Additional File: PC-MR post-processing methodology

This supplementary file presents new methods to analyze PC-MR velocity data using the principles of control volume analysis. PC-MR phase and magnitude images were imported into MATLAB for image processing. Spatiotemporal velocity values were derived from the phase images as follows. A static background region was manually selected to determine the phase value corresponding to zero velocity, computed as the average phase value over space and time in this rectangular region. The remaining velocity values were linearly scaled using Venc and the number of phase encoding steps of the data set. The standard deviation of phase values in this region provided an estimate of the velocity noise level, used to compute the signal to noise ratio (SNR). Custom software implemented in MATLAB was used to determine the region of interest and terms in the conservation equations as follows. A region of interest (ROI) was segmented from the PC-MR data sets. Ideally the ROI contains only pixels within the lumen of the vessel of interest and represents the portion of the control surface through which fluid flows. The ROI may be assumed static or a function of time. Figure 3 outlines the process used for static ROI segmentation. The simplest method entails examining a magnitude image, Figure 3(a). A threshold value, between zero and one, was selected to create a binary (black and white) image, Figure 3(b), from which the ROI was manually selected, leaving only the desired ROI, Figure 3(c). Terms in the conservation equations were estimated from velocity values within the ROI as follows. Of terms derived from PC-MR velocity measurements, the volume flow rate waveform is the simplest and most commonly computed. The product of image-normal or through-plane velocity, Vk i j, and area, ∆S , for a pixel, (i, j), is the volume flow rate through that pixel at the kth acquisition time. Summation of pixels within the ROI yields the volume flow in a given pathway (e.g. aqueduct, spinal canal, blood vessels, or flow phantom) at the kth instant. Data throughout the cardiac cycle allows the volume flow rate waveform, Q(t), to be estimated within the ROI for the k time intervals.