Abstract

One of the principal objectives of researchers in cancer treatment is to increase the fraction of chemotherapeutic molecules that reaches primary or metastatic malignancies. One possible avenue towards this goal is the coupling of the drug molecule with agents capable of identifying neoplasms, as is typically done with antibody-antigen complexation. While this has had some success, even a perfectly antibody guided therapeutic agent encounters significant complications in reaching the targeted neoplasms. Since these problems are mainly mechanical rather than biological in nature they cannot be dealt with by better biomarker technology. Jain and his coworkers have identified several such obstacles to delivery among them being the blood viscosity and the high interstitial pressures within tumors.

The analysis of Jain et al relates to large tumors and thus may not be appropriate to answer some of the questions of the clinical oncologist. In particular, the assumption that the fluid pressure is time independent limits the scope to large, slowly growing, dominantly necrotic tumors. Though the time scale for convection/diffusion of the macromolecules is very short compared to the typical doubling times for tumors, the assumption of time independence of the fluid pressure is in general not tenable since the pressure varies widely through the growth of the tumor and in particular depends on the tumor growth rate and the absence or presence of a necrotic core. In order to calculate the penetration properties of a chemotherapeutic agent, i.e. the concentration of drug in a tumor, we have used poroelastic constitutive assumptions together with spherical symmetry to obtain a pressure distribution that varies with the tumor’s age. Using this, we can obtain concentration profiles for the early stages of growth of the neoplasm. In fact, we show in Fig. 1 that in the initial growth phase of the tumor the concentration profile rises at first before decreasing with increasing age since the interstitial pressure is not high enough yet to act as a significant barrier to the delivery of the drug.

At present there is a lack of modeling in the area of drug distribution in cancer tumors. Developing better models is important because of their potential as quantitative tools in clinical oncology. Issues such as proper drug dosage, the timing of the insertion and the course of delivery (Fig. 2) are all features of a good model that could guide a practitioner in his work. Our model determines the tumor response as a function of it’s age and also the point at which convection no longer occurs in the majority of the tumor. The model could conceivably be used to determine when this type of therapy is no longer effective, thus saving medical resources and unnecessary chemotherapy side effects for patients.

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