Abstract

Tortuosity is an important geometric vessel parameter and among the first microvascular alterations observed in various retinopathies. In the current study, a quantitative vessel tortuosity index (VTI) based on a combination of local and global centerline features is presented. Performance of VTI and previously established tortuosity indices were compared against human observers’ evaluation of tortuosity. An image-processing pipeline was developed for application of VTI in retinal vessels imaged by optical coherence tomography angiography (OCTA) in perifoveal (6 mm × 6 mm) and parafoveal (3 mm × 3 mm) regions centered on the fovea. Forty-one subjects (12 healthy control (NC) and 29 sickle cell retinopathy (SCR)) and 10 subjects (5 NC and 5 SCR) were imaged in the perifoveal and parafoveal regions, respectively. The relationship between VTI and age was examined in the perifoveal regions in NC subjects. VTI was measured from the OCTA images and compared between NC and SCR subjects using generalized least square regression with and without adjusting for age and race. VTI was found to correlate better than the 4 previous indices with performance of human observers. In the perifoveal region, a significant correlation was observed between VTI and age (r = −0.4, P<0.001, N = 12). VTI was higher in SCR than NC subjects in perifoveal and parafoveal regions (P≤0.001). The results demonstrate that the proposed method shows promise for detection of increased tortuosity in vessels due to retinal disorders.

© 2017 Optical Society of America

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2017 (1)

2016 (6)

K. V. Chalam and K. Sambhav, “Optical coherence tomography angiography in retinal diseases,” J. Ophthalmic Vis. Res. 11(1), 84–92 (2016).
[Crossref] [PubMed]

W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

R. Annunziata, A. Kheirkhah, S. Aggarwal, P. Hamrah, and E. Trucco, “A fully automated tortuosity quantification system with application to corneal nerve fibres in confocal microscopy images,” Med. Image Anal. 32, 216–232 (2016).
[Crossref] [PubMed]

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
[Crossref] [PubMed]

M. Aghamohamadian-Sharbaf, H. R. Pourreza, and T. Banaee, “A novel curvature-based algorithm for automatic grading of retinal blood vessel tortuosity,” IEEE J. Biomed. Health Inform. 20(2), 586–595 (2016).
[Crossref] [PubMed]

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
[Crossref] [PubMed]

2015 (4)

R. F. Spaide, J. M. Klancnik, and M. J. Cooney, “Retinal vascular layers imaged by fluorescein angiography and optical coherence tomography angiography,” JAMA Ophthalmol. 133(1), 45–50 (2015).
[Crossref] [PubMed]

C. J. Sanfilippo, M. A. Klufas, D. Sarraf, and I. Tsui, “Optical coherence tomography angiography of sickle cell maculopathy,” Retin. Cases Brief Rep. 9(4), 360–362 (2015).
[PubMed]

A. Nagiel, S. R. Sadda, and D. Sarraf, “A promising future for optical coherence tomography angiography,” JAMA Ophthalmol. 133(6), 629–630 (2015).
[Crossref] [PubMed]

I. C. Han, M. Tadarati, and A. W. Scott, “Macular vascular abnormalities identified by optical coherence tomographic angiography in patients with sickle cell disease,” JAMA Ophthalmol. 133(11), 1337–1340 (2015).
[Crossref] [PubMed]

2013 (3)

A. A. Kalitzeos, G. Y. Lip, and R. Heitmar, “Retinal vessel tortuosity measures and their applications,” Exp. Eye Res. 106, 40–46 (2013).
[Crossref] [PubMed]

E. Bribiesca, “A measure of tortuosity based on chain coding,” Pattern Recognit. 46(3), 716–724 (2013).
[Crossref]

M. Tavakoli, R. P. Shahri, H. Pourreza, A. Mehdizadeh, T. Banaee, and M. H. B. Toosi, “A complementary method for automated detection of microaneurysms in fluorescein angiography fundus images to assess diabetic retinopathy,” Pattern Recognit. 46(10), 2740–2753 (2013).
[Crossref]

2012 (3)

A. Bhuiyan, B. Nath, K. Ramamohanarao, R. Kawasaki, and T. Y. Wong, “Automated analysis of retinal vascular tortuosity on color retinal images,” J. Med. Syst. 36(2), 689–697 (2012).
[Crossref] [PubMed]

H. Lei and G. E. Karniadakis, “Quantifying the rheological and hemodynamic characteristics of sickle cell anemia,” Biophys. J. 102(2), 185–194 (2012).
[Crossref] [PubMed]

Y. Jia, O. Tan, J. Tokayer, B. Potsaid, Y. Wang, J. J. Liu, M. F. Kraus, H. Subhash, J. G. Fujimoto, J. Hornegger, and D. Huang, “Split-spectrum amplitude-decorrelation angiography with optical coherence tomography,” Opt. Express 20(4), 4710–4725 (2012).
[Crossref] [PubMed]

2011 (5)

Q. V. Hoang, F. Y. Chau, M. Shahidi, and J. I. Lim, “Central macular splaying and outer retinal thinning in asymptomatic sickle cell patients by spectral-domain optical coherence tomography,” Am. J. Ophthalmol. 151, 990–994 (2011).

R. K. Murthy, S. Grover, and K. V. Chalam, “Temporal macular thinning on spectral-domain optical coherence tomography in proliferative sickle cell retinopathy,” Arch. Ophthalmol. 129(2), 247–249 (2011).
[Crossref] [PubMed]

M. B. Sasongko, T. Y. Wong, T. T. Nguyen, C. Y. Cheung, J. E. Shaw, and J. J. Wang, “Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy,” Diabetologia 54(9), 2409–2416 (2011).
[Crossref] [PubMed]

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
[Crossref] [PubMed]

D. Calvo, M. Ortega, M. G. Penedo, and J. Rouco, “Automatic detection and characterisation of retinal vessel tree bifurcations and crossovers in eye fundus images,” Comput. Methods Programs Biomed. 103(1), 28–38 (2011).
[Crossref] [PubMed]

2010 (1)

A. O. Fadugbagbe, R. Q. Gurgel, C. Q. Mendonça, R. Cipolotti, A. M. dos Santos, and L. E. Cuevas, “Ocular manifestations of sickle cell disease,” Ann. Trop. Paediatr. 30(1), 19–26 (2010).
[Crossref] [PubMed]

2008 (1)

E. Grisan, M. Foracchia, and A. Ruggeri, “A novel method for the automatic grading of retinal vessel tortuosity,” IEEE Trans. Med. Imaging 27(3), 310–319 (2008).
[Crossref] [PubMed]

2007 (1)

S. Koreen, R. Gelman, M. E. Martinez-Perez, L. Jiang, A. M. Berrocal, D. J. Hess, J. T. Flynn, and M. F. Chiang, “Evaluation of a computer-based system for plus disease diagnosis in retinopathy of prematurity,” Ophthalmology 114(12), e59–e67 (2007).
[Crossref] [PubMed]

2006 (1)

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

2005 (2)

R. Gelman, M. E. Martinez-Perez, D. K. Vanderveen, A. Moskowitz, and A. B. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. Vis. Sci. 46(12), 4734–4738 (2005).
[Crossref] [PubMed]

G. G. Emerson and G. A. Lutty, “Effects of sickle cell disease on the eye: clinical features and treatment,” Hematol. Oncol. Clin. North Am. 19(5), 957–973 (2005).
[Crossref] [PubMed]

2003 (1)

E. Bullitt, G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward, “Measuring tortuosity of the intracerebral vasculature from MRA images,” IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003).
[Crossref] [PubMed]

2001 (1)

J. S. Wolffsohn, G. A. Napper, S. M. Ho, A. Jaworski, and T. L. Pollard, “Improving the description of the retinal vasculature and patient history taking for monitoring systemic hypertension,” Ophthalmic Physiol. Opt. 21(6), 441–449 (2001).
[Crossref] [PubMed]

2000 (2)

G. Dougherty and J. Varro, “A quantitative index for the measurement of the tortuosity of blood vessels,” Med. Eng. Phys. 22(8), 567–574 (2000).
[Crossref] [PubMed]

C. U. Eze, R. Gupta, and D. L. Newman, “A comparison of quantitative measures of arterial tortuosity using sine wave simulations and 3D wire models,” Phys. Med. Biol. 45(9), 2593–2599 (2000).
[Crossref] [PubMed]

1999 (1)

W. E. Hart, M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson, “Measurement and classification of retinal vascular tortuosity,” Int. J. Med. Inform. 53(2-3), 239–252 (1999).
[Crossref] [PubMed]

1998 (1)

M. Matsumoto and T. Nishimura, “Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[Crossref]

1993 (1)

O. Smedby, N. Högman, S. Nilsson, U. Erikson, A. G. Olsson, and G. Walldius, “Two-dimensional tortuosity of the superficial femoral artery in early atherosclerosis,” J. Vasc. Res. 30(4), 181–191 (1993).
[Crossref] [PubMed]

1990 (1)

C. M. Wenn and D. L. Newman, “Arterial tortuosity,” Australas. Phys. Eng. Sci. Med. 13(2), 67–70 (1990).
[PubMed]

1982 (1)

D. Bracher, “Changes in peripapillary tortuosity of the central retinal arteries in newborns. A phenomenon whose underlying mechanisms need clarification,” Graefes Arch. Clin. Exp. Ophthalmol. 218(4), 211–217 (1982).
[Crossref] [PubMed]

1966 (2)

A. Kagan, E. Aureli, and J. Dobree, “A note on signs in the fundus oculi and arterial hypertension: conventional assessment and significance,” Bull. World Health Organ. 34(6), 955–960 (1966).
[PubMed]

R. B. Welch and M. F. Goldberg, “Sickle-cell hemoglobin and its relation to fundus abnormality,” Arch. Ophthalmol. 75(3), 353–362 (1966).
[Crossref] [PubMed]

Aggarwal, S.

R. Annunziata, A. Kheirkhah, S. Aggarwal, P. Hamrah, and E. Trucco, “A fully automated tortuosity quantification system with application to corneal nerve fibres in confocal microscopy images,” Med. Image Anal. 32, 216–232 (2016).
[Crossref] [PubMed]

Aghamohamadian-Sharbaf, M.

M. Aghamohamadian-Sharbaf, H. R. Pourreza, and T. Banaee, “A novel curvature-based algorithm for automatic grading of retinal blood vessel tortuosity,” IEEE J. Biomed. Health Inform. 20(2), 586–595 (2016).
[Crossref] [PubMed]

Alam, M.

Annunziata, R.

R. Annunziata, A. Kheirkhah, S. Aggarwal, P. Hamrah, and E. Trucco, “A fully automated tortuosity quantification system with application to corneal nerve fibres in confocal microscopy images,” Med. Image Anal. 32, 216–232 (2016).
[Crossref] [PubMed]

Aureli, E.

A. Kagan, E. Aureli, and J. Dobree, “A note on signs in the fundus oculi and arterial hypertension: conventional assessment and significance,” Bull. World Health Organ. 34(6), 955–960 (1966).
[PubMed]

Aylward, S. R.

E. Bullitt, G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward, “Measuring tortuosity of the intracerebral vasculature from MRA images,” IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003).
[Crossref] [PubMed]

Banaee, T.

M. Aghamohamadian-Sharbaf, H. R. Pourreza, and T. Banaee, “A novel curvature-based algorithm for automatic grading of retinal blood vessel tortuosity,” IEEE J. Biomed. Health Inform. 20(2), 586–595 (2016).
[Crossref] [PubMed]

M. Tavakoli, R. P. Shahri, H. Pourreza, A. Mehdizadeh, T. Banaee, and M. H. B. Toosi, “A complementary method for automated detection of microaneurysms in fluorescein angiography fundus images to assess diabetic retinopathy,” Pattern Recognit. 46(10), 2740–2753 (2013).
[Crossref]

Beevers, G.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

Berrocal, A. M.

S. Koreen, R. Gelman, M. E. Martinez-Perez, L. Jiang, A. M. Berrocal, D. J. Hess, J. T. Flynn, and M. F. Chiang, “Evaluation of a computer-based system for plus disease diagnosis in retinopathy of prematurity,” Ophthalmology 114(12), e59–e67 (2007).
[Crossref] [PubMed]

Bhuiyan, A.

A. Bhuiyan, B. Nath, K. Ramamohanarao, R. Kawasaki, and T. Y. Wong, “Automated analysis of retinal vascular tortuosity on color retinal images,” J. Med. Syst. 36(2), 689–697 (2012).
[Crossref] [PubMed]

Bracher, D.

D. Bracher, “Changes in peripapillary tortuosity of the central retinal arteries in newborns. A phenomenon whose underlying mechanisms need clarification,” Graefes Arch. Clin. Exp. Ophthalmol. 218(4), 211–217 (1982).
[Crossref] [PubMed]

Bribiesca, E.

E. Bribiesca, “A measure of tortuosity based on chain coding,” Pattern Recognit. 46(3), 716–724 (2013).
[Crossref]

Bullitt, E.

E. Bullitt, G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward, “Measuring tortuosity of the intracerebral vasculature from MRA images,” IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003).
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Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
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A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
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W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

Chau, F. Y.

Q. V. Hoang, F. Y. Chau, M. Shahidi, and J. I. Lim, “Central macular splaying and outer retinal thinning in asymptomatic sickle cell patients by spectral-domain optical coherence tomography,” Am. J. Ophthalmol. 151, 990–994 (2011).

Chen, X.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
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C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
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W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

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R. F. Spaide, J. M. Klancnik, and M. J. Cooney, “Retinal vascular layers imaged by fluorescein angiography and optical coherence tomography angiography,” JAMA Ophthalmol. 133(1), 45–50 (2015).
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Côté, B.

W. E. Hart, M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson, “Measurement and classification of retinal vascular tortuosity,” Int. J. Med. Inform. 53(2-3), 239–252 (1999).
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A. O. Fadugbagbe, R. Q. Gurgel, C. Q. Mendonça, R. Cipolotti, A. M. dos Santos, and L. E. Cuevas, “Ocular manifestations of sickle cell disease,” Ann. Trop. Paediatr. 30(1), 19–26 (2010).
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S. Koreen, R. Gelman, M. E. Martinez-Perez, L. Jiang, A. M. Berrocal, D. J. Hess, J. T. Flynn, and M. F. Chiang, “Evaluation of a computer-based system for plus disease diagnosis in retinopathy of prematurity,” Ophthalmology 114(12), e59–e67 (2007).
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E. Grisan, M. Foracchia, and A. Ruggeri, “A novel method for the automatic grading of retinal vessel tortuosity,” IEEE Trans. Med. Imaging 27(3), 310–319 (2008).
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Fulton, A. B.

R. Gelman, M. E. Martinez-Perez, D. K. Vanderveen, A. Moskowitz, and A. B. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. Vis. Sci. 46(12), 4734–4738 (2005).
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S. Koreen, R. Gelman, M. E. Martinez-Perez, L. Jiang, A. M. Berrocal, D. J. Hess, J. T. Flynn, and M. F. Chiang, “Evaluation of a computer-based system for plus disease diagnosis in retinopathy of prematurity,” Ophthalmology 114(12), e59–e67 (2007).
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R. Gelman, M. E. Martinez-Perez, D. K. Vanderveen, A. Moskowitz, and A. B. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. Vis. Sci. 46(12), 4734–4738 (2005).
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E. Bullitt, G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward, “Measuring tortuosity of the intracerebral vasculature from MRA images,” IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003).
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Ghasemi Falavarjani, K.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
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W. E. Hart, M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson, “Measurement and classification of retinal vascular tortuosity,” Int. J. Med. Inform. 53(2-3), 239–252 (1999).
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E. Grisan, M. Foracchia, and A. Ruggeri, “A novel method for the automatic grading of retinal vessel tortuosity,” IEEE Trans. Med. Imaging 27(3), 310–319 (2008).
[Crossref] [PubMed]

Grover, S.

R. K. Murthy, S. Grover, and K. V. Chalam, “Temporal macular thinning on spectral-domain optical coherence tomography in proliferative sickle cell retinopathy,” Arch. Ophthalmol. 129(2), 247–249 (2011).
[Crossref] [PubMed]

Gupta, R.

C. U. Eze, R. Gupta, and D. L. Newman, “A comparison of quantitative measures of arterial tortuosity using sine wave simulations and 3D wire models,” Phys. Med. Biol. 45(9), 2593–2599 (2000).
[Crossref] [PubMed]

Gurgel, R. Q.

A. O. Fadugbagbe, R. Q. Gurgel, C. Q. Mendonça, R. Cipolotti, A. M. dos Santos, and L. E. Cuevas, “Ocular manifestations of sickle cell disease,” Ann. Trop. Paediatr. 30(1), 19–26 (2010).
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Hamrah, P.

R. Annunziata, A. Kheirkhah, S. Aggarwal, P. Hamrah, and E. Trucco, “A fully automated tortuosity quantification system with application to corneal nerve fibres in confocal microscopy images,” Med. Image Anal. 32, 216–232 (2016).
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K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
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I. C. Han, M. Tadarati, and A. W. Scott, “Macular vascular abnormalities identified by optical coherence tomographic angiography in patients with sickle cell disease,” JAMA Ophthalmol. 133(11), 1337–1340 (2015).
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W. E. Hart, M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson, “Measurement and classification of retinal vascular tortuosity,” Int. J. Med. Inform. 53(2-3), 239–252 (1999).
[Crossref] [PubMed]

W. E. Hart, M. Goldbaum, B. Cote, P. Kube, and M. R. Nelson, “Automated measurement of retinal vascular tortuosity,” in Proceedings of the AMIA Annual Fall Symposium, (American Medical Informatics Association, 1997), 459.

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A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
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A. A. Kalitzeos, G. Y. Lip, and R. Heitmar, “Retinal vessel tortuosity measures and their applications,” Exp. Eye Res. 106, 40–46 (2013).
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Hess, D. J.

S. Koreen, R. Gelman, M. E. Martinez-Perez, L. Jiang, A. M. Berrocal, D. J. Hess, J. T. Flynn, and M. F. Chiang, “Evaluation of a computer-based system for plus disease diagnosis in retinopathy of prematurity,” Ophthalmology 114(12), e59–e67 (2007).
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J. S. Wolffsohn, G. A. Napper, S. M. Ho, A. Jaworski, and T. L. Pollard, “Improving the description of the retinal vasculature and patient history taking for monitoring systemic hypertension,” Ophthalmic Physiol. Opt. 21(6), 441–449 (2001).
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Q. V. Hoang, F. Y. Chau, M. Shahidi, and J. I. Lim, “Central macular splaying and outer retinal thinning in asymptomatic sickle cell patients by spectral-domain optical coherence tomography,” Am. J. Ophthalmol. 151, 990–994 (2011).

Högman, N.

O. Smedby, N. Högman, S. Nilsson, U. Erikson, A. G. Olsson, and G. Walldius, “Two-dimensional tortuosity of the superficial femoral artery in early atherosclerosis,” J. Vasc. Res. 30(4), 181–191 (1993).
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Hornegger, J.

Hsu, W.

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
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Huang, D.

Hubschman, J.-P.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
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A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
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Jabbar, A.-S.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
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Jaworski, A.

J. S. Wolffsohn, G. A. Napper, S. M. Ho, A. Jaworski, and T. L. Pollard, “Improving the description of the retinal vasculature and patient history taking for monitoring systemic hypertension,” Ophthalmic Physiol. Opt. 21(6), 441–449 (2001).
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Jia, Y.

Jiang, L.

S. Koreen, R. Gelman, M. E. Martinez-Perez, L. Jiang, A. M. Berrocal, D. J. Hess, J. T. Flynn, and M. F. Chiang, “Evaluation of a computer-based system for plus disease diagnosis in retinopathy of prematurity,” Ophthalmology 114(12), e59–e67 (2007).
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Jonas, J. B.

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
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A. Kagan, E. Aureli, and J. Dobree, “A note on signs in the fundus oculi and arterial hypertension: conventional assessment and significance,” Bull. World Health Organ. 34(6), 955–960 (1966).
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A. A. Kalitzeos, G. Y. Lip, and R. Heitmar, “Retinal vessel tortuosity measures and their applications,” Exp. Eye Res. 106, 40–46 (2013).
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Karniadakis, G. E.

H. Lei and G. E. Karniadakis, “Quantifying the rheological and hemodynamic characteristics of sickle cell anemia,” Biophys. J. 102(2), 185–194 (2012).
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A. Bhuiyan, B. Nath, K. Ramamohanarao, R. Kawasaki, and T. Y. Wong, “Automated analysis of retinal vascular tortuosity on color retinal images,” J. Med. Syst. 36(2), 689–697 (2012).
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R. Annunziata, A. Kheirkhah, S. Aggarwal, P. Hamrah, and E. Trucco, “A fully automated tortuosity quantification system with application to corneal nerve fibres in confocal microscopy images,” Med. Image Anal. 32, 216–232 (2016).
[Crossref] [PubMed]

Klancnik, J. M.

R. F. Spaide, J. M. Klancnik, and M. J. Cooney, “Retinal vascular layers imaged by fluorescein angiography and optical coherence tomography angiography,” JAMA Ophthalmol. 133(1), 45–50 (2015).
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Klein, R.

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
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K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
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C. J. Sanfilippo, M. A. Klufas, D. Sarraf, and I. Tsui, “Optical coherence tomography angiography of sickle cell maculopathy,” Retin. Cases Brief Rep. 9(4), 360–362 (2015).
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Kube, P.

W. E. Hart, M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson, “Measurement and classification of retinal vascular tortuosity,” Int. J. Med. Inform. 53(2-3), 239–252 (1999).
[Crossref] [PubMed]

W. E. Hart, M. Goldbaum, B. Cote, P. Kube, and M. R. Nelson, “Automated measurement of retinal vascular tortuosity,” in Proceedings of the AMIA Annual Fall Symposium, (American Medical Informatics Association, 1997), 459.

Lau, Q. P.

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
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C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
[Crossref] [PubMed]

Lei, H.

H. Lei and G. E. Karniadakis, “Quantifying the rheological and hemodynamic characteristics of sickle cell anemia,” Biophys. J. 102(2), 185–194 (2012).
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M. Alam, D. Thapa, J. I. Lim, D. Cao, and X. Yao, “Quantitative characteristics of sickle cell retinopathy in optical coherence tomography angiography,” Biomed. Opt. Express 8(3), 1741–1753 (2017).
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Lin, W.

E. Bullitt, G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward, “Measuring tortuosity of the intracerebral vasculature from MRA images,” IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003).
[Crossref] [PubMed]

Lip, G. Y.

A. A. Kalitzeos, G. Y. Lip, and R. Heitmar, “Retinal vessel tortuosity measures and their applications,” Exp. Eye Res. 106, 40–46 (2013).
[Crossref] [PubMed]

Liu, J. J.

Lutty, G. A.

G. G. Emerson and G. A. Lutty, “Effects of sickle cell disease on the eye: clinical features and treatment,” Hematol. Oncol. Clin. North Am. 19(5), 957–973 (2005).
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A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
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Martinez-Perez, M. E.

S. Koreen, R. Gelman, M. E. Martinez-Perez, L. Jiang, A. M. Berrocal, D. J. Hess, J. T. Flynn, and M. F. Chiang, “Evaluation of a computer-based system for plus disease diagnosis in retinopathy of prematurity,” Ophthalmology 114(12), e59–e67 (2007).
[Crossref] [PubMed]

R. Gelman, M. E. Martinez-Perez, D. K. Vanderveen, A. Moskowitz, and A. B. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. Vis. Sci. 46(12), 4734–4738 (2005).
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A. O. Fadugbagbe, R. Q. Gurgel, C. Q. Mendonça, R. Cipolotti, A. M. dos Santos, and L. E. Cuevas, “Ocular manifestations of sickle cell disease,” Ann. Trop. Paediatr. 30(1), 19–26 (2010).
[Crossref] [PubMed]

Miere, A.

W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

Minvielle, W.

W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

Mistry, P. D.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

Mitchell, P.

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
[Crossref] [PubMed]

Moskowitz, A.

R. Gelman, M. E. Martinez-Perez, D. K. Vanderveen, A. Moskowitz, and A. B. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. Vis. Sci. 46(12), 4734–4738 (2005).
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Murthy, R. K.

R. K. Murthy, S. Grover, and K. V. Chalam, “Temporal macular thinning on spectral-domain optical coherence tomography in proliferative sickle cell retinopathy,” Arch. Ophthalmol. 129(2), 247–249 (2011).
[Crossref] [PubMed]

Nagiel, A.

A. Nagiel, S. R. Sadda, and D. Sarraf, “A promising future for optical coherence tomography angiography,” JAMA Ophthalmol. 133(6), 629–630 (2015).
[Crossref] [PubMed]

Napper, G. A.

J. S. Wolffsohn, G. A. Napper, S. M. Ho, A. Jaworski, and T. L. Pollard, “Improving the description of the retinal vasculature and patient history taking for monitoring systemic hypertension,” Ophthalmic Physiol. Opt. 21(6), 441–449 (2001).
[Crossref] [PubMed]

Nath, B.

A. Bhuiyan, B. Nath, K. Ramamohanarao, R. Kawasaki, and T. Y. Wong, “Automated analysis of retinal vascular tortuosity on color retinal images,” J. Med. Syst. 36(2), 689–697 (2012).
[Crossref] [PubMed]

Nelson, M. R.

W. E. Hart, M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson, “Measurement and classification of retinal vascular tortuosity,” Int. J. Med. Inform. 53(2-3), 239–252 (1999).
[Crossref] [PubMed]

W. E. Hart, M. Goldbaum, B. Cote, P. Kube, and M. R. Nelson, “Automated measurement of retinal vascular tortuosity,” in Proceedings of the AMIA Annual Fall Symposium, (American Medical Informatics Association, 1997), 459.

Newman, D. L.

C. U. Eze, R. Gupta, and D. L. Newman, “A comparison of quantitative measures of arterial tortuosity using sine wave simulations and 3D wire models,” Phys. Med. Biol. 45(9), 2593–2599 (2000).
[Crossref] [PubMed]

C. M. Wenn and D. L. Newman, “Arterial tortuosity,” Australas. Phys. Eng. Sci. Med. 13(2), 67–70 (1990).
[PubMed]

Nguyen, T. T.

M. B. Sasongko, T. Y. Wong, T. T. Nguyen, C. Y. Cheung, J. E. Shaw, and J. J. Wang, “Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy,” Diabetologia 54(9), 2409–2416 (2011).
[Crossref] [PubMed]

Nilsson, S.

O. Smedby, N. Högman, S. Nilsson, U. Erikson, A. G. Olsson, and G. Walldius, “Two-dimensional tortuosity of the superficial femoral artery in early atherosclerosis,” J. Vasc. Res. 30(4), 181–191 (1993).
[Crossref] [PubMed]

Nishimura, T.

M. Matsumoto and T. Nishimura, “Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[Crossref]

Olsson, A. G.

O. Smedby, N. Högman, S. Nilsson, U. Erikson, A. G. Olsson, and G. Walldius, “Two-dimensional tortuosity of the superficial femoral artery in early atherosclerosis,” J. Vasc. Res. 30(4), 181–191 (1993).
[Crossref] [PubMed]

Ortega, M.

D. Calvo, M. Ortega, M. G. Penedo, and J. Rouco, “Automatic detection and characterisation of retinal vessel tree bifurcations and crossovers in eye fundus images,” Comput. Methods Programs Biomed. 103(1), 28–38 (2011).
[Crossref] [PubMed]

Parker, K. H.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

Pedrinelli, R.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

Penedo, M. G.

D. Calvo, M. Ortega, M. G. Penedo, and J. Rouco, “Automatic detection and characterisation of retinal vessel tree bifurcations and crossovers in eye fundus images,” Comput. Methods Programs Biomed. 103(1), 28–38 (2011).
[Crossref] [PubMed]

Pizer, S. M.

E. Bullitt, G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward, “Measuring tortuosity of the intracerebral vasculature from MRA images,” IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003).
[Crossref] [PubMed]

Pollard, T. L.

J. S. Wolffsohn, G. A. Napper, S. M. Ho, A. Jaworski, and T. L. Pollard, “Improving the description of the retinal vasculature and patient history taking for monitoring systemic hypertension,” Ophthalmic Physiol. Opt. 21(6), 441–449 (2001).
[Crossref] [PubMed]

Potsaid, B.

Pourreza, H.

M. Tavakoli, R. P. Shahri, H. Pourreza, A. Mehdizadeh, T. Banaee, and M. H. B. Toosi, “A complementary method for automated detection of microaneurysms in fluorescein angiography fundus images to assess diabetic retinopathy,” Pattern Recognit. 46(10), 2740–2753 (2013).
[Crossref]

Pourreza, H. R.

M. Aghamohamadian-Sharbaf, H. R. Pourreza, and T. Banaee, “A novel curvature-based algorithm for automatic grading of retinal blood vessel tortuosity,” IEEE J. Biomed. Health Inform. 20(2), 586–595 (2016).
[Crossref] [PubMed]

Ramamohanarao, K.

A. Bhuiyan, B. Nath, K. Ramamohanarao, R. Kawasaki, and T. Y. Wong, “Automated analysis of retinal vascular tortuosity on color retinal images,” J. Med. Syst. 36(2), 689–697 (2012).
[Crossref] [PubMed]

Rouco, J.

D. Calvo, M. Ortega, M. G. Penedo, and J. Rouco, “Automatic detection and characterisation of retinal vessel tree bifurcations and crossovers in eye fundus images,” Comput. Methods Programs Biomed. 103(1), 28–38 (2011).
[Crossref] [PubMed]

Ruggeri, A.

E. Grisan, M. Foracchia, and A. Ruggeri, “A novel method for the automatic grading of retinal vessel tortuosity,” IEEE Trans. Med. Imaging 27(3), 310–319 (2008).
[Crossref] [PubMed]

Sadda, S. R.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
[Crossref] [PubMed]

A. Nagiel, S. R. Sadda, and D. Sarraf, “A promising future for optical coherence tomography angiography,” JAMA Ophthalmol. 133(6), 629–630 (2015).
[Crossref] [PubMed]

Sambhav, K.

K. V. Chalam and K. Sambhav, “Optical coherence tomography angiography in retinal diseases,” J. Ophthalmic Vis. Res. 11(1), 84–92 (2016).
[Crossref] [PubMed]

Sanfilippo, C. J.

C. J. Sanfilippo, M. A. Klufas, D. Sarraf, and I. Tsui, “Optical coherence tomography angiography of sickle cell maculopathy,” Retin. Cases Brief Rep. 9(4), 360–362 (2015).
[PubMed]

Sarraf, D.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
[Crossref] [PubMed]

C. J. Sanfilippo, M. A. Klufas, D. Sarraf, and I. Tsui, “Optical coherence tomography angiography of sickle cell maculopathy,” Retin. Cases Brief Rep. 9(4), 360–362 (2015).
[PubMed]

A. Nagiel, S. R. Sadda, and D. Sarraf, “A promising future for optical coherence tomography angiography,” JAMA Ophthalmol. 133(6), 629–630 (2015).
[Crossref] [PubMed]

Sasongko, M. B.

M. B. Sasongko, T. Y. Wong, T. T. Nguyen, C. Y. Cheung, J. E. Shaw, and J. J. Wang, “Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy,” Diabetologia 54(9), 2409–2416 (2011).
[Crossref] [PubMed]

Schwartz, S. D.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
[Crossref] [PubMed]

Scott, A. W.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
[Crossref] [PubMed]

I. C. Han, M. Tadarati, and A. W. Scott, “Macular vascular abnormalities identified by optical coherence tomographic angiography in patients with sickle cell disease,” JAMA Ophthalmol. 133(11), 1337–1340 (2015).
[Crossref] [PubMed]

Shahidi, M.

Q. V. Hoang, F. Y. Chau, M. Shahidi, and J. I. Lim, “Central macular splaying and outer retinal thinning in asymptomatic sickle cell patients by spectral-domain optical coherence tomography,” Am. J. Ophthalmol. 151, 990–994 (2011).

Shahri, R. P.

M. Tavakoli, R. P. Shahri, H. Pourreza, A. Mehdizadeh, T. Banaee, and M. H. B. Toosi, “A complementary method for automated detection of microaneurysms in fluorescein angiography fundus images to assess diabetic retinopathy,” Pattern Recognit. 46(10), 2740–2753 (2013).
[Crossref]

Shaw, J. E.

M. B. Sasongko, T. Y. Wong, T. T. Nguyen, C. Y. Cheung, J. E. Shaw, and J. J. Wang, “Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy,” Diabetologia 54(9), 2409–2416 (2011).
[Crossref] [PubMed]

Smedby, O.

O. Smedby, N. Högman, S. Nilsson, U. Erikson, A. G. Olsson, and G. Walldius, “Two-dimensional tortuosity of the superficial femoral artery in early atherosclerosis,” J. Vasc. Res. 30(4), 181–191 (1993).
[Crossref] [PubMed]

Souied, E. H.

W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

Spaide, R. F.

R. F. Spaide, J. M. Klancnik, and M. J. Cooney, “Retinal vascular layers imaged by fluorescein angiography and optical coherence tomography angiography,” JAMA Ophthalmol. 133(1), 45–50 (2015).
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Stanton, A. V.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

Subhash, H.

Tadarati, M.

I. C. Han, M. Tadarati, and A. W. Scott, “Macular vascular abnormalities identified by optical coherence tomographic angiography in patients with sickle cell disease,” JAMA Ophthalmol. 133(11), 1337–1340 (2015).
[Crossref] [PubMed]

Tan, O.

Tavakoli, M.

M. Tavakoli, R. P. Shahri, H. Pourreza, A. Mehdizadeh, T. Banaee, and M. H. B. Toosi, “A complementary method for automated detection of microaneurysms in fluorescein angiography fundus images to assess diabetic retinopathy,” Pattern Recognit. 46(10), 2740–2753 (2013).
[Crossref]

Thapa, D.

Thom, S. A.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

Tokayer, J.

Toosi, M. H. B.

M. Tavakoli, R. P. Shahri, H. Pourreza, A. Mehdizadeh, T. Banaee, and M. H. B. Toosi, “A complementary method for automated detection of microaneurysms in fluorescein angiography fundus images to assess diabetic retinopathy,” Pattern Recognit. 46(10), 2740–2753 (2013).
[Crossref]

Trucco, E.

R. Annunziata, A. Kheirkhah, S. Aggarwal, P. Hamrah, and E. Trucco, “A fully automated tortuosity quantification system with application to corneal nerve fibres in confocal microscopy images,” Med. Image Anal. 32, 216–232 (2016).
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Tsui, I.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
[Crossref] [PubMed]

C. J. Sanfilippo, M. A. Klufas, D. Sarraf, and I. Tsui, “Optical coherence tomography angiography of sickle cell maculopathy,” Retin. Cases Brief Rep. 9(4), 360–362 (2015).
[PubMed]

Vanderveen, D. K.

R. Gelman, M. E. Martinez-Perez, D. K. Vanderveen, A. Moskowitz, and A. B. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. Vis. Sci. 46(12), 4734–4738 (2005).
[Crossref] [PubMed]

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G. Dougherty and J. Varro, “A quantitative index for the measurement of the tortuosity of blood vessels,” Med. Eng. Phys. 22(8), 567–574 (2000).
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Walldius, G.

O. Smedby, N. Högman, S. Nilsson, U. Erikson, A. G. Olsson, and G. Walldius, “Two-dimensional tortuosity of the superficial femoral artery in early atherosclerosis,” J. Vasc. Res. 30(4), 181–191 (1993).
[Crossref] [PubMed]

Wang, J. J.

M. B. Sasongko, T. Y. Wong, T. T. Nguyen, C. Y. Cheung, J. E. Shaw, and J. J. Wang, “Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy,” Diabetologia 54(9), 2409–2416 (2011).
[Crossref] [PubMed]

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
[Crossref] [PubMed]

Wang, K.

K. Ghasemi Falavarjani, A. W. Scott, K. Wang, I. C. Han, X. Chen, M. Klufas, J.-P. Hubschman, S. D. Schwartz, S. R. Sadda, D. Sarraf, and I. Tsui, “Correlation Of Multimodal Imaging In Sickle Cell Retinopathy,” Retina 36(Suppl 1), S111–S117 (2016).
[Crossref] [PubMed]

Wang, Q.

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
[Crossref] [PubMed]

Wang, Y.

Wang, Y. X.

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
[Crossref] [PubMed]

Wei, W. B.

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
[Crossref] [PubMed]

Welch, R. B.

R. B. Welch and M. F. Goldberg, “Sickle-cell hemoglobin and its relation to fundus abnormality,” Arch. Ophthalmol. 75(3), 353–362 (1966).
[Crossref] [PubMed]

Wenn, C. M.

C. M. Wenn and D. L. Newman, “Arterial tortuosity,” Australas. Phys. Eng. Sci. Med. 13(2), 67–70 (1990).
[PubMed]

Witt, N. W.

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
[Crossref] [PubMed]

Wolffsohn, J. S.

J. S. Wolffsohn, G. A. Napper, S. M. Ho, A. Jaworski, and T. L. Pollard, “Improving the description of the retinal vasculature and patient history taking for monitoring systemic hypertension,” Ophthalmic Physiol. Opt. 21(6), 441–449 (2001).
[Crossref] [PubMed]

Wong, T. Y.

A. Bhuiyan, B. Nath, K. Ramamohanarao, R. Kawasaki, and T. Y. Wong, “Automated analysis of retinal vascular tortuosity on color retinal images,” J. Med. Syst. 36(2), 689–697 (2012).
[Crossref] [PubMed]

M. B. Sasongko, T. Y. Wong, T. T. Nguyen, C. Y. Cheung, J. E. Shaw, and J. J. Wang, “Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy,” Diabetologia 54(9), 2409–2416 (2011).
[Crossref] [PubMed]

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
[Crossref] [PubMed]

Yang, J. Y.

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
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Yao, X.

You, B.

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
[Crossref] [PubMed]

Zambrowski, O.

W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

Zheng, Y.

C. Y. Cheung, Y. Zheng, W. Hsu, M. L. Lee, Q. P. Lau, P. Mitchell, J. J. Wang, R. Klein, and T. Y. Wong, “Retinal vascular tortuosity, blood pressure, and cardiovascular risk factors,” Ophthalmology 118(5), 812–818 (2011).
[Crossref] [PubMed]

ACM Trans. Model. Comput. Simul. (1)

M. Matsumoto and T. Nishimura, “Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator,” ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998).
[Crossref]

Am. J. Ophthalmol. (3)

Q. Wang, S. Chan, J. Y. Yang, B. You, Y. X. Wang, J. B. Jonas, and W. B. Wei, “Vascular density in retina and choriocapillaris as measured by optical coherence tomography angiography,” Am. J. Ophthalmol. 168, 95–109 (2016).
[Crossref] [PubMed]

Q. V. Hoang, F. Y. Chau, M. Shahidi, and J. I. Lim, “Central macular splaying and outer retinal thinning in asymptomatic sickle cell patients by spectral-domain optical coherence tomography,” Am. J. Ophthalmol. 151, 990–994 (2011).

W. Minvielle, V. Caillaux, S. Y. Cohen, F. Chasset, O. Zambrowski, A. Miere, and E. H. Souied, “Macular microangiopathy in sickle cell disease using optical coherence tomography angiography,” Am. J. Ophthalmol. 164, 137–144 (2016).

Ann. Trop. Paediatr. (1)

A. O. Fadugbagbe, R. Q. Gurgel, C. Q. Mendonça, R. Cipolotti, A. M. dos Santos, and L. E. Cuevas, “Ocular manifestations of sickle cell disease,” Ann. Trop. Paediatr. 30(1), 19–26 (2010).
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Arch. Ophthalmol. (2)

R. B. Welch and M. F. Goldberg, “Sickle-cell hemoglobin and its relation to fundus abnormality,” Arch. Ophthalmol. 75(3), 353–362 (1966).
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R. K. Murthy, S. Grover, and K. V. Chalam, “Temporal macular thinning on spectral-domain optical coherence tomography in proliferative sickle cell retinopathy,” Arch. Ophthalmol. 129(2), 247–249 (2011).
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Australas. Phys. Eng. Sci. Med. (1)

C. M. Wenn and D. L. Newman, “Arterial tortuosity,” Australas. Phys. Eng. Sci. Med. 13(2), 67–70 (1990).
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Biomed. Opt. Express (1)

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H. Lei and G. E. Karniadakis, “Quantifying the rheological and hemodynamic characteristics of sickle cell anemia,” Biophys. J. 102(2), 185–194 (2012).
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Comput. Methods Programs Biomed. (1)

D. Calvo, M. Ortega, M. G. Penedo, and J. Rouco, “Automatic detection and characterisation of retinal vessel tree bifurcations and crossovers in eye fundus images,” Comput. Methods Programs Biomed. 103(1), 28–38 (2011).
[Crossref] [PubMed]

Diabetologia (1)

M. B. Sasongko, T. Y. Wong, T. T. Nguyen, C. Y. Cheung, J. E. Shaw, and J. J. Wang, “Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy,” Diabetologia 54(9), 2409–2416 (2011).
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A. A. Kalitzeos, G. Y. Lip, and R. Heitmar, “Retinal vessel tortuosity measures and their applications,” Exp. Eye Res. 106, 40–46 (2013).
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D. Bracher, “Changes in peripapillary tortuosity of the central retinal arteries in newborns. A phenomenon whose underlying mechanisms need clarification,” Graefes Arch. Clin. Exp. Ophthalmol. 218(4), 211–217 (1982).
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IEEE J. Biomed. Health Inform. (1)

M. Aghamohamadian-Sharbaf, H. R. Pourreza, and T. Banaee, “A novel curvature-based algorithm for automatic grading of retinal blood vessel tortuosity,” IEEE J. Biomed. Health Inform. 20(2), 586–595 (2016).
[Crossref] [PubMed]

IEEE Trans. Med. Imaging (2)

E. Bullitt, G. Gerig, S. M. Pizer, W. Lin, and S. R. Aylward, “Measuring tortuosity of the intracerebral vasculature from MRA images,” IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003).
[Crossref] [PubMed]

E. Grisan, M. Foracchia, and A. Ruggeri, “A novel method for the automatic grading of retinal vessel tortuosity,” IEEE Trans. Med. Imaging 27(3), 310–319 (2008).
[Crossref] [PubMed]

Int. J. Med. Inform. (1)

W. E. Hart, M. Goldbaum, B. Côté, P. Kube, and M. R. Nelson, “Measurement and classification of retinal vascular tortuosity,” Int. J. Med. Inform. 53(2-3), 239–252 (1999).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (1)

R. Gelman, M. E. Martinez-Perez, D. K. Vanderveen, A. Moskowitz, and A. B. Fulton, “Diagnosis of plus disease in retinopathy of prematurity using Retinal Image multiScale Analysis,” Invest. Ophthalmol. Vis. Sci. 46(12), 4734–4738 (2005).
[Crossref] [PubMed]

J. Hypertens. (1)

A. D. Hughes, E. Martinez-Perez, A.-S. Jabbar, A. Hassan, N. W. Witt, P. D. Mistry, N. Chapman, A. V. Stanton, G. Beevers, R. Pedrinelli, K. H. Parker, and S. A. Thom, “Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension,” J. Hypertens. 24(5), 889–894 (2006).
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J. Med. Syst. (1)

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Figures (3)

Fig. 1
Fig. 1 Flow chart depicting steps for VTI assessment in retinal vessels in OCTA.
Fig. 2
Fig. 2 Visual demonstration of parameters extracted from a vessel centerline for VTI computation. (a) Angle between a line tangent to the centerline and a reference axis for the first centerline point. (b) Tangent lines for points along the centerline. SD of angles between each tangent line and the reference axis was computed. (c) Critical points (red circles) were determined based on changes in sign of slope of the tangent lines. (d) Magnitude of curve as ratio of arch length (LA) to the chord length (LC) between pairs of inflection points including centerline end points (red squares).
Fig. 3
Fig. 3 (a) OCTA images acquired in a NC (top row) and SCR (bottom row) subject in perifoveal regions. Example of a vessel segment endpoints is shown with red arrows (a; top row) (b) Vessel segmentation using k-means clustering. Example of a vessel segment endpoints selected on the binary image for centerline extraction are shown by red dots (b; top row). (c) Vessel endpoints (yellow circles) and centerlines (red lines) for VTI assessment. Mean VTI in the perifoveal region in the NC and SCR subjects were 0.41 and 0.71, respectively.

Tables (2)

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Table 1 Pearson’s rank correlation of human observes vs 5 tortuosity measures from a set of 25 randomly generated sinusoidal curves. VTI (vessel tortuosity index), density index (DI), non-linear curvature (Tnl), distance measure (DM), and integral of absolute curvature (Tc).

Tables Icon

Table 2 Subject’s demographics. M and F are abbreviations for male and female, respectively. W, AA and A stand for White, African American and Asian, respectively. OD and OS are right and left eye, respectively. SS, SC, and Sβ are abbreviations for sickle cell genotype HbS/HbS, HbS/HbC, and HbS/beta thalassemia, respectively. Bold indicates statistical significance.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E= j=1 k x i c i x i μ j 2 .
k(l)= dx( l ) dl d 2 y(l) d l 2 d 2 x( l ) d l 2 dy(l) dl ( ( dx(l) dl ) 2 + ( dy(l) dl ) 2 ) 3 2 .
M= 1 Ip+2 i=1 Ip+2 L Ai L Ci .
VTI= 0.1S D θ .N.M. L A L C .

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