Zone specific fractal dimension of retinal images as predictor of stroke incidence

Quantitative analysis of retinal vascular parameters changes in school-age children with refractive error using artificial intelligence

Aim

To quantitatively analyze the relationship between spherical equivalent refraction (SER) and retinal vascular changes in school-age children with refractive error by applying fundus photography combined with artificial intelligence (AI) technology and explore the structural changes in retinal vasculature in these children.

Methods

We conducted a retrospective case-control study, collecting data on 113 cases involving 226 eyes of schoolchildren aged 6-12 years who attended outpatient clinics in our hospital between October 2021 and May 2022. Based on the refractive spherical equivalent refraction, we categorized the participants into four groups: 66 eyes in the low myopia group, 60 eyes in the intermediate myopia group, 50 eyes in the high myopia group, and 50 eyes in the control group. All participants underwent a series of examinations, including naked-eye and best-corrected visual acuity, cycloplegic spherical equivalent refraction, intraocular pressure measurement, ocular axial measurement (AL), and color fundus photography. Using fundus photography, we quantitatively analyzed changes in the retinal vascular arteriovenous ratio (AVR), average curvature, and vascular density with AI technology. Data were analyzed using the χ2 test and one-way analysis of variance.

Results

The AVR in the low myopia group, moderate myopia group, high myopia group, and control group were 0.80 ± 0.05, 0.80 ± 0.04, 0.76 ± 0.04, and 0.79 ± 0.04, respectively, and the vessel densities were 0.1024 ± 0.0076, 0.1024 ± 0.0074, 0.0880 ± 0.0126, and 0.1037 ± 0.0143, respectively The difference between the AVR and vascular density in the high myopia group was statistically significant compared to the other three groups (p < 0.05). Linear correlation analysis showed a strong negative correlation between the spherical equivalent refraction and the ocular axis (r = -0.874, p < 0001), a moderate positive correlation between the spherical equivalent refraction and the vascular density (r = 0.527, p < 0001), and a moderate negative correlation between the ocular axis and the vascular density (r = -0.452, p < 0001).

Conclusion

Schoolchildren with high myopia showed a decreased AVR and decreased vascular density in the retinal vasculature. The AVR and vascular density may be early predictors of myopia progression.

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

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

Empirical retinal venous pulse wave velocity using modified photoplethysmography

OBJECTIVE

Using the novel imaging method of high-speed modified photoplethysmography we measured the retinal venous pulse wave velocity in a single case.

RESULTS

A healthy 30-year-old subject underwent high-speed modified photoplethysmography (120 frames per second) with simultaneous ophthalmodynamometry at 26 Meditron units. A video of the optic nerve was analyzed using custom software. A harmonic regression model was fitted to each pixel in the time series and used to quantify the retinal vascular pulse wave parameters. Retinal venous pulsation at the optic disc was observed as a complex dynamic wall motion, whereas contraction commenced at a point in the vein at the center of the optic disc, and progressed centrifugally. The empirically estimated retinal venous pulse wave velocity at this segment was approximately 22.24694 mm/s. This measurement provides an estimate for future studies in the field.

Retinal microvascular density modifications during the water drinking test

PURPOSE

The water drinking test (WDT) is a well-known stress test that increases intraocular pressure (IOP) momentarily and can indicate risk of glaucoma progression. This study focuses on correlating changes in the retinal microvascular plexus with the WDT in young healthy subjects.

METHODS

A total of 20 eyes of 20 healthy young subjects (mean age 24.37 ± 2.17 years) were included in this study. In our protocol, WDT consisted of drinking 1 L of water within 5 min. Outcome measures in this prospective observational study were mean arterial pressure (MAP), heart rate (HR), IOP, and retinal vessel density of both superficial and deep macular retina using optical coherence tomography angiography (OCTA), which were assessed before water ingestion and four times after at 15-min intervals. OCTA images were later quantified by fractal analysis (box counting [D_box]). One-way repeated measures analysis of variance (ANOVA) was used to assess the effects of WDT on each of the parameters.

RESULTS

The WDT resulted in significant peak changes of the following parameters compared to baseline: IOP: 15.63 ± 3.37 versus 18.38 ± 4.53 mmHg at 30 min, p < 0.001; HR: 75.74 ± 12.23 versus 64.95 ± 11.37 bpm at 15 min, p < 0.001; deep retinal vessel density 1.758 ± 0.14 versus 1.749 ± 0.16 at 15 min, p = 0.040.

CONCLUSIONS

Besides IOP elevation and systemic effects in HR, WDT is associated with temporary modifications of the deep vascular plexus in young healthy subjects.

CEPS: An Open Access MATLAB Graphical User Interface (GUI) for the Analysis of Complexity and Entropy in Physiological Signals

BACKGROUND

We developed CEPS as an open access MATLAB^® GUI (graphical user interface) for the analysis of Complexity and Entropy in Physiological Signals (CEPS), and demonstrate its use with an example data set that shows the effects of paced breathing (PB) on variability of heart, pulse and respiration rates. CEPS is also sufficiently adaptable to be used for other time series physiological data such as EEG (electroencephalography), postural sway or temperature measurements.

METHODS

Data were collected from a convenience sample of nine healthy adults in a pilot for a larger study investigating the effects on vagal tone of breathing paced at various different rates, part of a development programme for a home training stress reduction system.

RESULTS

The current version of CEPS focuses on those complexity and entropy measures that appear most frequently in the literature, together with some recently introduced entropy measures which may have advantages over those that are more established. Ten methods of estimating data complexity are currently included, and some 28 entropy measures. The GUI also includes a section for data pre-processing and standard ancillary methods to enable parameter estimation of embedding dimension m and time delay τ ('tau') where required. The software is freely available under version 3 of the GNU Lesser General Public License (LGPLv3) for non-commercial users. CEPS can be downloaded from Bitbucket. In our illustration on PB, most complexity and entropy measures decreased significantly in response to breathing at 7 breaths per minute, differentiating more clearly than conventional linear, time- and frequency-domain measures between breathing states. In contrast, Higuchi fractal dimension increased during paced breathing.

CONCLUSIONS

We have developed CEPS software as a physiological data visualiser able to integrate state of the art techniques. The interface is designed for clinical research and has a structure designed for integrating new tools. The aim is to strengthen collaboration between clinicians and the biomedical community, as demonstrated here by using CEPS to analyse various physiological responses to paced breathing.

Serotonergic psychedelics LSD & psilocybin increase the fractal dimension of cortical brain activity in spatial and temporal domains

Psychedelic drugs, such as psilocybin and LSD, represent unique tools for researchers investigating the neural origins of consciousness. Currently, the most compelling theories of how psychedelics exert their effects is by increasing the complexity of brain activity and moving the system towards a critical point between order and disorder, creating more dynamic and complex patterns of neural activity. While the concept of criticality is of central importance to this theory, few of the published studies on psychedelics investigate it directly, testing instead related measures such as algorithmic complexity or Shannon entropy. We propose using the fractal dimension of functional activity in the brain as a measure of complexity since findings from physics suggest that as a system organizes towards criticality, it tends to take on a fractal structure. We tested two different measures of fractal dimension, one spatial and one temporal, using fMRI data from volunteers under the influence of both LSD and psilocybin. The first was the fractal dimension of cortical functional connectivity networks and the second was the fractal dimension of BOLD time-series. In addition to the fractal measures, we used a well-established, non-fractal measure of signal complexity and show that they behave similarly. We were able to show that both psychedelic drugs significantly increased the fractal dimension of functional connectivity networks, and that LSD significantly increased the fractal dimension of BOLD signals, with psilocybin showing a non-significant trend in the same direction. With both LSD and psilocybin, we were able to localize changes in the fractal dimension of BOLD signals to brain areas assigned to the dorsal-attenion network. These results show that psychedelic drugs increase the fractal dimension of activity in the brain and we see this as an indicator that the changes in consciousness triggered by psychedelics are associated with evolution towards a critical zone.

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.

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.

Regional Patterns in Retinal Microvascular Network Geometry in Health and Disease

The study explores the regional differences in microvascular geometry between the optic disc (O) and the macular area (M) in health and disease. Skeletonized manually segmented vascular networks from 15 healthy, 15 retinas with diabetic retinopathy (DR), and 15 retinas with glaucoma from publicly available High-Resolution Fundus (HRF) image database were used. When visualized by a digital fundus camera, O has a substantial proportion of small arteries and larger arterioles, while M contains smaller arterioles at the periphery and avascular zone in the center. We hypothesized that in pathological conditions the vascular network remodelling patterns in these two regions may be different. The analysis of box-counting fractal dimension (Db), lacunarity (Λ), and microvascular density showed that in healthy retinas, Λ and vessel density were lower in the M compared to the O, while the Db did not change. In retinas with DR, the Db was the lowest in the M, which was different from all other groups. The vessel density followed this trend. Lacunarity was the highest in the O of DR group compared to all other groups. The results show that in DR various regions of retinal microvascular network remodel in a different manner and to different extent.

Retinal Microvascular Network and Microcirculation Assessments in High Myopia

PURPOSE

To investigate the changes of the retinal microvascular network and microcirculation in high myopia.

DESIGN

A cross-sectional, matched, comparative clinical study.

PARTICIPANTS

Twenty eyes of 20 subjects with nonpathological high myopia (28 ± 5 years of age) with a refractive error of -6.31 ± 1.23 D (mean ± SD) and 20 eyes of 20 age- and sex-matched control subjects (30 ± 6 years of age) with a refractive error of -1.40 ± 1.00 D were recruited.

METHODS

Optical coherence tomography angiography (OCTA) was used to image the retinal microvascular network, which was later quantified by fractal analysis (box counting [D_box], representing vessel density) in both superficial and deep vascular plexuses. The Retinal Function Imager was used to image the retinal microvessel blood flow velocity (BFV). The BFV and microvascular density in the myopia group were corrected for ocular magnification using Bennett's formula.

RESULTS

The density of both superficial and deep microvascular plexuses was significantly decreased in the myopia group in comparison to the controls (P < .05). The decrease of the microvessel density of the annular zone (0.6-2.5 mm), measured as D_box, was 2.1% and 2.9% in the superficial and deep vascular plexuses, respectively. Microvessel density reached a plateau from 0.5 mm to 1.25 mm from the fovea in both groups, but that in the myopic group was about 3% lower than the control group. No significant differences were detected between the groups in retinal microvascular BFV in either arterioles or venules (P > .05). Microvascular densities in both superficial (r = -0.45, P = .047) and deep (r = -0.54, P = .01) vascular plexuses were negatively correlated with the axial lengths in the myopic eye. No correlations were observed between BFV and vessel density (P > .05).

CONCLUSIONS

Retinal microvascular decrease was observed in the high myopia subjects, whereas the retinal microvessel BFV remained unchanged. The retinal microvascular network alteration may be attributed to ocular elongation that occurs with the progression of myopia. The novel quantitative analyses of the retinal microvasculature may help to characterize the underlying pathophysiology of myopia and enable early detection and prevention of myopic retinopathy.

Automatic Analysis of Retinal Vascular Parameters for Detection of Diabetes in Indian Patients with No Retinopathy Sign

This study has investigated the association between retinal vascular parameters with type II diabetes in Indian population with no observable diabetic retinopathy. It has introduced two new retinal vascular parameters: total number of branching angles (TBA) and average acute branching angles (ABA) as potential biomarkers of diabetes in an explanatory model. A total number of 180 retinal images (two (left and right) × two (ODC and MC) × 45 subjects (13 diabetics and 32 nondiabetics)) were analysed. Stepwise linear regression analysis was performed to model the association between type II diabetes with the best subset of explanatory variables (predictors), consisting of retinal vascular parameters and patients' demographic information. P value of the estimated coefficients (P < 0.001) indicated that, at α level of 0.05, the newly introduced retinal vascular parameters, that is, TBA and ABA together with CRAE, mean tortuosity, SD of branching angle, and VB, are related to type II diabetes when there is no observable sign of retinopathy.