Recently the Lumped Parameter Model (LPM) has been extended to three dimensions enabling fast calculations of full resist profiles. This resist model incorporates most of the lithographically significant physical phenomenon of resist systems. This model works well to match isolated and semi-isolated line resist systems. However, it is not very successful at matching contact hole or isolated trench resist systems. The reason for this mismatch can be traced to the influence of base quencher present in chemically amplified (CA) resists yet absent from the original LPM. The quencher effectively splits the aerial image into two complementary images. These two images (acid and base) simultaneously diffuse and react with each other. A single aerial image diffusion model cannot approximate the resulting coupled quenching-diffusion system. An improved LPM that incorporates quencher and its diffusion is presented. Successful implementation of this model requires solving the coupled quenching-diffusion system in a fast and accurate manner. Several solution methods are discussed. The agreement between the Lumped Parameter Model and a full CA resist model is greatly improved. This improvement will enable fast and more accurate calculations of resist affects on three-dimensional imaging bias.