A novel algorithm for refining cerebral vascular measurements in infants and adults

Abstract

Background:

Comprehensive quantification of intracranial vascular characteristics by vascular tracing provides an objective clinical assessment of vascular structure. However, weak signal or low contrast in small distal arteries, artifacts due to volitional motion, and vascular pulsation are challenges for accurate vessel tracing from 3D time-of-flight (3D-TOF) magnetic resonance angiography (MRA) images.

New Method:

A vascular measurement refinement algorithm is developed and validated for robust quantification of intracranial vasculature from 3D-TOF MRA. After automated vascular tracing, centerline positions, lumen radii and centerline deviations are jointly optimized to restrict traces to within vascular regions in the straightened curved planar reformation (CPR) views. The algorithm is validated on simulated vascular images and on repeat 3D-TOF MRA acquired from infants and adults.

Results:

The refinement algorithm can reliably estimate vascular radius and correct deviated centerlines. For the simulated vascular image with noise level of 1 and deviation of centerline of 3, the mean radius difference is below 15.3 % for scan-rescan reliability. Vascular features from repeated clinical scans show significantly improved measurement agreement, with intra-class correlation coefficient (ICC) improvement from 0.55 to 0.7 for infants and from 0.59 to 0.92 for adults.

Comparison with Existing Methods:

The refinement algorithm is novel because it utilizes straightened CPR views that incorporate information from the entire artery. In addition, the optimization corrects centerline positions, lumen radii and centerline deviations simultaneously.

Conclusions:

Intracranial vasculature quantification using a novel refinement algorithm for vascular tracing improves the reliability of vascular feature measurements in both infants and adults.

1. Introduction

Three dimensional Time-of-flight (3D-TOF) magnetic resonance angiography (MRA) allows visualization of intracranial vasculature without the need for exposure to ionizing radiation or contrast agents. This technique is widely used clinically (Choi et al., 2007; Bash et al., 2005; Kim et al., 2019). These image volumes contain a rich amount of information that can additionally be used to reconstruct whole-brain vascular maps using vascular tracing methods, as has been previously reported (Wright et al., 2013; Chen et al., 2018a). Artery tracing is not limited only to 3D-TOF MRA as it also has been used to quantify coronary arteries from computed tomography angiography (Wolterink et al., 2019), retinal arteries from optical coherence tomography (Lin et al., 2012) and the arteriole tree from photoacoustic microscopy (Li et al., 2017). These maps can provide comprehensive and quantitative measures of vascular structure and intensity characteristics, including vascular length, volume, tortuosity, and intensity, which are highly relevant to the study of pathology or blood flow conditions (Choi et al., 2007; Chen et al., 2019).

One characteristic of 3D-TOF MRA images, however, is that distal branches often have lower signal intensity and image contrast than proximal branches, due to MR imaging limitations. In addition, head movement and vascular pulsations can cause further image degradation in the form of motion artifacts and blurry vessel boundaries (Tsuruda et al., 1992; Carriero et al., 1994). These effects can make it challenging to produce whole brain quantitative measures that are robust and reliable. This is especially true in patients with compromised cerebral blood flow due to cardiovascular disease and in infants, where pulse rates are higher, vessels are more elastic, and intrinsic brain motion is more prominent.

One solution is to perform image correction after initial vascular tracing of the TOF MRA images. Segmentation correction by boundary refinement has been previously applied to various medical image segmentation tasks, such as manual refinements of liver and lung segmentations with virtual reality (Beichel et al., 2012; Sun et al., 2013a), infant gray-white boundaries (Kim et al., 2013) and computer-aided human interactions on luminal and external elastic lamina surfaces of coronary vessel segmentation from intravascular ultrasound images (Sun et al., 2013b). Manual correction of segmentation errors is timeconsuming and fraught with inter-rater inconsistencies, thus limiting applicability to large studies. Some automated refinement algorithms exist for other clinical applications, such as removing unwanted tissues with lung nodules using 3-D geodesic distance mapping (Diciotti et al., 2011), brain tumor boundary refinement using a parametric deformable model constrained by spatial relations (Khotanlou et al., 2009), and liver segmentation refinement with graph cut and probability mapping (Lu et al., 2017). These approaches usually take advantage of the geometrical shape of the segmentation target, so they might not be applicable to other clinical applications, such as artery traces refinements where the target shape is a tube.

For measurement refinement of vascular tracing, valuable neighboring voxel information along the centerline should be considered, which can improve the centerline locations and the smoothness of the radii of vessels for better vascular feature quantifications. Straightened curved planar reformation (CPR) of arteries (Kanitsar et al., 2003), or straightening the artery along its centerline, is used by clinicians and has been reported to be beneficial for coronary and renal artery stenosis detection (Ropers et al., 2003; Berg et al., 1998). The straightened CPR approach incorporates neighboring voxel information and therefore is better suited for global centerline refinement on whole arteries and correction of errors throughout the distal vascular tree.

In this paper, an automated vascular refinement algorithm is presented, based on straightened CPR, that provides robust vasculature quantification. Straightened CPR was used to incorporate information from surrounding voxels along the whole artery to better optimize artery centerline positions, lumen radii and centerline deviations. We evaluated the reliability of this approach to quantify whole-brain vascular features in infants and in adults.

2. Methods

2.1. Study population

3D-TOF vascular imaging data from five full-term infants, aged 8–15 months (11.6 ± 2.3 months), acquired during natural sleep, as well as five adults, aged 47–70 years (60.4 ± 9.5 years), were used for this study. All 3D-TOF acquisitions were acquired twice to assess scan-rescan reliability of our CPR measurement refinement algorithm. These data were acquired as part of several ongoing MR imaging projects approved by the UW Institutional Review Board; written informed consent was obtained from the parents of all infants and from all adult participants.

2.2. MRA data acquisition

3D TOF MRA data were acquired on a 3.0 T Philips MR scanner (Ingenia CX, Best, The Netherlands) located at the University of Washington Biomolecular Imaging Center. For adult subjects, a 3D-TOF MRA sequence with the following parameters was used: TR 14.7 ms, TE 3.5 ms, flip angle 18 degrees, axial plane slice thickness 1.4 mm, interpolated resolution 0.3 mm × 0.3 mm, Field of View (FOV) 190 mm × 190 mm, matrix size 360 × 228. The image volume encompassed a portion of the brain, with center lines going through anterior commissure-posterior commissure (AP-PC) line on sagittal survey and interhemispheric fissure on coronal and transverse survey images. The adult subject 3D-TOF MRA scans were repeated within 7.4 ± 0.5 days of the initial scan, and the image volume for the second scan was aligned with the placement from the first scan. For infant subjects, the following 3D-TOF MRA sequence parameters were used: TR 19.6 ms, TE 4.1 ms, flip angle 18 degrees, axial plane, slice thickness 1.4 mm, interpolated resolution 0.35 mm × 0.35 mm × 0.35 mm, FOV 150 mm × 150 mm, matrix size 216 × 214. In infants, the scan volume encompassed the entire brain with center lines going through AC-PC line and interhemispheric fissure on survey images, and the repeat scan for each infant was acquired within the same scan session.

2.3. Artery tracing

For all subjects, intracranial vasculature throughout the brain was traced using iCafe, a semi-automated artery tracing tool we have previously reported (Chen et al., 2018a; Chen et al., 2018b). In iCafe, arteries in TOF MRA are traced using an open-curve active contour model (Wang et al., 2011) and reconstructed as radius varying tubes, then labeled as one of the 24 anatomical types (Chen et al., 2018a; Chen et al., 2018b) so that comprehensive artery features can be extracted, such as distal artery length and volume of middle cerebral arteries.

As anticipated in infants, the artery centerline and estimated radii along the centerline were often found not to be accurate, due to voluntary and substantial physiological brain and vascular motion and weak signal strength in multiple regions. Fig. 1 shows an example of the maximum intensity projections (MIP) for one infant, along with the artery tracing produced using iCafe, as well as two examples where the estimated radius generated by the tracing does not appear to correspond well to the actual artery boundaries.

Fig. 1.

(a) MIPs from three directions for the MRA of an individual infant. (b) Artery tracing of this data using the iCafe (Chen et al., 2018a) tool. (c) Cross-sectional plane at the location indicated by the purple arrow with too large of an estimated radius (red circle). (d) Cross-sectional plane at the location indicated by the red arrow with too small of an estimated radius (red circle).

2.4. Vascular measurement refinement algorithm

For an individual artery segment, the vascular measurement refinement algorithm uses both the signal intensity gradient from the cross-sectional plane and neighboring information along the centerline, to improve artery boundary delineation and radius smoothness. First, a straightened CPR view is generated. Then, the artery tracing is optimized in three stages: 1) trace position optimization, 2) trace radius optimization, and 3) trace deviation correction.

2.4.1. Straightened CPR view generation

The directions along the centerline can be represented as normal vectors n_i = (x_i, y_i, z_i). Based on the orthogonal relations of normal directions and coordinate axes, the cross-sectional plane C_i (u, v) = (u•(x_u, y_u, z_u), v•(x_v, y_v, z_v)) for normal direction n_i can be generated from

$$\{\begin{array}{l}{x}_u=\frac{y_i^2+z_i^2}{\sqrt{{\left(y_i^2+z_i^2\right)}^2+x_i^2{y}_i^2+x_i^2{z}_i^2}}\hfill \\ y_u=-\frac{x_i{y}_i}{\sqrt{{\left(y_i^2+z_i^2\right)}^2+x_i^2{y}_i^2+x_i^2{z}_i^2}}\hfill \\ z_u=-\frac{x_i{z}_i}{\sqrt{{\left(y_i^2+z_i^2\right)}^2+x_i^2{y}_i^2+x_i^2{z}_i^2}}\hfill \\ x_v=0\hfill \\ y_v=\frac{z_i}{\sqrt{y_i^2+z_i^2}}\hfill \\ z_v=-\frac{y_i}{\sqrt{y_i^2+z_i^2}}\hfill \end{array}$$ (1)

when y_i and z_i are not zero at the same time. An illustrative graph is shown in Fig. 2.

Fig. 2.

Illustration graph for straightened CPR view generation. (a) a cross-sectional plane (blue rectangle) at center position p_j is defined by normal vector n_i, any target position can be defined in the cross-sectional plane by two orthogonal vectors u and v. (b) interpolated normal direction at the position between two center positions is the linear interpolation between two neighboring normal vectors p_j and p_j+1 according to their distances to center positions.

As the cross-sectional plane to a normal vector is not unique, x_v = 0 is chosen as one of the planes for convenience. Linear interpolation is used for fast generation of the cross-sectional plane of the image.

The straightened CPR image M (u, v) is generated as follows: v is the accumulated distance from the starting point of the trace, somewhere on the centerline between p_j and p_j+1, with distances of d₁ and d₂, the interpolated normal direction ${\widehat{n}}_i=\frac{d_1}{d_1+d_2}{n}_j+\frac{d_2}{d_1+d_2}{n}_{j+1}$. M (u, v = v_j) is the C_i (u = cos(θ), v = sin(θ)) derived from Eq. (1), where θ is the rotated view angle for the straightened CPR image.

As an example, straightened CPR views for one segment that includes the internal carotid artery and the middle cerebral artery viewed at 0, 45, 90, and 135 degrees are shown in Fig. 3.

Fig. 3.

Left: MIP view with selected trace in blue. Right: straightened CPR view at angles of 0, 45, 90, and 135°. The radius along the centerline is shown in blue in the straightened CPR 135° angle image.

2.4.2. Trace position refinement

The 3D position of points in the trace is refined using the optimization function considering losses for trace smoothness and their intensity.

$$\begin{gathered} L_1(p)=\sum _i{L}_1(p_i)=\sum _i\{w_{dist}({\Vert d_i\Vert }^{(1)}+\gamma {\Vert d_i\Vert }^{(2)} \\ +\gamma (d_{x,i}^{(2)}+d_{y,i}^{(2)}+d_{z,i}^{(2)}))-w_{int}\left[I_n(p_i)+I_s(p_i)\right]\} \end{gathered}$$ (2)

where the directional vector between two center points d_i = (p_i − p_i−1) = (d_x,i, d_y,i, d_z,i), and ‖d_i‖ denotes the length of the vector; I_n (p) and I_s (p) are intensity values of normalized (M_n) and segmented (M_s) straightened CPR images at position of p_i = (x_i, y_i, z_i). (1) and (2) represent 1st and 2nd order of derivative. Minimizing the derivative of the length of the distance vector ensures the even distribution of center points along the centerline, and minimizing the derivative of the x, y, z coordinates help to ensure the smooth coordinate transitions between neighboring center points. γ is the parameter to control the first and second order weights for derivatives, and is empirically chosen as 5, the same as the active contour models (Kass et al., 1988). Maximizing the intensities of center points on normalized and segmented straightened CPR images restricts the center points on the foreground of vascular images (lumen region of arteries). w_dist = 0.02 and w_int = 1 are weights for controlling the smoothness and intensity loss to the similar level.

2.4.3. Trace radius refinement

After the trace position refinement, centerline positions are fixed, and the radius of each point is refined using the following equation.

$$\begin{gathered} L_2(r)=\sum _i{L}_2\left(u_{l,i},u_{r,i},v_i\right)=\sum _i{L}_2\left(l\left(v_i\right),r\left(v_i\right),v_i\right) \\ =\sum _i{w}_{\text{smooth}}\left[l^{(1)}\left(v_i\right)+r^{(1)}\left(v_i\right)+\gamma l^{(2)}\left(v_i\right)+\gamma r^{(2)}\left(v_i\right)\right] \\ -w_{\mathrm{grad}}\left[M_u\left(l\left(v_i\right),v_i\right)+M_u\left(r\left(v_i\right),v_i\right)\right] \end{gathered}$$ (3)

where l(v) and r(v) are the left and right boundary for artery radius in straightened CPR image M_n. Minimizing the derivatives controls the smoothness of both sides of boundaries. M_u is the derivative of M_n in its horizontal direction. Maximizing the horizontal gradient intensity ensures the radius boundaries to fit the edge of luminal area in the arteries. w_smooth = 1 and w_grad = 50 are weights for controlling the smoothness and gradient loss to the similar level.

2.4.4. Trace deviation correction

Ideally, the mean location of the left and right radius boundaries $\frac{l(u,v)+r(u,v)}{2}$ in the straightened CPR image should always be in the vertical center of the straightened CPR image (v = v_m). Any deviation away from the vertical center in u direction $\mathbf{o}=\frac{l(v)+r(v)}{2}-v_m$ needs to be re-centered.

2.4.5. Iterative optimization from different angles

Arteries are iteratively optimized using straightened CPR images M_deg generated from multiple rotation angles {0,90,45,135}. The optimization process was repeated 3 times for this study. The Nelder-Mead algorithm (Gao and Han, 2012) was used for optimization.

2.5. Validation and reliability

The refinement algorithm was first validated on three simulated images for evaluating its performance on refining artery radii and correcting centerline deviations.

The first simulation has three artificial artery branches with various radius and directions. We traced the arteries using iCafe, then deviated the centerline and changed the radius of centerline points randomly. The refinement algorithm was applied to restore the traces.

The second simulation aimed to evaluate the robustness of the algorithm to different levels of deviations and noises. To simulate the MRA noise property, a random noise with a Rayleigh distribution of various noise levels l was added to a noise-free image of a simulated artery tree. The Rayleigh noise follows the probability density function of $f(x)=l\cdot x\cdot \exp (-\frac{x^2}{2})$. For simplicity, the simulation image has only one straight artery (along the z axis) in the image center with a constant radius of 5 and intensity of 1. The refinement algorithm was applied with images having different noise levels (0, 0.5, and 1 used in this study). To test the robustness of the refinement algorithm in correcting centerline deviations, the initial centerline of the artery was set to have various deviations to the real artery center with 0, 1, 2 and 3 pixels in both of the axes in the cross-sectional planes (x and y directions in this case). As the ground truth of the artery radii and centerline positions are known, the following metrics were used to evaluate the performance of the vascular measurement refinement algorithm compared with ground truth: mean radius difference in percentage, mean point deviation (in pixels), artery length difference in percentage.

The third simulation evaluated the smoothing effect of the algorithm on an artificial stenosis. On a regular artificial artery with radius of 10 pixels, we reduced the artery radius to 50 % in a short segment of stenosis with length of 2 pixel, 5 pixels, and 10 pixels. The refinement algorithm was applied to each stenosis to evaluate whether the algorithm smoothed over the stenosis.

The validated algorithm was then applied to the repeated artery tracings of 3D-TOF MRA scans for 5 infants and 5 adults. As ground truth could not be determined, the measurement agreement for radii in selected arterial regions from the two repeated scans were compared before and after applying the refinement algorithm. Higher measurement agreement between repeated scans was considered to more accurately approximate the actual radius. Considering different tracing conditions, where the number of points in each segment and connection of segments in bifurcations are different, radii from selected locations on ICA, M1, M2 and M3 segments were manually chosen. One radius was selected as the sample in each segment when the segment could be matched on the second scan. Sampled radii differences between the repeated scans, as well as intra-class correlation coefficient (ICC) and within-subject coefficient of variation (CV), were evaluated before and after the vascular refinement algorithm was applied.

3. Results

After applying the vascular refinement algorithm, artery traces from simulated images can be restored in various radius and directions (Fig. 4).

Fig. 4.

Refinement of a simulated artery trace with branches of varying radii and directions. (a) Ground truth traces. (b) Centerlines deviated randomly to test refinement algorithm restoration of the traces. (c) Traces after refinement.

The algorithm was robust within a range of simulated noise and deviation. The measurement differences from ground truth corrected to within a reasonable range, for this example, a mean radius difference of 9.1 % at a noise level of 1 and point deviation of 3 pixels. An example of artery traces before and after refinements is shown in Fig. 5. The performance for all the settings in the simulated image is shown in Fig. 6.

Fig. 5.

(a) One slice of simulated artery with radius of 5 pixels. (b) Slice of (a) with added Rayleigh noise of 0.5. (c) and (d) Straightened CPR view of the simulated artery at 0 and 90 degrees for initialized centerline with deviation of 3 pixels in x and y directions. Radius along the artery was indicated in dotted red lines in the straightened CPR image. (e) and (f) Straightened CPR view of the simulated artery at 0 and 90 degrees after vascular measurement refinement.

Fig. 6.

Feature difference after vascular measurement refinement on the simulated artery with different noise level and initial deviations of the centerline.

In our simulation, the algorithm will not smooth out stenosis if the stenosis length is within 5 pixels (1.5–1.75 mm using our current imaging protocol). However, a current limitation of this refinement approach is when there is sudden decrease in radius, the algorithm will consider the radius change as noise, and smooth it out. Results are displayed in Fig. 7.

Fig. 7.

Refinement algorithm modeling effects on artificial stenosis with different length of stenosis. Left: before, right: after artery refinement. Blue circles are showing the radius for each corresponding centerline points. Bottom: plot of radius difference with ground truth in the most stenotic point after refinement under different stenosis lengths.

The refinement algorithm was found to be effective at improving artery traces on 3D-TOF MRA images. In most cases, sudden changes of radius along the centerline, inaccurate radius boundary estimation due to weak MR signal, and tortuosity due to noise are minimized or resolved. One example from infants and one example from adults are shown in Fig. 8. In this example, improvement in the delineation of arteries is visibly improved in a number of regions, including the sudden change of radius on the left side of the anterior cerebral artery and middle cerebral artery, and the right side of posterior cerebral artery, as pointed out by the red arrows.

Fig. 8.

Characteristic arterytraces before and after vascular measurement refinement for an infant (top row) and adult (bottom row). Red arrows highlight several artery locations showing improvements.

Comparison of quantitative metrics of vascular features between the two scans for each subject revealed that vascular measurement refinements for TOF MRA scans improved the measurement correlations for all ten subjects. The reproducibility for overall quantitative assessments, and for individual segments, between repeated infant and adult scans before and after refinement are detailed in supplementary material. Artery radius differences measured between two repeated scans were significantly reduced using the refinement algorithm for both infants (p = 0.008) and adults (p = 0.048). ICC improved from 0.55 to 0.7 for infants, and from 0.59 to 0.92 for adults. CV decreased from 28.52 % to 19.71 % for infants, and from 26.65 % to 11.01 % for adults. Note that the adults had less motion and vascular pulsation than infants, so the artery boundary is sharper and more consistent between scans.

3.1. Discussion

Quantitative characterization of whole brain vascular structure has the potential to provide important and novel clinical information to evaluate the health status of the neurovascular system. Heretofore, limitations of imaging acquisition, as well as complications posed by specific patient populations, have substantially impacted the clinical reliability of these measurements. In this study, we present a vascular measurement refinement algorithm that uses straightened CPR to reduce measurement errors using quantitative intracranial artery tracing approaches, such as iCafe (Chen et al., 2018a). This refinement algorithm corrects for mistakes in artery traces derived from 3D-TOF MRA image volumes by incorporating both signal gradients and neighboring voxel information along the centerline. This algorithm was tested on both infants and adults. Infants, in particular pose a specific challenge to accurate quantification of intracranial vascular features. This refinement approach is shown to improve the measurement reliability of commonly used and clinically useful vascular metrics, such as artery radius in both subject populations. Straightened CPR view is considered an ideal platform for vascular measurement refinement, as the radius change along the centerline is represented as a smooth trace, which can be optimized using active contour models to ensure smoothness. Meanwhile, the gradients of signal intensities are represented in horizontal directions, which are easily adjustable. The joint optimization on both radius change smoothness and gradient maximization ensures good performance for vascular measurement refinement.

The refinement algorithm presented here was applied in conjunction with artery tracing performed by iCafe, a method previously reported by our lab. However, it is applicable to most other artery tracing algorithms based on TOF MRA images.

Our findings demonstrate that this refinement algorithm improves reliability of four common metrics of intracranial vasculature in both adults and in infants. These clinical imaging findings are in agreement with our simulated finding, as well.

With improved accuracy in quantifying artery characteristics throughout the brain, subtle changes between multiple time points can be identified and can potentially advance understanding of both brain development and disease progression, or regression. The ability to robustly quantify vasculature features in the presence of head motion and high brain and vascular pulsation allows for investigation of changes in blood flow and neurovascular structure associated with early life development. Similarly, reliable quantification of vascular features extracted from distal arteries in subjects with compromised cerebral flow may provide valuable quantitative blood flow information in cardiovascular disease research.

Several limitations exist in this study. First, the refinement algorithm was tested on ten subjects for measurement reliability. Validation and further refinement of the algorithm through studying larger population with varied blood flow conditions, artifacts, imaging resolutions and vascular diseases, especially with severe stenosis or sudden radius changes, will help to establish its clinical applicability. As the parameters used in the refinement algorithm were mainly chosen empirically, further systematic tuning might help to optimize performance. Finally, no quantitative performance comparisons were made with other refinement approaches developed to improve measurement reliability of other organs, as the applicability of those methods is uncertain, and they have not been developed for the tube shape of arteries.

3.2. Conclusion

In this study, development of a vascular measurement refinement algorithm based on straightened CPR that provides increased scan-rescan measurement reliability and vascular details for intracranial vasculature map quantification is presented. Measurement improvements provided by this approach have the potential to allow clinically useful vascular features to be more reliably and rapidly characterized and quantified in an objective manner. This vascular measurement refinement approach will facilitate new avenues of research for vascular imaging studies to explore brain vascular changes during early development and in the presence of vascular pathology.