Comparing Gradient Descent with Automatic Differentiation and Particle Swarm Optimization Techniques for Estimating Tumor Blood Flow Parameters in Contrast-Enhanced Imaging

In this preliminary report, two optimization approaches, gradient descent with automatic differentiation and particle swarm optimization, are presented, applied, and compared in an effort to leverage dynamic information collected during contrast-enhanced medical imaging of tumors to estimate four blood flow parameters: perfusion, permeability surface area product, volume of the plasma, and volume of the interstitial space. Using Fick’s law on a simple two-compartment model, the resulting PDEs are numerically integrated using a collocation method for a set of boundary and initial conditions and known values of the parameters, and the resulting tracer concentrations were spatially integrated to generate truth data of signal intensity as a function of time only. After using physical constraints on the boundaries to recover reasonable estimates for two of the parameters, the two optimization approaches are used in an attempt to recover estimates for the remaining two parameters. The resulting efficacy and efficiency of the two optimization approaches are compared.