The present disclosure provides systems and methods for rendering lesions on a geometric surface model of a geometric structure. The system includes a computer-based model construction system configured to create a three-dimensional (3D) texture map including a plurality of voxels each having a tissue necrosis value, increment the tissue necrosis values as a function of at least one parameter to generate a total tissue necrosis value for each voxel, render at least one lesion on the geometric surface model based on the total tissue necrosis values, and display the geometric surface model and the at least one rendered lesion.