Fractal Analysis of the Vascular Tree in the Human Retina

A universal mathematical model applied to the congenital ventral penile curvature

INTRODUCTION

The macroscopic dynamic of fetal penis development presents a pattern resembling the unfolding of a spiral, so congenital ventral penile curvature could indicate that this natural sequence has been interrupted. Our aim in this article is to offer a mathematical model of congenital ventral curvature of the penis.

MATERIALS AND METHODS

Five individuals who presented with congenital ventral penile curvature and three who presented with acquired penile ventral curvature due to Peyronie's disease were evaluated. The penises were photographed during an induced erection test and the penile curvature patterns were compared with an equiangular spiral. When an association was found, a potential relationship to the golden spiral-a type of equiangular spiral-was also assessed. The mathematical spiral relationships were analyzed using Wolfram CDF Player® (Logarithmic Spiral) and PhiMatrix® software. The Wolfram software generated logarithmic spirals equivalent to the penile curvature with appropriate mathematical values. The PhiMatrix software, which builds any golden spirals from golden rectangles, was used to check whether the spiral was golden as well as equiangular.

RESULTS

An equiangular spiral that was also golden was found in all cases of congenital ventral penile curvature. In contrast, none of the acquired penile ventral curvature cases showed a specific pattern.

CONCLUSION

Congenital ventral penile curvature has the mathematical pattern of a golden spiral. Our results offer a mathematical algorithm for potential use in surgical reconstruction procedures, regenerative medicine, tissue engineering, robotics, and body-machine interfaces.

Chronic Neovascular Central Serous Chorioretinopathy: A Stress/Rest Optical Coherence Tomography Angiography Study

PURPOSE

To compare optical coherence tomography-angiography (OCT-A) performed during physical exercise (stress OCT-A) to the basal examination (rest OCT-A) in the imaging of choroidal neovascularization (CNV) in patients with chronic central serous chorioretinopathy (CSCR).

DESIGN

Prospective, cohort study.

METHODS

This multicenter study included 29 consecutive patients with chronic CSCR and flat irregular pigment epithelium detachments (FIPEDs). All patients underwent rest and stress OCT-A (i.e., hand-grip test [HGT]). Systemic hemodynamic data were recorded during the examinations. Rest and stress OCT-A in the en-face and cross-sectional views were qualitatively compared to establish the degree of evidence of flow signals due to CNVs. The en-face angiograms underwent additional automated quantitative analysis to assess the rate of change in neovascular parameters during the stress condition.

RESULTS

Blood pressure significantly increased during the HGT (P = 0.001). Considering both the en-face and the cross-sectional images, CNV was identified in 13 eyes with the rest OCT-A and in 22 eyes with the stress OCT-A (P = 0.001). Cross-sectional imaging was more sensitive than en-face imaging in detecting neovascular blood flow signals under both rest (P = 0.125) and stress (P = 0.001) conditions. The quantitative analysis showed a significantly greater neovascular area and fractal dimension on the stress OCT-A (P = 0.002).

CONCLUSIONS

Performing OCT-A during HGT enhances the sensitivity of the examination in detecting CNV in chronic CSCR. The increased neovascular perfusion following the induced increase of blood pressure is consistent with choroidal blood flow dysregulation in patients with CSCR and indicates new areas of discussion about CNV in this disease.

Quantitative Optical Coherence Tomography Angiography Biomarkers in a Treat-and-Extend Dosing Regimen in Neovascular Age-Related Macular Degeneration

Purpose

To evaluate the association between quantitative optical coherence tomography angiography (OCT-A) parameters and clinical outcomes in treatment-naïve neovascular age-related macular degeneration (nAMD) patients treated with a treat-and-extend dosing regimen on a 12-month follow-up interval.

Methods

Observational, prospective study of consecutive patients. The treatment protocol was based on a loading dose of three anti-vascular endothelial growth factor (VEGF) intravitreal injections (IVI) followed by a treat-and-extend regimen. Eyes were evaluated by swept-source OCT-A at baseline, 1 month after the loading dose and at 12 months. A quantitative analysis was issued for fractal dimension (FD), lacunarity index (LAC), blood flow surface area (SA), and vessel density (VD). An association of these parameters with the anatomic response and functional responses, and IVI number at 12 months of follow-up was assessed. A level of significance α = 0.05 was considered.

Results

Sixty-four patients were included, 52 of whom (81%) completed the 12-month study protocol. The median number of injections at 12 months was 7 (P₂₅-P₇₅: 6-12). FD and SA were reduced 1 month after the loading dose of anti-VEGF (P < 0.001). The generalized linear models using baseline FD and baseline SA achieved the best performance in discriminating a lower treatment burden (area under the curve [AUC] = 0.78; 95% confidence interval [CI]: 0.64-0.91 and AUC = 0.76; 95% CI: 0.63-0.90, respectively).

Conclusions

Baseline OCT-A may provide useful biomarkers for the treatment burden in nAMD.

Translational Relevance

The application of fractal dimension and automatic blood flow area algorithms to OCT-A data can distinguish patients with distinct treatment burdens in the first year of nAMD.

Retinal vessel phenotype in patients with primary open-angle glaucoma

PURPOSE

To characterize the phenotype of retinal vessels using central retinal artery equivalent (CRAE), central retinal vein equivalent (CRVE), tortuosity and fractal dimension (FD) in primary open-angle glaucoma (POAG) subjects.

METHODS

This prospective case-control multicentre study included 61 POAG subjects and 61 controls matched for age, systemic hypertension and body mass index. Fundus images of the right eye were acquired using a non-mydriatic camera. Central retinal artery equivalent (CRAE), CRVE, arteriole-to-venule ratio, FD and tortuosity of the vascular network were measured using VAMPIRE software (Vessel Assessment and Measurement Platform for Images of the Retina). Primary open-angle glaucoma (POAG) patients underwent 24.2 sita-standard visual field and peri-papillary optical coherence tomography (OCT) examinations. Data were expressed as median and interquartile range (75-25th percentiles).

RESULTS

The control group was comparable to the POAG group for sex ratio, refraction and intraocular pressure. The mean CRAE and the mean CRVE were significantly lower in the POAG group than in the control group [150.5 (137.9; 157.1) μm versus 161.3 (154.0; 168.4) μm and 204.8 (190.1; 218.1) μm versus 233.5 (222.3; 246.9) μm, respectively; p < 0.001] and for fractal parameters as well. No significant difference was found for tortuosity between the two groups. There was a significant correlation between CRAE and retinal nerve fibre layer (RNFL) thickness (r = 0.27; p = 0.03). VAMPIRE parameters were not correlated with visual field indices.

CONCLUSION

Primary open-angle glaucoma (POAG) was associated with a narrowing of arterial and venous retinal vessels, a higher arteriole-to-venule ratio and lower values of FD. The relationship between CRAE and RNFL thickness needs further investigation.

Retinal vascular fractal dimension and cerebral blood flow, a pilot study

PURPOSE

Ocular and brain microcirculation share embryological and histological similarities. The retinal vascular fractal dimension (FD) is a marker of retinal vascular complexity of the vascular tree. The purpose of this study was to explore the relationship between cerebral blood flow (CBF), retinal vascular FD and other retinal vascular markers.

METHODS

Cross-sectional analysis comprising 26 individuals ≥65 years old from the Cognitive REServe and Clinical ENDOphenotype (CRESCENDO) cohort of relative healthy older adults. Retinal vascular FD was measured from fundus photographs by using the semi-automated Singapore Eye Vessel Assessment (SIVA) software. CBF was estimated using a 2D pulsed ASL MRI sequence. Associations between blood flow and retinal parameters were analysed using linear regression models adjusted for age and sex.

RESULTS

Cerebral blood flow was positively associated with venular FD (R²  = 0.32, p = 0.03). This association was stronger in the anterior versus posterior brain territories (R²  = 0.35 [p = 0.001] versus R²  = 0.16 [p = 0.07], respectively). Global CBF was correlated with arteriolar branching angle (R²  = 0.23, p = 0.01) and tortuosity (R²  = 0.20, p = 0.02). Global CBF was not correlated with other SIVA parameters.

CONCLUSIONS

Retinal venular complexity summarized by the FD was associated with cerebral blood flow as well as retinal arteriolar tortuosity and branching angle. Larger prospective clinical studies are needed to confirm these results.

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.

The fractal geometry of bronchial trees differs by strain in mice

Fractal biological structures are pervasive throughout the plant and animal kingdoms, with the mammalian lung being a quintessential example. The lung airway and vascular trees are generated during embryogenesis from a small set of building codes similar to Turing mechanisms that create robust trees ideally suited to their functions. Whereas the blood flow pattern generated by these fractal trees has been shown to be genetically determined, the geometry of the trees has not. We explored a newly established repository providing high-resolution bronchial trees from the four most commonly studied laboratory mice (B6C3F1, BALB/c, C57BL/6 and CD-1). The data fit a fractal model well for all animals with the fractal dimensions ranging from 1.54 to 1.67, indicating that the conducting airway of mice can be considered a self-similar and space-filling structure. We determined that the fractal dimensions of these airway trees differed by strain but not sex, reinforcing the concept that airway branching patterns are encoded within the DNA. The observations also highlight that future study design and interpretations may need to consider differences in airway geometry between mouse strains.NEW & NOTEWORTHY Similar to larger mammals such as humans, the geometries of the bronchial tree in mice are fractal structures that have repeating patterns from the trachea to the terminal branches. The airway geometries of the four most commonly studied mice are different and need to be considered when comparing results that employ different mouse strains. This variability in mouse airway geometries should be incorporated into computer models exploring toxicology and aerosol deposition in mouse models.

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.

Retinal vascular fractal dimension in bipolar disorder and schizophrenia

BACKGROUND

Bipolar disorder (BD) and schizophrenia (SCZ), are associated with greater vascular co-morbidities and adverse vascular events. Owing to shared developmental origins and morphology, retinal vasculature is a proxy assessment measure of the cerebral vasculature. Although retinal vascular fractal dimension (D_f), a measure of vascular geometry and complexity of branching, has been shown to be directly associated with cerebrovascular pathology, it has not been examined in SCZ and BD.

METHODS

We studied 277 participants (92 healthy volunteers, 98 SCZ, and 87 BD) from 18 to 50 years of age. Images were acquired by trained personnel using a non-mydriatic fundus camera and the retinal vascular D_f was calculated by the box-counting method using an automated algorithm. The average D_f across the left and right eyes were calculated.

RESULTS

Both SCZ and BD had significantly increased D_f compared to HV despite controlling for possible confounding factors. However, there was no significant difference between SCZ and BD. These findings suggest abnormal retinal vascular D_f in psychoses.

LIMITATIONS

The study design was cross-sectional, and patients were on medications. Confound of lifestyle factors such as diet and exercise, if any, was not controlled. Sub-group analysis between BD-I and BD-II was not performed in view of the small sample.

CONCLUSIONS

Considering the easy accessibility, affordability, and non-invasive nature of the examination, retinal vascular D_f could serve as a surrogate marker for cerebral vascular abnormality and could potentially identify BD and SCZ patients at risk of developing adverse vascular events.

3D Printable Vascular Networks Generated by Accelerated Constrained Constructive Optimization for Tissue Engineering

One of the greatest challenges in fabricating artificial tissues and organs is the incorporation of vascular networks to support the biological requirements of the embedded cells, encouraging tissue formation and maturation. With the advent of 3D printing technology, significant progress has been made with respect to generating vascularized artificial tissues. Current algorithms to generate arterial/venous trees are computationally expensive and offer limited freedom to optimize the resulting structures. Furthermore, there is no method for algorithmic generation of vascular networks that can recapitulate the complexity of the native vasculature for more than two trees, and export directly to a 3D printing format. Here, we report such a method, using an accelerated constructive constrained optimization approach, by decomposing the process into construction, optimization, and collision resolution stages. The new approach reduces computation time to minutes at problem sizes where previous implementations have reported days. With the optimality criterion of maximizing the volume of useful tissue which could be grown around such a network, an approach of alternating stages of construction and batch optimization of all node positions is introduced and shown to yield consistently more optimal networks. The approach does not place a limit on the number of interpenetrating networks that can be constructed in a given space; indeed we demonstrate a biomimetic, liver-like tissue model. Methods to account for the limitations of 3D printing are provided, notably the minimum feature size and infill at sharp angles, through padding and angle reduction, respectively.

Bioprinting Vasculature: Materials, Cells and Emergent Techniques

Despite the great advances that the tissue engineering field has experienced over the last two decades, the amount of in vitro engineered tissues that have reached a stage of clinical trial is limited. While many challenges are still to be overcome, the lack of vascularization represents a major milestone if tissues bigger than approximately 200 µm are to be transplanted. Cell survival and homeostasis is to a large extent conditioned by the oxygen and nutrient transport (as well as waste removal) by blood vessels on their proximity and spontaneous vascularization in vivo is a relatively slow process, leading all together to necrosis of implanted tissues. Thus, in vitro vascularization appears to be a requirement for the advancement of the field. One of the main approaches to this end is the formation of vascular templates that will develop in vitro together with the targeted engineered tissue. Bioprinting, a fast and reliable method for the deposition of cells and materials on a precise manner, appears as an excellent fabrication technique. In this review, we provide a comprehensive background to the fields of vascularization and bioprinting, providing details on the current strategies, cell sources, materials and outcomes of these studies.

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.

Retinal Microvascular and Neurodegenerative Changes in Alzheimer's Disease and Mild Cognitive Impairment Compared with Control Participants

PURPOSE

Evaluate and compare the retinal microvasculature in the superficial capillary plexus (SCP) in Alzheimer's disease (AD), mild cognitive impairment (MCI), and cognitively intact controls using OCT angiography. OCT parameters were also compared.

DESIGN

Cross-sectional study.

PARTICIPANTS

Seventy eyes from 39 AD participants, 72 eyes from 37 MCI participants, and 254 eyes from 133 control participants were enrolled.

METHODS

Participants were imaged using Zeiss Cirrus HD-5000 with AngioPlex (Carl Zeiss Meditec, Dublin, CA) and underwent cognitive evaluation with Mini-Mental State Examination.

MAIN OUTCOME MEASURES

Vessel density (VD) and perfusion density (PD) in the SCP within the Early Treatment Diabetic Retinopathy Study 6-mm circle, 3-mm circle, and 3-mm ring were compared between groups. Foveal avascular zone (FAZ) area, central subfield thickness (CST), macular ganglion cell-inner plexiform layer (GC-IPL) thickness, and peripapillary retinal nerve fiber layer (RNFL) thickness were also compared.

RESULTS

Alzheimer's participants showed significantly decreased SCP VD and PD in the 3-mm ring (P = 0.001 and P = 0.002, respectively) and 3-mm circle (P = 0.003 and P = 0.004, respectively) and decreased SCP VD in the 6-mm circle (P = 0.047) compared with MCI and significantly decreased SCP VD and PD in the 3-mm ring (P = 0.008 and P = 0.004, respectively) and 3-mm circle (P = 0.015 and P = 0.009, respectively) and SCP PD in the 6-mm circle (P = 0.033) when compared with cognitively intact controls. There was no difference in SCP VD or PD between MCI and controls (P > 0.05). FAZ area and CST did not differ significantly between groups (P > 0.05). Alzheimer's participants showed significantly decreased GC-IPL thickness over the inferior (P = 0.032) and inferonasal (P = 0.025) sectors compared with MCI and significantly decreased GC-IPL thickness over the entire (P = 0.012), superonasal (P = 0.041), inferior (P = 0.004), and inferonasal (P = 0.006) sectors compared to controls. MCI participants showed significantly decreased temporal RNFL thickness (P = 0.04) compared with controls.

CONCLUSIONS

Alzheimer's participants showed significantly reduced macular VD, PD, and GC-IPL thickness compared with MCI and controls. Changes in the retinal microvasculature may mirror small vessel cerebrovascular changes in AD.

A mathematical modelling analysis of the response of blood pressure and heart rate to submaximal exercise

Objective: According to Golden ratio (GR) and Fibonacci sequence, models of the organisation of various structures can be encountered in biology, medicine, architecture and engineering. Recent studies indicate that GR can be highlighted in the organisation and physiological functioning of the cardiovascular system. The aim of this study was to investigate the cardiovascular homeostasis during rest and exercise testing by determining the GR validity at the dynamic level of systolic and diastolic blood pressure (SBP, DBP) and heart rate (HR) values. Methods and Results: We used data obtained from a cardiovascular testing of a group of 236 young healthy subjects (mean age of 19.35 ± 1.92 years). We realised a double assessment of subjects (HR and BP), at rest and immediately after a six minutes submaximal exercise test (Astrand and Rhyming protocol). The investigated group showed a normal cardiovascular reactivity in subjects. GR harmonic rhythm can be identified in the correlation of hemodynamic parameters of HR and SBP, respectively of SBP and DBP, at rest. The differences between means of the ratios (SBP/HR and SBP/DBP), at rest and after effort, were statistically significant (p < .001), with a large effect size. Conclusions: We confirm that the rest state determines the harmonisation of SBP and HR, respectively, of SBP and DBP values, both ratios being very close to GR value. From the perspective of these cardiovascular parameters, the human body is designed to function in the harmonic regime at rest and to temporarily get out of synchronisation during exercise.

Peripapillary Microvascular and Neural Changes in Diabetes Mellitus: An OCT-Angiography Study

Purpose

To evaluate peripapillary vessel density and morphology in patients with diabetes mellitus (DM) without clinical signs of diabetic retinopathy (DR) and with mild, nonproliferative DR and to correlate with peripapillary nerve fiber layer (NFL) thickness.

Methods

One hundred seventeen eyes (34 healthy controls, 54 patients with DM without DR [noDR group] and 24 patients with mild DR [DR group]) were prospectively evaluated. All subjects underwent peripapillary and macular optical coherence tomography angiography (OCT-A). Peripapillary NFL thickness was also recorded. OCT-A slab of radial peripapillary plexus (RPC) and macular superficial capillary plexus (SCP) were analysed in order to calculate perfusion density (PD) and vessel density (VD). Further an image analysis of RPC slab was performed to identify number of branches (NoB) and total branches length (tBL).

Results

In peripapillary area there was a significant decrease in VD (P = 0.003), NoB (P < 0.001), and tBL (P < 0.001) in noDR group versus controls; PD values were not different among groups (P = 0.126); there was a significant decrease in average NFL thickness in DR versus controls (P = 0.008) and in the inferior quadrant in noDR group versus controls (P = 0.03); there was a significant correlation between OCT-A and NFL thickness values (ρ ranging from 0.19-0.57). In macular region PD and VD were decreased only in DR group (P < 0.05).

Conclusions

There are early changes in the peripapillary vessel morphology and VD of the RPC in patients with DM without DR that correlate to NFL thinning. Earlier changes in superficial vessel density are documented in the peripapillary than in the macular region. These data may confirm a coexistence of an early neuronal and microvascular damage in patients with DM without clinical signs of DR.

Novel Predictors of Visual Outcome in Anti-VEGF Therapy for Myopic Choroidal Neovascularization Derived Using OCT Angiography

PURPOSE

To explore novel prognostic factors associated with visual function and number of anti-vascular endothelial growth factor (VEGF) treatments in eyes with active myopic choroidal neovascularization (mCNV) using OCT angiography (OCTA).

DESIGN

Prospective case series.

PARTICIPANTS

Twenty-eight treatment-naïve eyes with active mCNV from 27 consecutive patients (mean age, 64.4 ± 11.1 years).

METHODS

All eyes received through injection a single loading dose of intravitreal aflibercept (IVA), followed by additional IVA on a pro re nata (PRN) basis during the subsequent 12 months. At baseline, OCTA images of a 3 × 3-mm macular cube were acquired using an OCTA scanner. On binarized and skeletonized OCTA images of the outer retinal layer, OCTA-derived baseline parameters of mCNV-including lesion size, vessel density, vessel length density (VLD), vessel diameter index, and fractal dimension (FD)-were measured and evaluated for correlation with 12-month best-corrected visual acuity (BCVA) and number of additional injections.

MAIN OUTCOME MEASURES

The primary and secondary outcomes were BCVA 12 months after initial treatment and number of additional injections, respectively.

RESULTS

There was no significant difference between baseline and 12-month BCVA (0.37 ± 0.30 and 0.30 ± 0.35 logarithm of the minimal angle of resolution, respectively; P = 0.23). The number of additional injections was 0.93 ± 1.02 (mean ± standard deviation). Baseline VLD, FD, and BCVA were correlated with 12-month BCVA (P = 0.02, r = 0.46; P = 0.02, r = 0.46; and P = 0.02, r = 0.45, respectively), and VLD also was correlated with the number of additional injections (P = 0.03, r = 0.42).

CONCLUSIONS

Exuberant mCNV, which is characterized by high VLD and FD derived using OCTA, is a predictor of poor visual outcomes after a single IVA injection followed by a PRN regimen. Only baseline VLD was correlated with the number of additional IVA injections, which indicates that this parameter could help to determine the optimal anti-VEGF treatment regimen for individual eyes with mCNV.

Biomarkers of Peripheral Nonperfusion in Retinal Venous Occlusions Using Optical Coherence Tomography Angiography

Purpose

To study the association between the assessment of central macular vascular layers by optical coherence tomography angiography (OCT-A) and peripheral nonperfusion evaluated by fluorescein angiography (FA) in patients with retinal venous occlusion (RVO).

Methods

Retrospective review of RVO patients without macular edema. Patients underwent a comprehensive ophthalmic examination including FA, spectral-domain OCT, and OCT-A. Significant ischemia was defined as nonperfusion areas superior or equal to the equivalent of one retinal quadrant on FA. Vascular density (VD) and foveal avascular zone were measured using AngioAnalytics software. Fractal dimension (FD) and lacunarity (LAC) were computed using an algorithm designed by MATLAB (MathWorks, Natick, MA). These variables were used to build a model that translates their association with OCT-A parameters.

Results

There were 48 eyes (48 patients) of which 19 had significant peripheral nonperfusion. Deep capillary plexus FD, VD, and LAC were associated with significant ischemia. In fact, regarding the association with this outcome, LAC alone had the highest area under the curve (AUC = 0.88) followed by FD (AUC = 0.85) and VD (AUC = 0.73). The multivariable model that included LAC and VD, adjusted by best-corrected visual acuity (BCVA) achieved the best performance for the identification of severe nonperfusion on wide-field FA (AUC = 0.93).

Conclusions

The characteristics of the central macular deep capillary plexus on OCT-A may be associated with peripheral nonperfusion on FA, particularly the combination of LAC and vessel density after adjusting by BCVA.

Translational Relevance

Fractal-based metrics applied to OCT-A may become a valuable marker of ischemia in RVO and help guide the clinical decision to perform invasive angiography.

Dendritic surface patterns from Bénard-Marangoni instabilities upon evaporation of a reactive ZnO nanofluid droplet: A fractal dimension analysis

We present a box counting fractal dimension (FD) analysis of the dendritic patterns obtained under conditions far from equilibrium via rapid evaporation of a sessile drop containing reactive ZnO nanoparticles. These dendrites were manifestations of solidified Bénard-Marangoni (BM) instability convection cells, and we previously noted that their complex hierarchical morphologies were superficially analogous to the foliage of red algae, Spanish dagger, or spider plant. The fractal dimension of the Bénard-Marangoni dendrites was found to vary in the range of 1.77-1.89 and also depend on the size of the Bénard-Marangoni cells. These fractal dimension results were correlated with the morphological details of the Bénard-Marangoni cells and ZnO particle characteristics, providing a quantitative description of such complex surface patterns emerging from the dynamic process of the Bénard-Marangoni instability.

Advanced Optical Coherence Tomography Angiography Analysis of Age-related Macular Degeneration Complicated by Onset of Unilateral Choroidal Neovascularization

PURPOSE

To analyze optical coherence tomography angiography (OCTA) quantitative features in patients affected by new-onset choroidal neovascularization (CNV) in 1 eye and early/intermediate age-related macular degeneration (AMD) in the fellow eye.

DESIGN

Case-control study.

METHODS

Setting: Clinical practice.

STUDY POPULATION

Thirty patients and 30 age-matched controls.

OBSERVATION PROCEDURES

Both cohorts underwent complete ophthalmologic examination, including best-corrected visual acuity (BCVA) measurement, biomicroscopy, fluorescein angiography (FA) and indocyanine green angiography (ICGA) examination, optical coherence tomography, and OCTA scans. The 1-way a test with Bonferroni correction was used to assess statistical significance and Tau Kendall's correlation analysis was performed.

MAIN OUTCOME MEASURES

BCVA, choroidal thickness, vessel density, vessel tortuosity, vessel dispersion. and vessel rarefaction.

RESULTS

Mean BCVA was 20/32 for CNV eyes and 20/20 for both fellow and control eyes. Choroidal thickness was 190.33 ± 63.98 μm for CNV eyes, 216.83 ± 50.31 μm for fellow eyes, and 310.52 ± 27.13 μm for controls. The quantitative analysis of retinal vessels revealed significant alterations, especially in the deep capillary plexus and radial peripapillary capillaries, both in CNV and in fellow eyes, compared with controls. In particular, decreased vessel density and tortuosity and increased dispersion and rarefaction were found. Several significant correlations were also found among the quantitative parameters adopted.

CONCLUSIONS

New postprocessing OCTA parameters are able to detect deep retinal vascular alterations quantitatively, in both CNV-affected and fellow eyes of patients with new-onset CNV. Further investigations are warranted in order to explore the validity of these new approaches on follow-up.

Quantitative optical coherence tomography angiography biomarkers for neovascular age-related macular degeneration in remission

Purpose

To characterize quantitative optical coherence tomography angiography (OCT-A) parameters in active neovascular age-related macular degeneration (nAMD) patients under treatment and remission nAMD patients.

Design

Retrospective, cross-sectional study.

Participants

One hundred and four patients of whom 72 were in Group 1 (active nAMD) and 32 in Group 2 (remission nAMD) based on SD-OCT (Spectral Domain OCT) qualitative morphology.

Methods

This study was conducted at the Centre Ophtalmologique de l’Odeon between June 2016 and December 2017. Eyes were analyzed using SD-OCT and high-speed (100 000 A-scans/second) 1050-nm wavelength swept-source OCT-A. Speckle noise removal and choroidal neovascularization (CNV) blood flow delineation were automatically performed. Quantitative parameters analyzed included blood flow area (Area), vessel density, fractal dimension (FD) and lacunarity. OCT-A image algorithms and graphical user interfaces were built as a unified tool in Matlab coding language. Generalized Additive Models were used to study the association between OCT-A parameters and nAMD remission on structural OCT. The models’ performance was assessed by the Akaike Information Criterion (AIC), Brier Score and by the area under the receiver operating characteristic curve (AUC). A p value of ≤ 0.05 was considered as statistically significant.

Results

Area, vessel density and FD were different (p<0.001) in the two groups. Regarding the association with CNV activity, Area alone had the highest AUC (AUC = 0.85; 95%CI: 0.77–0.93) followed by FD (AUC = 0.80; 95%CI: 0.71–0.88). Again, Area obtained the best values followed by FD in the AIC and Brier Score evaluations. The multivariate model that included both these variables attained the best performance considering all assessment criteria.

Conclusions

Blood flow characteristics on OCT-A may be associated with exudative signs on structural OCT. In the future, analyses of OCT-A quantitative parameters could potentially help evaluate CNV activity status and to develop personalized treatment and follow-up cycles.

Optical Coherence Tomography Angiography in Intermediate Uveitis

PURPOSE

To investigate the involvement of the retinal and choriocapillaris microvasculature in intermediate uveitis on optical coherence tomography angiography (OCT-A).

DESIGN

Case-control study.

METHODS

Patients and age-matched controls were imaged with swept-source OCT-A. Using ImageJ, superficial and deep retinal vasculature were semi-automatically analyzed for vessel (VD) and skeleton density (SD), vessel diameter index (VDI), and fractal dimension (FD). Choriocapillaris layer was automatically graded for mean signal intensity, signal intensity standard deviation, kurtosis of signal intensity distribution, and flow signal voids.

RESULTS

Twenty-nine intermediate uveitis eyes and 30 control eyes were included. Both superficial and deep retinal layers showed significant reduction in all OCT-A parameters (eg, superficial retinal layer: 0.31 vs 0.40 VD, 5.6e^-8 vs 6.4e^-8 SD, 5.4e⁶ vs 6.1e⁶ VDI, and 1.78 vs 1.79 FD, respectively, all P < .05). At the choriocapillaris layer a greater heterogeneity of perfusion with a shift toward a higher proportion of large confluent flow signal voids was present. Also in the absence of macular edema OCT-A parameters were reduced when compared with healthy controls (all parameters except for VDI in the superficial retinal layer and the choriocapillaris kurtosis and flow signal void analyses).

CONCLUSIONS

In intermediate uveitis, reduced vascular density and complexity in superficial as well as deep retinal layers and altered choriocapillaris perfusion are present. Moreover, these findings indicate impairment of the macular microvasculature even in the absence of macular edema. The results of our study may aid in the diagnosis as well as the monitoring of intermediate uveitis.

Microfluidics-Enabled Multimaterial Maskless Stereolithographic Bioprinting

A stereolithography-based bioprinting platform for multimaterial fabrication of heterogeneous hydrogel constructs is presented. Dynamic patterning by a digital micromirror device, synchronized by a moving stage and a microfluidic device containing four on/off pneumatic valves, is used to create 3D constructs. The novel microfluidic device is capable of fast switching between different (cell-loaded) hydrogel bioinks, to achieve layer-by-layer multimaterial bioprinting. Compared to conventional stereolithography-based bioprinters, the system provides the unique advantage of multimaterial fabrication capability at high spatial resolution. To demonstrate the multimaterial capacity of this system, a variety of hydrogel constructs are generated, including those based on poly(ethylene glycol) diacrylate (PEGDA) and gelatin methacryloyl (GelMA). The biocompatibility of this system is validated by introducing cell-laden GelMA into the microfluidic device and fabricating cellularized constructs. A pattern of a PEGDA frame and three different concentrations of GelMA, loaded with vascular endothelial growth factor, are further assessed for its neovascularization potential in a rat model. The proposed system provides a robust platform for bioprinting of high-fidelity multimaterial microstructures on demand for applications in tissue engineering, regenerative medicine, and biosensing, which are otherwise not readily achievable at high speed with conventional stereolithographic biofabrication platforms.

Angiogenic Factors produced by Hypoxic Cells are a leading driver of Anastomoses in Sprouting Angiogenesis-a computational study

Angiogenesis - the growth of new blood vessels from a pre-existing vasculature - is key in both physiological processes and on several pathological scenarios such as cancer progression or diabetic retinopathy. For the new vascular networks to be functional, it is required that the growing sprouts merge either with an existing functional mature vessel or with another growing sprout. This process is called anastomosis. We present a systematic 2D and 3D computational study of vessel growth in a tissue to address the capability of angiogenic factor gradients to drive anastomosis formation. We consider that these growth factors are produced only by tissue cells in hypoxia, i.e. until nearby vessels merge and become capable of carrying blood and irrigating their vicinity. We demonstrate that this increased production of angiogenic factors by hypoxic cells is able to promote vessel anastomoses events in both 2D and 3D. The simulations also verify that the morphology of these networks has an increased resilience toward variations in the endothelial cell's proliferation and chemotactic response. The distribution of tissue cells and the concentration of the growth factors they produce are the major factors in determining the final morphology of the network.

Investigation of microvascular morphological measures for skeletal muscle tissue oxygenation by image-based modelling in three dimensions

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, especially for skeletal muscle during exercise. Traditionally, microvascular oxygen supply capability is assessed by the analysis of morphological measures on transverse cross-sections of muscle, e.g. capillary density or capillary-to-fibre ratio. In this work, we investigate the relationship between microvascular structure and muscle tissue oxygenation in mice. Phase contrast imaging was performed using synchrotron radiation computed tomography (SR CT) to visualize red blood cells (RBCs) within the microvasculature in mouse soleus muscle. Image-based mathematical modelling of the oxygen diffusion from the RBCs into the muscle tissue was subsequently performed, as well as a morphometric analysis of the microvasculature. The mean tissue oxygenation was then compared with the morphological measures of the microvasculature. RBC volume fraction and spacing (mean distance of any point in tissue to the closest RBC) emerged as the best predictors for muscle tissue oxygenation, followed by length density (summed RBC length over muscle volume). The two-dimensional measures of capillary density and capillary-to-fibre ratio ranked last. We, therefore, conclude that, in order to assess the states of health of muscle tissue, it is advisable to rely on three-dimensional morphological measures rather than on the traditional two-dimensional measures.

Modelling of retinal vasculature based on genetically tuned parametric L-system

Structures of retinal blood vessels are of great importance in diagnosis and treatment of diseases that affect the eyes. Parametric Lindenmayer system (L-system) is one of the powerful rule-based methods that has a great capability for generating tree-like structures using simple rewriting rules. In this study, a novel framework, which can be used to model the retinal vasculature based on available images, has been proposed. This framework presents a solution to special instance of a general open problem, the L-system inverse problem, in which L-system rules should be obtained based on images representing a particular tree-like structure. In this study, genetic algorithm with a novel objective function based on feature matching and an L-system grammar comparison has been used along with nonlinear regression to solve the parametric L-system inverse problem. The resulting L-system growth rules have been employed to predict inaccessible vascular branches. Graphical and quantitative comparison between model results and target structures of different case studies reveals that the proposed framework can be used to generate the structure of retinal blood vessels accurately. Even in the cases lacking sufficient image data, it can provide acceptable predictions.

Morphological and functional properties of the conducting human airways investigated by in vivo computed tomography and in vitro MRI

The accurate representation of the human airway anatomy is crucial for understanding and modeling the structure-function relationship in both healthy and diseased lungs. The present knowledge in this area is based on morphometric studies of excised lung casts, partially complemented by in vivo studies in which computed tomography (CT) was used on a small number of subjects. In the present study, we analyzed CT scans of a cohort of healthy subjects and obtained comprehensive morphometric information down to the seventh generation of bronchial branching, including airway diameter, length, branching angle, and rotation angle. Although some of the geometric parameters (such as the child-to-parent branch diameter ratio) are found to be in line with accepted values, for others (such as the branch length-to-diameter ratio) our findings challenge the common assumptions. We also evaluated several metrics of self-similarity, including the fractal dimension of the airway tree. Additionally, we used phase-contrast magnetic resonance imaging (MRI) to obtain the volumetric flow field in the three-dimensional-printed airway model of one of the subjects during steady inhalation. This is used to relate structural and functional parameters and, in particular, to close the power-law relationship between branch flow rate and diameter. The diameter exponent is found to be significantly lower than in the usually assumed Poiseuille regime, which we attribute to the strong secondary (i.e., transverse) velocity component. The strength of the secondary velocity with respect to the axial component exceeds the levels found in idealized airway models and persists within the first seven generations. NEW & NOTEWORTHY We performed a comprehensive computed tomography-based study of the conductive airway morphology in normal human subjects, including branch diameter, length, and mutual angles. We found significant departure from classic homothetic relationships. We also carried out MRI measurements of the three-dimensional inspiratory flow in an anatomy-based model and directly assessed structure-function relationships that have so far been assumed. We found that strong secondary flows (i.e., transverse velocity components) persist through the first seven generations of bronchial branching.

Reproducibility of Vessel Density, Fractal Dimension, and Foveal Avascular Zone Using 7 Different Optical Coherence Tomography Angiography Devices

PURPOSE

To evaluate the reproducibility of parafoveal microvascular anatomy of 7 different optical coherence tomography angiography (OCT-A) devices by comparing vessel density (VD), fractal dimension (FD), and foveal avascular zone (FAZ) of superficial and deep capillary plexus in healthy volunteers.

DESIGN

Reliability analysis.

METHODS

Consecutive healthy volunteers presenting at the Eye Clinic, Department of Biomedical and Clinical Sciences, Luigi Sacco Hospital, University of Milan in the same clinic visit were imaged by 7 different OCT-A devices: Optovue RTVue XR Avanti (Optovue, Inc, Fremont, California, USA), prototype Spectralis OCT-A (Spectralis; Heidelberg Engineering, Heidelberg, Germany), AngioPlex (Cirrus 5000 HD-OCT; Carl Zeiss Meditec, Inc, Dublin, California, USA), prototype PlexElite (Carl Zeiss Meditec), RS-3000 Advance (Nidek, Gamagori, Japan), OCT-HS100 (Canon, Tokyo, Japan), and Revo NX (Optopol Technology SA, Zawiercie, Poland). OCT-A examinations were performed using a 3 × 3 mm volume scan pattern centered on the fovea. Mean VD, FD, and FAZ values between the instruments were compared.

RESULTS

The 7 different devices presented measurements with different mean values, with only a limited number of comparisons not significantly different between the instruments. Moreover, Bland-Altman analysis revealed that the limits of agreement for all the comparisons were not acceptable. Regression analysis was used in the development of tables to compare various devices, despite which large standard errors were found for both intercepts and slope conversion values.

CONCLUSIONS

Our results suggest that the comparison between instruments is nearly impossible and the set of measurements from the various instruments are not interchangeable regarding VD, FD, and FAZ for both the superficial and deep capillary plexus.

Comparison of retinal vascular geometry in obese and non-obese children

Purpose

Childhood obesity is associated with adult cardiometabolic disease. We postulate that the underlying microvascular dysfunction begins in childhood. We thus aimed to compare retinal vascular parameters between obese and non-obese children.

Methods

This was a cross-sectional study involving 166 children aged 6 to 12 years old in Malaysia. Ocular examination, biometry, retinal photography, blood pressure and body mass index measurement were performed. Participants were divided into two groups; obese and non-obese. Retinal vascular parameters were measured using validated software.

Results

Mean age was 9.58 years. Approximately 51.2% were obese. Obese children had significantly narrower retinal arteriolar caliber (F_(1,159) = 6.862, p = 0.010), lower arteriovenous ratio (F_(1,159) = 17.412, p < 0.001), higher venular fractal dimension (F_(1,159) = 4.313, p = 0.039) and higher venular curvature tortuosity (F_(1,158) = 5.166, p = 0.024) than non-obese children, after adjustment for age, gender, blood pressure and axial length.

Conclusions

Obese children have abnormal retinal vascular geometry. These findings suggest that childhood obesity is characterized by early microvascular abnormalities that precede development of overt disease. Further research is warranted to determine if these parameters represent viable biomarkers for risk stratification in obesity.

Retinal vascular imaging technology to monitor disease severity and complications in type 1 diabetes mellitus: A systematic review

OBJECTIVE

Type 1 diabetes mellitus (T1DM) is a major disease affecting a large number of young patients. In the recent years, retinal vascular imaging has provided an objective assessment of vascular health in patients with T1DM. Our study aimed to review the current literature on retinal vascular parameters in young patients with T1DM in order to understand the following: (i) How retinal vessels are affected in T1DM (ii) How such vascular changes can be predictive of future diabetic microvascular complications METHODS: We performed a systematic review and extracted relevant data from 17 articles.

RESULTS

We found significant correlations between retinal vessel changes and diabetes-related risk factors (eg, hypertension, hyperlipidemia, and obesity), diabetes-related features (eg, diabetes duration and glycemic control), and diabetes-related microvascular complications (eg, diabetic retinopathy, nephropathy, and neuropathy).

CONCLUSION

Our findings suggest that retinal microvasculature is associated with both disease severity and complications in young patients with T1DM.

Proliferative diabetic retinopathy characterization based on fractal features: Evaluation on a publicly available dataset

PURPOSE

Diabetic retinopathy (DR) is one of the most widespread causes of preventable blindness in the world. The most dangerous stage of this condition is proliferative DR (PDR), in which the risk of vision loss is high and treatments are less effective. Fractal features of the retinal vasculature have been previously explored as potential biomarkers of DR, yet the current literature is inconclusive with respect to their correlation with PDR. In this study, we experimentally assess their discrimination ability to recognize PDR cases.

METHODS

A statistical analysis of the viability of using three reference fractal characterization schemes - namely box, information, and correlation dimensions - to identify patients with PDR is presented. These descriptors are also evaluated as input features for training ℓ1 and ℓ2 regularized logistic regression classifiers, to estimate their performance.

RESULTS

Our results on MESSIDOR, a public dataset of 1200 fundus photographs, indicate that patients with PDR are more likely to exhibit a higher fractal dimension than healthy subjects or patients with mild levels of DR (P≤1.3×10-2). Moreover, a supervised classifier trained with both fractal measurements and red lesion-based features reports an area under the ROC curve of 0.93 for PDR screening and 0.96 for detecting patients with optic disc neovascularizations.

CONCLUSIONS

The fractal dimension of the vasculature increases with the level of DR. Furthermore, PDR screening using multiscale fractal measurements is more feasible than using their derived fractal dimensions. Code and further resources are provided at https://github.com/ignaciorlando/fundus-fractal-analysis.

Applying fractal analysis to pupil dilation for measuring complexity in a process monitoring task

This laboratory experiment was designed to use fractal dimension as a new method to analyze pupil dilation to evaluate the level of complexity in a multitasking environment. By using the eye-head integrated tracking system, we collected both pupil responses and head positions while participants conducted both process monitoring task and Multi-Attribute Task Battery (MATB-II) tasks. There was a significant effect of scenario complexity on a composite index of multitasking performance (Low Complexity » High Complexity). The fractal dimension of pupil dilation was also significantly influenced by complexity. The results clearly showed that the correlation between pupil dilation and multitasking performance was stronger when the pupil data was analyzed by using the fractal dimension method. The participants showed a higher fractal dimension when they performed a low complexity multitasking scenario. The findings of this research help us to advance our understanding of how to evaluate the complexity level of real-world applications by using pupillary responses.

Geometrical Complexity of Cortical Microvascularization in Moyamoya Disease

BACKGROUND

Dilatation of the microvascular diameter is recognized in moyamoya disease and referred to as microvascularization. The purpose of this study was to characterize the cortical microvascularization in moyamoya disease using imaging analysis, and to explore the developmental mechanism of the collateral network around the cortical surface.

METHODS

A total of 20 hemispheric sides of 14 patients with moyamoya disease were included in this study. From the intraoperative images, cortical surface images were extracted, and binary images were subsequently created. Then the ratio of the microvessels of the brain surface (vascular fraction; VF) and the box-counting fractal dimension (Db) values were calculated. The VF and Db values in the moyamoya disease group were then compared with those in atherosclerotic disease and nonischemic disease groups, and assessed in terms of clinical and radiologic factors.

RESULTS

VF was significantly higher in the moyamoya disease group compared with the atherosclerotic disease group, and Db was significantly higher in the moyamoya disease group compared with the atherosclerotic disease and nonischemic disease groups. In the moyamoya disease group, VF showed a moderate correlation with magnetic resonance angiography (MRA) score. Moreover, Db was significantly higher in the pediatric patients, in the presence of ischemic symptoms, and in the presence of ivy sign, and Db showed a moderate correlation with MRA score and cerebral blood flow in moyamoya disease.

CONCLUSIONS

In the patients with moyamoya disease, the cortical microvascularization exhibited increased Db and dilatation of the pial arteries. In moyamoya disease, cortical microvascularization is associated with clinical and radiologic factors. This microvascularization might be a compensatory mechanism in the ischemic condition in moyamoya disease.

Fractal characteristics of the microvascular network: A useful index to assess vascularization level of porous silk fibroin biomaterial

The neovascularization of biomaterials for tissue engineering is not only related to growth of capillaries but also involves appropriate hierarchy distribution of the microvessels. In this study, we proposed hierarchy distribution contrast method which can assess vascular transport capacity, in order to examine the hierarchy distribution of the neovessels during vascularization of the porous silk fibroin biomaterials implanted into rats and its evolution. The results showed that the fractal characteristics appeared toward the end of the vascularization stages, and the structure of the microvascular network after 3 weeks of implantation was similar to the fractal microvascular tree with bifurcation exponent x = 3 and fractal dimension D = 1.46, which became a sign of maturation of the regenerative vasculature. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 105A: 2276-2290, 2017.

Noninvasive Retinal Markers in Diabetic Retinopathy: Advancing from Bench towards Bedside

The retinal vascular system is the only part of the human body available for direct, in vivo inspection. Noninvasive retinal markers are important to identity patients in risk of sight-threatening diabetic retinopathy. Studies have correlated structural features like retinal vascular caliber and fractals with micro- and macrovascular dysfunction in diabetes. Likewise, the retinal metabolism can be evaluated by retinal oximetry, and higher retinal venular oxygen saturation has been demonstrated in patients with diabetic retinopathy. So far, most studies have been cross-sectional, but these can only disclose associations and are not able to separate cause from effect or to establish the predictive value of retinal vascular dysfunction with respect to long-term complications. Likewise, retinal markers have not been investigated as markers of treatment outcome in patients with proliferative diabetic retinopathy and diabetic macular edema. The Department of Ophthalmology at Odense University Hospital, Denmark, has a strong tradition of studying the retinal microvasculature in diabetic retinopathy. In the present paper, we demonstrate the importance of the retinal vasculature not only as predictors of long-term microvasculopathy but also as markers of treatment outcome in sight-threatening diabetic retinopathy in well-established population-based cohorts of patients with diabetes.

Impact of Multiple En Face Image Averaging on Quantitative Assessment from Optical Coherence Tomography Angiography Images

PURPOSE

To investigate the impact of multiple en face image averaging on quantitative measurements of the retinal microvasculature using optical coherence tomography angiography (OCTA).

DESIGN

Prospective, observational, cross-sectional case series.

PARTICIPANTS

Twenty-one healthy individuals with normal eyes.

METHODS

Macular OCTA images were acquired from all participants using the Zeiss Cirrus 5000 with Angioplex OCTA software (Carl Zeiss Meditec, Dublin, CA). Nine OCTA cube scans per eye were obtained and 9 superficial retinal layer (SRL) and deep retinal layer (DRL) en face OCTA image slabs were averaged individually after registration. Quantitative parameters from the retinal microvasculature were measured on binarized and skeletonized OCTA images and compared with single OCTA images without averaging.

MAIN OUTCOME MEASURES

Vessel density (VD), vessel length density (VLD), vessel diameter index (VDI), and fractal dimension (FD).

RESULTS

Participants with artifact or poor image quality were excluded, leaving 18 eyes for the analysis. After averaging, qualitatively there was apparent reduction in background noise, and fragmented vessels in the images before averaging became continuous with smoother walls and showed sharper contrast in both the SRL and DRL. Binarized and skeletonized derivates of these averaged images also showed fewer line fragments and dots in nonvascular areas and more continuous vessel images than those of images without averaging. In both SRL and DRL, VD (P = 0.0010 and P = 0.0003, respectively), VLD (P < 0.0001 for both), and FD (P < 0.0001 for both) significantly decreased and VDI significantly increased after averaging (P < 0.0001 for both).

CONCLUSIONS

Averaging of multiple en face OCTA images improves image quality and also significantly impacts quantitative measurements. Reducing noise that could be misinterpreted as flow and annealing discontinuous vessel segments seem to be major mechanisms by which averaging may be of benefit.

Effect of Axial Eye Length on Retinal Vessel Parameters in 6 to 12-Year-Old Malay Girls

PURPOSE

Retinal vessel analysis is affected by both systemic and ocular factors. Malays are the major ethnicity in South East Asia. Data on the retinal microvasculature in Malays is limited, especially among children. We aim to evaluate the influence of ocular biometry on retinal vessel parameters in young Malay girls.

METHODS

This was a cross-sectional, hospital-based study involving 86 Malay girls aged 6 to 12 years old in Hospital Universiti Sains Malaysia from 2015-2016. Ocular examination, refraction, biometry, retinal photography, and anthropometric measurements were performed. The central retinal arteriolar equivalent (CRAE), central retinal venular equivalent (CRVE) and overall fractal dimension (Df) were measured using validated computer-based methods (Singapore I vessel analyzer, SIVA version 3.0, Singapore). The associations of ocular biometry and CRAE, CRVE and Df were analyzed using multivariable analysis.

RESULTS

The mean CRAE, CRVE and Df in Malay girls were 171.40 (14.40) um, 248.02 (16.95) um and 1.42 (0.05) respectively. Each 1 mm increase in axial length was associated with a reduction of 4.25 um in the CRAE (p = 0.03) and a reduction of 0.02 in the Df (p = 0.02), after adjustment for age, blood pressure and body mass index. No association was observed between axial length and CRVE. Anterior chamber depth and corneal curvature had no association with CRAE, CRVE or Df.

CONCLUSION

Axial length affects retinal vessel measurements. Narrower retinal arterioles and reduced retinal fractal dimension were observed in Malay girls with longer axial lengths.

Retinal microvascular network alterations: potential biomarkers of cerebrovascular and neural diseases

Increasing evidence suggests that the conditions of retinal microvessels are indicators to a variety of cerebrovascular, neurodegenerative, psychiatric, and developmental diseases. Thus noninvasive visualization of the human retinal microcirculation offers an exceptional opportunity for the investigation of not only the retinal but also cerebral microvasculature. In this review, we show how the conditions of the retinal microvessels could be used to assess the conditions of brain microvessels because the microvascular network of the retina and brain share, in many aspects, standard features in development, morphology, function, and pathophysiology. Recent techniques and imaging modalities, such as optical coherence tomography (OCT), allow more precise visualization of various layers of the retina and its microcirculation, providing a "microscope" to brain microvessels. We also review the potential role of retinal microvessels in the risk identification of cerebrovascular and neurodegenerative diseases. The association between vision problems and cerebrovascular and neurodegenerative diseases, as well as the possible role of retinal microvascular imaging biomarkers in cerebrovascular and neurodegenerative screening, their potentials, and limitations, are also discussed.

Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

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

PURPOSE

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.

Growth, ageing and scaling laws of coronary arterial trees

Despite the well-known design principles of vascular systems, it is unclear whether the vascular arterial tree obeys some scaling constraints during normal growth and ageing in a given species. Based on the micro-computed tomography measurements of coronary arterial trees in mice at different ages (one week to more than eight months), we show a constant exponent of 3/4, but age-dependent scaling coefficients in a length-volume scaling law (Lc=K(length-volume) · Vc³/⁴; Lc is the crown length, Vc is the crown volume, K(length-volume) is the age-dependent scaling coefficient) during normal growth and ageing. The constant 3/4 exponent represents the self-similar fractal-like branching pattern (i.e. basic mechanism to regulate the development of vascular trees within a species), whereas the age-dependent scaling coefficients characterize the structural growth or resorption of vascular trees during normal growth or ageing, respectively. This study enhances the understanding of age-associated changes in vascular structure and function.