Dynamic analysis of proximal arteries of the ischemic foot

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Dynamic analysis of proximal arteries of

the ischemic foot

Boris Ponsioen

Supervisor: Dr. H. Marquering

Biomedical Engineering and Physics, AMC FNWI, Universiteit van Amsterdam

Bachelor Thesis Physics, 12 ec Student number: 10279806 July 17, 2014

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1 Summary

Critical Limb Ischaemia (CLI) is a combination of a severe lack of blood flow, rest pain and other non-healing complications. The prognosis for patients diagnosed with CLI is poor, often leading to loss of limb by amputation and with a survival rate of 45% in the first five years after initial onset of symptoms.

For diagnosis and during treatment of CLI, imaging technology is of great importance. 2D dynamic perfusion imaging can be used to visualize the blood flow and perfusion in the lower limb and can provide additional quantitative information, based on a region of interest drawn by the user. However, this type of analysis yields information about the blood flow in the larger arteries and the perfusion of the smaller vasculature combined.

In this study, we were interested in studying the blood flow in the larger proximal arteries separately. For this, we have developed a proof of concept of an algorithm that detects the arteries in a scan. This can be used to make calculations on the parameters describing the blood flow inside the arteries, such as the time to peak and area under curve of the signal intensity in time, along the path of the artery, instead of averaging over a larger area.

We demonstrate the performance of the algorithm in three cases and conclude with noting that the algorithm provides the desired results in most cases. However, a great amount of testing and development has to be done before a program such as ours can be used. For this, we discuss several possible improvements to the search algorithm.

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2 Samenvatting

Bij patienten met een ernstig verstoorde aanvoer van bloed naar de onderbenen en voeten, ook wel Critical Limb Ischaemia (CLI) genoemd indien het gecombineerd wordt met pijn bij de voet in rust en andere complicaties, moet er snel gehandeld worden. De diagnose CLI is ernstig en resulteert vaak in amputatie. Daarnaast overleeft 80% van de patiënten het eerste jaar en slechts 45% de eerste vijf jaar nadat de klachten verschijnen.

Een behandeloptie is in sommige gevallen revascularisatie, waarbij een afgesloten bloedvat opnieuw wordt geopend. Als dit het probleem niet verhelpt, wordt voornamelijk de pijn bestreden. CLI wordt vooral veroorzaakt door verstopping van de slagaders, atherosclerose genoemd, wat zelf is gerelateerd aan een aantal risicofactoren als diabetes, roken, hoge leeftijd en genetische aanleg.

Om de doorbloeding van de voet te onderzoeken, zijn er diverse scans mogelijk. De meest gebruikte is een serie van röntgenfoto’s met contrast. De contrastvloeistof

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maakt het bloed in de vaten zichtbaar, waarna in de serie foto’s de weg die het bloed aflegt in de tijd te vervolgen is. Deze foto’s kunnen ook gecombineerd worden in een enkele afbeelding, waarbij met kleuren wordt aangegeven hoe lang de contrastvloeistof nodig had om elke plek te bereiken. Zo is in één overzicht te zien hoe goed de voet wordt doorbloed en is ook duidelijk te zien of een revascularisatie effect heeft gehad.

Om dit verder te onderzoeken, moeten een aantal parameters die de doorbloeding beschrijven berekend worden. Hierbij wordt gekeken naar hoe de sterkte van het signaal in een bepaald punt verandert in de tijd als het contrast door het punt stroomt. De voornaamste parameters zijn time to peak (TTP) en area under curve (AUC). De TTP is de tijd die het contrast nodig heeft gehad om een bepaald punt te bereiken en de AUC beschrijft de totale hoeveelheid contrast dat door een punt stroomt. Deze parameters kunnen berekend worden in de huidige software door een gebied te tekenen in een scan, region of interest (ROI) genoemd, waarna het programma berekent hoe het bloed door dit gebied stroomt. Dit soort berekeningen nemen echter de doorbloeding van de grote en kleine vaten samen. Dit kan waardevolle informatie zijn en er wordt daarom op het moment veel onderzoek naar verricht, maar in dit onderzoek waren we geïnteresseerd in de stroming van alleen het bloed door de grotere vaten. Hiervoor hebben we een computerprogramma ontwikkeld die automatisch de vaten in het onderbeen detecteert. Nadat het deze gevonden heeft, kunnen er berekeningen worden gemaakt aan de stroming van het bloed door de vaten.

De werking van het programma wordt gedemonstreerd aan de hand van drie patiënten, waarvan twee een revascularisatie hebben ondergaan. Bij deze twee casussen worden scans die vóór de revascularisatie genomen zijn vergeleken met scans van erna.

Het programma is ontwikkeld om te onderzoeken wat de mogelijkheden zijn van deze vorm van analyse van de doorbloeding. Voordat een dergelijk programma daadwerkelijk toegepast kan worden, zal er nog veel aan doorontwikkeld en verbeterd moeten worden in volgend onderzoek. We sluiten af met enkele suggesties over het verbeteren van het huidige programma.

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3 Introduction

Critical limb ischaemia, characterized by a lack of blood flow in advanced stage, combined with rest pain and other non-healing complications, is a serious chronic condition with a poor prognosis. The main cause is atherosclerosis, which is linked to a number of risk factors, namely age, smoking and diabetes.

CLI requires immediate treatment in order to preserve the limb. Several en-dovascular options are available to reopen the blocked artery1_{. Nonetheless, in}

many cases amputation cannot be avoided. The survival rate is 80% in the first year after presentation of CLI, and continues at the same rate to 45% after five years2_{. Furthermore, the differences in outcome of revascularization}

procedures and treatment are large and not fully understood. To achieve better patient selection, not only anatomic factors should be taken into account, but also, more importantly, the physiological state of the limb3_{. This calls for new}

imaging techniques, some of which have become possible with current scanning technologies.

A number of scanning methods are used for diagnosis and during treatment of CLI, including CT angiography, Magnetic Resonance angiography and X-ray angiograms. These aid in the identification and localization of blockages in the arteries in the limb. The main goal of the treatment is to restore perfusion in the foot by improving blood flow in the arteries. To visualize the blood flow, a new imaging method has been developed, called 2D dynamic imaging, which combines a series of x-ray scans. With this method, the flow of the blood can be visualized in time.

Quantitative measurement of the changes in blood flow and perfusion due to treatment is possible with 2D dynamic imaging4,5. However, this provides a combination of information on blood flow in the larger arteries as well as microvascular perfusion, based on a drawn region of interest. In this study, we have developed a software program to identify the main arteries so they can be studied separately from the small blood vessels. A direct relation between change in perfusion in the whole foot and clinical outcome due to revascularization is not yet proven, although currently actively researched. Separate information on the change in blood flow in the main arteries could be of additional importance in this research.

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4 Background/Theory

4.1 2D Perfusion Imaging

For conventional imaging of the anatomy, the widely used standards are Computed Tomography (CT), based on x-ray imaging. The scans are quick, detailed, not expensive and equipment is available around the world. To gain information about the physiology, however, other types of scanning technology must be used. The area of nuclear medicine provides tools such as PET/SPECT to map the physiology inside the patient. But for analyzing the perfusion inside the lower limbs, among other parts of the body, the x-ray technology can still be of important use.

2D perfusion imaging is a type of imaging which uses digital subtraction angiog-raphy scans to map the perfusion of the blood vessels. Contrast is injected in the patient to visualize the artery lumen, after which a series of scans is made. This is possible due to the short scanning time per image of the x-ray angiography scans6.

To better visualize the arteries and the blood inside, subtraction is used. The scan series starts before the contrast arrives in the lower limb. This image is later subtracted from the other images in the series to hide the bones and other structures, leaving only the arteries and the blood with contrast agent to be visible7.

The scans are combined into an animation of the arrival of the contrast agent in the lower limb and the following flow of the blood towards the foot. Arteries with a disrupted blood flow are clearly visible in the scans and overall perfusion in smaller blood vessels can be assessed.

The clinical significance of the measurements of the perfusion in the lower limbs is currently being researched, focusing on it’s application in improving patient selection8. The direct result of the restoration of blood flow in a blocked artery is easily spotted, but the expected improvement in overall perfusion in the foot is much more difficult to measure. Accurate measurement of the change in blood flow speed and volume inside the proximal arteries after a revascularization procedure could provide an indication of the success of the procedure.

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4.2 Search algorithm analysis

2D perfusion imaging provides useful visual information for analysis of the blood flow in lower limbs. As in other visualization tools, 2D perfusion imaging does not yet provide accurate quantitative information on the microvasculature and actual perfusion of the organs. Computer programs for automatic analysis have been developed to acquire more quantitative information. The clinical value of their results has not yet been established, however.

An example of such a tool is currently being used5. This program combines the images in a scan series into a single image, in which color are used that correspond to the arrival time at each point. A proximal point inside an artery, for instance, may be colored red, while a more distal point is colored blue. This gives an overview of the perfusion in a single image.

Current software is able to calculate parameters such as time to peak and area under curve. These are based on a region of interest, drawn by the user. The advantage of such a calculation is that it is easy to use and runs fast. However, some information may be lost. Since these calculations are based on average characteristics over a larger area, regional changes cannot be analyzed.

One method to overcome this problem is to identify the blood flow in each artery separately, instead of averaging over a larger region. The latter type of analysis combines the perfusion of all the blood vessels, including the main arteries as well as micro-vascular circulation, treating the lower limb as an organ. In our type of analysis, it is possible to focus only on the main arteries, where we expect changes in flow after a revascularization procedure. We have developed a program which first employs a search algorithm that searches for the arteries in the scan. Once the proximal arteries have been identified, the parameters describing the blood flow can be calculated along the path of an artery.

4.3 X-ray imaging

At the base of this type of image analysis lies scanning technology that uses x-rays to reveal the anatomy of a patient. Variation in attenuation of the x-ray beams, depending on the tissue through which they travel, creates contrast in the image6. The characteristics of the tissue that influence the attenuation are quantified by the attenuation coefficient, usually denoted by the Greek letter µ. When x-rays travel through a medium with a constant attenuation coefficient, the

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intensity of the outgoing beam decreases approximately exponentially with the thickness of the medium. In media with a non-constant attenuation coefficient, we must integrate over the path to calculate the attenuation. In the resulting image, the intensity at a certain pixel and time step can be approximated by the following equation:

I(x, t) = I0 e−

R

µ(x,t)dl ₍₁₎

with I(x, t) the intensity at a pixel with position x at time t, I0 the intensity of

the x-ray beam at the source, µ the attenuation coefficient and l the path length of the x-rays.

5 Methods

For the analysis of the blood flow parameters in the main arteries, we have developed a software program. This program is able to identify the main arteries in a scan image and quantify the blood flow within an artery. The application is written in Ruby, a modern object-oriented scripting language, mainly known for its applications in web development. The language is, though not as fast as C and the like, also suitable for this research because of its easy to read syntax and powerful built-in methods.

This study focuses primarily on the proof of concept of this functionality. The program operates within the command line, without a graphical user interface. Such an interface can be added in a later stage and could have additional benefits.

5.1 Outline

The program follows an object-oriented approach to remain flexible when adding new components such as a (graphical) user interface, while relatively simple to read and understand.

Several components make up the program. The first part that runs, after initial configuration and loading of the images, is the search algorithm. This searches in a single image in a series for arteries and saves them as separate artery objects. These objects are briefly described in section 5.3. The second part consists of calculations and analysis of the blood flow inside these arteries.

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The focus lays on the former of the two parts, due to the proof-of-concept nature of this study. The calculations afterwards can be modified and more can be added in a later stage.

5.2 Image access

The program reads the image’s pixel intensity values directly. The greyscale value of each pixel can be read and written. As a result, the operations are straightforward, since the pixel greyscale values are simply integers between 0 and 256.

A scan series consists of a number of 2D images, with each image corresponding to a point in time. The images are read as 2D arrays of pixel values. In this way, an entire row or column is easily accessible. Ruby has many built-in array methods that can be used to manipulate the image data9.

5.3 Search algorithm

The search algorithm finds starting points in arteries by looking for peaks in signal intensity along a horizontal row of pixels. The pixel values within the row are thresholded: all values below a certain threshold are mapped to zero (black), and all values above mapped to the maximum value. The result is a series of pixel values of either 0 or 1, distributed in one or more peaks.

The user sets the number of arteries to search for. To find the starting points, the program sorts the peaks in the horizontal slice by width, assuming the widest peaks correspond to the arteries. Very narrow peaks can be caused by either smaller blood vessels or noise in the scan. The programs selects as many of the widest peaks as the user requires.

Once a starting point for an artery has been found, an algorithm runs that follows the path of the artery. It does this in an iterative fashion. At each iteration, points are selected in a circle around the current point. The pixel values around each candidate point are averaged and the candidate with the strongest signal value is chosen as the next point. A illustration of this process is given by figure 1. During this process, candidate points in the direction of the previous point are excluded.

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Figure 1: The searching algorithm illustrated. The grey path represents an artery. Each previous iteration in the search is represented by a dark red square, interpolated by lighter red squares. The blue arrows give the directions of the candidates for the next point, and the green square is the chosen next point.

are below a threshold, the search is terminated. This threshold is set by the user. Scans vary in contrast, as does the thickness of the arteries, therefore this threshold needs to be set correctly in each scan. In practice, the value of the threshold corresponds with the length of path that the program finds. When the edge of the image is reached, the algorithm stops as well.

The advantage of this method is that it works in all directions. Arteries in the scans may run horizontal at some locations, or even in upward direction. The searching process is repeated for each artery. From these sets of points, artery objects are created and stored for later use in calculations. An artery object contains an array with the coordinates of each point, along with helper functions, which can be extended in future versions of the program.

5.4 Usage and settings

As described above, the program runs inside the command line. The program is designed to run as much automatically as possible, though some parameters have to be set by the user, depending on the images in the scan.

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This setting determines at what minimum value the program should stop following an artery. This effectively controls the length of the part of the artery that is detected by the algorithm.

5.5 Analysis

To illustrate the possible applications of this program, we have added calculations of the time to peak and area under curve parameters of the blood flow inside the arteries.

Once the arteries of interest have been detected, the coordinates of the points in their paths are stored. Given a certain point in the images, the program finds the nearest point inside an artery. It then writes the pixel values of the same point in all images in the series to a file. This data represents the dynamic evolution of the contrast signal in the point.

When this calculation is also done on a second point downstream in the artery, information about the flow can be obtained by comparing the time to peak and area under curve.

The final step of the analysis is comparing the results of the described calculations before and after a revascularization procedure. The difference in flow in the proximal arteries can give an indication of the success of the procedure. Clinical outcome, however, can still differ from the results visible in the scans.

5.6 Application

The main purpose of this research is to assess the viability of this type of automatic image analysis. The starting point is the automatic detection of arteries in the scans. The separate calculation in each artery makes it possible to compare the changes in flow in a single artery of interest, rather than the perfusion in a region of interest around the artery. This information may be of more clinical significance than an overall calculation.

This study provides a proof of concept for automatic detection of arteries in a scan, to be used for evaluation of the state of the perfusion. With this as a starting point, more analysis modules can be added for different kinds of calculations inside these arteries.

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6 Results

For evaluation of the methods introduced in this study, several cases of critical limb ischaemia have been studied. Scans were made before and after a revascularization procedure and the program focused on the blood flow inside one of the proximal arteries.

6.1 Case 1

As an example, we include a case of a completely blocked proximal artery in the lower limb. We started with running the search algorithm on a suitable image in the scan before a revascularization procedure. The image and the results of the search are displayed in figure 2. As shown in the images, two of the proximal arteries are clearly visible, while a third is not, due to it being blocked.

Figure 2:The result of the searching algorithm

in case 1 before revascularization, with the detected arteries drawn by a green line.

Figure 3: Two points of interest in case 1

before revascularization selected for analysis of the blood flow, designated by green circles.

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Figure 4:The result of the searching algorithm in case 1 after revascularization, with the found arteries drawn by a green line.

Figure 5: Two points of interest in case 1 after

revascularization. The points, indicated by the green circles, are positioned as close to the points in figure 3 as possible.

The next step was to select two points inside an artery. Usually, the points are chosen at a proximal part of the arteries in the image. In this case, however, a more distal location was of more interest, for reason explained in the next paragraph. When given the pixel coordinates close to a point inside an arteries and a path length, the program finds the point in the artery, along with a second distal point at a distance equal to the given path length. The two point chosen in this case are drawn in figure 3. The exact locations of the points do not need to be set by the user, as the program looks for the point inside the artery that is closest to a given point.

The results of the revascularization procedure were significant, as is shown in 4. The blood flow in the most dorsal of the two previously active arteries is now completely transferred to the third artery, which has been opened during the revascularization procedure. The middle artery of the three seems to be unaffected by this change.

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We have chosen the two points at a more distal location, because the blood flow in the proximal arteries changed completely. Therefore, quantitative analysis in the proximal regions would not be very interesting. The results of the search algorithm in the scan after the procedure are shown in figure 4.

Lastly, the program collected the signal strength in the two points throughout the scan series in both the scans. In figures 6 and 7 the data is plotted. The continuous lines represent a smoothing of the data, by means of a moving average calculation. As expected, the time to peak is larger in the distal point, while the area under curve is smaller, in both plots.

Since the two proximal arteries, left and right in the image, seem to supply the same distal artery of blood, the change in blood flow in this part is a measure for the perfusion in the rest of the foot. Since the time to peak was reduced in the scan after the procedure, indicating faster blood flow, we may consider the procedure to be a slight success, although the dorsal proximal artery is no longer utilized.

Signal vs time in two points in case 1 before revascularization

Image index Si gn al in te nsi ty 0 20 40 60 100 120 140 160 180 200 Proximal point Distal point

Figure 6: Signal strength in two points of

in-terest in case 1 plotted against image index (signifying time). The continuous lines are smoothed data.

Signal vs time in two points in case 1 after revascularization

Image index Si gn al in te nsi ty 0 10 20 30 40 50 100 120 140 160 180 200 Proximal point Distal point

in-terest in case 1 plotted against image index.

6.2 Case 2

A different example is given by another case, in which a main artery in the patient’s lower limb was obstructed. An image of the series with the identified arteries drawn is shown in figure 8 and the points of interest are displayed in figure 9.

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Figure 8:The result of the searching algorithm in case 2 before revascularization, with the found arteries drawn by a green line.

before revascularization.

The patient underwent an revascularization procedure in an attempt to open the previously blocked artery. This procedure had a significant effect, extending the blood flow inside the artery to the heel of the foot. The new situation, along with the results of the search, are shown in figure 10 and the points of interest are visible in figure 11.

The signal strength through the two points of interest in time is plotted in figures 12 and 13. We have again smoothed the data, represented by the continuous lines.

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Figure 10: The result of the searching algo-rithm in case 2 after revascularization, with the found arteries drawn by a green line.

after revascularization.

Signal vs time in two points in case 2 before revascularization

Image index Si gn al in te nsi ty 0 10 20 30 40 50 60 70 100 120 140 160 Proximal point Distal point

interest in case 2 plotted against image index. The continuous lines are smoothed data.

Signal vs time in two points in case 2 after revascularization

Image index Si gn al in te nsi ty 0 10 20 30 40 50 90 100 110 120 130 140 150 160 Proximal point Distal point

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6.3 Case 3

To illustrate both the strength and weakness of the search algorithm, we have included a third case. In this case, we only used the search algorithm, since there is only one scan made. Therefore, we can not compare the perfusion and flow before and after a revascularization. We have included this case because of the complexity of the image. Three main arteries are visible, each containing several divisions leading to smaller arteries.

The results of the algorithm are shown in figure 14. In the settings, we have instructed the algorithm to search for three proximal arteries. The middle artery was particularly challenging to detect correctly, since it had a division into two branches of comparable thickness. The algorithm is programmed to chose the direction with the highest signal intensity, however further fine tuning of the settings may be necessary in cases similar to this case.

Figure 14: Performance of the search algorithm in case 3. Three arteries were detected and

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7 Discussion

We have shown the proof of concept by testing our algorithm with 17 cases, three of which are described above. In two of these cases, the search algorithm correctly followed the paths of the main arteries. These were scans of good quality with clearly defined main arteries, having a much greater thickness than smaller arteries.

The third case showed the performance of the search algorithm in a more complex image, where the thickness difference was less between the main arteries and their smaller branches. The results in figure 14 showed a correct detection of the main arteries in the upper region of the image. Although the paths of the left and right arteries were followed correctly, the search algorithm chose the incorrect direction at a bifurcation in the middle artery. This error may be attributed to the higher signal intensity in the chosen branch, despite it’s smaller thickness. Future versions of the algorithm improve on this functionality.

The results varied in some cases, depending mostly on image quality. The search algorithm performs better on images with higher contrast, as expected. In practice this means that images that are good enough for humans to use, with reasonably clearly defined blood vessels, should work with this program. For most of these the standard settings can be used, but some cases require some tweaking of the parameters. In future versions of this program, it may be possible to set these parameters automatically.

More variations in performance were found in the part of the program that calculates the blood flow parameters. In most cases, the calculations seemed to be reasonable. An example of a calculation by this algorithm in case 1 is shown in figures 6 and 7. In each plot, the data is as expected: the signal arrived at the distal point later and with less volume. The difference between the two plots, due to a revascularization, is more subtle. Although the peak is wider in figure 7, there seems to be no measurable delay in time to peak in the distal point, compared to the proximal point. Since there was a slight delay visible in figure 6, we suspect a faster flow after the procedure.

The plots of the second case show a less clear result. After the same amount of smoothing as used in the previous case, the signal appears irregular, with no clear peak visible. Therefore, such a case shows that an automatic calculation of the time to peak would not always be reliable. There does not seem to be a significant change in blood flow after the procedure, except a slightly smaller peak. This could indicate that the blood flow decreases in the center artery as

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the artery on the left is reopened during the procedure, provided that the amount of injected contrast agent remains the same.

However, since differences in time to peak between two points in the same artery were very small in some cases, we were not able to prove the accuracy of these calculations. While this study focused on the concept of applying a search algorithm on the scans - leaving the calculations as mere demonstrations of a possible application - we can provide a few suggestions for optimizing such as calculation program.

A possible explanation for inaccuracies in the calculations are the positions of the points of interest. The program chooses the second point automatically at a certain distance, set by the user, distal of the first point. This reduces error in the comparison of different scans, since the arteries are often at a different location. However, since the flow is calculated in points (pixels), variation in artery width influence the calculation. We have tried correcting for these variations by calculating the width at the points of interest, but due to the small size of the arteries, with a typical width of 2-4 pixels, the variations could not be accurately taken into account.

More accurate and sophisticated modules for analysis have yet to be developed to work with our program. Further study with such applications is needed to determine the usefulness of this program and its concept of analyzing perfusion per artery.

8 Conclusion

We have tested the program with several test cases. The three cases described in the results section show the performance of the search algorithm, as well as a possible application of the program in the first two cases.

As seen in figures 2, 4, 8 and 10, the search algorithm followed the paths of the arteries. In an image where the arteries branch of into other arteries with a thickness that approaches the thickness of the main branch, the algorithm was not always successful. An example of such a case is given by case 3, as shown in figure 14. Since these situations mainly occur in distal regions of the arteries in the lower limb, this potential problem is of less significance for the focus of this study, namely the flow in the proximal arteries.

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flow in the main arteries in the lower limb. Once the arteries are correctly identified, the flow in the arteries can be carefully analyzed. Additionally, the search algorithm runs fast on normal hardware, making the setup of the program as quick as drawing a region of interest, if not quicker. A long way of testing and improving a search algorithm such as ours is still ahead, as well as the need for proper modules for the calculations. We have shown the possibilities of a search algorithm and developed a proof of concept for such an algorithm.

9 References

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3 _{M.S. Conte, Journal of Vascular Surgery 57, (2013).}

4 _{M. Giordano, Perfusion Imaging in the Peripheral Vasculature Using}

Interven-tional C-Arm Systems (Utrecht University, 2013).

5

http://www.medical.philips.com:80/wpd.aspx?p=/main/products/interventional_ xray/product/interventional_radiology/interventional_tools/2d_perfusion. wpd, (Accessed july 2014).

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Dynamic analysis of proximal arteries of the ischemic foot

Dynamic analysis of proximal arteries of

the ischemic foot

Contents

1

Summary

2

Samenvatting

3

Introduction

4

Background/Theory

5

Methods

6

Results

7

Discussion

8

Conclusion

9

References