1. A system that measures perfusion through a volume of tissue, the system comprising: a non-transitory memory to store computer-executable instructions; and a processor that executes the computer-executable instructions to at least: receive an ultrasound signal response of a contrast agent within a volume of tissue as a function of time, wherein the contrast agent is infused into a patient's vasculature at a constant rate, wherein the volume of tissue comprises a and a geometry, wherein the geometry is a rectangular prism with a corresponding length, width, and height; determine a probabilistic constant based on the geometry of the volume of tissue; determine a ratio of mean velocity to mean path length based on the ultrasound signal response at a first time representing a transitory intensity and a second time corresponding to a steady state intensity; determine a tissue density of the volume of tissue; and determine a mean perfusion through the volume of tissue based on the probabilistic constant, the ratio of mean velocity to mean path length, the tissue density, the width, and the height.