Fractal Analysis of the Vascular Tree in the Human Retina

Self-similarity logic: a common pattern in the vascular and nervous systems

Vascular and neuronal networks are examples of body structures created by processes of branching morphogenesis, showing a similar architecture. Like vascular network morphogenesis, where morphology adapts to the amount of flow, neuronal branching dynamics also can be modulated by neural activity. Axon branching, indeed, often occurs as a dynamic process that involves branch addition and branch retraction. Self-similarity logic characterizes both the nervous and the vascular system. From a morphologic point of view, the self-similarity of the vascular system is straightforward, being the result of a hierarchical sequence of bifurcations, leading to a structure which can be considered strictly self-similar.

Association between retinal vascular fractal dimensions and retinopathy of prematurity: an AI-assisted retrospective case-control study

PURPOSE

The main objective of this study was to analyze the fractal dimensions (D(f)) of retinal vasculature in premature infants with retinopathy of prematurity (ROP) and determine their correlation with ROP severity.

METHODS

We conducted a single-center retrospective case-control study involving 641 premature patients with ROP (641 eyes) and 684 normal preterm infants (684 eyes) matched for corrected gestational age (CGA). Computer-assisted techniques were used to quantify peripapillary retinal vascular D(f), vessel tortuosity (VT), and vessel width (VW).

RESULTS

Compared to the normal preterm groups, patients with ROP exhibited a significant increase in retinal vascular D(f) by 0.0061 (P = 0.0002). Subgroup analyses revealed a significant association between increasing ROP severity and increased retinal vascular D(f) (P < 0.05). Multivariable-adjusted ordered logistic regression models demonstrated that retinal vascular D(f) (aOR: 3.307, P < 0.0001) was significantly independent and associated with ROP severity. For every 0.1 increase in D(f), the probability of ROP requiring intervention increased by 33.07%. Multiple linear regression models indicated a significant positive correlation between D(f) and VT, as well as VW around the optic disc (P < 0.0001). For every 1 (104 cm-3) increase in VT, D(f) increased by 0.0010. Similarly, for every 1 (μm) increase in VW, D(f) increased by 0.0025.

CONCLUSIONS

Our findings suggest that increased D(f) in retinal vessels is a pathological characteristic of ROP. This increase may be attributed to the curvature and width of the retinal vasculature in infants with ROP. Quantitative measurement of retinal vascular D(f) could serve as a valuable vascular indicator for assessing the severity of ROP.

Fractal Changes of the Retinal Microvasculature in Birdshot Chorioretinopathy

BACKGROUND AND OBJECTIVE

Retinal vascular disorders are associated with lower fractal dimension (FD). We analyzed FD in birdshot chorioretinopathy (BSCR).

PATIENTS AND METHODS

This was a retrospective cohort study. We performed optical coherence tomography angiography (OCTA) and analyzed FD of the superficial capillary plexus (SCP), deep capillary plexus (DCP), and choriocapillaris (CC) using ImageJ. For each vascular layer, we analyzed the presence of BSCR, subjects' age, sex, and presence of diabetes mellitus to determine which may predict lower FD.

RESULTS

We compared 28 eyes (14 patients) with BSCR to 34 control eyes (17 patients). Mean FD of BSCR was lower in SCP (1.584 [± 0.126] vs 1.706 [± 0.118], P < 0.001), DCP (1.637 [± 0.134] vs 1.780 [± 0.096], P < 0.001), and CC (1.884 [± 0.063] vs 1.917 [± 0.047], P = 0.036). FD of SCP was lower per increasing year (0.005 [P = 0.014]). Male patients had lower FD-DCP (0.101 [P = 0.043]).

CONCLUSION

In BSCR, fractal analysis showed significant involvement of the SCP, DCP, and to a lesser extent the CC. [Ophthalmic Surg Lasers Imaging Retina 2024;55:646-651.].

Fractal Changes of the Retinal Microvasculature in Syphilitic Uveitis

PURPOSE

To quantify chorioretinal microvascular damage and recovery post-treatment in patients with acute syphilitic posterior placoid chorioretinitis (ASPPC) using fractal dimension (FD).

METHODS

Retrospective cohort study of patients with serologically confirmed syphilitic uveitis. We obtained optical coherence tomography angiography (OCTA) scans at baseline and follow-up after intravenous penicillin treatment and computed FD of the superficial capillary plexus (SCP), deep capillary plexus (DCP), and choriocapillaris (CC) using ImageJ.

RESULTS

We enrolled seven patients with ASPPC (11 eyes), and 17 control subjects (34 eyes). Pre-treatment averages of FD-SCP, FD-DCP, and FD-CC were: 1.672 (±0.115), 1.638 (±0.097), and 1.72 (±0.137); post-treatment: 1.760 (±0.071), 1.764 (±0.043), and 1.898 (±0.047). After treatment FD-CC increased in all 11 eyes with an average of 0.163 (p = 0.003); FD-DCP increased in 10 (91%) eyes with an average of 0.126 (p = 0.003); and FD-SCP increased in seven (64%) eyes with an average of 0.089 (p = 0.059). Compared to the post-treatment FD values in the syphilitic group, controls had similar FD-SCP (p = 0.266), FD-DCP (p = 0.078), and FD-CC (p = 0.449).

CONCLUSIONS

CC and DCP are mostly affected in ASPPC with minimal changes in the SCP. All vascular layers FD recovered after completing antibiotic treatment.

Segmentation and multiparametric evaluation of corneal whorl-like nerves for in vivo confocal microscopy images in dry eye disease

OBJECTIVE

To establish an automated corneal nerve analysis system for corneal in vivo confocal microscopy (IVCM) images from both the whorl-like corneal nerves in the inferior whorl (IW) region and the straight ones in the central cornea and to characterise the geometric features of cornea nerves in dry eye disease (DED).

METHODS AND ANALYSIS

An encoder-decoder-based semi-supervised method was proposed for corneal nerve segmentation. This model's performance was compared with the ground truth provided by experienced clinicians, using Dice similarity coefficient (DSC), mean intersection over union (mIoU), accuracy (Acc), sensitivity (Sen) and specificity (Spe). The corneal nerve total length (CNFL), tortuosity (CNTor), fractal dimension (CNDf) and number of branching points (CNBP) were used for further analysis in an independent DED dataset including 50 patients with DED and 30 healthy controls.

RESULTS

The model achieved 95.72% Acc, 97.88% Spe, 80.61% Sen, 75.26% DSC, 77.57% mIoU and an area under the curve value of 0.98. For clinical evaluation, the CNFL, CNBP and CNDf for whorl-like and straight nerves showed a significant decrease in DED patients compared with healthy controls (p<0.05). Additionally, significantly elevated CNTor was detected in the IW in DED patients (p<0.05). The CNTor for straight corneal nerves, however, showed no significant alteration in DED patients (p>0.05).

CONCLUSION

The proposed method segments both whorl-like and straight corneal nerves in IVCM images with high accuracy and offered parameters to objectively quantify DED-induced corneal nerve injury. The IW is an effective region to detect alterations of multiple geometric indices in DED patients.

Stress sensitivity analysis of vuggy porous media based on two-scale fractal theory

Interparticle pore space and vugs are two different scales of pore space in vuggy porous media. Vuggy porous media widely exists in carbonate reservoirs, and the permeability of this porous media plays an important role in many engineering fields. It has been shown that the change of effective stress has important effects on the permeability of vuggy porous media. In this work, a fractal permeability model for vuggy porous media is developed based on the fractal theory and elastic mechanics. Besides, a Monte Carlo simulation is also implemented to obtain feasible values of permeability. The proposed model can predict the elastic deformation of the fractal vuggy porous media under loading stress, which plays a crucial role in the variations of permeability. The predicted permeability data based on the present fractal model are compared with experimental data, which verifies the validity of the present fractal permeability model for vuggy porous media. The parameter sensitivity analysis indicates that the permeability of stress-sensitivity vuggy porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, Young's modulus, and Poisson's ratio.

Role of optical coherence tomography angiography in the evaluation of peripheral ischemia in retinal vein occlusion

In the last decade, optical coherence tomography angiography (OCTA) has become part of the clinical management of retinal vein occlusion (RVO), proving in itself a useful technique for both the prediction of visual acuity (VA) outcomes and the risk of complications. In fact, OCTA has been proven a valid imaging technique in detailed assessment of foveal and parafoveal microvascular status in both acute and chronic RVO. Quantitative OCTA data have shown a significant correlation not only with final VA but also with the extension of peripheral ischemia, which represents a major risk factor for macular edema recurrence and neovascularization onset. Finally, wide-field OCTA represents a promising noninvasive technique for the assessment of peripheral ischemia. The aim of this review is to report the main literature findings about microvascular changes and clinical applications of OCTA in the context of RVO-induced peripheral ischemia.

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.

Retinal vascular structure independently predicts the initial treatment response in neovascular age-related macular degeneration

PURPOSE

Prediction of the early treatment response is important in neovascular age-related macular degeneration (nAMD). Hence, we aimed to test if non-invasive measurements of the retinal vascular structure were able to predict a successful outcome of initial intravitreal treatment.

METHODS

In 58 eyes of 58 patients with treatment-naïve nAMD, advanced markers of retinal vascular structure were measured by Singapore I Vessel Assessment prior to initial intravitreal treatment with three monthly injections of aflibercept with subsequently categorization of patients as full treatment responders (FTR) or non/partial treatment responders (N/PR), with the former defined as loosing fewer than five Early Treatment Diabetic Retinopathy Study letters and having no residual intra- or subretinal fluid or macular haemorrhage.

RESULTS

Of 54 eyes attending follow-up, 44.4% were categorized as FTR. Patients with FTR were older (81.5 vs. 77 years, p = 0.04), and prior to treatment those eyes had a lower retinal arteriolar fractal dimension (Fd) (1.21 vs. 1.24 units, p = 0.02) and venular length-diameter ratio (LDR) (7.3 vs. 15.9 units, p = 0.006), but did not differ with respect to other retinal vascular parameters. In multiple logistic regression models, a lower chance of FTR was independently predicted by a higher retinal venular LDR (odds ratio [OR] 0.91, 95% CI 0.82-0.99, p = 0.03, for each 1 unit increment) and marginally by a higher retinal arteriolar Fd (OR 0.83, 95% CI 0.68-1.00, p = 0.05, for each 0.01 unit increment).

CONCLUSION

Retinal venular LDR independently predicted the initial treatment response in nAMD. If confirmed by long-term, prospective studies, this might help to guide treatment.

The diploic venous system in Homo neanderthalensis and fossil Homo sapiens: A study using high-resolution computed tomography

OBJECTIVES

The diploic venous system has been hypothesized to be related to human brain evolution, though its evolutionary trajectory and physiological functions remain largely unclear. This study examines the characteristics of the diploic venous channels (DCs) in a selection of well-preserved Homo neanderthalensis and Upper Paleolithic Homo sapiens crania, searching for the differences between the two taxa and exploring the associations between brain anatomy and DCs.

MATERIALS AND METHODS

Five H. neanderthalensis and four H. sapiens fossil specimens from Western Europe were analyzed. Based on Micro-CT scanning and 3D reconstruction, the distribution pattern and draining orifices of the DCs were inspected qualitatively. The size of the DCs was quantified by volume calculation, and the degree of complexity was quantified by fractal analyses.

RESULTS

High-resolution data show the details of the DC structures not documented in previous studies. H. neanderthalensis and H. sapiens specimens share substantial similarities in the DCs. The noticeable differences between the two samples manifest in the connecting points surrounding the frontal sinuses, parietal foramina, and asterional area.

DISCUSSION

This study provides a better understanding of the anatomy of the DCs in H. neanderthalensis and H. sapiens. The connection patterns of the DCs have potential utility in distinguishing between the two taxa and in the phylogenetic and taxonomic discussion of the Neandertal-like specimens with controversial taxonomic status.

Fractal analysis of the macular region in healthy eyes using swept-source optical coherence tomography angiography

PURPOSE

This cross-sectional observational study evaluated the relationship between retinal vascular fractal dimension (FD) and age, as well as other vascular parameters in healthy eyes using swept-source optical coherence tomography angiography (SS-OCTA).

METHODS

The study cohort consisted of 222 eyes of 116 healthy participants with no ocular or systemic disease. SS-OCTA images were captured and analyzed using the Plex Elite 9000 and software tools available in the advanced retinal imaging (ARI) network hub. The retinal vascular layers were defined by the instrument's automatic retinal layer segmentation. The fractal analysis was performed on the superficial capillary plexus (SCP), deep capillary plexus (DCP), and the whole retina. Grayscale OCTA images were standardized and binarized using ImageJ and fractal box-counting analyses were performed using Fractalyse software. Pearson's correlation was used to analyze the correlation between FD and retinal vascular parameters.

RESULTS

The results showed that FD values were significantly higher in the 6 mm ring and the whole 6 × 6 scan region when compared to the 1 mm ETDRS central subfield. The correlation between age and FD was weak with a significant positive correlation between age and FD of the SCP in the 6 mm ring and between age and FD of the DCP in the 1 mm ring. Overall, differences in FD values in these healthy eyes were extremely small regardless of age or macular location.

CONCLUSION

FD values in normal eyes show little variation with age and are relatively stable across the macula. This suggests that FD values may not need adjustment for age or location when evaluated in the context of retinal disease.

Retinal vessel geometry in patients with idiopathic epiretinal membrane

We investigated the associations between retinal vascular geometric measurements and idiopathic epiretinal membrane (ERM). Whether changes in retinal vascular geometry are independent of systemic cardiovascular risk factors was also evaluated. This retrospective, cross sectional study included 98 patients with idiopathic ERM, and 99 healthy age-matched controls. Quantitative retinal vascular parameters were measured from digital retinal fundus photographs using a semi-automated computer-assisted program. Multivariate logistic regression analyses were performed to evaluate associations between retinal vascular geometric parameters and the presence of idiopathic ERM after adjusting for systemic cardiovascular risk factors. There was no significant difference in the baseline characteristics of the two groups, except that the ERM group had a higher proportion of females than the control group. In multivariate regression analyses, female sex (odds ratio [OR] 0.402; 95% CI 0.196-0.802; P = 0.011), wider retinal venular caliber (OR 16.852; 95% CI 5.384-58.997; P < 0.001) and decreased total fractal dimension (OR 0.156; 95% CI 0.052-0.440; P = 0.001) were associated with idiopathic ERM. Idiopathic ERM was associated with alterations in global retinal microvascular geometric parameters, wider retinal venules, and less complex vascular branching patterns, independent of cardiovascular risk factors.

Image processing and quantification analysis for optical coherence tomography angiography in epiretinal membrane

BACKGROUND

To explore image processing methods for optical coherence tomography angiography (OCTA) of the epiretinal membrane (ERM), and to evaluate the impact of ERM on vision by analyzing the retinal vasculature.

METHODS

Thirty eyes of 30 patients with idiopathic ERM who underwent OCTA were retrospectively evaluated. Image processing of OCTA, including the Mexican hat filter (MHF) and exclusion of the foveal avascular zone (FAZ), was attempted using Fiji. OCTA parameters, including vessel density (VD), fractal dimension (FD), and vessel tortuosity (VT), were measured for large vessels only, capillaries only, and the whole vasculature. Pearson correlation analysis was used to evaluate the correlations between best-corrected visual acuity (BCVA) and OCTA parameters.

RESULTS

The correlations between BCVA and retinal vasculature were much increased when the capillaries only instead of the whole vasculature was used for analysis. Both higher VD and FD of capillaries were correlated with better BCVA, and MHF largely increased their correlations (P < 0.0001 for both). In contrast, both higher VD and FD of the large vessels were associated with poorer BCVA (P = 0.042 and 0.049, respectively). A higher VT of capillaries was correlated with better BCVA, and both MHF and exclusion of the FAZ were necessary to reveal their correlations (P = 0.028) CONCLUSIONS: Separation of large vessels and capillaries was necessary to reveal the correlation between retinal vasculature and BCVA in ERM. MHF was necessary to elucidate all microvascular parameters of capillaries, and exclusion of the FAZ was mandatory for evaluation of VT.

Numerical prediction of portal hypertension by a hydrodynamic blood flow model combing with the fractal theory

Portal hypertension (PH) can cause a series of complications, therefore, early prediction of PH is important. Traditional diagnostic methods are harmful to the human body, while other non-invasive methods are inaccurate and lack physical meaning. Combining various fractal theories and flow laws, we establish a complete portal system blood flow model from the Computed Tomography (CT) and angiography images. The portal vein pressure (PP) is obtained by the flow rate data from the Doppler ultrasound and the pressure-velocity relationship is established by the model. Three normal participants and 12 patients with portal hypertension were divided into three groups. For the three normal participants (Group A), their mean PP calculated by the model is 1752 Pa, falling into the normal range of PP. The mean PP of three patients with portal vein thrombosis (Group B) is 2357 Pa; and for the 9 patients with cirrhosis (Group C), their mean PP is 2915 Pa. These results validate the classification performance of the model. Moreover, the blood flow model can give early warning parameters of the corresponding portal vein trunk and portal vein microtubules for thrombosis and liver cirrhosis. This model presents the complete process of blood flow from sinusoids to the portal vein, adapts to the diagnosis of portal hypertension of thrombosis and liver cirrhosis, and provides a new method for noninvasive portal vein pressure detection from the perspective of biomechanics.

Retinal vascular fractal dimension measurements in patients with obstructive sleep apnea syndrome: a retrospective case-control study

STUDY OBJECTIVES

We performed a case-control study to investigate the correlation between the apnea-hypopnea index (AHI) and the retinal vascular fractal dimension (FD).

METHODS

We selected 527 individuals who underwent polysomnography during health checkups at the Huadong Sanatorium from January to December 2021 as the study population, of whom 468 were included and 59 were excluded. All participants underwent a detailed health examination, including medical history assessment, physical examination, assessment of lifestyle factors, fundus photography, and laboratory examinations. The retinal vasculature was quantitatively assessed using Singapore I Vessel Assessment (SIVA) software. The relationship between the AHI and the retinal vessel quantitative was examined by multiple linear regression analyses and restricted cubic spline.

RESULTS

Among the 468 studied individuals, the average age was 51.51 (43-58) years, with 369 (78.85%) men and 99 (21.15%) women. According to the AHI indicator, 355 individuals were diagnosed with obstructive sleep apnea (OSA) syndrome, with an average AHI of 17.00 (9.200-30.130) events/h; 113 individuals were classified as controls, with an average AHI of 2.13 (0.88-3.63) events/h. In multiple linear regression, following varying degrees of adjustment for confounding factors, FD was reduced by 0.013 (P = .012; 95% confidence interval [CI]: -0.024 to -0.003), FD arteriole (FDa) was reduced by 0.013 (P = .019; 95% CI: -0.024 to -0.002), and FD venule (FDv) was reduced by 0.014 (P = .08; 95% CI: -0.024 to -0.004) in the high-AHI group compared with the low-AHI group. All tests for trend P values were < .05. The restricted cubic spline in the overall OSA population and the individuals without diabetes revealed a U-shaped pattern of decreasing, then increasing, FD, FDa, and FDv with a rising AHI. In the OSA individual with diabetes, FD, FDa, and FDv gradually decreased with increasing AHI.

CONCLUSIONS

The FD is associated with AHI in OSA individuals. The link between AHI and FD varied for OSA individuals with and without diabetes.

CITATION

Wang J, Chen T, Qi X, Li Y, Yang X, Meng X. Retinal vascular fractal dimension measurements in patients with obstructive sleep apnea syndrome: a retrospective case-control study. J Clin Sleep Med. 2023;19(3):479-490.

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 parameters, cortical cerebral microinfarcts, and their interaction with cognitive impairment

BACKGROUND

Quantitative changes in retinal vessels and thinning of optic nerves have been associated with subclinical (atherosclerosis, inflammation) and clinical age-related brain pathologies (stroke and neurodegeneration). However, data on the association between both retinal vascular and neuronal parameters with cortical cerebral microinfarcts (CMIs) and how these factors jointly influence cognition are lacking.

AIM

We investigated the association of retinal vascular and neuronal changes with CMIs on 3 T MRI and explored their interaction with cognitive impairment in a memory-clinic population.

METHODS

A total of 538 participants were included. Retinal vascular parameters (caliber, tortuosity, and fractal dimension) were measured from retinal fundus photographs using a semi-automated computer-assisted program. Retinal nerve fiber layer (RNFL) and ganglion cell-inner plexiform layer (GC-IPL) thicknesses were obtained from optical coherence tomography. Cortical CMIs were defined as hypointense on T1-weighted MRI, <5 mm in diameter and restricted to the cortex. Cognition was assessed using Clinical Dementia Rating Sum-of-Boxes (CDR-SoB) score and detailed neuropsychological test. Multivariable regression analysis was conducted adjusting for age, sex, hypertension, hyperlipidemia, diabetes mellitus, smoking, diagnosis, white matter hyperintensities volume, lacunes, and cerebral microbleeds.

RESULTS

Larger venular caliber (Rate ratios (RR): 1.15, 95% CI: 1.01-1.38, p = 0.014), increased venular fractal dimension (RR: 1.58, 95% CI: 1.31-1.91, p ⩽ 0.001), increased venular tortuosity (RR: 1.54, 95% CI: 1.35-1.75, p ⩽ 0.001), and thinner GC-IPL (RR: 1.24, 95% CI: 1.13-1.36, p ⩽ 0.001) were associated with CMI counts. Among individuals in highest tertile of retinal parameters, a significant interaction was observed between venular tortuosity (RR: 1.12, 95% CI: 1.02-1.22, p-interaction = 0.014) and GC-IPL (RR: 1.05, 95% CI: 1.01-1.11, p-interaction < 0.001) with CMIs on CDR-SoB.

CONCLUSION

Retinal vascular and neuronal parameters are associated with cortical CMIs, and persons with both pathologies are likely to have cognitive impairment. Further studies may be warranted to evaluate the clinical utility of retinal parameters and CMI in risk prediction for cognitive dysfunction.

Fractal Dimension of Peripapillary Vasculature in Primary Open-Angle Glaucoma

PURPOSE

To compare the fractal dimensions of the peripapillary microvasculature as obtained by optical coherence tomography angiography (OCTA) between primary open-angle glaucoma (POAG) and controls.

METHODS

Optic nerve head and peripapillary area images were taken using the 20° × 20°-scan of Spectralis OCTA (Heidelberg Engineering) in 97 subjects (64 POAG patients, 33 control patients). The optic nerve head microvasculature was evaluated according to predefined slabs: the superficial vascular complex (SVC) and the avascular complex (AVC). The en face image of each slab was processed by ImageJ software (National Institutes of Health) in order to calculate the vessel density and the fractal dimension using the box-counting method. For comparison, the peripapillary retinal nerve fiber layer (RNFL) thickness was obtained from Spectralis OCT circle scans. The utilities of the parameters for discriminating between the POAG and control groups were assessed using areas under the receiver operating characteristic curves (AUCs).

RESULTS

The SVC fractal dimension was lower in the POAG than in the control group (p < 0.001), while AVC showed no intergroup difference (p = 0.563). The fractal dimension showed a good correlation with the vessel density in both SVC and AVC (both p < 0.001). In a multivariable regression analysis, the SVC fractal dimension was negatively correlated with age (p < 0.001) and axial length (p < 0.001) and positively correlated with average RNFL thickness (p < 0.001), while the AVC fractal dimension was positively correlated with the Bruch's membrane opening size (p = 0.013). In terms of diagnostic utility, the AUC was significantly larger for the average RNFL thickness (AUC, 0.889) than for the SVC fractal dimension (AUC, 0.772; p = 0.008).

CONCLUSIONS

The fractal dimension of SVC was associated with the average RNFL thickness and was reduced in POAG patients. Fractal dimension analysis could be used in evaluating peripapillary vascularity by OCTA.

Visualizing the spatiotemporal pattern of yolk sac membrane vascular network by enhanced local fractal analysis

OBJECTIVE

To establish methods for providing a comprehensive and detailed description of the spatial distribution of the vascular networks, and to reveal the spatiotemporal pattern of the yolk sac membrane vascular network during the angiogenic procedure.

METHODS

Addressing the limitations in the conventional local fractal analysis, an improved approach, named scanning average local fractal dimension, was proposed. This method was conducted on 6 high-resolution vascular images of the yolk sac membrane for 3 eggs at two stages (E3 and E4) to characterize the spatial distribution of the complexity of the vascular network.

RESULTS

With the proposed method, the spatial distribution of the complexity of the yolk sac membrane vascular network was visualized. From E3 to E4, the local fractal dimension increased in 3 eggs, 1.80 ± 0.02 vs. 1.85 ± 0.02, 1.72 ± 0.03 vs. 1.83 ± 0.02, and 1.77 ± 0.03 vs. 1.82 ± 0.02, respectively. The mean local fractal dimension in the most distal area from the embryo proper was the lowest at E3 while the highest at E4. At E3, the most peaks of the local fractal dimension were located in the vein territories and shifted to artery territories at E4.

CONCLUSIONS

The spatial distribution of the complexity of the yolk sac membrane vascular network exhibited diverse patterns at different stages. In addition from E3 to E4, the increment of complexity at the intersection areas between arteries and sinus terminalis was with the most advance. This is consistent with the physiologic evidence. The present work provides a potential approach for investigating the spatiotemporal pattern of the angiogenic process.

Repeatability and Reproducibility of Retinal Fractal Dimension Measured with Swept-Source Optical Coherence Tomography Angiography in Healthy Eyes: A Proof-of-Concept Study

The retinal vascular network fractal dimension (FD) could be a promising imaging biomarker. Our objective was to evaluate its repeatability and reproducibility in healthy eyes. A cross-sectional study was undertaken with young, healthy volunteers who had no reported cardiac risk factors or ocular disease history. For each participant, three SS-OCTA images (12 × 12 mm) were acquired using the Plex Elite 9000 (Carl Zeiss Meditec AG, Jena, Germany) by two ophthalmologists. Automated segmentation was obtained from both the superficial and deep capillary plexuses. FD was estimated by box counting. The intraclass correlation coefficients (ICC) were used as measures for repeatability and reproducibility. A total of 43 eyes of healthy volunteers were included. The mean ± standard deviation (SD) age was 30 ± 6.2 years. The results show good repeatability. The ICC was 0.722 (95% CI, 0.541–0.839) in the superficial capillary plexus and 0.828 (95% CI, 0.705–0.903) in the deep capillary plexus. For reproducibility, the ICC was 0.651 (95% CI, 0.439–0.795) and 0.363 (95% CI, 0.073–0.596) at the superficial and deep capillary plexus, respectively. In this study, the FD of the vascular network measured via SS-OCTA showed good repeatability and reproducibility in healthy participants.

Deciphering Stomach Myoelectrical Slow Wave Conduction Patterns via Confocal Imaging of Gastric Pacemaker Cells and Fractal Geometry

Interstitial Cells of Cajal (ICC) are specialized gastrointestinal (GI) pacemaker cells that generate and actively propagate slow waves of depolarization (SWs) of the muscularis propria. SWs regulate the motility of the GI tract necessary for digestion, absorption of nutrients, and elimination of waste. Within the gastric wall, there are three main inter-connected layers of ICC networks: longitudinal muscle ICC (ICC-LM), myenteric plexus ICC (ICC-MP) & circumferential muscle (ICC-CM). Fractal structural parameters such as Fractal Dimension (FD), Lacunarity and Succolarity, have many advantages over physically-based parameters when it comes to characterizing the complex architectures of ICC networks. The analysis of networks of ICC throughout the proximal and distal murine gastric antrum with the FD and Lacunarity metrics was previously performed. Although the application of Succolarity is relatively nascent compared to the FD and Lacunarity; nevertheless, numerous studies have demonstrated the capability of this fractal measure to extract information from images associated with flow by which neither the FD nor Lacunarity are capable of discerning. In this study, Succolarity analysis of ICC-MP and ICC-CM networks were performed with confocal images taken across the proximal and distal murine antrum. Our findings demonstrated the Succolarity of ICC-MP and ICC-CM varied with directions and antral regions. The Succolarity of ICC-MP did not vary considerably with direction, however, Succolarity was higher in the aboral direction with 0.2113 ±0.1589, and 0.0637 ±0.0822 in the proximal and distal antrum, respectively. The overall Succolarity of ICC-MP was significantly higher than that of ICC-CM in the proximal antrum ( 0.1580±0.1325 vs [Formula: see text]) and in the distal antrum ( 0.0449 ±0.0409 vs [Formula: see text]). Clinical Relevance-Modeling SWs conduction patterns via image analysis of detailed ICC networks help to facilitate an improved understanding of the mechanisms underpinning GI myoelectric activity and the diseases associated with its dysfunction.

Association between retinal vascular measures and brain white matter lesions in schizophrenia

OBJECTIVE

Recent studies have examined retinal vascular abnormalities in schizophrenia as retinal vascular imaging is a non-invasive proxy to cerebral microvasculature. However, relation between retinal vascular abnormalities and brain structure is not well examined in schizophrenia. Hence in this study, for the first time, we examined the relationship between retinal vascular measures and brain white matter lesions in schizophrenia. We examined brain white matter lesions as they are considered a predictive marker for future adverse cerebrovascular event.

METHODS

We acquired retinal vascular images of both eyes using a non-mydriatic camera and calculated retinal vascular diameter, tortuosity, trajectory and fractal dimension using validated methods. All patients underwent Magnetic Resonance Imaging of bran and we computed white matter hypo-intensities using Freesurfer software. We performed a linear regression analysis to examine the relationship between white matter hypo-intensities and retinal vascular measures controlling for age, sex, fasting blood sugar, creatinine, whole-brain volume, and antipsychotic dose.

RESULTS

The regression model was significant in Schizophrenia patients (R=0.983;R2 =0.966;-F=10.849;p = 0.008) but not in healthy volunteers (R=0.828;R2 =0.686;F=0.182; p = 0.963). Among the retinal vascular measures, arterial tortuosity (β = 0.963;p-0.002), tortuosity (β = -1.002;p = 0.001) and fractal dimension (β = -0.688;p = 0.014) were significant predictors of white matter lesions.

DISCUSSION

The current study's findings support the conclusion that retinal vascular fractal dimension and tortuosity are associated with changes in cerebral white matter and may be considered proxy markers for cerebral microvasculature in schizophrenia. Considering the relationship between white matter lesions and stroke, these observations could have important clinical implications to screen schizophrenia patients for risk of adverse cerebrovascular event.

Analysis of Regional Variations of the Interstitial Cells of Cajal in the Murine Distal Stomach Informed by Confocal Imaging and Machine Learning Methods

Introduction

The network of Interstitial Cells of Cajal (ICC) plays a plethora of key roles in maintaining, coordinating, and regulating the contractions of the gastrointestinal (GI) smooth muscles. Several GI functional motility disorders have been associated with ICC degradation. This study extended a previously reported 2D morphological analysis and applied it to 3D spatial quantification of three different types of ICC networks in the distal stomach guided by confocal imaging and machine learning methods. The characterization of the complex changes in spatial structure of the ICC network architecture contributes to our understanding of the roles that different types of ICC may play in post-prandial physiology, pathogenesis, and/or amelioration of GI dsymotility- bridging structure and function.

Methods

A validated classification method using Trainable Weka Segmentation was applied to segment the ICC from a confocal dataset of the gastric antrum of a transgenic mouse, followed by structural analysis of the segmented images.

Results

The machine learning model performance was compared to manually segmented subfields, achieving an area under the receiver-operating characteristic (AUROC) of 0.973 and 0.995 for myenteric ICC (ICC-MP; n = 6) and intramuscular ICC (ICC-IM; n = 17). The myenteric layer in the distal antrum increased in thickness (from 14.5 to 34 μm) towards the lesser curvature, whereas the thickness decreased towards the lesser curvature in the proximal antrum (17.7 to 9 μm). There was an increase in ICC-MP volume from proximal to distal antrum (406,960 ± 140,040 vs. 559,990 ± 281,000 μm³; p = 0.000145). The % of ICC volume was similar for ICC-LM and for ICC-CM between proximal (3.6 ± 2.3% vs. 3.1 ± 1.2%; p = 0.185) and distal antrum (3.2 ± 3.9% vs. 2.5 ± 2.8%; p = 0.309). The average % volume of ICC-MP was significantly higher than ICC-IM at all points throughout sample (p < 0.0001).

Conclusions

The segmentation and analysis methods provide a high-throughput framework of investigating the structural changes in extended ICC networks and their associated physiological functions in animal models.

Relationship of fractal analysis in retinal microvascularity with demographic and diagnostic parameters

Problems and diseases with eye are common in diabetic patients. Early diagnosis and detection of various diseases like retinopathy, neuropathy and nephropathy is crucial in diabetic patients. Certain demographic and diagnostic parameters play a significant role in predicting diseases related to diabetes. Development of a novel diagnostic method which helps to predict the disease by establishing a significant correlation with the demographic and diagnostic parameters is of prime importance. This study proposes a new methodology in which retinal fractals are obtained for the images and the derived retinal fractals are analysed to aid in disease prediction. This study comprises of images from patients with retinopathy, non retinopathy, neuropathy, nephropathy and hypertension. The proposed research is carried out in two aspects: 1) to correlate the retinal fractals of retinopathy and non retinopathy images with certain demographic and diagnostic parameters and interpret its significance, and 2) to exhibit a relationship between the retinal fractals and various diseases/addictive habit to facilitate the prediction of the disease/addictive habit. Hausdorff fractal dimension (HFD) was applied and higher fractal dimension was obtained for healthy cases. Then using Statistical Package for the Social Sciences (SPSS) various statistical parameters and significance were calculated to analyse the relationship. Analysis results showed that fractal value helped in distinguishing between the retinopathy and non retinopathy conditions. It also helped in diagnosing the presence and absence of hypertension. Correlation analysis between certain demographic parameters and fractal value showed a positive correlation whereas few exhibited negative correlation.

Choroidal neovascularization activity and structure by optical coherence tomography angiography in age related macular degeneration

Background. In economically developed countries, age-related macular degeneration (AMD) is the leading cause of visual disability among the population of the older age group. The main criterion for the anti-VEGF treatment of neovascular AMD is the activity of choroidal neovascularization (CNV), which is determined by its confi guration. The search for optimal criteria for quantifying the state of the macular region in order to decide on the appointment of anti-VEGF therapy continues.Aim: improving the effi ciency of diagnosis and treatment of AMD based on the assessment of the configuration of vascular system on the “Key to Diagnosis II” platform.Material and methods. The study included 341 patients: 64 % (218 patients, 267 eyes) with non-neovascular AMD, 36 % (123 patients, 174 eyes) – with neovascular AMD. 56 patients (58 eyes) had active type I CNV. Group 1A – active CNV before treatment (9 patients, 9 eyes), group 1B – non-active CNV after treatment with antiVEGF (9 patients, 9 eyes); control group – 10 patients (10 eyes) without AMD. Analysis of OCT-angio images of choriocapillaries included the isolation of CNV, its area, fractal dimension (Df) and the complexity of the vascular system (CVS) counting.Results. Group 1A: Df – 1.5871 ± 0.05, CVS – 2.29 ± 0.29, area – 11734 ± 4866; group 1B: Df – 1.6462 ± 0.08, CVS – 1.65 ± 0.18, area – 6797 ± 3818; control: Df – 1.9167 ± 0.06, CVS – 1, area – 0. Significant differences were found for CVS (p = 0.0003). Df correlates with the CNV area (p = 0.7) and is probably an unreliable parameter due to incomplete visualization of active CNV.Conclusions. CVS is a quantitative biomarker for determining the activity of type 1 CNV in patients with AMD and can serve as a parameter for convolutional neural networks training for automated analysis of OCT angiography images based on the “Key to Diagnosis II” platform

Macular Vascular Geometry Changes With Sex and Age in Healthy Subjects: A Fundus Photography Study

Purpose: To characterize the sex- and age-related alterations of the macular vascular geometry in a population of healthy eyes using fundus photography.

Methods: A cross-sectional study was conducted with 610 eyes from 305 healthy subjects (136 men, 169 women) who underwent fundus photography examination and was divided into four age groups (G1 with age ≤ 25 years, G2 with age 26–35 years, G3 with age 36–45 years, and G4 with age ≥ 46 years). A self-developed automated retinal vasculature analysis system allowed segmentation and separate multiparametric quantification of the macular vascular network according to the Early Treatment Diabetic Retinopathy Study (ETDRS). Vessel fractal dimension (D_f), vessel area rate (VAR), average vessel diameter (D_m), and vessel tortuosity (τ_n) were acquired and compared between sex and age groups.

Results: There was no significant difference between the mean age of male and female subjects (32.706 ± 10.372 and 33.494 ± 10.620, respectively, p > 0.05) and the mean age of both sexes in each age group (p > 0.05). The D_f, VAR, and D_m of the inner ring, the D_f of the outer ring, and the D_f and VAR of the whole macula were significantly greater in men than women (p < 0.001, p < 0.001, p < 0.05, respectively). There was no significant change of τ_n between males and females (p > 0.05). The D_f, VAR, and D_m of the whole macula, the inner and outer rings associated negatively with age (p < 0.001), whereas the τ_n showed no significant association with age (p > 0.05). Comparison between age groups observed that D_f started to decrease from G2 compared with G1 in the inner ring (p < 0.05) and D_f, VAR, and D_m all decreased from G3 compared with the younger groups in the whole macula, inner and outer rings (p < 0.05).

Conclusion: In the healthy subjects, macular vascular geometric parameters obtained from fundus photography showed that D_f, VAR, and D_m are related to sex and age while τ_n is not. The baseline values of the macular vascular geometry were also acquired for both sexes and all age groups.

OCTAVA: An open-source toolbox for quantitative analysis of optical coherence tomography angiography images

Optical coherence tomography angiography (OCTA) performs non-invasive visualization and characterization of microvasculature in research and clinical applications mainly in ophthalmology and dermatology. A wide variety of instruments, imaging protocols, processing methods and metrics have been used to describe the microvasculature, such that comparing different study outcomes is currently not feasible. With the goal of contributing to standardization of OCTA data analysis, we report a user-friendly, open-source toolbox, OCTAVA (OCTA Vascular Analyzer), to automate the pre-processing, segmentation, and quantitative analysis of en face OCTA maximum intensity projection images in a standardized workflow. We present each analysis step, including optimization of filtering and choice of segmentation algorithm, and definition of metrics. We perform quantitative analysis of OCTA images from different commercial and non-commercial instruments and samples and show OCTAVA can accurately and reproducibly determine metrics for characterization of microvasculature. Wide adoption could enable studies and aggregation of data on a scale sufficient to develop reliable microvascular biomarkers for early detection, and to guide treatment, of microvascular disease.

Differentiating features of OCT angiography in diabetic macular edema

The purpose of current study was to evaluate different optical coherence tomography angiography (OCTA) metrics in eyes with diabetic retinopathy with and without diabetic macular edema (DME). In this retrospective study, macular OCTA images of eyes with non-proliferative or proliferative diabetic retinopathy were evaluated. Vascular density, vascular complexity and non-perfusion densities were compared between eyes with and without DME. One-hundred-thirty-eight eyes of 92 diabetic patients including 49 eyes with DME were included. In multivariate analysis, the presence of DME was positively associated with geometric perfusion deficit (GPD) in superficial capillary plexus (SCP), capillary non-perfusion (CNP) of SCP, and GPD in deep capillary plexus (DCP) (all P < 0.05). In eyes with DME, central foveal thickness was associated with VD ratio (SCP/DCP) (P = 0.001) and FAZ area (P = 0.001). In conclusion, in eyes with diabetic retinopathy, the presence of DME was associated with more extensive capillary non-perfusion compared to those with no macular edema.

Comparison of optical coherence tomography angiography metrics in primary angle-closure glaucoma and normal-tension glaucoma

To investigate the peripapillary vascular metrics in early normal tension glaucoma (NTG) and early primary angle closure glaucoma (PACG) eyes using optical coherence tomography angiography (OCT-A). One or both eyes of each subject were imaged for a 3 × 3 mm peripapillary region by swept-source OCT-A (DRI-OCT Triton, Topcon, Japan) and assessed by an automated MATLAB program. OCT-A metrics including circumpapillary vessel density (cpVD) and fractal dimension (cpFD) were compared. Their association with visual field (VF) parameters and retinal nerve fiber layer (RNFL) thickness were determined. Sixty-eight eyes of 51 PACG, 68 eyes of 48 NTG, and 68 eyes of 49 control subjects were cross-sectionally analyzed. NTG eyes had significantly lower global cpVD (52.369 ± 0.781%) compared with PACG eyes (55.389 ± 0.721%, P = 0.004) that had comparable disease severity and average RNFL thickness. Multivariable analysis revealed that, for PACG and NTG eyes, decreased cpVD ([PACG] β = -4.242; CI: -8.120, -0.363 vs [NTG] β = -5.531; CI: -9.472, -1.590) and cpFD ([PACG] β = -8.894;CI: -11.925, -5.864 vs [NTG] β = -12.064; CI: -17.095, -6.932) were associated with decreased RNFL thickness (all P ≤ 0.032); with a stronger association between decrease cpFD and decreased RNFL thickness in NTG eyes (P = 0.028). Decreased cpVD was associated with decrease mean deviation (MD) in NTG eyes (β = -0.707; CI: -1.090, -0.324; P ≤ 0.001) and not associated with the visual field parameters in PACG eyes. Early NTG had lower global cpVD compared with early PACG, despite similar disease severity and average RNFL thickness.

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.

Optical coherence tomography (OCT) angiolytics: a review of OCT angiography quantitative biomarkers

Optical coherence tomography angiography (OCTA) provides a non-invasive method to obtain angiography of the chorioretinal vasculature leading to its recent widespread adoption. With a growing number of studies exploring the use of OCTA, various biomarkers quantifying the vascular characteristics have come to light. In the current report, we summarize the biomarkers currently described for retinal and choroidal vasculature using OCTA systems and the methods used to obtain them. Further, we present a critical review of these methods and key findings in common retinal diseases and appraise future directions, including applications of artificial intelligence in OCTA .

Nonclinical research areas of future importance for clinical therapies: Exploring the concepts of nonlinearity in dentistry

Linear system analysis has been dominating medical and dental research, and most of the research achievements in these fields have come from applying a reductionist view of nature. However, biologic systems are fundamentally nonlinear with highly composite dynamics made up of numerous interacting elements and feedback loops, therefore studying them as linear models may not result in an accurate representation of their true features. The authors reviewed and utilized some of the principles of chaos and nonlinearity and extended them to clinical dentistry, from cracked tooth and flare-up after root canal procedures to the outcome of clinical treatments. Utilization of the concepts of chaos and sensitive dependence on initial conditions, and the concepts of self-organization, stigmergy, and fractals may help us to understand some of the puzzles that have not been solved by conventional linear models. The goal of this paper is to present some areas within nonclinical research that we believe will have important roles in the development of future clinical examination methods and therapies.

Quantitative Optical Coherence Tomography Angiography Biomarkers for Alport Syndrome

PURPOSE

The aim of this study was to evaluate microvascular abnormalities of patients with Alport syndrome (AS) using optical coherence tomography angiography (OCT-A) quantitative biomarkers.

METHODS

This was cross sectional, prospective evaluation of consecutive patients with AS and healthy subjects. AS diagnosis was performed by the genetic test. All participants underwent a retinal vasculature evaluation by spectral-domain optical coherence tomography (SD-OCT) and OCT-A of the macula. Quantitative analysis included whole vascular density, foveal avascular zone area, fractal dimension (FD), and lacunarity (LAC).

RESULTS

Ninety-four eyes were included in this study, 45 eyes from patients with AS and 49 eyes from healthy subjects. The pathogenic mutation in the COL4A5 gene on the chromosome X was found in 14 patients; the pathogenic autosomal recessive mutations in the COL4A3 gene were found in 9 patients. Quantitative evaluation demonstrated a significant difference between AS and healthy subjects on LAC of the superficial capillary plexus and deep capillary plexus (DCP) (p < 0.001 and p < 0.001, respectively) and on FD in the DCP (p < 0.001).

CONCLUSION

The DCP Alport patients have a higher vessel nonuniformity than DCP of healthy subjects. We hypothesize that endothelial cell lesion in the setting of low resistance at the DCP circuit could lead to long-term structural disorganization.

CHARACTERIZATION BY FRACTAL DIMENSION ANALYSIS OF THE RETINAL CAPILLARY NETWORK IN PARKINSON DISEASE

PURPOSE

To characterize retinal capillary complexity by optical coherence tomography angiography in Parkinson disease.

METHOD

Twenty-five Parkinson disease patients and 25 age- and gender-matched healthy controls were recruited. Optical coherence tomography angiography and optical coherence tomography imaged the superficial and deep retinal capillary plexuses and retinal structure. Retinal capillary skeleton density, retinal capillary perfusion density, and fractal dimension analysis of retinal capillary complexity were performed in the total annular zone and quadrant sectors. The thickness of retinal nerve fiber layer, ganglion cell layer and inner plexiform layer, and total retinal thickness were extracted from retinal structural images. Relationships among the retinal capillaries, retinal structure, and clinical parameters were analyzed.

RESULTS

The superficial retinal capillary plexus in Parkinson disease patients had lower retinal capillary skeleton and perfusion densities and capillary complexity in the total annular zone and all quadrant sectors compared with healthy control subjects. The deep retinal capillary plexus retinal capillary complexity was decreased in the total annular zone and the superior and inferior quadrants. The retinal capillary complexity in the inferior quadrant was negatively correlated with the best-corrected visual acuity and disease duration (r = -0.61, r = -0.43, respectively, both P < 0.05).

CONCLUSION

As determined by fractal analysis, retinal capillary complexity can be an objective biomarker in Parkinson disease.

COMPARISON BETWEEN SEVERAL OPTICAL COHERENCE TOMOGRAPHY ANGIOGRAPHY DEVICES AND INDOCYANINE GREEN ANGIOGRAPHY OF CHOROIDAL NEOVASCULARIZATION

PURPOSE

To compare indocyanine green angiography and four different optical coherence tomography angiography (OCTA) devices and to test their reproducibility in the evaluation of choroidal neovascularization (CNV).

METHODS

This study was an observational case series of Type 1 and Type 2 CNV presenting at the Eye Clinic, Department of Biomedical and Clinical Sciences, Luigi Sacco Hospital, University of Milan, imaged with indocyanine green angiography and four different OCTA devices: prototype PlexElite (Carl Zeiss Meditec), prototype Spectralis OCTA (Spectralis; Heidelberg Engineering, Heidelberg, Germany), Optovue RTVue XR Avanti (Optovue, Inc, Fremont, CA), and AngioPlex (Cirrus 5000 HD-OCT; Carl Zeiss Meditec, Inc, Dublin, CA). Optical coherence tomography angiography examinations were performed using a 3 × 3-mm or 6 × 6-mm volume scan pattern to capture the full lesion. The mean area of CNV, vessel density, and fractal dimension were compared between the devices.

RESULTS

Seventeen eyes of 17 patients with CNV were enrolled. The CNV area was significantly larger in indocyanine green angiography than in the OCTA devices. Moreover, the four different instruments produced measurements with different mean values of CNV area, vessel density, and fractal dimension. The Bland-Altman analysis revealed that the limits of agreement for the comparisons were not acceptable.

CONCLUSION

The choroidal neovascularization area is larger when imaged with standard indocyanine green angiography than with different OCTA devices with different algorithms, wavelengths, and scan patterns. The differences between several OCTA devices in the evaluation of quantitative parameters of CNV, such as CNV area, vessel density, and fractal dimension, suggest the necessity to standardize OCTA measurements for research and clinical practice.

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 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.

QUANTITATIVE OPTICAL COHERENCE TOMOGRAPHY ANGIOGRAPHY FEATURES OF INACTIVE MACULAR NEOVASCULARIZATION IN AGE-RELATED MACULAR DEGENERATION

PURPOSE

To compare quantitative optical coherence tomography angiography parameters between treatment-naïve quiescent macular neovascularizations (MNVs) and previously treated nonexudative Type 1 MNVs, in patients with age-related macular degeneration.

METHODS

The eyes included in the study were analyzed by fluorescein angiography, indocyanine green angiography, spectral-domain optical coherence tomography, and optical coherence tomography angiography. According to their medical history and multimodal imaging evaluation, Type 1 MNVs were divided into 2 groups: 1) treatment-naïve quiescent MNVs; 2) previously treated nonexudative Type 1 MNVs. Quantitative optical coherence tomography angiography parameters, including perfusion density (PD), fractal dimension (FD), and lacunarity (LAC) were calculated. Receiver operating characteristic curves, showing the ability of PD, FD, and LAC to discriminate between the two MNV groups, were built.

RESULTS

Twenty-two eyes with treatment-naïve quiescent MNVs and 20 eyes with MNVs previously treated nonexudative Type 1 MNVs were analyzed. Mean FD and LAC were statistically different between the two study groups (P < 0.05). Lacunarity showed the best discrimination ability, followed by FD and PD (area under curve = 0.83, 0.78, 0.62, respectively).

CONCLUSION

Results suggest that FD and LAC may be useful optical coherence tomography angiography biomarkers to objectively discriminate inactive MNVs with different prognosis, such as treatment-naïve quiescent MNVs and previously treated nonexudative Type 1 MNVs, in age-related macular degeneration patients.

FRACTAL DIMENSION AND OPTICAL COHERENCE TOMOGRAPHY ANGIOGRAPHY FEATURES OF THE CENTRAL MACULA AFTER REPAIR OF RHEGMATOGENOUS RETINAL DETACHMENTS

PURPOSE

Patients with macula-off rhegmatogenous retinal detachments (RRDs) may have suboptimal visual recovery, despite successful reattachment due to various reasons. This study was performed to evaluate the retinal microvasculature in subjects undergoing surgery for RRD using optical coherence tomography angiography.

METHODS

In this case-control study, the analysis of optical coherence tomography angiography findings of 19 eyes of 19 patients (15 men) who underwent RRD surgery at a tertiary institute were compared with 19 eyes of 19 age- and sex-matched healthy subjects with no known ocular disease. 3 × 3-mm optical coherence tomography angiography scans were obtained at 3 months postoperatively and analyzed. Optical coherence tomography angiography images of patients with RRD and control subjects were analyzed for capillary density index and fractal dimensions.

RESULTS

Mean age of the patients was 40.21 years, and the mean age of controls was 43.73 years. Eight eyes underwent scleral buckling alone, and 11 eyes underwent primary vitrectomy with gas tamponade (C3F8 gas) for macula-off RRD. None of the eyes had redetachment during the follow-up at 3 months. Mean capillary density index among patients was 33.28% ± 0.99% and 34.06% ± 2.22% in the superficial and deep retinal plexuses, respectively, compared with 36.11% ± 1.29% and 37.52% ± 1.24% among controls (P < 0.001). The mean fractal dimension was lower among subjects compared with controls (1.46 vs. 1.61 in the superficial plexus, P < 0.001; 1.58 vs. 1.64 in the deep plexus, P < 0.001).

CONCLUSION

Optical coherence tomography angiography demonstrates significant reduction in mean capillary density index and fractal dimension in patients after surgery for RRD in our patients. Thus, reduction in vascular perfusion and branching pattern identified using novel analysis techniques on optical coherence tomography angiography images may provide an insight into the reasons for suboptimal visual gain after RRD surgery.

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.

OCT-Angiography as a reliable prognostic tool in laser-treated proliferative diabetic retinopathy: The RENOCTA Study

PURPOSE

To quantitatively assess retinal neovascularizations (RNVs) in proliferative diabetic retinopathy (PDR) before and after photocoagulative laser treatment (PLT) using Optical Coherence Tomography Angiography (OCT-A).

METHODS

Consecutive patients with PDR were examined with fluorescein angiography (FA) and OCT-A before and after PLT. Baseline and after-treatment FA images were quantitatively analyzed to assess both the RNVs area and leakage area. On OCT-A RNVs area, vascular perfusion density (VPD), vessel length density (VLD) and fractal dimension were computed. VPD of the full-retina OCT-A underneath the RNV was determined to evaluate potential laser-induced changes in vascular perfusion.

RESULTS

Fifteen eyes of 13 patients with PDR were enrolled. The mean area of the RNVs was 0.47 ± 0.50 mm² in the baseline OCT-A and 0.32 ± 0.40 mm² in the post-treatment assessment (p = 0.0002). The mean RNV VPD of RNV was 2% ± 4% in pre-treatment and 1% ± 1% for the post-treatment (p = 0.0001). The mean VLD of RNV was 7.26 ± 1.53 at baseline and 6.64 ± 1.65 in the post treatment (p = 0.0002). A significant difference in terms of mean RNVs area and VPD reduction between eyes that needed additional treatment and those that did not (~40% vs ~20%; p < 0.05), was observed. Mean VPD of full-retinal thickness OCT-angiogram was 55% ± 10% for the pre-treatment and 53% ± 8% for the post treatment scan (p = 0.02).

CONCLUSION

The quantitative OCT-A assessment of laser-induced changes of RNVs can be a useful non-invasive approach for determining treatment efficacy. A reduction of RNVs area or VPD ⩾ 40% might reveal those eyes that won't require additional treatment. Retinal perfusion impairment seemed to progress independently from the treatment.

Combined Multi-Modal Assessment of Glaucomatous Damage With Electroretinography and Optical Coherence Tomography/Angiography

Purpose

To compare the diagnostic performance and to evaluate the interrelationship of electroretinographical and structural and vascular measures in glaucoma.

Methods

For 14 eyes of 14 healthy controls and 15 eyes of 12 patients with glaucoma ranging from preperimetric to advanced stages optical coherence tomography (OCT), OCT-angiography (OCT-A), and electrophysiological measures (multifocal photopic negative response ratio [mfPhNR] and steady-state pattern electroretinography [ssPERG]) were applied to assess changes in retinal structure, microvasculature, and function, respectively. The diagnostic performance was assessed via area-under-curve (AUC) measures obtained from receiver operating characteristics analyses. The interrelation of the different measures was assessed with correlation analyses.

Results

The mfPhNR, ssPERG amplitude, parafoveal (pfVD) and peripapillary vessel density (pVD), macular ganglion cell inner plexiform layer thickness (mGCIPL) and peripapillary retinal nerve fiber layer thickness (pRNFL) were significantly reduced in glaucoma. The AUC for mfPhNR was highest among diagnostic modalities (AUC: 0.88, 95% confidence interval: 0.75-1.0, P < 0.001), albeit not statistically different from that for macular (mGCIPL: 0.76, 0.58-0.94, P < 0.05; pfVD: 0.81, 0.65-0.97, P < 0.01) or peripapillary imaging (pRNFL: 0.85, 0.70-1.0, P < 0.01; pVD: 0.82, 0.68-0.97, P < 0.01). Combined functional/vascular measures yielded the highest AUC (mfPhNR-pfVD: 0.94, 0.85-1.0, P < 0.001). The functional/structural measure correlation (mfPhNR-mGCIPL correlation coefficient [rs]: 0.58, P = 0.001; mfPhNR-pRNFL rs: 0.66, P < 0.001) was stronger than the functional-vascular correlation (mfPhNR-pfVD rs: 0.29, P = 0.13; mfPhNR-pVD rs: 0.54, P = 0.003).

Conclusions

The combination of ERG measures and OCT-A improved diagnostic performance and enhanced understanding of pathophysiology in glaucoma.

Translational Relevance

Multimodal assessment of glaucoma damage improves diagnostics and monitoring of disease progression.

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.

Microvascular Phenotyping in the Maastricht Study: Design and Main Findings, 2010-2018

Microvascular dysfunction (MVD) is a common pathophysiological change that occurs in various diseases, such as type 2 diabetes mellitus (T2DM), heart failure, dementia, and depression. Recent technical advances have enabled noninvasive measurement and quantification of microvascular changes in humans. In this paper, we describe the protocols of the microvascular measurements applied in the Maastricht Study, an ongoing prospective, population-based cohort study of persons aged 40–75 years being carried out in the southern part of the Netherlands (baseline data assessment, November 2010–January 2020). The study includes a variety of noninvasive measurements in skin, retina, brain, and sublingual tissue, as well as plasma and urine biomarker assessments. Following this, we summarize our main findings involving these microvascular measurements through the end of 2018. Finally, we provide a brief perspective on future microvascular investigations within the framework of the Maastricht Study.

Long-term follow-up of quiescent choroidal neovascularisation associated with age-related macular degeneration or pachychoroid disease

AIMS

To evaluate the long-term progression of quiescent type 1 choroidal neovascularisation (CNV) associated with age-related macular degeneration (AMD) or with pachychoroid disease.

METHODS

All cases of quiescent type 1 CNV with a minimum follow-up of 12 months seen at the Department of Ophthalmology of University Paris Est, Creteil and at the Centre Ophtalmologique de l'Odeon, Paris, between June 2009 and December 2018 were retrospectively reviewed. Optical coherence tomography angiography (OCT-A) of eyes not showing CNV activation during 24 months was evaluated for quantitative analyses of CNV status biomarkers (fractal dimension, lacunarity, vessel density, aspect ratio, CNV area).

RESULTS

A total of 67 eyes (65 patients, 43 females, mean age 76.63±9.7 years) with quiescent CNV and a mean follow-up of 49.56±27.3 (12-112) months were included. Of 28 eyes showing activation of quiescent CNV, 12 eyes with pachychoroid-associated CNV showed reduced visual loss (-3.28 ETDRS letters, p=0.7 vs -13.03 ETDRS letters, p=0.02), greater choroidal thinning (-59.5 µm, p=0.03 vs - 16.36 µm, p=0.3) and needed less antivascular endothelial growth factor intravitreal injections (IVI) (0.09 vs 0.21, p=0.01) than 16 eyes with AMD-associated CNV. CNV area was the only OCT-A biomarker to significantly change during 24 months in inactive quiescent CNV (+29.5%, p=0.01, in pachychoroid group and +27.1%, p=0.03, in the AMD group).

CONCLUSION

In the long-term follow-up, inactive quiescent CNV showed an increase of CNV area without significant changes of the other OCT-A biomarkers. Quiescent type 1 CNV undergoing activation showed greater response to IVI when associated to pachychoroid.

Fractal analysis of retinal vasculature in normal subjects on ultra-wide field fluorescein angiography

AIM

To evaluate the fractal feature of the retinal vasculature of normal eyes on a stereographic projected and montaged ultra-wide field (UWF) fluorescein angiography (FA).

METHODS

Prospective, observational, cross-sectional study. Totally 59 eyes of 31 normal subjects were imaged using the Optos 200Tx. Images obtained at different gaze angles stereographically projected and montaged. The early-phase UWF FA frames were processed to segment the retinal vasculature and the results were exported as binary masks. The fractal dimension (FD) was calculated using the box-counting method.

RESULTS

The global FD for the entire retina was 1.6±0.04, with no difference between males and females (1.59±0.04 vs 1.61±0.04, P=0.084) or between right and left eyes (1.6±0.04 vs 1.6±0.05, P=0.61). FD was non-uniformly distributed among four quadrants (P<0.001) and decreased as the distance from the fovea increased (P<0.001). A negative association was observed between FD and age (R=-0.37, P=0.006), and this relationship was observed in the posterior and mid-peripheral retina (P<0.05) but absent in far-periphery (P>0.05).

CONCLUSION

Fractal geometry is non-uniformly distributed across the retina in normal eyes and decreases from the fovea to the far-periphery. Subjects with an older age tend to have a smaller FD, however, the FD in the far-periphery does not appear to be influenced by age.

Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood-gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions (DF) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined DF values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded DF values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess-Murray law or 'the principle of minimum work'.