May 2007
Volume 48, Issue 5
Free
Clinical and Epidemiologic Research  |   May 2007
The Association between Retinal Vascular Network Geometry and Cognitive Ability in an Elderly Population
Author Affiliations
  • Niall Patton
    From the Princess Alexandra Eye Pavilion, Edinburgh, United Kingdom; the
  • Alison Pattie
    School of Philosophy, Psychology and Language Sciences and the
  • Tom MacGillivray
    Wellcome Trust Clinical Research Facility, Western General Hospital, Edinburgh, United Kingdom; and the
  • Tariq Aslam
    From the Princess Alexandra Eye Pavilion, Edinburgh, United Kingdom; the
  • Baljean Dhillon
    From the Princess Alexandra Eye Pavilion, Edinburgh, United Kingdom; the
  • Alan Gow
    School of Philosophy, Psychology and Language Sciences and the
  • John M. Starr
    Department of Geriatric Medicine, Royal Victoria Hospital, University of Edinburgh, Edinburgh, United Kingdom; the
  • Lawrence J. Whalley
    Department of Mental Health, University of Aberdeen, Clinical Research Centre, Royal Cornhill Hospital, Aberdeen, United Kingdom.
  • Ian J. Deary
    School of Philosophy, Psychology and Language Sciences and the
Investigative Ophthalmology & Visual Science May 2007, Vol.48, 1995-2000. doi:10.1167/iovs.06-1123
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      Niall Patton, Alison Pattie, Tom MacGillivray, Tariq Aslam, Baljean Dhillon, Alan Gow, John M. Starr, Lawrence J. Whalley, Ian J. Deary; The Association between Retinal Vascular Network Geometry and Cognitive Ability in an Elderly Population. Invest. Ophthalmol. Vis. Sci. 2007;48(5):1995-2000. doi: 10.1167/iovs.06-1123.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

purpose. To test the hypothesis that parameters of retinal vascular network geometry are significantly associated with cognition.

methods. Three hundred twenty-one community-dwelling, surviving participants in the Scottish Mental Survey of 1932 from the Lothian region of Scotland (Lothian Birth Cohort 1921; all born in 1921 and aged approximately 83 when tested) underwent fundus photography and the following psychometric tests: Wechsler Logical Memory, Verbal Fluency, and Raven’s Standard Progressive Matrices. In addition, a general cognitive ability score (g) was obtained from these three correlated tests of cognition. The following parameters of the retinal vascular network geometry were measured: central retinal arterial and venular equivalents (CRAE and CRVE, respectively), arteriovenous ratio (AVR), suboptimality of the median branching coefficient (BC), and median angle of the five most proximal arteriolar bifurcations. General linear modeling (GLM; analysis of covariance [ANCOVA]) was used to measure associations, with gender, APOE e4 status, presence of diabetes, smoking status (current, ex-, or never), and history of cerebrovascular disease as fixed factors and the following covariables: IQ at age 11, logMAR (logarithm of the minimum angle of resolution) near visual acuity of the better-seeing eye, years of full-time formal education, occupational social class category, systolic and diastolic blood pressure, and alcohol units per week.

results. Deviation of the median BC from optimality was significantly associated with general cognitive ability (g) (η2 = 0.034, P = 0.02) and verbal fluency (η2 = 0.037, P = 0.01), whereas deviation of the angle at arteriolar bifurcations from optimality was significantly associated with logical memory (η2 = 0.026, P = 0.03). CRAE, CRVE, and AVR did not contribute significantly to any cognitive test scores.

Conclusions

The association of suboptimal retinal vascular network geometry and cognition was shown in this study. It supports the concept that the retinal microvasculature acts as a surrogate marker for the cerebral microvasculature.

Cognitive aging is a large personal and societal burden, with large individual differences, and it is important to find the determinants of change in cognition with age. 1 Variation in vascular disease contributes to cognitive ability differences in old age, 2 and a possible window on vascular status is provided by the retinal vessels. The retinal microcirculation is the only vasculature that can be visualized and photographed in vivo in humans. Epidemiologic studies have used computerized retinal image analysis to detect associations between the retinal microvasculature and systemic cardiovascular disease (Hubbard LD et al. IOVS 1992;33:ARVO Abstract 804). 3 4 5 6 Based on the homology between the retinal and cerebral microcirculations 7 and the knowledge that cognitive disease relates to the state of the cerebral vasculature, 8 9 10 it has been speculated that variation in the retinal vasculature contributes to individual differences in cognitive abilities among older people. 11 12 However, in previous studies addressing this question it was not possible to control for prior or premorbid cognitive ability, which is known to account for a substantial proportion of the variance in cognitive function scores in old age. 13 14 Therefore, the investigators were prevented from assessing definitively whether vascular factors account for variation in age-related change in cognitive abilities. In addition, in previous studies it was not possible to control for other potential important variables, such as visual acuity and apolipoprotein E (APOE) status. The presence of retinopathy in diabetes accounts for approximately 14% of cognitive variance (fluid intelligence, information processing, and attention ability), after adjustment for age and estimated premorbid IQ. 15 This was an exploratory observational study of the association between quantifiable parameters of the retinal vasculature and cognition in a well-defined, elderly (age 83 years) population, the most of whom underwent IQ testing at age 11 years. We introduce the novel concept of suboptimality (both of bifurcation angles and junctional branching coefficients) to provide quantitative parameters of retinal vascular network geometry. 
Methods
Ethics approval was obtained from the local (Lothian) ethics review committee, and all participants gave full-informed written consent before entry into the study. The study complied with the Declaration of Helsinki on the procedures for research involving human subjects. 
Lothian Birth Cohort 1921 Sample
The group under study were a mostly noninstitutionalized sample whose general mental ability was measured when the participants were aged approximately 11 years. In 1932, under the auspices of the Scottish Council for Research in Education (SCRE), it was decided to survey the mental ability of all Scottish children born in 1921 (the 1932 Scottish Mental Survey [SMS1932]). 16 Between 1999 and 2001, attempts were made to trace and contact individuals born in 1921 and residing within the Lothian region of Scotland (principally the City of Edinburgh). A total of 550 people were successfully traced and are described as the Lothian Birth Cohort 1921 (LBC1921). This group has already provided information on cognitive associations in aging. 17 In the present study, in which we used data from a new, second wave of data collection within old age, we examined the association between cognition and retinal vascular network geometry. In 2003, 454 members of the LBC1921 cohort were again contacted, by mail. Ten subjects had died, 13 were not reachable, 16 withdrew after being contacted, and 80 were unable (mostly due to current illness or disability) or unwilling to take part. Three hundred thirty-five agreed to take part, and 321 were tested for this study. Of the 321, 303 were community dwelling, 16 were in sheltered housing, and 2 were in nursing homes. All subjects attended between December 2003 and September 2005 for repeat cognitive function testing and retinal photography (all performed during one visit). Repeat cognitive function tests were performed by one of two authors (AP tested the majority and AG the remainder). In addition, visual assessments and retinal photography were performed. 
Cognitive Tests
The Moray House Test.
Mental ability at age 11 was tested with The Moray House Test, 16 which was administered as a group test with a 45-minute time limit. It has a maximum score of 76. It contains many verbal reasoning items and also some numerical, spatial, and abstract reasoning items. 
Mini Mental State Examination.
The MMSE is a brief, quantitative measure of cognitive status in adults. 18 It is a widely used method for assessing cognitive status among older people and especially as a screening test for dementia. An MMSE score of <24 is often used to indicate significant cognitive impairment. Its role in our study is to give an overview of the limited degree of significant cognitive impairment in the LBC1921 sample. 
Logical Memory: Immediate Recall and Delayed Recall.
Logical Memory is a subtest of the Revised Wechsler Memory Scale (WMS-R). 19 Participants are scored on how completely they recall two short stories with 25 ideas. Participants were read the two thematically independent stories (designated A and B) and were asked to recall each story immediately after hearing it. This was the immediate recall element: Logical Memory I. After an approximately 30-minute delay, the participants were asked to recall both stories, without hearing the details again. This tested the delayed recall element: Logical Memory II. 
Controlled Oral Word Association Test (COWAT): Verbal Fluency Test.
The COWAT Verbal Fluency test assesses the capacity of an individual for word generation. 20 The subject is asked to produce as many words as possible beginning with three particular letters (C, F, and L were used in the present study) in a time of 1 minute for each letter. Performance of this phonemic fluency task involves the creation of appropriate strategies for word retrieval, which is an important component of executive function. 21  
Raven’s Standard Progressive Matrices.
Raven’s Standard Progressive Matrices 22 is a test of nonverbal reasoning and is a particularly good indicator of general cognitive ability. 23 The test was designed to measure a person’s ability to reason by induction. The allocated time limit for the test was 20 minutes, and the number of correctly completed items comprised the score (maximum score, 60). 
General Cognitive Ability Score (g).
In addition to the mentioned individual cognitive tests, a measure of general cognitive ability (g) was generated by extracting a component that reflected the variance shared by logical memory, verbal fluency, and Raven’s Progressive Matrices. A general cognitive factor typically accounts for approximately 50% of the variance when a diverse battery of cognitive tests are given to a healthy population sample. 24 The correlations (Pearson’s r) among the three tests here were (all P < 0.001): Raven verbal fluency = 0.36; Raven logical memory = 0.40; and verbal fluency-logical memory = 0.28. Principal components analysis revealed one component, accounting for 56.5% of the total variance. Scores on this first unrotated principal component were saved as general mental ability (g) scores. Loadings of the three tests on the g factor were all high, further validating its being used in the study: Raven = 0.79; verbal fluency = 0.71; and logical memory = 0.74. 
Retinal Photography
Participants had 1% tropicamide drops administered approximately 20 minutes before image capture. Both pupils were dilated if possible. If, after inspection at 20 minutes, pupillary dilatation was insufficient, then a further 1% tropicamide dose was given. Subsequent to this, fundus photography was performed. Color photographs (35 mm) photographs were taken with a mydriatic fundus camera (Kowa Pro 1 professional fundus camera; Kowa, Tokyo, Japan) with a 50° field of view centered on the optic disc. After film processing (Provia 100F; Fujifilm, Tokyo, Japan), the 35-mm photographs were then digitally scanned at 3200 dpi (model 3200 Perfect Scanner; Epson Seiko, Nagano, Japan) and stored in tagged image file format (TIFF). Using this resolution, medium-sized retinal vessels tended to measure approximately 20 to 30 pixels in diameter. RGB (red-green-blue) images were converted to grayscale and contrast enhanced (contrast-limited adaptive histogram equalization). 
Parameters of Retinal Vascular Network Geometry
All parameters of retinal vascular network geometry were measured by one individual (NP) who used a custom-written (by TM) software package (written in MatLab; The Mathworks Inc., Natick, NA) computing environment. Retinal vessel widths (summarized as the central retinal arterial equivalent [CRAE], central retinal venular equivalent [CRVE], and the arteriovenous ratio [AVR]) were recorded for each individual. In addition, optimality of the retinal arteriolar bifurcation geometry was measured. 
Measurements of Retinal Vessel Caliber.
The six largest arterioles and venules were measured within a circular zone defined as between 0.5 and 1 disc diameter from the optic disc edge. The microdensitometric technique used to measure vessel width has been described. 25 To summarize these widths, we calculated the CRAE by using a formula we devised, which is based on that reported by Knudtson et al. 26 but incorporates the degree of asymmetry between retinal arterioles in combining individual retinal arterioles. 25 In addition, the CRVE was calculated according to the formula devised by Knudtson et al., 26 but using a branching coefficient (BC) constant of 1.22, as previously calculated by the authors 25 (as this more approximates the theoretical optimum of 1.26). Finally, the AVR was the quotient of the CRAE/CRVE. For retinal vessel caliber measurements, intraobserver reliability of the AVR was measured in 20 randomly chosen fundus images. The intraclass correlation coefficient (ICC) was 0.932, with coefficient of repeatability ± 0.058. 
Optimality at Arteriolar Bifurcation Geometry.
Vascular topographical geometry, far from being a totally random network, has a tendency to conform to optimal principals, to minimize physical properties such as power losses and volume across the vascular network. 27 28 29 30 31 32 In 1926, Murray calculated that 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 (i.e., the junction exponent = 3, known eponymously as Murray’s law). An alternative way to express Murray’s law is to use the BC:  
\[\mathrm{Branching\ coefficient}\ (\mathrm{BC}){=}(\mathrm{D}_{1}^{2}{+}\mathrm{D}_{2}^{2})/\mathrm{D}_{0}^{2}\]
where D0 is the width of the trunk vessel, and D1 and D2 are the widths of the two branch vessels. 
By differential calculus, it can be shown that to minimize work across the retinal vasculature, the BC should approximate 1.26 (= 21/3). Hence, we measured the median BC of the five most proximal arteriolar junctions. Rather than express the absolute BC, we measured, more relevantly, the degree of deviation of the BC from optimality (i.e., 1.26). The root mean square of the median BC was calculated and a square root transform performed to normalize the data. Because of the variable quality of the fundus images in an elderly population, intraobserver reliability of the median BC using microdensitometry was moderate for peripheral vessel measurements (ICC = 0.552; coefficient of repeatability = 0.67). Using micrometric techniques to measure peripheral junctional vessel widths improved the intraobserver reliability (ICC = 0.650; coefficient of repeatability = 0.54). The direct micrometric technique involved selecting the area that contained the vessel junction to be measured as a region of interest, which then opened in a new window. This window was then maximized to standardize the resolution for the area of interest that contained the vessel junction. Using a visual evaluation of the edges of the vessels, the user selected two points of the trunk vessel, each one of which represented one edge. Using this same technique, the process was then repeated for each of the two respective branches. After selection of the six edge points, the diameter of the trunk and the two branch vessel widths would be calculated by the computer and displayed in pixel units. Although micrometric measurements have been described as less accurate than microdensitometric techniques in measuring retinal vessel width, precision was more important than accuracy for our purposes. 
To calculate the bifurcation angle (ω), a region of interest within the grayscale-enhanced digital image was magnified in a separate window, and the angle between the two daughter arterioles was calculated by using the cosine rule. This calculation was performed for the five most proximal arteriolar junctions and the median angle calculated. Both theoretical and empiric studies have shown an optimized arteriolar bifurcation geometry of approximately 75°, to minimize work across the vascular network. Thus, the root mean square of the difference of the median angle from 75° was calculated. Again, a square root transform of the data was used to normalize the data, before parametric analysis. The intraobserver reliability of the bifurcation angle (ω) was ICC = 0.959 (n= 20) and the coefficient of repeatability = 10.4°. 
Measures of Static Visual Function
Distance visual acuity (VA) was measured by using the logarithm of the minimum angle of resolution [logMAR] chart at 6 m. Both eye acuities were measured if possible, with the subjects wearing appropriate spectacle correction. However, no new refractions were performed. If spectacles were not available, pinhole visual acuity was used as the best corrected acuity. In addition, near visual acuity was measured in both eyes with a near logMAR acuity chart at 30 cm. Finally, contrast sensitivity according to a Pelli-Robson chart at 1 m was measured. All tests were performed under standardized conditions of illumination. The associations of visual function with cognition are not discussed herein but will be published in a later report. Near visual acuity was used as a covariable when assessing the relationship between retinal vascular network geometry and cognition. 
Subjects had sitting blood pressure measured with a manual sphygmomanometer and the systolic and diastolic arterial blood pressure was recorded (in mm Hg). In addition, history of cerebrovascular disease, presence of diabetes, a self-estimate of alcohol units per week, and smoking status (never, ex-smoker, and current) was recorded. The individuals in this present study had had apolipoprotein E (APOE) genotyping 33 performed some years previously. 
Statistical Analysis
Inspection of the cognitive test results revealed normal distributions. Likewise, the CRAE, CRVE, and AVR followed normal distributions. The root mean square deviations of the median angle and BC from optimality were positively skewed and underwent square root transformation to normalize the data. General linear modeling (GLM; analysis of covariance [ANCOVA]) was used with the cognitive test scores as dependent variables. Gender, APOE ε4 allele status, presence of diabetes, history of cerebrovascular disease, and smoking status were fixed effects. The following were covariables: Moray House Test (IQ) score at age 11 in 1932, logMAR near visual acuity of the better-seeing eye, years of full-time formal education, occupational social class category, systolic and diastolic blood pressure (mm Hg), and alcohol units per week. Statistical significance was set at P < 0.05. Eta squared (η2) values were used to convey effect sizes (SPSS ver. 8.0; SPSS Inc. Chicago, IL). 
Results
There were 145 (45.2%) men and 176 (54.8%) women, and all were either 83 or 84 years old. All were of white ethnic origin. Mean (±SD) distance visual acuity was 0.23 (0.17), near visual acuity was 0.36 (0.17), and contrast sensitivity was 1.28 (0.3). Of the 321, 289 (132 [45.7%] men; 157 [54.3%] women) had fundus images of sufficient quality to analyze some of the retinal vascular parameters. A total of 32 images (13 men and 19 women) were of insufficient quality to perform any analysis. In all of the remaining 289 individuals, the parameters of CRAE, CRVE, and AVR were measured. For deviation of the median BC and angles from optimality, n= 226 (i.e., 63 images that were able to provide a measure of CRAE, CRVE, and AVR were either of too poor quality to analyze all five proximal arteriolar junctions, or less than five proximal arteriolar junctions were evaluable within the 50° field). For the cognitive tests, a small number of tests (four or fewer) were not performed on all the 321 subjects. 
The distribution of MMSE scores in the LBC1921 group showed that most of the individuals had near-to-ceiling scores (mean, 28.1 [1.94 SD]), with only a very small proportion having an MMSE score below 24 (n = 9). 
The mean (±SD) for each of the three individual cognitive test results are shown in Table 1 . There were no significant differences between cognitive test scores (P > 0.05 for all) in those individuals who had some parameters of retinal vasculature measured (n= 289) and those who had insufficiently good images (n = 32) to measure any of the parameters of retinal vasculature. 
The mean (± SD) of the retinal vascular network parameters are also in Table 1 . For the vessel width measurements, the values in pixels translate into the following values in micrometers, to aid comparison with other studies, based on an assumption of the average optic disc diameter (approximately 400 pixels) being equal to 1850 μm: CRAE = 187 μm and CRVE = 243 μm. Mean (SD) near logMAR visual acuity of the better-seeing eye was 0.36 (0.18). Mean systolic blood pressure (mean [SD]) was 164.93 mm Hg (28.25), and mean diastolic blood pressure was 83.88 mm Hg (13.58). Twenty-five (7.8%) individuals had a history of cerebrovascular disease, and 21 (6.5%) had diabetes. One hundred fifty-four (48%) never smoked, 144 (45%) were ex-smokers, and 21 (7%) were current smokers. Mean alcohol units per week were 6.1 (10.86). 
Measuring Associations between Cognition and Retinal Vascular Parameters
Of the 289 individuals who were subject to some form of retinal vascular measurement, 22 had no record of their Moray House Test score at age 11, 7 had no APOE allele status, and 2 had no data for social class category and years of full-time formal education. Mean (± SD) Moray House Test scores at age 11 were 47.4 (11.6). Median length (years) of full-time formal education was 10 (interquartile range, 9–12). Social class categories were as follows: professional occupation (n = 76); managerial/technical (n = 128); skilled manual (n = 109); partly skilled occupation (n = 3); unskilled occupation (n = 3). APOE genotype status was as follows: ε2 ε2 (n = 1); ε2 ε3 (n = 48); ε2 ε4 (n = 10); ε3 ε3 (n = 188); ε3 ε4 (n = 65); ε4 ε4 (n = 2). 
CRAE, CRVE, and AVR did not contribute significantly to any cognitive test scores (Table 2)
Absolute values of the BC (for g, F = 0.06, P = 0.80, η2 < 0.001; for verbal fluency, F = 0.95, P = 0.33, η2 = 0.006; for logical memory, F = 0.08, P = 0.77, η2 = 0.001; for Raven’s Progressive Matrices, F = 0.06, P = 0.81, η2 < 0.001) and angle at arteriolar bifurcations (for g, F = 0.00, P = 0.98, η2 < 0.001; for verbal fluency, F = 0.47, P = 0.48, η2 = 0.003, for logical memory, F = 0.484, P = 0.48, η2 = 0.003; for Raven’s progressive matrices, F = 0.05, P = 0.82, η2 < 0.001) were not associated with cognition. 
Deviation of the median BC from optimality was significantly associated with general cognitive ability (g) (F = 6.08, P = 0.02, η2 = 0.034; Table 2 ). The following were the other individual contributions to variation in g: Moray House Test at age 11, F = 37.07, P < 0.001, η2 = 0.18; gender, F = 0.83, P = 0.77, η2 <.01; logMAR near visual acuity, F = 8.55, P = 0.004, η2 = 0.05; APOE ε4 allele status, F = 3.87, P = 0.05, η2 = 0.02; presence of diabetes, F = 0.90, P = 0.34, η2 <.01; history of cerebrovascular disease, F = 0.05, P = 0.95, η2 <.01; smoking status, F = 0.80, P = 0.45, η2 <.01; systolic blood pressure, F = 3.66, P = 0.06, η2 = 0.02; diastolic blood pressure, F = 0.17, P = 0.68, η2 <.01; alcohol units per week, F = 0.54, P = 0.46, η2 <.01; years of full-time formal education, F = 2.43, P = 0.12, η2 = 0.01; and social class category, F = 0.18, P = 0.67, η2 <.01. 
Deviation of the median BC from optimality was also significantly associated with verbal fluency (F = 6.64, P = 0.01, η2 = 0.037; Table 2 ), and there was a statistical trend with Raven’s matrices (P = 0.09). 
Deviation of the angle at arteriolar bifurcations from optimality was significantly associated only with logical memory (F = 4.67, P = 0.03, η2 = 0.026; Table 2 ). The following were the other individual contributions to variation in logical memory: Moray House Test at age 11, F = 12.07, P = 0.001, η2 = 0.07; gender, F = 3.68, P = 0.06, η2 = 0.02; logMAR near visual acuity, F = 1.17, P = 0.28, η2 <.01; APOE ε4 allele status, F = 3.10, P = 0.08, η2 = 0.02; presence of diabetes, F = 0.25, P = 0.61, η2 <.01; history of cerebrovascular disease, F = 0.70, P = 0.50, η2 <.01; smoking status, F = 0.68, P = 0.51, η2 <.01; systolic blood pressure, F = 0.42, P = 0.52, η2 <.01; diastolic blood pressure, F = 0.34, P = 0.56, η2 <.01; alcohol units per week, F = 1.27, P = 0.26, η2 <.01; years of full-time formal education, F = 0.04, P = 0.84, η2 <.01; social class category, F = 0.26, P = 0.61, η2 <.01. 
Discussion
In the models tested in the present study, the significant, independent contributors to general cognitive function in old age were mental ability at age 11, deviation from optimality of the retinal vascular network, near visual acuity, and APOE ε4 allele status. In addition, suboptimality of angles at arteriolar bifurcations was associated with the cognitive domain of verbal declarative memory after adjustment for mental ability at age 11. The effect size, in these relatively healthy older people, was small, with retinal indices contributing approximately 2% to 3% of the variance in some cognitive scores, but this approximates to the same as APOE genotype. 33 The ARIC (Atherosclerosis Risk in Communities) study also found a relationship between the presence of focal retinopathy and cognition (memory recall, digit symbol subtest, and verbal fluency) in a middle-aged population, 12 and this relationship was still present in nondiabetic participants only. However, in our study, rather than measure presence of focal retinopathy, we attempted to measure quantifiable parameters of the retinal vasculature, viz. retinal vessel widths and features of retinal arteriolar bifurcation geometry. 
The association of suboptimal BC with 3.4% of the variance in g after controlling for IQ at age 11 may be interpreted as suboptimal BC’s contributing to individual differences in cognitive change between age 11 and age 83. 34 Although only the verbal fluency component of g reached statistical significance with the suboptimality of the BC, there was a statistical trend (P < 0.10) of association with Raven’s Progressive Matrices. No association was evident between the BC and logical memory. Verbal fluency and Raven’s progressive matrices represent the cognitive domains of executive function and nonverbal reasoning. Executive functioning in particular may be expected to be reflected by the state of the cerebral small vessels, and hence in the retinal microvasculature. Impairment of executive function and attention are believed to be characteristic of vascular cognitive impairment 2 and is governed by the prefrontal systems of the brain. 35 Buffon et al. 36 recently described the cognitive profile of patients with CADASIL, which represents the archetypal cerebral small vessel disease. They found executive dysfunction among almost 90% of patients. 
Knudtson et al. 26 were the first to use the concept of the branching coefficient to summarize retinal vessel widths into the CRAE and CRVE. More recently, Witt et al. 37 have used the principle of suboptimality of peripheral arteriolar junctions to detect an association with mortality due to ischemic heart disease (but not stroke). In addition, Chapman et al. 38 have used the principle of suboptimality to detect an association between peripheral vascular disease and suboptimality of retinal arteriolar junctional exponents (an alternative measure of vessel bifurcation geometry). These measures are all based on Murray’s principle of minimum work and volume across a vascular network, which predicts an ideal BC of 1.26. Deviation above or below this value results in cost in one or other of these entities, and hence this is the basis for our use of unidirectional suboptimality of the BC from an idealized value rather than an absolute value. 
Relatively few studies have explored relationships between arteriolar bifurcation geometrical angles and cardiovascular disease. Retinal arteriolar bifurcation angles have been found to be reduced in persons with hypertension, 39 those of advanced age, 40 and low-birth-weight males. 41 Birth weight is also independently associated with cognitive ability. 42 No relationship was reported between vascular bifurcation angles (of the five most proximal arteriolar junctions) and peripheral vascular disease, compared with healthy control subjects. 40 However, these studies employed absolute retinal arteriolar angles, rather than deviation from optimality. 
Murray predicted that to minimize the principle of work across the vascular network, the angles between two vessels at a bifurcation should approximate to 75°, 28 and studies corroborate that mean bifurcation angles approximate to 75°. 43 44 45 Additional work by Frame and Sarelius 44 has shown that angles are not constant and “anatomically invariant,” but change significantly with blood flow and that the resultant increase in vessel caliber results in changes of angles of up to 50°. Further, this change is not unidirectional (i.e., some angles decrease while others increase, and therefore we recorded change from optimality rather than absolute values). 
Our finding of no association with summary measures of vascular width (CRAE, CRVE, and AVR) and cognition concurs with the ARIC study, 12 although that was a much larger study involving a middle-aged, much more heterogeneous population, and the cognitive function tests were not performed at the same time as retinal photography. In addition, the investigators were unable to control for earlier cognition or visual function. However, their study confirmed an association between retinal microvascular abnormalities (focal retinopathy: e.g., hemorrhages, microaneurysms, and exudates) and cognition. One of the conclusions drawn from the ARIC study was that retinal vascular features associated with blood–retinal barrier breakdown (microaneurysms, retinal hemorrhages) had the strongest association with cognition, suggesting an important potential pathophysiological mechanism of cognitive impairment. Griffith et al. 45 46 have shown that the endothelium plays a significant role in optimization of vascular geometry, by nitric oxide (NO) and endothelin-1 release, and hence alteration from vascular network optimality may reflect endothelial dysfunction. In addition, altered optimal geometry is associated with altered shear stress across that network, which may further compound the effects on the vascular endothelium 47 48 and result in endothelial inflammation through increased expression of proinflammatory genes, 49 50 increased production of superoxide and hydrogen peroxide free radicals, 50 and decreased levels of important intracellular antioxidants such as glutathione peroxidase. 51 The area of greatest wall shear stress has been determined both in vivo and by computational fluid dynamics as occurring within one vessel diameter of a vessel branch. 52 Thus, as a generalized objective measure of retinal vascular network geometry, it is possible that branching coefficients and bifurcation angles relate to vascular inflammation and blood–retinal barrier breakdown more than do measures of generalized vessel width and hence relate to cognition in a fashion similar to focal retinopathy. 
Caution must be exercised in interpreting the findings from the present exploratory study, as some of the tests of cognition did not relate to changes in vascular geometry and further studies of suboptimal retinal vascular geometry are necessary to determine the potential usefulness of these measures as markers of microangiopathy. In addition, studies relating known markers of cerebral small vessel disease (such as cerebral white matter lesions and lacunar infarcts, known to be associated with cognition 14 and features of retinal vessels 53 54 55 56 ) with parameters of retinal arteriolar geometry are required. Furthermore, because this was an exploratory study, statistical adjustment for multiple hypothesis testing was not performed. Future larger confirmatory studies are planned. 
A limitation of our study is that the quality of the retinal photography in this elderly population was not ideal, due to the prevalence of medial opacities. This resulted in not being able to measure every parameter of retinal vascular network geometry in every individual, although we tried to optimize our computerized image analysis to obtain as many measurements in as many individuals as possible. Furthermore, we used micrometric, rather than microdensitometric, techniques to measure peripheral retinal vessel widths that were used to calculate the median BC. However, micrometric techniques were more reliable in this set of fundus images, and any systematic bias for measuring vessels wider or narrower due to the use of micrometry would be balanced by using a coefficient with which differences would likely cancel each other out. Finally, of the original surviving cohort contacted to participate in the study, 133 of the 454 subjects contacted did not participate for one reason or another, which could introduce a degree of selection bias. 
In conclusion, in an elderly, independently living population of North European individuals with predominantly normal cognitive ageing, there was an association between suboptimality of the retinal arteriolar bifurcation junctional geometry and cognition. In particular, suboptimality of the branching coefficients was associated with general cognitive ability and verbal fluency, and suboptimality of the bifurcation angle was associated with verbal declarative memory. Our findings support the concept that the retinal microvasculature acts as a surrogate marker for the cerebral microvasculature and offers retinal vascular imaging as a potential approach to the noninvasive study and measurement of the consequences of cerebral microvascular disease. 
 
Table 1.
 
Descriptive Statistics of the Individual Cognition Tests and Parameters of Retinal Vascular Network Geometry
Table 1.
 
Descriptive Statistics of the Individual Cognition Tests and Parameters of Retinal Vascular Network Geometry
Mean SD Range
Logical memory 32.6 14.3 1–75
Raven’s matrices 29.9 9.0 6–51
Verbal fluency 39.7 12.7 11–77
CRAE (pixels) 40.61 5.77 26.74–64.54
CRVE (pixels) 52.60 6.83 33.95–78.46
AVR 0.77 0.11 0.55–1.21
Median BC 1.32 0.21 0.88–1.99
Median angle (deg.) 71.91 9.69 48.3–104.60
Table 2.
 
General Linear Models for Tests of Cognition with Parameters of Retinal Vascular Network Geometry
Table 2.
 
General Linear Models for Tests of Cognition with Parameters of Retinal Vascular Network Geometry
Cognitive Ability Score (g) Logical Memory Verbal Fluency Ravens Progressive Matrices
CRAE 0.25 (0.62) 0.26 (0.61) 3.86 (0.06) 0.10 (0.75)
CRVE 0.47 (0.49) 0.26 (0.61) 0.53 (0.47) 0.05 (0.82)
AVR 0.01 (0.92) 0.47 (0.49) 1.65 (0.20) 0.11 (0.74)
Suboptimal branching coefficient 6.08 (0.02, 0.034) 0.60 (0.44) 6.64 (0.01, 0.037) 2.85 (0.09)
Suboptimal angles 1.29 (0.26) 4.67 (0.03, 0.026) 0.76 (0.38) 1.14 (0.28)
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Table 1.
 
Descriptive Statistics of the Individual Cognition Tests and Parameters of Retinal Vascular Network Geometry
Table 1.
 
Descriptive Statistics of the Individual Cognition Tests and Parameters of Retinal Vascular Network Geometry
Mean SD Range
Logical memory 32.6 14.3 1–75
Raven’s matrices 29.9 9.0 6–51
Verbal fluency 39.7 12.7 11–77
CRAE (pixels) 40.61 5.77 26.74–64.54
CRVE (pixels) 52.60 6.83 33.95–78.46
AVR 0.77 0.11 0.55–1.21
Median BC 1.32 0.21 0.88–1.99
Median angle (deg.) 71.91 9.69 48.3–104.60
Table 2.
 
General Linear Models for Tests of Cognition with Parameters of Retinal Vascular Network Geometry
Table 2.
 
General Linear Models for Tests of Cognition with Parameters of Retinal Vascular Network Geometry
Cognitive Ability Score (g) Logical Memory Verbal Fluency Ravens Progressive Matrices
CRAE 0.25 (0.62) 0.26 (0.61) 3.86 (0.06) 0.10 (0.75)
CRVE 0.47 (0.49) 0.26 (0.61) 0.53 (0.47) 0.05 (0.82)
AVR 0.01 (0.92) 0.47 (0.49) 1.65 (0.20) 0.11 (0.74)
Suboptimal branching coefficient 6.08 (0.02, 0.034) 0.60 (0.44) 6.64 (0.01, 0.037) 2.85 (0.09)
Suboptimal angles 1.29 (0.26) 4.67 (0.03, 0.026) 0.76 (0.38) 1.14 (0.28)
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