BACKGROUND: Hypertension may increase tortuosity or twistedness of arteries. We applied a centerline extraction algorithm and tortuosity metric to magnetic resonance angiography (MRA) brain images to quantitatively measure the tortuosity of arterial vessel centerlines. The most commonly used arterial tortuosity measure is the distance factor metric (DFM). This study tested a DFM based measurement's ability to detect increases in arterial tortuosity of hypertensives using existing images. Existing images presented challenges such as different resolutions which may affect the tortuosity measurement, different depths of the area imaged, and different artifacts of imaging that require filtering. METHODS: The stability and accuracy of alternative centerline algorithms was validated in numerically generated models and test brain MRA data. Existing images were gathered from previous studies and clinical medical systems by manually reading electronic medical records to identify hypertensives and negatives. Images of different resolutions were interpolated to similar resolutions. Arterial tortuosity in MRA images was measured from a DFM curve and tested on numerically generated models as well as MRA images from two hypertensive and three negative control populations. Comparisons were made between different resolutions, different filters, hypertensives versus negatives, and different negative controls. RESULTS: In tests using numerical models of a simple helix, the measured tortuosity increased as expected with more tightly coiled helices. Interpolation reduced resolution-dependent differences in measured tortuosity. The Korean hypertensive population had significantly higher arterial tortuosity than its corresponding negative control population across multiple arteries. In addition one negative control population of different ethnicity had significantly less arterial tortuosity than the other two. CONCLUSIONS: Tortuosity can be compared between images of different resolutions by interpolating from lower to higher resolutions. Use of a universal negative control was not possible in this study. The method described here detected elevated arterial tortuosity in a hypertensive population compared to the negative control population and can be used to study this relation in other populations.

The enhancement of small vessels in MRA imaging is an important problem. In this paper, we propose using local maximum mean (LMM) processing to enhance the detectability of small vessels. At each voxel in the original three-dimensional (3-D) data set, the LMM over the line segments in the cube centered at the voxel is taken and used to form the 3-D LMM data set. The maximum intensity projection (MIP) is then applied to the LMM data to produce the two-dimensional (2-D) LMM-MIP image. Through LMM processing, the variance of background tissue is reduced, thus increasing the detectability of small vessels. Moreover, the single bright voxels are suppressed and the disconnected small vessels can be connected. However, the LMM processing widens the larger, brighter vessels. To keep the advantages provided by both the LMM-MIP and MIP images, it is proposed that weight functions be used to combine them. The performance of the LMM-MIP algorithm is analyzed and compared with the performance of the MIP algorithm under three measures: The vessel voxel projection probability, the vessel receiver operating characteristic (ROC) curve and the vessel-tissue contrast-to-noise ratio (CNR). Closed forms of the three measures are obtained. It is shown that the LMM-MIP algorithm improves the detectability of small vessels under all three measures. The longer the projection path and the larger the CNR of the original data, then the greater the improvement. Confirming the theoretical analysis, results of an experiment utilizing practical MRA data demonstrate the improved visual quality of small vessels.

The maximum intensity projection (MIP) is a popularly used algorithm for display of MRA images, but its performance has not been rigorously analyzed before. In this paper, four measures are proposed for the performance of the MIP algorithm and the quality of images projected from three-dimensional (3-D) data, which are vessel voxel projection probability, vessel detection probability, false vessel probability, and vessel-tissue contrast-to-noise ratio (CNR). As side products, vessel-missing probability, vessel receiver operating characteristics (ROC's), and mean number of false vessels are also studied. Based on the assumptions that the intensities of vessel, tissue, and noise along a projection path are independent Gaussian, these measures are derived and obtained all in closed forms. All the measures are functions of explicit parameters: vessel-to-tissue noise ratio (VTNR) and CNR of 3-D data prior to the MIP, vessel diameter, and projection length. It is shown that the MIP algorithm increases the CNR of large vessels whose CNR prior to the MIP is high and whose diameters are large. The increase in CNR increases with projection path length. On the other hand, all the proposed measures indicate that the small vessels that have low CNR prior to the MIP and small diameters suffer from the MIP. The performance gets worse as projection path length increases. All measures demonstrate a better performance when the vessel diameter is larger. Other properties and possible applications of the derived measures are also discussed.