Simulation of daily soft multifocal contact lenses using SimVis Gekko: from in-vitro and computational characterization to clinical validation

Multifocal contact lenses (MCLs) are one of the solutions to correct presbyopia, but their adoption is not widespread. To address this situation, visual simulators can be used to refine the adaptation process. This study aims to obtain accurate simulations for a visual simulator (SimVis Gekko; 2EyesVision) of daily soft MCL designs from four manufacturers. In-vitro characterization of these MCLs-several powers and additions- was obtained using NIMO TR-1504. From the averaged relative power profiles across powers, phase maps were reconstructed and the Through-Focus Visual Strehl metric was calculated for each MCL design. The SimVis Gekko simulation corresponding to each MCL design was obtained computationally and bench-validated. Finally, the MCL simulations were clinically validated involving presbyopic patients. The clinical validation results show a good agreement between the SimVis Gekko simulations and the real MCLs for through-focus visual acuity (TF-VA) curves and VA at three real distances. All MCL designs showed a partial correlation higher than 0.90 and a Root Mean Square Error below 0.07 logMAR between the TF-VA of simulations and Real MCLs across subjects. The validity of the simulation approach using SimVis Gekko and in-vitro measurements was confirmed in this study, opening the possibility to accelerate the adaptation of MCLs.

Long-range frequency-domain optical delay line based on a spinning tilted mirror for low-cost ocular biometry

Optical biometers are routinely used to measure intraocular distances in ophthalmic applications such as cataract surgery planning or myopia monitoring. However, due to their high cost and reduced transportability, access to them for screening and surgical planning is still limited in low-resource and remote settings. To increase patients' access to optical biometry we propose a novel low-cost frequency-domain optical delay line (FD-ODL) based on an inexpensive stepper motor spinning a tilted mirror, for integration into a time-domain (TD)-biometer, amenable to a compact footprint. In the proposed FD-ODL, the axial scan range and the A-scan rate are decoupled from one another, as the former only depends on the spinning mirror tilt angle, while the A-scan rate only depends on the motor shaft rotational speed. We characterized the scanning performance and specifications for two spinning mirror tilt angles, and compared them to those of the standard, more expensive FD-ODL implementation, employing a galvanometric scanner for group delay generation. A prototype of the low-cost FD-ODL with a 1.5 deg tilt angle, resulting in an axial scan range of 6.61 mm and an A-scan rate of 10 Hz was experimentally implemented and integrated in a dual sample beam optical low-coherence reflectometry (OLCR) setup with a detour unit to replicate the measurement window around the anterior segment and the retina. The intraocular distances of a model eye were measured with the proposed low-cost biometer and found to be in good agreement with those acquired by a custom swept-source optical coherence tomography (SS-OCT) system and two commercial biometers, validating our novel design.

Optical beam scanner with reconfigurable non-mechanical control of beam position, angle, and focus for low-cost whole-eye OCT imaging

Whole-eye optical coherence tomography (OCT) imaging is a promising tool in ocular biometry for cataract surgery planning, glaucoma diagnostics and myopia progression studies. However, conventional OCT systems are set up to perform either anterior or posterior eye segment scans and cannot easily switch between the two scan configurations without adding or exchanging optical components to account for the refraction of the eye's optics. Even in state-of-the-art whole-eye OCT systems, the scan configurations are pre-selected and cannot be dynamically reconfigured. In this work, we present the design, optimization and experimental validation of a reconfigurable and low-cost optical beam scanner based on three electro-tunable lenses, capable of non-mechanically controlling the beam position, angle and focus. We derive the analytical theory behind its control. We demonstrate its use in performing alternate anterior and posterior segment imaging by seamlessly switching between a telecentric focused beam scan to an angular collimated beam scan. We characterize the corresponding beam profiles and record whole-eye OCT images in a model eye and in an ex vivo rabbit eye, observing features comparable to those obtained with conventional anterior and posterior OCT scanners. The proposed beam scanner reduces the complexity and cost of other whole-eye scanners and is well suited for 2-D ocular biometry. Additionally, with the added versatility of seamless scan reconfiguration, its use can be easily expanded to other ophthalmic applications and beyond.

Poster Session: Perceived image quality of natural images through different bifocal corrections after adaptation to sharp or blur

Simultaneous Vision, present in bifocal and multifocal contact or intraocular lenses, is a common clinical strategy for presbyopia. Neural adaptation is known to occur, but it is not predictable nor well understood. Previous works have studied the short-term neural adaptation to bifocal images using Adaptive Optics and digital convolutions of a face image (with pure defocus and simultaneous images) as adaptation images, and also as test images for perceptual judgments (Radhakrishnan et al., 2014). In this study, we use a programmable see-through head-mounted visual simulator (SimVis Gekko) to analyze the effect of neural adaptation on the perceived image quality of different bifocal corrections (BC) with different balances of energy between far and near, and for different transitions between adaptation and test. Eight subjects judged a video sequence of urban natural images, through two monofocal corrections (0 and 3D) and nine BCs (far/near balance from 90/10 to 10/90 and an addition of 3.00D), optically simulated monocularly. Two initial adaptation states of 10s were used: 0.00D-SHARP and 3.00D-BLUR, followed a transition from these states to the BC that can be ABRUPT (with 1, 5 or 30s of adaptation), or SMOOTH (linear transition lasting 1, 5 or 30s). Our results show a significant increase in perceptual quality after adaptation to BLUR, particularly for intermediate energy balances. However, subjects are quite insensitive to the type and duration of the transition.

Multifocal contact lens vision simulated with a clinical binocular simulator

PURPOSE

The purpose of this study is to compare the binocular visual perception of participants wearing multifocal contact lenses and these same lens designs viewed through a temporal multiplexing visual simulator.

METHODS

Visual performance and perceived visual quality at various distances were obtained in 37 participants wearing soft M-CLs and through the SimVis Gekko programmed with the same lenses. In a pilot study (n = 10) visual performance was measured in terms of LogMAR visual acuity (VA) at far (4 m), intermediate (64 cm) and near (40 cm) distances and through-focus VA (TFVA) curves with the simulated M-CLs. In the follow-up study (n = 27), LogMAR VA at far, intermediate and near distances were measured both with the actual and simulated M-CLs. Perceived visual quality was measured in both studies using the Multifocal Acceptance Score (MAS-2EV), and a Participants Reported Outcomes Vision questionnaire. Differences between the metrics obtained with simulated and actual lenses were obtained.

RESULTS

Both actual and simulated M-CLs increased depth-of-focus by a similar amount. Mean LogMAR VA differences with actual and simulated M-CLs ranged between 4 and 6 letters (0.08 ± 0.01, 0.12 ± 0.01 and 0.10 ± 0.01, for far, intermediate and near distances, respectively). MAS-2EV average score differences with actual and simulated M-CLs ranged between -1.00 and + 4.25. Average MAS-2EV scores were not correlated significantly with VA. However, MAS-2EV (average and individual scores) were highly correlated to visual quality questionnaire responses (p < 0.005).

CONCLUSIONS

A simultaneous vision simulator accurately represented vision with M-CLs both VA at various distances and perceived visual quality, as measured in a clinical setting. The MAS-2EV metric accurately captured participant reported outcomes of standard vision questionnaires. The combination of SimVis Gekko and MAS-2EV has the potential to largely reduce chair time in M-CLs fitting.

Closed-loop experimental optimization of tunable lenses

Tunable lenses (TLs) are optical devices that can change their optical power in response to an electrical signal. In many applications, they are often pushed to or beyond their temporal limits. Fast periodic and/or abrupt variations of the optical power induce undesired distortions in their transient response and produce a decrease in their performance. A low-cost focimetry system, along with a custom closed-loop iterative optimization algorithm, was developed to (1) characterize a TL's response at high speed and (2) optimize their performance in realistic TL working conditions. A significant lens performance improvement was found in about 23 iterations with a decrease in the area under the error curve and an improved effective time. Applying the closed-loop optimization algorithm in a depth scanning experiment enhanced the image quality. Quantitatively, the image quality was evaluated using the structural similarity index metric that improves in individual frames, on average, from 0.345 to 0.895.

Multifocal acceptance score to evaluate vision: MAS-2EV

We present a new metric (Multifocal Acceptance Score, MAS-2EV) to evaluate vision with presbyopic corrections. The MAS-2EV is based on a set of images representing natural visual scenes at day and night conditions projected in far and near displays, and a near stereo target. Subjects view and score the images through different binocular corrections (monofocal corrections at far; bifocal corrections; monovision and modified monovision) administered with soft contact lenses (in cyclopleged young subjects) or with a binocular simultaneous vision simulator (in presbyopic and cyclopleged young subjects). MAS-2EV scores are visually represented in the form of polygons, and quantified using different metrics: overall visual quality, visual degradation at far, visual benefit at near, near stereo benefit, visual imbalance near-far, overall visual imbalance and a combined overall performance metric. We have found that the MAS-2EV has sufficient repeatability and sensitivity to allow differentiation across corrections with only two repetitions, and the duration of the psychophysical task (3 min for subject/condition/correction) makes it useable in the clinic. We found that in most subjects binocular bifocal corrections produce the lowest visual imbalance, and the highest near stereo benefit. 46.67% of the subjects ranked binocular bifocal corrections first, and 46.67% of the subjects ranked monovision first. MAS-2EV, particularly in combination with visual simulators, can be applied to select prospective presbyopic corrections in patients prior to contact lens fitting or intraocular lens implantation.

Optical and Visual Quality With Physical and Visually Simulated Presbyopic Multifocal Contact Lenses

Purpose

As multifocal contact lenses (MCLs) expand as a solution for presbyopia correction, a better understanding of their optical and visual performance becomes essential. Also, providing subjects with the experience of multifocal vision before contact lens fitting becomes critical, both to systematically test different multifocal designs and to optimize selection in the clinic. In this study, we evaluated the ability of a simultaneous vision visual simulator (SimVis) to represent MCLs.

Methods

Through focus (TF) optical and visual quality with a center-near aspheric MCL (low, medium and high near adds) were measured using a multichannel polychromatic Adaptive Optics visual simulator equipped with double-pass, SimVis (temporal multiplexing), and psychophysical channels to allow measurements on-bench and in vivo. On bench TF optical quality of SimVis-simulated MCLs was obtained from double-pass (DP) images and images of an E-stimulus using artificial eyes. Ten presbyopic subjects were fitted with the MCL. Visual acuity (VA) and DP retinal images were measured TF in a 4.00 D range with the MCL on eye, and through SimVis simulations of the same MCLs on the same subjects.

Results

TF optical (on bench and in vivo) and visual (in vivo) quality measurements captured the expected broadening of the curves with increasing add. Root mean square difference between real and SimVis-simulated lens was 0.031/0.025 (low add), 0.025/0.015 (medium add), 0.019/0.011 (high add), for TF DP and TF LogMAR VA, respectively. A shape similarity metric shows high statistical values (lag κ = 0), rho = 0.811/0.895 (low add), 0.792/0.944 (medium add), and 0.861/0.915 (high add) for TF DP/LogMAR VA, respectively.

Conclusions

MCLs theoretically and effectively expand the depth of focus. A novel simulator, SimVis, captured the through-focus optical and visual performance of the MCL in most of the subjects. Visual simulators allow subjects to experience vision with multifocal lenses prior to testing them on-eye.

Translational Relevance

Simultaneous visual simulators allow subjects to experience multifocal vision non-invasively. We demonstrated equivalency between real multifocal contact lenses and SimVis-simulated lenses. The results suggest that SimVis is a suitable technique to aid selection of presbyopic corrections in the contactology practice.

Tunable lenses: dynamic characterization and fine-tuned control for high-speed applications

Tunable lenses are becoming ubiquitous, in applications including microscopy, optical coherence tomography, computer vision, quality control, and presbyopic corrections. Many applications require an accurate control of the optical power of the lens in response to a time-dependent input waveform. We present a fast focimeter (3.8 KHz) to characterize the dynamic response of tunable lenses, which was demonstrated on different lens models. We found that the temporal response is repetitive and linear, which allowed the development of a robust compensation strategy based on the optimization of the input wave, using a linear time-invariant model. To our knowledge, this work presents the first procedure for a direct characterization of the transient response of tunable lenses and for compensation of their temporal distortions, and broadens the potential of tunable lenses also in high-speed applications.

Experimental validations of a tunable-lens-based visual demonstrator of multifocal corrections

The Simultaneous Vision simulator (SimVis) is a visual demonstrator of multifocal lens designs for prospective intraocular lens replacement surgery patients and contact lens wearers. This programmable device employs a fast tunable lens and works on the principle of temporal multiplexing. The SimVis input signal is tailored to mimic the optical quality of the multifocal lens using the theoretical SimVis temporal profile, which is evaluated from the through-focus Visual Strehl ratio metric of the multifocal lens. In this paper, for the first time, focimeter-verified on-bench validations of multifocal simulations using SimVis are presented. Two steps are identified as being critical to accurate SimVis simulations. Firstly, a new iterative approach is presented that improves the accuracy of the theoretical SimVis temporal profile for three different multifocal intraocular lens designs - diffractive trifocal, refractive segmented bifocal, and refractive extended depth of focus, while retaining a low sampling. Secondly, a fast focimeter is used to measure the step response of the tunable lens, and the input signal is corrected to include the effects of the transient behavior of the tunable lens. It was found that the root-mean-square of the difference between the estimated through-focus Visual Strehl ratio of the multifocal lens and SimVis is not greater than 0.02 for all the tested multifocal designs.

Temporal multiplexing to simulate multifocal intraocular lenses: theoretical considerations

Fast tunable lenses allow an effective design of a portable simultaneous vision simulator (SimVis) of multifocal corrections. A novel method of evaluating the temporal profile of a tunable lens in simulating different multifocal intraocular lenses (M-IOLs) is presented. The proposed method involves the characteristic fitting of the through-focus (TF) optical quality of the multifocal component of a given M-IOL to a linear combination of TF optical quality of monofocal lenses viable with a tunable lens. Three different types of M-IOL designs are tested, namely: segmented refractive, diffractive and refractive extended depth of focus. The metric used for the optical evaluation of the temporal profile is the visual Strehl (VS) ratio. It is shown that the time profiles generated with the VS ratio as a metric in SimVis resulted in TF VS ratio and TF simulated images that closely matched the TF VS ratio and TF simulated images predicted with the M-IOL. The effects of temporal sampling, varying pupil size, monochromatic aberrations, longitudinal chromatic aberrations and temporal dynamics on SimVis are discussed.

Static and dynamic crystalline lens accommodation evaluated using quantitative 3-D OCT

Custom high-resolution high-speed anterior segment spectral domain Optical Coherence Tomography (OCT) provided with automatic quantification and distortion correction algorithms was used to characterize three-dimensionally (3-D) the human crystalline lens in vivo in four subjects, for accommodative demands between 0 to 6 D in 1 D steps. Anterior and posterior lens radii of curvature decreased with accommodative demand at rates of 0.73 and 0.20 mm/D, resulting in an increase of the estimated optical power of the eye of 0.62 D per diopter of accommodative demand. Dynamic fluctuations in crystalline lens radii of curvature, anterior chamber depth and lens thickness were also estimated from dynamic 2-D OCT images (14 Hz), acquired during 5-s of steady fixation, for different accommodative demands. Estimates of the eye power from dynamical geometrical measurements revealed an increase of the fluctuations of the accommodative response from 0.07 D to 0.47 D between 0 and 6 D (0.044 D per D of accommodative demand). A sensitivity analysis showed that the fluctuations of accommodation were driven by dynamic changes in the lens surfaces, particularly in the posterior lens surface.

In vivo human crystalline lens topography

Custom high-resolution high-speed anterior segment spectral domain optical coherence tomography (OCT) was used to characterize three-dimensionally (3-D) the human crystalline lens in vivo. The system was provided with custom algorithms for denoising and segmentation of the images, as well as for fan (scanning) and optical (refraction) distortion correction, to provide fully quantitative images of the anterior and posterior crystalline lens surfaces. The method was tested on an artificial eye with known surfaces geometry and on a human lens in vitro, and demonstrated on three human lenses in vivo. Not correcting for distortion overestimated the anterior lens radius by 25% and the posterior lens radius by more than 65%. In vivo lens surfaces were fitted by biconicoids and Zernike polynomials after distortion correction. The anterior lens radii of curvature ranged from 10.27 to 14.14 mm, and the posterior lens radii of curvature ranged from 6.12 to 7.54 mm. Surface asphericities ranged from -0.04 to -1.96. The lens surfaces were well fitted by quadrics (with variation smaller than 2%, for 5-mm pupils), with low amounts of high order terms. Surface lens astigmatism was significant, with the anterior lens typically showing horizontal astigmatism ([Formula: see text] ranging from -11 to -1 µm) and the posterior lens showing vertical astigmatism ([Formula: see text] ranging from 6 to 10 µm).

Quantitative OCT-based corneal topography in keratoconus with intracorneal ring segments

Custom high-resolution high-speed anterior segment spectral domain Optical Coherence Tomography (OCT) was used to characterize three-dimensionally (3-D) corneal topography in keratoconus before and after implantation of intracorneal ring segments (ICRS). Previously described acquisition protocols were followed to minimize the impact of the motions of the eye. The collected set of images was corrected from distortions: fan (scanning) and optical (refraction). Custom algorithms were developed for automatic detection and classification of volumes in the anterior segment of the eye, in particular for the detection and classification of the implanted ICRS. Surfaces were automatically detected for quantitative analysis of the corneal elevation maps (fitted by biconicoids and Zernike polynomials) and pachymetry. Automatic tools were developed for the estimation of the 3-D positioning of the ICRS. The pupil center reference was estimated from the segmented iris volume. The developed algorithms are illustrated in a keratoconic eye (grade III) pre- and 30 days post-operatively after implantation of two triangular-section, 0.3-mm thick Ferrara ring segments. Quantitative corneal topographies reveal that the ICRS produced a flattening of the anterior surface, a steepening of the posterior surface, meridional differences in the changes in curvature and asphericity, and increased symmetry of the anterior topography. Optical distortion correction through the ICRS (of a different refractive index from the cornea) allowed accurate pachymetric estimates, which showed increased thickness in the ectatic area as well as in peripheral corneal areas. Automatic tools allowed estimation of the depth of the implanted ICRS ring, as well as its rotation with respect to the pupil plane. Anterior segment sOCT provided with fan and optical distortion correction and analysis tools is an excellent instrument for evaluating and monitoring keratoconic eyes and for the quantification of the changes produced by ICRS treatment.

Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging

We present an optimization method to retrieve the gradient index (GRIN) distribution of the in-vitro crystalline lens from optical path difference data extracted from OCT images. Three-dimensional OCT images of the crystalline lens are obtained in two orientations (with the anterior surface up and posterior surface up), allowing to obtain the lens geometry. The GRIN reconstruction method is based on a genetic algorithm that searches for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens. Computer simulations showed that, for noise of 5 μm in the surface elevations, the GRIN is recovered with an accuracy of 0.003 and 0.010 in the refractive indices of the nucleus and surface of the lens, respectively. The method was applied to retrieve three-dimensionally the GRIN of a porcine crystalline lens in vitro. We found a refractive index ranging from 1.362 in the surface to 1.443 in the nucleus of the lens, an axial exponential decay of the GRIN profile of 2.62 and a meridional exponential decay ranging from 3.56 to 5.18. The effect of GRIN on the aberrations of the lens also studied. The estimated spherical aberration of the measured porcine lens was 2.87 μm assuming a homogenous equivalent refractive index, and the presence of GRIN shifted the spherical aberration toward negative values (-0.97 μm), for a 6-mm pupil.

Combining coma with astigmatism can improve retinal image over astigmatism alone

We demonstrate that certain combinations of non-rotationally symmetric aberrations (coma and astigmatism) can improve retinal image quality over the condition with the same amount of astigmatism alone. Simulations of the retinal image quality in terms of Strehl Ratio, and measurements of Visual Acuity under controlled aberrations with adaptive optics were performed, varying defocus, astigmatism and coma. Astigmatism ranged between 0 and 1.5D. Defocus ranged typically between -1 and 1D. The amount of coma producing best retinal image quality (for a given relative angle between astigmatism and coma) was computed and the amount was found to be different from zero in all cases (except for 0D of astigmatism). For example, for a 6mm pupil, in the presence of 0.5D of astigmatism, a value of coma of 0.23mum produced (for best focus) a peak improvement in Strehl Ratio by a factor of 1.7, over having 0.5D of astigmatism alone. The improvement holds over a range of >1.5D of defocus and peak improvements were found for amounts of coma ranging from 0.15mum to 0.35mum. We measured VA under corrected high order aberrations, astigmatism alone (0.5D) and astigmatism in combination with coma (0.23mum), with and without adaptive optics correction of all the other aberrations, in two subjects. We found that the combination of coma with astigmatism improved decimal VA by a factor of 1.28 (28%) and 1.47 (47%) in both subjects, over VA with astigmatism alone when all the rest of aberrations were corrected. Nevertheless, in the presence of typical normal levels of HOA the effect of the coma/astigmatism interaction is considerably diminished.

Dynamic accommodation with simulated targets blurred with high order aberrations

High order aberrations have been suggested to play a role in determining the direction of accommodation. We have explored the effect of retinal blur induced by high order aberrations on dynamic accommodation by measuring the accommodative response to sinusoidal variations in accommodative demand (1-3D). The targets were blurred with 0.3 and 1mum (for a 3-mm pupil) of defocus, coma, trefoil and spherical aberration. Accommodative gain decreased significantly when 1-mum of aberration was induced. We found a strong correlation between the relative accommodative gain (and phase lag) and the contrast degradation imposed on the target at relevant spatial frequencies.

Visual performance with real-life tasks under adaptive-optics ocular aberration correction

We measured the effect of the correction of the natural aberrations of the eye by means of adaptive optics on the subject's performance on three different visual tasks: subjective sharpness assessment of natural images, familiar face recognition, and facial expression recognition. Images were presented through a dedicated psychophysical channel and viewed through an electromagnetic deformable mirror. Experiments were performed on 17 normal subjects. Ocular aberrations (astigmatism and higher order aberrations) were reduced on average from 0.366 +/- 0.154 to 0.101 +/- 0.055 mum for a 5-mm pupil diameter. On average, subjects considered to be sharper 84 +/- 14% of the images viewed under AO correction, and there was a significant correlation between the amount of corrected aberrations and the percentage of images that the subject considered sharper when observed under AO-corrected aberrations. In all eyes (except one), AO correction improved familiar face recognition, by a factor of x1.13 +/- 0.12 on average. However, AO correction did not improve systematically facial expression recognition.

Accommodative lag and fluctuations when optical aberrations are manipulated

We evaluated the accommodative response to a stimulus moving from 0 to 6 D following a staircase function under natural, corrected, and induced optical aberrations, using an adaptive-optics (AO) electromagnetic deformable mirror. The accommodative response of the eye (through the mirror) and the change of aberrations were measured on 5 subjects using a Hartmann-Shack wavefront sensor operating at 12.8 Hz. Five conditions were tested: (1) natural aberrations, (2) AO correction of the unaccommodated state and induction (over 6-mm pupils) of (3) +1 microm and (4) -1 microm of spherical aberration and (5) -2 microm of vertical coma. Four subjects showed a better accommodative response with AO correction than with their natural aberrations. The induction of negative spherical aberration also produced a better accommodative response in the same subjects. Accommodative lag increased in all subjects when positive spherical aberration and coma were induced. Fluctuations of the accommodative response (computed during each 1-D period of steady accommodation) increased with accommodative response when high-order aberrations were induced. The largest fluctuations occurred for induced negative spherical aberration and the smallest for natural and corrected aberrations. The study demonstrates that aberrations influence accommodative lag and fluctuations of accommodation and that correcting aberrations improves rather than compromises the accommodative response.

Influence of adaptive-optics ocular aberration correction on visual acuity at different luminances and contrast polarities

We evaluated the visual benefit of correcting astigmatism and high-order aberrations with adaptive optics (AO) on visual acuity (VA) measured at 7 different luminances (ranging from 0.8 to 50 cd/m(2)) and two contrast polarities (black letters on white background, BoW, and white letters on black background, WoB) on 7 subjects. For the BoW condition, VA increased with background luminance in both natural and AO-corrected conditions, and there was a benefit of AO correction at all luminances (by a factor of 1.29 on average across luminances). For WoB VA increased with foreground luminance but decreased for the highest luminances. In this reversed polarity condition AO correction increased VA by a factor of 1.13 on average and did not produce a visual benefit at high luminances. The improvement of VA (averaged across conditions) was significantly correlated (p = 0.04) with the amount of corrected aberrations (in terms of Strehl ratio). The improved performance with WoB targets with respect to BoW targets is decreased when correcting aberrations, suggesting a role of ocular aberrations in the differences in visual performance between contrast polarities.