STENOSIS DETECTION IN INTERNAL CAROTID AND VERTEBRAL ARTERIES WITH THE USE OF DIAMETERS ESTIMATED FROM MRI DATA

Background. Magnetic resonance imaging (MRI) offers the opportunity to quantify the vessel diameters in vivo. This technique can have a breakthrough impact on the evaluation, risk stratification and therapeutical planning in hemodynamic-related pathologies, e.g., arterial stenosis. However, its applicability in clinics is limited due to the complex post-processing required to extract the information and the difficulty to synthesize the obtained data into clinical useful parameters. Objective. In this work, we use the vessel diameter distribution along its central line obtained with the use of MRI technology in order to detect the existence of stenosis in internal carotid arteries (ICA) and vertebral arteries (VA) with the minimal amount of False Negative predictions and to estimate the efficiency of therapy. Methods. Special normalized and smoothed characteristics will be used to develop the stenosis detection criteria which can be used for every artery separately and for both vessels simultaneously. Linear and non-linear characteristics were used to increase the reliability of diagnostics. Study is based on the Receiver Operating Characteristics (ROC) and optimization methods. Real diameter data of 10 patients (80 data sets) were used. Results. To detect stenosis, three different criteria have been proposed, based on the optimal smoothing parameters of vessel diameter distributions and the corresponding threshold values for linear and nonlinear characteristics. The use of the developed criteria allows increasing the reliability of stenosis detection. Conclusions. Different linear, non-linear, smoothed and non-smoothed parameters and ROC were applied to detect stenosis in internal carotid and vertebral arteries. It was shown that smoothed data are necessary for VA and the criterion applicable both for VA and ICA. For ICA it is possible to use initial (unsmoothed) data. Only one False Positive case was detected for every artery. Results of application of proposed criteria are presented, tested and discussed. For VA it is possible to use criteria 1 and 2 and smoothed normalized diameter data. For ICA criterion 2 can be recommended to detect long enough narrowing areas. To detect short zones of stenosis in ICA, the criterion 3 is useful, since it uses the non-smoothed diameter data.


Introduction
In this paper, we discuss the automatic detection of stenosis from the estimated diameters of cross-sectional areas of a blood vessel. Such a detection problem can appear at the quantification stage of Computerized Angiography that is based on digital image processing and important in conventional radiology. The survey [1] contains a profound overview of stenosis detection methods. The algorithms discussed there have been developed for the coronary artery stenosis detection, but in principle, they can also be used for diagnosing stenosis of other types of arteries, such as cervical arteries that are of our main interest here.
Among the methods overviewed in the above mentioned survey, the algorithm proposed in [2] outperforms the others and can be considered as state-of-the-art one. In this algorithm, the stenoses are subsequently detected and quantified by computing the relative change between the estimated and expected diameter profiles.
One important requirement formulated in [1] states that a fully automatic algorithm should be able to identify stenosis-free arteries with high specificity (above 0.6) to not overwhelm with a considerable amount of false positive detections. Note that although on the datasets considered in our study, the algorithm proposed in [2] performs even better than it has been reported in [1], for some types of arteries the specificity 0.636 exhibited by the algorithm is too close to the above indicated low limit of 0.6.
Thus, it would be desirable to further improve the stenosis detection performance. The present study is aimed at addressing this need.

Information collection
In this research we use the data of patients suffering a spontaneous cervical artery dissection until 2017, who were treated at the Department of Neurology, Medical University of Innsbruck, within the ReSect-study [3]. We selected the data of 10 patients with stenotic cervical artery dissection at the study baseline (date A). All patients received 3T whole body magnetic resonance angiography (MRA) at the Neuroimaging Research Core Facility of the Medical University of Innsbruck, equipped with a 3T whole body system (Verio, Siemens, Erlangen, Germany) employing a 12-channel head coil and an additional neck-coil. The right and left internal carotid arteries (ICA) and vertebral arteries (VA) were segmented from the MRA images using ITK-SNAP program (www.itksnap.org) [4]. For the determination of the diameter and position data from the segmentations at baseline (date A) and follow-up (date B) we used VMTK program (www.vmtk.org). After segmentation only the cases with a clear diagnosis were used for testing stenosis detection algorithms. Consequently, the data of 38 ICA and 39 VA were analyzed.
It must be noted that problem of vessel segmentation with the use of MRI data is complicated and requires a lot of effort and appropriate skills [5][6][7][8][9][10][11][12]. In particular, a hydrodynamics-based algorithm was proposed in [11] for automatic segmentations of large vessels, calculations of their radius and other characteristics versus distance along the central line.

Normalized and smoothed characteristics
Different patients and even one patient before and after treatment may have substantially different sets for a characteristic j с (e.g., artery diameter ), j d its averaged values of c and root-mean-square deviations: In particular, the average diameter of VA increased by 33% after the patient P1 treatment. In order to develop universal criteria (applicable for different patients), we will use the normalized characteristics according to the following formula: To diminish the noise, we will use also smoothed and smoothed normalized characteristics: ; Where w is the width of smoothing (in particular, w = 0 means using the initial distributions without any smoothing); i n is number of indexes between j = i  w, j > 0 and j = i + w, j < n + 1; and n is the number of elements in a data set (can be different for different patients and arteries). We will try to use different values of the width of smoothing in order to find the optimal and universal stenosis detection criteria.

Deviations from average values
Similar to [13], we will treat a zone of possible stenosis as a narrowing between two adjacent points with average values of the characteristic. If the minimal value of a characteristic in this area min T is smaller than certain threshold, the stenosis is flagged. Thus, for every characteristic the value of deviation min || VT  will be calculated with the use of developed Matlab code.
To compare the results, we will use also the deviations of non-normalized characteristics min || vt  and a special criterion k, calculated according to the formula: In the cases, when there are no two adjacent points with average values of the characteristic, the value of deviation and criterion k are supposed to be zero.

Use of Receiver Operating Characteristic
To compare the effectiveness of criteria we will use Receiver Operating Characteristic (ROC) methods. In particular, we will calculate the area under the ROC curve (AUC), sensitivity (SE), specificity (SP), positive predictive value PPV and F 1 score according to the known formulas [ Here TN is the total number of true negative predictions; TP is the total number of true positive To calculate these characteristics, 39 data sets were used for VA (without P10-A-left, diagnosis "closed") and 38 data sets for ICA (without P2-Bright and P5-B-left, diagnosis "improved"). Thus, to develop the reliable criteria, we will use only cases with a clear stenosis diagnosis (yes or no). Later we will discuss mentioned above unclear cases and their influence on the results.
It is very important to have a criterion minimizing not only the number of errors (FP + FN), but also the number of FN diagnoses. With the use of such approach we will minimize the number of really ill persons, who are not identified. The developed Mathlab code minimizes FP + FN, searches the cases with FN = 0, calculates the corresponding values of thresholds and indicates the number of the set with the false positive prediction.

Different criteria applied for VA diameter distribution
The results of calculations with the use of VA diameter data sets are presented in Figs for normalized and non-normalized diameter respectively. In both ranges the false positive prediction correspond to the same data set (P1-B-right). With the use of k-parameter the number of errors is greater than 1 (FP + FN > 1) for all 0 100 w  (see Fig. 3  2) calculate the average value of the smoothed diameter t and the critical value 0.89 t according to some common value of threshold, shown in Fig. 1.
3) plot both values on the graph with diameter distributions (blue and red straight lines); 4) the regions of smoothed diameter distributions (black lines) located under two intersections of straight blue lines and under straight red lines can be treated as zones of possible stenosis.
The use of this criterion is illustrated in Figs. 4-6. Blue markers and lines represent the initial diameters, bold black lines show the smoothed diameter distributions.

Using criterion 1 to detect stenosis in internal carotid arteries
The criterion 1 was developed with the use of VA diameter distributions, which can be treated as learning data sets. To test this criterion, more VA data is necessary. We can try to use this criterion for ICA data, even understanding the difference in shapes and sizes of these two arteries. In particular, the precision of diameter data must be greater for ICA (therefore ICA data needs less smoothing), since the average cross section area of ICA is larger and contains more pixels at the same resolution.
Criterion 1 was applied for 40 ICA diameter data sets. Even after using a more precise value of threshold 0.

Development and testing of the common criterion 2 applicable both for vertebral arteries and internal carotid arteries
The results of testing the criterion 1 on ICA data sets can be improved with the use of smaller values of the depth of smoothing, since high values of AUC and only one FP error occur in VA at rather large range of w (see Fig. 1). We can try to develop a common criterion 2, which can be applicable for both arteries and yield better testing results. For this purpose we will use the ROC results for ICA data shown in Fig. 8

) plot both values on the graph with diameter distributions (blue and red straight lines); 4) the regions of smoothed diameter distributions (black lines) located under two intersections of blue lines and under red lines can be treated as zones of possible stenosis.
Application of this criterion for both arteries (77 data sets) yields only two FP cases (one per each artery) and the values SE = 1; SP = 0.969; PPN = 0.867; F 1 = 0.929. An example of criterion 2 application for VA data sets is shown in Fig. 9. The application of this criterion to the ICA data is presented in the next Section.

4) the regions of smoothed diameter distributions (black lines) located under two intersections of blue dashed lines and under red dashed lines can be treated as zones of possible stenosis.
Some applications of criteria 2 and 3 to ICA diameter data sets are shown in Figs. 10-12 (blue bold and dashed lines are very close for these cases). It can be seen that application of different criteria can give different results in some cases.

Comparison with the previous results
The algorithm by Shahzad et al. [2] was applied for the same VA and ICA data sets. The calculated ROC characteristics are presented in Table 2.
The optimized values are shown in brackets. Comparison of Tables 1 and 2 demonstrates that criterion 2 ensures higher values of all the characteristics for both arteries.

Possible errors in diagnosis
In order to check the Matlab code and possible errors in medical diagnosis, we have calculated the ROC characteristics assuming the existing stenosis in the case P1-B-right. The results are shown in Fig. 13. It can be seen that for the smoothing range depth 15 46 w  there are no errors and AUC = F 1 = 1. It is interesting to note that in the case P1-B-right, the stenosis is also flagged with the use of the non-linear characteristics presented below. The results of computations show that there is only this FP error for 6 24. w  We have also calculated the ROC characteristics assuming the existing stenosis in ICA for cases P2-B-right and P5-B-left (labeled as "improved"). The results are shown in Fig. 14. It can be seen that the number of errors increases for all values of the smoothing depth. In particular, the minimal number of FN cases is two.
Use of the non-linear characteristics in order to improve the reliability of predictions.    (see, e.g., [11]). Another very important blood flow characteristicpressure gradientis connected with the squared cross-section area, i.e., 4 i d (see, e.g., [12]).
Two series of computations were performed with the use of smoothed normalized cross-section area ( 2 i d ) and smoothed normalized squared crosssection area ( 4 i d ). The results showed that a unique FN or FP error exists both for VA and ICA for some ranges of the smoothing width shown in Table 3. No cases without any errors were revealed. For normalized diameter of ICA there are two ranges of the smoothing width, corresponding to a unique FP error, which occurs in different patients (see Table 3). For smoothed normalized squared cross-section area ( 4 i d ) of ICA, there are two ranges of the smoothing width, corresponding to a unique FN error, which occurs in the same patient (see Table 3).

Conclusions
Different linear, non-linear, smoothed, and non-smoothed parameters and receiver operating characteristic (ROC) were applied to detect stenosis in vertebral and internal carotid arteries. Real diameter data of 10 patients (80 data sets were used).
Three different criteria were proposed for stenosis detection. It was shown that smoothed data are necessary for VA and the criterion applicable both for VA and ICA. For ICA it is possible to use initial (unsmoothed) data. Only one False Positive case was detected for every artery.

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Results of application of proposed criteria are presented, tested and discussed. For VA it is possible to use criteria 1 and 2 and smoothed normalized diameter data. For ICA criterion 2 can be recommended to detect long enough narrowing areas. To detect short zones of stenosis in ICA, the criterion 3 is useful, since it uses the non-smoothed diameter data.
To minimize the number of FN cases we recommend to use both the criteria 1 and 2 for VA and both the criteria 2 and 3 for ICA. It would be useful to develop corresponding user-friendly interface.