic potential and is regulated by MAPK signaling. , 2012, Cancer research.