Low blood SNR makes detecting small vessels, measuring slow flow rates, and assessing blood perfusion without contrast administration challenging. A potential approach is to use Variance of Acceleration (VoA) imaging, which has been demonstrated previously in humans in vivo for monitoring subcutaneous bleeding and delineating intraplaque hemorrhage. We hypothesize that, without the addition of contrast agents, VoA can detect slow flow in small vessels for perfusion assessment. Experiments were performed on an ATS 700-D 527 calibrated flow phantom (vessel diameter of 1 mm, flow rates of 0-53 cm/s) and in the surgically exteriorized right kidneys of 3 pigs (2M/1F, mean body weight of 74.4 ± 9.3 kg) at baseline and after inducing ischemia. In the phantom, logVoA increased in the vessel with increasing flow rate, and it remained constant in the background. LogVoA values were higher in the background with versus without the ARF excitation. Similarly, logVoA values were higher in the vessel, particularly for flow rates < 12 cm/s, with versus without ARF excitation. Vessel CNR by logVoA was higher with versus without ARF excitation for flow rates < 12 cm/s, and CNR by logVoA was greater than CNR by power Doppler for all flow rates. Additionally, logVoA was statistically significantly greater at baseline than ischemia in all three in vivo pig kidneys. Finally, logVoA delineates a 1.25 mm-diameter vessel in a pig renal cortex in vivo, while power Doppler does not. These results suggest that logVoA could support contrast-free detection of slow blood flow in small vessels and in vivo perfusion assessment.