A mathematical model is developed to study the localization
characteristics of anti-cancer agents in solid tumors.  The model is
general enough that it may be applied to many chemotherapeutic
approaches to cancer treatment, but is firmly based on the biology of
a particular new and promising two-step drug targeting strategy.
Singular perturbation techniques are used to approximate the solution
away from the capillary wall and in the boundary layer at the
capillary-tissue interface.
  The solution to the full system of partial differential equations
can also be approximated by an ordinary differential equation
formulation whose solution provides a good analytic expression for the
total concentration of conjugate in the tumor.  From this result key
parameters are isolated; the effects of the tumor vasculature, binding
kinetics, and administration schedule are investigated; and the
critical parameters that influence the retention of the agent in the
tumor are determined.  The model predicts that conjugate localizes
best in well vascularized tissue, but is retained longer in poorly
vascularized sections of the tumor.  Also, reducing the dissociation
rate by half almost doubles the half-life in the tumor. Comparisons of
the model predictions with experimental observations are made and an
excellent correlation exists.