Abstract
Gliomas are diffuse and invasive brain tumors with the nefarious ability to evade even seemingly draconian treatment measures. Here we introduce a simple mathematical model for drug delivery of chemotherapeutic agents to treat such a tumor. The model predicts that heterogeneity in drug delivery related to variability in vascular density throughout the brain results in an apparent tumor reduction based on imaging studies despite continual spread beyond the resolution of the imaging modality. We discuss a clinical example for which the model-predicted scenario is relevant. The analysis and results suggest an explanation for the clinical problem of the long-standing confounding observation of shrinkage of the lesion in certain areas of the brain with continued growth in other areas.
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REFERENCES
Blinkov, S. M. and I. I. Glezer (1968). The human brain in figures and tables: a quantitative handbook. Basic Books, Inc, Plenum Press, New York.
Burgess, P. K., P. M. Kulesa, J. D. Murray and E. C. Alvord, Jr. (1997). The interactive of growth rates and diffusion coefficients in a three-dimensional mathematical model of gliomas. Journal of Neuropathology and Experimental Neurology 56(6): 704–713.
Coddington, E. A. and N. Levinson (1972). Theory of Ordinary Differential Equations. McGraw-Hill, New York.
Cook, J., D. E. Woodward, P. Tracqui, G. T. Bartoo, J. D. Murray and E. C. Alvord, Jr. (1995). The modeling of diffusive tumours. Journal of Biological Systems 3(4): 937–945.
Cruywagen, G. C., D. E. Woodward, P. Tracqui, G. T. Bartoo, J. D. Murray and E. C. Alvord, Jr. (1995). The modeling of diffusive tumours. Journal of Biological Systems 3(4): 937–945.
Kroll, R. A., M. A. Pagel, L. Muldoon, S. Roman-Goldstein and E. A. Neuwelt (1996). Increasing volume of distribution to the brain with interstitial infusion: dose, rather than convection, might be the most important factor. Neurosurgery 38(4): 746–754.
Magnus, W. and S. Winkler (1966). Hill's Equation. Dover, New York.
Murray, J.D. (2002). Mathematical Biology II: Spatial Models and Biomedical Applications. Springer-Verlag, New York.
Shigesada, N. and K. Kawasaki (1997). Biological Invasions: Theory and Practice. Oxford University Press.
Swanson, K.R. (1999). Mathematical modeling of the growth and control of tumors. PhD thesis, University of Washington.
Swanson, K. R., E. C. Alvord, Jr. and J. D. Murray (2000). A quantitative model for differential motility of gliomas in grey and white matter. Cell Proliferation 33: 317–329.
Swanson, K. R., E. C. Alvord, Jr. and J. D. Murray (2002). Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. British Journal of Cancer 86: 14–18.
Tracqui, P., G. C. Cruywagen, D. E. Woodward, G. T. Bartoo, J. D. Murray and E. C. Alvord, Jr. (1995). A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth. Cell Proliferation 28: 17–31.
Woodward, D. E., J. Cook, P. Tracqui, G. C. Cruywagen, J. D. Murray and E. C. Alvord, Jr. (1996). A mathematical model of glioma growth: the effect of extent of surgical resection. Cell Proliferation 29: 269–288.
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Swanson, K.R., Alvord, E.C. & Murray, J.D. Quantifying Efficacy of Chemotherapy of Brain Tumors with Homogeneous and Heterogeneous Drug Delivery. Acta Biotheor 50, 223–237 (2002). https://doi.org/10.1023/A:1022644031905
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DOI: https://doi.org/10.1023/A:1022644031905