| We present a multi-scale mathematical and in silico framework for therapeutics delivery to cancerous lesions. First, we outline the essential issues, spanning from the scale of the entire organism, whose liver, lungs, and kidneys immediately engage in detoxification and elimination, down through the tumoral, the cellular, and finally the genetic scale, where a myriad of molecular mechanisms relentlessly seeks to purge the cell and its organelles of cytotoxic charge. Then we present the core of the framework: a two-dimensional, multiscale model of carcinogenesis due to Zheng et al. [104], capable of simulating cancerous progression from avascular growth through neo-vascularization and into the later stages of invasive morphology. Using this model we present a simulation of the growth of a perfused region of glioblastoma multiforme (a highly malignant brain tumor), demonstrating a striking correspondence of characteristics with those found in vivo. Following this we incorporate our own tumoral-scale model of chemotherapeutic treatment, graphically and quantitatively demonstrating several of the previously discussed issues, such as inhomogenous drug delivery through impaired vasculature and diffusional obstacles, and shedding new light on a long-standing, controversial hypothesis of Rakesh Jain [48, 50, 49]. Finally, we formulate a model for cellular-scale therapeutics transport, again demonstrating relevant issues.; Although modeling of various components of drug delivery, such as tumoral hemodynamics, nanoparticle drug release, and cell resistance mechanisms, has been previously carried out, the simulations we perform represent the first time such models have been incorporated into a multi-dimensional, multi-scale framework. This work represents only a first step in the construction of an integrated model of therapeutics delivery. Collaboration is in progress among members of the Cristini Biomedical Simulation Laboratory at UCI and members of the Fruehauf Oncological Experimental Laboratory at UCIMC, where in vitro and in vivo testing of the mathematical and in silico models is proceeding. The desired end is a virtual cancer simulator capable of accurately simulating cancerous progression through its many stages and predicting the effects of therapeutic intervention. |
