Evaluating Descriptive Metrics of the Human Cone Mosaic

Purpose: To evaluate how metrics used to describe the cone mosaic change in response to simulated photoreceptor undersampling (i.e., cell loss or misidentification). Methods: Using an adaptive optics ophthalmoscope, we acquired images of the cone mosaic from the center of fixation to 10° along the temporal, superior, inferior, and nasal meridians in 20 healthy subjects. Regions of interest (n = 1780) were extracted at regular intervals along each meridian. Cone mosaic geometry was assessed using a variety of metrics − density, density recovery profile distance (DRPD), nearest neighbor distance (NND), intercell distance (ICD), farthest neighbor distance (FND), percentage of six-sided Voronoi cells, nearest neighbor regularity (NNR), number of neighbors regularity (NoNR), and Voronoi cell area regularity (VCAR). The “performance” of each metric was evaluated by determining the level of simulated loss necessary to obtain 80% statistical power. Results: Of the metrics assessed, NND and DRPD were the least sensitive to undersampling, classifying mosaics that lost 50% of their coordinates as indistinguishable from normal. The NoNR was the most sensitive, detecting a significant deviation from normal with only a 10% cell loss. Conclusions: The robustness of cone spacing metrics makes them unsuitable for reliably detecting small deviations from normal or for tracking small changes in the mosaic over time. In contrast, regularity metrics are more sensitive to diffuse loss and, therefore, better suited for detecting such changes, provided the fraction of misidentified cells is minimal. Combining metrics with a variety of sensitivities may provide a more complete picture of the integrity of the photoreceptor mosaic

Repeatability of \u3cem\u3eIn Vivo\u3c/em\u3e Parafoveal Cone Density and Spacing Measurements

Purpose. To assess the repeatability and measurement error associated with cone density and nearest neighbor distance (NND) estimates in images of the parafoveal cone mosaic obtained with an adaptive optics scanning light ophthalmoscope (AOSLO).Methods. Twenty-one participants with no known ocular pathology were recruited. Four retinal locations, approximately 0.65[degrees] eccentricity from the center of fixation, were imaged 10 times in randomized order with an AOSLO. Cone coordinates in each image were identified using an automated algorithm (with or without manual correction) from which cone density and NND were calculated. Owing to naturally occurring fixational instability, the 10 images recorded from a given location did not overlap entirely. We thus analyzed each image set both before and after alignment.Results. Automated estimates of cone density on the unaligned image sets showed a coefficient of repeatability of 11,769 cones/mm2 (17.1%). The primary reason for this variability appears to be fixational instability, as aligning the 10 images to include the exact same retinal area results in an improved repeatability of 4358 cones/mm2 (6.4%) using completely automated cone identification software. Repeatability improved further by manually identifying cones missed by the automated algorithm, with a coefficient of repeatability of 1967 cones/mm2 (2.7%). NND showed improved repeatability and was generally insensitive to the undersampling by the automated algorithm.Conclusions. As our data were collected in a young, healthy population, this likely represents a best-case estimate for corresponding measurements in patients with retinal disease. Similar studies need to be carried out on other imaging systems (including those using different imaging modalities, wavefront correction technology, and/or image analysis software), as repeatability would be expected to be highly sensitive to initial image quality and the performance of cone identification algorithms. Separate studies addressing intersession repeatability and interobserver reliability are also needed

Open Source Software for Automatic Detection of Cone Photoreceptors in Adaptive Optics Ophthalmoscopy Using Convolutional Neural Networks

Imaging with an adaptive optics scanning light ophthalmoscope (AOSLO) enables direct visualization of the cone photoreceptor mosaic in the living human retina. Quantitative analysis of AOSLO images typically requires manual grading, which is time consuming, and subjective; thus, automated algorithms are highly desirable. Previously developed automated methods are often reliant on ad hoc rules that may not be transferable between different imaging modalities or retinal locations. In this work, we present a convolutional neural network (CNN) based method for cone detection that learns features of interest directly from training data. This cone-identifying algorithm was trained and validated on separate data sets of confocal and split detector AOSLO images with results showing performance that closely mimics the gold standard manual process. Further, without any need for algorithmic modifications for a specific AOSLO imaging system, our fully-automated multi-modality CNN-based cone detection method resulted in comparable results to previous automatic cone segmentation methods which utilized ad hoc rules for different applications. We have made free open-source software for the proposed method and the corresponding training and testing datasets available online

Chaos in Time Dependent Variational Approximations to Quantum Dynamics

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large N (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos correcte

Automatic Detection of Cone Photoreceptors In Split Detector Adaptive Optics Scanning Light Ophthalmoscope Images

Quantitative analysis of the cone photoreceptor mosaic in the living retina is potentially useful for early diagnosis and prognosis of many ocular diseases. Non-confocal split detector based adaptive optics scanning light ophthalmoscope (AOSLO) imaging reveals the cone photoreceptor inner segment mosaics often not visualized on confocal AOSLO imaging. Despite recent advances in automated cone segmentation algorithms for confocal AOSLO imagery, quantitative analysis of split detector AOSLO images is currently a time-consuming manual process. In this paper, we present the fully automatic adaptive filtering and local detection (AFLD) method for detecting cones in split detector AOSLO images. We validated our algorithm on 80 images from 10 subjects, showing an overall mean Dice’s coefficient of 0.95 (standard deviation 0.03), when comparing our AFLD algorithm to an expert grader. This is comparable to the inter-observer Dice’s coefficient of 0.94 (standard deviation 0.04). To the best of our knowledge, this is the first validated, fully-automated segmentation method which has been applied to split detector AOSLO images

Evaluating Outer Segment Length as A Surrogate Measure of Peak Foveal Cone Density

Adaptive optics (AO) imaging tools enable direct visualization of the cone photoreceptor mosaic, which facilitates quantitative measurements such as cone density. However, in many individuals, low image quality or excessive eye movements precludes making such measures. As foveal cone specialization is associated with both increased density and outer segment (OS) elongation, we sought to examine whether OS length could be used as a surrogate measure of foveal cone density. The retinas of 43 subjects (23 normal and 20 albinism; aged 6–67 years) were examined. Peak foveal cone density was measured using confocal adaptive optics scanning light ophthalmoscopy (AOSLO), and OS length was measured using optical coherence tomography (OCT) and longitudinal reflectivity profile-based approach. Peak cone density ranged from 29,200 to 214,000 cones/mm2(111,700 ± 46,300 cones/mm2); OS length ranged from 26.3 to 54.5 μm (40.5 ± 7.7 μm). Density was significantly correlated with OS length in albinism (p \u3c 0.0001), but not normals (p = 0.99). A cubic model of density as a function of OS length was created based on histology and optimized to fit the albinism data. The model includes triangular cone packing, a cylindrical OS with a fixed volume of 136.6 μm3, and a ratio of OS to inner segment width that increased linearly with increasing OS length (R2 = 0.72). Normal subjects showed no apparent relationship between cone density and OS length. In the absence of adequate AOSLO imagery, OS length may be used to estimate cone density in patients with albinism. Whether this relationship exists in other patient populations with foveal hypoplasia (e.g., premature birth, aniridia, isolated foveal hypoplasia) remains to be seen

Assessing the Spatial Relationship Between Fixation and Foveal Specializations

Increased cone photoreceptor density, an avascular zone (FAZ), and the displacement of inner retinal neurons to form a pit are distinct features of the human fovea. As the fovea provides the majority of our vision, appreciating how these anatomical specializations are related is important for understanding foveal development, normal visual function, and retinal disease. Here we evaluated the relationship between these specializations and their location relative to the preferred retinal locus of fixation (PRL). We measured foveal pit volume, FAZ area, peak cone density, and location of the PRL in 22 subjects with normal vision using optical coherence tomography and adaptive optics scanning light ophthalmoscopy. Foveal pit volume was positively correlated with FAZ area; however, peak cone density was not correlated with pit volume. In addition, there was no systematic offset of the location of any of these specializations relative to PRL, and there was no correlation between the magnitude of the offset from PRL and the corresponding foveal specialization measurements (pit volume, FAZ area, peak cone density). The standard deviation of our PRL measurements was consistent with previous measurements of fixational stability. These data provide insight into the sequence of events during foveal development and may have implications for visual function and retinal disease

Relationship Between the Foveal Avascular Zone and Foveal Pit Morphology

Purpose.To assess the relationship between foveal pit morphology and size of the foveal avascular zone (FAZ). Methods. Forty-two subjects were recruited. Volumetric images of the macula were obtained using spectral domain optical coherence tomography. Images of the FAZ were obtained using either a modified fundus camera or an adaptive optics scanning light ophthalmoscope. Foveal pit metrics (depth, diameter, slope, volume, and area) were automatically extracted from retinal thickness data, whereas the FAZ was manually segmented by two observers to extract estimates of FAZ diameter and area. Results. Consistent with previous reports, the authors observed significant variation in foveal pit morphology. The average foveal pit volume was 0.081 mm3 (range, 0.022 to 0.190 mm3). The size of the FAZ was also highly variable between persons, with FAZ area ranging from 0.05 to 1.05 mm2 and FAZ diameter ranging from 0.20 to 1.08 mm. FAZ area was significantly correlated with foveal pit area, depth, and volume; deeper and broader foveal pits were associated with larger FAZs. Conclusions. Although these results are consistent with predictions from existing models of foveal development, more work is needed to confirm the developmental link between the size of the FAZ and the degree of foveal pit excavation. In addition, more work is needed to understand the relationship between these and other anatomic features of the human foveal region, including peak cone density, rod-free zone diameter, and Henle fiber layer

Subclinical Photoreceptor Disruption in Response to Severe Head Trauma

Commotio retinae is a transient opacification of the retina due to outer retinal disruption occurring in a contrecoup fashion after blunt trauma.Histological studies in animals and humans after ocular blunt trauma have revealed that disruption occurs at the level of the photoreceptor outer segments and retinal pigment epithelium.Recent reports using optical coherence tomography (OCT) have shown detectable disruption at the level of the photoreceptor inner segment/outer segment junction and retinal pigment epithelium and that these changes may be reversible over time with restoration of normal outer retinal architecture.However, the resolution of existing OCT technology may not be sensitive enough to detect photoreceptor disruption. Adaptive optics (AO) imaging systems enable cellular-resolution imaging of the human retina, and there is a growing number of cases where deficits have been visible on AO images but not on OCT. Herein, we report a case of subclinical photoreceptor disruption after head trauma as seen by an AO scanning ophthalmoscope (AOSO) but not apparent clinically or on spectral-domain OCT (SD-OCT)

Resumming the large-N approximation for time evolving quantum systems

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is $L(x,\dot{x}) = (1/2) \sum_{i=1}^{N} \dot{x}_i^2 - (g/8N) [ \sum_{i=1}^{N} x_i^2 - r_0^2 ]^{2}$. The key to these approximations is to treat both the $x$ propagator and the $x^2$ propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the $x^2$ propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact $x^2$ propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest $N$ better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are separately liste