Characterisation of the neovascularisation process in diabetic retinopathy by means of fractal geometry: diagnostic implications

Predictive Factors of Visual Outcome in Treatment-Naïve Diabetic Macular Edema: Preliminary Results from the Clinical Study "FOVEA"

Diabetic macular edema (DME) is a common cause of vision impairment in diabetic retinopathy. The aim of this study was to analyze the relationship between visual outcome and anatomic changes detected by traditional multimodal retinal imaging and optical coherence tomography angiography (OCTA) in DME eyes under treatment with Aflibercept.

METHODS

Sixty-six DME eyes of 62 patients under treatment with intravitreal Aflibercept and with one-year follow-up were enrolled. All participants underwent a full ophthalmic evaluation, including best correct visual acuity (BCVA) measurement, spectral-domain optical coherence tomography, fluorescein angiography and OCTA, both at baseline and final examination. Fractal OCTA analysis of the superficial and deep capillary plexus (SCP and DCP) was performed to estimate vascular perfusion density and lacunarity (LAC).

RESULTS

At the final examination, there was a significant improvement in terms of BCVA and central macular thickness (CMT). Furthermore, eyes with CMT <373 µm at baseline reached the higher BCVA at the last follow-up. Eyes with CMT ≥373 µm and DCP LAC <0.41 reached a higher final BCVA, if compared with eyes showing the same CMT but higher initial LAC.

CONCLUSION

A 12-month treatment with intravitreal Aflibercept for DME resulted in significant visual and anatomic improvement. Multimodal retinal imaging, together with fractal OCTA analysis, may provide useful biomarkers, predictive of visual outcome in DME.

Qualitative and quantitative evaluation of diabetic choroidopathy using ultra-widefield indocyanine green angiography

To investigate angiographic characteristic features of diabetic choroidopathy, as well as choroidal vascular density (CVD) and fractal dimension (CFD) in diabetic eyes and controls using ultra-widefield (UWF) indocyanine green angiography (ICGA). All patients underwent UWF fluorescein angiography and ICGA. Using imageJ software, CVD and CFD was analyzed. SFCT was assessed using spectral-domain optical coherence tomography. The image parameters were compared based on the DR stage and the presence of diabetic macular edema (DME). One-hundred six eyes from 63 patients (59.11 ± 16.31 years; male [%]: 23 [36.5%]) were included in the DM group, and 40 eyes from 22 subjects were included in the control group. The DM group had a mean age of 59.11 ± 16.31 years and a mean HbA1c percentage of 7.72 ± 1.28%. The most common ICGA findings of DC were choroidal hyperpermeability (57.5%), hypofluorescent spots (48.1%). Salt and pepper pattern (19.8%), inverted inflow phenomenon (3.8%), choroidal arterial tortuosity (24.5%), and late choroidal non-perfusion (6.6%) were more common in advanced DR. The CVD, CFD, and SFCT increased as the DR severity progressed. The DME group had a significantly higher CFD and SFCT than the non-DME group (P < 0.001 and P = 0.019, respectively). The qualitative and quantitative UWF ICGA image analysis revealed that choroidal blood vessels became dilated, complex, and hyperpermeable as the DR progressed. These features of diabetic choroidopathy (DC) were more severe in eyes with DME than the non-DME eyes.

Optical coherence tomography angiography reveals progressive worsening of retinal vascular geometry in diabetic retinopathy and improved geometry after panretinal photocoagulation

Purpose

To quantify vessel tortuosity and fractal dimension of the superficial capillary plexus (SCP) of the macula in different stages of diabetic retinopathy (DR), and following panretinal photocoagulation (PRP) using optical coherence tomography angiography (OCTA).

Methods

75 eyes of 75 subjects were divided into five groups; healthy controls, diabetes with no clinical DR, non-proliferative diabetic retinopathy (NPDR), proliferative diabetic retinopathy (PDR) and patients who received PRP for PDR (PDR+PRP).For vessel tortuosity, SCP slabs from 3x3 mm macular OCTA scans were processed using imageJ (NIH, USA), where large perifoveal vessels were traced and their length was measured with tortuosity calculated as the ratio between the actual length and the straight Euclidean length. For fractal dimension, SCP slabs were processed and imported to Fractalyse (ThéMA, France), where box-counting analyses produced fractal dimension values.

Results

We found a significant difference in vessel tortuosity and fractal dimension between the five groups (one-way ANOVA, p < 0.001both). NPDR and PDR had significantly more tortuous vessels and lower fractal dimension compared to healthy controls (Tukey HSD: p = 0.02, 0.015,0.015 and <0.001, respectively). Fractal dimension was also significantly lower in NPDR and PDR compared to eyes with no clinical DR (p <0.001 both), and in PDR compared to NPDR (p = 0.014). Following PRP, vessel tortuosity was significantly lower and fractal dimension was higher in PDR+PRP compared to PDR (p = 0.001 and 0.031, respectively).

Conclusions

We used macular OCTA scans to demonstrate significantly higher perifoveal large vessel tortuosity, and lower fractal dimension in NPDR and PDR compared to healthy controls. Vessel tortuosity shows more dramatic normalization than fractal dimension and could be explored as a sensitive marker for successful PRP.

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.

Fractal characterization of retinal microvascular network morphology during diabetic retinopathy progression

OBJECTIVE

The study aimed to characterize morphological changes of the retinal microvascular network during the progression of diabetic retinopathy.

METHODS

Publicly available retinal images captured by a digital fundus camera from DIARETDB1 and STARE databases were used. The retinal microvessels were segmented using the automatic method, and vascular network morphology was analyzed by fractal parametrization such as box-counting dimension, lacunarity, and multifractals.

RESULTS

The results of the analysis were affected by the ability of the segmentation method to include smaller vessels with more branching generations. In cases where the segmentation was more detailed and included a higher number of vessel branching generations, increased severity of diabetic retinopathy was associated with increased complexity of microvascular network as measured by box-counting and multifractal dimensions, and decreased gappiness of retinal microvascular network as measured by lacunarity parameter. This association was not observed if the segmentation method included only 3-4 vessel branching generations.

CONCLUSIONS

Severe stages of diabetic retinopathy could be detected noninvasively by using high resolution fundus photography and automatic microvascular segmentation to the high number of branching generations, followed by fractal analysis parametrization. This approach could improve risk stratification for the development of microvascular complications, cardiovascular disease, and dementia in diabetes.

Fractal dimension and lacunarity analysis of retinal microvascular morphology in hypertension and diabetes

Hypertension and diabetes mellitus represent modifiable risk factors for vascular disease. They cause microvascular remodeling, and ultimately result in end-organ damage. Therefore, development of methods for noninvasive quantification of the effects of hypertension and diabetes mellitus on microvasculature is of paramount importance. The two goals of the study were: 1) to characterize the geometric complexity and inhomogeneity of retinal vasculature in hypertensive retinopathy (HR) and in proliferative diabetic retinopathy (PDR) by using box counting fractal dimension and lacunarity analysis, and 2) to determine if the combination of these two parameters can be used to describe differences in the vascular tree geometry between HR and PDR. The extended set of retinal images from the publicly available STARE database was manually segmented by our expert, validated, and made available for other researchers to use. The healthy retinal vascular network has a higher complexity (fractal dimension) compared to that in HR and in PDR. However, there is no difference in microvascular complexity between HR and PDR. The inhomogeneity of the retinal microvascular tree (lacunarity) was higher in PDR compared to HR. Lacunarity and fractal dimension together quantitatively characterize microvascular geometry in the retina with higher specificity than fractal analysis alone.

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

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

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

PURPOSE

To investigate inter-eye agreement in retinal vascular fractal dimension (FD) in patients with type 1 diabetes.

METHODS

In a cross-sectional study, both eyes were exained in 178 patients with type 1 diabetes. All vessels in a zone 0.5-2.0 disc diameters from the optic disc were traced and FD calculated with the box-counting method using SIVA-Fractal semiautomatic software. The modified Early Treatment Diabetic Retinopathy Study (ETDRS) scale was used to grade diabetic retinopathy (DR). Pitman's test of difference in variance was used to calculated inter-eye agreement in FD according to level of DR.

RESULTS

Mean age and duration of diabetes was 37.0 years and 29.5 years, respectively, and 49.4% of participants were male. Mean FD of right and left eyes was 1.4540 and 1.4472, respectively. FD did not differ between eyes in patients with no or non-proliferative DR (NPDR) in both eyes. This was true for patients with the same level of DR in both eyes (n = 74, p = 0.73), as well as for patients in which the ETDRS level of DR between the eyes differed by 1 (n = 43, p = 0.99) or more (n = 9, p = 0.53). In patients treated for proliferative DR in one eye, FD was significantly lower in this eye compared to the other (n = 10, p = 0.03).

CONCLUSION

FD did not differ significantly between the two eyes of patients with no DR or NPDR, despite differences in severity of DR.

Morphometric analysis of cryofixed muscular tissue for intraoperative consultation

For diagnostic purposes, cryofixation of tissues is a daily routine technique to investigate rapidly about the presence of tumours during a surgical procedure in patients. We performed morphometric analysis of cryofixed muscular tissues according to different techniques. About 1,000 muscle fibers and 1,493 nuclei, were automatically examined. After freezing, ice tissue interfaces shrinkage of the cells were present. Liquid isopentane or liquid nitrogen produced a statistical increase of fractal dimension, D, of the ice-tissue interfaces, P < 0.001 respect to the formalin-fixed samples, cryofixation performed inside the cryostat chamber at t = -20°C produced a D value close to the formalin-fixed samples. Shrinkage of the muscle fibers was higher in the samples cryofixed inside the cryostat chamber (P < 0.001). Cryofixation inside cryostat or by liquid nitrogen caused decreases of the nuclei dimensions and altered nuclear morphology (P < 0.01), liquid isopentane appeared not affecting the nuclei of the fibers. Cryofixation inside the cryostat chamber produced the highest shrinkage but it was reduced performing cryofixation in liquid nitrogen or isopentane. Freezing damage inside the muscle cells was absent in the samples cryofixed inside the cryostat, it was present after cryofixation by liquid nitrogen or isopentane. Subcellular components like the nuclei were preserved by isopentane. This paper present, for the first time, an objective method able to quantify and characterize the damages produced by cryofixation in biological sample for intraoperative consultation.

Retinal vascular fractal dimension, childhood IQ, and cognitive ability in old age: the Lothian Birth Cohort Study 1936

Purpose

Cerebral microvascular disease is associated with dementia. Differences in the topography of the retinal vascular network may be a marker for cerebrovascular disease. The association between cerebral microvascular state and non-pathological cognitive ageing is less clear, particularly because studies are rarely able to adjust for pre-morbid cognitive ability level. We measured retinal vascular fractal dimension (D_f) as a potential marker of cerebral microvascular disease. We examined the extent to which it contributes to differences in non-pathological cognitive ability in old age, after adjusting for childhood mental ability.

Methods

Participants from the Lothian Birth Cohort 1936 Study (LBC1936) had cognitive ability assessments and retinal photographs taken of both eyes aged around 73 years (n = 648). IQ scores were available from childhood. Retinal vascular D_f was calculated with monofractal and multifractal analysis, performed on custom-written software. Multiple regression models were applied to determine associations between retinal vascular D_f and general cognitive ability (g), processing speed, and memory.

Results

Only three out of 24 comparisons (two eyes × four D_f parameters × three cognitive measures) were found to be significant. This is little more than would be expected by chance. No single association was verified by an equivalent association in the contralateral eye.

Conclusions

The results show little evidence that fractal measures of retinal vascular differences are associated with non-pathological cognitive ageing.

Genetic algorithm based feature selection combined with dual classification for the automated detection of proliferative diabetic retinopathy

Proliferative diabetic retinopathy (PDR) is a condition that carries a high risk of severe visual impairment. The hallmark of PDR is the growth of abnormal new vessels. In this paper, an automated method for the detection of new vessels from retinal images is presented. This method is based on a dual classification approach. Two vessel segmentation approaches are applied to create two separate binary vessel map which each hold vital information. Local morphology features are measured from each binary vessel map to produce two separate 4-D feature vectors. Independent classification is performed for each feature vector using a support vector machine (SVM) classifier. The system then combines these individual outcomes to produce a final decision. This is followed by the creation of additional features to generate 21-D feature vectors, which feed into a genetic algorithm based feature selection approach with the objective of finding feature subsets that improve the performance of the classification. Sensitivity and specificity results using a dataset of 60 images are 0.9138 and 0.9600, respectively, on a per patch basis and 1.000 and 0.975, respectively, on a per image basis.

Hypoxia in vascular networks: a complex system approach to unravel the diabetic paradox

In this work we model the extent of hypoxia in the diabetic retina as a function of the area affected by vessel disruption. We find two regimes that differ on the ratio between the area of disrupted vasculature and the area of tissue in hypoxia. In the first regime the hypoxia is localized in the vicinity of the vascular disruption, while in the second regime there is a generalized hypoxia in the affected tissue. The transition between these two regimes occurs when the tissue area affected by individual sites of vessel damage is on the order of the square of the characteristic irrigation length in the tissue (the maximum distance that an irrigated point in the tissue is from an existing vessel). We observe that very high levels of hypoxia are correlated with the rupture of larger vessels in the retina, and with smaller radii of individual sites of vessel damage. Based on this property of vascular networks, we propose a novel mechanism for the transition between the nonproliferative and the proliferative stages in diabetic retinopathy.

The relationship of retinal vessel diameters and fractal dimensions with blood pressure and cardiovascular risk factors

BACKGROUND

This study aimed to investigate the correlation between quantitative retinal vascular parameters such as central retinal arteriolar equivalent (CRAE) and retinal vascular fractal dimension (D(f)), and cardiovascular risk factors in the Chinese Han population residing in the in islands of southeast China.

METHODOLOGY/PRINCIPLE FINDINGS

In this cross-sectional study, fundus photographs were collected and semi-automated analysis software was used to analyze retinal vessel diameters and fractal dimensions. Cardiovascular risk factors such as relevant medical history, blood pressure (BP), lipids, and blood glucose data were collected. Subjects had a mean age of 51.9 ± 12.0 years and included 812 (37.4%) males and 1,357 (62.6%) females. Of the subjects, 726 (33.5%) were overweight, 226 (10.4%) were obese, 272 (12.5%) had diabetes, 738 (34.0%) had hypertension, and 1,156 (53.3%) had metabolic syndrome. After controlling for the effects of potential confounders, multivariate analyses found that age (β = 0.06, P = 0.008), sex (β = 1.33, P = 0.015), mean arterial blood pressure (β = -0.12, P<0.001), high-sensitivity C-reactive protein (β = -0.22, P = 0.008), and CRVE (β = 0.23, P<0.001) were significantly associated with CRAE. Age (β = -0.0012, P < 0.001), BP classification (prehypertension: β = -0.0075, P = 0.014; hypertension: β = -0.0131, P = 0.002), and hypertension history (β = -0.0007, P = 0.009) were significantly associated with D(f).

CONCLUSIONS/SIGNIFICANCE

D(f) exhibits a stronger association with BP than CRAE. Thus, D(f) may become a useful indicator of cardiovascular risk.

Fractal-based analysis of optical coherence tomography data to quantify retinal tissue damage

BACKGROUND

The sensitivity of Optical Coherence Tomography (OCT) images to identify retinal tissue morphology characterized by early neural loss from normal healthy eyes is tested by calculating structural information and fractal dimension. OCT data from 74 healthy eyes and 43 eyes with type 1 diabetes mellitus with mild diabetic retinopathy (MDR) on biomicroscopy was analyzed using a custom-built algorithm (OCTRIMA) to measure locally the intraretinal layer thickness. A power spectrum method was used to calculate the fractal dimension in intraretinal regions of interest identified in the images. ANOVA followed by Newman-Keuls post-hoc analyses were used to test for differences between pathological and normal groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of each parameter to discriminate between eyes of pathological patients and normal healthy eyes.

RESULTS

Fractal dimension was higher for all the layers (except the GCL + IPL and INL) in MDR eyes compared to normal healthy eyes. When comparing MDR with normal healthy eyes, the highest AUROC values estimated for the fractal dimension were observed for GCL + IPL and INL. The maximum discrimination value for fractal dimension of 0.96 (standard error =0.025) for the GCL + IPL complex was obtained at a FD ≤ 1.66 (cut off point, asymptotic 95% Confidence Interval: lower-upper bound = 0.905-1.002). Moreover, the highest AUROC values estimated for the thickness measurements were observed for the OPL, GCL + IPL and OS. Particularly, when comparing MDR eyes with control healthy eyes, we found that the fractal dimension of the GCL + IPL complex was significantly better at diagnosing early DR, compared to the standard thickness measurement.

CONCLUSIONS

Our results suggest that the GCL + IPL complex, OPL and OS are more susceptible to initial damage when comparing MDR with control healthy eyes. Fractal analysis provided a better sensitivity, offering a potential diagnostic predictor for detecting early neurodegeneration in the retina.

Hemoglobin is associated with retinal vascular fractals in type 1 diabetes patients

PURPOSE

Retinal vascular fractal dimension, a measure of the density of the retinal vasculature, has been suggested as a marker of systemic microvascular disorders in diabetes. As hemoglobin concentration is tightly related to vascular physiology and hypoxia, the hypothesis was that hemoglobin concentration would be associated with retinal vascular fractals in a relevant population.

METHODS

In a cross-sectional study of 204 long-term type 1 diabetes patients from a population-based cohort, retinal digital photos were captured and graded for fractal dimension (Df) by International Retinal Imaging Software - Fractal (IRIS-Fractal). Df was calculated from a disc-centered retinal photo from the right eye. Hemoglobin concentrations were measured using routine equipment.

RESULTS

Of 175 patients with gradable images, median age was 57.7 years and median duration of diabetes was 42 years. Median retinal Df was 1.4606 (inter-quartile range 0.0264). A positive correlation was found between hemoglobin concentration and retinal vascular Df (r = 0.23, p = 0.0018). In a multiple linear regression model, Df was associated with hemoglobin (coefficient 0.0054 per 1.0 mmol/L increase in hemoglobin, p = 0.01) and age (coefficient -0.0046 for each 10-year increase in age, p = 0.04).

CONCLUSION

Hemoglobin correlated independently with retinal vascular fractals indicating a relationship between hemoglobin availability and retinal vascular structure.

Automated detection of proliferative diabetic retinopathy using a modified line operator and dual classification

Proliferative diabetic retinopathy (PDR) is a condition that carries a high risk of severe visual impairment. The hallmark of PDR is neovascularisation, the growth of abnormal new vessels. This paper describes an automated method for the detection of new vessels in retinal images. Two vessel segmentation approaches are applied, using the standard line operator and a novel modified line operator. The latter is designed to reduce false responses to non-vessel edges. Both generated binary vessel maps hold vital information which must be processed separately. This is achieved with a dual classification system. Local morphology features are measured from each binary vessel map to produce two separate feature sets. Independent classification is performed for each feature set using a support vector machine (SVM) classifier. The system then combines these individual classification outcomes to produce a final decision. Sensitivity and specificity results using a dataset of 60 images are 0.862 and 0.944 respectively on a per patch basis and 1.00 and 0.90 respectively on a per image basis.

Detection of neovascularization based on fractal and texture analysis with interaction effects in diabetic retinopathy

Diabetic retinopathy is a major cause of blindness. Proliferative diabetic retinopathy is a result of severe vascular complication and is visible as neovascularization of the retina. Automatic detection of such new vessels would be useful for the severity grading of diabetic retinopathy, and it is an important part of screening process to identify those who may require immediate treatment for their diabetic retinopathy. We proposed a novel new vessels detection method including statistical texture analysis (STA), high order spectrum analysis (HOS), fractal analysis (FA), and most importantly we have shown that by incorporating their associated interactions the accuracy of new vessels detection can be greatly improved. To assess its performance, the sensitivity, specificity and accuracy (AUC) are obtained. They are 96.3%, 99.1% and 98.5% (99.3%), respectively. It is found that the proposed method can improve the accuracy of new vessels detection significantly over previous methods. The algorithm can be automated and is valuable to detect relatively severe cases of diabetic retinopathy among diabetes patients.

Automated detection of proliferative retinopathy in clinical practice

Timely intervention for diabetic retinopathy (DR) lessens the possibility of blindness and can save considerable costs to health systems. To ensure that interventions are timely and effective requires methods of screening and monitoring pathological changes, including assessing outcomes. Fractal analysis, one method that has been studied for assessing DR, is potentially relevant in today’s world of telemedicine because it provides objective indices from digital images of complex patterns such as are seen in retinal vasculature, which is affected in DR. We introduce here a protocol to distinguish between nonproliferative (NPDR) and proliferative (PDR) changes in retinal vasculature using a fractal analysis method known as local connected dimension (D_conn) analysis. The major finding is that compared to other fractal analysis methods, D_conn analysis better differentiates NPDR from PDR (p = 0.05). In addition, we are the first to show that fractal analysis can be used to differentiate between NPDR and PDR using automated vessel identification. Overall, our results suggest this protocol can complement existing methods by including an automated and objective measure obtainable at a lower level of expertise that experts can then use in screening for and monitoring DR.

Eye complications and markers of morbidity and mortality in long-term type 1 diabetes

The incidence of type 1 diabetes is rising all over the world. Furthermore, the increased life-expectancy of type 1 diabetic patients is likely to cause a higher number of diabetes-related micro- and macrovascular complications in the years to come. In order to examine the level of long-term complications in type 1 diabetes as well as potential markers of micro- and macroangiopathy, a population-based cohort of Danish type 1 diabetic patients was examined in order to achieve the following aims: 1. To evaluate diabetic retinopathy as a long-term marker of all-cause mortality in type 1 diabetes (Paper I). 2. To estimate the long-term incidence and associated risk factors of blindness (Paper II) and cataract surgery (Paper III) in type 1 diabetes. 3 To use retinal vascular analyses in order to investigate the associations of long-term micro- and macrovascular complications and retinal vascular diameters (Paper IV) and retinal fractals (Paper V) in type 1 diabetes. 4. To examine N-terminal pro brain natriuretic peptide (Paper VI) and osteoprotegerin (Paper VII) as non-invasive markers of micro- and macrovascular complications in type 1 diabetes. In Paper I it was a major finding that, despite a mean age of only 38.3 years at baseline, 44.7% of the patients died during the 25-year follow-up. Patients who had proliferative retinopathy as well as proteinuria at the baseline examination had a significantly higher mortality. For these, the 10-year survival was only 22.2%. As demonstrated in Paper II, blindness is an important issue in type 1 diabetes. The 25-year cumulative incidence of blindness was 7.5%. Glycaemic regulation and maculopathy at baseline were both identified as risk factors of blindness. Finally, mortality was higher in patients who went blind during the follow-up. Cataract surgery is quite common in type 1 diabetes. In Paper III a 25-year cumulative incidence of 20.8% was found. Adjusted for mortality, this was even higher (29.4%). As compared to patients without diabetes, cataract surgery takes place approximately 20 years earlier in type 1 diabetic patients. Age and maculopathy at baseline were both identified as predictors of cataract surgery. In Paper IV it was demonstrated that patients with retinal arteriolar narrowing were 2.17 and 3.17 times more likely to have nephropathy and macrovascular disease, respectively. This was an important finding that suggests that retinal fundus photos may be used in order to predict the risk of non-ophthalmological complications in type 1 diabetes. Retinal fractal analysis is another way to evaluate the vascular system of the retina. In Paper V we found associations between retinal fractal and microvascular - but not macrovascular--disease. For instance, patients with lower fractal dimensions were more likely to have proliferative retinopathy (OR 1.45, 95% CI 1.04-2.03) and neuropathy (OR 1.42, 95% CI 1.01-2.01). NT-proBNP is likely to be a future predictor of diabetes-related complications. In Paper VI higher levels of NT-proBNP were related to nephropathy (OR 5.03, 95% CI 1.77-14.25), neuropathy (OR 4.08, 95% CI 1.52-10.97) and macrovascular disease (OR 5.84, 95% CI 1.65-20.74). These associations should be confirmed in future prospective studies. As opposed to NT-proBNP, osteoprotegerin is less likely to be a predictor of either micro- or macrovascular disease in type 1 diabetes. As demonstrated in Paper VII, even though association between higher levels of OPG and nephropathy were found in an age- and sex-adjusted model (OR 2.54, 95% CI 1.09-5.90), this was no longer statistically significant when other factors were taken into account. Overall, it was demonstrated that various complications such as mortality, blindness and cataract surgery were high in type 1 diabetes. Furthermore, retinal arteriolar narrowing, decreased retinal fractals and plasma NT-proBNP were associated with various micro- and macrovascular complications. If confirmed by prospective studies, these modalities may be used in order to identify patients at risk of diabetes-related complications. This could, ultimately, lead to decreased mortality and morbidity in type 1 diabetic patients.

Retinal vascular fractal dimension measurement and its influence from imaging variation: results of two segmentation methods

AIM

To assess the influences of imaging variation (different photographic angle) on the measurement of retinal vascular fractal dimension (D(f)), using two segmentation methods.

MATERIALS AND METHODS

Nonlinear orthogonal projection segmentation (International Retinal Imaging Software-Fractal, termed IRIS-Fractal) and curvature-based segmentation (Singapore Institute Vessel Assessment-Fractal, termed SIVA-Fractal) methods were used to measure D(f) and were assessed for their reproducibility in detecting retinal vessels of 30 stereoscopic pairs of optic disc color images. Each pair was taken from the same eye with slightly different angles of incidence. Each photograph of the pairs had subtle variations in brightness between areas temporal and nasal to the optic disc.

RESULTS

Intragrader reproducibility of D(f) measurement was similar (intraclass correlation 0.81 and 0.96, respectively) for IRIS-Fractal and SIVA-Fractal. Within-image pair Pearson's correlation coefficients (r) of D(f) measurements were moderate for both methods (0.57 and 0.48, respectively).

CONCLUSIONS

Both nonlinear orthogonal projection and curvature-based retinal vessel segmentation methods were found to be sensitive to variations in image brightness, resulting from iris shadowing associated with different angle of photographic incidence.

Lens opacity and refractive influences on the measurement of retinal vascular fractal dimension

PURPOSE

To examine the influence of lens opacity and refraction on the measurement of retinal vascular fractal dimension (Df).

METHODS

  Optic disc photographs (right eyes) of 3654 baseline Blue Mountains Eye Study participants (aged 49-97) were digitized. Retinal vascular Df was quantified using a computer-based program. Summated severity scores for nuclear, cortical and posterior subcapsular (PSC) cataract were assessed from lens photographs. Refraction data were converted to spherical equivalent refraction (SER), as sum spherical plus 0.5 cylinder power. Axial length was measured at 10-year follow-up examinations using an IOL master.

RESULTS

  Mean Df of the retinal vasculature was 1.444±0.023 for 2859 eligible participants. Increasing lens opacity scores were associated with significant reduction in Df (β=-0.0030, p<0.0001). Both cortical and PSC cataract involving central lens area were associated with reduced Df, after controlling for confounding factors (p(trend) ≤0.0105). Increasing myopia severity was associated with reduced Df after adjusting for lens opacity scores and other confounders (p(trend) <0.0001). The slope of Df decrease per SER reduction was 0.0040 in eyes with SER≤-4D, compared to -0.0016 in eyes with SER>-4D. For axial length quintiles, there were no significant differences in mean Df in all groups except a reduction in the fifth quintile (axial length ≥24.15mm) (all p<0.05).

CONCLUSION

  Ocular media opacity independently influenced retinal vascular Df measurement, but we found no evidence supporting any refractive axial magnification effect on this measure. Myopic refraction ≤-4D was associated with a reduction in Df, suggesting rarefaction of retinal vasculature associated with high myopia.

Retinal vascular fractal dimension and risk of early diabetic retinopathy: A prospective study of children and adolescents with type 1 diabetes

OBJECTIVE

To examine the prospective association of retinal vascular fractal dimension with diabetic retinopathy risk in young people with type 1 diabetes.

RESEARCH DESIGN AND METHODS

This was a hospital-based prospective study of 590 patients aged 12-20 years with type 1 diabetes free of retinopathy at baseline. All patients had seven-field retinal photographs taken of both eyes. Incident retinopathy was ascertained from retinal photographs taken at follow-up visits. Fractal dimension was measured from baseline photographs using a computer-based program following a standardized protocol.

RESULTS

Over a mean +/- SD follow-up period of 2.9 +/- 2.0 years, 262 participants developed mild nonproliferative diabetic retinopathy (15.0 per 100 person-years). After adjusting for age, sex, diabetes duration, A1C, and other risk factors, we found no association between retinal vascular fractal dimension and incident retinopathy.

CONCLUSIONS

Retinal vascular fractal dimension was not associated with incident early diabetic retinopathy in this sample of children and adolescents with type 1 diabetes.

Quantitative assessment of early diabetic retinopathy using fractal analysis

OBJECTIVE

Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes.

RESEARCH DESIGN AND METHODS

We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol.

RESULTS

In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber.

CONCLUSIONS

Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

Fractal analysis of the retinal vascular network in fundus images

Complexity of the retinal vascular network is quantified through the measurement of fractal dimension. A computerized approach enhances and segments the retinal vasculature in digital fundus images with an accuracy of 94% in comparison to the gold standard of manual tracing. Fractal analysis was performed on skeletonized versions of the network in 40 images from a study of stroke. Mean fractal dimension was found to be 1.398 (with standard deviation 0.024) from 20 images of the hypertensives sub-group and 1.408 (with standard deviation 0.025) from 18 images of the non-hypertensives subgroup. No evidence of a significant difference in the results was found for this sample size. However, statistical analysis showed that to detect a significant difference at the level seen in the data would require a larger sample size of 88 per group.

A reliability study of fractal analysis of the skeletonised vascular network using the "box-counting" technique

Binary vascular networks of the human retina were obtained by computerized processing of digital fundus images. Fractal analysis was performed on skeletonised versions. The effect of three parameters in the vascular segmentation and skeletonization algorithm was quantified, with threshold level found to have the greatest influence. The results were compared to fractal analysis of skeletons derived by manual tracing. The mean difference in fractal dimension between 2 observers is 0.004 (0.3%) and the coefficient of repeatability is +/- 0.050 (3.4%). Between a single observer and the computerized approach the mean difference is 0.012 (0.8%) and the coefficient is +/- 0.038 (2.6%). The computerized approach demonstrated a superior reliability compared to manual segmentation.

Fractal-based automatic localization and segmentation of optic disc in retinal images

In this paper, we proposed a novel algorithm to detect optic disc location in retinal images. Optic disc is a bright disk area and all major blood vessels and nerves originate from it. With its high fractal dimension of blood vessel, optic disc can be easily differentiated from other bright regions such as hard exudates and artifacts. Compared with existing algorithms, ours has much lower computational cost and is more robust. With its location known, segmentation of optic disc can be done with simple local histogram analysis. The algorithm can be valuable for automated processing for early stage retinal disease.

Fractal and Fourier analysis of the hepatic sinusoidal network in normal and cirrhotic rat liver

The organization of the hepatic microvascular network has been widely studied in recent years, especially with regard to cirrhosis. This research has enabled us to recognize the distinctive vascular patterns in the cirrhotic liver, compared with the normal liver, which may explain the cause of liver dysfunction and failure. The aim of this study was to compare normal and cirrhotic rat livers by means of a quantitative mathematical approach based on fractal and Fourier analyses performed on photomicrographs and therefore on discriminant analysis. Vascular corrosion casts of livers belonging to the following three experimental groups were studied by scanning electron microscopy: normal rats, CCl(4)-induced cirrhotic rats and cirrhotic rats after ligation of the bile duct. Photomicrographs were taken at a standard magnification; these images were used for the mathematical analysis. Our experimental design found that use of these different analyses reaches an efficiency of over 94%. Our analyses demonstrated a higher complexity of the normal hepatic sinusoidal network in comparison with the cirrhotic network. In particular, the morphological changes were more marked in the animals with bile duct-ligation cirrhosis compared with animals with CCl(4)-induced cirrhosis. The present findings based on fractal and Fourier analysis could increase our understanding of the pathophysiological alterations of the liver, and may have a diagnostic value in future clinical research.

Retinal image analysis: concepts, applications and potential

As digital imaging and computing power increasingly develop, so too does the potential to use these technologies in ophthalmology. Image processing, analysis and computer vision techniques are increasing in prominence in all fields of medical science, and are especially pertinent to modern ophthalmology, as it is heavily dependent on visually oriented signs. The retinal microvasculature is unique in that it is the only part of the human circulation that can be directly visualised non-invasively in vivo, readily photographed and subject to digital image analysis. Exciting developments in image processing relevant to ophthalmology over the past 15 years includes the progress being made towards developing automated diagnostic systems for conditions, such as diabetic retinopathy, age-related macular degeneration and retinopathy of prematurity. These diagnostic systems offer the potential to be used in large-scale screening programs, with the potential for significant resource savings, as well as being free from observer bias and fatigue. In addition, quantitative measurements of retinal vascular topography using digital image analysis from retinal photography have been used as research tools to better understand the relationship between the retinal microvasculature and cardiovascular disease. Furthermore, advances in electronic media transmission increase the relevance of using image processing in 'teleophthalmology' as an aid in clinical decision-making, with particular relevance to large rural-based communities. In this review, we outline the principles upon which retinal digital image analysis is based. We discuss current techniques used to automatically detect landmark features of the fundus, such as the optic disc, fovea and blood vessels. We review the use of image analysis in the automated diagnosis of pathology (with particular reference to diabetic retinopathy). We also review its role in defining and performing quantitative measurements of vascular topography, how these entities are based on 'optimisation' principles and how they have helped to describe the relationship between systemic cardiovascular disease and retinal vascular changes. We also review the potential future use of fundal image analysis in telemedicine.

Optic nerve head segmentation

Reliable and efficient optic disk localization and segmentation are important tasks in automated retinal screening. General-purpose edge detection algorithms often fail to segment the optic disk due to fuzzy boundaries, inconsistent image contrast or missing edge features. This paper presents an algorithm for the localization and segmentation of the optic nerve head boundary in low-resolution images (about 20 microns/pixel). Optic disk localization is achieved using specialized template matching, and segmentation by a deformable contour model. The latter uses a global elliptical model and a local deformable model with variable edge-strength dependent stiffness. The algorithm is evaluated against a randomly selected database of 100 images from a diabetic screening programme. Ten images were classified as unusable; the others were of variable quality. The localization algorithm succeeded on all bar one usable image; the contour estimation algorithm was qualitatively assessed by an ophthalmologist as having Excellent-Fair performance in 83% of cases, and performs well even on blurred images.

Progress towards automated diabetic ocular screening: a review of image analysis and intelligent systems for diabetic retinopathy

Patients with diabetes require annual screening for effective timing of sight-saving treatment. However, the lack of screening and the shortage of ophthalmologists limit the ocular health care available. This is stimulating research into automated analysis of the reflectance images of the ocular fundus. Publications applicable to the automated screening of diabetic retinopathy are summarised. The review has been structured to mimic some of the processes that an ophthalmologist performs when examining the retina. Thus image processing tasks, such as vessel and lesion location, are reviewed before any intelligent or automated systems. Most research has been undertaken in identification of the retinal vasculature and analysis of early pathological changes. Progress has been made in the identification of the retinal vasculature and the more common pathological features, such as small aneurysms and exudates. Ancillary research into image preprocessing has also been identified. In summary, the advent of digital data sets has made image analysis more accessible, although questions regarding the assessment of individual algorithms and whole systems are only just being addressed.

Is fractal geometry useful in medicine and biomedical sciences?

Fractal geometry has become very useful in the understanding of many phenomena in various fields such as astrophysics, economy or agriculture and recently in medicine. After a brief intuitive introduction to the basis of fractal geometry, the clue is made about the correlation between Df and the complexity or the irregularity of a structure. However, fractal analysis must be applied with certain caution in natural objects such as bio-medical ones. The cardio-vascular system remains one of the most important fields of application of these kinds of approach. Spectral analysis of the R-R interval, morphology of the distal coronary arteries constitute two examples. Other very interesting applications are founded in bacteriology, medical imaging or ophthalmology. In our institution, we apply fractal analysis in order to quantitate angiogenesis and other vascular processes.

Fractals in pathology

Many natural objects, including most objects studied in pathology, have complex structural characteristics and the complexity of their structures, for example the degree of branching of vessels or the irregularity of a tumour boundary, remains at a constant level over a wide range of magnifications. These structures also have patterns that repeat themselves at different magnifications, a property known as scaling self-similarity. This has important implications for measurement of parameters such as length and area, since Euclidean measurements of these may be invalid. The fractal system of geometry overcomes the limitations of the Euclidean geometry for such objects and measurement of the fractal dimension gives an index of their space-filling properties. The fractal dimension may be measured using image analysis systems and the box-counting, divider (perimeter-stepping) and pixel dilation methods have all been described in the published literature. Fractal analysis has found applications in the detection of coding of coding regions in DNA and measurement of the space-filling properties of tumours, blood vessels and neurones. Fractal concepts have also been usefully incorporated into models of biological processes, including epithelial cell growth, blood vessel growth, periodontal disease and viral infections.

Corneal vascularisation and its relation to the physical properties of the tissue: a fractal analysis

Various pathological conditions may cause vascularisation of the normally avascular and transparent cornea. The purpose of this study was to investigate the fractal geometry of corneal vascularisation and relate it to different growth models which may have implications for the understanding of fundamental processes involved in vasculogenesis. Photographs of 12 cases of severe superficial corneal vascularisation were obtained from accidentally alkali burned eyes long after the acute inflammatory reaction was over. The fractal dimension of these vessel patterns was calculated by means of the density-density-correlation function method to be D = 1.893 +/- 0.044 (m +/- sd) (n = 12). It is in excellent agreement with percolation models. The results suggest the importance of the surface characteristics of the invading cells as well as that of the extracellular matrix and the related interaction between them.

Mechanisms in retinal vasculogenesis: an analysis of the spatial branching site correlation

Starting from fractal dimension calculations of retinal vessel patterns, different growth models and related mechanisms have been suggested to simulate retinal vasculogenesis. A comprehensive view of this topic does not exist. In order to elucidate this question the spatial correlation of the vessel branching sites of the embryonic vessel pattern has been studied. During development of the retinal vasculature within the nerve fiber layer a modification of the branching characteristics can be observed. This result supports theories which suggest a close relation between the vessel propagation and the structure and surface characteristics of the invading vascular cells and the retinal tissue. Arterio-venous differentiation, however, may be dominated by diffusion processes.