Multifractal nature of ocular aberration dynamics of the human eye

The random walk of accommodation fluctuations

The focusing distance of the eye fluctuates during accommodation. However, the visual role of these accommodation fluctuations is not yet fully understood. The fluctuation complexity is one of the obstacles to this long standing challenge in visual science. In this work we seek to develop a statistical approach that i) accurately describes experimental measurements and ii) directly generates randomized and realistic simulations of accommodation fluctuations for use in future experiments. To do so we use the random walk approach, which is usually appropriate to describe the dynamics of systems that combine both randomness and memory.

High temporal resolution aberrometry in a 50-eye population and implications for adaptive optics error budget

We formed a database gathering the wavefront aberrations of 50 healthy eyes measured with an original custom-built Shack-Hartmann aberrometer at a temporal frequency of 236 Hz, with 22 lenslets across a 7-mm diameter pupil, for a duration of 20 s. With this database, we draw statistics on the spatial and temporal behavior of the dynamic aberrations of the eye. Dynamic aberrations were studied on a 5-mm diameter pupil and on a 3.4 s sequence between blinks. We noted that, on average, temporal wavefront variance exhibits a n^-2 power-law with radial order n and temporal spectra follow a f^-1.5 power-law with temporal frequency f. From these statistics, we then extract guidelines for designing an adaptive optics system. For instance, we show the residual wavefront error evolution as a function of the number of corrected modes and of the adaptive optics loop frame rate. In particular, we infer that adaptive optics performance rapidly increases with the loop frequency up to 50 Hz, with gain being more limited at higher rates.

Evaluation of the training objectives with surface electromyography

In this work, the multifractal analysis of the kinesiological surface electromyographic signal is proposed. The goal was to investigate the level of neuromuscular activation during complex movements on the laparoscopic trainer. The basic issue of this work concerns the changes observed in the signal obtained from the complete beginner in the field of using laparoscopic tools and the same person subjected to the series of training. To quantify the complexity of the kinesiological surface electromyography, the nonlinear analysis technique, namely, the multifractal detrended fluctuation analysis, was adopted. The analysis was based on the parameters describing the multifractal spectrum – the Hurst exponent – and the spectrum width. The statistically significant differences for a selected group of muscles at the different states (before and after training) are presented. In addition, as the base case, the relaxation state was considered and compared with the working states.

Multifractal analysis for nutritional assessment

The concept of multifractality is currently used to describe self-similar and complex scaling properties observed in numerous biological signals. Fractals are geometric objects or dynamic variations which exhibit some degree of similarity (irregularity) to the original object in a wide range of scales. This approach determines irregularity of biologic signal as an indicator of adaptability, the capability to respond to unpredictable stress, and health. In the present work, we propose the application of multifractal analysis of wavelet-transformed proton nuclear magnetic resonance (¹H NMR) spectra of plasma to determine nutritional insufficiency. For validation of this method on ¹H NMR signal of human plasma, standard deviation from classical statistical approach and Hurst exponent (H), left slope and partition function from multifractal analysis were extracted from ¹H NMR spectra to test whether multifractal indices could discriminate healthy subjects from unhealthy, intensive care unit patients. After validation, the multifractal approach was applied to spectra of plasma from a modified crossover study of sulfur amino acid insufficiency and tested for associations with blood lipids. The results showed that standard deviation and H, but not left slope, were significantly different for sulfur amino acid sufficiency and insufficiency. Quadratic discriminant analysis of H, left slope and the partition function showed 78% overall classification accuracy according to sulfur amino acid status. Triglycerides and apolipoprotein C3 were significantly correlated with a multifractal model containing H, left slope, and standard deviation, and cholesterol and high-sensitivity C-reactive protein were significantly correlated to H. In conclusion, multifractal analysis of ¹H NMR spectra provides a new approach to characterize nutritional status.

Chaos in ocular aberration dynamics of the human eye

Since the characterization of the eye's monochromatic aberration fluctuations in 2001, the power spectrum has remained the most widely used method for analyzing their dynamics. However, the power spectrum does not capture the complexities of the fluctuations. We measured the monochromatic aberration dynamics of six subjects using a Shack-Hartmann sensor sampling at 21 Hz. We characterized the dynamics using techniques from chaos theory. We found that the attractor embedding dimension for all aberrations, for all subjects, was equal to three. The embedding lag averaged across aberrations and subjects was 0.31 ± 0.07 s. The Lyapunov exponent of the rms wavefront error was positive for each subject, with an average value of 0.44 ± 0.15 µm/s. This indicates that the aberration dynamics are chaotic. Implications for future modeling are discussed.

Adaptive optics with pupil tracking for high resolution retinal imaging

Adaptive optics, when integrated into retinal imaging systems, compensates for rapidly changing ocular aberrations in real time and results in improved high resolution images that reveal the photoreceptor mosaic. Imaging the retina at high resolution has numerous potential medical applications, and yet for the development of commercial products that can be used in the clinic, the complexity and high cost of the present research systems have to be addressed. We present a new method to control the deformable mirror in real time based on pupil tracking measurements which uses the default camera for the alignment of the eye in the retinal imaging system and requires no extra cost or hardware. We also present the first experiments done with a compact adaptive optics flood illumination fundus camera where it was possible to compensate for the higher order aberrations of a moving model eye and in vivo in real time based on pupil tracking measurements, without the real time contribution of a wavefront sensor. As an outcome of this research, we showed that pupil tracking can be effectively used as a low cost and practical adaptive optics tool for high resolution retinal imaging because eye movements constitute an important part of the ocular wavefront dynamics.