Heterogeneity of monoclonal antibody distribution and radiation dose in tumors: a modeling analysis.

For successful use of monoclonal antibodies and their conjugates for diagnosis and therapy, it is helpful to understand both macroscopic and microscopic aspects of antibody distribution. Antibody distribution in a tumor is simulated by splicing together information on global pharmacokinetics, transport across the capillary wall, diffusive penetration through the tumor interstitial space, and antigen-antibody interaction. One interesting implication of this simulation is a microscopic dosimetry for radioimmunotherapy. The information of microscopic radioconjugate distribution will enable us to calculate absorbed dose in a tumor at the microscopic scale. The first step is to simulate the spatial antibody concentration profile in a tumor as a function of time after intravenous (bolus) injection, using reasonable values for the parameters involved. The second step is to calculate, also as a function of time, the absorbed radiation dose distribution resulting from each concentration profile. Parameter values for IgG pharmacology and a radiation point source function for I-131 are used to explore the effect of affinity on the antibody distribution and consequent absorbed dose in the tumor. The geometry simulated corresponds to a spherical nodule of densely packed tumor cells. Absorbed doses are calculated for radiation from a single nodule and for a cubic lattice of such nodules. This modeling analysis demonstrates that 1) antigen-antibody binding in tumors can retard antibody percolation; 2) high antibody affinity at a given dose tends to decrease antibody percolation and result in a heterogeneous distribution; 3) heterogeneous antibody distribution results in heterogeneous absorbed dose. This is more apparent in the case of radiation from a single nodule or small tumors. PERC and PERC-RAD, the computer program packages developed for these analyses, provide a convenient and flexible way to assess the impact of macroscopic and microscopic parameters on the distribution of immunoconjugates (PERC) and the consequent absorbed radiation dose in tumors (PERC-RAD). This mathematical model and the general principles developed here can be applied as well as to other biological ligands and beta-emitters.