Fractal analysis of retinal vessels suggests that a distinct vasculopathy causes lacunar stroke

Microvascular network alterations in the retina of patients with Alzheimer's disease

BACKGROUND

Although cerebral small-vessel disease has been implicated in the development of Alzheimer's disease (AD), the cerebral microcirculation is difficult to visualize directly in vivo. Because the retina provides a noninvasive window to assess the microcirculation, we determined whether quantitatively measured retinal microvascular parameters are associated with AD.

METHODS

We conducted a case-control study (case:control matching ≈ 1:2). Retinal photographs were analyzed using a computer program, and a spectrum of quantitative retinal microvascular parameters (caliber, fractal dimension, tortuosity, and bifurcation) were measured. Logistic regression models were used to compute the odds ratio (OR) and 95% confidence interval for AD adjusting for age, gender, ethnicity, smoking, hypertension, diabetes, hypercholesterolemia, and history of myocardial infarction.

RESULTS

We included 136 demented patients with AD and 290 age-gender-race-matched controls. Persons with narrower venular caliber (OR per standard deviation [SD] decrease, 2.01 [1.27-3.19]), decreased arteriolar and venular fractal dimension (OR per SD decrease 1.35 [1.08-1.68], 1.47 [1.17-1.84], respectively) and increased arteriolar and venular tortuosity (OR per SD increase, 1.84 [1.40-2.31], 1.94 [1.48-2.53], respectively) were more likely to have AD. These associations still persisted when only AD cases without a history of cerebrovascular disease were included.

CONCLUSIONS

Patients with AD have altered microvascular network in the retina (narrower retinal venules and a sparser and more tortuous retinal vessels) compared with matched nondemented controls. These changes in retinal microvasculature may reflect similar pathophysiological processes in cerebral microvasculature in the brains of patients with AD.

Age-related rarefaction in retinal vasculature is not linear

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

Cerebral microbleeds and the risk of mortality in the general population

Presence of cerebral microbleeds indicates underlying vascular brain disease and has been implicated in lobar hemorrhages and dementia. However, it remains unknown whether microbleeds also reflect more systemic vascular burden. We investigated the association of microbleeds with all-cause and cardiovascular related mortality in the general population. We rated the brain magnetic resonance imaging scans of 3979 Rotterdam Scan Study participants to determine presence, number, and location of microbleeds. Cox proportional hazards models, adjusted for age, sex, subcohort, vascular risk factors, and other MRI markers of cerebral vascular disease, were applied to quantify the association of microbleeds with mortality. After a mean follow up of 5.2 (±1.1) years, 172 (4.3 %) people had died. Presence of microbleeds, and particularly deep or infratentorial microbleeds, was significantly associated with an increased risk of all-cause mortality [sex-, age-, subcohort adjusted hazard ratio (HR) 2.27; CI 1.50-3.45], independent of vascular risk factors (HR 1.87; 95 % CI 1.20-2.92). The presence of deep or infratentorial microbleeds strongly associated with the risk of cardiovascular related mortality (HR 4.08; CI 1.78-9.39). Mortality risk increased with increasing number of microbleeds. The presence of microbleeds, particularly multiple microbleeds and those in deep or infratentorial regions, indicates an increased risk of mortality, independent of other MRI markers of cerebral vascular disease. Our data suggest that microbleeds may mark severe underlying vascular pathology associated with poorer survival.

Retinal Microvascular Changes and Risk of Stroke

Background and Purpose—

To examine the relationship between retinal microvascular measures and incident stroke in an Asian Malay population.

Methods—

We conducted a prospective, population-based cohort study of Asian Malay persons 40 to 80 years at baseline. Retinal microvascular signs were assessed from baseline retinal photographs including quantitative retinal microvascular parameters (caliber, branching angle, tortuosity, and fractal dimension) and qualitative retinopathy signs. Incident stroke cases were identified during the follow-up period. Cox proportional-hazards regression and incremental usefulness analysis (calibration, discrimination, and reclassification) were performed.

Results—

A total of 3189 participants were free of prevalent stroke at baseline. During the follow-up (median, 4.41 years), 51 (1.93%) participants had an incident stroke event. In Cox proportional-hazards models adjusting for established stroke predictors (age, sex, systolic blood pressure, total cholesterol, low-density lipoprotein cholesterol, smoking, glycosylated hemoglobin, and antihypertensive medication), retinopathy (hazard ratio, 1.94; 95% confidence interval, 1.01–3.72) and larger retinal venular caliber (hazard ratio, 3.28; 95% confidence interval, 1.30–8.26, comparing fourth versus first quartiles) were associated with risk of stroke. Compared with the model with only established risk factors, the addition of retinal measures improved the prediction of stroke (C-Statistic 0.826 versus 0.792; P =0.017) and correctly reclassified 5.9% of participants with incident stroke and 3.4% of participants with no incident stroke.

Conclusions—

Retinal microvascular changes are related to an increased risk of stroke in Asian Malay, consistent with data from white populations. Retinal imaging improves the discrimination and stratification of stroke risk beyond that of established risk factors by a significant but small margin.

Automated segmentation and fractal analysis of high-resolution non-invasive capillary perfusion maps of the human retina

The retina provides a window to study the pathophysiology of cerebrovascular diseases. Pathological retinal microvascular changes may reflect microangiopathic processes in the brain. Recent advances in optical imaging techniques have enabled the imaging of the retinal microvasculature at the capillary level, and the generation of high-resolution, non-invasive capillary perfusion maps (nCPMs) with the Retinal Function Imager (RFI). However, the lack of quantitative analyses of the nCPMs may limit the wider application of the method in clinical research. The goal of this project was to demonstrate the feasibility of automated segmentation and fractal analysis of nCPMs. We took two nCPMs of each subject in a group of 6 healthy volunteers and used our segmentation algorithm to do the automated segmentation for monofractal and multifractal analyses. The monofractal dimension was 1.885±0.020, and the multifractal dimension was 1.876±0.010 (P=0.108). The coefficient of repeatability was 0.070 for monofractal analysis and 0.026 for multifractal analysis. This study demonstrated that the automatic segmentation of nCPMs is feasible for fractal analyses. Both monofractal and multifractal analyses yielded similar results. The quantitative analyses of microvasculature at the capillary level may open up a new era for studying microvascular diseases such as cerebral small vessel disease.

Retinal vessel tortuosity in response to hypobaric hypoxia

PURPOSE

Retinal vascular tortuosity is associated with retinopathy of differing etiologies, including hypertension, diabetes, and hypoxia. However, detailed understanding of the underlying pathophysiology is lacking. The aim of this study was to map changes in tortuosity associated with hypoxia at high altitude, and to determine the influence of sildenafil and an antioxidant preparation on altitude-induced tortuosity.

METHODS

We measured the tortuosity of retinal vessels using a semi-automated method in 35 young, healthy subjects exposed to hypobaric hypoxia for 7 days at 5200 m, and compared the measurements to those from the same vessels at sea level. These subjects simultaneously took part in a randomized double-blind placebo-controlled trial of sildenafil and antioxidant. Comparison of tortuosity between these subgroups was performed.

RESULTS

High altitude was associated with the development of retinal tortuosity in individual vessels. A nonsignificant trend suggests this is limited by prophylaxis with sildenafil or antioxidant.

CONCLUSIONS

Retinal vessel tortuosity increases rapidly at high altitude. We suggest that retinal vessel tortuosity at altitude may result from increased sheer stress causing elongation of vessel segments and that this might be limited by agents that act to preserve nitric oxide dependent vasodilation.

TRIAL REGISTRATION NUMBERS

NCT00664001, NCT00627965.

Quantification of left ventricular trabeculae using fractal analysis

BACKGROUND

Left ventricular noncompaction (LVNC) is a myocardial disorder characterized by excessive left ventricular (LV) trabeculae. Current methods for quantification of LV trabeculae have limitations. The aim of this study is to describe a novel technique for quantifying LV trabeculation using cardiovascular magnetic resonance (CMR) and fractal geometry. Observing that trabeculae appear complex and irregular, we hypothesize that measuring the fractal dimension (FD) of the endocardial border provides a quantitative parameter that can be used to distinguish normal from abnormal trabecular patterns.

METHODS

Fractal analysis is a method of quantifying complex geometric patterns in biological structures. The resulting FD is a unitless measure index of how completely the object fills space. FD increases with increased structural complexity. LV FD was measured using a box-counting method on CMR short-axis cine stacks. Three groups were studied: LVNC (defined by Jenni criteria), n=30(age 41±13; men, 16); healthy whites, n=75(age, 46±16; men, 36); healthy blacks, n=30(age, 40±11; men, 15).

RESULTS

In healthy volunteers FD varied in a characteristic pattern from base to apex along the LV. This pattern was altered in LVNC where apical FD were abnormally elevated. In healthy volunteers, blacks had higher FD than whites in the apical third of the LV (maximal apical FD: 1.253±0.005 vs. 1.235±0.004, p<0.01) (mean±s.e.m.). Comparing LVNC with healthy volunteers, maximal apical FD was higher in LVNC (1.392±0.010, p<0.00001). The fractal method was more accurate and reproducible (ICC, 0.97 and 0.96 for intra and inter-observer readings) than two other CMR criteria for LVNC (Petersen and Jacquier).

CONCLUSIONS

FD is higher in LVNC patients compared to healthy volunteers and is higher in healthy blacks than in whites. Fractal analysis provides a quantitative measure of trabeculation and has high reproducibility and accuracy for LVNC diagnosis when compared to current CMR criteria.

Retinal microvasculature as a model to study the manifestations of hypertension

The retinal vasculature allows direct noninvasive visualization of the body's mircrovasculature. Because the retina and other end organs (brain and kidney) share similar anatomical features and physiological properties, the retinal vessels offer a unique and easily accessible window to study the health and disease of the human microcirculation. Advanced retinal vascular imaging technologies have been developed to allow a more objective and precise assessment of retinal vascular changes. The changes in the retinal vasculature associated with hypertension can be broadly divided into 3 groups: (1) classic retinal vascular changes in response to blood pressure (referred to as hypertensive retinopathy signs), (2) changes in retinal vascular caliber, and (3) changes in more global geometrical patterns of the retina. In this review, we summarize the current understanding of the relationship between retinal vascular changes and blood pressure, the evidence for the retinal vasculature as a biological model to study the manifestation and early pathogenic correlates of hypertension, the latest advances in retinal vascular imaging technologies, and the future opportunities and challenges of retinal vascular imaging. We suggest that further development of retinal vascular analyses and standardized measurement protocols, evaluation of the clinical use of retinal vascular imaging in assessing cardiovascular risk prediction, and using retinal vascular imaging to test antihypertensive treatments will allow the translation of retinal vascular imaging as a tool to improve the diagnosis, prognosis, and management of hypertension in clinical practice.

Skin graft vascular maturation and remodeling: a multifractal approach to morphological quantification

OBJECTIVE

One important contributor to tissue graft viability is angiogenic maturation of the graft tissue bed. This study uses scale-invariant microvascular morphological quantification to track vessel maturation and remodeling in a split-thickness skin-grafting model over 21 days, comparing the results to classical techniques.

METHODS

Images from a previous study of split-thickness skin grafting in rats were analyzed. Microvascular morphology (fractal and multifractal dimensions, lacunarity, and vessel density) within fibrin interfaces of samples over time was quantified using classical semi-automated methods and automated multifractal and lacunarity analyses.

RESULTS

Microvessel morphology increased in density and complexity, from three to seven days after engraftment and then regressed by 21 days. Vessel density increased from 0.07 on day 3 to 0.20 on day 7 and then decreased to 0.06 on day 21. A similar trend was seen for the fractal dimension that increased from 1.56 at three days to 1.77 at seven days then decreased to 1.57 by 21 days. Vessel diameters did not change whereas complexity and density did, signaling remodeling.

CONCLUSIONS

This new automated analysis identified design parameters for tissue engraftment and could be used in other models of graft vessel biology to track proliferation and pruning of complex vessel beds.

Retinal vascular fractal dimension and its relationship with cardiovascular and ocular risk factors

PURPOSE

To examine the influence of a range of cardiovascular risk factors and ocular conditions on retinal vascular fractal dimension in the Singapore Malay Eye Study.

DESIGN

Population-based cross-sectional study.

METHODS

Fractal analysis of the retinal vessels is a method to quantify the global geometric complexity of the retinal vasculature. Retinal vascular fractal dimension (D(f)) and caliber were measured from retinal photographs using a computer-assisted program. D(f) and arteriolar caliber were combined to form a retinal vascular optimality score (ranging from 0 to 3). Data on cardiovascular and ocular factors were collected from all participants based on a standardized protocol.

RESULTS

Two thousand nine hundred thirteen (88.8% of 3280 participants) persons had retinal photographs of sufficient quality for the measurement. The mean D(f) was 1.405 (standard deviation, 0.046; interquartile range, 1.243 to 1.542). In the multiple linear regression analysis, after controlling for gender, serum glucose, intraocular pressure, anterior chamber depth, and retinal vascular caliber, smaller D(f) was associated independently with older age (standardized regression coefficient [sβ] = -0.311; P < .001), higher mean arterial blood pressure (sβ = -0.085; P < .001), a more myopic spherical equivalent (sβ = 0.152; P < .001), and presence of cataract (sβ = -0.107; P < .001). Retinal vascular optimality score was associated significantly with higher mean arterial blood pressure (P > .001 for trend).

CONCLUSIONS

Age, blood pressure, refractive error, and lens opacity had significant influence on retinal vascular fractal measurements. A new score of retinal vascular optimality combining fractals and caliber showed strong association with blood pressure. Quantitative analysis of retinal vasculature therefore may provide additional information on microvascular architecture and optimality.

Retinal vascular geometry in Asian persons with diabetes and retinopathy

PURPOSE

Our purpose was to examine the relationship of retinal vascular parameters with diabetes and retinopathy in an older Asian population.

METHODS

Retinal photographs from participants of a population-based survey of Asian Malay persons aged 40-80 years were analyzed. Specific retinal vascular parameters (tortuosity, branching angle, fractal dimension, and caliber) were measured using a semiautomated computer-based program. Diabetes was defined as random plasma glucose ≥ 11.1 mmol/liter, the use of diabetes medication, or physician-diagnosed diabetes. Retinopathy signs were graded from photographs using the modified Airlie House classification system.

RESULTS

A total of 2735 persons were included in the study. Persons with diabetes (n = 594) were more likely to have straighter (less tortuous) arterioles and wider arteriolar and venular caliber than those without diabetes (n = 2141). Among subjects with diabetes, those with retinopathy had wider venular caliber than those without retinopathy (211.3 versus 204.9 mm, p = .001). Among nondiabetic subjects, however, those with retinopathy had more tortuous venules than those without retinopathy [5.19(×10(4)) versus 4.27(×10(4)), p < .001].

CONCLUSIONS

Retinal vascular parameters varied by diabetes and retinopathy status in this older Asian cohort. Our findings suggest that subtle alterations in retinal vascular architecture are influenced by diabetes.

Regional leptomeningeal score on CT angiography predicts clinical and imaging outcomes in patients with acute anterior circulation occlusions

BACKGROUND AND PURPOSE

The regional leptomeningeal score is a strong and reliable imaging predictor of good clinical outcomes in acute anterior circulation ischemic strokes and can therefore be used for imaging based patient selection. Efforts to determine biological determinants of collateral status are needed if techniques to alter collateral behavior and extend time windows are to succeed.

MATERIALS AND METHODS

This was a retrospective Institutional Review Board-approved study of patients with acute ischemic stroke and M1 middle cerebral artery+/- intracranial internal carotid artery occlusion at our center from 2003 to 2009. The rLMC score is based on scoring pial and lenticulostriate arteries (0, no; 1, less; 2, equal or more prominent compared with matching region in opposite hemisphere) in 6 ASPECTS regions (M1-6) plus anterior cerebral artery region and basal ganglia. Pial arteries in the Sylvian sulcus are scored 0, 2, or 4. Good clinical outcome was defined as mRS ≤ 2 at 90 days.

RESULTS

The analysis included 138 patients: 37.6% had a good (17-20), 40.5% a medium (11-16), and 21.7% a poor (0-10) rLMC score. Interrater reliability was high, with an intraclass correlation coefficient of 0.87 (95% CI, 0.77%-0.95%). On univariate analysis, no single vascular risk factor was associated with the presence of poor rLMCs (P ≥ .20 for all comparisons). In multivariable analysis, the rLMC score (good versus poor: OR, 16.7; 95% CI, 2.9%-97.4%; medium versus poor: OR, 9.2, 95% CI, 1.7%-50.6%), age (< 80 years), baseline ASPECTS (≥ 8), and clot burden score (≥ 8) were independent predictors of good clinical outcome.

CONCLUSIONS

The rLMC score is a strong imaging parameter on CT angiography for predicting clinical outcomes in patients with acute ischemic strokes.

Fractal analysis reveals reduced complexity of retinal vessels in CADASIL

The Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL) affects mainly small cerebral arteries and leads to disability and dementia. The relationship between clinical expression of the disease and progression of the microvessel pathology is, however, uncertain as we lack tools for imaging brain vessels in vivo. Ophthalmoscopy is regarded as a window into the cerebral microcirculation. In this study we carried out an ophthalmoscopic examination in subjects with CADASIL. Specifically, we performed fractal analysis of digital retinal photographs. Data are expressed as mean fractal dimension (mean-D), a parameter that reflects complexity of the retinal vessel branching. Ten subjects with genetically confirmed diagnosis of CADASIL and 10 sex and age-matched control subjects were enrolled. Fractal analysis of retinal digital images was performed by means of a computer-based program, and the data expressed as mean-D. Brain MRI lesion volume in FLAIR and T1-weighted images was assessed using MIPAV software. Paired t-test was used to disclose differences in mean-D between CADASIL and control groups. Spearman rank analysis was performed to evaluate potential associations between mean-D values and both disease duration and disease severity, the latter expressed as brain MRI lesion volumes, in the subjects with CADASIL. The results showed that mean-D value of patients (1.42±0.05; mean±SD) was lower than control (1.50±0.04; p = 0.002). Mean-D did not correlate with disease duration nor with MRI lesion volumes of the subjects with CADASIL. The findings suggest that fractal analysis is a sensitive tool to assess changes of retinal vessel branching, likely reflecting early brain microvessel alterations, in CADASIL patients.

Fractal immunology and immune patterning: potential tools for immune protection and optimization

Fractals are self-similar geometric patterns that are inherently embedded throughout nature. Their discovery and application have produced significant benefits across a wide variety of biomedical applications. Recently, complex physiological systems (e.g., neurological, respiratory, cardiovascular) have been shown to exhibit fractal dimensions that are capable of distinguishing among physiologic function versus dysfunction and, in turn, health versus disease. Additionally, fractal data suggest that the immune system operates under similar patterned relationships, and this is in keeping with the recent findings that immune-based diseases are organized according to specific patterns. This review considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain holistic information on immune-environment interactions. The potential uses of both synthetic and artificial immune systems for improved protection of the biological immune system are also discussed. The addition of holistic measures of immune status to currently collected biomarkers of immunotoxicity has the potential to increase the effectiveness of health risk assessment. The objective of extending fractal physiology analyses to the immune system would be to promote immune optimization as a public health benefit, which would include improved: (1) immunotoxicity testing and effective health risk reduction and (2) measures of effective immune management for children, adults, and aged individuals.

Angioarchitectural heterogeneity in human glioblastoma multiforme: a fractal-based histopathological assessment

There is currently no standard technique to objectively quantify the microvascularization of brain tumors. Fractal analysis has been proposed as a useful descriptor of tumor microvascularity. Standardization of the fractal analysis methodology could offer a new tool for this type of characterization. In this study, we applied fractal analysis to the characterization of the different angioarchitectures found in specimens of glioblastoma multiforme (GBM), the most common and most malignant type of human brain tumor. A retrospective series of 114 primary GBM specimens was carried out. To quantify neoplastic microvascularity, the level of two-dimensional geometrical complexity of the microvascular patterns was assessed using the box-counting algorithm, which estimates the microvascular fractal dimension (mvFD). mvFD makes information on the non-Euclidean space filled by vessels embedded in the tumor microenvironment available because it depends on vessel number, shape, magnitude and distribution pattern. A mean mvFD value of 1.44 ± 0.17 (range: 1.06-1.87) was found. The coefficient of variation was 44%. The high geometric variability, found objectively, in these samples reflects the angioarchitectural heterogeneity underlying GBM. The present study shows that angioarchitectural subtypes can be identified by mvFD, making this parameter a potential tool for quantifying different neoplastic microvascular patterns.

Multifractal and lacunarity analysis of microvascular morphology and remodeling

OBJECTIVE

Classical measures of vessel morphology, including diameter and density, are employed to study microvasculature in endothelial membrane labeled mice. These measurements prove sufficient for some studies; however, they are less well suited for quantifying changes in microcirculatory networks lacking hierarchical structure. We demonstrate that automated multifractal analysis and lacunarity may be used with classical methods to quantify microvascular morphology.

METHODS

Using multifractal analysis and lacunarity, we present an automated extraction tool with a processing pipeline to characterize 2D representations of 3D microvasculature. We apply our analysis on four tissues and the hyaloid vasculature during remodeling.

RESULTS

We found that the vessel networks analyzed have multifractal geometries and that kidney microvasculature has the largest fractal dimension and the lowest lacunarity compared to microvasculature networks in the cortex, skin, and thigh muscle. Also, we found that, during hyaloid remodeling, there were differences in multifractal spectra reflecting the functional transition from a space filling vasculature which nurtures the lens to a less dense vasculature as it regresses, permitting unobstructed vision.

CONCLUSION

Multifractal analysis and lacunarity are valuable additions to classical measures of vascular morphology and will have utility in future studies of normal, developing, and pathological tissues.