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Perivascular Spaces Segmentation in Brain MRI Using Optimal 3D Filtering

Lucia Ballerini, Ruggiero Lovreglio, Maria del C. Valdes-Hernandez, Joel Ramirez, Bradley J. MacIntosh, Sandra E. Black, Joanna M. Wardlaw

arXiv:1704.07699v1cs.CV

TL;DR

Visual PVS ratings are subject to observer variation, despite the relevance of PVS burden to neurological conditions. This paper optimizes 3D Frangi filtering with ordered-logit models and reports that automatically segmented PVS counts and volumes agree with visual ratings.

  • Problem

    Visual PVS burden ratings are prone to observer variation, while PVS enlargement is associated with SVD features, cognitive impairment, and inflammation.

    Source: §I · p. 1

  • Method

    The method uses 3D Frangi filtering, with ordered-logit models to optimize its parameters from visual ratings, and applies ROI masks to reduce false positives.

    Source: B. Image Preprocessing · p. 4, §VI · p. 7

  • Results

    Automatically segmented PVS count and volume agree with visual ratings.

    Source: §VI · p. 7

  • Takeaways & Limitations

    Quantitative PVS count and volume are described as more suitable for longitudinal studies than visual ratings, which can have ceiling or floor effects.

    Source: §VI · p. 7

    The method requires high-resolution, quasi-isotropic structural MRI, and inaccurate ROI masks can lead it to detect gray-matter boundaries and gyri as PVS.

    Source: §VI · p. 7

Abstract

from arXiv · show

Perivascular Spaces (PVS) are a recently recognised feature of Small Vessel Disease (SVD), also indicating neuroinflammation, and are an important part of the brain's circulation and glymphatic drainage system. Quantitative analysis of PVS on Magnetic Resonance Images (MRI) is important for understanding their relationship with neurological diseases. In this work, we propose a segmentation technique based on the 3D Frangi filtering for extraction of PVS from MRI. Based on prior knowledge from neuroradiological ratings of PVS, we used ordered logit models to optimise Frangi filter parameters in response to the variability in the scanner's parameters and study protocols. We optimized and validated our proposed models on two independent cohorts, a dementia sample (N=20) and patients who previously had mild to moderate stroke (N=48). Results demonstrate the robustness and generalisability of our segmentation method. Segmentation-based PVS burden estimates correlated with neuroradiological assessments (Spearman's $\rho$ = 0.74, p $<$ 0.001), suggesting the great potential of our proposed method

I. INTRODUCTION

PVS are small, fluid-filled structures whose enlargement is associated with SVD features, cognitive impairment, and inflammation, while visual burden ratings are subject to observer variation. The paper proposes a segmentation approach for enlarged PVS using 3D Frangi filtering and ordered-logit calibration against visual ratings.

I. INTRODUCTION

  • PVS are fluid-filled spaces along penetrating cerebral vessels that appear as small 3D tubular structures, generally under 3 mm in diameter.They are dark on T1-weighted and bright on T2-weighted MRI.Source: §I · p. 1
  • PVS enlargement is associated with other SVD features, cognitive impairment, and inflammation, while visual rating scales are prone to observer variation, particularly in the centrum semiovale.PVS can coexist there with other neuroradiological SVD features that confound identification.Source: §I · p. 1
  • Existing automatic approaches either require user intervention or rely on 7T training labels, limiting their practical fit to clinical research using 1.5T or 3T MRI and neuroradiologist ratings.The authors also note that normal PVS and deep medullary veins can confound visualization at 7T.Source: §I · p. 1
  • The proposed approach uses ordered-logit models to estimate Frangi filter parameters from visual ratings while accounting for rating uncertainty and interobserver variability.The authors calibrate models to each dataset’s rating scale and combine filtered T1 and T2 images.Source: §I · p. 2

II. MATERIALS

The paper uses dementia and mild-stroke cohorts and two visual PVS rating scales, with modified rating protocols described for its analyses. Its methods use those ratings to optimize a 3D Frangi-filter segmentation in the absence of accurate computational ground truth.

II. MATERIALS

  • The Sunnybrook Dementia Study and Mild Stroke Study provide the two datasets; Table I summarizes the MRI sequences relevant to PVS assessment in each.The cohorts comprise patients with an Alzheimer’s-disease-typical historical profile and patients with lacunar or mild cortical stroke features, respectively.Source: §II · p. 2, Table I · p. 2

III. METHODS

  • The proposed method applies 3D Frangi filtering and uses an ordered-logit model to optimize filter parameters from visual PVS ratings, accounting for measurement uncertainty without computational ground truth.The model relates PVS number to rating categories.Source: §III · p. 2

A. Visual Ratings of PVS

  • The Wardlaw and Patankar scales rate PVS burden in the centrum semiovale using ordered categories, and the study uses modified versions with standardized slice increments and category ranges.Assessors used T2 for primary identification, T1 for confirmation, and PD for rejection as needed; the evaluation included selected deep-gray structures but excluded sub-insular regions.Source: A. Visual Ratings of PVS · p. 2

B. Frangi filter

The Frangi filter uses second-order image structure to score vessel-like voxels across scales. Its response criteria distinguish tubular structures by Hessian eigenvalue patterns and by whether the structure is bright or dark.

B. Frangi filter

  • Frangi analyzes second-order image derivatives arranged in the Hessian matrix H_s(v) to describe voxel vesselness.The matrix contains the image’s second derivatives along and across spatial axes.Source: B. Frangi filter · pp. 2–3
  • For bright 3D tubular structures, the smallest-magnitude Hessian eigenvalue is near zero while the other two have similar magnitudes; dark structures reverse the sign conditions.The filter’s sensitivity to its eigenvalue measures is controlled by α, β, and c.Source: B. Frangi filter · p. 3
  • Responses across scales from s_min to s_max are combined, with the minimum and maximum scales chosen for the sizes of structures expected in the image.Source: B. Frangi filter · p. 3

C. Ordered Logit Models

The ordered-logit model links an ordinal rating to independent variables through a latent continuous score divided by thresholds. It represents measurement uncertainty through a logistic error term and expresses class membership probabilistically.

C. Ordered Logit Models

  • The ordered-logit model represents ordinal outcome y using a latent continuous variable y* partitioned by thresholds μ_i into ordered classes.The model’s parameters include β and the thresholds μ_i.Source: C. Ordered Logit Models · p. 3
  • The logistic error component has expected value zero and variance π/3, allowing the model to account for measurement uncertainty in ordinal data.Source: C. Ordered Logit Models · p. 3
  • Because y* is not deterministic, the model estimates the probability that an observation belongs to each class rather than assigning class membership from a fixed latent value.In this paper, the ordinal outcome is the PVS rating class and the independent variable is PVS count.Source: C. Ordered Logit Models · p. 3

IV. IMPLEMENTATION ISSUES

The ordered logit models were calibrated on synthetic PVS counts assigned to rating classes, with separate estimates for the Wardlaw and modified Patankar scales.

A. Model Calibration

  • 1,000 synthetic PVS counts were sampled from a log-normal distribution reflecting observed distributions, perturbed with normal noise, and assigned rating classes for model calibration.The perturbation used a normal distribution with standard deviation one.Source: A. Model Calibration · p. 4, Figure 3 · p. 4
  • For Wardlaw ratings, the estimated ordered logit parameters were β = 0.514 and thresholds µ0 = −2.840, µ1 = 5.708, µ2 = 10.497, and µ3 = 20.040.The classes corresponded to none, 1–10, 11–20, 21–40, and >40 PVS.Source: A. Model Calibration · p. 4, Figure 4 · p. 4
  • For the modified Patankar scale, the estimated parameters were β = 1.906 and thresholds µ0 = 2.269, µ1 = 9.569, µ2 = 18.995, and µ3 = 28.639.The classes corresponded to none, 1–5, 6–10, 11–15, and >15 PVS.Source: A. Model Calibration · p. 4, Figure 5 · p. 4

B. Image Preprocessing

Preprocessing generated ROI masks and a conservative PVS-mask estimate, with the analysis focused on the centrum semiovale.

B. Image Preprocessing

  • Fuzzy C-means clustering of T1 images assigned voxels to background, CSF, GM, and WM classes; combined CSF and GM voxels formed a mask for false-positive minimization.The centrum semiovale was defined as white matter superior to the lateral ventricles beneath the cortex; the study focused on this region rather than the basal ganglia because ROI masks were available for it.Source: B. Image Preprocessing · p. 4
  • Lesion Explorer PVS masks required acceptance criteria on both T1 and T2 and rejection criteria on PD, with cortical GM segmentation dilated by one voxel.These safeguards addressed imaging artifacts, differentiation from lacunar infarcts, registration errors, and partial-volume effects.Source: B. Image Preprocessing · p. 4
  • The resulting masks were a relatively conservative estimate of overall PVS burden, limiting their utility as ground truth for segmentation optimization.Source: B. Image Preprocessing · p. 4

C. Parameter Optimization

The method optimized Frangi-filter scales and threshold using rating-linked PVS counts, then assessed correspondence with visual ratings across cases.

C. Parameter Optimization

  • After reslicing MRI volumes to 1 mm isotropic voxels, the pipeline thresholded Frangi responses and retained 3D connected components with lengths between 3 and 50 mm.Voxels with F(v) larger than threshold t were retained to form initial binary PVS masks.Source: C. Parameter Optimization · p. 4
  • The Wardlaw count was derived from the automatically selected centrum-semiovale slice with the highest PVS density, while the Patankar count used 3D connected components across the whole centrum semiovale.Source: C. Parameter Optimization · p. 5
  • The optimization varied Frangi scales smin and smax and threshold t, keeping α = 0.5, β = 0.5, and c = 500 fixed because earlier optimization produced similar results at higher computational cost.Source: C. Parameter Optimization · p. 5
  • For each case, ordered-logit probabilities for five rating classes were computed from its PVS count, and the expert-assigned class probability contributed to the log-likelihood to maximize.The log-likelihood sums the logarithms of the selected probabilities across cases.Source: C. Parameter Optimization · p. 5

D. Model Validation

  • Voxelwise mask agreement could not be assessed because manual PVS segmentations were unavailable, and comparison with other methods was unfeasible across different resolutions, protocols, and cohorts.Manual annotation of these small structures was considered very time-consuming.Source: D. Model Validation · p. 5
  • Validation used Spearman’s ρ, and assessed correspondence of total PVS count and volume with visual ratings.Source: D. Model Validation · p. 5

V. EXPERIMENTS AND RESULTS

The experiments optimized 3D Frangi filter parameters using ratings from the SDS cohort. The fitted settings were broadly similar across modified rating scales, while another rater’s original Wardlaw ratings produced a different fit.

A. Experiments

  • The modified Wardlaw and Patankar rating-scale models had similar optimal parameters: both used smin = 1.4 and smax = 3.2, while t1 was 0.96 versus 0.95 and t2 was 0.35.Optimization used imaging datasets from 20 subjects selected from the Sunnybrook Dementia Study (SDS).Source: A. Experiments · p. 5
  • The minimum Frangi scale (smin) was the most significant parameter, while threshold choices played a smaller role across scale combinations.Source: A. Experiments · p. 5
  • Using the third rater’s original Wardlaw ratings yielded different optimal settings: smin = 0.2, smax = 2, t1 = 0.96, and t2 = 0.1.Source: A. Experiments · p. 5
  • The likelihood-plot trends indicated that the model adapted to the rater and selected parameters for the PVS that rater counted.Source: A. Experiments · p. 5

B. Qualitative Evaluation

The Frangi-based method detected tiny PVS that a conservative threshold method missed. Quantitative comparisons showed correlations with visual ratings, with results varying by rating and assessment measure.

B. Qualitative Evaluation

C. Quantitative Evaluation

  • Spearman’s ρ was 0.58 (p = 0.006) for modified Wardlaw and 0.71 (p = 0.0004) for modified Patankar ratings from the second rater, while count or volume comparisons showed low or no significant correlation.Source: C. Quantitative Evaluation · p. 6

B. Qualitative Evaluation

C. Quantitative Evaluation

  • Spearman’s ρ = 0.74 (p = 0.0002) for segmentation results versus original Wardlaw ratings; PVS total count and volume correlated with visual scores at ρ = 0.67 (p = 0.001) and ρ = 0.53 (p = 0.015), respectively.Source: C. Quantitative Evaluation · p. 6

D. Application to alternative acquisitions

The method was applied to T2-cube MRI in the Mild Stroke Study, with parameters optimized on 20 patients and tested on 48. Count and volume estimates correlated with visual ratings, supporting generalizability in this cohort.

D. Application to alternative acquisitions

VI. CONCLUSIONS

Automatically segmented PVS count and volume agree with visual ratings, and the method shows promise for quantitative assessment across sites. Its use is bounded by preprocessing-mask accuracy, MRI resolution, and image noise.

VI. CONCLUSIONS

  • The 3D Frangi method captures PVS running longitudinally and transversally in conventional MRI, while ordered-logit tuning uses ratings without computational ground truth.Its 3D segmentation avoids the double-counting limitations of slice-based methods.Source: §VI · p. 7
  • The method depends on accurate preprocessing ROI masks and high-resolution quasi-isotropic MRI; noisy images were excluded because tubular noise could be segmented as PVS.Source: §VI · p. 7
  • Automatically segmented PVS count and volume agree with visual ratings, and the method is free from inter- and intra-rater variability.The authors say more testing is needed in a wider range of subjects, including those with high burdens of other ageing and neuroinflammation features.Source: §VI · p. 7
  • Quantitative PVS volume and count are described as more suitable than visual ratings for longitudinal studies, which can show ceiling or floor effects.Accurate segmentation may also support analysis of PVS spatial distribution, orientation, density, and relationships with other SVD markers.Source: §VI · pp. 7–8
  • The authors report excellent multi-centre reproducibility and describe this as the first multicentre study of PVS segmentation.Source: §VI · p. 8
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