Creating an Automated Blood Vessel. Diameter Tracking Tool

Transcription

1 Medical Biophysics 3970Z 6 Week Project: Creating an Automated Blood Vessel Diameter Tracking Tool Peter McLachlan April 2, 2013 Introduction In order to meet the demands of tissues the body modulates local blood flow. Blood flow is primarily controlled in the microcirculation by changing the arteriole diameter. Measuring blood flow is an important metric for many physiologically relevant conditions including sepsis and cancer. Manual diameter measurements can be obtained after video recording using software like ImageJ or on the fly using electronic calipers [1]. These methods are time consuming and error prone, respectively, making automated software measurement desirable. Automated diameter measurement from initial seed points has been performed on videos of blood vessels flowing horizontally [1]. It is desirable to reproduce this process for vessels at an arbitrary orientation. This project attempts to achieve automated diameter measurements from video sequences featuring vessels at an arbitrary two-dimensional direction.

2 Theory Blood flow is modulated to meet metabolic demands and so is an important factor for many biophysical models. Blood flow can be quantified in the simplest way using Ohm s law, which states that blood flow is proportional to the blood pressure and inversely proportional to the resistance of the vessel. Q = P R (1) Note that, according to Poiseuille s law, the resistance is dependent on many factors including the vessel length, the fluid viscosity and importantly the radius, giving the Poiseuille s flow equation. Q = P π r4 8Lη (2) According to Poiseuille s law flow equation, as radius appears to the fourth power, blood flow is more sensitive to changes in radius than changes to the pressure, length or viscosity. Consequently, blood vessel radius, or diameter, is of particular interest when studying vascular behavior. Gold standard blood vessel diameter measurements from in vivo videos are obtained manually. This is effective however it is time very time consuming as projects may require multiple experiments each with videos of tens of thousands of video frames per experiment. This lengthy process begs for automation using image processing software. Lee et al. have produced a method for automated diameter measurements from initial diameter seed points within in vivo vascular videos for purely horizontal vessels [1]. The horizontal vessel videos were obtained by rotating the camera to the direction of the blood vessel before video recording and by numerical phantom creation.

3 It is desirable to generalize this process to vessels at any orientation since videos of vascular networks may feature multiple blood vessels at various orientations. This project attempts to achieve the goal of diameter measurements from automated video feature tracking of moving vessels at an arbitrary two-dimensional direction following a similar algorithm to Lee et al. Methods The overall programming flow is depicted in figure 1 showing the major functions of the developed software to take an in vivo microvessel video and output automated diameter measurements for all frames. Figure 1: Flow chart of software tasks performed to obtain diameter measurements from an in vivo vascular video Image Registration For this project frames for in vivo vascular videos must first undergo image registration. Image registration is a process with the goal of aligning multiple images taken at different times [1,2]. Consecutive frames in the video sequence are subject to tissue motion due to animal breathing and responses to experimental interventions. To obtain accurate measurements it will be necessary to align all images as much as possible. To do this each frame in the video sequence is compared to the

4 first image, the reference, and the between that frame and the reference similarity is measured. There are many metric for similarity that can be used and in fact other methods of image registration all together. For this study the two-dimensional normalized cross correlation was used. The amplitude of the normalized cross-correlation between two images, I 1 and I 2, is given by Equation 3 [3,4]. m 1 norm_corr (I 1, I 2 ) = i=0 n 1 I 1(i, j)(i 2 (i, j) I 2 ) σ 1 σ 2 j=0 (3) The following tasks were accomplished in order to create the registered video sequence. Using the built-in MATLAB function NORMXCORR2 the normalized correlation coefficient was calculated exhaustively for all positions of overlap between each image and the reference image (the first image in the sequence) [4]. The peak correlation amplitude was determined and the corresponding offset positions were used to create a new shifted, or registered, image offset from the original with any empty sections padded with pixels of value zero. This process was performed for all frames in the video sequence. Vessel Diameter Measurement and Feature Tracking To begin diameter measurement the diameter in the first video frame is determined from seed points defined by the user in the MATLAB interface. The Euclidean distance is calculated between the points as given by Equation 4. d 2 = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 (4) The frame by frame process of obtaining diameter measurements from a vascular video sequence given initial seed points is depicted in Figure 2. From the seed points declared on the n th frame an input sub-region was created on frame (n+1) and a base sub-region was created on the nth frame shown in Figure 2. The shifts between these regions were used to calculate movement of the points

5 indicating the boundary of the blood vessel with two-dimensional cross-correlation just as with image registration. Initial seed points were picked by the expert observer to be just on inside edge of the blood vessel at the intersection of the blue line and the black input rectangle. In other words the control point is located at the midpoint of the vertical edge of the square closest to the vessel. Other relative positions between the control points and the input rectangles are possible. Figure 2: Base regions (white) and input regions (black) of a video frame. Note that seed points in this image are placed outside of the lumen during testing. Typical results feature the seeds point at the outer most edge of the lumen. Seed points for frame (n+1) were calculated when the independent shifts were added to the n th frame seed points. From these new points the diameter for frame (n+1) was also calculated. In this was diameters were calculated for the entire video sequence according to Figure 3. Figure 3: Flow chart of feature tracking algorithm

6 Vessel diameter was calculated sequentially from the initial seed points provided that there was a reasonable peak correlation. The software was written that if the peak correlation amplitude was calculated to be less than 0.5 the user was notified of a poor correlation and the correlation offset was set to zero. In this event the seed points of the previous frame become those of the next frame unchanged. To validate the automated measurements gold standard expert manual measurements were obtained using ImageJ. The diameter measurement software was then run using the same initial seed points as the diameter points measured in the first frame of the expert manual measurements. Results Image registration of the video sequence, using the first image as the reference, produced correlation amplitudes of about 0.8 on average that declined slightly through the sequence. Frame 1 auto-correlated and the normalized cross correlation function in MATLAB, NORMXCORR2, provided it a correlation amplitude of zero. Likewise, frame zero is given a correlation amplitude of one by the same function. Figure 4: Correlation amplitudes for each video sequence frame performed with normalized cross-correlation

7 Automated vessel diameter measurements matched well to expert manual measurements using the same initial seed points. The average absolute error was 1.5 microns which, given the average diameter of the vessel is 35 microns, represents an error of roughly 5 percent. Correlation amplitudes for both control points are plotted against frame showing typically good correlations, close to unity, however with periods of poor correlation near the beginning and end of the sequence and corresponding to periods of increased absolute error. Figure 5: Automated and expert manual vessel diameter measurements, sub-region correlation amplitudes and the absolute difference between automated and expert manual diameter measurements Discussion Image Registration

8 Image registration using normalized cross-correlation produced seemingly low correlation amplitudes of approximately 0.8 and visually did not remove all of the tissue motion from the video sequence. The correlation amplitude declined slightly as the frame number increased. This may be due to each frame image differing slightly from the reference due to vessel dilation or contraction and background tissue motion. This may be a limitation of the normalized cross-correlation image registration method. Also the correlation coefficients of one and zero for the first two frames indicate demonstrate a possible error in the image registration implementation or the limitation of the NORMXCORR2 MATLAB function. These results indicates that a different method may provide superior image registration. It is assumed that using a better registration process will enable more accurate diameter measurements in the future. Discrete Fourier Transform (DFT) image registration may be a more robust method of registration [2]. It has been performed and has provided qualitatively better image registration but so far this registered sequence has not been used to perform diameter measurements in this study. Automated Diameter Measurements For some frames the region around Control Point 2, in the automated method, produced zero correlation amplitudes. The reason for this is unknown at this point but hypothesized to be an artefact of motion of the tissue in the video that was not sufficiently minimized by image registration. This video sequence was a portion of a longer sequence that featured a number of frames where the video was largely out of focus due to tissue response to a tetanic stimulus. It is desirable to be able to track diameters continuously before and after such an event. As a starting point this problem was ignored and the work focussed on the post-stimulus portion of the video sequence as this did feature most of the vessel dilation and subsequent relaxation to its resting diameter.

9 Initial seed points were picked by the expert observer to be just on inside edge of the blood vessel. The corresponding input rectangles were then positioned as described with the control point on the midpoint of the vertical edge facing the vessel. Note that positioning the input rectangle in this way may be suboptimal as some of the interior of the vessel will be inside of the input rectangle. Since the vascular blood is flowing, the image of this region is constantly changing and could contribute to spurious correlations or decrease correlation amplitudes. Alternatively, input rectangles could be positioned to have the control point at a vertex minimizing the area of the input rectangle overlapping the blood vessel. Applying these alternative approaches to handling control points should be explored in future work. Input regions were observed to drift into the blood vessel during some runs of the software. It is hypothesized that this is due to overlap of the region with the blood vessel causing correlations to areas further within the vessel. Input regions drifts were also observed along the vessel wall. To overcome these problems in the future we hope that modifying the position of the input patch to the diameter control point can minimize the overlap with the blood vessel and hence produce more stable positions of the input regions. All correlations were computed using a single video sequence and using only normalized cross correlation similarity metric. In the future it is desirable attempt automated diameter measurements on many different video sequence using varied imaging modalities. It is hypothesized that some similarity metrics may perform better across the board or at least for certain imaging modalities. A possible source of error includes any possible motion away or towards the camera by the tissue. Tissue motion towards the camera would have the effect of an apparent but erroneous change in

10 vessel diameter. It is an open question to quantify the significance of this effect and if it may be detected by analyzing size changes of static structures in the background tissue. In the future it is desirable expand the functionality of the software to be able to measure multiple vessels and to measure multiple a vessel in multiple regions of interest. If multiple measurements of a single vessel are performed some post-hoc removal of spurious results may be possible and could help to validate consistency of the results. Measuring changes in diameter of multiple vessels in a vascular bed may also be important for physiological studies. It has been shown that accurate automated diameter measurements are achievable from a video sequence of a blood vessel at one particular non-horizontal orientation within 5 percent accuracy. This builds on the work of Lee et al. However, to further generalize this result to vessels at any orientation testing of the software with further video sequences with vessels at multiple directions is required. Discrete periods with large absolute errors of about 6 microns (17 percent of typical diameter) were seen and are considered unsatisfactory. It will be necessary to attempt to minimize those errors potentially with the techniques previously mentioned (adjusted input rectangle positioning, other similarity metric, improved image registration, post-hoc measurement run selection). Conclusion The software was able to successfully stabilized tissue motion in sequences through image registration with reasonable correlation amplitudes. However it is believed that better registration can be achieved in the future.

11 The software is capable of making automated diameter measurements within a small degree of error when compared to expert manual measurements undesirable periods exhibiting large errors are observed. Some post-hoc analysis and selection of accurate results may be necessary to identify periods of poor measurements. Acknowledgements Dr. Graham Fraser Dr. Dwayne Jackson Nicole Novielli References [1] Lee, J., Jirapatnakul, A., Reeves, A., Crowe, W., Sarelius, I. Vessel Diameter Measurement from Intravital Microscopy. Annals of Biomedical Engineering, Vol. 37, No. 5, May 2009 (2009) p [2] Brown, L. G. A survey of image registration techniques. ACM Comput. Surv. 24(4): , 1992 [3] J. P. Lewis. Fast Normalized Cross-Correlation. Industrial Light & Magic, 1995 [3] J. P. Lewis, Fast Template Matching. Vision Interface, p , 1995