Hemodynamically significant stenosis of the internal carotid artery (ICA) is usually diagnosed by elevated velocities in a region of luminal narrowing. Many other significant diagnoses can be made based upon lower-than-normal velocities. Analysis of the combinations of low ICA velocity, abnormal ICA waveform, and abnormal velocities and waveforms in ipsilateral or contralateral ICA, common carotid artery, and vertebral arteries can allow diagnosis of significant vascular or valvular disease from the heart to the brain.