Elsevier

Computers & Graphics

Volume 69, December 2017, Pages 116-130
Computers & Graphics

Technical Section
Uncertainty visualization for interactive assessment of stenotic regions in vascular structures

https://doi.org/10.1016/j.cag.2017.10.002Get rights and content

Highlights

  • We developed a non-obstructive and non-animated approach to visually encode uncertainty in 3D shapes.

  • We demonstrated that our approach is favorable in comparison to state-of-the-art methods using transparency or animation.

  • We developed 3 different implementations of 3D uncertainty visualization to encode different aspects of surface variability.

  • We developed a 2D quantitative visual analysis system for uncertainty within selected stenotic regions.

  • We embedded our methods within a fully functional pipeline based on probabilistic segmentation for uncertainty modeling.

Abstract

Stenosis refers to the thinning of the inner surface (lumen) of vascular structures. Detecting stenoses and correctly estimating their degree is crucial in clinical settings for proper treatment planning. Such a planning involves a visual assessment, which in case of vascular structures is frequently based on 3D visual representations of the vessels. However, since vessel segmentation is affected by various sources of errors and noise in the imaging and image processing pipeline, it is crucial to capture and visually convey the uncertainty in a 3D visual representation. Moreover, it is crucial to quantify how much this uncertainty affects the calculated stenotic degree, since different severities lead to different treatments. We propose a novel approach for visualizing the shape deviation of different probability levels in vascular data, where the probability levels are computed from a probabilistic segmentation approach. Our non-obstructive visual encoding is based on rendering a single opaque surface representing a probability level of the cumulative distribution function around the vessels’ centerline. The surface rendering is enhanced with cumulative information about other levels. To do so, we traverse the probability space by applying an iterative projection method both inwards and outward until we reach surface variability within a given margin. We capture the shape variability between the different probability levels using the lengths of the projection lines, the change in angular directions, and the distortion of a parametrization. They are visually encoded using color and texture mapping. Furthermore, we allow for an interactive selection of a region of interest that automatically calculates the stenotic degree and how much the uncertainty affects the most likely result. We analyze our approach in comparison to state-of-the-art methods with medical experts in a study using both real magnetic resonance (MR) and computed tomography (CT) angiography data of vertebral arteries with stenoses as well as on MR angiography data with synthetically added stenoses and stenotic uncertainties. We evaluate how well our approach can guide medical experts in their assessment of the uncertainty in vertebral stenoses.

Introduction

A main aspect of the clinical assessment of vascular structures is to detect aneurysms or stenoses, i.e., abnormal dilations or narrowings of its inner surface (lumen). Cloud and Markus [1] report that approximately one quarter of ischemic strokes involve the posterior or vertebrobasilar circulation and particularly stenosis of the vertebral artery may account for up to 20% of posterior circulation ischemic strokes. To make the correct treatment decision, the clinicians visually inspect the lumen extracted from 3D CT or MR angiography data or obtained from 2D color-coded Duplex sonography to detect and assess stenoses and their degree of severity.

The severity of the stenosis is of crucial importance for the medical experts to make a treatment decision. While the treatment of asymptomatic patients with significant stenosis is subject to controversy, some investigators believe that high-grade stenosis of the vertebral arteries (greater than 70%) require endovascular treatment in case of a recurrent transient ischemic attack or brain infarction despite optimal conservative treatment [2].

While clinicians are trained to operate on the acquired 2D image slices and to interpret them directly, this process is challenging and requires a lot of expertise. Such investigations may lead to misdiagnoses or missing the vessel abnormalities altogether depending on the slice orientations, the distance between consecutive slices, and the time invested. In a workshop we conducted with five clinicians these issues were pointed out and the value of 3D visualizations in conjunction with 2D slice viewing was acknowledged. 3D vessel visualizations relies on a correct and precise extraction and display of the vessel walls. Unfortunately, there are many sources of uncertainty in the medical visualization pipeline [3] like noise errors, imaging artifacts, and assumptions made during image processing and segmentation, which negatively affect the correct extraction of the lumen. For example, in Fig. 1 three possible shapes of a stenotic vessel are shown in a 2D representation using contour lines. If a clinician is confronted with just one of those contour lines, the treatment decision may vary significantly depending on which is shown. In fact, Lundström et al. [4] reported that a slight modification of the transfer function used for volume visualization may result in a significantly different shape in the vessels, which may lead to a wrong treatment. Hence, the visual representation of the lumen shall capture and convey the uncertainty in the lumen shape and, in particular, the degree of the stenosis. There are different ways of capturing uncertainty. Its mathematical description is typically a probability distribution function or its anti-derivative, a cumulative distribution function. In Fig. 1, three different probability levels of such a cumulative distribution function are shown, similar to [5]. Areas where the three lines are close together indicate certain boundary information, while areas where the lines diverge indicate uncertainty in the shape of the vessel. The objectives of this paper are to introduce an interactive uncertainty-aware visual analysis system of stenotic regions in vascular structures including (1) a 3D visualization for easy detection of stenotic regions, (2) an intuitive assessment of the degree of uncertainty within the 3D setting, (3) a quantitative 2D visual assessment of the severity of a stenosis and its uncertainty within an interactively selected region of interest, and (4) a numerical outcome of the stenosis severity investigation from the interactive 2D visual analysis.

Our contributions include: (1) A non-obstructive and non-animated approach to visually encode uncertainty of 3D shapes. It is based on rendering a single (the most likely) surface and projecting the variation (i.e., the uncertainty) around it onto the surface using color or texture mapping. We demonstrate that our approach is favorable in comparison to state-of-the-art methods using transparency [5] or animation [4]. (2) Three different implementations of 3D uncertainty visualization within our approach that encode different aspects of surface variability. (3) A 2D quantitative visual analysis system for uncertainty within selected stenotic regions including angular uncertainty representation and numerical outputs. (4) Embedding the 3D and 2D analysis methods within a fully functional pipeline based on probabilistic segmentation for uncertainty modeling. (5) An evaluation of our methods in comparison to state-of-the-art approaches with two medical experts.

Section snippets

Related work

When dealing with medical imaging data, uncertainty of tissue shapes is typically estimated using probabilistic segmentation that generates for each voxel an n-dimensional probability vector that indicates the probability that the respective voxel belongs to one of the n segments. We also make use of probabilistic segmentation within our approach. Fuzzy segmentation procedures, such as the fuzzy c-means [6] or modified fuzzy c-means [7], or some Bayesian algorithms, such as the maximum a

Interactive uncertainty-aware visual analysis approach

Our interactive visual analysis tool for vascular stenoses starts with a 3D visualization of the vessels. This allows for an easy understanding of the vessels’ shape and location within the anatomical context. The focus of this paper is about conveying the uncertainty within the vessels’ shape. The 3D visualization presents color- or texture-mapped opaque surface renderings, where the color or texture encodes the degree of uncertainty. Opaque surface renderings allow for a good depth and shape

Angiography data

Throughout the study, we have used real CT and MR angiography data with certain vertebral stenosis but also shape differences at various areas along the vessels. We used one MR scan with a resolution of 384x512x88 and a voxel size of 0.586x0.586x0.7 mm3 (spanning 22.5x30x6.2 cm3) and a quite severe vertebral artery stenosis of ~50% (i.e., the lumen of the vessel is thinning to about half its diameter). One of the CT scans had a resolution of 512x512x330 and a voxel size of 0.432x0.432x1 mm3

Definitions

Let D be a spatial domain and X a continuous random variable. Then, the probability density function fX(p) describes the relative likelihood for the random variable to have a given value at point p ∈ D. Moreover, the cumulative distribution function FX(p) is the anti-derivative of the probability density function fX(p). For a one-dimensional domain D ∈ R, we can write FX(p):=pfX(u)du.

Our goal is to visualize the probability density function fX(p) or the cumulative distribution function FX(p)

2D Interactive visual analysis of ROI

After the user has selected a ROI within the 3D visual analysis, the ROI is shown using a 2D visualization. The 2D visualization is based on a cut through the vessel’s lumen along the vessel centerline [18]. The resulting slice is shown by mapping colors to the probability field values, see (Fig. 9. By default, a grayscale color map is used, but this can be adjusted interactively. Moreover, as we do not have occlusion problems in a 2D representation, we can explicitly encode the probability

Results and discussion

Fig. 11 shows our 3D visualization methods when applied to a synthetic stenosis when uncertainty is present and when uncertainty is not present. The first row shows the 25%, 50%, and 75% probability surfaces of the certain stenosis, while the third row shows the same surfaces from the uncertain stenosis. The second and fourth row of the image show our respective visualizations using these levels. For the certain case, the surfaces change equally everywhere between the different probability

Initial user study

We have evaluated our tool with two medical experts. One of them is a neurologist and has been working in the field of neurovascular imaging for 15 years. His area of expertise is atheroscleoris of the aorta and carotid artery bifurcation. He is in particular familiar with imaging methods such as modern vascular MR angiography and high-resolution 2D Duplex sonography. The other expert is a practicing physician with 6 years of experience in neurovascular imaging with a focus on imaging of

Conclusion and future work

We presented a system for visualizing and quantifying uncertainty for better assessment of stenotic regions in vascular structures. We used our system on real MR and CT angiography data and evaluated it with medical experts. To generate data with ground truth, we also generated synthetic uncertainties by modifying real MR volumes.

Our 3D visualization renders a single opaque probability surface and conveys the information about the variability around it by projecting information of the

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