Unwrapping phase in 3D MR phase contrast angiograms

The phase of a MR signal can provide important information about magnetic field inhomogeneity, or be used to map the velocity of blood flow. However, phase images can contain artifacts due to phase wrapping when the imaged signal lies outside the 2 pi range (i.e. outside the velocity encoding range for PCA) and is wrapped back on itself. For example, in 3D PCA sequences it might be necessary to deliberately reduce the encoding range to better discern small or slow flowing vessels causing aliasing in higher velocity regions. In this paper we show that we can quickly and reliably correct for such artifacts and gain a factor of two in the imaged dynamic range. Using an automatic filtering based method, we derive a statement of the certainty of the phase signal at each point to control an iterative decision process. This algorithm does not require the user to supply a threshold and is non-causal in the sense that it does not rely on finding good regions which is a drawback of methods reported elsewhere. After a detailed description of our algorithm, we present results of phase unwrapping in both phantom and clinical data. We show the method to be effective even in low signal to noise images and when the single-wrap-only assumption is violated. We illustrate a clinical use of our method in simulating bolus injection from PCA velocity data.