Features and Determinants of Lacune Shape
Relationship With Fiber Tracts and Perforating Arteries
Background and Purpose—Lacunes are a major manifestation of cerebral small vessel disease. Although still debated, the morphological features of lacunes may offer mechanistic insights. We systematically analyzed the shape of incident lacunes in cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy, a genetically defined small vessel disease.
Methods—A total of 88 incident lacunes from 57 patients were segmented from 3-dimensional T1 magnetic resonance images and 3 dimensionally reconstructed. Anatomic location, diameter, volume, surface area, and compactness of lacunes were assessed. The shape was analyzed using a size, orientation, and position invariant spectral shape descriptor. We further investigated the relationship with perforating arteries and fiber tracts.
Results—Lacunes were most abundant in the centrum semiovale and the basal ganglia. Diameter, volume, and surface area of lacunes in the basal ganglia and centrum semiovale were larger than in other brain regions. The spectral shape descriptor revealed a continuum of shapes with no evidence for distinct classes of lacunes. Shapes varied mostly in elongation and planarity. The main axis and plane of lacunes were found to align with the orientation of perforating arteries but not with fiber tracts.
Conclusions—Elongation and planarity are the primary shape principles of lacunes. Their main axis and plane align with perforating arteries. Our findings add to current concepts on the mechanisms of lacunes.
Lacunes are a key manifestation of cerebral small vessel disease (SVD). They can be visualized on magnetic resonance imaging (MRI) as cerebrospinal fluid (CSF)–isointense cavities and are commonly described as round or ovoid with a maximum diameter of 15 mm.1,2 However, their exact characteristics in terms of size, shape, and anatomic distribution are still debated.3–5 Previous studies proposed specific shape categories by classifying lacunes or lacunar infarcts as spheroid, ovoid, slab, stick, and even more complex shapes.3,6,7 However, these studies were based on visual ratings and the existence of distinct classes of lacunes has never been firmly established.
The determinants of lacune shape are largely unknown. A small case series on acute lacunar infarcts suggested underlying vessel anatomy as a determining factor.8 However, this has not been explored for chronic, cavitated lesions. Also, it has been suggested that Wallerian degeneration of white-matter fibers is involved in cavitation of lacunes, causing shapes to extend along fiber tracts.7 Another unresolved issue is the upper size limit of lacunes. The most widely used criterion to differentiate lacunes form other, typically larger CSF-isointense cavities, such as those resulting from striatocapsular infarcts,9 is a maximum diameter of 15 mm. However, there is little information on whether this is applicable to all imaging planes in 3-dimensions (3D).4
In the current longitudinal study, we systematically investigated incident lacunes using in vivo MRI. The shape was analyzed with an unbiased approach using a spectral shape descriptor (Laplace–Beltrami spectrum).10,11 We further assessed the effect of anatomic location, the orientation of perforating vessels, and the orientation of fiber tracts on the lacune shape.
A major challenge in studying lacunes is the distinction from enlarged perivascular spaces and CSF-filled cavities not caused by SVD, but eg, by cardioembolism, artery-to-artery embolism, or local atheroma of the parent artery.1,9,12 To account for these aspects, we focused on incident lacunes and on subjects with genetically defined SVD.
Subjects were drawn from an ongoing prospective 2-center study (Klinikum der Universität München, Germany and Hopital Lariboisière, Paris, France) encompassing 365 cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy patients.13–16 Follow-up visits were scheduled at 18, 36, and 54 months. Details of the study design have been described elsewhere.13 Two hundred seventy-six patients had at least 1 follow-up and thus were included in the study. The ethics committees of both participating centers approved the protocol. Written and informed consent was obtained from all subjects.
MRI and Preprocessing
All patients were scanned on 1.5-T scanners (Siemens Vision [Munich, n=56] or General Electric Medical Systems Signa [Paris, n=588; Munich, n=243]). The sequence parameters have previously been described13 (Table I in the online-only Data Supplement). All 3DT1 follow-up images were registered to the baseline scan and normalized nonlinearly to Montreal Neurological Institute (MNI) 152 space using tools from the Functional MRI of the Brain Software Library (FSL)17,18 as described previously.13
Identification of Incident Lacunes
Newly appearing CSF-isointense cavities were identified on follow-up scans using difference imaging and Jacobian maps calculated in comparison with the preceding scan. This procedure has been described in detail13 and revealed a total of 99 incident cavities in the cerebral hemispheres in 63 patients. Infratentorial cavities (n=4, all of them in the cerebellum) were not included in the analysis because of the lack of available atlas data. Five cavities were excluded because they had a tubular structure with a diameter <3 mm, strongly indicative of perivascular spaces. Six additional lesions had to be excluded because of incomplete cavitation (n=3), concomitant large vessel stroke (n=2), or insufficient image contrast (n=1). The final sample consisted of 88 incident lacunes detected in 57 cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy patients and provided the basis for all subsequent analyses.
Segmentation of Lacunes
Lacunes were segmented from 3DT1 images using a seed-growing algorithm, implemented in a custom software tool, developed using MATLAB (R2013b, The MathWorks, Natick, MA; details are given in online-only Data Supplement).
Creation of Surface Meshes
The surfaces of lacunes were represented by triangular boundary meshes created from the segmented lacunes using BrainVISA with standard settings.19,20 The vertex density of the meshes was adapted to the image resolution such that edges in the meshes were shorter than voxel edges. Only for visualization, lacunes were smoothed using the iso2mesh toolbox21 in Matlab with a low-pass filter. For visualization in MNI space, lacune meshes were transformed by nonlinear transformations of vertex coordinates using FSL. The normalization parameters were those received by normalizing the corresponding T1 scan to MNI 152 space.
The anatomic location of lacunes was rated on T1-weighted scans by 2 experienced raters (B.G., M. Duering) using the following 4 categories: basal ganglia, centrum semiovale, corpus callosum, and other. Corpus callosum was defined as a separate category to account for the spatial constraints of this anatomic structure. The agreement between raters was good (Cohen κ of 0.806). In the case of disagreement, a consensus was reached between the 2 raters.
We determined the following metrics calculated in native space: lacune volume, surface area, maximum diameter, axial diameter, and compactness. Volume, surface area, and compactness were calculated from the lacune mesh using BrainVISA. The maximum diameter of each lacune was calculated as the maximum distance of all possible pairs of vertices in the respective surface mesh. The axial diameter (ie, maximum diameter in the axial imaging plane) was calculated as the maximum distance between intersection points of the surface mesh with any axial plane. Details on calculation of basic characteristics are described in the online-only Data Supplement.
Spectral Shape Descriptors
To obtain an observer-independent measure of shape, we calculated the Laplace–Beltrami spectrum from the lacune mesh in native space using the ShapeDNA tool.10 This tool defines the Laplace–Beltrami spectrum as the family of eigenvalues found by solving the Laplace eigenvalue problem (Helmholtz equation). The eigenvalues in the Laplace–Beltrami spectrum build an ordered series. Eigenvalues with a lower ordinal position represent shape changes on a larger scale (low frequency), and eigenvalues with a higher ordinal position represent changes on a smaller scale (high frequency). We restricted the analysis to the first 10 eigenvalues because we considered the most relevant shape information to be related to large-scale (low frequency) shape changes.11 For similar considerations, eigenvalues were divided by their ordinal position in the spectrum.10,22
To reduce dimensionality of the Laplace–Beltrami spectrum, we used principal component (PC) analysis. Lacunes were then represented in a space defined by the first 3 PCs to search for subtypes (clusters) of lacunes with different shapes.
Principal Axes and Simplified Geometric Measures
To provide a more intuitive representation of lacune shape, we used the measures suggested by Westin et al24 for the geometric analysis of diffusion tensors. A tensor can be used to mathematically describe an ellipsoid, and the measures suggested by Westin et al24 indicate how close the corresponding ellipsoid is to the generic cases of a line (linear anisotropy), a plane (planar anisotropy), or a sphere (sphericity), respectively. We calculated these measures from the principal axes of the incident lacunes (online-only Data Supplement). Although more complex shape features (eg, bends and cone-like shapes) of lacunes would not be captured by the measures suggested by Westin et al24, they still can give a good approximation of their linear, planar, and spherical shape component. We used this approximation to get a more intuitive representation of the major shape principles represented by the spectral shape descriptor. In particular, we looked for correlations between the geometric measures suggested by Westin et al24 and the first 3 PCs, resulting from the PC analysis on the eigenvalues of the spectral shape descriptor.
Perforating Artery and Fiber Tract Orientation
The orientation of perforating arteries and white-matter tracts at the centroid of each lacune was defined using an atlas of arterial vascularization25 and a probabilistic atlas of the 20 major white-matter tracts in MNI space (Johns Hopkins University-International Consortium for Brain Mapping [JHU-ICBM] tracts).26 We developed a graphical user interface in Matlab to align slices from the vessel atlas with slices from the MNI template and to manually determine orientation vector for the perforating artery and white-matter tract at the centroid (the geometric center) of each lacune (details are given in the online-only Data Supplement). The resulting orientation vectors were then reverse transformed into native space. The agreement between raters was good for both perforating arteries (intraclass correlation coefficient, 0.741) and white-matter tracts (intraclass correlation coefficient, 0.919). The orientation of perforators and white-matter tracts could be determined for 74 and 53 lacunes, respectively. Lacunes in subcortical grey matter were not rated for tract orientation.
Relationship Between Lacune Shape and Perforating Artery/Fiber Tract Orientation
To assess the relationship between lacune shapes and vascular anatomy, we calculated 2 types of angles: the angles between the main axis of the lacunes (defined as their longest principal axis) and the orientation vector of perforating arteries at the centroid of the lacunes and the angles between the main plane of the lacunes (the plane defined by their longest and second longest principal axes) and the orientation vector of perforating arteries. We then tested whether the distributions for these 2 types of angles were different from a random distribution using the χ2 goodness-of-fit test. Similarly, the relationship between lacune shapes and fiber tract orientation was assessed by calculating the corresponding angles with the orientation vectors of the fiber tracts.
Statistical analyses were conducted with the R software package (version 3.1.0).27 The basic characteristics of lacunes and lacune loadings on the first 3 PCs of the ShapeDNA were compared across anatomic locations using the Kruskal–Wallis test. P values were corrected for multiple comparisons (8 tests) using the Bonferroni method. Significant results were followed by post hoc tests using pairwise Wilcoxon signed-rank tests with the Bonferroni method for adjusting P values. Linear regression was used to assess the relationship between the PCs of the spectral shape analysis and the simplified geometric measures.
The demographic features, vascular risk factors, and clinical and imaging characteristics of the 57 cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy patients with incident lacunes are reported in the Table. Symptoms were reported for 18 lacunes (20.5%; Table). Hence, the majority of lesions were clinically silent. Figure 1 depicts the anatomic distribution and shape characteristics of all incident lacunes (n=88) projected on a single glass brain in standard space (Movie I in the online-only Data Supplement).
Characteristics of Incident Lacunes
Lacunes were most abundant in the centrum semiovale (n=30) and the basal ganglia region (n=27). They were also present in other brain regions (corpus callosum, frontal/occipital pole; n=30), whereas the temporal lobe was relatively spared (n=1).
A comparison of basic lacune features across all anatomic locations showed significant differences in maximum diameter (H=15.76; P=0.01), volume (H=17.25; P=0.005), and surface area (H=18.76; P=0.002; Table II in the online-only Data Supplement). Post hoc pairwise comparisons (Figure 2) showed that lacunes in the basal ganglia and centrum semiovale were significantly larger compared with lacunes in the corpus callosum or other regions.
Spectral Shape Analysis
Global shape variations of lacunes were analyzed on the basis of a spectral shape descriptor, the Laplace–Beltrami spectrum. In PC analysis, the first 3 components explained 79.7% of the variance in the spectral shape descriptor, with 60.8% explained by the first component and 10.7% by the second. There was no difference in the first 3 PCs across anatomic locations (Table II in the online-only Data Supplement). As illustrated in Figure 3A, lacune shape varied continuously along the PCs without indication for clustering or subgroups.
To obtain a more intuitive representation of the shape principles captured by the first 3 PCs, we compared each PC with the following simplified geometric measures: linear anisotropy (elongation), planar anisotropy (planarity), and sphericity. PC1 is well represented by linear anisotropy (Figure 3B; adjusted R2=86.11; P=7.58×10−39). PC2 is best represented by planar anisotropy (Figure 3C; adjusted R2=32.93%; P=3.06×10−9). Other correlations were less strong (Figure II in the online-only Data Supplement). Figure 3D gives representative examples of lacunes plotted along PC1 and PC2. As can be seen from this analysis, elongation and planarity were the primary determinants of lacune shape.
Relationship With Perforating Arteries and White-Matter Tracts
To identify potential determinants of lacune shape, we next explored the spatial relationship between lacune geometry and both perforating arteries and white-matter tracts. Specifically, we examined the distribution of angles between the main lacune axis (for elongation) or main lacune plane (for planarity) and orientation vectors for perforating arteries and white-matter tracts.
Small angles between perforating arteries and the main lacune axis were more common than large angles (Figure 4A). The results were significantly different from a random distribution (χ2=36.68; df=8; P=1.32×10−5). Similarly, small angles between perforating arteries and the main lacune plane were more common than large angles (χ2=53.06; df=8; P=1.05×10−8; Figure 4B). For fiber tracts, the calculated angles did not differ from a random distribution (main axis: χ2=12.38; df=8; P=0.135; main plane: χ2=11.26; df=8; P=0.187). Hence, lacunes tend to align along perforating arteries.
Maximum Diameters of Lacunes in 3D and 2D
Routine clinical evaluation of lacunes is usually performed in 2D on axial slices, and an axial diameter of <15 mm is commonly used to distinguish lacunes from other CSF-isointense cavities. Figure 5 illustrates that 9 (10.2%) of the 88 lacunes had maximum diameters >15 mm. However, when analyzed in an axial imaging plane, only 1 lacune (1.1%) exceeded the 15-mm threshold.
This study in a well-characterized cohort of patients with genetically defined SVD shows that incident lacunes are distributed along a continuum of shapes, primarily defined by 2 geometric measures: elongation and planarity. Our study further demonstrates that lacunes tend to align with the orientation of perforating arteries. Lacunes in the basal ganglia and centrum semiovale were larger compared with other brain regions. These findings add to current concepts on the characteristics and mechanisms of lacunes.
We found elongation to be the predominant shape principle of lacunes regardless of anatomic location, and we found lacunes to be aligned with perforating arteries. This fits with a previous small case series of patients with acute lacunar infarcts that described linear structures on MRI or computed tomography consistent with alterations in or around perforating arteries.8 Our findings extend this observation from single cases to a systematic analysis in a large sample and to chronic cavitated lesions. We further addressed tract degeneration as a potential determinant of lacune shape. Recent studies have demonstrated secondary degeneration of white-matter tracts and remote grey matter after subcortical infarcts.28–31 It was further suggested that these secondary changes influence lacune shape.7 We found no relationship between lacune shape and fiber tract orientation. Hence, our observations suggest that the development of lacunes is primarily determined by mechanisms in or around perforating vessels, rather than by secondary effects, such as Wallerian degeneration.
Our finding of a continuum of shapes suggests that the development of lacunes is modulated by factors varying gradually and without relationship to a certain brain region. Again, one of these factors may be found in vascular anatomy. A postmortem study on lenticulostriate arteries demonstrated considerable interindividual and interhemispheric variability in branching patterns,32 and a similar degree of variability can be expected for centrum semiovale perforators. Thus, the continuum of lacune shapes may, in part, reflect variations in vascular branching patterns. Detailed studies assessing individual vascularization patterns in vivo before a lacune develops are needed to verify our hypothesis but are still methodologically challenging.33,34
The current study also has implications for diagnostic imaging. We show that the usual size criterion for lacunes (<15 mm) is valid when applied to images obtained in the axial plane. However, in a considerable proportion of lacunes, the maximum diameter in 3D exceeded 15 mm. This should be taken into account when inspecting imaging planes other than axial.
Our study has several strengths. First, we studied a well-defined cohort with genetically defined SVD. Thus, we are confident that our results are not contaminated by other causes of small cystic infarcts, such as cardiac or artery-to artery embolism. Second, we used advanced protocols for lacune detection and focused on incident lacunes, thus excluding enlarged perivascular spaces. Another strength is the application of a spectral shape descriptor that is invariant to scale, rotation, and translation.10 This enabled an unbiased and observer-independent approach without a priori assumptions on shape.
Our study also has limitations. The orientation of perforating arteries was derived from a single–subject atlas.25 Although being the best source for determining vessel anatomy in humans to date, this atlas does not account for individual differences, thereby adding noise and possibly reducing effect size. One might speculate that the relationship between perforating arteries and lacune shape is even stronger than observed in our study. Similarly, using an atlas for white-matter tract anatomy instead of individual tractography might have reduced our power to detect the relationship between tract orientation and lacune shape. Also, although the tract atlas is still state-of-the-art, it is prone to artifacts related to crossing fibers as an inherent limitation of diffusion tensor–based tractography. For this reason, we limited the tract analysis to areas where a clear and consistent tract orientation can be assigned.
It remains open whether the features and determinants of lacune shape observed here are generalizable to nongenetic SVDs. Previous studies on shape characteristics have focused on acute infarcts rather than lacunes,3–6 and we are not aware of any studies that have looked at the determinants of shape features. Of note, however, conducting similar analyses in sporadic patients will be difficult because of the known challenges in excluding competing vascular etiologies, such as atheroma of the parent artery or embolisms from proximal sources.
We thank Denis Rivière for assistance with the implementation of processing steps done in BrainVISA.
Sources of Funding
This work was supported by an FP6 European Research Area Network NEURON grant (01 EW1207) and the Vascular Dementia Research Foundation.
Continuing medical education (CME) credit is available for this article. Go to http://cme.ahajournals.org to take the quiz.
The online-only Data Supplement is available with this article at http://stroke.ahajournals.org/lookup/suppl/doi:10.1161/STROKEAHA.116.012779/-/DC1.
- Received January 15, 2016.
- Revision received March 1, 2016.
- Accepted March 4, 2016.
- © 2016 American Heart Association, Inc.
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