Multifractal analysis of human retinal vessels

Analysis of the Retinal and Choroidal Vasculature Using Ultrawidefield Fundus Imaging in Mild Cognitive Impairment and Normal Cognition

Purpose

To utilize ultrawidefield (UWF) imaging to evaluate retinal and choroidal vasculature and structure in individuals with mild cognitive impairment (MCI) compared with that of controls with normal cognition.

Design

Prospective cross sectional study.

Participants

One hundred thirty-one eyes of 82 MCI patients and 230 eyes of 133 cognitively normal participants from the Eye Multimodal Imaging in Neurodegenerative Disease Study.

Methods

A scanning laser ophthalmoscope (California, Optos Inc) was used to obtain UWF fundus color images. Images were analyzed with the Vasculature Assessment Platform for Images of the Retina UWF (VAMPIRE-UWF 2.0, Universities of Edinburgh and Dundee) software.

Main outcome measures

Imaging parameters included vessel width gradient, vessel width intercept, large vessel choroidal vascular density, vessel tortuosity, and vessel fractal dimension.

Results

Both retinal artery and vein width gradients were less negative in MCI patients compared with controls, demonstrating decreased rates of vessel thinning at the periphery (P < 0.001; P = 0.027). Retinal artery and vein width intercepts, a metric that extrapolates the width of the vessel at the center of the optic disc, were smaller in MCI patients compared with that of controls (P < 0.001; P = 0.017). The large vessel choroidal vascular density, which quantifies the vascular area versus the total choroidal area, was greater in MCI patients compared with controls (P = 0.025).

Conclusions

When compared with controls with normal cognition, MCI patients had thinner retinal vasculature manifested in both the retinal arteries and the veins. In MCI, these thinner arteries and veins attenuated at a lower rate when traveling toward the periphery. MCI patients also had increased choroidal vascular density.

Financial Disclosures

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Retinal Fractal Dimension Is a Potential Biomarker for Systemic Health-Evidence From a Mixed-Age, Primary-Care Population

Purpose

To investigate whether fractal dimension (FD), a retinal trait relating to vascular complexity and a potential "oculomics" biomarker for systemic disease, is applicable to a mixed-age, primary-care population.

Methods

We used cross-sectional data (96 individuals; 183 eyes; ages 18-81 years) from a university-based optometry clinic in Glasgow, Scotland, to study the association between FD and systemic health. We computed FD from color fundus images using Deep Approximation of Retinal Traits (DART), an artificial intelligence-based method designed to be more robust to poor image quality.

Results

Despite DART being designed to be more robust, a significant association (P < 0.001) between image quality and FD remained. Consistent with previous literature, age was associated with lower FD (P < 0.001 univariate and when adjusting for image quality). However, FD variance was higher in older patients, and some patients over 60 had FD comparable to those of patients in their 20s. Prevalent systemic conditions were significantly (P = 0.037) associated with lower FD when adjusting for image quality and age.

Conclusions

Our work suggests that FD as a biomarker for systemic health extends to mixed-age, primary-care populations. FD decreases with age but might not substantially decrease in everyone. This should be further investigated using longitudinal data. Finally, image quality was associated with FD, but it is unclear whether this finding is measurement error caused by image quality or confounded by age and health. Future work should investigate this to clarify whether adjusting for image quality is appropriate.

Translational Relevance

FD could potentially be used in regular screening settings, but questions around image quality remain.

Three-Dimensional Fractal Analysis of the Interstitial Cells of Cajal Networks of Gastrointestinal Tissue Specimens

Introduction

Several functional gastrointestinal disorders (FGIDs) have been associated with the degradation or remodeling of the network of interstitial cells of Cajal (ICC). Introducing fractal analysis to the field of gastroenterology as a promising data analytics approach to extract key structural characteristics that may provide insightful features for machine learning applications in disease diagnostics. Fractal geometry has advantages over several physically based parameters (or classical metrics) for analysis of intricate and complex microstructures that could be applied to ICC networks.

Methods

In this study, three fractal structural parameters: Fractal Dimension, Lacunarity, and Succolarity were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy; respectively of three types of gastric ICC network structures from a flat-mount transgenic mouse stomach.

Results

The Fractal Dimension of ICC in the longitudinal muscle layer was found to be significantly lower than ICC in the myenteric plexus and circumferential muscle in the proximal, and distal antrum, respectively (both p < 0.0001). Conversely, the Lacunarity parameters for ICC-LM and ICC-CM were found to be significantly higher than ICC-MP in the proximal and in the distal antrum, respectively (both p < 0.0001). The Succolarity measures of ICC-LM network in the aboral direction were found to be consistently higher in the proximal than in the distal antrum (p < 0.05).

Conclusions

The fractal parameters presented here could go beyond the limitation of classical metrics to provide better understanding of the structural-functional relationship between ICC networks and the conduction of gastric bioelectrical slow waves.

Ultra-Widefield Imaging of the Retinal Macrovasculature in Parkinson Disease Versus Controls With Normal Cognition Using Alpha-Shapes Analysis

Purpose

To investigate retinal vascular characteristics using ultra-widefield (UWF) scanning laser ophthalmoscopy in Parkinson disease (PD).

Methods

Individuals with an expert-confirmed clinical diagnosis of PD and controls with normal cognition without PD underwent Optos California UWF imaging. Patients with diabetes, uncontrolled hypertension, glaucoma, dementia, other movement disorders, or known retinal or optic nerve pathology were excluded. Images were analyzed using Vasculature Assessment and Measurement Platform for Images of the Retina (VAMPIRE-UWF) software, which describes retinal vessel width gradient and tortuosity, provides vascular network fractal dimensions, and conducts alpha-shape analysis to further characterize vascular morphology (complexity, Opαmin; spread, OpA).

Results

In the PD cohort, 53 eyes of 38 subjects were assessed; in the control cohort, 51 eyes of 33 subjects were assessed. Eyes with PD had more tortuous retinal arteries in the superotemporal quadrant (P = 0.043). In eyes with PD, alpha-shape analysis revealed decreased OpA, indicating less retinal vasculature spread compared to controls (P = 0.032). Opαmin was decreased in PD (P = 0.044), suggesting increased vascular network complexity. No differences were observed in fractal dimension in any region of interest.

Conclusions

This pilot study suggests that retinal vasculature assessment on UWF images using alpha-shape analysis reveals differences in retinal vascular network spread and complexity in PD and may be a more sensitive metric compared to fractal dimension.

Translational Relevance

Retinal vasculature assessment using these novel methods may be useful in understanding ocular manifestations of PD and the development of retinal biomarkers.

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Vessels characteristics in familial exudative vitreoretinopathy and retinopathy of prematurity based on deep convolutional neural networks

Purpose

The purpose of this study was to investigate the quantitative retinal vascular morphological characteristics of Retinopathy of Prematurity (ROP) and Familial Exudative Vitreoretinopathy (FEVR) in the newborn by the application of a deep learning network with artificial intelligence.

Methods

Standard 130-degree fundus photographs centered on the optic disc were taken in the newborns. The deep learning network provided segmentation of the retinal vessels and the optic disc (OD). Based on the vessel segmentation, the vascular morphological characteristics, including avascular area, vessel angle, vessel density, fractal dimension (FD), and tortuosity, were automatically evaluated.

Results

201 eyes of FEVR, 289 eyes of ROP, and 195 eyes of healthy individuals were included in this study. The deep learning system of blood vessel segmentation had a sensitivity of 72% and a specificity of 99%. The vessel angle in the FEVR group was significantly smaller than that in the normal group and ROP group (37.43 ± 5.43 vs. 39.40 ± 5.61, 39.50 ± 5.58, P = 0.001, < 0.001 respectively). The normal group had the lowest vessel density, the ROP group was in between, and the FEVR group had the highest (2.64 ± 0.85, 2.97 ± 0.92, 3.37 ± 0.88 respectively). The FD was smaller in controls than in the FEVR and ROP groups (0.984 ± 0.039, 1.018 ± 0.039 and 1.016 ± 0.044 respectively, P < 0.001). The ROP group had the most tortuous vessels, while the FEVR group had the stiffest vessels, the controls were in the middle (11.61 ± 3.17, 8.37 ± 2.33 and 7.72 ± 1.57 respectively, P < 0.001).

Conclusions

The deep learning technology used in this study has good performance in the quantitative analysis of vascular morphological characteristics in fundus photography. Vascular morphology was different in the newborns of FEVR and ROP compared to healthy individuals, which showed great clinical value for the differential diagnosis of ROP and FEVR.

A narrative review of retinal vascular parameters and the applications (Part I): Measuring methods

The retina is often used to evaluate the vascular health status of eyes and the whole body directly and noninvasively in vivo. Retinal vascular parameters included caliber, tortuosity and fractal dimension. These variables represent the density or geometric characteristics of the vascular network apart from reflecting structural changes in the retinal vessel system. Currently, these parameters are often used as indicators of retinal disease, cardiovascular and cerebrovascular disease. Advanced digital fundus photography apparatus and computer-assisted analysis techniques combined with artificial intelligence, make the quantitative calculation of these parameters easier, objective, and labor-saving.

Fine-mapping of retinal vascular complexity loci identifies Notch regulation as a shared mechanism with myocardial infarction outcomes

There is increasing evidence that the complexity of the retinal vasculature measured as fractal dimension, Df, might offer earlier insights into the progression of coronary artery disease (CAD) before traditional biomarkers can be detected. This association could be partly explained by a common genetic basis; however, the genetic component of Df is poorly understood. We present a genome-wide association study (GWAS) of 38,000 individuals with white British ancestry from the UK Biobank aimed to comprehensively study the genetic component of Df and analyse its relationship with CAD. We replicated 5 Df loci and found 4 additional loci with suggestive significance (P < 1e-05) to contribute to Df variation, which previously were reported in retinal tortuosity and complexity, hypertension, and CAD studies. Significant negative genetic correlation estimates support the inverse relationship between Df and CAD, and between Df and myocardial infarction (MI), one of CAD's fatal outcomes. Fine-mapping of Df loci revealed Notch signalling regulatory variants supporting a shared mechanism with MI outcomes. We developed a predictive model for MI incident cases, recorded over a 10-year period following clinical and ophthalmic evaluation, combining clinical information, Df, and a CAD polygenic risk score. Internal cross-validation demonstrated a considerable improvement in the area under the curve (AUC) of our predictive model (AUC = 0.770 ± 0.001) when comparing with an established risk model, SCORE, (AUC = 0.741 ± 0.002) and extensions thereof leveraging the PRS (AUC = 0.728 ± 0.001). This evidences that Df provides risk information beyond demographic, lifestyle, and genetic risk factors. Our findings shed new light on the genetic basis of Df, unveiling a common control with MI, and highlighting the benefits of its application in individualised MI risk prediction.

The impact of the image conversion factor and image centration on retinal vessel geometric characteristics

Background

This study aims to use fundus image material from a long-term retinopathy follow-up study to identify problems created by changing imaging modalities or imaging settings (e.g., image centering, resolution, viewing angle, illumination wavelength). Investigating the relationship of image conversion factor and imaging centering on retinal vessel geometric characteristics (RVGC), offers solutions for longitudinal retinal vessel analysis for data obtained in clinical routine.

Methods

Retinal vessel geometric characteristics were analyzed in scanned fundus photographs with Singapore-I-Vessel-Assessment using a constant image conversion factor (ICF) and an individual ICF, applying them to macula centered (MC) and optic disk centered (ODC) images. The ICF is used to convert pixel measurements into μm for vessel diameter measurements and to establish the size of the measuring zone. Calculating a constant ICF, the width of all analyzed optic disks is included, and it is used for all images of a cohort. An individual ICF, in turn, uses the optic disk diameter of the eye analyzed. To investigate agreement, Bland-Altman mean difference was calculated between ODC images analyzed with individual and constant ICF and between MC and ODC images.

Results

With constant ICF (n = 104 eyes of 52 patients) the mean central retinal equivalent was 160.9 ± 17.08 μm for arteries (CRAE) and 208.7 ± 14.7.4 μm for veins (CRVE). The individual ICFs resulted in a mean CRAE of 163.3 ± 15.6 μm and a mean CRVE of 219.0 ± 22.3 μm. On Bland–Altman analysis, the individual ICF RVGC are more positive, resulting in a positive mean difference for most investigated parameters. Arteriovenous ratio (p = 0.86), simple tortuosity (p = 0.08), and fractal dimension (p = 0.80) agreed well between MC and ODC images, while the vessel diameters were significantly smaller in MC images (p &lt; 0.002).

Conclusion

Scanned images can be analyzed using vessel assessment software. Investigations of individual ICF versus constant ICF point out the asset of utilizing an individual ICF. Image settings (ODC vs. MC) were shown to have good agreement.

Retinal capillary microvessel morphology changes are associated with vascular damage and dysfunction in cerebral small vessel disease

Cerebral small vessel disease (SVD) is a cause of stroke and dementia. Retinal capillary microvessels revealed by optical coherence tomography angiography (OCTA) are developmentally related to brain microvessels. We quantified retinal vessel density (VD) and branching complexity, investigating relationships with SVD lesions, white matter integrity on diffusion tensor imaging (DTI) and cerebrovascular reactivity (CVR) to CO2 in patients with minor stroke. We enrolled 123 patients (mean age 68.1 ± SD 9.9 years), 115 contributed retinal data. Right (R) and left (L) eyes are reported. After adjusting for age, eye disease, diabetes, blood pressure and image quality, lower VD remained associated with higher mean diffusivity (MD) (standardized β; R -0.16 [95%CI -0.32 to -0.01]) and lower CVR (L 0.17 [0.03 to 0.31] and R 0.19 [0.02 to 0.36]) in normal appearing white matter (NAWM). Sparser branching remained associated with sub-visible white matter damage shown by higher MD (R -0.24 [-0.08 to -0.40]), lower fractional anisotropy (FA) (L 0.17 [0.01 to 0.33]), and lower CVR (R 0.20 [0.02 to 0.38]) in NAWM. OCTA-derived metrics provide evidence of microvessel abnormalities that may underpin SVD lesions in the brain.

Y-27632 Impairs Angiogenesis on Extra-Embryonic Vasculature in Post-Gastrulation Chick Embryos

Y-27632 inhibits Rho-associated coiled-coil-containing protein kinase (ROCK) signaling, which is involved in various embryonic developmental processes, including angiogenesis, by controlling actin cytoskeleton assembly and cell contractility. Administration of Y-27632 impairs cytoskeletal arrangements in post-gastrulation chick embryos, leading to ventral body wall defects (VBWDs). Impaired angiogenesis has been hypothesized to contribute to VBWDs. ROCK is essential in transmitting signals downstream of vascular endothelial growth factor (VEGF). VEGF-mediated angiogenesis induces gene expressions and alterations of the actin cytoskeleton upon binding to VEGF receptors (VEGFRs). The aim of this study was to investigate effects of Y-27632 on angiogenesis in post-gastrulation chick embryos during early embryogenesis. After 60 h incubation, embryos in shell-less culture were treated with Y-27632 or vehicle for controls. Y-27632-treated embryos showed reduced extra-embryonic blood vessel formation with impaired circulation of the yolk sac, confirmed by fractal analysis. Western blot confirmed impaired ROCK downstream signaling by decreased expression of phosphorylated myosin light chain. Interestingly, RT-PCR demonstrated increased gene expression of VEGF and VEGFR-2 1 h post-treatment. Protein levels of VEGF were higher in Y-27632-treated embryos at 8 h following treatment, whereas no difference was seen in membranes. We hypothesize that administration of Y-27632 impairs vessel formation during angiogenesis, which may contribute to failure of VWB closure, causing VBWDs.

Retinal Vascular Changes in Alzheimer's Dementia and Mild Cognitive Impairment: A Pilot Study Using Ultra-Widefield Imaging

Purpose

Retinal microvascular abnormalities measured on retinal images are a potential source of prognostic biomarkers of vascular changes in the neurodegenerating brain. We assessed the presence of these abnormalities in Alzheimer's dementia and mild cognitive impairment (MCI) using ultra-widefield (UWF) retinal imaging.

Methods

UWF images from 103 participants (28 with Alzheimer's dementia, 30 with MCI, and 45 with normal cognition) underwent analysis to quantify measures of retinal vascular branching complexity, width, and tortuosity.

Results

Participants with Alzheimer's dementia displayed increased vessel branching in the midperipheral retina and increased arteriolar thinning. Participants with MCI displayed increased rates of arteriolar and venular thinning and a trend for decreased vessel branching.

Conclusions

Statistically significant differences in the retinal vasculature in peripheral regions of the retina were observed among the distinct cognitive stages. However, larger studies are required to establish the clinical importance of our findings. UWF imaging may be a promising modality to assess a larger view of the retinal vasculature to uncover retinal changes in Alzheimer's disease.

Translational Relevance

This pilot work reports an investigation into which retinal vasculature measurements may be useful surrogate measures of cognitive decline, as well as technical developments (e.g., measurement standardization), that are first required to establish their recommended use and translational potential.

Lower fractal dimension of retinal vessel for patients with Birdshot chorioretinopathy

PURPOSE

To identify the retinal vessel vasculature parameters associated with birdshot chorioretinopathy (BSCR).

METHODS

This retrospective observational study included 28 prevalent cases of BSCR with a median time from diagnosis of 6 years and 28 controls matched for age, arterial hypertension, diabetes and refraction. Forty-five-degree fundus images of both dilated eyes were acquired with a fundus camera (Canon CR-2, Tokyo, Japan). The summary diameter of the arterial retinal vessels (central retinal artery equivalent, CRAE), venous retinal vessels (central retinal vein equivalent, CRVE), vascular tortuosity and fractal dimension (FD) were measured using VAMPIRE software. Retinal vasculitis was characterized using fluorescein angiography and active choroiditis using indocyanine green angiography.

RESULTS

At baseline, BSCR was associated with lower FD compared with matched controls (mean difference, -0.04; 95% confidence interval [CI], -0.06 to -0.02, p < 0.001). No other VAMPIRE parameters (CRAE, CRVE, arterial and venous tortuosity) differed. Among BSCR patients, retinal vein vasculitis was associated with higher CRAE (mean difference, 21 μ; 95% CI, 2.6-40, p = 0.03), venous tortuosity (geometric mean ratio, 1.79; 95% CI, 1.18-2.72, p = 0.007) and FD (mean difference, -0.04; 95% CI, -0.06 to -0.01, p = 0.007). Resolution of retinal vein vasculitis during follow-up was paralleled by decrease in CRAE, CRVE and venous tortuosity values and increase in venous FD, respectively.

CONCLUSION

BSCR is associated with lower FD value, suggesting that chronic retinal inflammation induces microvascular remodelling. Efficient treatment of retinal vasculitis may reverse changes in retinal vascular parameters. Changes in retinal vascular parameters could be potentially useful for assessing patients with BSCR disease.

Retinal vessel multifractals predict pial collateral status in patients with acute ischemic stroke

OBJECTIVES

Pial collateral blood flow is a major determinant of the outcomes of acute ischemic stroke. This study was undertaken to determine whether retinal vessel metrics can predict the pial collateral status and stroke outcomes in patients.

METHODS

Thirty-five patients with acute stroke secondary to middle cerebral artery (MCA) occlusion underwent grading of their pial collateral status from computed tomography angiography and retinal vessel analysis from retinal fundus images.

RESULTS

The NIHSS (14.7 ± 5.5 vs 10.1 ± 5.8, p = 0.026) and mRS (2.9 ± 1.6 vs 1.9 ± 1.3, p = 0.048) scores were higher at admission in patients with poor compared to good pial collaterals. Retinal vessel multifractals: D0 (1.673±0.028vs1.652±0.025, p = 0.028), D1 (1.609±0.027vs1.590±0.025, p = 0.044) and f(α)max (1.674±0.027vs1.652±0.024, p = 0.019) were higher in patients with poor compared to good pial collaterals. Furthermore, support vector machine learning achieved a fair sensitivity (0.743) and specificity (0.707) for differentiating patients with poor from good pial collaterals. Age (p = 0.702), BMI (p = 0.422), total cholesterol (p = 0.842), triglycerides (p = 0.673), LDL (p = 0.952), HDL (p = 0.366), systolic blood pressure (p = 0.727), HbA1c (p = 0.261) and standard retinal metrics including CRAE (p = 0.084), CRVE (p = 0.946), AVR (p = 0.148), tortuosity index (p = 0.790), monofractal Df (p = 0.576), lacunarity (p = 0.531), curve asymmetry (p = 0.679) and singularity length (p = 0.937) did not differ between patients with poor compared to good pial collaterals.

CONCLUSIONS

This is the first translational study to show increased retinal vessel multifractal dimensions in patients with acute ischemic stroke and poor pial collaterals. A retinal vessel classifier was developed to differentiate between patients with poor and good pial collaterals and may allow rapid non-invasive identification of patients with poor pial collaterals.

Distinct fatty acid redistribution and textural changes in the brain tissue upon the static magnetic field exposure

We observed different outcomes upon the subacute exposure to the 128 mT highly homogeneous static magnetic field (SMF) when its orientation was (i) aligned with the vertical component of the geomagnetic field; (ii) in the opposite direction. We employed the fatty acids (FA) composition and digital image analyses (DIA) to provide insights into the underlying processes and examine the possible weak SMF effects. Swiss-Webster male mice were whole-body exposed for 1 h/day over five days. Brain tissue's thin liquid chromatography resulted in brain FA composition, indicating a possible sequence of changes due to the SMF exposure. Quantitative DIA accurately assessed different image parameters. Delicate textural changes were revealed in the group where pathohistological or biochemical alterations have not been detected. DIA-based biological markers seem to be very promising for studying delicate tissue changes, which results from the high sensitivity and wide availability of DIA.

Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution

Branching patterns are ubiquitous in nature; consequently, over the years many researchers have tried to characterize the complexity of their structures. Due to their hierarchical nature and resemblance to fractal trees, they are often thought to have fractal properties; however, their non-homogeneity (i.e., lack of strict self-similarity) is often ignored. In this paper we review and examine the use of the box-counting and sandbox methods to estimate the fractal dimensions of branching structures. We highlight the fact that these methods rely on an assumption of self-similarity that is not present in branching structures due to their non-homogeneous nature. Looking at the local slopes of the log–log plots used by these methods reveals the problems caused by the non-homogeneity. Finally, we examine the role of the canopies (endpoints or limit points) of branching structures in the estimation of their fractal dimensions.

Morphological characteristics of retinal vessels in eyes with high myopia: Ultra-wide field images analyzed by artificial intelligence using a transfer learning system

Purpose

The purpose of this study is to investigate the retinal vascular morphological characteristics in high myopia patients of different severity.

Methods

317 eyes of high myopia patients and 104 eyes of healthy control subjects were included in this study. The severity of high myopia patients is classified into C0-C4 according to the Meta Analysis of the Pathologic Myopia (META-PM) classification and their vascular morphological characteristics in ultra-wide field imaging were analyzed using transfer learning methods and RU-net. Correlation with axial length (AL), best corrected visual acuity (BCVA) and age was analyzed. In addition, the vascular morphological characteristics of myopic choroidal neovascularization (mCNV) patients and their matched high myopia patients were compared.

Results

The RU-net and transfer learning system of blood vessel segmentation had an accuracy of 98.24%, a sensitivity of 71.42%, a specificity of 99.37%, a precision of 73.68% and a F1 score of 72.29. Compared with healthy control group, high myopia group had smaller vessel angle (31.12 ± 2.27 vs. 32.33 ± 2.14), smaller fractal dimension (Df) (1.383 ± 0.060 vs. 1.424 ± 0.038), smaller vessel density (2.57 ± 0.96 vs. 3.92 ± 0.93) and fewer vascular branches (201.87 ± 75.92 vs. 271.31 ± 67.37), all P < 0.001. With the increase of myopia maculopathy severity, vessel angle, Df, vessel density and vascular branches significantly decreased (all P < 0.001). There were significant correlations of these characteristics with AL, BCVA and age. Patients with mCNV tended to have larger vessel density (P < 0.001) and more vascular branches (P = 0.045).

Conclusion

The RU-net and transfer learning technology used in this study has an accuracy of 98.24%, thus has good performance in quantitative analysis of vascular morphological characteristics in Ultra-wide field images. Along with the increase of myopic maculopathy severity and the elongation of eyeball, vessel angle, Df, vessel density and vascular branches decreased. Myopic CNV patients have larger vessel density and more vascular branches.

Quantitative Biomarkers for Cancer Detection Using Contrast-Free Ultrasound High-Definition Microvessel Imaging: Fractal Dimension, Murray's Deviation, Bifurcation Angle & Spatial Vascularity Pattern

A growing body of evidence indicates that there is a strong correlation between microvascular morphological features and malignant tumors. Therefore, quantification of these features might allow more accurate differentiation of benign and malignant tumors. The main objective of this research project is to improve the quantification of microvascular networks depicted in contrast-free ultrasound microvessel images. To achieve this goal, a new series of quantitative microvessel morphological parameters are introduced for differentiation of breast masses using contrast-free ultrasound-based high-definition microvessel imaging (HDMI). Using HDMI, we quantified and analyzed four new parameters: 1) microvessel fractal dimension (mvFD), a marker of tumor microvascular complexity; 2) Murray's deviation (MD), the diameter mismatch, defined as the deviation from Murray's law; 3) bifurcation angle (BA), abnormally decreased angle; and 4) spatial vascular pattern (SVP), indicating tumor vascular distribution pattern, either intratumoral or peritumoral. The new biomarkers have been tested on 60 patients with breast masses. Validation of the feature's extraction algorithm was performed using a synthetic data set. All the proposed parameters had the power to discriminate the breast lesion malignancy (p < 0.05), displaying BA as the most sensitive test, with a sensitivity of 90.6%, and mvFD as the most specific test, with a specificity of 92%. The results of all four new biomarkers showed an AUC = 0.889, sensitivity of 80% and specificity of 91.4% In conclusion, the added value of the proposed quantitative morphological parameters, as new biomarkers of angiogenesis within breast masses, paves the way for more accurate breast cancer detection with higher specificity.

2D alpha-shapes to quantify retinal microvasculature morphology and their application to proliferative diabetic retinopathy characterisation in fundus photographs

The use of 2D alpha-shapes (α-shapes) to quantify morphological features of the retinal microvasculature could lead to imaging biomarkers for proliferative diabetic retinopathy (PDR). We tested our approach using the MESSIDOR dataset that consists of colour fundus photographs from 547 healthy individuals, 149 with mild diabetic retinopathy (DR), 239 with moderate DR, 199 pre-PDR and 53 PDR. The skeleton (centrelines) of the automatically segmented retinal vasculature was represented as an α-shape and the proposed parameters, complexity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Op\alpha }_{min}$$\end{document}Opαmin), spread (OpA), global shape (VS) and presence of abnormal angiogenesis (Grad_α) were computed. In cross-sectional analysis, individuals with PDR had a lower \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Op\alpha }_{min}$$\end{document}Opαmin, OpA and Grad_α indicating a vasculature that is more complex, less spread (i.e. dense) and the presence of numerous small vessels. The results show that α-shape parameters characterise vascular abnormalities predictive of PDR (AUC 0.73; 95% CI [0.73 0.74]) and have therefore potential to reveal changes in retinal microvascular morphology.

Age-related changes in the fractal dimension of the retinal microvasculature, effects of cardiovascular risk factors and smoking behaviour

Purpose

This cross‐sectional study investigates the association between retinal vessel complexity and age and studies the effects of cardiovascular health determinants.

Methods

Retinal vessel complexity was assessed by calculating the box‐counting fractal dimension (D_f) from digital fundus photographs of 850 subjects (3–97 years). All photographs were labelled as ‘non‐pathological’ by the treating ophthalmologist.

Results

Statistical models showed a significantly decreasing relationship between age and D_f (linear: R‐squared = 0.1897, p < 0.0001; quadratic: R‐squared = 0.2343, p < 0.0001; cubic: R‐squared = 0.2721, p < 0.0001), with the cubic regression model offering the best compromise between accuracy and model simplicity. Multivariate cubic regression showed that age, spherical equivalent and smoking behaviour have an effect (p < 0.0001) on D_f. A significantly increasing effect of the number of pack‐years on D_f was observed (effect: 0.0004, p = 0.0017), as well as a significantly decreasing effect of years since tobacco abstinence (effect: −0.0149, p < 0.0001).

Conclusion

We propose using a cubic trend with age, refractive error and smoking behaviour when interpreting retinal vessel complexity.

Vessel Evaluation in Patients with Primary Open-Angle Glaucoma, Normal Tension Glaucoma and Healthy Controls

Purpose

To compare changes in central retinal arterial equivalent (CRAE), central retinal vein equivalent (CRVE), arteriovenous ratio (AVR), tortuosity and fractal dimension in primary open-angle glaucoma (POAG), normal-tension glaucoma (NTG) and in a control group (CG) on fundus photographs. Further, to provide further evidence of vascular change in glaucoma patients using a novel method of tortuosity.

Patients and Methods

The primary endpoint was the change in CRAE, CRVE, AVR, fractal dimension and tortuosity of the retinal vasculature from baseline, retrospectively analyzed from 2011 to 2017 at the University Eye Hospital Tuebingen. Fundus photos of POAG (N = 49), NTG (N = 38) and CG (N = 18) were computer evaluated and analyzed in the quantities mentioned above.

Results

CRAE in NTG and POAG and CRVE in NTG significantly decreased (P = 0.02, P = 0.01; P = 0.03) whereas CRVE in POAG increased insignificantly (P = 0.72). In NTG, AVR decreased significantly (P = 0.05), but to a lesser extent than in POAG (P < 0.001). In CG, CRAE decreased insignificantly (P = 0.10), CRVE decreased significantly (P = 0.03) and AVR increased insignificantly (P = 0.77). In POAG tortuosity calculated using standard methods as well as our novel method, increased significantly (P = 0.015-0.04), whereas it did not occur in NTG (P = 0.18-0.57) and CG (P = 0.11-0.21). Fractal dimensions in POAG decreased significantly (P = 0.001-0.002), whereas in NTG and CG changes were insignificant (P = 0.33-0.92).

Conclusion

Based on a retrospective analysis of fundus photographs, specific retinal vasculature features of the retinal vasculature display significant alterations associated with NTG and POAG. The assessment of tortuosity using our novel method was consistent with previously established methods for analyzing tortuosity.

Retinal arteriolar tortuosity and fractal dimension are associated with long-term cardiovascular outcomes in people with type 2 diabetes

AIMS/HYPOTHESIS

Our aim was to determine whether quantitative retinal traits in people with type 2 diabetes are independently associated with incident major cardiovascular events including CHD and stroke.

METHODS

A total of 1066 men and women with type 2 diabetes, aged 65-74 years, were followed up over 8 years in the population-based Edinburgh Type 2 Diabetes Study. Using retinal photographs taken at baseline and specialist software, a number of quantitative retinal traits were measured, including arteriolar and venular widths and tortuosity as well as fractal dimension (a measure of the branching pattern complexity of the retinal vasculature network). Incident CHD events occurring during follow-up included fatal and non-fatal myocardial infarction, first episodes of angina and coronary interventions for CHD. Incident cerebrovascular events included fatal and non-fatal stroke or transient ischaemic attack. Cox proportional hazard regression analyses were performed to identify the association of the retinal traits with cardiovascular events in the population with retinal data available (n = 1028).

RESULTS

A total of 200 participants had an incident cardiovascular event (139 CHD and 61 cerebrovascular events). Following adjustment for age and sex, arteriolar tortuosity and fractal dimension were associated with cerebrovascular events (HR 1.27 [95% CI 1.02, 1.58] and HR 0.74 [95% CI 0.57, 0.95], respectively), including with stroke alone (HR 1.30 [95% CI 1.01, 1.66] and HR 0.73 [95% CI 0.56, 0.97], respectively). These associations persisted after further adjustment for established cardiovascular risk factors (HR 1.26 [95% CI 1.01, 1.58] and HR 0.73 [95% CI 0.56, 0.94], respectively). Associations generally reduced in strength after a final adjustment for the presence of diabetic retinopathy, but the association of fractal dimension with incident cerebrovascular events and stroke retained statistical significance (HR 0.73 [95% CI 0.57, 0.95] and HR 0.72 [95% CI 0.54, 0.97], respectively). Associations of retinal traits with CHD were generally weak and showed no evidence of statistical significance.

CONCLUSIONS/INTERPRETATION

Arteriolar tortuosity and fractal dimension were associated with incident cerebrovascular events, independent of a wide range of traditional cardiovascular risk factors including diabetic retinopathy. These findings suggest potential for measurements of early retinal vasculature change to aid in the identification of people with type 2 diabetes who are at increased risk from stroke.

Imaging the Retinal Vasculature

Advances in retinal imaging are enabling researchers and clinicians to make precise noninvasive measurements of the retinal vasculature in vivo. This includes measurements of capillary blood flow, the regulation of blood flow, and the delivery of oxygen, as well as mapping of perfused blood vessels. These advances promise to revolutionize our understanding of vascular regulation, as well as the management of retinal vascular diseases. This review provides an overview of imaging and optical measurements of the function and structure of the ocular vasculature. We include general characteristics of vascular systems with an emphasis on the eye and its unique status. The functions of vascular systems are discussed, along with physical principles governing flow and its regulation. Vascular measurement techniques based on reflectance and absorption are briefly introduced, emphasizing ways of generating contrast. One of the prime ways to enhance contrast within vessels is to use techniques sensitive to the motion of cells, allowing precise measurements of perfusion and blood velocity. Finally, we provide a brief introduction to retinal vascular diseases.

Development of Novel Fractal Method for Characterizing the Distribution of Blood Flow in Multi-Scale Vascular Tree

Blood perfusion is an important index for the function of the cardiovascular system and it can be indicated by the blood flow distribution in the vascular tree. As the blood flow in a vascular tree varies in a large range of scales and fractal analysis owns the ability to describe multi-scale properties, it is reasonable to apply fractal analysis to depict the blood flow distribution. The objective of this study is to establish fractal methods for analyzing the blood flow distribution which can be applied to real vascular trees. For this purpose, the modified methods in fractal geometry were applied and a special strategy was raised to make sure that these methods are applicable to an arbitrary vascular tree. The validation of the proposed methods on real arterial trees verified the ability of the produced parameters (fractal dimension and multifractal spectrum) in distinguishing the blood flow distribution under different physiological states. Furthermore, the physiological significance of the fractal parameters was investigated in two situations. For the first situation, the vascular tree was set as a perfect binary tree and the blood flow distribution was adjusted by the split ratio. As the split ratio of the vascular tree decreases, the fractal dimension decreases and the multifractal spectrum expands. The results indicate that both fractal parameters can quantify the degree of blood flow heterogeneity. While for the second situation, artificial vascular trees with different structures were constructed and the hemodynamics in these vascular trees was simulated. The results suggest that both the vascular structure and the blood flow distribution affect the fractal parameters for blood flow. The fractal dimension declares the integrated information about the heterogeneity of vascular structure and blood flow distribution. In contrast, the multifractal spectrum identifies the heterogeneity features in blood flow distribution or vascular structure by its width and height. The results verified that the proposed methods are capable of depicting the multi-scale features of the blood flow distribution in the vascular tree and further are potential for investigating vascular physiology.

Quantitative Parameters from OCT Angiography in Patients with Diabetic Retinopathy and in Those with Only Peripheral Retinopathy Compared with Control Participants

Purpose

To describe the differences in a range of quantitative OCT angiography (OCTA) metrics across early stages of diabetic retinopathy (DR), providing robust effect estimates as well as sensitivity and specificity.

Design

Cross-sectional study with population-based sampling.

Participants

Four hundred forty-one eyes from 296 individuals: 328 control eyes (no diabetes mellitus [DM] and no DR), 55 eyes with DM and no DR, and 58 eyes with early nonproliferative DR.

Methods

Multimodal retinal imaging included color fundus photography, color Optomap ultra-widefield imaging, and spectral-domain OCT (Spectralis OCT2; Heidelberg Engineering GmbH) with the OCTA module. All images were graded for the presence and severity of DR features. OCTA images were assessed manually for inclusion based on quality. Binary OCTA metrics were assessed after 3-dimensional projection artifact removal including from the nerve fiber layer vascular plexus, superficial vascular plexus (SVC), and deep vascular plexus (DVC) by Early Treatment Diabetic Retinopathy Study (ETDRS) grid, foveal avascular zone (FAZ) area, FAZ minimum and maximum diameter, perimeter length, and circularity.

Main Outcome Measures

Diabetes mellitus and DR status and presence or absence of DR in the retinal periphery.

Results

The reduction in vessel densities in participants with DM and manifest DR compared with control participants tended to be twice that of those with DM, but no DR, compared with control participants. Some evidence of spatial heterogeneity in vessel reductions was found in those yet to develop DR, whereas those with manifest DR had significant reductions across the ETDRS grid. The FAZ perimeter and circularity were impacted most significantly by DM, and those with DR showed decreased multispectral fractal dimensions compared with control participants. Eyes with peripheral DR had reduced vessel density compared with those with DM and no DR only in the superior outer, temporal inner, and temporal outer regions in the DVC and SVC. The area under the receiver operating characteristic curve ranged between 0.48 and 0.73.

Conclusions

Significant differences in OCTA metrics can be found in those with DM before manifest DR using commercially available equipment with minimal image postprocessing. Although diagnostic performance was poor, these metrics may be useful for measuring change over time in clinical trials.

Retinal microvascular complexity comparing mono- and multifractal dimensions in relation to cardiometabolic risk factors in a Middle Eastern population

PURPOSE

Metrics that capture changes in the retinal microvascular structure are relevant in the context of cardiometabolic disease development. The microvascular topology is typically quantified using monofractals, although it obeys more complex multifractal rules. We study mono- and multifractals of the retinal microvasculature in relation to cardiometabolic factors.

METHODS

The cross-sectional retrospective study used data from 3000 Middle Eastern participants in the Qatar Biobank. A total of 2333 fundus images (78%) passed quality control and were used for further analysis. The monofractal (D_f ) and five multifractal metrics were associated with cardiometabolic factors using multiple linear regression and were studied in clinically relevant subgroups.

RESULTS

D_f and multifractals are lowered in function of age, and D_f is lower in males compared to females. In models corrected for age and sex, D_f is significantly associated with BMI, insulin, systolic blood pressure, glycated haemoglobin (HbA1c), albumin, LDL and total cholesterol concentrations. Multifractals are negatively associated with systolic and diastolic blood pressure, glucose and the WHO/ISH cardiovascular risk score. D_f was higher, and multifractal curve asymmetry was lower in diabetic patients (HbA1c > 6.5%) compared to healthy individuals (HbA1c < 5.7%). Insulin resistance (insulin ≥ 23 mcU/mL) was associated with significantly lower D_f values.

CONCLUSION

One or more fractal metrics are in association with sex, age, BMI, systolic and diastolic blood pressure and biochemical blood measurements in a Middle Eastern population study. Follow-up studies aiming at investigating retinal microvascular changes in relation to cardiometabolic risk should analyse both monofractal and multifractal metrics for a more comprehensive microvascular picture.

Retinal venular tortuosity and fractal dimension predict incident retinopathy in adults with type 2 diabetes: the Edinburgh Type 2 Diabetes Study

AIMS/HYPOTHESIS

Our aim was to determine whether a range of prespecified retinal vessel traits were associated with incident diabetic retinopathy in adults with type 2 diabetes.

METHODS

In the prospective observational cohort Edinburgh Type 2 Diabetes Study of 1066 adults with type 2 diabetes, aged 60-75 years at recruitment, 718 were free from diabetic retinopathy at baseline. Baseline retinal traits including vessel widths, tortuosity (curvature) and fractal dimensions (network complexity), were quantified using fundus camera images and semiautomated software, and analysed using logistic regression for their association with incident diabetic retinopathy over 10 years.

RESULTS

The incidence of diabetic retinopathy was 11.4% (n = 82) over 10 years. After adjustment for a range of vascular and diabetes-related risk factors, both increased venular tortuosity (OR 1.51; 95% CI 1.15, 1.98; p = 0.003) and decreased fractal dimension (OR 0.75; 95% CI 0.58, 0.96; p = 0.025) were associated with incident retinopathy. There was no evidence of an association with arterial tortuosity, and associations between measurements of vessel widths and retinopathy lost statistical significance after adjustment for diabetes-related factors and vascular disease. Adding venular tortuosity to a model including established risk factors for diabetic retinopathy (HbA_1c, BP and kidney function) improved the discriminative ability (C statistic increased from 0.624 to 0.640, p = 0.013), but no such benefit was found with fractal dimension.

CONCLUSIONS/INTERPRETATION

Increased retinal venular tortuosity and decreased fractal dimension are associated with incident diabetic retinopathy, independent of classical risk factors. There is some evidence that venular tortuosity may be a useful biomarker to improve the predictive ability of models based on established retinopathy risk factors, and its inclusion in further risk prediction modelling is warranted.

On the quantitative effects of compression of retinal fundus images on morphometric vascular measurements in VAMPIRE

BACKGROUND AND OBJECTIVES

This paper reports a quantitative analysis of the effects of joint photographic experts group (JPEG) image compression of retinal fundus camera images on automatic vessel segmentation and on morphometric vascular measurements derived from it, including vessel width, tortuosity and fractal dimension.

METHODS

Measurements are computed with vascular assessment and measurement platform for images of the retina (VAMPIRE), a specialized software application adopted in many international studies on retinal biomarkers. For reproducibility, we use three public archives of fundus images (digital retinal images for vessel extraction (DRIVE), automated retinal image analyzer (ARIA), high-resolution fundus (HRF)). We generate compressed versions of original images in a range of representative levels.

RESULTS

We compare the resulting vessel segmentations with ground truth maps and morphological measurements of the vascular network with those obtained from the original (uncompressed) images. We assess the segmentation quality with sensitivity, specificity, accuracy, area under the curve and Dice coefficient. We assess the agreement between VAMPIRE measurements from compressed and uncompressed images with correlation, intra-class correlation and Bland-Altman analysis.

CONCLUSIONS

Results suggest that VAMPIRE width-related measurements (central retinal artery equivalent (CRAE), central retinal vein equivalent (CRVE), arteriolar-venular width ratio (AVR)), the fractal dimension (FD) and arteriolar tortuosity have excellent agreement with those from the original images, remaining substantially stable even for strong loss of quality (20% of the original), suggesting the suitability of VAMPIRE in association studies with compressed images.

Retinal image measurements and their association with chronic kidney disease in Chinese patients with type 2 diabetes: the NCD study

AIMS

Retinal and renal microcirculations are known to share similar physiological changes during early diabetes because of abnormal glucose metabolism and other processes. The retinal vasculature therefore may serve as potential biomarker for the early identification of those at high risk of chronic kidney disease (CKD) in diabetes.

METHODS

Data from 1925 patients (aged 49.0 ± 10.3) with type 2 diabetes were analyzed. Various retinal image measurements (RIMs) were collected using a validated fully automated computer program. Multiple logistic regressions were performed to investigate the correlation between RIMs and CKD.

RESULTS

In logistic regression adjusting for multiple variables, wider venular calibers in the central and middle zones and narrower arteriolar caliber in the central zone were associated with CKD (p < 0.001, p = 0.020, and p < 0.001, respectively). Increased arteriolar tortuosity was associated with CKD (p = 0.035). Multiple image texture measurements were also significantly associated with CKD.

CONCLUSIONS

Renal dysfunction in type 2 diabetes was associated with various retinal image measurements. These non-invasive image measurements may serve as potential biomarkers for the early identification and monitoring of individuals at high risk of CKD in the course of diabetes.

Retinal Vasculature Fractal and Stroke Mortality

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.

Retinal Vascular Fractal Dimensions and Their Association with Macrovascular Cardiac Disease

INTRODUCTION

As the only part of the human vasculature, the retina is available for direct, noninvasive inspection. Retinal vascular fractal dimension (DF) is a method to measure the structure of the retinal vascular tree, with higher noninteger values between 1 and 2 representing a more complex and dense retinal vasculature. Retinal vascular structure has been associated with a variety of systemic diseases, and this study examined the association of DF and macrovascular cardiac disease in a case-control design.

METHODS

Retinal fundus photos were captured with Topcon TRC-50X in 38 persons that had coronary artery bypass grafting (CABG, cases) and 37 cardiovascular healthy controls. The semiautomatic software VAMPIRE was used to measure retinal DF.

RESULTS

Patients with CABG had lower DF of the retinal main venular vessels compared to the control group (1.15 vs. 1.18, p = 0.01). In a multivariable regression model adjusted for gender and age, eyes in the fourth quartile with higher DF were less likely to have CABG compared to patients in the first (OR, 7.20; 95% confidence interval: 1.63-31.86; p = 0.009) and second (OR, 8.25; 95% confidence interval: 1.70-40.01; p = 0.009) quartiles.

CONCLUSIONS

This study demonstrates that lower complexity of main venular vessels associates with higher risk of having CABG. The research supports the hypothesis that the retinal vascular structure can be used to assess nonocular macrovascular disease.

Macular vessel density, branching complexity and foveal avascular zone size in normal tension glaucoma

The aim of this study was to investigate the relationship between glaucoma severity and perifoveal vessel density (pfVD), branching complexity, and foveal avascular zone (FAZ) size in normal tension glaucoma (NTG). 31 patients with NTG washed out of glaucoma medications were subjected to tests including; intraocular pressure measurement; standard automated perimetry; optical coherence tomography (OCT) measurement of macular ganglion cell complex (mGCC), inner macular thickness (IMT) and circumpapillary retinal nerve fibre layer (cpRNFL); and OCT angiography measurement of pfVD, FAZ perimeter and multispectral fractal dimensions (MSFD). Eyes with more severe glaucoma had significantly thinner mGCC and cpRNFL and lower pfVD. MD decreased by 0.4 dB (95% CI 0.1 to 0.6 dB, P = 0.007) for every 1% decrease in pfVD. Lower MSFD was observed in eyes with lower pfVD and in patients with systemic hypertension. Multivariable analysis, accounting for age and OCTA quality, found lower pfVD remained significantly associated with thinner IMT, thinner mGCC and worse MD but not with MSFD. pfVD was reduced in NTG and was diminished in eyes with worse MD. Macular vessel branching complexity was not related to severity of visual field loss but was lower in patients with systemic hypertension.

Investigating Vascular Complexity and Neurogenic Alterations in Sectoral Regions of the Retina in Patients With Cognitive Impairment

Evidence is accumulating that cognitive function, and visual impairment may be related. In this pilot study, we investigated whether multifractal dimension and lacunarity analyses performed in sectoral regions of the retina may reveal changes in patients with cognitive impairment (CI) that may be masked in the study considering the whole retinal branching pattern. Prospective age-matched subjects (n = 69) with and with no CI and without the presence of any ophthalmic history were recruited (age > 55+ years). The Montreal Cognitive Assessment (MoCA) was used to measure CI, and full-field electroretinogram (ERG) was performed. Also, visual performance exams were conducted using the Rabin cone contrast test (CCT). Quantification of the retinal structure was performed in retinal fundus images [45^o field of view (FOV), optic disk centered] with excellent quality for all individuals [19 healthy controls (HC) and 20 patients with CI] after evaluating the inclusion and exclusion criteria in all study participants recruited (n = 69). The skeletonized vasculature network that comprised the whole branching pattern observable in the full 45° FOV was obtained for each image and divided into nine equal regions (superotemporal, superior, superonasal, macular, optic disk, nasal, inferotemporal, inferior, and inferonasal). The multifractal behavior was analyzed by calculating the generalized dimension Dq (Do, D1, and D2), the lacunarity parameter (Λ), and singularity spectrum f(α) in the nine sectoral skeletonized images as well as in the skeletons that comprised the whole branching pattern observable in the full 45° FOV. The analyses were performed using the ImageJ program together with the FracLac plug-in. Independent sample t-tests or Mann Whitney U test and Pearson correlation coefficient were used to find associations between all parameters in both groups. The effect size (Cohen’s d) of the difference between both groups was also assessed. A p-value < 0.05 was considered statistically significant. Significant correlations between multifractal and Λ parameters with the MoCA and implicit time ERG-parameter were observed in the regional analysis. In contrast, no trend was found when considering the whole retinal branching pattern. Analysis of combined structural-functional parameters in sectoral regions of the retina, instead of individual retinal biomarkers, may provide a useful clinical marker of CI.

Global assessment of arteriolar, venular and capillary changes in normal tension glaucoma

Microcirculatory insufficiency has been hypothesized in glaucoma pathogenesis. There is a scarcity of data to comprehensively examine the changes in retinal microvasculature and its role in normal tension glaucoma (NTG). We conducted a cross-sectional case-control study and included 168 eyes from 100 NTG patients and 68 healthy subjects. Quantitative retinal arteriolar and venular metrics were measured from retinal photographs using a computer-assisted program. Radial peripapillary capillary network was imaged with OCT-A and quantitative capillary metrics (circumpapillary vessel density (cpVD) and circumpapillary fractal dimension (cpFD)) were measured with a customized MATLAB program. We found that NTG was associated with decreased arteriolar and venular tortuosity, arteriolar branching angle, cpVD and cpFD. Decreased venular caliber, arteriolar and venular branching angles, cpVD and cpFD were associated with thinner average RNFL thickness. Decreased arteriolar and venular branching angles, cpVD and cpFD were also associated with worse standard automated perimetry measurements (mean deviation and visual field index). Compared with retinal arteriolar and venular metrics, regression models based on OCT-A capillary metrics consistently showed stronger associations with NTG and structural and functional measurements in NTG. We concluded that NTG eyes showed generalized microvascular attenuations, in which OCT-A capillary metrics attenuations were more prominent and strongly associated with NTG.

A recommended "minimum data set" framework for SD-OCT retinal image acquisition and analysis from the Atlas of Retinal Imaging in Alzheimer's Study (ARIAS)

INTRODUCTION

We propose a minimum data set framework for the acquisition and analysis of retinal images for the development of retinal Alzheimer's disease (AD) biomarkers. Our goal is to describe methodology that will increase concordance across laboratories, so that the broader research community is able to cross-validate findings in parallel, accumulate large databases with normative data across the cognitive aging spectrum, and progress the application of this technology from the discovery stage to the validation stage in the search for sensitive and specific retinal biomarkers in AD.

METHODS

The proposed minimum data set framework is based on the Atlas of Retinal Imaging Study (ARIAS), an ongoing, longitudinal, multi-site observational cohort study. However, the ARIAS protocol has been edited and refined with the expertise of all co-authors, representing 16 institutions, and research groups from three countries, as a first step to address a pressing need identified by experts in neuroscience, neurology, optometry, and ophthalmology at the Retinal Imaging in Alzheimer's Disease (RIAD) conference, convened by the Alzheimer's Association and held in Washington, DC, in May 2019.

RESULTS

Our framework delineates specific imaging protocols and methods of analysis for imaging structural changes in retinal neuronal layers, with optional add-on procedures of fundus autofluorescence to examine beta-amyloid accumulation and optical coherence tomography angiography to examine AD-related changes in the retinal vasculature.

DISCUSSION

This minimum data set represents a first step toward the standardization of retinal imaging data acquisition and analysis in cognitive aging and AD. A standardized approach is essential to move from discovery to validation, and to examine which retinal AD biomarkers may be more sensitive and specific for the different stages of the disease severity spectrum. This approach has worked for other biomarkers in the AD field, such as magnetic resonance imaging; amyloid positron emission tomography; and, more recently, blood proteomics. Potential context of use for retinal AD biomarkers is discussed.

Association between the retinal vascular network and retinal nerve fiber layer in the elderly: The Montrachet study

PURPOSE

To investigate the association between the characteristics of the retinal vascular network in the elderly and retinal nerve fiber layer (RNFL) thickness in a population-based study.

METHODS

We conducted a population-based study, the Montrachet study (Maculopathy Optic Nerve, nuTRition neurovAsCular, and HEarT disease), in participants aged ≥ 75 years. RNFL thickness was assessed with spectral-domain optical coherence tomography (SD-OCT). Analysis of the retinal vascular network was performed by means of the Singapore "I" Vessel Assessment (SIVA) software based on fundus photography.

RESULTS

Data from 970 participants were suitable for analysis. Patients with optic neuropathy were excluded. In multivariable analysis, each standard deviation (SD) decrease in the caliber of the six largest arterioles and veins in zone B and the six largest arterioles and veins in zone C was associated with a decrease in global RNFL thickness (β = -1.62 μm, P = 0.001; β = -2.39 μm, P < 0.001; β = -1.56 μm, P = 0.002; and β = -2.64 μm, P < 0.001, respectively).

CONCLUSIONS

Our study found that decreased retinal vessels caliber were associated with a decreased RNFL thickness in the elderly without optic neuropathy.

Remodeling mechanisms determine size distributions in developing retinal vasculature

The development of retinal blood vessels has extensively been used as a model to study vascular pattern formation. To date, various quantitative measurements, such as size distribution have been performed, but the relationship between pattern formation mechanisms and these measurements remains unclear. In the present study, we first focus on the islands (small regions subdivided by the capillary network). We quantitatively measured the island size distribution in the retinal vascular network and found that it tended to exhibit an exponential distribution. We were able to recapitulate this distribution pattern in a theoretical model by implementing the stochastic disappearance of vessel segments around arteries could reproduce the observed exponential distribution of islands. Second, we observed that the diameter distribution of the retinal artery segment obeyed a power law. We theoretically showed that an equal bifurcation branch pattern and Murray’s law could reproduce this pattern. This study demonstrates the utility of examining size distribution for understanding the mechanisms of vascular pattern formation.

Teratogenesis in the chick embryo following post-gastrulation exposure to Y-27632 -effect of Y-27632 on embryonic development

The pyridine derivative Y-27632 inhibits Rho-associated coiled-coil-containing protein kinase (ROCK) signaling, which is involved in numerous developmental processes during embryogenesis, primarily by controlling actin-cytoskeleton assembly and cell contractility. Somite formation requires rearrangement of the cytoskeleton and assists in major morphological mechanisms, including ventral body wall formation. Administration of Y-27632 impairs cytoskeletal arrangements in post-gastrulation chick embryos leading to ventral body wall defects (VBWD) at later stages of development. The aim of this study was to investigate the effect of Y-27632 on somite development in post-gastrulation chick embryos during early embryogenesis. After 60 h incubation, embryos in shell-less culture were treated with Y-27632 or vehicle for controls. Following administration, abnormality rates were assessed. In treatment groups, embryos showed a kinked longitudinal body axis. Western blot confirmed impaired ROCK downstream signaling by decreased expression of phosphorylated cofilin-2. Histology, Lysotracker studies and RT-PCR demonstrated increased cell death in somites, the neural tube and the ectoderm. RT-PCR and Western blot of factors known to be involved during somitogenesis revealed reduced expression in the treatment group compared to controls. We hypothesize that administration of Y-27632 disrupts somite development causing axial kinking and embryo malformation, which may lead to VBWD.

Association of Retinal Microvascular Characteristics With Short-term Memory Performance in Children Aged 4 to 5 Years

IMPORTANCE

Neurocognitive functions develop rapidly in early childhood and depend on the intrinsic cooperation between cerebral structures and the circulatory system. The retinal microvasculature can be regarded as a mirror image of the cerebrovascular circulation.

OBJECTIVE

To investigate the association between retinal vessel characteristics and neurological functioning in children aged 4 to 5 years.

DESIGN, SETTING, AND PARTICIPANTS

In this cohort study, mother-child pairs were recruited at birth from February 10, 2010, to June 24, 2014, and renewed consent at their follow-up visit from December 10, 2014, to July 13, 2018. Participants were followed up longitudinally within the prospective Environmental Influence on Aging in Early Life birth cohort. A total of 251 children underwent assessment for this study. Data were analyzed from July 17 to October 30, 2019.

MAIN OUTCOMES AND MEASURES

Retinal vascular diameters, the central retinal arteriolar equivalent (CRAE), central retinal venular equivalent (CRVE), vessel tortuosity, and fractal dimensions were determined. Attention and psychomotor speed, visuospatial working memory, and short-term visual recognition memory were assessed by the Cambridge Neuropsychological Test Automated Battery, including the following tasks: Motor Screening (MOT), Big/Little Circle (BLC), Spatial Span (SSP), and Delayed Matching to Sample (DMS).

RESULTS

Among the 251 children included in the assessment (135 girls [53.8%]; mean [SD] age, 4.5 [0.4] years), for every 1-SD widening in CRVE, the children performed relatively 2.74% (95% CI, -0.12 to 5.49; P = .06) slower on the MOT test, had 1.76% (95% CI, -3.53% to -0.04%; P = .04) fewer correct DMS assessments in total, and made 2.94% (95% CI, 0.39 to 5.29; P = .02) more errors given a previous correct answer in the DMS task on multiple linear regression modeling. For every 1-SD widening in CRAE, the total percentage of errors and errors given previous correct answers in the DMS task increased 1.44% (95% CI, -3.25% to 0.29%; P = .09) and 2.30% (95% CI, -0.14% to 4.61%; P = .07), respectively. A 1-SD higher vessel tortuosity showed a 4.32% relative increase in latency in DMS task performance (95% CI, -0.48% to 9.12%; P = .07). Retinal vessel characteristics were not associated with BLC and SSP test outcomes.

CONCLUSIONS AND RELEVANCE

These findings suggest that children's microvascular phenotypes are associated with short-term memory and that changes in the retinal microvasculature may reflect neurological development during early childhood.

Automated diagnosis and quantitative analysis of plus disease in retinopathy of prematurity based on deep convolutional neural networks

BACKGROUND

The purpose of this study was to develop an automated diagnosis and quantitative analysis system for plus disease. The system provides a diagnostic decision but also performs quantitative analysis of the typical pathological features of the disease, which helps the physicians to make the best judgement and communicate the decisions.

METHODS

The deep learning network provided segmentation of the retinal vessels and the optic disc (OD). Based on the vessel segmentation, plus disease was classified and tortuosity, width, fractal dimension and vessel density were evaluated automatically.

RESULTS

The trained network achieved a sensitivity of 95.1% with 97.8% specificity for the diagnosis of plus disease. For detection of preplus or worse, the sensitivity and specificity were 92.4% and 97.4%. The quadratic weighted k was 0.9244. The tortuosities for the normal, preplus and plus groups were 3.61 ± 0.08, 5.95 ± 1.57 and 10.67 ± 0.50 (10⁴  cm^-3 ). The widths of the blood vessels were 63.46 ± 0.39, 67.21 ± 0.70 and 68.89 ± 0.75 μm. The fractal dimensions were 1.18 ± 0.01, 1.22 ± 0.01 and 1.26 ± 0.02. The vessel densities were 1.39 ± 0.03, 1.60 ± 0.01 and 1.64 ± 0.09 (%). All values were statistically different among the groups. After treatment for plus disease with ranibizumab injection, quantitative analysis showed significant changes in the pathological features.

CONCLUSIONS

Our system achieved high accuracy of diagnosis of plus disease in retinopathy of prematurity. It provided a quantitative analysis of the dynamic features of the disease progression. This automated system can assist physicians by providing a classification decision with auxiliary quantitative evaluation of the typical pathological features of the disease.

Systematic Review on Fractal Dimension of the Retinal Vasculature in Neurodegeneration and Stroke: Assessment of a Potential Biomarker

Introduction: Ocular manifestations in several neurological pathologies accentuate the strong relationship between the eye and the brain. Retinal alterations in particular can serve as surrogates for cerebral changes. Offering a “window to the brain,” the transparent eye enables non-invasive imaging of these changes in retinal structure and vasculature. Fractal dimension (FD) reflects the overall complexity of the retinal vasculature. Changes in FD could reflect subtle changes in the cerebral vasculature that correspond to preclinical stages of neurodegenerative diseases. In this review, the potential of this retinal vessel metric to serve as a biomarker in neurodegeneration and stroke will be explored.

Methods: A literature search was conducted, following the PRISMA Statement 2009 criteria, in four large bibliographic databases (Pubmed, Embase, Web Of Science and Cochrane Library) up to 12 October 2019. Articles have been included based upon their relevance. Wherever possible, level of evidence (LOE) has been assessed by means of the Oxford Centre for Evidence-based Medicine Level of Evidence classification.

Results: Twenty-one studies were included for qualitative synthesis. We performed a narrative synthesis and produced summary tables of findings of included papers because methodological heterogeneity precluded a meta-analysis. A significant association was found between decreased FD and neurodegenerative disease, mainly addressing cognitive impairment (CI) and dementia. In acute, subacute as well as chronic settings, decreased FD seems to be associated with stroke. Differences in FD between subtypes of ischemic stroke remain unclear.

Conclusions: This review provides a summary of the scientific literature regarding the association between retinal FD and neurodegenerative disease and stroke. Central pathology is associated with a decreased FD, as a measure of microvascular network complexity. As retinal FD reflects the global integrity of the cerebral microvasculature, it is an attractive parameter to explore. Despite obvious concerns, mainly due to a lack of methodological standardization, retinal FD remains a promising non-invasive and low-cost diagnostic biomarker for neurodegenerative and cerebrovascular disease. Before FD can be implemented in clinic as a diagnostic biomarker, the research community should strive for uniformization and standardization.

Multifractal-based lacunarity analysis of trabecular bone in radiography

This study presents textural characterization techniques for effective osteoporosis diagnosis using bone radiograph images. The automatic classification of osteoporosis and healthy (control) cases using bone radiograph images in this work presents a major challenge as the images show no visual differences for both cases. The proposed work utilizes multifractals to characterize the trabecular bone texture in the radiographs. Initially, Holder exponents are computed, then Hausdorff dimensions are determined, which quantify the global regularity of the pixels. Finally, lacunarity is computed from the Hausdorff dimensions. Performance metrics show that estimating lacunarity from the Hausdorff dimensions, rather than the input image, directly helps in achieving better textural characterization of bone radiographs, leading to better performance in osteoporosis classification. The proposed lacunarity-based trabecular bone textural characterization method is compared with other multifractal-based methods for trabecular bone textural characterization, such as box-counting and regularization dimensions. The proposed method is also evaluated with the textural characterization of a bone radiograph challenge dataset to demonstrate its effectiveness compared to the other methods used in the challenge.

Retinal Vessel Phenotype in Patients with Nonarteritic Anterior Ischemic Optic Neuropathy

PURPOSE

The pathophysiology of nonarteritic anterior ischemic optic neuropathy (NAION) is not completely understood. Studies of the retinal vasculature phenotype in patients with NAION could help us to understand vascular abnormalities associated with the disease.

DESIGN

Retrospective case series with matched control subjects.

METHODS

Study population: 57 patients with NAION and 57 control subjects matched to NAION patients for sex, age, systemic hypertension, diabetes, and obstructive sleep apnea syndrome between September 2007 and July 2017.

MAIN OUTCOME MEASURES

All patients and control subjects underwent a complete ocular examination and 45° funduscopic color photographs. The widths of the 6 largest arteries in zone B (between 0.5 and 1 optic disc diameter from the optic disc), summarized by the central retinal artery equivalent (CRAE), the widths of the 6 largest veins in zone B, summarized by the central retinal vein equivalent (CRVE), the arteriole to venule ratio, tortuosity, and fractal dimension were measured on the 2 groups using Vessel Assessment and Measurement Platform for Images of the Retina, a software tool for efficient semiautomatic quantification of the retinal vasculature morphology in fundus camera images. The Wilcoxon signed-rank test and MacNemar χ² test for paired sample and generalized estimating equations for modeling the Vessel Assessment and Measurement Platform for Images of the Retina parameters as dependent variables were used.

RESULTS

CRVE and fractal dimension (D0a) were significantly higher in the NAION group when compared with the control group, whereas the arteriole to venule ratio and vascular tortuosity were significantly lower. Compared with control subjects, acute NAION yielded an increased CRAE value (174 ± 33 vs 160 ± 13 μm) while resolution NAION yielded a decreased CRAE value (152 ± 12 vs 156 ± 33 μm). Acute NAION yielded an increased CRVE value (244 ± 35 vs 210 ± 21 μm) while resolution NAION yielded an unchanged CRVE value. We found no difference between groups for age, refraction, optic disc diameter, CRAE, or fractal dimension.

CONCLUSIONS

Retinal vascular parameters were different in our sample between NAION and control patients, especially at the acute stage of the disease. Our results suggest a normalization of the same parameters at the resolution stage.

Distinguishing cognitive impairment by using singularity spectrum and lacunarity analysis of the retinal vascular network

The development of effective therapies for cognitive impairment (CI), especially due to Alzheimer's disease, demands diagnosing the condition during the prodromal phase. The diagnosis of CI involves expensive and invasive methods, such as positron emission tomography and cerebrospinal fluid assessment via spinal tap. Hence, a comparatively lower cost and noninvasive method of diagnosis is imperative. The human retina is an extension of the brain characterized by similarities in vascular and neural structures. The complications of CI are not only limited to the brain but also affect the retina for which the loss of retinal ganglion cells has been associated with neurodegeneration in the brain. The loss of retinal ganglion cells in individuals with CI may be related to reduced vascular demand and a potential remodeling of the retinal vascular branching complexity. Retinal imaging biomarkers may provide a low cost and noninvasive alternative for the diagnosis of CI. In this study, the retinal vascular branching complexity of patients with CI was characterized using the singularity spectrum multifractal dimension and lacunarity parameter. A reduced vascular branching complexity was observed in subjects with CI when compared to age- and sex-matched cognitively healthy controls. Significant associations were also found between retinal vascular and functional parameters.

Network-based features for retinal fundus vessel structure analysis

Retinal fundus imaging is a non-invasive method that allows visualizing the structure of the blood vessels in the retina whose features may indicate the presence of diseases such as diabetic retinopathy (DR) and glaucoma. Here we present a novel method to analyze and quantify changes in the retinal blood vessel structure in patients diagnosed with glaucoma or with DR. First, we use an automatic unsupervised segmentation algorithm to extract a tree-like graph from the retina blood vessel structure. The nodes of the graph represent branching (bifurcation) points and endpoints, while the links represent vessel segments that connect the nodes. Then, we quantify structural differences between the graphs extracted from the groups of healthy and non-healthy patients. We also use fractal analysis to characterize the extracted graphs. Applying these techniques to three retina fundus image databases we find significant differences between the healthy and non-healthy groups (p-values lower than 0.005 or 0.001 depending on the method and on the database). The results are sensitive to the segmentation method (manual or automatic) and to the resolution of the images.

Multifractal and lacunarity analyses of microvascular morphology in eyes with diabetic retinopathy: A projection artifact resolved optical coherence tomography angiography study

OBJECTIVE

To evaluate the degree of microvascular impairment in DR using multifractal and lacunarity analyses and to compare the diagnostic ability between traditional Euclidean measures (fovea avascular zone area and vessel density) and fractal geometric features.

METHODS

This retrospective cross-sectional study included a total of 143 eyes of 94 patients with different stages of DR. The retinal microvasculature was imaged by projection removed OCTA. We examined the degree of association between fractal metrics of the retinal microvasculature and DR severity. The area under the ROC curve was used to estimate the diagnostic performance.

RESULTS

With increasing DR severity, the multifractal spectrum shifted toward the left bottom and exhibited less left skewness and asymmetry. The vessel density, multifractal features, and lacunarity measured from the DCP were strongly associated with DR severity. The multifractal feature D₅ showed the highest diagnostic ability. The combination of multifractal features further improved the discriminating power.

CONCLUSIONS

Multifractal and lacunarity analyses can be potentially valuable tools for assessment of microvascular impairments in DR. Multifractal geometric parameters exhibit a better discriminatory performance than Euclidean measures, particularly for detection of the early stages of DR.

Investigating Multimodal Diagnostic Eye Biomarkers of Cognitive Impairment by Measuring Vascular and Neurogenic Changes in the Retina

Previous studies have demonstrated that cognitive impairment (CI) is not limited to the brain but also affects the retina. In this pilot study, we investigated the correlation between the retinal vascular complexity and neurodegenerative changes in patients with CI using a low-cost multimodal approach. Quantification of the retinal structure and function were conducted for every subject (n = 69) using advanced retinal imaging, full-field electroretinogram (ERG) and visual performance exams. The retinal vascular parameters were calculated using the Singapore Institute Vessel Assessment software. The Montreal Cognitive Assessment was used to measure CI. Pearson product moment correlation was performed between variables. Of the 69 participants, 32 had CI (46%). We found significantly altered microvascular network in individuals with CI (larger venular-asymmetry factor: 0.7 ± 0.2) compared with controls (0.6 ± 0.2). The vascular fractal dimension was lower in individuals with CI (capacity, information and correlation dimensions: D₀, D_1, and D₂ (mean ± SD): 1.57 ± 0.06; 1.56 ± 0.06; 1.55 ± 0.06; age 81 ± 6years) vs. controls (1.61 ± 0.03; 1.59 ± 0.03; 1.58 ± 0.03; age: 80 ± 7 years). Also, drusen-like regions in the peripheral retina along with pigment dispersion were noted in subjects with mild CI. Functional loss in color vision as well as smaller ERG amplitudes and larger peak times were observed in the subjects with CI. Pearson product moment correlation showed significant associations between the vascular parameters (artery-vein ratio, total length-diameter ratio, D₀, D₁, D₂ and the implicit time (IT) of the flicker response but these associations were not significant in the partial correlations. This study illustrates that there are multimodal retinal markers that may be sensitive to CI decline, and adds to the evidence that there is a statistical trend pointing to the correlation between retinal neuronal dysfunction and microvasculature changes suggesting that retinal geometric vascular and functional parameters might be associated with physiological changes in the retina due to CI. We suspect our analysis of combined structural-functional parameters, instead of individual biomarkers, may provide a useful clinical marker of CI that could also provide increased sensitivity and specificity for the differential diagnosis of CI. However, because of our study sample was small, the full extent of clinical applicability of our approach is provocative and still to be determined.

Vascular amounts and dispersion of caliber-classified vessels as key parameters to quantitate 3D micro-angioarchitectures in multiple myeloma experimental tumors

Blood vessel micro-angioarchitecture plays a pivotal role in tumor progression, metastatic dissemination and response to therapy. Thus, methods able to quantify microvascular trees and their anomalies may allow a better comprehension of the neovascularization process and evaluation of vascular-targeted therapies in cancer. To this aim, the development of a restricted set of indexes able to describe the arrangement of a microvascular tree is eagerly required. We addressed this goal through 3D analysis of the functional microvascular network in sulfo-biotin-stained human multiple myeloma KMS-11 xenografts in NOD/SCID mice. Using image analysis, we show that amounts, spatial dispersion and spatial relationships of adjacent classes of caliber-filtered microvessels provide a near-linear graphical “fingerprint” of tumor micro-angioarchitecture. Position, slope and axial projections of this graphical outcome reflect biological features and summarize the properties of tumor micro-angioarchitecture. Notably, treatment of KMS-11 xenografts with anti-angiogenic drugs affected position and slope of the specific curves without degrading their near-linear properties. The possibility offered by this procedure to describe and quantify the 3D features of the tumor micro-angioarchitecture paves the way to the analysis of the microvascular tree in human tumor specimens at different stages of tumor progression and after pharmacologic interventions, with possible diagnostic and prognostic implications.