Integrative mathematical oncology

Abstract

Cancer research attracts broad resources and scientists from many disciplines, and has produced some impressive advances in the treatment and understanding of this disease. However, a comprehensive mechanistic view of the cancer process remains elusive. To achieve this it seems clear that one must assemble a physically integrated team of interdisciplinary scientists that includes mathematicians, to develop mathematical models of tumorigenesis as a complex process. Examining these models and validating their findings by experimental and clinical observations seems to be one way to reconcile molecular reductionist with quantitative holistic approaches and produce an integrative mathematical oncology view of cancer progression.

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Figure 1: Mathematical models and multiple processes.
Figure 2: Cancer is multiscale.
Figure 3: The hybrid discrete continuum model.
Figure 4: Simulated tumour growth using the hybrid discrete continuum model.
Figure 5: A three-dimensional simulation of tumour growth in a grainy extracellular matrix.

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Acknowledgements

The authors gratefully acknowledge the support of the Integrative Cancer Biology Program funded by the National Cancer Institute.

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Correspondence to Alexander R. A. Anderson or Vito Quaranta.

Supplementary information

Supplementary information S1 (movie)

Tumour growth in a uniform ECM (cf. Figure 4a) All of the 2 dimensional simulations show the spatio–temporal evolution of all four variables in a 1cm2 domain: tumour cells (upper left), proteinase (upper right), nutrient (lower left) and ECM (lower right) over a period of approximately 3 months. Cell colouration relates to either the tumour cell-cell adhesion status (low=blue, medium=cyan, high=yellow, very high=orange) or if the cell is dead (dark brown). Colouration of the other variables is done using the hot colourmap (high=white, medium=red, low=black) to represent varying concentrations. All parameters used in the simulations are identical with the exception of the different microenvironments. (MOV 4942 kb)

Supplementary information S2 (movie)

Tumour growth in a grainy ECM (cf. Figure 4b) All of the 2 dimensional simulations show the spatio–temporal evolution of all four variables in a 1cm2 domain: tumour cells (upper left), proteinase (upper right), nutrient (lower left) and ECM (lower right) over a period of approximately 3 months. Cell colouration relates to either the tumour cell–cell adhesion status (low=blue, medium=cyan, high=yellow, very high=orange) or if the cell is dead (dark brown). Colouration of the other variables is done using the hot colourmap (high=white, medium=red, low=black) to represent varying concentrations. All parameters used in the simulations are identical with the exception of the different microenvironments. (MOV 5892 kb)

Supplementary information S3 (movie)

Tumour growth under low nutrient conditions (cf. Figure 4c) All of the 2 dimensional simulations show the spatio–temporal evolution of all four variables in a 1cm2 domain: tumour cells (upper left), proteinase (upper right), nutrient (lower left) and ECM (lower right) over a period of approximately 3 months. Cell colouration relates to either the tumour cell–cell adhesion status (low=blue, medium=cyan, high=yellow, very high=orange) or if the cell is dead (dark brown). Colouration of the other variables is done using the hot colourmap (high=white, medium=red, low=black) to represent varying concentrations. All parameters used in the simulations are identical with the exception of the different microenvironments. (MOV 827 kb)

Supplementary information S4 (movie)

A sequence of slices through the 3–dimensional tumour shown in Fig. 5. Colouration reflects different levels of cell density (green=low, red=high.)Each of the 3 dimensional simulations are simply different renderings of the same final tumour morphology after growth in a grainy ECM domain 0.5cm3 for approximately 1.5 months. (MOV 2070 kb)

Supplementary information S5 (movie)

A sequence of slices building up the 3–dimensional tumour shown in Fig. 5. Colouration is only used to try to distinguish different individual cells and has no other meaning.Each of the 3 dimensional simulations are simply different renderings of the same final tumour morphology after growth in a grainy ECM domain 0.5cm3 for approximately 1.5 months. (MOV 1699 kb)

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Anderson, A., Quaranta, V. Integrative mathematical oncology. Nat Rev Cancer 8, 227–234 (2008). https://doi.org/10.1038/nrc2329

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