The retinal vasculature is the only microcirculation that can be visualized in vivo in humans and analysis of the retinal vessels can provide potentially valuable disease biomarkers. It is well established that the morphology of retinal blood vessels changes with ocular disease such as diabetic retinopathy.1 The retina is an extension of the diencephalon, and there are retinal blood vessel changes associated with certain brain pathologies such as small vessel disease2 and early Alzheimer’s disease.3 There have also been associations between retinal vessel changes and cognitive impairment.4 The intricate relationship between retinal structure, brain pathology, and cognition has resulted in several studies3,5 investigating how the retinal nerve fiber layer (RNFL) contributes to variation in these phenotypes.
The RNFL is formed by the expansion of the fibers of the optic nerve. Because the retinal vessels lie on top of the RNFL, defects in the RNFL are associated with changes in retinal vessel morphology (eg, reduced RNFL thickness is associated with narrower retinal vessel caliber).5 The RNFL is a sensitive structure and processes such as high intraocular pressure,6 inflammation,7 and hypoxia8 can damage the layer. Thinning of the RNFL has been associated with ocular diseases such as glaucoma,6 retinitis pigmentosa,9 and diabetic retinopathy.10 RNFL thinning is also associated with neurological diseases such as multiple sclerosis7 and Alzheimer’s disease.3 There is also a physiological thinning of the RNFL associated with advancing age.11 In addition, a study has shown a positive association between RNFL thickness and cognitive ability in healthy, young individuals.12
Although they are intimately juxtaposed, there has been little research into the relationship between RNFL and retinal vascular topography in patients without glaucoma. By studying this relationship, we aim to understand how the retinal blood and nerve layers are associated.
Patients and Methods
One hundred and one participants (59 men and 42 women) from the Lothian Birth Cohort 1936 (LBC1936)13 were examined for this project. This was a subgroup of the LBC1936’s participants who agreed to have their RNFL thickness measured after being contacted by mail. All participants were born in 1936 and the mean age when RNFL thickness was measured was 72.89 years (standard deviation 0.28).
The RNFL measurement was performed with mydriasis by experienced operators using a Stratus optical coherence tomography machine (Carl Zeiss, Ltd., Cambridge, UK). The fast RNFL scan protocol acquires three repeated sets of 256 measurements (total of 768 data points) in a circular sweep of a standardized diameter of 3.4 mm around the optic disc. The examiner centered the aiming circle around the optic disc each time and the polarization was optimized to maximize the reflective signal. The acquired RNFL measurements could be further subdivided into four areas representing the superior, temporal, inferior, and nasal quadrants. Each individual scan produced data for each quadrant and scans were combined to form an overall mean for each eye. All 101 participants had their right eye RNFL thickness measured and 32 participants had their left eye measured. There was no systematic measurement error between the left and right eye measurements when a subpopulation of patients was tested.
Color fundus photographs were taken of both eyes using a Canon non-mydriatic camera (CR-DGi; Canon USA, Inc., Lake Success, NY) at 45° field of view in 2000.
Morphological Measurements of Retinal Vessels
Branching Coefficient. The most efficient circulation across a vascular network can be achieved if blood flow is proportional to the cubed power of the vessel’s radius (Murray’s law).14 An alternative way to express Murray’s law is to use the branching coefficient that states the sum of the branch vessel’s cross-sectional areas squared divided by the trunk vessel’s cross-sectional area squared should have a theoretical optimal value of 1.26. This value represents the most efficient way for a vessel to branch to reduce power losses and drag.
Bifurcation Angle. The bifurcation angle is the angle subtended between two daughter vessels at a vascular junction. Studies have shown an optimal value of 75° in the arteries and arterioles.15 Retinal arteriolar bifurcation angles are shown to be reduced in hypertension, increasing age, and low birth weight males.16
Branching coefficients and bifurcation angles were measured by one individual (MEG) using a custom-image was then manually checked to identify accurate arteriolar and venule nodes within 3° of branching.
The VAMPIRE software detected between 3 and 8 bifurcations for both arterioles and venules for each fundus image and, from these bifurcations, the arteriole and venule branching coefficient and arteriole bifurcation angle were noted. Deviation from the optimum (1.26 for arteriole and venule branching coefficient and 75° for arteriole bifurcation angle) was then calculated. The root mean square of the 3 to 8 values was calculated for the three parameters and then the square root of the root mean square was taken. This approach meant that each image analyzed produced one value for each of the three parameters (ie, arteriole branching coefficient, venule branching coefficient, and arteriole bifurcation angle).
Fractal Analysis. Fractal analysis describes the degree of branching complexity of a structure.18 Retinal blood vessels may have different properties in different regions of the retina, so that different characteristics can be found depending on the location or scale of the measurement considered (this type of pattern is known as a geometrical multifractal). Fractal dimensions of image objects can be measured using computational approaches.
Fractal measures were available for 58 of the right eyes that were used as the sample size for the correlation analysis. A module of the VAMPIRE program was run on the image set. Binary vascular networks of the human retina were obtained from the digital photographs so that each photograph was transformed into a purely black and white image (with white corresponding to vessel and black to nonvessel). The vessel maps were then skeletonized based on iterative deletion of pixels to reduce vessels to their center lines. Two sets of data were returned when performing fractal analysis: results for analysis of the vessel maps (fractal vessel map) and results for analysis of the skeletons (fractal skeleton). The fractal vessel map parameter uses a box counting technique for measuring the fractal value. Fractal analysis values were obtained (Dq = 0) with and without vessel width information retained.
Exploratory scatter plots of RNFL thickness versus the vascular network parameters were generated using Microsoft Excel (Microsoft Corp., Redmond, WA). SPSS 14 software (SPSS, Inc., Chicago, IL) was used for related tests of normality and for calculating coefficients and corresponding P values. A principal component analysis with varimax rotation was run on potential retinal predictors followed by a regression analysis to see which retinal parameters predicted RNFL.
The retinal vascular parameters were analyzed in both the left and right eyes of the participants so that comparisons could be made between the left and right eye vascular morphology. No results were obtained in 58 of the 202 retinal photographs that were analyzed. This was due to either poor image quality or inability of the software to identify enough bifurcation points (at least 3 required for arterioles and venules). The mean value, standard deviation, and range for each vascular network parameter are given in Table 1. The overall average arteriole branching coefficient was 1.31 (hypothesized optimal theoretical value: 1.26), with an average of 1.31 for men and 1.29 for women. The overall average venule branching coefficient was 1.18, with an average of 1.21 for men and 1.19 for women. For arteriole and venule branching coefficients, we found no significant difference between the left and right eyes or between genders. The overall average arteriole bifurcation angle was 70.1° (hypothesized optimal theoretical value: 75°), and the average was 69.8° for men and 70.5° for women. For arteriole bifurcation, we found no significant difference between the left and right eyes or for male and female values.
Table 1: Mean Values, Standard Deviation, and Range for Each Vascular Network Parameter
Seventy-eight of the total participants were able to have both RNFL and all retinal morphological parameters (apart from fractal analysis) measured. Of these, 59 were right eyes and 19 were both left and right eyes. Fractal measures were available for 58 of the right eyes, which became the sample size for the regression analysis.
The RNFL variable met the Kolmogorov–Smirnov criterion for normality (P = .2). We tested the correlations between RNFL thickness and retinal vessel parameters (ie, on fractal vessel map, fractal skeleton map, arteriole branching coefficient, venule branching coefficient, and arteriole bifurcation angle). Table 2 shows correlations between retinal vessel variables and RNFL thickness. The only significant association was between branching coefficient and RNFL thickness (r = 0.249, P = .028). The direction of association was such that greater deviation from optimality of the coefficient was associated with thicker RNFL. The coefficient was similar whether parametric or nonparametric correlation was used.
Table 2: Pearson Correlation Between RNFL Thickness and Each Vascular Network Parameter Prior to Removal of the Nonsignificant Predictors
Our study found that the average arteriole and venule branching coefficient was 1.31 and 1.18, respectively (hypothesized optimal theoretical value = 1.26) and the average arteriole bifurcation angle was 70.1° (hypothesized optimal theoretical value of 75°). The main finding of the study was that suboptimality of arteriole branching coefficient was associated with a thicker RNFL. To our knowledge, no study has previously investigated this relationship before.
The positive correlation between suboptimality of arteriole branching coefficient and thicker RNFL was unexpected. Thinner RNFL has previously been found to be associated with diseased states such as ocular hypertension,6 optic neuritis,19 and Alzheimer’s disease.3 We had expected the same with increasing suboptimality of the arteriole branching coefficient. Therefore, we suggested that optical coherence tomography-based biomarker metrics require further study to better define their relationship with retinal neurovascular imaging and anatomy.
The arteriole and venule branching coefficient show considerable variation from the expected value (1.26)14 and large variance within the measurements. This may be an indication of the limitation of the VAMPIRE software that may have resulted from the quantification of three-dimensional structures from two-dimensional images and the accuracy of blood vessel segmentation. The finding of reduced average arteriole bifurcation of 70.1° could be expected because previous studies have shown reduction in the bifurcation angle associated with advanced age.20 The great range in bifurcation angle is unlikely to be due to software error, as demonstrated by a previous study21 that showed angles can change up to 50° due to local changes in blood flow. The range and mean of the bifurcation angle parameter therefore supports existing literature concerning bifurcation angles and the changes that occur with age.
Another limitation of the study was that the level of refractive error was not controlled. This is important because RNFL thickness decreases with increasing myopia.22 However, it has been noted that myopia rates decrease with age23 and, therefore, in the elderly Lothian Birth Cohort population the role of myopia affecting the results is not as significant as if the same study was done on a younger population. A further limitation was that not all branching points were picked up by the software and some that were picked up were not correctly identified. This meant that only 3 bifurcation points were picked up in some retinal photographs and in others there were up to 8, meaning that varying numbers of bifurcations were measured in each retinal photograph when calculating the root mean square. There was also a problem with the clarity of retinal photographs because 40 photographs were not analyzed due to poor quality. This may have been partially due to the presence of media opacities such as cataracts in some of the patients.
The RNFL and arteriole branching coefficient correlation has provided a new insight into the possible ways retinal blood vessels and nerves interact in healthy eyes. Further studies of suboptimal retinal vascular geometry and comparative studies of RNFL thickness in healthy and diseased eyes are needed to better understand the complex relationship between the retinal blood vessels and the retina. There is a need for larger scale studies to be performed and investigate the link between retinal vascular metrics and optical coherence tomography measures, especially retinal ganglion layer profiles. Further studies will provide insight into how these biomarkers change in health and disease, and how they may be used as a surrogate marker in the study of brain neurovasculature.
Our study found that the range and mean of the branching coefficient and bifurcation angle largely support existing literature concerning retinal morphological parameters and their changes with age. However, the main finding was that suboptimality of arteriole branching coefficient was associated with a thicker RNFL. No study has investigated this relationship before and our results showed an unexpected direction of association that needs more research to validate and confirm.
- Batterbury M, Bowling B, Murphy C. Ophthalmology: An Illustrated Colour Text. London: Churchill Livingstone; 2009.
- Doubal FN, MacGillivray TJ, Hokke PE, Dhillon B, Dennis MS, Wardlaw JM. Differences in retinal vessels support a distinct vasculopathy causing lacunar stroke. Neurology. 2009;72:1773–1778. doi:10.1212/WNL.0b013e3181a60a71 [CrossRef]
- Berisha F, Feke GT, Trempe CL, McMeel JW, Schepens CL. Retinal abnormalities in early Alzheimer’s disease. Invest Ophthalmol Vis Sci. 2007;48:2285–2289. doi:10.1167/iovs.06-1029 [CrossRef]
- Ding J, Patton N, Deay IJ, et al. Retinal microvascular abnormalities and cognitive dysfunction: a systematic review. Br J Ophthalmol. 2008;92:1017–1025. doi:10.1136/bjo.2008.141994 [CrossRef]
- Zheung Y, Cheung N, Aung T, Mitchell P, He M, Wong TY. Relationship of retinal vascular caliber with rnfl thickness: the singapore malay eye study. Invest Ophthalmol Vis Sci. 2009;50:4091–4096. doi:10.1167/iovs.09-3444 [CrossRef]
- Townsend KA, Wollstein G, Schuman JS, et al. Imaging of the retinal nerve fiber layer for glaucoma. Br J Ophthalmol. 2009;93:139–143. doi:10.1136/bjo.2008.145540 [CrossRef]
- Talman LS, Bisker ER, Sackel DJ, et al. Longitudinal study of vision and retinal nerve fiber layer thickness in multiple sclerosis. Ann Neurol. 2010;67:749–760.
- Kargi SH, Altin R, Koksal M, et al. Retinal nerve fibre layer measurements are reduced in patients with obstructive sleep apnoea syndrome. Eye (Lond). 2005;19:575–579. doi:10.1038/sj.eye.6701582 [CrossRef]
- Walia S, Fishman GA, Edward DP, Lindeman M. Retinal nerve fiber layer defects in RP patients. Invest Ophthalmol Vis Sci. 2007;48:4748–4752. doi:10.1167/iovs.07-0404 [CrossRef]
- Cabrera DeBuc D, Somfai GM. Early detection of retinal thickness changes in diabetes using OCT. Med Sci Monit. 2010;16:15–21.
- Alamouti B, Funk J. Retinal thickness decreases with age: an OCT study. Br J Ophthalmol. 2003;87:899–901. doi:10.1136/bjo.87.7.899 [CrossRef]
- van Koolwijk LM, Despriet DD, Van Duijn CM, et al. Association of cognitive functioning with retinal nerve fiber layer thickness. Invest Ophthalmol Vis Sci. 2009;50:4576–4580. doi:10.1167/iovs.08-3181 [CrossRef]
- Deary IJ, Gow AJ, Taylor MD, et al. The Lothian Birth Cohort 1936: a study to examine influences on cognitive ageing from age 11 to age 70 and beyond. BMC Geriatrics. 2007;7:28. doi:10.1186/1471-2318-7-28 [CrossRef]
- Murray CD. The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol. 1926;9:835–841. doi:10.1085/jgp.9.6.835 [CrossRef]
- Lee JY, Lee SJ. Murray’s law and bifurcation angle in the arterial micro-circulation system and their application to the design of microfluidics. Microfluid Nanofluidics. 2009;8(1):85–95. doi:10.1007/s10404-009-0454-1 [CrossRef]
- Chapman N, Mohamudally A, Cerutti A, et al. Retinal vascular network architecture in low birth weight men. J Hypertens. 1997;15:1449–1453. doi:10.1097/00004872-199715120-00012 [CrossRef]
- Perez-Rovira A, MacGillivray T, Trucco E, et al. VAMPIRE: Vessel Assessment and Measurement Platform for Images of the Retina. Presented at the 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society. ; August 30, 2011. ; Boston, MA. .
- Avakian A, Kalina RE, Sage EH, et al. Fractal analysis of region-based vascular change in the normal and proliferative diabetic retina. Curr Eye Res. 2002;24:274–280. doi:10.1076/ceyr.24.4.274.8411 [CrossRef]
- Trip SA, Schlottmann PG, Jones SJ, et al. Optic nerve atrophy and retinal nerve fibre layer thinning following optic neuritis: evidence that axonal loss is a substrate of MRI-detected atrophy. Neuromage. 2006;31:286–293. doi:10.1016/j.neuroimage.2005.11.051 [CrossRef]
- Stanton AV, Mullaney P, Mee F, et al. A method for quantifying retinal microvascular alterations associated with blood pressure and age. J Hypertens. 1995;13:41–48. doi:10.1097/00004872-199501000-00008 [CrossRef]
- Frame MD, Sarelius IH. Arteriolar bifurcation angles vary with position and when flow is changed. Microvasc Res. 1993;46:190–205. doi:10.1006/mvre.1993.1046 [CrossRef]
- Kang SH, Hong SW, Im SK, Lee SH, Ahn MD. Effect of myopia on the thickness of the retinal nerve fiber layer measured by Cirrus HD optical coherence tomography. Invest Ophthalmol Vis Sci. 2010;51:4075–4083. doi:10.1167/iovs.09-4737 [CrossRef]
- Wensor M, McCarty CA, Taylor HR. Prevalence and risk factors of myopia in Victoria, Australia. Arch Ophthalmol. 1999;117:658–663. doi:10.1001/archopht.117.5.658 [CrossRef]
Mean Values, Standard Deviation, and Range for Each Vascular Network Parameter
|Vascular Network Parameters||Mean||Standard Deviation||Range|
|Arteriole branching coefficient|
| Right eyes||1.29||0.379|
| Left eyes||1.32||0.432|
|Venule branching coefficient|
| Right eyes||1.19||0.343|
| Left eyes||1.18||0.262|
|Arteriole bifurcation angle (°)|
| Right eyes||70.0||17.9|
| Left eyes||70.7||18.5|
|Fractal vessel map|
Pearson Correlation Between RNFL Thickness and Each Vascular Network Parameter Prior to Removal of the Nonsignificant Predictors
|Vascular Network Parameters||Pearson Correlation With RNFL Thickness|
|Arteriole branching coefficient||r = 0.249, P = .028|
|Arteriole bifurcation angle||r = −0.123, P = .317|
|Fractal vessel map||r = 0.234, P = .106|
|Fractal skeleton||r = 0.204, P = .159|
Figure 1. Retinal photograph (A) before and (B) after automatic detection of blood vessels.