Clinical validation of an algorithm to correct the error in the keratometric estimation of corneal power for normal eyes

To validate clinically an algorithm for correcting the error in the keratometric estimation of corneal power by using a variable keratometric index of refraction (nk) in a normal healthy population.

Evaluating approximations generated by the GNG3D method for mesh simplification

In this paper we present different error measurements with the aim to evaluate the quality of the approximations generated by the GNG3D method for mesh simplification. The first phase of this method consists on the execution of the GNG3D algorithm, described in the paper. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces thus obtaining the optimized mesh. The implementation of three error functions, named Eavg, Emax, Esur, permitts us to control the error of the simplified model, as it is shown in the examples studied.

Applying reactive models to column experiments to assess the hydrogeochemistry of seawater intrusion: optimising ACUAINTRUSION and selecting cation exchange coefficients with PHREEQC

Three sets of laboratory column experimental results concerning the hydrogeochemistry of seawater intrusion have been modelled using two codes: ACUAINTRUSION (Chemical Engineering Department, University of Alicante) and PHREEQC (U.S.G.S.). These reactive models utilise the hydrodynamic parameters determined using the ACUAINTRUSION TRANSPORT software and fit the chloride breakthrough curves perfectly. The ACUAINTRUSION code was improved, and the instabilities were studied relative to the discretisation. The relative square errors were obtained using different combinations of the spatial and temporal steps: the global error for the total experimental data and the partial error for each element. Good simulations for the three experiments were obtained using the ACUAINTRUSION software with slight variations in the selectivity coefficients for both sediments determined in batch experiments with fresh water. The cation exchange parameters included in ACUAINTRUSION are those reported by the Gapon convention with modified exponents for the Ca/Mg exchange. PHREEQC simulations performed using the Gains-Thomas convention were unsatisfactory, with the exchange coefficients from the database of PHREEQC (or range), but those determined with fresh water – natural sediment allowed only an approximation to be obtained. For the treated sediment, the adjusted exchange coefficients were determined to improve the simulation and are vastly different from those from the database of PHREEQC or batch experiment values; however, these values fall in an order similar to the others determined under dynamic conditions. Different cation concentrations were simulated using two different software packages; this disparity could be attributed to the defined selectivity coefficients that affect the gypsum equilibrium. Consequently, different calculated sulphate concentrations are obtained using each type of software; a smaller mismatch was predicted using ACUAINTRUSION. In general, the presented simulations by ACUAINTRUSION and PHREEQC produced similar results, making predictions consistent with the experimental data. However, the simulated results are not identical to the experimental data; sulphate (total S) is overpredicted by both models, most likely due to such factors as the kinetics of gypsum, the possible variations in the exchange coefficients due to salinity and the neglect of other processes.

Minimizing the IOL Power Error Induced by Keratometric Power

Purpose. To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometric index (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL power calculation (PIOLadj). Methods. A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power calculation (named PIOLadj). Theoretical differences ($PIOL) between the new proposed formula (PIOLadj) and which is obtained through Gaussian optics (PIOL Gauss) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOL power calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared with Haigis, HofferQ, Holladay, and SRK/T formulas. Results. A theoretical PIOL underestimation greater than 0.5 diopters was present in most of the cases when nk = 1.3375 was used. If nkadj was used for Pc calculation, a maximal calculated error in $PIOL of T0.5 diopters at corneal vertex in most cases was observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL power calculation (PIOLadj) could be valid with effective lens position optimization nondependent of the corneal power. Conclusions. The use of a single value of nk for Pc calculation can lead to significant errors in PIOL calculation that may explain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using the new PIOLadj based on the algorithm of nkadj.

Selective SWIFT-R. A Flexible Software-Based Technique for Soft Error Mitigation in Low-Cost Embedded Systems

Commercial off-the-shelf microprocessors are the core of low-cost embedded systems due to their programmability and cost-effectiveness. Recent advances in electronic technologies have allowed remarkable improvements in their performance. However, they have also made microprocessors more susceptible to transient faults induced by radiation. These non-destructive events (soft errors), may cause a microprocessor to produce a wrong computation result or lose control of a system with catastrophic consequences. Therefore, soft error mitigation has become a compulsory requirement for an increasing number of applications, which operate from the space to the ground level. In this context, this paper uses the concept of selective hardening, which is aimed to design reduced-overhead and flexible mitigation techniques. Following this concept, a novel flexible version of the software-based fault recovery technique known as SWIFT-R is proposed. Our approach makes possible to select different registers subsets from the microprocessor register file to be protected on software. Thus, design space is enriched with a wide spectrum of new partially protected versions, which offer more flexibility to designers. This permits to find the best trade-offs between performance, code size, and fault coverage. Three case studies have been developed to show the applicability and flexibility of the proposal.

Algorithm for Correcting the Keratometric Error in the Estimation of the Corneal Power in Eyes With Previous Myopic Laser Refractive Surgery

Purpose: To calculate theoretically the errors in the estimation of corneal power when using the keratometric index (nk) in eyes that underwent laser refractive surgery for the correction of myopia and to define and validate clinically an algorithm for minimizing such errors. Methods: Differences between corneal power estimation by using the classical nk and by using the Gaussian equation in eyes that underwent laser myopic refractive surgery were simulated and evaluated theoretically. Additionally, an adjusted keratometric index (nkadj) model dependent on r1c was developed for minimizing these differences. The model was validated clinically by retrospectively using the data from 32 myopic eyes [range, −1.00 to −6.00 diopters (D)] that had undergone laser in situ keratomileusis using a solid-state laser platform. The agreement between Gaussian (PGaussc) and adjusted keratometric (Pkadj) corneal powers in such eyes was evaluated. Results: It was found that overestimations of corneal power up to 3.5 D were possible for nk = 1.3375 according to our simulations. The nk value to avoid the keratometric error ranged between 1.2984 and 1.3297. The following nkadj models were obtained: nkadj= −0.0064286r1c + 1.37688 (Gullstrand eye model) and nkadj = −0.0063804r1c + 1.37806 (Le Grand). The mean difference between Pkadj and PGaussc was 0.00 D, with limits of agreement of −0.45 and +0.46 D. This difference correlated significantly with the posterior corneal radius (r = −0.94, P < 0.01). Conclusions: The use of a single nk for estimating the corneal power in eyes that underwent a laser myopic refractive surgery can lead to significant errors. These errors can be minimized by using a variable nk dependent on r1c.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

Relationship among Corneal Biomechanics, Refractive Error, and Axial Length

Purpose: To evaluate the relationship between different ocular and corneal biomechanical parameters in emmetropic and ametropic healthy white children. Methods: This study included 293 eyes of 293 healthy Spanish children (135 boys and 158 girls), ranging in age from 6 to 17 years. Subjects were divided according to the refractive error: control (emmetropia, 99 children), myopia (100 children), and hyperopia (94 children) groups. In all cases, corneal hysteresis (CH) and corneal resistance factor (CRF) were evaluated with the Ocular Response Analyzer system. Axial length (AL) and mean corneal power were also measured by partial coherence interferometry (IOLMaster), and central corneal thickness (CCT) and anterior chamber depth were measured by anterior segment optical coherence tomography (Visante). Results: Mean (±SD) CH and CRF were 12.12 (±1.71) and 12.30 (±1.89) mm Hg, respectively. Mean (±SD) CCT was 542.68 (±37.20) μm and mean (±SD) spherical equivalent was +0.14 (±3.41) diopters. A positive correlation was found between CH and CRF (p < 0.001), and both correlated as well with CCT (p < 0.0001). Corneal resistance factor was found to decrease with increasing age (p = 0.01). Lower levels of CH were associated with longer AL and more myopia (p < 0.001 and p = 0.001, respectively). Higher values of CH were associated with increasing hyperopia. Significant differences in CH were found between emmetropic and myopic groups (p < 0.001) and between myopic and hyperopic groups (p = 0.011). There were also significant differences in CRF between emmetropic and myopic groups (p = 0.02). Multiple linear regression analysis showed that lower CH and CRF significantly associated with thinner CCT, longer AL, and flatter corneal curvature. Conclusions: The Ocular Response Analyzer corneal biomechanical properties seem to be compromised in myopia from an early age, especially in high myopia.

New Approach for Correction of Error Associated With Keratometric Estimation of Corneal Power in Keratoconus

The aim of this study was to obtain the exact value of the keratometric index (nkexact) and to clinically validate a variable keratometric index (nkadj) that minimizes this error. Methods: The nkexact value was determined by obtaining differences (DPc) between keratometric corneal power (Pk) and Gaussian corneal power (PGauss c ) equal to 0. The nkexact was defined as the value associated with an equivalent difference in the magnitude of DPc for extreme values of posterior corneal radius (r2c) for each anterior corneal radius value (r1c). This nkadj was considered for the calculation of the adjusted corneal power (Pkadj). Values of r1c ∈ (4.2, 8.5) mm and r2c ∈ (3.1, 8.2) mm were considered. Differences of True Net Power with PGauss c , Pkadj, and Pk(1.3375) were calculated in a clinical sample of 44 eyes with keratoconus. Results: nkexact ranged from 1.3153 to 1.3396 and nkadj from 1.3190 to 1.3339 depending on the eye model analyzed. All the nkadj values adjusted perfectly to 8 linear algorithms. Differences between Pkadj and PGauss c did not exceed 60.7 D (Diopter). Clinically, nk = 1.3375 was not valid in any case. Pkadj and True Net Power and Pk(1.3375) and Pkadj were statistically different (P , 0.01), whereas no differences were found between PGauss c and Pkadj (P . 0.01). Conclusions: The use of a single value of nk for the calculation of the total corneal power in keratoconus has been shown to be imprecise, leading to inaccuracies in the detection and classification of this corneal condition. Furthermore, our study shows the relevance of corneal thickness in corneal power calculations in keratoconus.

Estimation of the Central Corneal Power in Keratoconus: Theoretical and Clinical Assessment of the Error of the Keratometric Approach

Purpose: The aim of this study was to analyze theoretically the errors in the central corneal power calculation in eyes with keratoconus when a keratometric index (nk) is used and to clinically confirm the errors induced by this approach. Methods: Differences (DPc) between central corneal power estimation with the classical nk (Pk) and with the Gaussian equation (PGauss c ) in eyes with keratoconus were simulated and evaluated theoretically, considering the potential range of variation of the central radius of curvature of the anterior (r1c) and posterior (r2c) corneal surfaces. Further, these differences were also studied in a clinical sample including 44 keratoconic eyes (27 patients, age range: 14–73 years). The clinical agreement between Pk and PGauss c (true net power) obtained with a Scheimpflug photography–based topographer was evaluated in such eyes. Results: For nk = 1.3375, an overestimation was observed in most cases in the theoretical simulations, with DPc ranging from an underestimation of 20.1 diopters (D) (r1c = 7.9 mm and r2c = 8.2 mm) to an overestimation of 4.3 D (r1c = 4.7 mm and r2c = 3.1 mm). Clinically, Pk always overestimated the PGauss c given by the topography system in a range between 0.5 and 2.5 D (P , 0.01). The mean clinical DPc was 1.48 D, with limits of agreement of 0.71 and 2.25 D. A very strong statistically significant correlation was found between DPc and r2c (r = 20.93, P , 0.01). Conclusions: The use of a single value for nk for the calculation of corneal power is imprecise in keratoconus and can lead to significant clinical errors.

Error induced by the estimation of the corneal power and the effective lens position with a rotationally asymmetric refractive multifocal intraocular lens

AIM: To evaluate the prediction error in intraocular lens (IOL) power calculation for a rotationally asymmetric refractive multifocal IOL and the impact on this error of the optimization of the keratometric estimation of the corneal power and the prediction of the effective lens position (ELP). METHODS: Retrospective study including a total of 25 eyes of 13 patients (age, 50 to 83y) with previous cataract surgery with implantation of the Lentis Mplus LS-312 IOL (Oculentis GmbH, Germany). In all cases, an adjusted IOL power (PIOLadj) was calculated based on Gaussian optics using a variable keratometric index value (nkadj) for the estimation of the corneal power (Pkadj) and on a new value for ELP (ELPadj) obtained by multiple regression analysis. This PIOLadj was compared with the IOL power implanted (PIOLReal) and the value proposed by three conventional formulas (Haigis, Hoffer Q and Holladay). RESULTS: PIOLReal was not significantly different than PIOLadj and Holladay IOL power (P>0.05). In the Bland and Altman analysis, PIOLadj showed lower mean difference (-0.07 D) and limits of agreement (of 1.47 and -1.61 D) when compared to PIOLReal than the IOL power value obtained with the Holladay formula. Furthermore, ELPadj was significantly lower than ELP calculated with other conventional formulas (P<0.01) and was found to be dependent on axial length, anterior chamber depth and Pkadj. CONCLUSION: Refractive outcomes after cataract surgery with implantation of the multifocal IOL Lentis Mplus LS-312 can be optimized by minimizing the keratometric error and by estimating ELP using a mathematical expression dependent on anatomical factors.

A Belief System's Organization Based on a Computational Model of the Dynamic Context: First Approximation

In this article we present a model of organization of a belief system based on a set of binary recursive functions that characterize the dynamic context that modifies the beliefs. The initial beliefs are modeled by a set of two-bit words that grow, update, and generate other beliefs as the different experiences of the dynamic context appear. Reason is presented as an emergent effect of the experience on the beliefs. The system presents a layered structure that allows a functional organization of the belief system. Our approach seems suitable to model different ways of thinking and to apply to different realistic scenarios such as ideologies.

S-SETA: Selective Software-Only Error-Detection Technique Using Assertions

Software-based techniques offer several advantages to increase the reliability of processor-based systems at very low cost, but they cause performance degradation and an increase of the code size. To meet constraints in performance and memory, we propose SETA, a new control-flow software-only technique that uses assertions to detect errors affecting the program flow. SETA is an independent technique, but it was conceived to work together with previously proposed data-flow techniques that aim at reducing performance and memory overheads. Thus, SETA is combined with such data-flow techniques and submitted to a fault injection campaign. Simulation and neutron induced SEE tests show high fault coverage at performance and memory overheads inferior to the state-of-the-art.