Klosterboer and Rutledge developed a mathematical model for photothermographic systems consisting of silver halide grains, silver carboxylates, development chemistry and binder. The Klosterboer-Rutledge (K-R) model incorporates several simplifying assumptions, the most limiting of which is the assumption that the spheres of influence do not overlap. This assumption effectively restricts the validity of the model to low grain-number densities. The model has now been modified to remove this restriction resulting in a more general model that resolves the discrepancy between the Klosterboer-Rutledge model and the observed dependence of D_MAX, contrast and speed on grain-number density. The Klosterboer-Rutledge model also treats the spheres of influence as spheres with perfectly sharp boundaries. The generalized model was derived with an arbitrarily shaped region of influence thereby extending the validity to more realistic model films. In addition, other simplifying assumptions were addressed to complete the generalization of the K-R model.