Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.

PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.

Correcting the errors: Volatility forecast evaluation using high-frequency data and realized volatilities

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit recent nonparametric asymptotic distributional results, are both easy-to-implement and highly accurate in empirically realistic situations. We also illustrate that properly accounting for the measurement errors in the volatility forecast evaluations reported in the existing literature can result in markedly higher estimates for the true degree of return volatility predictability.

Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry.

We present an analytical method that yields the real and imaginary parts of the refractive index (RI) from low-coherence interferometry measurements, leading to the separation of the scattering and absorption coefficients of turbid samples. The imaginary RI is measured using time-frequency analysis, with the real part obtained by analyzing the nonlinear phase induced by a sample. A derivation relating the real part of the RI to the nonlinear phase term of the signal is presented, along with measurements from scattering and nonscattering samples that exhibit absorption due to hemoglobin.

Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition.

In this paper, we propose generalized sampling approaches for measuring a multi-dimensional object using a compact compound-eye imaging system called thin observation module by bound optics (TOMBO). This paper shows the proposed system model, physical examples, and simulations to verify TOMBO imaging using generalized sampling. In the system, an object is modulated and multiplied by a weight distribution with physical coding, and the coded optical signal is integrated on to a detector array. A numerical estimation algorithm employing a sparsity constraint is used for object reconstruction.

Measurements of nonlinear refractive index in scattering media.

We have recently developed a spectral re-shaping technique to simultaneously measure nonlinear refractive index and nonlinear absorption. In this technique, the information about the nonlinearities is encoded in the frequency domain, rather than in the spatial domain as in the conventional Z-scan method. Here we show that frequency encoding is much more robust with respect to scattering. We compare spectral re-shaping and Z-scan measurements in a highly scattering environment and show that reliable spectral re-shaping measurements can be performed even in a regime that precludes standard Z-scans.

Enhancing imaging systems using transformation optics.

We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.

Division of labor in frontal eye field neurons during presaccadic remapping of visual receptive fields.

Our percept of visual stability across saccadic eye movements may be mediated by presaccadic remapping. Just before a saccade, neurons that remap become visually responsive at a future field (FF), which anticipates the saccade vector. Hence, the neurons use corollary discharge of saccades. Many of the neurons also decrease their response at the receptive field (RF). Presaccadic remapping occurs in several brain areas including the frontal eye field (FEF), which receives corollary discharge of saccades in its layer IV from a collicular-thalamic pathway. We studied, at two levels, the microcircuitry of remapping in the FEF. At the laminar level, we compared remapping between layers IV and V. At the cellular level, we compared remapping between different neuron types of layer IV. In the FEF in four monkeys (Macaca mulatta), we identified 27 layer IV neurons with orthodromic stimulation and 57 layer V neurons with antidromic stimulation from the superior colliculus. With the use of established criteria, we classified the layer IV neurons as putative excitatory (n = 11), putative inhibitory (n = 12), or ambiguous (n = 4). We found that just before a saccade, putative excitatory neurons increased their visual response at the RF, putative inhibitory neurons showed no change, and ambiguous neurons increased their visual response at the FF. None of the neurons showed presaccadic visual changes at both RF and FF. In contrast, neurons in layer V showed full remapping (at both the RF and FF). Our data suggest that elemental signals for remapping are distributed across neuron types in early cortical processing and combined in later stages of cortical microcircuitry.

Frontal eye field neurons assess visual stability across saccades.

The image on the retina may move because the eyes move, or because something in the visual scene moves. The brain is not fooled by this ambiguity. Even as we make saccades, we are able to detect whether visual objects remain stable or move. Here we test whether this ability to assess visual stability across saccades is present at the single-neuron level in the frontal eye field (FEF), an area that receives both visual input and information about imminent saccades. Our hypothesis was that neurons in the FEF report whether a visual stimulus remains stable or moves as a saccade is made. Monkeys made saccades in the presence of a visual stimulus outside of the receptive field. In some trials, the stimulus remained stable, but in other trials, it moved during the saccade. In every trial, the stimulus occupied the center of the receptive field after the saccade, thus evoking a reafferent visual response. We found that many FEF neurons signaled, in the strength and timing of their reafferent response, whether the stimulus had remained stable or moved. Reafferent responses were tuned for the amount of stimulus translation, and, in accordance with human psychophysics, tuning was better (more prevalent, stronger, and quicker) for stimuli that moved perpendicular, rather than parallel, to the saccade. Tuning was sometimes present as well for nonspatial transaccadic changes (in color, size, or both). Our results indicate that FEF neurons evaluate visual stability during saccades and may be general purpose detectors of transaccadic visual change.

Exploring the role of the substantia nigra pars reticulata in eye movements.

Experiments that demonstrated a role for the substantia nigra in eye movements have played an important role in our understanding of the function of the basal ganglia in behavior more broadly. In this review we explore more recent experiments that extend the role of the substantia nigra pars reticulata from a simple gate for eye movements to include a role in cognitive processes for eye movements. We review recent evidence suggesting that basal ganglia nuclei beyond the substantia nigra may also play a role in eye movements and the cognitive events leading up to the production of eye movements. We close by pointing out some unresolved questions in our understanding of the relationship of basal ganglia nuclei and eye movements.

The Rational Adolescent: Strategic Information Processing during Decision Making Revealed by Eye Tracking.

Adolescence is often viewed as a time of irrational, risky decision-making - despite adolescents' competence in other cognitive domains. In this study, we examined the strategies used by adolescents (N=30) and young adults (N=47) to resolve complex, multi-outcome economic gambles. Compared to adults, adolescents were more likely to make conservative, loss-minimizing choices consistent with economic models. Eye-tracking data showed that prior to decisions, adolescents acquired more information in a more thorough manner; that is, they engaged in a more analytic processing strategy indicative of trade-offs between decision variables. In contrast, young adults' decisions were more consistent with heuristics that simplified the decision problem, at the expense of analytic precision. Collectively, these results demonstrate a counter-intuitive developmental transition in economic decision making: adolescents' decisions are more consistent with rational-choice models, while young adults more readily engage task-appropriate heuristics.

Dynamics of visual receptive fields in the macaque frontal eye field.

Neuronal receptive fields (RFs) provide the foundation for understanding systems-level sensory processing. In early visual areas, investigators have mapped RFs in detail using stochastic stimuli and sophisticated analytical approaches. Much less is known about RFs in prefrontal cortex. Visual stimuli used for mapping RFs in prefrontal cortex tend to cover a small range of spatial and temporal parameters, making it difficult to understand their role in visual processing. To address these shortcomings, we implemented a generalized linear model to measure the RFs of neurons in the macaque frontal eye field (FEF) in response to sparse, full-field stimuli. Our high-resolution, probabilistic approach tracked the evolution of RFs during passive fixation, and we validated our results against conventional measures. We found that FEF neurons exhibited a surprising level of sensitivity to stimuli presented as briefly as 10 ms or to multiple dots presented simultaneously, suggesting that FEF visual responses are more precise than previously appreciated. FEF RF spatial structures were largely maintained over time and between stimulus conditions. Our results demonstrate that the application of probabilistic RF mapping to FEF and similar association areas is an important tool for clarifying the neuronal mechanisms of cognition.

Similar prevalence and magnitude of auditory-evoked and visually evoked activity in the frontal eye fields: implications for multisensory motor control.

Saccadic eye movements can be elicited by more than one type of sensory stimulus. This implies substantial transformations of signals originating in different sense organs as they reach a common motor output pathway. In this study, we compared the prevalence and magnitude of auditory- and visually evoked activity in a structure implicated in oculomotor processing, the primate frontal eye fields (FEF). We recorded from 324 single neurons while 2 monkeys performed delayed saccades to visual or auditory targets. We found that 64% of FEF neurons were active on presentation of auditory targets and 87% were active during auditory-guided saccades, compared with 75 and 84% for visual targets and saccades. As saccade onset approached, the average level of population activity in the FEF became indistinguishable on visual and auditory trials. FEF activity was better correlated with the movement vector than with the target location for both modalities. In summary, the large proportion of auditory-responsive neurons in the FEF, the similarity between visual and auditory activity levels at the time of the saccade, and the strong correlation between the activity and the saccade vector suggest that auditory signals undergo tailoring to match roughly the strength of visual signals present in the FEF, facilitating accessing of a common motor output pathway.

A subcortical source of visual input to the frontal eye field

Many neurons in the frontal eye field (FEF) exhibit visual responses and are thought to play important roles in visuosaccadic behavior. The FEF, however, is far removed from striate cortex. Where do the FEF's visual signals come from? Usually they are reasonably assumed to enter the FEF through afferents from extrastriate cortex. Here we show that, surprisingly, visual signals also enter the FEF through a subcortical route: a disynaptic, ascending pathway originating in the intermediate layers of the superior colliculus (SC). We recorded from identified neurons at all three stages of this pathway (n=30-40 in each sample): FEF recipient neurons, orthodromically activated from the SC; mediodorsal thalamus (MD) relay neurons, antidromically activated from FEF and orthodromically activated from SC; and SC source neurons, antidromically activated from MD. We studied the neurons while monkeys performed delayed saccade tasks designed to temporally resolve visual responses from presaccadic discharges. We found, first, that most neurons at every stage in the pathway had visual responses, presaccadic bursts, or both. Second, we found marked similarities between the SC source neurons and MD relay neurons: in both samples, about 15% of the neurons had only a visual response, 10% had only a presaccadic burst, and 75% had both. In contrast, FEF recipient neurons tended to be more visual in nature: 50% had only a visual response, none had only a presaccadic burst, and 50% had both a visual response and a presaccadic burst. This suggests that in addition to their subcortical inputs, these FEF neurons also receive other visual inputs, e.g. from extrastriate cortex. We conclude that visual activity in the FEF results not only from cortical afferents but also from subcortical inputs. Intriguingly, this implies that some of the visual signals in FEF are pre-processed by the SC.

The frontal eye field sends predictively remapped visual signals to the superior colliculus

We perceive a stable visual world even though saccades often move our retinas. One way the brain may achieve a stable visual percept is through predictive remapping of visual receptive fields: just before a saccade, the receptive field of many neurons moves from its current location ("current receptive field") to the location it is expected to occupy after the saccade ("future receptive field"). Goldberg and colleagues found such remapping in cortical areas, e.g. in the frontal eye field (FEF), as well as in the intermediate layers of the superior colliculus (SC). In the present study we investigated the source of the SC's remapped visual signals. Do some of them come from the FEF? We identified FEF neurons that project to the SC using antidromic stimulation. For neurons with a visual response, we tested whether the receptive field shifted just prior to making a saccade. Saccadic amplitudes were chosen to be as small as possible while clearly separating the current and future receptive fields; they ranged from 5-30 deg. in amplitude and were directed contraversively. The saccadic target was a small red spot. We probed visual responsiveness at the current and future receptive field locations using a white spot flashed at various times before or after the saccade. Predictive remapping was indicated by a visual response to a probe flashed in the future receptive field just before the saccade began. We found that many FEF neurons projecting to the SC exhibited predictive remapping. Moreover, the remapping was as fast and strong as any previously reported for FEF or SC. It is clear, therefore, that remapped visual signals are sent from FEF to SC, providing direct evidence that the FEF is one source of the SC's remapped visual signals. Because remapping requires information about an imminent saccade, we hypothesize that remapping in FEF depends on corollary discharge signals such as those ascending from the SC through MD thalamus (Sommer and Wurtz 2002).