Dielectric parameters, blood perfusion rate, and the temperature interval across which the tissue changes phase were found to have the most significant impact on MWA model outputs. The latent heat of tissue water vaporization and the volumetric heat capacity of the vaporized tissue were recognized as the least influential parameters. Uncertainties in model outputs identified in this study can be incorporated to provide probabilistic maps of expected ablation outcome for patient-specific treatment planning.
This paper presents new results for the modulus of families of walks on a graph-a discrete analog of the modulus of curve families due to Beurling and Ahlfors. Particular attention is paid to the dependence of the modulus on its parameters. Modulus is shown to generalize (and interpolate among) three important quantities in graph theory: shortest path, effective resistance, and maxflow or min-cut.
The notion of p-modulus of a family of objects on a graph is a measure of the richness of such families. We develop the notion of minimal subfamilies using the method of Lagrangian duality for p-modulus. We show that minimal subfamilies have at most |E| elements and that these elements carry a weight related to their "importance" in relation to the corresponding p-modulus problem. When p = 2, this measure of importance is in fact a probability measure and modulus can be thought as trying to minimize the expected overlap in the family.
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