Vascular Fractal Dimension Research Articles

Compound speckle model detects anti-angiogenic tumor response in preclinical nonlinear contrast-enhanced ultrasonography.

This paper proposes a method for analyzing the first-order speckle statistics of nonlinear contrast-enhanced ultrasound images from tumors. Contrast signal intensity is modeled as a compound distribution of exponential probability density functions with a gamma weighting function. The gamma probability weighting function serves as an approximation for log-normally distributed flow velocities in a vascular network. The model was applied to sub-harmonic bolus-injection images acquired from a mouse breast cancer xenograft model treated with murine version bevacizumab. The area under curve produced using the compound statistical model could more accurately discriminate anti-VEGF-treated tumors from untreated tumors than conventional contrast-enhanced ultrasound image processing. This result was validated with gold standard histological measures of microvascular density. Fractal vessel geometry was estimated using the gamma weighting function and tested against micro-CT perfusion casting. Treated tumors had a significantly lower vascular fractal dimension than control tumors. Vascular complexity estimated using the ultrasound compound statistical model performed similarly to micro-CT fractal dimension for discriminating treated from control tumors. The proposed technique can quantify tumor perfusion and provide an index of vascular complexity, making it a potentially useful addition for clinical detection of vascular normalization in anti-angiogenic trials.

PS 05-88 THE RELATIONSHIP OF RETINAL VESSEL DIAMETERS AND FRACTAL DIMENSIONS WITH BLOOD PRESSURE AND CARDIOVASCULAR RISK FACTORS

Objective: This study aimed to investigate the correlation between quantitative retinal vascular parameters such as central retinal arteriolar equivalent (CRAE) and retinal vascular fractal dimension [D(f)], and cardiovascular risk factors in the Chinese Han population residing in the in islands of southeast China. Design and Method: In this cross-sectional study, fundus photographs were collected and semi-automated analysis software was used to analyze retinal vessel diameters and fractal dimensions. Cardiovascular risk factors such as relevant medical history, blood pressure (BP), lipids, and blood glucose data were collected. Results: Subjects had a mean age of 51.9612.0 years and included 812 (37.4%) males and 1,357 (62.6%) females. Of the subjects, 726 (33.5%) were overweight, 226 (10.4%) were obese, 272 (12.5%) had diabetes, 738 (34.0%) had hypertension, and 1,156 (53.3%) had metabolic syndrome. After controlling for the effects of potential confounders, multivariate analyses found that age (β = 0.06, P = 0.008), sex (β = 1.33, P = 0.015), mean arterial blood pressure (β = −0.12, P < 0.001), high-sensitivity C-reactive protein (β = −0.22, P = 0.008), and CRVE (β = 0.23, P < 0.001) were significantly associated with CRAE. Age (β = −0.0012, P < 0.001), BP classification (prehypertension: β = −0.0075, P = 0.014; hypertension: β = −0.0131, P = 0.002), and hypertension history (β = −0.0007, P = 0.009) were significantly associated with D(f). Conclusions: D(f) exhibits a stronger association with BP than CRAE. Thus, D(f) may become a useful indicator of cardiovascular risk.

Quantitative analysis of vascular colonisation and angio-conduction in porous silicon-substituted hydroxyapatite with various pore shapes in a chick chorioallantoic membrane (CAM) model

The development of scaffolds for bone filling of large defects requires an understanding of angiogenesis and vascular guidance, which are crucial processes for bone formation and healing. There are few investigations on the ability of a scaffold to support blood vessel guidance and it this is of great importance because it relates to the quality and dispersion of the blood vessel network. This work reports an analysis of vascularisation of porous silicon-substituted hydroxyapatite (SiHA) bioceramics and the effects of pore shape on vascular guidance using an expedient ex ovo model, the chick embryo chorioallantoic membrane (CAM) assay. Image analysis of vascularised implants assessed the vascular density, fractal dimension and diameter of blood vessels at two different scales (the whole ceramic and pores alone) and was performed on model SiHA ceramics harbouring pores of various cross-sectional geometries (circles, square, rhombus, triangles and stars). SiHA is a biocompatible material which allows the conduction of blood vessels on its surface. The presence of pores did not influence angiogenesis related-parameters (arborisation, fractal dimension) but pore geometry affected the blood vessel guidance and angio-conductive potential (diameter and number of the blood vessels converging toward the pores). The measured angles of pore cross-section modulated the number and diameter of blood vessels converging to pores, with triangular pores appearing of particular interest. This result will be used for shaping ceramic scaffolds with specific porous architecture to promote vascular colonisation and osteointegration. Statement of SignificanceAn expedient and efficient method, using chick embryo chorioallantoic membrane (CAM) assays, has been set up to characterise quantitatively the angiogenesis and the vascular conduction in scaffolds. This approach complements the usual cell culture assays and could replace to a certain extent in vivo experiments. It was applied to silicon-substituted hydroxyapatite porous bioceramics with various pore shapes. The material was found to be biocompatible, allowing the conduction of blood vessels on its surface. The presence of pores does not influence the angiogenesis but the pore shape affects the blood vessel guidance and angio-conductive potential. Pores with triangular cross-section appear particularly attractive for the further design of scaffolds in order to promote their vascular colonisation and osteointegration and improve their performances.

Inter-Eye Agreement in Measurement of Retinal Vascular Fractal Dimension in Patients with Type 1 Diabetes Mellitus

ABSTRACTPurpose: To investigate inter-eye agreement in retinal vascular fractal dimension (FD) in patients with type 1 diabetes.Methods: In a cross-sectional study, both eyes were exained in 178 patients with type 1 diabetes. All vessels in a zone 0.5–2.0 disc diameters from the optic disc were traced and FD calculated with the box-counting method using SIVA-Fractal semiautomatic software. The modified Early Treatment Diabetic Retinopathy Study (ETDRS) scale was used to grade diabetic retinopathy (DR). Pitman’s test of difference in variance was used to calculated inter-eye agreement in FD according to level of DR.Results: Mean age and duration of diabetes was 37.0 years and 29.5 years, respectively, and 49.4% of participants were male. Mean FD of right and left eyes was 1.4540 and 1.4472, respectively. FD did not differ between eyes in patients with no or non-proliferative DR (NPDR) in both eyes. This was true for patients with the same level of DR in both eyes (n = 74, p = 0.73), as well as for patients in which the ETDRS level of DR between the eyes differed by 1 (n = 43, p = 0.99) or more (n = 9, p = 0.53). In patients treated for proliferative DR in one eye, FD was significantly lower in this eye compared to the other (n = 10, p = 0.03).Conclusion: FD did not differ significantly between the two eyes of patients with no DR or NPDR, despite differences in severity of DR.

Reliability of Using Retinal Vascular Fractal Dimension as a Biomarker in the Diabetic Retinopathy Detection.

The retinal fractal dimension (FD) is a measure of vasculature branching pattern complexity. FD has been considered as a potential biomarker for the detection of several diseases like diabetes and hypertension. However, conflicting findings were found in the reported literature regarding the association between this biomarker and diseases. In this paper, we examine the stability of the FD measurement with respect to (1) different vessel annotations obtained from human observers, (2) automatic segmentation methods, (3) various regions of interest, (4) accuracy of vessel segmentation methods, and (5) different imaging modalities. Our results demonstrate that the relative errors for the measurement of FD are significant and FD varies considerably according to the image quality, modality, and the technique used for measuring it. Automated and semiautomated methods for the measurement of FD are not stable enough, which makes FD a deceptive biomarker in quantitative clinical applications.

A prospective case-control study to investigate retinal microvascular changes in acute dengue infection

Dengue infection can affect the microcirculation by direct viral infection or activation of inflammation. We aimed to determine whether measured retinal vascular parameters were associated with acute dengue infection. Patients with acute dengue were recruited from Communicable Diseases Center, Singapore and age-gender-ethnicity matched healthy controls were selected from a population-based study. Retinal photographs were taken on recruitment and convalescence. A spectrum of quantitative retinal microvascular parameters (retinal vascular caliber, fractal dimension, tortuosity and branching angle) was measured using a semi-automated computer-based program. (Singapore I Vessel Assessment, version 3.0). We included 62 dengue patients and 127 controls. Dengue cases were more likely to have wider retinal arteriolar and venular calibers (158.3 μm vs 144.3 μm, p < 0.001; 227.7 μm vs 212.8 μm, p < 0.001; respectively), higher arteriolar and venular fractal dimensions (1.271 vs 1.249, p = 0.002; 1.268 vs. 1.230, p < 0.001, respectively), higher arteriolar and venular tortuosity (0.730 vs 0.546 [x104], p < 0.001; 0.849 vs 0.658 [x104], p < 0.001; respectively), compared to controls. Resolution of acute dengue coincided with decrease in retinal vascular calibers and venular fractal dimension. Dengue patients have altered microvascular network in the retina; these changes may reflect pathophysiological processes in the immune system.

Retinal Vascular Fractals Correlate With Early Neurodegeneration in Patients With Type 2 Diabetes Mellitus.

To investigate the correlation between the retinal vascular fractal dimension (Fd) and neurodegenerative changes in patients with no or mild diabetic retinopathy (DR). In this cross-sectional study we examined 103 patients with type 2 diabetes mellitus (T2DM) with no or mild DR. In a randomly selected eye of each patient, Fd was calculated using SIVA-Fractal, a specialized semiautomatic software. Retinal neurodegeneration was evaluated by Topcon 3D OCT-2000 spectral-domain optical coherence tomography (OCT) and by a RETI-scan multifocal ERG (mf-ERG) system in rings one to six. Level of DR was determined by a single trained grader in seven-field fundus photos according to the Early Treatment Diabetic Retinopathy Study (ETDRS) scale. Mean age and duration of T2DM were 62.3 and 11.6 years, respectively; 46.6% were men. Mean Fd was 1.413 (range, 1.278-1.509) and ETDRS levels were 10 (42.7%), 20 (35.0%), and 35 (22.3%), respectively. Fd correlated inversely with mf-ERG implicit time of ring one (r = -0.25, P = 0.01) and present diabetic neuropathy (P = 0.02), and positively with OCT ganglion cell layer (GCL) thickness (r = 0.20, P = 0.04). In a multivariable linear regression model, Fd was associated with mf-ERG implicit time of ring one (coefficient -0.0021/ms, P = 0.040) and the presence of diabetic neuropathy (coefficient -0.0209 for neuropathy present versus absent, P = 0.041). In patients with T2DM and no or minimal DR, independent correlations were found between early vascular and neurogenic changes. Thus, retinal vascular fractal analysis might be considered as a tool to identify patients with early neurodegenerative retinal changes.

GW26-e1287 Aortic stiffness is associated with the central retinal arteriolar equivalent and retinal vascular fractal dimension in a population along the southeastern coast of China

GW26-e1287 Aortic stiffness is associated with the central retinal arteriolar equivalent and retinal vascular fractal dimension in a population along the southeastern coast of China

Retinal vascular fractal dimension, childhood IQ, and cognitive ability in old age: the Lothian Birth Cohort Study 1936.

PurposeCerebral microvascular disease is associated with dementia. Differences in the topography of the retinal vascular network may be a marker for cerebrovascular disease. The association between cerebral microvascular state and non-pathological cognitive ageing is less clear, particularly because studies are rarely able to adjust for pre-morbid cognitive ability level. We measured retinal vascular fractal dimension (D f) as a potential marker of cerebral microvascular disease. We examined the extent to which it contributes to differences in non-pathological cognitive ability in old age, after adjusting for childhood mental ability.MethodsParticipants from the Lothian Birth Cohort 1936 Study (LBC1936) had cognitive ability assessments and retinal photographs taken of both eyes aged around 73 years (n = 648). IQ scores were available from childhood. Retinal vascular D f was calculated with monofractal and multifractal analysis, performed on custom-written software. Multiple regression models were applied to determine associations between retinal vascular D f and general cognitive ability (g), processing speed, and memory.ResultsOnly three out of 24 comparisons (two eyes × four D f parameters × three cognitive measures) were found to be significant. This is little more than would be expected by chance. No single association was verified by an equivalent association in the contralateral eye.ConclusionsThe results show little evidence that fractal measures of retinal vascular differences are associated with non-pathological cognitive ageing.

Aortic stiffness is associated with the central retinal arteriolar equivalent and retinal vascular fractal dimension in a population along the southeastern coast of China.

The objective of this study was to evaluate the association of the central retinal arteriolar equivalent (CRAE) and the retinal vascular fractal dimension, two quantitative parameters that reflect microcirculation, with aortic stiffness. In this cross-sectional study, we identified the cardiovascular risk factors in 2169 subjects using a health questionnaire, physical examinations and laboratory examinations. We evaluated the aortic stiffness using noninvasive brachial-ankle pulse wave velocity (baPWV) and assessed the microcirculatory alterations with CRAE and retinal vascular fractal dimension, which were measured using fundus photography and semiautomatic quantitative software, respectively. The increase in baPWV (Q1-Q4) correlated with an increased likelihood of the central retinal artery narrowing and a reduction in the retinal vascular fractal dimension. Further adjustment of the cardiovascular risk factors diminished the association between baPWV and CRAE, but increased the association between baPWV and retinal vascular fractal dimension. Elevated baPWV correlates with reduced CRAE and retinal vascular fractal dimension. Such a finding supports macrocirculation- and microcirculation-associated hypotheses.

Retinal microvascular abnormalities and risk of renal failure in Asian populations.

BackgroundRetinal microvascular signs may provide insights into the structure and function of small vessels that are associated with renal disease. We examined the relationship of retinal microvascular signs with both prevalent and incident end-stage renal disease (ESRD) in a multi-ethnic Asian population.MethodsA total of 5763 subjects (aged ≥40 years) from two prospective population-based studies (the Singapore Malay Eye Study and the Singapore Prospective Study) were included for the current analysis. Retinopathy was graded using the modified Airlie House classification system. Retinal vascular parameters were measured using computer-assisted programs to quantify the retinal vessel widths (arteriolar and venular caliber) and retinal vascular network (fractal dimension). Data on ESRD was obtained by record linkage with the ESRD cases registered by National Registry of Diseases Office, Singapore. Multi-variable adjusted regression analyses were performed to assess the associations of baseline retinal vascular parameters and prevalent and incident ESRD.ResultsAt baseline, 21(0.36%) persons had prevalent ESRD. During a median follow-up of 4.3 years, 33 (0.57%) subjects developed ESRD. In our analyses, retinopathy was associated with prevalent ESRD (multi-variable adjusted odds ratio [OR], 3.21, 95% confidence interval [CI]: 1.28–8.05) and incident ESRD (multi-variable adjusted hazard ratio [HR], 2.51, 95%CI: 1.14–5.54). This association was largely seen in person with diabetes (HR, 2.60, 95%CI: 1.01–6.66) and not present in persons without diabetes (HR, 1.65, 95%CI: 0.14–18.98). Retinal arteriolar caliber, retinal venular caliber and retinal vascular fractal dimension were not associated with ESRD.ConclusionRetinopathy signs in persons with diabetes are related to an increased risk of ESRD; however, other microvascular changes in the retina are not associated with ESRD.

Two-dimensional neovascular complexity is significantly higher in nontumor prostate tissue than in low-risk prostate cancer.

PurposeProstate cancer is the most frequent cancer in men in Europe. A major focus in urology is the identification of new biomarkers with improved accuracy in patients with low-risk prostate cancer. Here, we evaluated two-dimensional neovascular complexity in prostate tumor and nontumor biopsy cores by use of a computer-aided image analysis system and assessed the correlations between the results and selected clinical and pathological parameters of prostate carcinoma.Materials and MethodsA total of 280 prostate biopsy sections from a homogeneous series of 70 patients with low-risk prostate cancer (Gleason score 3+3, prostate-specific antigen [PSA]<10 ng/mL, and clinical stage T1c) who underwent systematic biopsy sampling and subsequent radical prostatectomy were analyzed. For each biopsy, 2-µm sections were treated with CD34 antibodies and were digitized by using an image analysis system that automatically estimates the surface fractal dimension.ResultsOur results showed that biopsy sections without cancer were significantly more vascularized than were tumors. No correlations were found between the vascular surface fractal dimension and patient's age, PSA and free-to-total PSA ratios, pathological stage, Gleason score, tumor volume, vascular invasion, capsular penetration, surgical margins, and biochemical recurrence.ConclusionsThe value of angiogenesis in prostate cancer is still controversial. Our findings suggest that low-risk prostate cancer tissues are less vascularized than are nontumor tissues. Further studies are necessary to understand whether angiogenesis is a hallmark of intermediate- and high-risk prostate cancer.

The relationship of retinal vessel diameters and fractal dimensions with blood pressure and cardiovascular risk factors.

BackgroundThis study aimed to investigate the correlation between quantitative retinal vascular parameters such as central retinal arteriolar equivalent (CRAE) and retinal vascular fractal dimension (D(f)), and cardiovascular risk factors in the Chinese Han population residing in the in islands of southeast China.Methodology/Principle FindingsIn this cross-sectional study, fundus photographs were collected and semi-automated analysis software was used to analyze retinal vessel diameters and fractal dimensions. Cardiovascular risk factors such as relevant medical history, blood pressure (BP), lipids, and blood glucose data were collected. Subjects had a mean age of 51.9±12.0 years and included 812 (37.4%) males and 1,357 (62.6%) females. Of the subjects, 726 (33.5%) were overweight, 226 (10.4%) were obese, 272 (12.5%) had diabetes, 738 (34.0%) had hypertension, and 1,156 (53.3%) had metabolic syndrome. After controlling for the effects of potential confounders, multivariate analyses found that age (β = 0.06, P = 0.008), sex (β = 1.33, P = 0.015), mean arterial blood pressure (β = −0.12, P<0.001), high-sensitivity C-reactive protein (β = −0.22, P = 0.008), and CRVE (β = 0.23, P<0.001) were significantly associated with CRAE. Age (β = −0.0012, P<0.001), BP classification (prehypertension: β = −0.0075, P = 0.014; hypertension: β = −0.0131, P = 0.002), and hypertension history (β = −0.0007, P = 0.009) were significantly associated with D(f).Conclusions/SignificanceD(f) exhibits a stronger association with BP than CRAE. Thus, D(f) may become a useful indicator of cardiovascular risk.

Hemoglobin is Associated with Retinal Vascular Fractals in Type 1 Diabetes Patients

Purpose: Retinal vascular fractal dimension, a measure of the density of the retinal vasculature, has been suggested as a marker of systemic microvascular disorders in diabetes. As hemoglobin concentration is tightly related to vascular physiology and hypoxia, the hypothesis was that hemoglobin concentration would be associated with retinal vascular fractals in a relevant population.Methods: In a cross-sectional study of 204 long-term type 1 diabetes patients from a population-based cohort, retinal digital photos were captured and graded for fractal dimension (Df) by International Retinal Imaging Software – Fractal (IRIS-Fractal). Df was calculated from a disc-centered retinal photo from the right eye. Hemoglobin concentrations were measured using routine equipment.Results: Of 175 patients with gradable images, median age was 57.7 years and median duration of diabetes was 42 years. Median retinal Df was 1.4606 (inter-quartile range 0.0264). A positive correlation was found between hemoglobin concentration and retinal vascular Df (r = 0.23, p = 0.0018). In a multiple linear regression model, Df was associated with hemoglobin (coefficient 0.0054 per 1.0 mmol/L increase in hemoglobin, p = 0.01) and age (coefficient −0.0046 for each 10-year increase in age, p = 0.04).Conclusion: Hemoglobin correlated independently with retinal vascular fractals indicating a relationship between hemoglobin availability and retinal vascular structure.

Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus: the Danish Cohort of Pediatric Diabetes 1987 (DCPD1987).

Fractal analysis of the retinal vasculature provides a global measure of the complexity and density of retinal vessels summarised as a single variable: the fractal dimension. We investigated fractal dimensions as long-term predictors of microvasculopathy in type 1 diabetes. We included 180 patients with type 1 diabetes in a 16 year follow-up study. In baseline retinal photographs (from 1995), all vessels in a zone 0.5-2.0 disc diameters from the disc margin were traced using Singapore Institute Vessel Assessment-Fractal image analysis software. Artefacts were removed by a certified grader, and fractal dimensions were calculated using the box-counting method. At follow-up (in 2011), diabetic neuropathy, nephropathy and proliferative retinopathy were assessed and related to baseline fractal dimensions in multiple regressions adjusted for sex and baseline age, diabetes duration, HbA1c, BP, BMI, vibration perception threshold, albuminuria, retinopathy and vessel diameters. Mean baseline age and diabetes duration were 21.0 and 13.4 years, respectively, and of patients 50.0% were males. The mean fractal dimension was 1.3817. The 16 year incidences of neuropathy, nephropathy and proliferative retinopathy were 10.8%, 8.0% and 27.9%, respectively. Multiple regression analyses showed a lower fractal dimension to significantly predict incident neuropathy (OR 1.17 per 0.01 fractal dimension decrease [95% CI 1.01, 1.36]), nephropathy (OR 1.40 per 0.01 fractal dimension decrease [95% CI 1.10, 1.79]) and proliferative retinopathy (OR 1.22 per 0.01 fractal dimension decrease [95% CI 1.09, 1.37]). The retinal vascular fractal dimension is a shared biomarker of diabetic microvasculopathy, thus indicating a possible common pathogenic pathway. Retinal fractal analysis therefore is a potential tool for risk stratification in type 1 diabetes.

Measurement of Macular Fractal Dimension Using a Computer-Assisted Program

Macular diseases may be associated with an altered retinal vasculature. We describe and test new software for the measurement of retinal vascular fractal dimension to quantify the complexity of retinal vasculature at the macula (D mac) and to compare this with fractal dimension measured around the optic disc (D disc). A total of 342 macular-centered and optic disc-centered digital retinal photographs from 171 subjects was selected randomly from a population-based study. Retinal vascular fractional dimension (Df) was measured by two trained graders using a computer-assisted program (SIVA-FA, software version 1.0, National University of Singapore) on macula-centered (D mac) and optic disc-centered (D disc) photographs, to assess intergrader reliability. Measurements were repeated after two weeks to determine intragrader reliability. A separate 50 pairs of consecutively repeated images were selected and measured using SIVA-FA to assess intrasession reliability. Reliability analyses were conducted using intraclass correlation coefficients (ICC), and multiple linear regression analyses were performed to compare factors associated with D mac and D disc measurements. The mean (SD) D mac and D disc values were 1.453 (0.060) and 1.484 (0.043), respectively, and were highly correlated (r = 0.70, P < 0.001). Intragrader, intergrader, and intrasession reliability for both Df measures was high (ICCs ranging from 0.88-0.99). In multiple regression analyses, age (both β = -0.03, P < 0.001) and hypertension (β = -0.02, P = 0.011; β = -0.02, P = 0.021, respectively) were independently associated with D mac and D disc. The complexity of the retinal vasculature in the macula can be measured reliably and may be a useful tool to study parafoveal vascular networks in macula diseases, such as diabetic maculopathy.

Retinal Vascular Parameter Variations in Patients With Human Immunodeficiency Virus

To compare the retinal vascular parameters in patients with human immunodeficiency virus (HIV) infection with normal controls, and to determine the relationship between retinal vascular parameters and HIV-related blood biomarkers (CD4(+) T-lymphocytes count, presence of HIV RNA). Case-control study of eighty-five patients with HIV on follow-up at the Communicable Disease Center, Singapore, and 251 age-, sex-, and race-matched normal healthy controls (case: control matching ≈ 1:3) selected from the Singapore Epidemiology of Eye Disease program were included in this study. Standardized retinal photographs were taken from patients and controls. Trained technicians measured quantitative retinal vascular parameters (retinal vascular caliber, branching angle, tortuosity, and fractal dimension) with a semiautomated computer-based program following a standardized protocol. HIV-patients had more tortuous arterioles (0.77 × [10(4)] vs. 0.59 × [10(4)], P < 0.001) and venules (0.90 × [10(4)] vs. 0.74 × [10(4)], P < 0.001), compared with healthy normal subjects. Amongst the HIV-patients, increasing HIV viral loads were associated with decreased retinal arteriolar caliber (P trend = 0.009) and decreased arteriolar-venular ratio (P trend = 0.025). Our study showed that patients with HIV have significant variations in retinal vasculature. Retinal vascular imaging may offer further insight into the pathophysiology behind HIV-related vascular disease in future.

Relationship Between Retinal Vascular Geometry With Retinal Nerve Fiber Layer and Ganglion Cell-Inner Plexiform Layer in Nonglaucomatous Eyes

To examine the relationship between retinal vascular geometric parameters with retinal nerve fiber layer (RNFL) and ganglion cell-inner plexiform layer (GC-IPL) parameters in nonglaucomatous subjects. Study subjects were identified from the Singapore Chinese Eye Study (SCES), a population-based survey of Singaporean Chinese aged 40 to 80 years. All subjects underwent standardized systemic and ocular examinations. Nonglaucomatous eyes were defined as eyes with normal, reliable visual field results. Retinal vascular parameters (retinal vascular fractal dimension, tortuosity, and caliber) were measured from retinal photographs by using a computer-assisted program, according to a standardized protocol. Spectral-domain optical coherence tomography (SD-OCT) was used to measure RNFL and macular GC-IPL thicknesses. A total of 352 nonglaucomatous subjects with gradable retinal photographs and OCT images were included for the final analyses. In multiple regression analyses, after adjusting for age, sex, hypertension, diabetes, axial length, disc area, and OCT signal strength; decreased retinal vascular fractal dimension (β = -1.60, P = 0.002), narrower retinal arteriolar caliber (β = -1.60, P = 0.001), and venular caliber (β = -1.97, P < 0.001) were independently associated with thinner average RNFL thickness. In addition, decreased retinal vascular fractal dimension (β = -0.77, P = 0.017) and decreased retinal venular tortuosity (β = -0.63, P = 0.042) were independently associated with thinner average GC-IPL thickness after adjusting for age, sex, hypertension, diabetes, axial length, and OCT signal strength. Rarefaction, vasoconstriction, and straightening of the retinal vasculature are associated with thinner RNFL and GC-IPL thickness. This information may potentially provide further insights on the role of vascular processes in glaucoma development and progression.

Age-related rarefaction in retinal vasculature is not linear

The fractal dimension is a global measure of complexity and is useful for quantifying anatomical structures, including the retinal vascular network. A previous study found a linear declining trend with aging on the retinal vascular fractal dimension (DF); however, it was limited to the older population (49 years and older). This study aimed to investigate the possible models of the fractal dimension changes from young to old subjects (10–73 years). A total of 215 right-eye retinal samples, including those of 119 (55%) women and 96 (45%) men, were selected. The retinal vessels were segmented using computer-assisted software, and non-vessel fragments were deleted. The fractal dimension was measured based on the log–log plot of the number of grids versus the size. The retinal vascular DF was analyzed to determine changes with increasing age. Finally, the data were fitted to three polynomial models. All three models are statistically significant (Linear: R2 = 0.1270, 213 d.f., p < 0.001, Quadratic: R2 = 0.1536, 212 d.f., p < 0.001, Cubic: R2 = 0.1529, 211 d.f., p < 0.001). The quadratic regression is significantly better than the linear regression (p < 0.001); however, the increase in R2 from the quadratic model to the cubic model is not significant (p = 0.97). These results suggest that the decreasing trend of the fractal dimension associated with aging is better explained by the quadratic model than by the linear and cubic models in a sample with a broader age spectrum.

Blood pressure and retinal small arteries

Blood pressure and retinal small arteries