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British Journal of Medicine and Medical Research

British Journal of Medicine and Medical Research, ISSN: 2231-0614,Vol.: 4, Issue.: 16 (01-10 June)


Original Research Article


Mathematical Model of Colorectal Cancer with Monoclonal Antibody Treatments



L.G. dePillis1*, H. Savage2 and A. E. Radunskaya3
1Department of Mathematics, Harvey Mudd College, Claremont, California, USA.
2Graduate Group in Immunology, University of California, Davis, Davis, California, USA.
3Department of Mathematics, Pomona College, Claremont, California, USA.




We present a new mathematical model of colorectal cancer growth and its response to monoclonalantibody (mAb) therapy. Although promising, most mAb drugs are still in trial phases, and the possible variations in the dosing schedules of those currently approved for use have not yet been thoroughly explored. To investigate the effectiveness of current mAb treatment schedules, and to test hypothetical treatment strategies, we have created a system of nonlinear ordinary differential equations (ODEs) to model colorectal cancer growth and treatment. The model includes tumor cells, elements of the host’s immune response, and treatments. Model treatments include the chemotherapy agent irinotecan and one of two monoclonal antibodies - cetuximab, which is FDAapproved for colorectal cancer, and panitumumab, which is still being evaluated in clinical trials. The model incorporates patient-specific parameters to account for individual variations in immune system strength and in medication efficacy against the tumor. We have simulated outcomes for groups of virtual patients on treatment protocols for which clinical trial data are available, using a range of biologically reasonable patient-specific parameter values. Our results closely match clinical trial results for these protocols. We also simulated experimental dosing schedules, and have found new schedules which, in our simulations, reduce tumor size more effectively than current treatment schedules. Additionally, we examined the system’s equilibria and sensitivity to parameter values. In the absence of treatment, tumor evolution is most affected by the intrinsic tumor growth rate and carrying capacity. When treatment is introduced, tumor growth is most affected by drugspecific PK/PD parameters.


Keywords :

Colorectal cancer; Mathematical model; Monoclonal antibody; Immunotherapy; Mixed chemo-immunotherapy; Simulated cohort study; In silico tumor growth.


Full Article - PDF    Page 3101-3131    Article Metrics


DOI : 10.9734/BJMMR/2014/8393

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