Physical properties of the microenvironment influence penetration of drugs into tumors. Here, we develop a mathematical model to predict the outcome of chemotherapy based on the physical laws of diffusion. The most important parameters in the model are the volume fraction occupied by tumor blood vessels and their average diameter. Drug delivery to cells, and kill thereof, are mediated by these microenvironmental properties and affected by the diffusion penetration distance after extravasation. To calculate parameter values we fit the model to histopathology measurements of the fraction of tumor killed after chemotherapy in human patients with colorectal cancer metastatic to liver (coefficient of determination R 2 = 0.94). To validate the model in a different tumor type, we input patient-specific model parameter values from glioblastoma; the model successfully predicts extent of tumor kill after chemotherapy (R 2 = 0.7-0.91). Toward prospective clinical translation, we calculate blood volume fraction parameter values from in vivo contrastenhanced computed tomography imaging from a separate cohort of patients with colorectal cancer metastatic to liver, and demonstrate accurate model predictions of individual patient responses (average relative error = 15%). Here, patient-specific data from either in vivo imaging or histopathology drives output of the model's formulas. Values obtained from standard clinical diagnostic measurements for each individual are entered into the model, producing accurate predictions of tumor kill after chemotherapy. Clinical translation will enable the rational design of individualized treatment strategies such as amount, frequency, and delivery platform of drug and the need for ancillary non-drug-based treatment.colorectal cancer liver metastasis | glioblastoma multiforme histopathology | contrast CT | patient drug response | mathematical modeling P redicting the effects of chemotherapeutic drugs on tumor behavior in patients is vital to advancing knowledge in the fight against cancer. Computational methods of "mathematical pathology" developed through quantitative analysis of human tumor tissue have the potential to provide predictions of treatment outcomes in the clinical setting (1). Here, we develop our model using colorectal cancer (CRC) metastatic to liver from one cohort of patients as an example of intratumor perfusion properties. We then assess the general applicability of our model to predict response in other tumor types, that is, glioblastoma multiforme (GBM). We prospectively apply our model in vivo to a third cohort of subjects with metastatic CRC to liver using pretreatment contrast-enhanced computed tomography (CT) scans followed by correlation histopathology after treatment and surgical excision.CRC metastatic to liver can be treated by surgical resection in the majority of cases. Metastases too large or numerous for primary excision are first treated with chemotherapy and then excised if possible, because chemotherapy alone is rarely curative (2, 3). This strategy works,...

A quantitative understanding of the advantages of nanoparticle-based drug delivery vis-à-vis conventional free drug chemotherapy has yet to be established for cancer or other disease despite numerous investigations. Here, we employ first-principles cell biophysics, drug pharmaco-kinetics and drug pharmaco-dynamics to model the delivery of doxorubicin (DOX) to hepatocellular carcinoma (HCC) tumor cells and predict the resultant experimental cytotoxicity data. The fundamental, mechanistic hypothesis of our mathematical model is that the integrated history of drug uptake by the cells over time of exposure, which sets the cell death rate parameter, and the uptake rate are the sole determinants of dose response relationship. A universal solution of the model equations is capable of predicting the entire, nonlinear dose response of the cells to any drug concentration based on just two separate measurements of these cellular parameters. This analysis reveals that nanocarrier-mediated delivery overcomes resistance to free drug because of improved cellular uptake rates, and that dose response curves to nanocarrier mediated drug delivery are equivalent to those for free-drug, but “shifted to the left,” i.e., lower amounts of drug achieve the same cell kill. We then demonstrate the model’s general applicability to different tumor and drug types, and cell-exposure time courses by investigating HCC cells exposed to cisplatin and 5-fluorouracil, breast cancer MCF-7 cells exposed to DOX, and pancreatic adenocarcinoma PANC-1 cells exposed to gemcitabine. The model will help in the optimal design of nanocarriers for clinical applications and improve the current, largely empirical understanding of in vivo drug transport and tumor response.

The kinesins have long been known to drive microtubule-based transport of sub-cellular components, yet the mechanisms of their attachment to cargo remain a mystery. Several different cargo-receptors have been proposed based on their in vitro binding affinities to kinesin-1. Only two of these—phosphatidyl inositol, a negatively charged lipid, and the carboxyl terminus of the amyloid precursor protein (APP-C), a trans-membrane protein—have been reported to mediate motility in living systems. A major question is how these many different cargo, receptors and motors interact to produce the complex choreography of vesicular transport within living cells. Here we describe an experimental assay that identifies cargo–motor receptors by their ability to recruit active motors and drive transport of exogenous cargo towards the synapse in living axons. Cargo is engineered by derivatizing the surface of polystyrene fluorescent nanospheres (100 nm diameter) with charged residues or with synthetic peptides derived from candidate motor receptor proteins, all designed to display a terminal COOH group. After injection into the squid giant axon, particle movements are imaged by laser-scanning confocal time-lapse microscopy. In this report we compare the motility of negatively charged beads with APP-C beads in the presence of glycine-conjugated non-motile beads using new strategies to measure bead movements. The ensuing quantitative analysis of time-lapse digital sequences reveals detailed information about bead movements: instantaneous and maximum velocities, run lengths, pause frequencies and pause durations. These measurements provide parameters for a mathematical model that predicts the spatiotemporal evolution of distribution of the two different types of bead cargo in the axon. The results reveal that negatively charged beads differ from APP-C beads in velocity and dispersion, and predict that at long time points APP-C will achieve greater progress towards the presynaptic terminal. The significance of this data and accompanying model pertains to the role transport plays in neuronal function, connectivity, and survival, and has implications in the pathogenesis of neurological disorders, such as Alzheimer’s, Huntington and Parkinson’s diseases.

The prediction of optimal times of separation as a function of the applied electrical field and cation valence have been studied for the case of field flow fractionation [Martin M., Giddings J. C., J. Phys. Chem. 1981, 85, 727] with charged solutes. These predictions can be very useful to a priori design or identify optimal operating conditions for a Couette-based device for field flow fractionation when the orthogonal field is an electrical field. Mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accomplished after the role of the capillary geometrical dimensions on the applied electrical field equations has been assessed [Oyanader M. A., Arce P., Electrophoresis 2005; 26, 2857]. Moreover, explicit analytical expressions are derived for the effective parameters, i.e. diffusivity and convective velocity as functions of the applied (orthogonal) electrical field. These effective transport parameters are used to study the effect of the cation valence of the solutes and of the magnitude of the applied orthogonal electrical field on the values of the optimal time of separation. These parameters play a significant role in controlling the optimal separation time, leading to a family of minimum values, for particular magnitudes of the applied orthogonal electrical field.

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