Visual perception of surface curvature. The spin variation and its physiological implications

In the context of the models of structure from motion visual processing, we propose that the optic-flow field is a source of information for the perception of the curvature of a smooth surface in motion. In particular, it is shown how the spin variation (SV), a second spatial derivative of the retinal velocity field, is mathematically related to the curvature of the surface. Under the hypothesis that the visual system relies on SV to analyse the structure of a moving surface, a neural scheme for SV detection is proposed and psychophysical predictions are developed. Results obtained on artificial images show that the SV scheme presents a rather weak sensitivity to noise in conditions of low image velocity.     

Behavior of Cells in Rotating Electric Fields with Account to Surface Charges and Cell Structures

The behavior of a single biological cell in a rotating electric field is investigated both theoretically and experimentally. The torque acting on the cell is calculated. The dependence of the torque on electric cell properties (the dielectric constants, the conductivities, and the surface charges of the cell components) and the field frequency is discussed. The dependence of the rotation velocity on the field frequency shows a typical resonance behavior. It is discussed in which manner the single rotation extrema are related to the different homogeneous cell compartments (cytoplasm, cell membrane, and cell wall). It is shown that the cell surface charge shifts the resonance frequency and influences the absolute value of rotation velocity.     

家兔的开环及闭环视动震颤（OKN）研究

研究了家兔闭环及开环状态的ＯＫＮ反应。闭环时,ＯＫＮ眼动速度与刺激速度成正比,增益接近１。当固定受刺激眼形成开环状态时,ＯＫＮ眼动速度远大于刺激速度,增益可达１０２左右,说明ＯＫＮ系统是由运动跟踪的负反馈机制控制的;刺激范围缩小则眼动反应减弱,表明ＯＫＮ系统对运动信息具有空间总和作用;以视野中不同高度的局部刺激时,发现视网膜中央视带比周边部对ＯＫＮ刺激的敏感性高;单光点刺激视带中央可诱发出清楚的ＯＫＮ反应,这为临床上应用ＯＫＮ客观测定视网膜功能和运动感知提供了可能性。     

Retinal ganglion cell type, size, and spacing can be specified independent of homotypic dendritic contacts

In Brn3b(-/-) mice, where 80% of retinal ganglion cells degenerate early in development, the remaining 20% include most or all ganglion cell types. Cells of the same type cover the retinal surface evenly but tile it incompletely, indicating that a regular mosaic and normal dendritic field size can be maintained in the absence of contact among homotypic cells. In Math5(-/-) mice, where only approximately 5% of ganglion cells are formed, the dendritic arbors of at least two types among the residual ganglion cells are indistinguishable from normal in shape and size, even though throughout development they are separated by millimeters from the nearest neighboring ganglion cell of the same type. It appears that the primary phenotype of retinal ganglion cells can develop without homotypic contact; dendritic repulsion may be an end-stage mechanism that fine-tunes the dendritic arbors for more efficient coverage of the retinal surface.     

Frame of reference transformations in motion perception during smooth pursuit eye movements

Smooth pursuit eye movements change the retinal image velocity of objects in the visual field. In order to change from a retinocentric frame of reference into a head-centric one, the visual system has to take the eye movements into account. Studies on motion perception during smooth pursuit eye movements have measured either perceived speed or perceived direction during smooth pursuit to investigate this frame of reference transformation, but never both at the same time. We devised a new velocity matching task, in which participants matched both perceived speed and direction during fixation to that during pursuit. In Experiment 1, the velocity matches were determined for a range of stimulus directions, with the head-centric stimulus speed kept constant. In Experiment 2, the retinal stimulus speed was kept approximately constant, with the same range of stimulus directions. In both experiments, the velocity matches for all directions were shifted against the pursuit direction, suggesting an incomplete transformation of the frame of reference. The degree of compensation was approximately constant across stimulus direction. We fitted the classical linear model, the model of Turano and Massof (2001) and that of Freeman (2001) to the velocity matches. The model of Turano and Massof fitted the velocity matches best, but the differences between de model fits were quite small. Evaluation of the models and comparison to a few alternatives suggests that further specification of the potential effect of retinal image characteristics on the eye movement signal is needed.     

Binocular depth perception mechanisms in tongue-projecting salamanders

Tongue-projecting salamanders (Bolitoglossini) combine extreme speed and high precision in prey capture. They possess all requirements for stereoscopic depth perception: frontally oriented eyes, a substantial amount of direct ipsilateral projection in addition to the contralateral one, and binocularly driven neurons. Extracellular recordings were made from retinal afferents in the tectum as well as from the somata of tectal neurons. RF-sizes of afferents and tectal neurons were determined, and the response properties of tectal neurons were tested under monocular and binocular conditions with stimuli of different size and velocity. While RF-sizes and response properties of binocular neurons during binocular and contralateral stimulation were similar, ipsilaterally stimulated neurons exhibited much smaller RFs, lower spike rates and different size preferences.Furthermore, the contralateral retinotectal projection from one eye and the ipsilateral from the other are in register. While retinal afferents are distributed linearly over the tectal surface, most tectal neurons are activated by a retinal area corresponding to the frontal visual field; this results in a magnification of this region. The two monocular receptive fields of binocular neurons exhibit zero disparities (horopter) at distances that coincide with the maximum reach of the tongue. We hypothesize that bolitoglossine salamanders (as well as amphibians in general) make use of two kinds of disparities: (1) between the maps in the left and right tectal hemisphere, coding for the lateral eccentricity of an object, and (2) between the ipsilateral and contralateral retinotectal map, coding for the distance. The presence of substantial direct ipsilateral afferents in bolitoglossine salamanders appears to be the basis for a fast computation of object distance, which is characteristic of these animals.Abbreviations Ax/Ay coordinates of a recorded afference - Nx/Ny coordinates of a recorded neuron - RF receptive field - RFc contralateral receptive field - RFi ipsilateral receptive field - RFx/RFy coordinates of a receptive field center - RGC retinal ganglion cell     

Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics.     

Geometry of binocular vision and a model for stereopsis

If a binocular observer looks at surfaces, the disparity is a continuous vector field defined on the manifold of cyclopean visual directions. We derive this field for the general case that the observer is presented with a curved surface and fixates an arbitrary point. We expand the disparity field in the neighbourhood of a visual direction. The first order approximation can be decomposed into congruences, similarities and deformations. The deformation component is described by the traceless part of the symmetric part of the gradient of the disparity. The deformation component carries all information concerning the slant of a surface element that is contained in the disparity field itself; it is invariant for changes of fixation, differential cyclotorsion and uniform aniseikonia. The deformation component can be found from a comparison of the orientation of surface details in the left and right retinal images. The theory provides a geometric explanation of the percepts obtained with uniform and oblique meridional aniseikonia. We utilize the geometric theory to construct a mechanistic model of stereopsis that obviates the need for internal zooming mechanisms, but nevertheless is insensitive to differential cyclotorsion or uniform aniseikonia.     

Doppler Optical Coherence Tomography of Retinal Circulation

Noncontact retinal blood flow measurements are performed with a Fourier domain optical coherence tomography (OCT) system using a circumpapillary double circular scan (CDCS) that scans around the optic nerve head at 3.40 mm and 3.75 mm diameters. The double concentric circles are performed 6 times consecutively over 2 sec. The CDCS scan is saved with Doppler shift information from which flow can be calculated. The standard clinical protocol calls for 3 CDCS scans made with the OCT beam passing through the superonasal edge of the pupil and 3 CDCS scan through the inferonal pupil. This double-angle protocol ensures that acceptable Doppler angle is obtained on each retinal branch vessel in at least 1 scan. The CDCS scan data, a 3-dimensional volumetric OCT scan of the optic disc scan, and a color photograph of the optic disc are used together to obtain retinal blood flow measurement on an eye. We have developed a blood flow measurement software called "Doppler optical coherence tomography of retinal circulation" (DOCTORC). This semi-automated software is used to measure total retinal blood flow, vessel cross section area, and average blood velocity. The flow of each vessel is calculated from the Doppler shift in the vessel cross-sectional area and the Doppler angle between the vessel and the OCT beam. Total retinal blood flow measurement is summed from the veins around the optic disc. The results obtained at our Doppler OCT reading center showed good reproducibility between graders and methods (<10%). Total retinal blood flow could be useful in the management of glaucoma, other retinal diseases, and retinal diseases. In glaucoma patients, OCT retinal blood flow measurement was highly correlated with visual field loss (R²>0.57 with visual field pattern deviation). Doppler OCT is a new method to perform rapid, noncontact, and repeatable measurement of total retinal blood flow using widely available Fourier-domain OCT instrumentation. This new technology may improve the practicality of making these measurements in clinical studies and routine clinical practice.     

Chasing a dummy target: smooth pursuit and velocity control in male blowflies

Male blowflies chase and catch other flies in fast acrobatic flights. To unravel the underlying control system, we presented a black moving sphere instead of a real fly as a pursuit target. By varying the size and speed of the target, we were able to systematically analyse the decisive visual determinants that guide chasing behaviour. Flies pursue targets of a wide range of sizes and velocities. The percentage of pursuits resulting in target capture decreases with increasing target size and speed. Chasing male flies adjust their forward velocity depending on the retinal size of the target, indicating that retinal size is a relevant input variable of the control system. The chasing fly focuses the target with great accuracy in the frontal part of its visual field by means of a smooth pursuit control system using the retinal position of the target to determine the flight direction. We conclude that for a comprehensive understanding of chasing control different time lags in the control systems of angular and forward velocity together with the impact of inertia on fly movements need to be taken into account.     

Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera)

Bees and wasps are known to use a visual representation of the nest environment to guide the final approach to their nest. It is also known that they acquire this representation during an orientation flight performed on departure.A detailed film analysis shows that orientation flights in solitary wasps of the genus Cerceris consist of a systematic behavioural sequence: after lift-off from the nest entrance, wasps fly in ever increasing arcs around the nest. They fly along these arcs obliquely to their long axis and turn so that the nest entrance is held in the left or right visual field at retinal positions between 30° and 70° from the midline. Horizontal distance from the nest and height above ground increase throughout an orientation flight so that the nest is kept at retinal elevations between 45° and 60° below the horizon. The wasps' rate of turning is constant at between 100°/s and 200°/s independent of their distance from the nest and their ground velocity increases with distance. The consequence of this is that throughout the flight wasps circle at a constant angular velocity around the nest.Orientation flights are strongly influenced by landmark lay-out. Wasps adjust their flight-path and their orientation in a way that allows them to fixate the nest entrance and to hold the closest landmark in their frontal visual field.The orientation flight generates a specific topography of motion parallax across the visual field. This could be used by wasps to acquire a series of snapshots that all contain the nest position, to acquire snapshots of close landmarks only (distance filtering), to exclude shadow contours from their visual representation (figure-ground discrimination) or to gain information on the distance of landmarks relative to the nest.     

Apparent position governs contour-element binding by the visual system

An assumption inherent in many models of visual space is that the spatial coordinates of retinal cells implicitly give rise to the perceptual code for position. The results of the experiments reported here, in which it is shown that retinally non-veridical locations of contour elements are used by the visual system for contour-element binding, lend support to a different view. The visual system does not implicitly code position with reference to the labelled locations of retinal cells, but dynamically extracts spatial position from the aggregate result of local computations. These computations may include local spatial relationships between retinal cells, but are not confined to them; other computations, including position derived from local velocity cues, are combined to code the position of objects in the visual world.     

Mathematical principles in afferent visual neurons: Differentiation,integration and transient proportionality related to receptive fields and shift-effect

The dual reciprocal and antagonistic organization of B- and D-neurons of the afferent visual system is obtained using differentiation and integration as mathematical equivalents of visual information processing by an impulse frequency code. The spatial and temporal derivatives lead to the transient responses. A constant and a time-dependent term proportional to the luminance distribution describe the sustained response components and the shift-effect of retinal on- and off-center ganglion cells. Receptive field properties of lateral geniculate cells and their antagonistic shift-effect are obtained by passing the retinal output, i.e. the difference between B- and D-neurons' activity, once again through the same operations. However, the factor of proportionality is applied to the retina alone. The surprisingly small difference between retinal and geniculate receptive field properties on the one hand and the dramatic change from a synergistic to an antagonistic shift-effect on the other hand are thereby explained. The theory offers an understanding of a a possible functional significance of the shift-effect as a mechanism of transientrestoration of visual information, which prevents the system from total fading by means of shifts of the retinal image, normally produced by eye movements.     

Hyperspectral computed tomographic imaging spectroscopy of vascular oxygen gradients in the rabbit retina in vivo

Diagnosis of retinal vascular diseases depends on ophthalmoscopic findings that most often occur after severe visual loss (as in vein occlusions) or chronic changes that are irreversible (as in diabetic retinopathy). Despite recent advances, diagnostic imaging currently reveals very little about the vascular function and local oxygen delivery. One potentially useful measure of vascular function is measurement of hemoglobin oxygen content. In this paper, we demonstrate a novel method of accurately, rapidly and easily measuring oxygen saturation within retinal vessels using in vivo imaging spectroscopy. This method uses a commercially available fundus camera coupled to two-dimensional diffracting optics that scatter the incident light onto a focal plane array in a calibrated pattern. Computed tomographic algorithms are used to reconstruct the diffracted spectral patterns into wavelength components of the original image. In this paper the spectral components of oxy- and deoxyhemoglobin are analyzed from the vessels within the image. Up to 76 spectral measurements can be made in only a few milliseconds and used to quantify the oxygen saturation within the retinal vessels over a 10-15 degree field. The method described here can acquire 10-fold more spectral data in much less time than conventional oximetry systems (while utilizing the commonly accepted fundus camera platform). Application of this method to animal models of retinal vascular disease and clinical subjects will provide useful and novel information about retinal vascular disease and physiology.     

A novel function for Hedgehog signalling in retinal pigment epithelium differentiation

Sonic hedgehog is involved in eye field separation along the proximodistal axis. We show that Hh signalling continues to be important in defining aspects of the proximodistal axis as the optic vesicle and optic cup mature. We show that two other Hedgehog proteins, Banded hedgehog and Cephalic hedgehog, related to the mouse Indian hedgehog and Desert hedgehog, respectively, are strongly expressed in the central retinal pigment epithelium but excluded from the peripheral pigment epithelium surrounding the ciliary marginal zone. By contrast, downstream components of the Hedgehog signalling pathway, Gli2, Gli3 and X-Smoothened, are expressed in this narrow peripheral epithelium. We show that this zone contains cells that are in the proliferative state. This equivalent region in the adult mammalian eye, the pigmented ciliary epithelium, has been identified as a zone in which retinal stem cells reside. These data, combined with double labelling and the use of other retinal pigment epithelium markers, show that the retinal pigment epithelium of tadpole embryos has a molecularly distinct peripheral to central axis. In addition, Gli2, Gli3 and X-Smoothened are also expressed in the neural retina, in the most peripheral region of the ciliary marginal zone, where retinal stem cells are found in Xenopus, suggesting that they are good markers for retinal stem cells. To test the role of the Hedgehog pathway at different stages of retinogenesis, we activated the pathway by injecting a dominant-negative form of PKA or blocking it by treating embryos with cyclopamine. Embryos injected or treated at early stages display clear proximodistal defects in the retina. Interestingly, the main phenotype of embryos treated with cyclopamine at late stages is a severe defect in RPE differentiation. This study thus provides new insights into the role of Hedgehog signalling in the formation of the proximodistal axis of the eye and the differentiation of retinal pigment epithelium.     

Retinoschisin (RS1), the protein encoded by the X-linked retinoschisis gene, is anchored to the surface of retinal photoreceptor and bipolar cells through its interactions with a Na/K ATPase-SARM1 complex

Retinoschisin or RS1 is a discoidin domain-containing protein encoded by the gene responsible for X-linked retinoschisis (XLRS), an early onset macular degeneration characterized by a splitting of the retina. Retinoschisin, expressed and secreted from photoreceptors and bipolar cells as a homo-octameric complex, associates with the surface of these cells where it serves to maintain the cellular organization of the retina and the photoreceptor-bipolar synaptic structure. To gain insight into the role of retinoschisin in retinal cell adhesion and the pathogenesis of XLRS, we have investigated membrane components in retinal extracts that interact with retinoschisin. Unlike the discoidin domain-containing blood coagulation proteins Factor V and Factor VIII, retinoschisin did not bind to phospholipids or retinal lipids reconstituted into unilamellar vesicles or immobilized on microtiter plates. Instead, co-immunoprecipitation studies together with mass spectrometric-based proteomics and Western blotting showed that retinoschisin is associated with a complex consisting of Na/K ATPase (alpha3, beta2 isoforms) and the sterile alpha and TIR motif-containing protein SARM1. Double labeling studies for immunofluorescence microscopy confirmed the co-localization of retinoschisin with Na/K ATPase and SARM1 in photoreceptors and bipolar cells of retina tissue. We conclude that retinoschisin binds to Na/K ATPase on photoreceptor and bipolar cells. This interaction may be part of a novel SARM1-mediated cell signaling pathway required for the maintenance of retinal cell organization and photoreceptor-bipolar synaptic structure.     

Looking into the water with a facet eye

The apparent velocity and apparent size of objects approaching an animal strongly depend on their size, their position within the visual field and on the path along which they move. It also makes a considerable difference whether both the animal and the objects are in air, or whether the animal looks from one medium into the other, as is the case in animals that live at the water surface. To systematically investigate this situation we calculated apparent velocity and size in the midsagittal plane of approaching objects of flat horizontal, rodlike vertical and spherical shape. We confine our investigation to object movements along straight horizontal and vertical paths and consider the situation for eyes with and without acute zones. The apparent velocity of an approaching object is low in the far field and increases rapidly close to the eye in both air and water. Along horizontal paths and close to the animal it is higher in water than in air. Along vertical paths and close to the animal it is higher in air than in water. Both relationships are exaggerated when there is an acute zone for vertical resolution along the animal's horizon. Boundary curves are calculated along which an approaching object is seen by a linearly increasing number of receptors. The change of apparent size is characterized by the density of these lines. Below the water surface the change of apparent size is similar to that of the apparent velocity. The apparent size of a horizontally elongated object approaching along a horizontal path increases steadily, that of a vertically elongated object along a vertical line initially increases, but can decrease again near the water surface. An acute zone substantially changes the shape and density of these contour lines. The biological consequences of these effects are discussed.     

Consequences for retinal growth when vision occurs in S2 space

We postulate that the process of vision occurs in the S2 space. The retina is endowed with the topology of a part of a two-sphere S2, roughly, the topology of a hemisphere. There is a corresponding topology on the tectal surface, induced by the anatomy of the retino-tectal connections. Our analysis predicts the experimentally observed "near-neighbour" relationships between points in the visual field and their representation in the tectum. Further, in this context, topological arguments are presented to indicate that if the normal developing retinal disc in goldfish undergoes a process of deformation, a discontinuity is generated at the retinal surface. This discontinuity makes the differential patterns of the retinal and tectal tissues more compatible, and also enables the retina (which grows throughout the life of the animal) to conveniently connect to the tectum.