Skip to main content

Abstract

Background and Purpose:

Fractal analysis is a method of quantifying the branching complexity and density of the retinal vessels. We hypothesized that reduced fractal dimension, signifying a sparser vascular network, is associated with long-term stroke mortality.

Methods:

We examined the relationship of fractal dimension and stroke mortality in a prospective, population-based cohort of 3143 participants aged 49 years or older. Fractal dimension was measured from digitized fundus photographs using a computer-automated method. Stroke mortality was documented from Australian National Death Index records. We defined reduced fractal dimension as values in the lowest quartile.

Results:

Over 12 years, there were 132 (4.2%) stroke-related deaths. Stroke-related mortality was higher in participants with reduced fractal dimension (lowest quartile) compared with the highest quartile (7.7% versus 1.3%, P<0.01). After controlling for age, gender, smoking, blood pressure, history of stroke, and other factors, participants with reduced fractal dimension had higher stroke mortality (hazard ratio, 2.42 [95% CI, 1.15–5.07], lowest versus highest quartile). When modeled as a continuous variable, reduced fractal dimension was associated with increased stroke mortality (multivariable-adjusted hazard ratio, 1.26 [95% CI, 1.06–1.51], per SD decrease).

Conclusions:

Reduced retinal vascular fractal dimension is independently associated with 12-year stroke mortality. Reduced fractal dimension may indicate cerebral tissue hypoxia and increased risk of stroke.

Introduction

Stroke is the fifth most frequent cause of death and the leading cause of disability in the United States.1 The cause of stroke involves macrovascular and microvascular causes. There is considerable homology in the retinal and cerebral microcirculations,2 and retinal microvascular changes may reflect similar changes in the cerebral microcirculation.3–8 The branching pattern of the retinal vessels can be investigated using fractal analysis, which quantifies the complexity and density of the branching vascular network and summarizes it as a global index, the fractal dimension (Df).7,9 Greater fractal dimension indicates increased branching complexity and is visible as a denser vascular network, while reduced fractal dimension indicates sparser and more rarefied vascular network.7,9
We previously reported retinal vascular fractal dimension is reduced in persons with hypertension, demonstrating an empirical relationship of sparser vascular architecture with blood pressure (BP).7 We conducted a small case-control pilot study which showed reduced fractal dimension was associated with short-term risk of stroke,10 and a cross-sectional study by other investigators showed similar results.11 We hypothesized that persons with reduced retinal vascular fractal are at increased risk of cerebrovascular events such as stroke and tested our hypothesis in a large prospective population-based cohort study.

Methods

Study Population

The data that support the findings of this study are available from the corresponding author upon reasonable request. We examined the relationship of retinal vascular fractal (Df) and stroke mortality in the Blue Mountains Eye Study, a prospective, population-based cohort of predominantly Whites aged 49 years or older at the commencement of the study in 1992.7 Baseline participants (n=3654) represented 82.4% of eligible potential participants living in 2 postcode areas in the Blue Mountains, New South Wales, Australia. This study was conducted according to the recommendations of the Declaration of Helsinki and was approved by the Western Sydney Area Human Ethics Committee and the University of Sydney Human Ethics committee. Written, informed consent was obtained from all participants. The study population comprised 3143 participants (86.0%) who had baseline retinal photographs suitable for measuring Df.

Retinal Photography and Measurement of Fractal Dimension

At the baseline examination, 30° retinal photographs of the optic disc, macula, and other retinal fields of both eyes were taken after pupil dilation using a Zeiss FF3 fundus camera (Carl Zeiss, Oberkochen, Germany). Optic disc-centered photographs were digitized in monochrome and used to measure 2 parameters: fractal dimension of the retinal vasculature and retinal vessel caliber. Measurement was performed by trained graders.
The program to measure fractal dimension, International Retinal Imaging Software—Fractal, is described elsewhere.7 Briefly, digital monochrome disk-centered images of the right eye fundus were viewed on two 21-inch monitors allowing image displays at 1280×1024 resolution. Trained graders examined the images, determined the radius of the optic disk, and cropped a circular area 3.5 optic disk radii surrounding the center of the optic disk. Cropping of a consistently defined area provides measures comparable among different images of the same individual taken at different time points, or among dissimilar individuals. International Retinal Imaging Software—Fractal then automatically generated a skeletonized line tracing of the retinal vessels from the image (Figure) which the grader examined and compared with the original cropped image to identify and erase artifacts that were occasionally erroneously included in the skeletonized line tracing such as alpha peripapillary atrophy, choroidal vessels, and pigment abnormalities. Df was then calculated from the refined skeletonized line tracing using the box-counting method, an established method of measuring fractal dimension of structures that are not perfectly self-similar, such as the real-life retinal vasculature.12,13 All measurements were performed by a single grader with high intragrader reliability (intraclass correlation coefficient, 0.95).
Figure. Fractal pattern of retinal vessels. The upper series shows an eye with higher fractal dimension (Df=1.442) and more complex branching pattern, while the lower series shows one with reduced fractal dimension (Df=1.423) and less complex branching pattern (vascular rarefaction). The participant whose eye is shown in the upper series died from stroke 7 y later.
Retinal arteriolar and venular calibers were also measured from photographs using a separate computer program (IVAN, University of Wisconsin), described elsewhere.14 Individual vessel caliber measurements were combined into summary indices referred to as central retinal artery equivalent and central retinal vein equivalent, which represented the estimated mean retinal arteriolar and venular caliber of the eye. As previously reported, intra- and inter-grader grading agreement was high, with quadratic weighted κ values ranging from 0.80 to 0.93.14 Further details are given elsewhere.14 Data from the right eye was used in these analyses.

Measurement of Other Variables

Systolic and diastolic BP measurements were taken concurrently at the baseline visit. A single BP measurement using the same mercury sphygmomanometer with appropriate adult cuff size was taken of each participant following at least 10 minutes of being seated. We adapted the 2003 World Health Organization guidelines15 to define hypertension, taking as hypertensive grade 2 or above (severe hypertension) if the subject was previously diagnosed as hypertensive and currently using antihypertensive medications, or had a systolic BP ≥160 mm Hg or diastolic BP ≥100 mm Hg at examination. We defined diabetes as a physician diagnosis of diabetes, or a fasting blood sugar ≥7 mmol/L. Serum total cholesterol and HDL (high-density lipoprotein) cholesterol were measured from casual (United States) or fasting blood specimens (Australia) using standard procedures. We obtained self-reported history of angina and acute myocardial infarction from face-to-face interviews and defined history of stroke if either of these conditions was present. These definitions are described in detail in other reports.16

Assessment of Stroke Mortality

We determined stroke mortality based on deaths and causes of death from the Australian National Death Index.16 Causes of death in the National Death Index database are collected from death certificates, which are completed by the physician in attendance, coroner or medical examiner, regardless of whether the death occurred in a hospital or in the community. This is recorded using International Classification of Diseases (ICD) codes. Stroke death was defined if any of the following codes from ICD-9 and ICD-10 were included in the causes of death (ICD-9: 430.0–438.9, and ICD-10: I60.0–I69.9). Australian National Death Index data has high sensitivity and specificity for vascular mortality (92.5% and 89.6%, respectively).17 The census cutoff for CHD death was December 31, 2005 (12-year follow-up).

Statistical Analysis

We divided the baseline population into quartiles of Df and assessed the risk of stroke mortality in each quartile. Reduced Df was defined as Df in the smallest (lowest) quartile. We used Cox regression to estimate hazard ratios (HR) and 95% CI. The initial multivariable models adjusted for age, gender, body mass index, mean arterial BP, diabetes, current smoking, history of stroke or coronary heart disease, HDL cholesterol, and triglycerides. The second model further adjusted for retinal arteriolar and venular calibers. The proportional hazards assumption was tested with respect to the time period variable, namely visual inspection of the log cumulative hazard plots and adding time-dependent variables into the first multivariable model. Age violated the proportional hazards assumption and hence was modeled as a strata variable (in 10-year categories). Prespecified subgroup analyses were performed, after stratification by gender, hypertension, and diabetes.

Results

Of 3143 participants at baseline, 132 (4.2%) died from stroke-related causes over the 12 year follow-up period. Table 1 shows the baseline characteristics of patients by quartiles of Df. The Figure shows the skeletonized vessel tracing of a participant who died from stroke compared with a normal control who did not die from stroke. The reduced Df can be seen as a reduction in the complexity of the branching network.
Table 1. Baseline Characteristics of Participants in the Blue Mountains Eye Study
Baseline characteristics by quartiles of fractal dimension (Df)
 Q1 (n=838)Q2 (n=839)Q3 (n=838)Q4 (n=839)P value
Df range1.323–1.4281.428–1.4441.444–1.4571.457–1.506 
Mean age, y (SD)71.2 (9.6)66.0 (8.8)64.1 (8.4)61.3 (7.8)<0.0001
Male, %39.3%41.8%47%46.2%0.0037
Mean systolic BP, mm Hg (SD)151.8 (23.4)146.6 (21.2)144.6 (19.7)140.2 (19.4)<0.0001
Mean diastolic BP, mm Hg (SD)83.8 (10.5)83.7 (10.3)83.6 (10.0)82.5 (9.6)0.015
Body mass index, kg/m2 (SD)25.6 (4.5)26.0 (4.4)26.6 (4.8)26.4 (4.4)<0.0001
Plasma HDL cholesterol, mmol/L (SD)1.46 (0.43)1.46 (0.44)1.41 (0.43)1.40 (0.45)0.0004
BP medications37.2%30.2%33.1%26.5%<0.0001
Diabetes, %10.0%6.3%7.4%6.9%0.47
Current smoking, %11.0%15.0%14.3%20.4%<0.0001
History of previous stroke, %7.3%5.5%3.2%3.4%0.0001
History of coronary heart disease, %18.5%14.3%15.1%15.6%0.1
Retinal vein occlusion, %2.6%1.9%1.4%1.3%0.22
Diabetic retinopathy, %3.0%1.8%2.3%2.0%0.38
Mean arteriolar caliber182 (18.6)186.1 (17.4)188.2 (17.1)192.6 (17.6)<0.0001
Mean venular caliber219.2 (20.1)223.7 (20.5)226.7 (18.9)231.2 (20.4)<0.0001
BP indicates blood pressure; and HDL, high-density lipoprotein.
Stroke-related mortality was almost 6-fold higher in participants in the lowest quartile of Df, compared with participants in the largest quartile (P<0.01, Table 2). After adjustment for age, sex, mean arterial BP, smoking and other covariates, the association remained significant with multivariable-adjusted HR, 2.42 (95% CI, 1.15–5.07); P trend=0.03. After further adjustment for retinal arteriolar and venular caliber, those in the lowest quartile of Df compared with the highest quartile, had an ≈2-fold greater risk of stroke mortality. When modeled as a continuous variable, decreased Df was associated with increased stroke mortality with multivariable-adjusted HR, 1.26 (95% CI, 1.06–1.51) per SD Df decrease. These associations remained similar with further adjustment for retinal arteriolar and venular calibers. We constructed additional multivariable analyses adjusting for retinal vascular disorders such as retinal vein occlusion and diabetic retinopathy. The final multivariable model adjusted for age, sex, body mass index, mean arterial BP, smoking history, diabetes, history of stroke or coronary heart disease, triglycerides and high-density cholesterol, retinal vein occlusion, diabetic retinopathy (Table 2). The findings further strengthened, with multivariable-adjusted HR, 2.41 (95% CI, 1.15–5.07); P=0.02 comparing the lowest Df with the highest.
Table 2. Df and Risk of Stroke Mortality
DfRisk of stroke mortality (95% CI)
% (n) stroke mortalityAge-sex adjusted HRP valueMultivariable-adjusted HR*P valueMultivariable-adjusted HRP valueMultivariable-adjusted HRP value
First quartile7.73 (64)2.32 (1.19–4.53)0.012.42 (1.15–5.07)0.022.21 (1.04–4.70)0.042.41 (1.15–5.07)0.02
Second quartile4.46 (37)1.88 (0.95–3.73)0.071.96 (0.92–4.16)0.081.82 (0.85–3.88)0.121.96 (0.92–4.17)0.08
Third quartile3.49 (29)1.85 (0.92–3.72)0.081.94 (0.90–4.19)0.091.88 (0.87–4.07)0.111.96 (0.91–4.23)0.09
Fourth quartile1.33 (11)1.0 (referent)1.0 (referent)1.0 (referent)1.0 (referent)
P for trend0.02 0.03 0.06 0.03 
Per SD decrease 1.24 (1.06–1.45)0.011.26 (1.06–1.51)0.011.26 (1.03–1.53)0.021.26 (1.05–1.50)0.01
Df indicates fractal dimension; and HR, hazard ratio.
*
Multivariable analyses adjusted for age, sex, body mass index, mean arterial blood pressure, smoking history, diabetes, history of stroke or coronary heart disease, triglycerides, and high-density cholesterol.
Additionally adjusted for retinal arteriolar and venular calibers.
Multivariable analyses adjusted for age, sex, body mass index, mean arterial blood pressure, smoking history, diabetes, history of stroke or coronary heart disease, triglycerides and high-density cholesterol, retinal vein occlusion, and diabetic retinopathy.
The association of Df with stroke mortality was strongest in men (multivariable HR, 4.17 [95% CI, 1.22–14.29]) and nonsignificant in women (multivariable-adjusted HR, 1.38 [95% CI, 0.61–3.14]; Table 3). The P value for the interaction between gender and the association of Df with stroke mortality was nonsignificant(P>0.05). The association was similar in participants with and without a history of stroke, although it was nonsignificant in both groups.
Table 3. Df and Risk of Stroke Mortality by Subgroups
Risk of stroke mortality (95% CI)*
SubgroupsStroke mortality rate (%)Multivariable-adjusted HRP valueMultivariable-adjusted HRP value
Men57/1362 (4.2)4.17 (1.22–14.29)0.023.94 (1.14–13.51)0.03
Women75/1781 (4.2)1.38 (0.61–3.14)0.441.25 (0.54–2.90)0.60
No hypertension23/911 (2.5)NANANANA
Hypertension109/2232 (4.9)1.55 (0.76–3.17)0.231.43 (0.69–2.95)0.33
Diabetes12/245 (4.9)NANANANA
No diabetes120/2898 (4.1)1.92 (0.97–3.79)0.061.73 (0.86–3.46)0.12
No history of stroke or CHD96/2558 (3.8)2.11 (0.91–4.93)0.081.78 (0.75–4.20)0.19
History of stroke or CHD36/585 (6.2)2.05 (0.67–6.29)0.212.02 (0.65–6.25)0.23
No history of Stroke114/2985 (3.9)1.88 (0.92–3.83)0.081.65 (0.80–3.41)0.17
History of Stroke16/145 (11.03)2.21 (0.24–20.0)0.482.34 (0.24–23.28)0.46
CHD indicates coronary heart disease; Df, fractal dimension; HR, hazard ratio; and NA, not applicable due to small numbers.
*
Smallest vs largest fractal dimension quartile.
Multivariable analyses adjusted for age, sex, body mass index, mean arterial blood pressure, smoking history, diabetes, history of stroke, or coronary heart disease.
Additionally adjusted for retinal arteriolar and venular calibers.
We performed supplementary analyses with additional adjustment for use of antihypertensive medications in multivariable models. The results remained similar, with multivariable HR, 2.39 (95% CI, 1.14–5.02) comparing participants in the lowest Df quartile with the highest, and multivariable HR, 1.26 (95% CI, 1.05–1.50) per SD decrease in Df when modeled as a continuous variable.
We also performed propensity score matching to reduce the effects of any skewed baseline variables. Before propensity score matching, the initial multivariable HR comparing the lowest Df with the highest was HR, 2.42 (95% CI, 1.15–5.07); P=0.02, Table 2. After propensity score matching, the HR remained similar at 2.49 (95% CI, 1.01–6.13), P=0.04.

Discussion

The retinal vascular fractal dimension, or Df, is a global measure of retinal vascular branching complexity and density.7,9 We hypothesized that reduced Df, representing a sparser microvascular network, is an indicator of tissue hypoxia in the retina (and brain) and would be associated with incident stroke mortality. We tested the hypothesis in a population-based cohort of 3143 older individuals and found that reduced Df was associated with higher rates of stroke mortality. Multivariable adjustment for age, gender, smoking, BP, history of stroke, and other risk factors attenuated this relationship, but reduced Df remained independently associated with stroke mortality.
There are few studies for direct comparison. We previously conducted a pilot case-control study of a subsample (n=312, 10%) of our cohort and found reduced Df was associated with 5-year incident stroke.10 Our current study now extended to the entire cohort over a longer time period confirms these findings and provides more precise risk estimates after adjustment for confounders. A case-control study in Singaporean Chinese found reduced Df was associated with prevalent ischemic stroke compared with controls without stroke,11 in line with our study results. Other studies have found more conflicting results but had limitations. For example, a study in Asian Malays did not detect any association between Df and 5-year incident stroke, but the study was limited by small numbers of incident stroke cases (n=51).18 Another case-control study found lacunar stroke was associated with larger Df,19 while another similarly designed study reported lacunar stroke associated with reduced Df.20 The control group in both these studies was participants with other forms of stroke, and the results may not be directly applicable to our study.
Stroke is closely associated with cognitive dysfunction and may share similar pathophysiology. Our findings are consistent with reports that reduced Df is associated with Alzheimer disease21 and cognitive impairment.22 In patients with type 1 diabetes, reduced Df predicts microvascular complications such as diabetic retinopathy, neuropathy, and nephropathy,23 but not macrovascular complications such as stroke.24 Again this may have been limited by the small number of participants with type 1 diabetes studied (n=208). Reduced Df has also been linked with increased prevalence of cerebral microbleeds,25 supporting a link with cerebral dysfunction. A recent cross-sectional study found reduced arteriolar Df associated with magnetic resonance imaging evidence of small vessel disease.26 Reduced Df is associated in cross-sectional studies with lacunar stroke, as well as with large vessel and cardioembolic stroke,11,27 both of which have high mortality. The association with the latter 2 conditions may drive the association in our study of reduced Df and stroke mortality.
Our study does not provide a means to determine the mechanism(s) linking reduced Df in the retinal microvasculature with increased stroke mortality. However, we may speculate that this association may reflect similar changes in retinal and cerebral microcirculations. The loss of branching complexity of small vessels may impair collateral circulation and consequently lead to tissue hypoxia and loss of collateral blood flow in the case of arterial occlusion, which in turn increases the risk of stroke and stroke mortality.28 Reduced Df is clinically visible as rarefaction of the microcirculation and loss of vascular density, and occurs with aging, hypertension, and other vascular diseases.29–32 The endothelium may mediate these changes as it plays a major role in maintaining vascular bifurcations.33,34 Narrower retinal arterioles and wider retinal venules may be early markers of microvascular damage that have been consistently shown to predict vascular disease.3,35,36 However, after adjustment for retinal vascular calibers in our analyses, the association of reduced Df with stroke mortality remained similar, signifying that Df conveys additional prognostic information independent of vascular calibers. A recent study of a knock-in mouse model of the rare autosomal dominant syndrome, Retinal Vasculopathy With Cerebral Leukoencephalopathy and Systemic Manifestations, showed an association of retinal microvascular abnormalities with increased susceptibility to experimental stroke and mortality, further supporting a link between retinal vascular changes and stroke mortality.37
Whether reduced Df can be used clinically to improve stroke prediction need further investigation. A meta-analysis of retinal vessel calibers and incident stroke has found that while wider retinal venules is consistently associated with increased risk of stroke, the additional prognostic information over and above that of traditional cardiovascular risk factors was modest.36 Further work is needed to confirm our findings and evaluate the clinical utility of Df as a cardiovascular risk marker. Future studies would benefit from collecting data on stroke subtype, to determine if Df is associated with ischemic or hemorrhagic stroke, or both.
In subgroup analyses the association of Df with stroke mortality was present in men but not in women. These results should be taken as hypothesis-generating. There is some evidence that cardiovascular risk may vary by gender. Retinal vessel calibers are more predictive of incident coronary heart disease in women than men,35 in line with evidence that microvascular disease plays a more prominent role in coronary microvascular dysfunction in women. There is less evidence for gender differences in stroke although a systematic review has suggested men have a higher rate of incident stroke than women.38 This was postulated to be related to several possibilities including the protective effects of estrogen on cerebral circulation, genetic factors, differences in BP and other cerebrovascular risk factors such as ischemic heart disease, peripheral artery disease, and smoking, all of which are more prevalent in males.39
Our results add to growing evidence that retinal Df may be a useful biomarker of stroke risk. However several methodological issues need to be addressed before Df can be considered for clinical application. Different methodological techniques have been used to measure Df, with considerable variation in the retinal area sampled, use of different algorithms, use of different calculation techniques (eg, box counting, Higuchi method, spectrum, or Fourier method), and semi or fully automated analysis depending on degree of input from graders. This has been well covered in a recent review.40 The methodology used in this report is the most widely used, particularly in analyses of association with neurological conditions.40 Nonetheless, there is limited agreement between different methods41 and standardized measurement of quantitative retinal parameters such as Df is desirable to improve reproducibility.
Our study has several strengths including a prospective design with long follow-up of a large cohort, masked, and objective measurement of Df, multivariable adjustment for confounders, and assessment of stroke mortality with validated death records. The following limitations deserve mention. First, we measured Df in the retinal microcirculation rather than cerebral microcirculation and assumed that changes in the former mirror changes in the latter. This may be a reasonable assumption as histological studies demonstrate similar changes in cerebral and retinal microcirculation with hypertension.42 Second, we did not assess or confirm cases of stroke and used stroke-related mortality as the outcome. This may miss participants with milder strokes and transient ischemic attack who would have been censored in our analyses. This may act to reduce the magnitude of effect we report. Third, we measured total fractal dimension of both arterioles and venules. There is some evidence reduced arteriolar rather than venular fractal dimension is associated with cerebral microbleeds,25,26 and higher arteriolar Df may be associated with larger cortical volume, whereas higher venular Df may be associated with lower cortical volume in patients with HIV.43 Venular Df may also be a more sensitive indicator of age-related rarefaction of vasculature.43 Recent evidence has shown that the molecular and cellular regulation of superficial and deep, as well as arterial, venous and capillary blood vessels in the retina differs, and are differently affected by hypertension and other vascular diseases such as diabetes.44 Our method does not reflect the deep vascular networks which may limit the information gathered. Separating the components of Df into superficial and deep, as well arterial and venular, may thus be useful in future studies and provide insights into pathophysiology. As Df is a dynamic measure and changes with age, there is a possibility of misclassification as Df evolves from the baseline measure over the study period. Future studies could control for this by measuring Df at different study points. Finally, atrial fibrillation is an important cause of severe stroke and, therefore, stroke mortality, but we did not collect data on this condition. Future studies should take this into account.
In summary, we report that older persons with reduced retinal fractal dimension had a higher long-term risk of stroke mortality independent of age, gender, smoking, BP, and other risk factors. Reduced retinal vascular fractal may indicate relative retinal (and cerebral) tissue hypoxia and hence increased risk of stroke mortality.

Acknowledgments

We acknowledge the participants of the Blue Mountains Eye Study and thank them for their contributions.

Footnote

Nonstandard Abbreviations and Acronyms

BP
blood pressure
Df
fractal dimension
HDL
high-density lipoprotein
HR
hazard ratio
ICD
International Classification of Disease

References

1.
Go AS, Mozaffarian D, Roger VL, Benjamin EJ, Berry JD, Blaha MJ, Dai S, Ford ES, Fox CS, Franco S, et al; American Heart Association Statistics Committee and Stroke Statistics Subcommittee. Executive summary: heart disease and stroke statistics–2014 update: a report from the American Heart Association. Circulation. 2014;129:399–410. doi: 10.1161/01.cir.0000442015.53336.12
2.
Baker ML, Hand PJ, Wang JJ, Wong TY. Retinal signs and stroke: revisiting the link between the eye and brain. Stroke. 2008;39:1371–1379. doi: 10.1161/STROKEAHA.107.496091
3.
Wong TY, Mitchell P. Hypertensive retinopathy. N Engl J Med. 2004;351:2310–2317. doi: 10.1056/NEJMra032865
4.
Qiu C, Cotch MF, Sigurdsson S, Klein R, Jonasson F, Klein BE, Garcia M, Jonsson PV, Harris TB, Eiriksdottir G, et al. Microvascular lesions in the brain and retina: the age, gene/environment susceptibility-Reykjavik study. Ann Neurol. 2009;65:569–576. doi: 10.1002/ana.21614
5.
Mitchell P, Wang JJ, Wong TY, Smith W, Klein R, Leeder SR. Retinal microvascular signs and risk of stroke and stroke mortality. Neurology. 2005;65:1005–1009. doi: 10.1212/01.wnl.0000179177.15900.ca
6.
Lindley RI, Wang JJ, Wong MC, Mitchell P, Liew G, Hand P, Wardlaw J, De Silva DA, Baker M, Rochtchina E, et al; Multi-Centre Retina and Stroke Study (MCRS) Collaborative Group. Retinal microvasculature in acute lacunar stroke: a cross-sectional study. Lancet Neurol. 2009;8:628–634. doi: 10.1016/S1474-4422(09)70131-0
7.
Liew G, Wang JJ, Cheung N, Zhang YP, Hsu W, Lee ML, Mitchell P, Tikellis G, Taylor B, Wong TY. The retinal vasculature as a fractal: methodology, reliability, and relationship to blood pressure. Ophthalmology. 2008;115:1951–1956. doi: 10.1016/j.ophtha.2008.05.029
8.
Kwa VI, van der Sande JJ, Stam J, Tijmes N, Vrooland JL; Amsterdam Vascular Medicine Group. Retinal arterial changes correlate with cerebral small-vessel disease. Neurology. 2002;59:1536–1540. doi: 10.1212/01.wnl.0000033093.16450.5c
9.
Patton N, Aslam TM, MacGillivray T, Deary IJ, Dhillon B, Eikelboom RH, Yogesan K, Constable IJ. Retinal image analysis: concepts, applications and potential. Prog Retin Eye Res. 2006;25:99–127. doi: 10.1016/j.preteyeres.2005.07.001
10.
Kawasaki R, Che Azemin MZ, Kumar DK, Tan AG, Liew G, Wong TY, Mitchell P, Wang JJ. Fractal dimension of the retinal vasculature and risk of stroke: a nested case-control study. Neurology. 2011;76:1766–1767. doi: 10.1212/WNL.0b013e31821a7d7d
11.
Ong YT, De Silva DA, Cheung CY, Chang HM, Chen CP, Wong MC, Wong TY, Ikram MK. Microvascular structure and network in the retina of patients with ischemic stroke. Stroke. 2013;44:2121–2127. doi: 10.1161/STROKEAHA.113.001741
12.
Stosić T, Stosić BD. Multifractal analysis of human retinal vessels. IEEE Trans Med Imaging. 2006;25:1101–1107. doi: 10.1109/tmi.2006.879316
13.
Mainster MA. The fractal properties of retinal vessels: embryological and clinical implications. Eye (Lond). 1990;4(Pt 1):235–241. doi: 10.1038/eye.1990.33
14.
Sherry LM, Wang JJ, Rochtchina E, Wong T, Klein R, Hubbard L, Mitchell P. Reliability of computer-assisted retinal vessel measurementin a population. Clin Exp Ophthalmol. 2002;30:179–182. doi: 10.1046/j.1442-9071.2002.00520.x
15.
Whitworth JA; World Health Organization, International Society of Hypertension Writing Group. 2003 World Health Organization (WHO)/International Society of Hypertension (ISH) statement on management of hypertension. J Hypertens. 2003;21:1983–1992. doi: 10.1097/00004872-200311000-00002
16.
Wang JJ, Liew G, Klein R, Rochtchina E, Knudtson MD, Klein BE, Wong TY, Burlutsky G, Mitchell P. Retinal vessel diameter and cardiovascular mortality: pooled data analysis from two older populations. Eur Heart J. 2007;28:1984–1992. doi: 10.1093/eurheartj/ehm221
17.
Magliano D, Liew D, Pater H, Kirby A, Hunt D, Simes J, Sundararajan V, Tonkin A. Accuracy of the Australian National Death Index: comparison with adjudicated fatal outcomes among Australian participants in the long-term intervention with pravastatin in ischaemic disease (LIPID) study. Aust N Z J Public Health. 2003;27:649–653. doi: 10.1111/j.1467-842x.2003.tb00615.x
18.
Cheung CY, Tay WT, Ikram MK, Ong YT, De Silva DA, Chow KY, Wong TY. Retinal microvascular changes and risk of stroke: the Singapore Malay Eye Study. Stroke. 2013;44:2402–2408. doi: 10.1161/STROKEAHA.113.001738
19.
Cheung N, Liew G, Lindley RI, Liu EY, Wang JJ, Hand P, Baker M, Mitchell P, Wong TY; Multi-Center Retina & Stroke Study Collaborative Group. Retinal fractals and acute lacunar stroke. Ann Neurol. 2010;68:107–111. doi: 10.1002/ana.22011
20.
Doubal FN, MacGillivray TJ, Patton N, Dhillon B, Dennis MS, Wardlaw JM. Fractal analysis of retinal vessels suggests that a distinct vasculopathy causes lacunar stroke. Neurology. 2010;74:1102–1107. doi: 10.1212/WNL.0b013e3181d7d8b4
21.
Williams MA, McGowan AJ, Cardwell CR, Cheung CY, Craig D, Passmore P, Silvestri G, Maxwell AP, McKay GJ. Retinal microvascular network attenuation in Alzheimer’s disease. Alzheimers Dement (Amst). 2015;1:229–235. doi: 10.1016/j.dadm.2015.04.001
22.
Ong YT, Hilal S, Cheung CY, Xu X, Chen C, Venketasubramanian N, Wong TY, Ikram MK. Retinal vascular fractals and cognitive impairment. Dement Geriatr Cogn Dis Extra. 2014;4:305–313. doi: 10.1159/000363286
23.
Broe R, Rasmussen ML, Frydkjaer-Olsen U, Olsen BS, Mortensen HB, Peto T, Grauslund J. Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus: the Danish cohort of pediatric diabetes 1987 (DCPD1987). Diabetologia. 2014;57:2215–2221. doi: 10.1007/s00125-014-3317-6
24.
Grauslund J, Green A, Kawasaki R, Hodgson L, Sjølie AK, Wong TY. Retinal vascular fractals and microvascular and macrovascular complications in type 1 diabetes. Ophthalmology. 2010;117:1400–1405. doi: 10.1016/j.ophtha.2009.10.047
25.
McGrory S, Ballerini L, Doubal FN, Staals J, Allerhand M, Valdes-Hernandez MDC, Wang X, MacGillivray T, Doney ASF, Dhillon B, et al. Retinal microvasculature and cerebral small vessel disease in the Lothian Birth Cohort 1936 and Mild Stroke Study. Sci Rep. 2019;9:6320. doi: 10.1038/s41598-019-42534-x
26.
Hilal S, Ong YT, Cheung CY, Tan CS, Venketasubramanian N, Niessen WJ, Vrooman H, Anuar AR, Chew M, Chen C, et al. Microvascular network alterations in retina of subjects with cerebral small vessel disease. Neurosci Lett. 2014;577:95–100. doi: 10.1016/j.neulet.2014.06.024
27.
Wu HQ, Wu H, Shi LL, Yu LY, Wang LY, Chen YL, Geng JS, Shi J, Jiang K, Dong JC. The association between retinal vasculature changes and stroke: a literature review and Meta-analysis. Int J Ophthalmol. 2017;10:109–114. doi: 10.18240/ijo.2017.01.18
28.
Kwa VI, Lopez OL. Fractal analysis of retinal vessels: peeping at the tree of life? Neurology. 2010;74:1088–1089. doi: 10.1212/WNL.0b013e3181d7d917
29.
Stanton AV, Wasan B, Cerutti A, Ford S, Marsh R, Sever PP, Thom SA, Hughes AD. Vascular network changes in the retina with age and hypertension. J Hypertens. 1995;13(12 Pt 2):1724–1728.
30.
Lipsitz LA, Goldberger AL. Loss of ‘complexity’ and aging. Potential applications of fractals and chaos theory to senescence. JAMA. 1992;267:1806–1809.
31.
Hughes AD, Martinez-Perez E, Jabbar AS, Hassan A, Witt NW, Mistry PD, Chapman N, Stanton AV, Beevers G, Pedrinelli R, et al. Quantification of topological changes in retinal vascular architecture in essential and malignant hypertension. J Hypertens. 2006;24:889–894. doi: 10.1097/01.hjh.0000222759.61735.98
32.
Ab Hamid F, Che Azemin MZ, Salam A, Aminuddin A, Mohd Daud N, Zahari I. Retinal vasculature fractal dimension measures vessel density. Curr Eye Res. 2016;41:823–831. doi: 10.3109/02713683.2015.1056375
33.
Sherman TF, Popel AS, Koller A, Johnson PC. The cost of departure from optimal radii in microvascular networks. J Theor Biol. 1989;136:245–265. doi: 10.1016/s0022-5193(89)80162-6
34.
Griffith TM, Edwards DH. Basal EDRF activity helps to keep the geometrical configuration of arterial bifurcations close to the Murray optimum. J Theor Biol. 1990;146:545–573. doi: 10.1016/s0022-5193(05)80378-9
35.
McGeechan K, Liew G, Macaskill P, Irwig L, Klein R, Klein BE, Wang JJ, Mitchell P, Vingerling JR, Dejong PT, et al. Meta-analysis: retinal vessel caliber and risk for coronary heart disease. Ann Intern Med. 2009;151:404–413. doi: 10.7326/0003-4819-151-6-200909150-00005
36.
McGeechan K, Liew G, Macaskill P, Irwig L, Klein R, Klein BE, Wang JJ, Mitchell P, Vingerling JR, de Jong PT, et al. Prediction of incident stroke events based on retinal vessel caliber: a systematic review and individual-participant meta-analysis. Am J Epidemiol. 2009;170:1323–1332. doi: 10.1093/aje/kwp306
37.
Mulder IA, Rubio-Beltran E, Ibrahimi K, Dzyubachyk O, Khmelinskii A, Hoehn M, Terwindt GM, Wermer MJH, MaassenVanDenBrink A, van den Maagdenberg AMJM. Increased mortality and vascular phenotype in a knock-in mouse model of retinal vasculopathy with cerebral leukoencephalopathy and systemic manifestations. Stroke. 2020;51:300–307. doi: 10.1161/STROKEAHA.119.025176
38.
Appelros P, Stegmayr B, Terént A. Sex differences in stroke epidemiology: a systematic review. Stroke. 2009;40:1082–1090. doi: 10.1161/STROKEAHA.108.540781
39.
Krause DN, Duckles SP, Pelligrino DA. Influence of sex steroid hormones on cerebrovascular function. J Appl Physiol (1985). 2006;101:1252–1261. doi: 10.1152/japplphysiol.01095.2005
40.
Lemmens S, Devulder A, Van Keer K, Bierkens J, De Boever P, Stalmans I. Systematic review on fractal dimension of the retinal vasculature in neurodegeneration and stroke: assessment of a potential biomarker. Front Neurosci. 2020;14:16. doi: 10.3389/fnins.2020.00016
41.
McGrory S, Taylor AM, Pellegrini E, Ballerini L, Kirin M, Doubal FN, Wardlaw JM, Doney ASF, Dhillon B, Starr JM, et al. Towards standardization of quantitative retinal vascular parameters: comparison of SIVA and VAMPIRE measurements in the Lothian birth cohort 1936. Transl Vis Sci Technol. 2018;7:12. doi: 10.1167/tvst.7.2.12
42.
Goto I, Katsuki S, Ikui H, Kimoto K, Mimatsu T. Pathological studies on the intracerebral and retinal arteries in cerebrovascular and noncerebrovascular diseases. Stroke. 1975;6:263–269. doi: 10.1161/01.str.6.3.263
43.
Crystal HA, Holman S, Lui YW, Baird AE, Yu H, Klein R, Rojas-Soto DM, Gustafson DR, Stebbins GT. Association of the fractal dimension of retinal arteries and veins with quantitative brain MRI measures in HIV-infected and uninfected women. PLoS One. 2016;11:e0154858. doi: 10.1371/journal.pone.0154858
44.
Yang JM, Park CS, Kim SH, Noh TW, Kim JH, Park S, Lee J, Park JR, Yoo D, Jung HH, et al. Dll4 suppresses transcytosis for arterial blood-retinal barrier homeostasis. Circ Res. 2020;126:767–783. doi: 10.1161/CIRCRESAHA.119.316476

eLetters(0)

eLetters should relate to an article recently published in the journal and are not a forum for providing unpublished data. Comments are reviewed for appropriate use of tone and language. Comments are not peer-reviewed. Acceptable comments are posted to the journal website only. Comments are not published in an issue and are not indexed in PubMed. Comments should be no longer than 500 words and will only be posted online. References are limited to 10. Authors of the article cited in the comment will be invited to reply, as appropriate.

Comments and feedback on AHA/ASA Scientific Statements and Guidelines should be directed to the AHA/ASA Manuscript Oversight Committee via its Correspondence page.

Information & Authors

Information

Published In

Go to Stroke
Go to Stroke
Stroke
Pages: 1276 - 1282
PubMed: 33611944

Versions

You are viewing the most recent version of this article.

History

Received: 21 July 2020
Revision received: 28 November 2020
Accepted: 12 January 2021
Published online: 22 February 2021
Published in print: April 2021

Permissions

Request permissions for this article.

Keywords

  1. fractals
  2. hypertension
  3. hypoxia
  4. microcirculation
  5. retinal vessels

Subjects

Authors

Affiliations

Centre for Vision Research, Westmead Institute for Medical Research, University of Sydney, Australia (G.L., B.G., A.J.W., G.B.M., P.M.).
Bamini Gopinath, PhD
Centre for Vision Research, Westmead Institute for Medical Research, University of Sydney, Australia (G.L., B.G., A.J.W., G.B.M., P.M.).
Andrew J. White, MD, PhD
Centre for Vision Research, Westmead Institute for Medical Research, University of Sydney, Australia (G.L., B.G., A.J.W., G.B.M., P.M.).
George Burlutsky, MapplStat
Centre for Vision Research, Westmead Institute for Medical Research, University of Sydney, Australia (G.L., B.G., A.J.W., G.B.M., P.M.).
Tien Yin Wong, MD, PhD
Duke-NUS Medical School, National University of Singapore (T.Y.W.).
Singapore Eye Research Institute, Singapore National Eye Center (T.Y.W.).
Paul Mitchell, MD, PhD
Centre for Vision Research, Westmead Institute for Medical Research, University of Sydney, Australia (G.L., B.G., A.J.W., G.B.M., P.M.).

Notes

For Sources of Funding and Disclosures, see page 1281.
Correspondence to: Gerald Liew, MD, PhD, Centre for Vision Research, The Westmead Institute for Medical Research, University of Sydney, Westmead Hospital, 176 Hawkesbury Rd, Westmead, NSW Australia 2145. Email [email protected]

Disclosures

Disclosures None.

Sources of Funding

This study was funded by Australian National Health & Medical Research Council (NHMRC), Project grant IDs: 153948, 211069, and 302068.

Metrics & Citations

Metrics

Citations

Download Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Select your manager software from the list below and click Download.

  1. Retinal vascular fingerprints predict incident stroke: findings from the UK Biobank cohort study, Heart, (heartjnl-2024-324705), (2025).https://doi.org/10.1136/heartjnl-2024-324705
    Crossref
  2. Population-based Normative Reference for Retinal Microvascular Atlas, Ophthalmology Science, (100723), (2025).https://doi.org/10.1016/j.xops.2025.100723
    Crossref
  3. Associations of Retinal Microvascular Density and Fractal Dimension with Glaucoma: A Prospective Study from UK Biobank, Ophthalmology Science, 5, 2, (100661), (2025).https://doi.org/10.1016/j.xops.2024.100661
    Crossref
  4. Comparative analysis of retinal microvascular parameters in healthy individuals with or without carotid artery stenosis or plaque, European Journal of Ophthalmology, (2024).https://doi.org/10.1177/11206721241291224
    Crossref
  5. Retinal Vascular Measurements and Mortality Risk: Evidence From the UK Biobank Study, Translational Vision Science & Technology, 13, 1, (2), (2024).https://doi.org/10.1167/tvst.13.1.2
    Crossref
  6. Retinal artery to vein ratio is associated with cerebral microbleeds in individuals with type 1 diabetes, Journal of Hypertension, 42, 6, (1039-1047), (2024).https://doi.org/10.1097/HJH.0000000000003690
    Crossref
  7. Correlation between retinal vascular geometric parameters and pathologically diagnosed type 2 diabetic nephropathy, Clinical Kidney Journal, 17, 8, (2024).https://doi.org/10.1093/ckj/sfae204
    Crossref
  8. Predicting systemic diseases in fundus images: systematic review of setting, reporting, bias, and models’ clinical availability in deep learning studies, Eye, 38, 7, (1246-1251), (2024).https://doi.org/10.1038/s41433-023-02914-0
    Crossref
  9. Retinal Microvasculature Causally Affects the Brain Cortical Structure: A Mendelian Randomization Study, Ophthalmology Science, 4, 6, (100465), (2024).https://doi.org/10.1016/j.xops.2024.100465
    Crossref
  10. Retinal imaging for the assessment of stroke risk: a systematic review, Journal of Neurology, 271, 5, (2285-2297), (2024).https://doi.org/10.1007/s00415-023-12171-6
    Crossref
  11. See more
Loading...

View Options

View options

PDF and All Supplements

Download PDF and All Supplements

PDF/EPUB

View PDF/EPUB
Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Personal login Institutional Login
Purchase Options

Purchase this article to access the full text.

Purchase access to this article for 24 hours

Retinal Vasculature Fractal and Stroke Mortality
Stroke
  • Vol. 52
  • No. 4

Purchase access to this journal for 24 hours

Stroke
  • Vol. 52
  • No. 4
Restore your content access

Enter your email address to restore your content access:

Note: This functionality works only for purchases done as a guest. If you already have an account, log in to access the content to which you are entitled.

Figures

Tables

Media

Share

Share

Share article link

Share

Comment Response