CIA PROJECT
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The Atherosclerosis Project
The atherosclerosis project is a part of the CIA project, which is a joined venture between the Image group at ITU and the Center for Clinical and Basic Research in Ballerup.
Problem formulation for the project
The goal of the project is the developement of a mass-screening tool, well-suited for quantifying the extend of calcific deposits in the lumbar aorta of postmenopausal women, i. e. women whose ovaries have seized to produce female sex-steroids (estrogen). Although several simple methods have been proposed for the semi-quantitative grading of aortic calcification, these methods may have limitations especially in capturing small changes in the progression of atherosclerosis. Furthermore, the evaluation depends on the investigator / technician involved, and does not take the changes of the interluminal expansion or the calcium density of the individual plaques into account.
A mass-screening tool has to deliver reliable and easily reproducible data which should give information regarding the degree of calcification, as well as the density progression of the individual plaques. In order to make such a diagnostic tool available to the broad public, an easy, cost-efficient solution has to be found, which suggests 2D x-rays. The problem associated with common x-rays though, is that soft tissue, and thus a healthy aorta, is not visible. This means, that the inference of the calcification index and progression has to rely solely on the visible calcific deposits in the aorta.
What is atherosclerosis
The process of aorta calcification is started by an irritation of the outer cell-layer of the innermost tissue of the artery – the endothelium. Once this irritation is detected, various mechanisms of the immune-system take over. White blood cells (monocytes) rush to the injured tissue and infiltrate the wall of the artery; the blood cells undergo a metamorphic process while they infiltrate and become now macrophages. This leads to the appearance of macrophage-derived foam cells, which are laden with lipids; i.e., fatty elements.
When the white blood cells keep on rushing to the irritated tissue, the lipid-core that has accumulated underneath the endothelium, increases in size and causes eventually the swelling to rupture (see Fig. 1). This rupturing in turn triggers another process of the defensive mechanisms – platelet aggregation. Platelets play a major role in wound healing, since they possess the ability to ‘glue’ themselves to wounded tissue and to each other, thereby forming a platelet plug. This form for plug is formed shortly after the just mentioned rupturing, closing the wound. The negative kickback of this process is that parts of this plug can break away from the artery wall and cause smaller blood vessels to be blocked.
Figure 1: Structure of an unstable human atherosclerotic plaque
Medical background studies
Autopsy studies of 600+ middle-aged adults in the 1950s reported highly significant positive associations between the degree of abdominal calcification and the presence of calcified plaque in the coronary arteries. The resulting data suggested that a high correlation between abdominal aortic calcification and advanced coronary atherosclerosis had to be present in the living population. This was motivation enough for a follow-up study involving 1049 men and 1466 women (mean age, 61 years at baseline) who were followed from 1967 to 1989, in order to further the understanding of the impact of abdominal arterial calcific deposits on the prediction of cardiovascular disease (CVD) and coronary heart disease (CHD).
The follow-up study concluded that the presence of abdominal aortic calcium is generally associated with an increased risk of subsequent coronary heart disease and cardiovascular disease, independently of traditional cardiovascular risk factors (confounders). It showed that calcification in the abdominal aorta anterior to the first four lumbar vertebrae was common and affected 2/3 of the study population. It also produced strong evidence that imaging of vascular calcification using lumbar radiographs provides an important prognostic tool to help assess the risk of CVD.
Angle of attack
The project for solving our ambitious task is delt up in three main phases:
1) Locating the aorta
2) Devising a new method for the assessment of the degree of atherosclerotic plaque, that allows to monitor progression as well as density of individual plaques
3) Finding the calcified areas
Phase 1: Locating the aorta
We approached this problem by employing Active Shape Modelling, which basically consists of translating, scaling, and rotating the shapes so that they overlap and only the pure shape information is left. From this shape model is then the mean shape extracted. Onto the mean shape are the possible modes of variation projected, thus yielding the entire shape spectrum.
Figure 2: Left: The red lines denote the aorta annotated by the expert, the yellow lines denote the mean shape, and the blue lines show our prediction. Middle: The prediction model achieves an overlap of 92%. Right: The mean shape accounts for only 73% of the original area.
We built a prediction model, that allows us to compute the most plausible shape, an example result can be seen in Fig. 2. From a dataset of 90 images we can predict 89% of the area of the original aorta with a standard deviation of 5.5%.
Phase 2: Devising a new method for the assessment of the degree of calcification
The idea behind our approach is to simulate how a calcified image would have looked like non-calcified, by inpainting all the calcified areas, a technique used in image restoration as well as postprocessing of film. The difference between the calcified and the non-calcified image then yield the new calcification index.
Using a randomization process we generated an area of a certain width at each chosen segment, compared this area to the data provided by the physician and inpainted the area, whenever the area did not overlap with an actual calcification. In case of an overlap, the segment was simply discarded and a new choice, based on the just mentioned parameters was made. This procedure was iterated for each width 80 times, and the width varied from 10 to 100 pixels. The individual inpainted images were then compared to the respective original images, thus providing us with a function of how well the inpainting process could recreate the background of an image dependent on the width of an area (see Fig. 3).
Figure 3: The standard deviation of the difference in pixel intensities for each of the 80 datasets is displayed as a function of width. The regression line for the std can be expressed as std = 0.299 × width.
Visual inspection of our initial experiments with inpainting of calcified areas made it clear that the inpainting procedure was biased by minute calcific deposits just outside the annotated areas . These calcific rests were missed by the physician and became only apparent when zooming in to pixel-level. Since the inpainting method relies entirely on boundary information, we had to expand the annotated areas in order to avoid faulty results as much as possible.
Thus, the next step was to iterate the inpainting process for each calcified area of an image, so that each area was dilated with a mask (we used a disk) that grew in size proportional to the number of iteration (see Fig. 4). From these computations we extracted the result that produced the maximum signal-to-noise ratio.
Figure 4: Inpainting on image nr. 0201. Left: Inpainting mask for the undilated calcified area. Second-from-left: The inpainted region of interest shows an almost homogeneous structure, that is biased by the remaining calcification on the border (arrow). third-from-left: The difference of the original and the inpainted region of interest. Third-from-right: Inpainting mask for the maximally dilated calcified area. Second-from-right: The inpainted region of interest is far larger than the calcified area. Right: The difference of the original and the inpainted region of interest.
In order to assess the quality of our method, we summed up all the differences for the respective areas for each image and plotted them in sorted order against the respective scoring systems of the standard procedure (see Fig.5). From the graphs in Figure 5 it is apparent that our method offers more possibilty for discerning the different stages of plaque development than the standard procedure. In the case of the lowest calcified image all the scores of the standard procedure have the value of one, whereas our score is 29.9 ± 7.7, thus much more explicit for even the mildest calcification. For the moderate calcifications, it is impossible to gather any conclusive information from the standard procedure. Where our method scored an interval of [280 - 430], the standard procedure maintains its value of 3 for the 4-score, a value of 5 for the 8-score and even drops from an 8 to a 7 for the 24-score, due to the measurements of length only.
Figure 5: The three graphs depict the relationship between the respective scoring systems of the standard procedure and the total differences resulting from our inpainting method.
Phase 3: Finding the calcified areas
For this last phase we can probably achieve reasonnable results by employing some sort of classification scheme. This future work will initially be based on the assumption of a Gaussian population, such that the class-conditional densities for the multivariate normal can be expressed as
where i = 1,….,k. Since we only need two classes ( calcified and non-calcified ) an initial, rough labelling will be computeable by using
where L(.) denotes the expected loss in the posterior distribution when assigning an observation x to a class πi.