Antibody therapies for cancer have been developed because of their ability to specifically target tumor cells that have up-regulated, altered, or inappropriately expressed antigens on their surface. This specific binding provides an advantage over traditional chemotherapeutics by enabling antibodies to accumulate in neoplastic tissue while largely sparing normal tissue. However, the large size of these molecules and rapid binding in tumor tissue, combined with the abnormal physiology of tumors, causes slow, heterogeneous uptake (Jain, 1999
). The antibody dose in the tumor is often insufficient to mediate a significant therapeutic response, and poor microdistribution leaves many cells with little to no treatment.
The distribution of antibodies in tumors is a complex, erratic process. Vascularized tumors have a network of poorly formed vessels throughout a highly disorganized, heterogeneous cluster of tumor and multiple stromal cell types (Dvorak, 1986
). Due to several biological mediators secreted locally, the tumor blood vessels are often much more permeable than normal capillaries, and, with a lack of efficient lymphatic drainage, this leads to elevated interstitial pressure and elimination of the normal pressure gradients between the tissue and vessel (Boucher et al., 1990
). With the loss of pressure across the capillary wall, these vessels are susceptible to collapse from the growth and solid stress of the surrounding cancerous tissue, causing areas of low vessel density and necrosis (Boucher & Jain, 1992
). The disrupted pressure gradients and malformed, tortuous paths of vessels (Ahlstrom et al., 1988
) interfere with blood flow patterns, causing temporary cessation and even reversal of flow direction. Poor blood flow and avascular regions give rise to hypoxia, making some areas more resistant to radiation and chemotherapeutics (Vaupel et al., 2001
). Once antibodies exit the blood vessel, they face a variety of other transport barriers. The lack of convection means these macromolecular drugs rely primarily on diffusion to extravasate and move through the tissue. Within the tumor interstitium, variations in extracellular matrix and cell density cause heterogeneous diffusion (Jain, 1999
). Rapid binding to antigen immobilizes these drugs almost immediately, causing perivascular localization, and differences in local antigen density further vary the local concentration even in regions that are efficiently targeted (Aquino et al., 2004
Given the stochastic development of the vasculature and complexity of targeting in tumors, modeling the uptake is an unwieldy task. Significant intra- and inter-tumor variability, even more so in the clinic (Scott et al., 2005
) than in animal models, can further complicate modeling attempts. Despite these complexities, simplified models can still provide a basic understanding of the most important parameters for designing experiments, interpreting data, and developing strategies to improve targeting (Bertuzzi et al., 2008
; Fujimori et al., 1989
). These models are equally useful in determining which assumptions have not been met when tumor uptake is significantly different than anticipated, and whether these differences can be exploited.
The purpose of developing this model is to create a mechanistic description of total antibody uptake in a tumor based on the dominant principles controlling localization. We have previously developed a simplified model of transport in micrometastases and around individual blood vessels in solid tumors (Thurber et al., 2008a
; Thurber et al., 2007
). These models showed that the ratio of extravasation of antibodies from the blood vessels to the rate at which they diffuse within the tissue (Biot number) is very low (< 0.01 for most targeting molecules). We show here that this results in the total uptake from the vessels being almost independent from the microscopic distribution. This reduction in dimensionality allows a compartmental model to describe the total antibody in the tumor, even though the tumor is not well-mixed (i.e. not homogeneous). The result is a simple analytical model that clearly delineates the major factors controlling tumor uptake and can be used by non-modeling researchers to estimate the time course of antibody uptake in solid tumors. Ideally this will be used in conjunction with experiments to further our understanding and develop improvements in targeting.