Presentation on theme: "* This work was done as part of the Capstone chemical engineering class at the University of Oklahoma ** Capstone undergraduate students A mathematical."— Presentation transcript:
* This work was done as part of the Capstone chemical engineering class at the University of Oklahoma ** Capstone undergraduate students A mathematical model is used to determine appropriate timing of an existing cancer treatment based on attaching monoclonal antibodies (mAb) to single-walled carbon nanotubes (SWNT) for breast cancer cells. The mathematical model predicts the initial dosage for intravenous injection and near-infrared (NIR) radiation emission intensity and timing as a function of the tumor volume. Monoclonal antibodies are produced by one type of immune cell. They are used to specifically target cancer cells. Single-walled carbon nanotubes are graphite sheets rolled into a cylinder. Strong absorption of NIR radiation is one of their unique properties. Researchers have recently conjugated mAbs to SWNTs to target breast cancer cells. By using a NIR laser, the localized heating due to the high thermal conductivity of SWNTs led to successful eradication of the cancer cells 1. Single-walled carbon nanotube HER2 receptor (on breast cancer cells) Abstract Cancer cell The functionalization of SWNTs with mAbs serves to deliver SWNTs to the cancer site for phototherapy. Functionalizing SWNTs with mAbs Introduction Sources Shao, N., Lu, S., et al., Integrated molecular targeting of IGF1T and HER2 surface receptors and destruction of breast cancer cells using single wall carbon nanotubes, Nanotechnology (2007), 18:1-9. University of Maine, Department of Chemistry, Monoclonal antibody Linker molecule Surfactant SWNT Monoclonal antibody Crossing Barriers Due to their small size, nanosystems have been shown to overcome biological barriers, such as the blood-brain barrier, which makes them attractive for cancer therapy. Mathematical Modeling for Tumor Targeting Plasma & Lymph Flow Diagram Two Subcompartments Model Immunoglobulin IgG is dispersed to the vascular and interstitial spaces through plasma flow. Their half-life is determined by the FcRn receptor in endothelial cells. This model describes the catabolic process of IgG through its internalization into the organ and tissues. The two-pore model shows how mAbs travel through the organs and tissues. It also explains the diffusion of mAbs into the interstitium through the blood vessel wall. Two-pore Model k int : Rate constant of internalization k cat : Rate constant for lysosomal degradation k rec : Rate constant for recycling of Fc-Rn bound C m : Concentration of catabolites CL org : Catabolite clearance rate J v : Fluid flux α L, α S : Fraction of bulk fluid Concentration of mAbs in the Body Begin NIR irradiation We have successfully modeled the initial dosage requirement of the drug as a function of tumor volume the required time for NIR emission following injection the temperature gradient of the tumor during NIR irradiation the required time for tumor cell damage Based on the temperature gradient of the tumor during irradiation, damage to the surrounding normal cells will be minimal. It is not desirable to have the tumor cells reach temperatures above 80°C due to bubbling of the tumor and subsequent damage to surrounding normal cells. Therefore, an irradiation time of three minutes is sufficient for eradication of tumor cells.. Shao, N., Lu, S., Wickstrom, E., and Panchapakesan, B., Integrated molecular targeting of IGF1T and HER2 surface receptors and destruction of breast cancer cells using single wall carbon nanotubes, Nanotechnology (2007), 18:1-9. 2. Davda, J. P., Jain, M., Batra, S. K., Gwilt, P. R., Robinson, D. H., A physiologically based pharmacokinetic (PBPK) model to characterize and perdict the disposition of monoclonal antibody CC49 and its single chain Fv constructs, International Immunopharmacology (2008) 8:401-413. 3. Meyskens, F., Thomson, S., Moon, T., Quantitation of the Number of Cells within Tumor Colonies in Semisolid Medium and Their Growth as Oblate Spheroids, Cancer Research (1984), 271-277. 4. G. Z. Ferl, A. M. Wu, J. J. Distefano III, A predictive model of therapeutic monoclonal antibody dynamics and regulation by the newnatal Fc Receptor (FcRn), Annals of Biomedical Engineering (2005) 33( 11): 1640-1652. We would like to thank the following for their guidance and help in our project: Chiranth Srinivasan, Dr. Daniel Resasco, Dr. Lance Lobban, Dr. Liang Zhang, Dr. Barbara Safiejko-Mroczka, and Kevin Bagnall. Conclusions Acknowledgements References Photothermal Therapy Temperature Gradient of the Tumor Cell at Various Irradiation Times t = 1 mint = 2 mint = 3 min Number of cells in a colonies TV = 10 mlTV= 15 mlTV = 20 mlTV = 25 ml 1.09E+091.51E+091.89E+092.26E+09 Energy used (W) 0.480.720.951.19 218.36301.12378.25451.44 Number of SWNT required 1.06E+111.58E+112.11E+112.64E+11 4.83E+136.66E+138.36E+139.98E+13 Total amount of SWNT (mol) 1.75E-132.63E-133.50E-134.38E-13 8.01E-111.11E-101.39E-101.66E-10 Maximum TC value of antibodies (%) 7.214.943.753.02 Initial dose SWNT required (mole) 2.43E-125.32E-129.35E-121.45E-11 1.11E-092.24E-093.70E-095.49E-09 Initial dose antibody used (mole) 1.11E-092.50E-094.00E-096.00E-09
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