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The progress of nanoparticle (NP)-based drug delivery has been hindered by an inability toestablish structure-activity relationships in vivo. Here, using stable, monosized, radiolabeled,mesoporous silica nanoparticles (MSNs), we apply an integrated SPECT/CT imaging andmathematical modeling approach to understand the combined effects of MSN size, surfacechemistry and routes of administration on biodistribution and clearance kinetics in healthyrats. We show that increased particle size from ~32- to ~142-nm results in a monotonicdecrease in systemic bioavailability, irrespective of route of administration, with correspondingaccumulation in liver and spleen. Cationic MSNs with surface exposed amines (PEI)have reduced circulation, compared to MSNs of identical size and charge but with shieldedamines (QA), due to rapid sequestration into liver and spleen. However, QA show greatertotal excretion than PEI and their size-matched neutral counterparts (TMS). Overall, weprovide important predictive functional correlations to support the rational design ofnanomedicines.

Cancer continues to be among the leading healthcare problems worldwide, and efforts continue not just to find better drugs, but also better drug delivery methods. The need for delivering cytotoxic agents selectively to cancerous cells, for improved safety and efficacy, has triggered the application of nanotechnology in medicine. This effort has provided drug delivery systems that can potentially revolutionize cancer treatment. Nanocarriers, due to their capacity for targeted drug delivery, can shift the balance of cytotoxicity from healthy to cancerous cells. The field of cancer nanomedicine has made significant progress, but challenges remain that impede its clinical translation. Several biophysical barriers to the transport of nanocarriers to the tumor exist, and a much deeper understanding of nano-bio interactions is necessary to change the status quo. Mathematical modeling has been instrumental in improving our understanding of the physicochemical and physiological underpinnings of nanomaterial behavior in biological systems. Here, we present a comprehensive review of literature on mathematical modeling works that have been and are being employed towards a better understanding of nano-bio interactions for improved tumor delivery efficacy.