Detection of clustered anomalies in single-voxel morphometry as a rapid automated method for identifying intracranial aneurysms

Unruptured intracranial aneurysms (UIAs) are prevalent neurovascular anomalies which, in rare circumstances, rupture to create a catastrophic subarachnoid haemorrhage. Although surgical management can reduce rupture risk, the majority of IAs exist undiscovered until rupture. Current computer-aided UIA diagnoses sensitively detect and measure UIAs within cranial angiograms, but remain limited to low specificities whose output requires considerable neuroradiologist interpretation not amenable to broad screening efforts. To address these limitations, we propose an analysis which interprets single-voxel morphometry of segmented neurovasculature to identify UIAs. Once neurovascular anatomy of a specified resolution is segmented, interrelationships between voxel-specific morphometries are estimated and spatially-clustered outliers are identified as UIA candidates. Our automated solution detects UIAs within magnetic resonance angiograms (MRA) at unmatched 86% specificity and 81% sensitivity using 3 minutes on a conventional laptop. Our approach does not rely on interpatient comparisons or training datasets which could be difficult to amass and process for rare incidentally discovered UIAs within large MRA files, and in doing so, is versatile to user-defined segmentation quality, to detection sensitivity, and across a range of imaging resolutions and modalities. We propose this method as a unique tool to aid UIA screening, characterisation of abnormal vasculature in at-risk patients, morphometry-based rupture risk prediction, and identification of other vascular abnormalities. Graphical Abstract Highlights Rapid and automated detection of unruptured intracranial aneurysms (UIAs) in MRAs Highly specific, sensitive UIA detection to reduce radiologist input for screening Detection is versatile to image resolution, modality and has tuneable mm sensitivity


Abstract 23
Unruptured intracranial aneurysms (UIAs) are prevalent neurovascular anomalies which, in rare 24 circumstances, rupture to create a catastrophic subarachnoid haemorrhage. Although surgical 25 management can reduce rupture risk, the majority of IAs exist undiscovered until rupture. Current 26 computer-aided UIA diagnoses sensitively detect and measure UIAs within cranial angiograms, but 27 remain limited to low specificities whose output requires considerable neuroradiologist interpretation 28 not amenable to broad screening efforts. To address these limitations, we propose an analysis which 29 interprets single-voxel morphometry of segmented neurovasculature to identify UIAs. Once 30 neurovascular anatomy of a specified resolution is segmented, interrelationships between voxel-specific 31 morphometries are estimated and spatially-clustered outliers are identified as UIA candidates. Our 32 automated solution detects UIAs within magnetic resonance angiograms (MRA) at unmatched 86% 33 specificity and 81% sensitivity using 3 minutes on a conventional laptop. Our approach does not rely 34 on interpatient comparisons or training datasets which could be difficult to amass and process for rare 35 incidentally discovered UIAs within large MRA files, and in doing so, is versatile to user-defined 36 segmentation quality, to detection sensitivity, and across a range of imaging resolutions and modalities. 37 We propose this method as a unique tool to aid UIA screening, characterisation of abnormal vasculature 38 in at-risk patients, morphometry-based rupture risk prediction, and identification of other vascular 39 abnormalities. 40 41 Graphical Abstract 42

Introduction 43
Intracranial aneurysms (IAs) are bulging, weak outpouchings of arteries that supply blood in the brain. 44 IAs are relatively common (2% to 5% prevalence; Figure 1A,B) but rarely discovered prior to incident 45 (International Study of Unruptured Intracranial Aneurysms (ISUIA), 2003). While most unruptured IAs 46 (UIAs) are asymptomatic, between 0.25% and 1% spontaneously rupture resulting in a subarachnoid 47 Herein, we present an image analysis method based on a single-voxel morphometry approach to rapidly, 77 automatically, and specifically identify UIAs. Our algorithm automatically reconstructs 3D 78 presentations of patient neurovasculature from MRA, CTA, or DSA image datasets, then seeks to 79 identify UIA candidates based on three voxel morphometry attributes: distance from vessel centreline, 80 distance from vessel edge, and distance from image base. Identified UIA location and size are measured 81 and validated against clinician measurement. We analysed a cohort of 29 TOF MRAs presenting UIAs 82 who are benchmarked against 705 healthy TOF MRAs. Our automated algorithm is unique in its rapid 83 analysis of large 3D datasets without the need for training data or interpatient comparisons, its high and 84 tuneable specificity and sensitivity to identify fine features for clinical observation, and its versatility 85 in analysing a range of MRA resolutions as well as CTA  patients harbouring UIAs were monitored over several years so that a total of 29 aneurysm-containing 93 TOF MRAs were imaged. The UIA parent vessel, location, and dimensions were described within 94 radiology reports and annotated within 2D slices of the image as illustrated in Figure S1. pipeline with several distinct steps, as illustrated in Figure 2 and detailed in the following subsections. 103 104 2.1. Global segmentation of a neurovascular mask (Auto-Segmentation) 105 Initially a universal threshold value was calculated to segment intravascular blood from surrounding 106 cranial tissue ( Figure 3A). All voxel intensities throughout the CTA, DSA, or TOF-MRA image were 107 linearly divided into = 50 bins from maximal to minimal voxel intensity, similar to Nyúl et al., 108 2000. Voxel intensity brightness, x, belonging to different tissue types, such as dim extravascular soft 109 tissue versus bone versus bright intravascular blood, was estimated by a sum of lognormal distributions 110 ( Figure 3B) as previously performed for MRA images (Forkert et al., 2012): 111  With tissue content scalar and tissue intensity mean and standard deviation . Voxel intensities 113 throughout the image were estimated as the sum of these lognormal distributions. In CTA images all 3 114 aforementioned tissue types could be detected simultaneously, 1+2+3 , while in TOF MRA and DSA 115 images only intravascular and extravascular tissue could be distinguished, 1+2 . The six or nine 116 parameters of 1+2 or 1+2+3 were fit by minimising normalised error to the log voxel intensity of 117 histogram bin 3 to 48 as to avoid overexposed and underexposed inconsistencies (removing = 4% 118 of bins from either end). A threshold value, , was calculated to segment vessels from the brain tissue:  Identification of centrepoints via mask erosion, connecting adjacent centrepoints bottom-to-top into a network of branches, and measuring branch lengths and bifurcation points to detect centrepath length. (D) A voxel-specific polynomial regression was individually fit to measure the correlation between voxel distance from centreline (radius) versus voxel distance from vessel edge (depth) and voxel distance from base (path) for each image. (E) The error of actual voxel radius from expected voxel radius was measured and (F) outliers which were spatially-clustered together were identified as aneurysmal candidates, (G) overlaid in red over segmented mask image intensities with UIA region inset. The algorithm required 3 minutes to execute.

Evaluating single-voxel morphology (Mask Processing and Centreline Estimation) 126
Once the neurovascular mask is segmented, centrepoints are defined via a 3D medial surface thinning 127 operation after filling closed voxel holes in the image. These centrepoints were then dilated and 128 annealed together using a = 2 voxel rolling ball, and then centrepoints were re-identified in order 129 to remove overestimated and overlapping small vessels using a range of binary morphological 130 operations. A centreline was then connected through neighbouring centrepoints starting with the 131 centrepoint in the lowest (most caudal) axial plane. When the next nearest unallocated centrepoint was 132 further than = 1mm away, the terminal end of that vessel branch had been reached and the 133 centreline for a new vessel was evaluated from the next lowest centrepoint. Branch endpoints between 134 = 1mm and ℎ = 2mm away from a previously allocated centrepoint were then connected to 135 form the full neurovascular tree. Once completed, an interconnected branch network of centrelines 136 through the segmented neurovascular mask was formed ( Figure 3C).

138
Voxels within the vascular mask were evaluated using a range of morphometric properties: taking the 139 vascular voxel as reference, indicates the distance to vessel centreline, distance to edge, and 140 distance to the carotid vessel, defined as the nearest terminal centrepoint at the bottom of the mask 141 ( Figure 3D). The first two properties were calculated using Euclidean distance operations performed on 142 Boolean matricies between the neurovascular model and points defining the vessel centrelines. The 143 third distance operation required sorting individual vessel branches' distance to the bottom of the 144 vascular tree. Since many vessel branches intersect with many other vessel branches at multiple points, 145 a combinatorial approach identified the tree branch path network which minimised total mask across 146 all intersecting branch entrances and exits. 147 148

Identifying aneurysms as outlier voxel clusters (Morphometry and Outlier Detection) 149
Each voxel's three morphometries formed a consistent relationship. That is, the distance of a voxel from 150 the vessel centreline ( ) depended on how far it was from the vessel edge ( ) as well as its distance 151 away from the base of the mask ( ) ( Figure 3E). A voxel far from the vessel centreline was more likely 152 to be near the vessel edge and these distances were larger nearer the thick carotid arteries and not thin 153 terminal cranial vessels. This relationship was characterised through fitting a polynomial regression 154 through all voxels within the neurovascular masks (>10,000 voxels). For speed, a polynomial regression 155 was used to estimate a voxel's centreline distance ( ) which was first-order in its edge distance ( ) 156 and fourth-order in its base distance ( ). Several other global and local polynomial regressions (loess) 157 were compared but either exhibited a worse regression fit or prohibitively long processing times, 158 respectively. Clusters of voxels which had centreline distances inaccurately predicted by our ℎ( , ) 159 regression were treated as outliers and considered to belong to either noncylindrical or inadequately 160 large vessel anatomies, suggestive of vascular regions that may be aneurysm candidates ( Figure 3F,E). 161 Since this outlier detection is based on a single patient image and not a large dataset of patients, it can 162 be particularly universal to anatomical and imaging differences.

164
The definition of these voxel cluster outliers, or aneurysm candidates, can be tailored for high or low 165 detection sensitivity based on user demand and clinical application. For our multi-repository validation 166 we identified aneurysm candidates as voxel clusters beyond the polynomial regression's = 96% 167 confidence interval and larger than = 17.3ℎ( , ) + 1.5 mm 3 to allow for aneurysm detection 168 in large central as well as small peripheral vessels. Voxel centreline distance estimated from ℎ( , ) 169 typically varied from 1.5 mm at the carotid artery base to 0 mm at the terminal ends of peripheral 170 arteries. We later demonstrate how users can decrease and to increase detection sensitivity 171 for small or emergent aneurysmal buds. 172 173

Refining poorly-segmented neurovascular masks (Optional Local Resegmentation) 174
For poor quality images with under-or over-saturated cranial images, it may be difficult to analyse 175 morphometry due to a fusing of adjacent vessels or an inaccurate capture of the aneurysm shape ( Figure  176 4A). In such cases, a more accurate segmentation can be achieved through re-estimating the 177 segmentation threshold for many small regions throughout the vessel structure. However, this more 178 accurate local segmentation comes at the price of increased time and experimentally evaluated 179 parameters. This local segmentation procedure proceeds by evaluating the vessel centrepoints produced 180 from Section 2.2 and drawing spherical neighbourhoods around these centrepoints for re-segmentation. 181 Next, successive centrepoints neighbourhood are considered until all their contained vessel masks have 182 been re-segmented. Finally, the remaining image space is also re-segmented based on the threshold 183 assigned to each voxel's closest neighbourhood, which allows for significant mask growth.

185
The diameter of these spherical neighbourhoods must be large enough to consider the thickest vessel 186 diameter while sampling frequency along the centrepoints must be fine enough to not allow 187 unconsidered gaps. To ensure adequate neighbourhood overlap, sampling frequency was dictated by 188 spherical neighbourhood centroid spacing scaled to sphere and vessel radius: 189 Where is the desired spherical neighbourhood radius, is the calculated vessel mask radius, and 191 is a user-defined scalar between 0 and 1 adjusting neighbourhood overlap, where = 1 would 192 allow neighbourhoods to overlap just enough to encompass the current vessel radius. Spherical 193 neighbourhoods which are too large or too infrequent would limit the effectiveness of the local 194  Figures 2 and 3 is rapid, sensitive, and specific, it struggles with large convoluted neurovascular masks with overlapping vasculature. When a more detailed mask and IA identification is required at the expense of increased computational time, additional pipeline refinements can be performed. (B) A local resegmentation can be performed which recalculates the threshold of the neurovascular mask within spherical neighborhoods along the previous centrelines, and then expands those thresholds into the remainder of the image. This resegmentation serves to cull vessel thicknesses within overlapping high-signal regions and enhance the vessel mask into regions with low signal and can be iterated as desired. (C) A mask refinement can be performed which surveys an aneurysmal candidate and deletes vessel centrelines which enter an aneurysm to provide a more complete IA segmentation.
segmentation, but small or frequent neighbourhoods create unnecessary computational burden. Our 195 masks appeared to work best with = 2.75 mm and = 0.5 to allow for re-segmented masks to 196 grow in dim peripheral regions but also shrink in bright carotid regions ( Figure 4B).

198
Spherical neighbourhoods can predominately be comprised of brain tissue near shrinkingly small 199 vessels, resulting in only one lognormal distribution of low voxel intensities and skewing the calculation 200 of a threshold value to extremely low values for re-segmentation, causing brain tissue to be interpreted 201 as vessels. are deleted, the UIA detection is re-run at the original threshold sensitivity ( Figure 4C).

218
Our image analysis approach is conventional in specifying which morphometry attributes are indicative 219 of UIAs but also mimics machine learning approaches by identifying unique patterns in single-voxel 220 morphometries for each image. In doing so, our algorithm becomes adaptable to image quality and 221 detection accuracy inputs. Our image processing steps require user-selected parameters (Table 1) which 222 must be validated to be widely applicable but whose detection sensitivity can also be adjusted to detect 223 fine or coarse aneurysmal candidate regions. Correspondingly, we validate the accuracy and 224 demonstrate the versatility of our statistical approach herein. 225 226 3.1. Rapid automated IA detection is sensitive and specific 227 The sensitivity of this algorithm was validated over a cohort of patients presenting to the Royal Brisbane 228 and Women's Hospital (RBWH) between 2009 and 2019 who harboured an UIA imaged by TOF MRA 229 (14 patients, 29 TOF MRA images). Several patients were imaged on more than one occasion to monitor 230 aneurysmal shape changes over time and assess rupture risk for surgical decision-making. Accuracy of 231 algorithm-identified aneurysm location and size was validated by interventional radiologists asked to 232 retrospectively annotate, measure, and comment on unedited TOF MRA image slices while blinded to 233 the algorithm's detection as illustrated in Figure S1. The specificity of this algorithm was validated over 234 a cohort of 27 patients not identified to have an intracranial aneurysm using TOF MRA and DSA. To provide a fair comparison, all validations were performed with identical parameters, which also 244 ensured the algorithm was fully automated. The speed of the algorithm varied between 1.5 and 12 min 245 primarily depending on image resolution (which affected image matrix size), and neurovascular mask 246 volume (which affected time-intensive binary distance operations). The 734 TOF MRAs varied across 247 10 image resolutions from 0.26 to 0.80 mm/voxel ( Figure S2). Median processing times per TOF MRA 248 image were 5.2 min, 2.7 min, and 2.0 min for RBWH, MIDAS, and IXI datasets respectively.

250
There was a clear trend between XY image resolution and segmented mask volume and length. This 251 trend led to the under-segmentation of low-resolution TOF MRA images within the IXI and MIDAS 252 repository datasets creating large neurovascular masks containing additional peripheral vessels 253 irrelevant for aneurysmal identification such as venous sinuses and torcula. An exponential relationship 254 between XY image resolution and the thresholding parameter was defined to normalise segmentation 255 across resolutions ( Figure 5, Figure S2). Without normalisation, images from MIDAS and IXI 256 repositories were significantly different to RBWH with respect to mask length and volume. After 257 normalisation, mask lengths were more equal between repositories.

259
The algorithm's identification achieved 81% sensitivity and 86% specificity, correctly identifying UIAs UIAs appeared within small overlapping peripheral arteries, especially for low-resolution images, such 266 as the M3 and M4 segments in the anterior cerebral artery (as illustrated in Figure S3). 267 268

Detection pipeline is versatile to imaging resolution and MRA, CTA, or DSA modalities 269
This algorithm was principally developed for TOF MRA imaging, which represents a promising 270 technique to 3D image intracranial vasculature without the use of intravenous contrast or x-ray 271 radiation. However, many patients are unable to be imaged via MRA, including those who have 272 Table 1: Summary of algorithm parameters. These algorithm parameters are grouped into the pipeline steps specified in Figure 2 and throughout methodology Section 2. Values are provided as a guide to replicate the algorithm performance in this paper but can be changed based on user preferences. Detection sensitivity was lowered in Figure 7 to demonstrate the impact of varied detection sensitivity. This algorithm was applied to abnormal and normal CTA and DSA images in Figure 6. These 3D 278 images frequently have much higher XY resolution (0.15 -0.30 mm/voxel) but lower Z resolution (1.0 279 -2.0 mm/voxel) which can cause artefacts for vessels coarsely resolved in the Z-dimension. Even so, 280 the algorithm was able to segment and identify UIAs within MRA, CTA, and DSA datasets, indicating 281 its versatility across imaging modalities and clinical needs. 282 283

Adjustable detection sensitivity can identify early budding aneurysms 284
The algorithm can be tailored to suit specific clinical needs by adjusting two sensitivity parameters: the 285 error threshold ( ) and the size threshold ( ) which identify outliers as candidate aneurysm 286 regions. During algorithm validation and in Figure 5, these sensitivity parameters were kept constant 287 across the 3 patient datasets and more than 700 patient images. However, sensitivity can be improved 288  Figure S2.
at the cost of specificity (false-positive aneurysm detection) by decreasing the minimum error or cluster 289 size of candidate aneurysm regions to highlight small or slightly bulging intracranial vessels. While 290 these bulging regions may be false positives generated by atypically tortuous neurovasculature or 291 imaging or segmentation artefacts, lowering these detection thresholds could be useful to suggest 292 potential small, difficult-to-spot, or secondary UIAs for radiological assessment.

294
To demonstrate the utility of this algorithm's tuneable sensitivity, we identified a patient harbouring an 295 UIA which was monitored over 5 TOF MRA imaging sessions between 2012 and 2018. During the 296 initial visit in 2012, a large 4 x 3 mm saccular aneurysm was discovered on the left peripheral 297 communicating artery and was monitored over the following 6 years. In 2018, a second bilateral 298 aneurysm was discovered which led to a surgical decision of intervention. Using our algorithm at Figure  299 5's validation sensitivity, we identified the same UIAs at the same timepoints as the clinicians identified. 300 We then repeated our algorithm using a heightened sensitivity which detected abnormal voxel clusters 301 Neurovasculature was imaged using right-hemisphere DSA (first row) before being rushed to surgery for endovascular coil placement. Later, this patient was imaged using TOF MRA with a large artefact at the location of the prior aneurysm (second row, red dotted circle). (B) Neurovasculature was imaged using TOF MRA or CTA for both brain hemispheres on the same date. Columns, from left to right, include original medical image mean intensity projection, voxel intensity histogram fit to the sum of 2 or 3 lognormal regressions, segmented soft tissue, bone, and/or vasculature masks, and mask voxel intensity heatmap with identified aneurysms. Measured UIA dimensions from CTA or DSA appear inaccurate, highlighted in red text. Abbreviation S.T. corresponds to 'soft tissue'. larger than 0.7 mm 3 . Using this sensitivity, we could observe 302 the growth of a small bulging region (0.9 -2.9 mm 3 ) at the 303 same location that the bilateral aneurysm would form 6 years 304 earlier, with no other false-positives detected (Figure 7). 305 While such small regional voxel abnormalities may often 306 occur due to imaging artefact or normal variances within 307 neurovascular anatomy, such a sensitive identification could 308 identify regions of radiologic interest similar to those 309 performed in recent computer-aided diagnosis approaches 310 ( Previous computer-aided diagnoses have reached high levels 314 of sensitivity but have done so exhibiting very low specificity, 315 incorrectly detecting several false-positive UIAs per image. 316 These approaches still require substantial radiological 317 interpretation to exclude these false-positives and may not 318 improve the number of medical images a radiologist can 319 assess within a certain amount of time. Furthermore, detection 320 rates vary between radiologists and neuroradiologists and our 321 approach enables an unbiased detection and characterisation 322 of UIAs at mm 3 resolution (Okahara et al., 2002). This user-323 adjustable approach will better provide both high-specificity 324 screening of UIA presence and high-sensitivity UIA 325 characterisation toward reduced radiologist workloads. 326

Discussion 327
We propose a new method to identify UIAs within 3D medical 328 angiograms, principally within widely-used TOF MRAs 329 (Thompson et al., 2015). The key innovations of our method 330 include high sensitivity with high specificity and user-defined 331 versatility while utilising large 3D medical images 332 independent of interpatient comparison. Our method reaches 333 at least an 81% sensitivity and 86% specificity, on-par with 334 conventional computer aided MRA diagnoses achieving up to 335 83.6% sensitivity and 75% specificity, while analysing MRAs 2019). One recent approach identified UIAs inside small 343 ~30mm vessel segments with 88.5% sensitivity and 98.5% 344 Figure 7: Single-case longitudinal study of an emerging second UIA. Patient neurovasculature was imaged using TOF MRA over five monitoring sessions across six years. The initial four sessions monitored any shape changes from a large burst saccular aneurysm within the right hemisphere (50 mm 3 final size). On the final monitoring session, a second bilateral aneurysm was detected within the left hemisphere (20 mm 3 final size) which led to the decision to operate. Implementing the 'mask refinement' option and an UIA detection sensitivity of 0.7 mm 3 , the emergence of a bulging region was detected in the location of the second aneurysm up to 6 years (4 imaging appointments) prior to its clinical identification by a radiologist.
specificity, but required 8 hours to manually segment each neurovascular model into pieces (Yang et 345 al., 2020). These machine learning approaches rely on large training datasets which may be difficult to 346 acquire and time-consuming to train for 3D angiograms of incidentally-discovered UIAs. Altogether, 347 computer-aided diagnosis have only increased radiologist diagnosis sensitivity from 64% to 69% and 348 have not reduced radiologist interpretation time (Miki et  The detection of UIAs prior to rupture allows for careful management to avoid haemorrhage. 379 Fortunately, the incidental discovery of UIAs is becoming more frequent due to the increased use and 380 resolution of MRA, a neurovascular imaging technique which does not require intravenous contrast or 381 x-ray radiation (Thompson et al., 2015). While MRA may be a promising angiography technique to 382 screen for UIAs in patients with a strong family history or those presenting migraines (Micieli and 383 Kingston, 2019), it would be laborious, expensive, and unfeasible to engage expert neuroradiologists to 384 review large numbers of cranial angiograms within a publicly-funded clinical imaging department (Z. 385 Shi et al., 2020). In addition, once a UIA is discovered the surgical decision-making process remains 386 'complex and controversial' where as many as 58.3% of UIA patients undergo neuro or endovascular 387 surgery (International Study of Unruptured Intracranial Aneurysms (ISUIA), 2003). While rupture risk 388 is associated with UIA size and location aspect ratio, neck-to-body ratio, and intra-UIA fluid dynamics aneurysms (top right). The poor resolution images segment anterior cerebral arteries that comprise only 574 a few voxels in diameter, and due to their low resolution, these arteries appear to overlap during 575 segmentation, creating false-positive artefacts. 576