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

Dynamical Properties and Chaos Synchronization in a Fractional-Order Two-Stage Colpitts Oscillator

In this paper, the dynamics and synchronization of a fractional-order four dimensional nonlinear system based on a twostage Colpitts oscillator is investigated, using the Grünwald-Letnikov method. The study of the fractional-order stability of the equilibrium states of the system is carried out. The bifurcation diagram confirms the occurrence of Hopf bifurcation in the proposed system when the fractional-order passes a sequence of critical values, and reveals in addition various bifurcation scenarios including period-doubling and interior crisis transitions to chaos. In order to promote chaos-based fractional-order synchronization of this type of oscillators, a synchronization strategy based upon the design of a nonlinear state observer is successfully adapted. Numerical simulations are performed to demonstrate the effectiveness and applicability of the proposed technique