- Email: [email protected]
A pilot study using “ROPtool” to quantify plus disease in retinopathy of prematurity
Letters to the Editor A PILOT STUDY USING “ROPtool” TO QUANTIFY PLUS DISEASE IN RETINOPATHY OF PREMATURITY To the Editor: I have concerns about Wallace et al’s1 definition of tortuosity as the longer path taken by a blood vessel relative to a “smooth curve” that can be drawn by choosing points about every 40 pixels along the vessel path and then connecting the dots. To be sure, this approach is an improvement over Wallace’s first algorithm,2 which compared the length of the vessel path to the distance between the beginning and the end of the vessel in question (the so-called distance metric [DM]),3 which could lead to a falsely elevated measure of tortuosity in a gradually curving vessel. However, the authors’ current algorithm is still prone to error. Figure 1 shows several examples of vessel paths with tortuosity calculated according to Wallace’s algorithm using ImageJ.4 Figure 1A shows a vessel with a single sine-wave cycle followed by a straight line segment. Figure 1B shows a vessel with a single higher frequency sine-wave cycle of the same amplitude followed by a straight line segment. Figure 1C has two cycles of a sine-wave of the same frequency and amplitude as shown in Figure 1B. Figure 1D shows a lower frequency sine-wave of the same amplitude. When one compares the ratio of the vessel path to the smooth curve based on defining points 40 pixels apart along the vessel path, the descending order of tortuosity is: 1A ⬎⬎ 1D, 1D slightly greater than 1C, and 1C slightly greater than 1B. By contrast, my (and probably most people’s) visual perception of tortuosity would suggest that 1C ⬎ 1B ⬎ 1A ⬎ 1D. The error in measuring tortuosity resulted from choosing a sine wave (in Figure 1B and C) that has a peak-to-trough vessel length of roughly twice the 40 pixel distance chosen by the authors as the interval between defining points for their smooth curve. The resultant smooth curve approximated the higher frequency sinusoidal vessel paths in Figure 1B and C so closely that the algorithm failed to detect the high tortuosity. Bullitt et al3 have previously shown in a study of tortuosity of cerebral vasculature that the simple DM could be improved by multiplying DM by the number of inflection points along the vessel path to derive an inflection count metric (ICM) that more accurately reflects vessel tortuosity. However, the ICM was inaccurate in cases of vessels with coil configuration because these have no inflection points. The sum of the angles metric (SOAM) derived by measuring the angle between adjacent vectors along the vessel path, summing those angles, and normalizing by total vessel length seems to provide very good correlation with vessel tortuosity.3 Although the SOAM algorithm had trouble measuring the tortuosity of sine waves with very high ampli-
J AAPOS 2007;11:630-631. Published online October 29, 2007. Copyright © 2007 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/2007/$35.00 ⫹ 0
630
FIG 1. Different vessel paths ( black line) with tortuosity calculated according to Wallace’s algorithm as the ratio of length of vessel path to length of a “smooth curve” (red line) defined by points 40 pixels apart along the vessel path. (E) A potential alternative approach with a “smooth curve” based on the general direction of overall vessel pattern.
tudes (10, 20, and 40) combined with a higher frequency (3) as compared with the DM or ICM, it is doubtful that retinal vessels with such characteristics exist. One can also argue whether sine waves with such high amplitudes and high frequencies are in fact tortuous if they approximate a saw-tooth wave pattern with straight lines that abruptly change in direction at the peaks. The problem with the DM or variations thereof is that it runs counter to most observers’ intuitive sense of tortuosity as somehow related to curvature along a vessel path rather than the greater length of a tortuous vessel’s path.3,5 It is possible that some variation of the DM such as the smooth curve envisioned by the authors may yet be combined with SOAM. However, any new smooth curve algorithm would need to demonstrate greater generalizability to curves of varying dimensions and should probably not rely on specific pixel distances between defining points of a smooth curve that can be undermined by a tortuous vessel with just the right parameters. Perhaps a smooth curve such as shown in Figure 1E that traverses the general direction of the tortuous vessel would prove more useful.5 However, it remains to be seen whether such a smooth curve can be generated automatically and consistently for different vessels without operator input on the defining points of the smooth curve.
Journal of AAPOS
Volume 11 Number 6 / December 2007
Michael B. Yang, MD Abrahamson Pediatric Eye Institute Cincinnati Children’s Hospital Cincinnati, Ohio References 1. Wallace DK, Zhao Z, Freedman SF. A pilot study using “ROPtool” to quantify plus disease in retinopathy of prematurity. J AAPOS 2007; 11:381-7. 2. Wallace DK, Jomier J, Aylward SR, Landers MB. Computer-automated quantification of plus disease in retinopathy of prematurity. J AAPOS 2003;7:126-30. 3. Bullitt E, Gerig G, Pizer SM, Line W, Aylward SR. Measuring tortuosity of the intracerebral vasculature from MRA images. IEEE Trans Med Imaging 2003;22:1163-71. 4. Rasband WS, ImageJ. US National Institutes of Health, Bethesda, MD, http://rsb.info.nih.gov/ij/, 1997-2007. 5. Hart WE, Goldbaum M, Cote B, Kube P, Nelson MR. Measurement and classification of retinal vascular tortuosity. Int J Med Inform 1999;53:239-52. doi:10.1016/j.jaapos.2007.08.004
REPLY: To the Editor: We thank Dr. Yang for his interest in our work, and we are pleased to respond to the individual points he raises. First, he is concerned about our “definition of tortuosity as the longer path taken by a blood vessel relative to a smooth curve that can be drawn by choosing points about every 40 pixels along the vessel path and then connecting the dots.” We regret that we did not describe our technique in more detail in our article,1 because he has misinterpreted how our smooth curves were generated. They were not made by connecting “points” or “dots” along the vessel. Instead, smooth curves were generated by interpolating the points using a spline, which is a special function defined piecewise by polynomials. In other words, a spline is a polynomial curve that travels through a set of given points. Therefore, the links between points are not straight lines as illustrated in Dr. Yang’s Figure 1, and his calculations of the tortuosities that would result if our algorithm were applied to his sine-wave examples are incorrect. Second, he suggests that we use the sum of the angle metric instead of our tortuosity measure because it “seems to provide very good correlation with vessel tortuosity.” We chose our measure of tortuosity primarily because of its ability to detect clinically relevant tortuosity. Expert judgment of retinal blood vessel tortuosity is probably driven by small wiggles as opposed to large curves. Capowski et al2 showed that a numeric index based on the five highest tortuosity values of very short vessel segments was a sensitive indicator of tortuosity. We showed in this pilot study that our algorithm has excellent accuracy in comJ AAPOS 2007;11:631. Copyright © 2007 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/2007/$35.00 ⫹ 0
Journal of AAPOS
Letters to the Editor
631
parison to consensus of experienced examiners. Results of a much larger study comparing ROPtool to individual examiners will soon be published.3 Third, Dr. Yang suggests that his alternative approach illustrated in his Figure 1E may be an improvement over our method of calculating tortuosity. However, it is impossible to evaluate his method without any reference to the size of the vessel. (In our article, we stated that an average major vessel had four to five points along its length from which a smooth curve was generated.) If the segment shown in his Figure 1E is the entire length of a retinal blood vessel, then it is one that simply “meanders” and is not really very tortuous. In such a case, tortuosity would be grossly overestimated using the red line illustrated as a smooth curve comparison. If it is a short vessel segment (eg, two optic disk diameters in length), then it is indeed a very tortuous vessel, and it would be correctly measured as such using the red line illustrated as its comparison. In that case, ROPtool’s tortuosity algorithm would generate a very similar red line and would appropriately calculate a high tortuosity index. Finally, in the interest of keeping the methods section of our article succinct, we did not include details of a small study that we conducted prior to settling on the optimum space between points used for generating our smooth curves. In that study, one of us (ZZ) generated curves using three different distances between points along the vessels. Two of us (DKW and SFF), who were masked to these distances, independently chose the one smooth curve among three that best represented the path that a normal (nontortuous) vessel would take. Our consensus was that the best smooth curves were generated from points roughly 40 pixels apart, and these results were incorporated into our algorithm. As we strive to improve ROPtool, we plan to link a clinical parameter (such as optic nerve size) to the distance between points. This method will standardize the distance so that ROPtool will be able to analyze photographs with different magnifications and resolutions. Ultimately, we hope to develop an accurate, nearly automated, user-friendly program that will allow analysis of an image and determination of plus or preplus disease in 1 minute or less. David K. Wallace, MD, MPH Zheen Zhao, PhD Sharon F. Freedman, MD Duke University, Durham, North Carolina References 1. Wallace DK, Zhao Z, Freedman SF. A pilot study using “ROPtool” to quantify plus disease in retinopathy of prematurity. J AAPOS 2007; 11:381-7. 2. Capowski JJ, Kylstra JA, Freedman SF. A numeric index based on spatial frequency for the tortuosity of retinal vessels and its application to plus disease in retinopathy of prematurity. Retina 1995;15:490-500. 3. Wallace DK, Freedman SF, Zhao Z, Jung SH. Accuracy of “ROPTool” versus individual examiners in assessing retinal vascular tortuosity. Arch Ophthalmol in press 2007. doi:10.1016/j.jaapos.2007.09.003
J AAPOS 2007;11:630-631. Published online October 29, 2007. Copyright © 2007 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/2007/$35.00 ⫹ 0
630
FIG 1. Different vessel paths ( black line) with tortuosity calculated according to Wallace’s algorithm as the ratio of length of vessel path to length of a “smooth curve” (red line) defined by points 40 pixels apart along the vessel path. (E) A potential alternative approach with a “smooth curve” based on the general direction of overall vessel pattern.
tudes (10, 20, and 40) combined with a higher frequency (3) as compared with the DM or ICM, it is doubtful that retinal vessels with such characteristics exist. One can also argue whether sine waves with such high amplitudes and high frequencies are in fact tortuous if they approximate a saw-tooth wave pattern with straight lines that abruptly change in direction at the peaks. The problem with the DM or variations thereof is that it runs counter to most observers’ intuitive sense of tortuosity as somehow related to curvature along a vessel path rather than the greater length of a tortuous vessel’s path.3,5 It is possible that some variation of the DM such as the smooth curve envisioned by the authors may yet be combined with SOAM. However, any new smooth curve algorithm would need to demonstrate greater generalizability to curves of varying dimensions and should probably not rely on specific pixel distances between defining points of a smooth curve that can be undermined by a tortuous vessel with just the right parameters. Perhaps a smooth curve such as shown in Figure 1E that traverses the general direction of the tortuous vessel would prove more useful.5 However, it remains to be seen whether such a smooth curve can be generated automatically and consistently for different vessels without operator input on the defining points of the smooth curve.
Journal of AAPOS
Volume 11 Number 6 / December 2007
Michael B. Yang, MD Abrahamson Pediatric Eye Institute Cincinnati Children’s Hospital Cincinnati, Ohio References 1. Wallace DK, Zhao Z, Freedman SF. A pilot study using “ROPtool” to quantify plus disease in retinopathy of prematurity. J AAPOS 2007; 11:381-7. 2. Wallace DK, Jomier J, Aylward SR, Landers MB. Computer-automated quantification of plus disease in retinopathy of prematurity. J AAPOS 2003;7:126-30. 3. Bullitt E, Gerig G, Pizer SM, Line W, Aylward SR. Measuring tortuosity of the intracerebral vasculature from MRA images. IEEE Trans Med Imaging 2003;22:1163-71. 4. Rasband WS, ImageJ. US National Institutes of Health, Bethesda, MD, http://rsb.info.nih.gov/ij/, 1997-2007. 5. Hart WE, Goldbaum M, Cote B, Kube P, Nelson MR. Measurement and classification of retinal vascular tortuosity. Int J Med Inform 1999;53:239-52. doi:10.1016/j.jaapos.2007.08.004
REPLY: To the Editor: We thank Dr. Yang for his interest in our work, and we are pleased to respond to the individual points he raises. First, he is concerned about our “definition of tortuosity as the longer path taken by a blood vessel relative to a smooth curve that can be drawn by choosing points about every 40 pixels along the vessel path and then connecting the dots.” We regret that we did not describe our technique in more detail in our article,1 because he has misinterpreted how our smooth curves were generated. They were not made by connecting “points” or “dots” along the vessel. Instead, smooth curves were generated by interpolating the points using a spline, which is a special function defined piecewise by polynomials. In other words, a spline is a polynomial curve that travels through a set of given points. Therefore, the links between points are not straight lines as illustrated in Dr. Yang’s Figure 1, and his calculations of the tortuosities that would result if our algorithm were applied to his sine-wave examples are incorrect. Second, he suggests that we use the sum of the angle metric instead of our tortuosity measure because it “seems to provide very good correlation with vessel tortuosity.” We chose our measure of tortuosity primarily because of its ability to detect clinically relevant tortuosity. Expert judgment of retinal blood vessel tortuosity is probably driven by small wiggles as opposed to large curves. Capowski et al2 showed that a numeric index based on the five highest tortuosity values of very short vessel segments was a sensitive indicator of tortuosity. We showed in this pilot study that our algorithm has excellent accuracy in comJ AAPOS 2007;11:631. Copyright © 2007 by the American Association for Pediatric Ophthalmology and Strabismus. 1091-8531/2007/$35.00 ⫹ 0
Journal of AAPOS
Letters to the Editor
631
parison to consensus of experienced examiners. Results of a much larger study comparing ROPtool to individual examiners will soon be published.3 Third, Dr. Yang suggests that his alternative approach illustrated in his Figure 1E may be an improvement over our method of calculating tortuosity. However, it is impossible to evaluate his method without any reference to the size of the vessel. (In our article, we stated that an average major vessel had four to five points along its length from which a smooth curve was generated.) If the segment shown in his Figure 1E is the entire length of a retinal blood vessel, then it is one that simply “meanders” and is not really very tortuous. In such a case, tortuosity would be grossly overestimated using the red line illustrated as a smooth curve comparison. If it is a short vessel segment (eg, two optic disk diameters in length), then it is indeed a very tortuous vessel, and it would be correctly measured as such using the red line illustrated as its comparison. In that case, ROPtool’s tortuosity algorithm would generate a very similar red line and would appropriately calculate a high tortuosity index. Finally, in the interest of keeping the methods section of our article succinct, we did not include details of a small study that we conducted prior to settling on the optimum space between points used for generating our smooth curves. In that study, one of us (ZZ) generated curves using three different distances between points along the vessels. Two of us (DKW and SFF), who were masked to these distances, independently chose the one smooth curve among three that best represented the path that a normal (nontortuous) vessel would take. Our consensus was that the best smooth curves were generated from points roughly 40 pixels apart, and these results were incorporated into our algorithm. As we strive to improve ROPtool, we plan to link a clinical parameter (such as optic nerve size) to the distance between points. This method will standardize the distance so that ROPtool will be able to analyze photographs with different magnifications and resolutions. Ultimately, we hope to develop an accurate, nearly automated, user-friendly program that will allow analysis of an image and determination of plus or preplus disease in 1 minute or less. David K. Wallace, MD, MPH Zheen Zhao, PhD Sharon F. Freedman, MD Duke University, Durham, North Carolina References 1. Wallace DK, Zhao Z, Freedman SF. A pilot study using “ROPtool” to quantify plus disease in retinopathy of prematurity. J AAPOS 2007; 11:381-7. 2. Capowski JJ, Kylstra JA, Freedman SF. A numeric index based on spatial frequency for the tortuosity of retinal vessels and its application to plus disease in retinopathy of prematurity. Retina 1995;15:490-500. 3. Wallace DK, Freedman SF, Zhao Z, Jung SH. Accuracy of “ROPTool” versus individual examiners in assessing retinal vascular tortuosity. Arch Ophthalmol in press 2007. doi:10.1016/j.jaapos.2007.09.003