Microbubble ultrasound contrast agents (UCAs) have been extensively used in medical ultrasound for enhancing the echo components from blood vessels. However, their ultimate promise of enhancing the echoes from the microvasculature with high specificity remains unfulfilled using existing methods. We have previously shown that the Volterra filter can be used to enhance UCA echo components from flow channels with dimensions similar to peripheral vessels, e.g. the carotid artery. In this paper, we investigate a new receiver architecture based on an adaptive third-order Volterra Filter (VF) in conjunction with beamformed echo data from imaging tumor microvasculature in vivo. It is shown that the cubic and quadratic components of the VF provide significant enhancement of the UCA echoes from the tumor compared to the echoes from the same tissue regions in the absence of the UCA. We describe an adaptive recursive least squares (RLS) implementation of the VF and give examples of the contrast enhancement. Further enhancement of the UCA contrast is achieved by applying a dynamic statistical decision rule that produces a parameter we refer to as the temporal perfusion index (TPI). The TPI rewards transient echo oscillations while rejecting tissue motion and noise variation. These in vivo results demonstrate the potential for advanced signal processing in increasing the sensitivity and specificity of medical ultrasound in imaging tissue perfusion, a form of functional imaging.