A systems approach for tumor pharmacokinetics

Abstract

Recent advances in genome inspired target discovery, small molecule screens, development of biological and nanotechnology have led to the introduction of a myriad of new differently sized agents into the clinic. The differences in small and large molecule delivery are becoming increasingly important in combination therapies as well as the use of drugs that modify the physiology of tumors such as anti-angiogenic treatment. The complexity of targeting has led to the development of mathematical models to facilitate understanding, but unfortunately, these studies are often only applicable to a particular molecule, making pharmacokinetic comparisons difficult. Here we develop and describe a framework for categorizing primary pharmacokinetics of drugs in tumors. For modeling purposes, we define drugs not by their mechanism of action but rather their rate-limiting step of delivery. Our simulations account for variations in perfusion, vascularization, interstitial transport, and non-linear local binding and metabolism. Based on a comparison of the fundamental rates determining uptake, drugs were classified into four categories depending on whether uptake is limited by blood flow, extravasation, interstitial diffusion, or local binding and metabolism. Simulations comparing small molecule versus macromolecular drugs show a sharp difference in distribution, which has implications for multi-drug therapies. The tissue-level distribution differs widely in tumors for small molecules versus macromolecular biologic drugs, and this should be considered in the design of agents and treatments. An example using antibodies in mouse xenografts illustrates the different in vivo behavior. This type of transport analysis can be used to aid in model development, experimental data analysis, and imaging and therapeutic agent design.

Figure 1. Example molecules and model structure.

(A) Space filling models of oxygen, FDG, doxorubicin, and an IgG for size comparison. (B) Diagram of a Krogh cylinder labeled with the four fundamental steps in tumor localization.

Figure 2. Simulation results for different class agents.

(A) Oxygen simulation in region with closely space vessels (50 µm Krogh radius) showing decreasing axial concentration due to poor blood flow (top). With the Krogh radius increased to 200 µm, the radial gradients show diffusion limited uptake for oxygen (bottom). (B) Antibody uptake is heterogeneous due to rapid binding relative to diffusion, and the lack of axial gradients indicates blood flow is not limiting (top). An epifluorescence image of an A431 tumor xenograft slice 24 hrs after 30 µg of cetuximab-VivoTag 680 was injected intravenously shows the perivascular distribution of the antibody (bottom). (C) The blood flow, extravasation, and diffusion are faster than cellular uptake for the class IV agent FDG resulting in homogenous distribution in the interstitium (top). This occurs even with heterogeneous cellular uptake as demonstrated by the intracellular FDG-6-phosphate in the same simulation (bottom).

Figure 3. Class variation with antibodies.

Mice with HT-29 tumor on the left side and A431 tumors on the right side were injected with 30 µg (left) or 300 µg (right) of cetuximab-VT680. The lower dose is subsaturating, so uptake is limited by delivery from the vasculature with similar uptake in both tumors. At saturating doses, the uptake is limited by the number of binding sites, and uptake is statistically higher in the A431 xenografts, which express EGFR at a much higher level. The reported p values are from a two-tailed t-test.

Figure 4. Class variation in time and multi-agent simulations.

The plasma profile along the length of the vessel is shown for the first 12 minutes for FDG (A) and an antibody (B). The axial gradients indicate a transient blood flow limitation (class I) for FDG while the antibody evenly fills the blood volume. (C) A joint simulation of oxygen (color scale) and a monoclonal antibody (z-axis) show differential uptake. The antibody is delivered to regions not reached by the blood flow limited oxygen, and other regions are well oxygenated with no antibody. (D) Similarly, a pretargeting simulation with higher antibody dose (z-axis) and reacting secondary agent (color scale) shows some regions targeted by the primary antibody may be missed by the rapidly cleared and blood flow limited small molecule secondary agent.