Power Calculation Method Research Articles

Congenital cataract surgery: long-term refractive outcomes of a new intraocular lens power correction formula.

The final refraction after intraocular lens (IOL) implantation remains a challenge in the management of paediatric cataracts. No consensual guidelines exist for the choice of IOL power. The aim of this study was to validate a method of IOL power calculation by evaluating the final refractive error in all patients with IOL implantation operated at our institution. We retrospectively studied all children under 7 years of age who underwent cataract surgery with IOL implantation at our institution between 2010 and 2015. Intraocular lens (IOL) power was calculated as follows: After B-scan determination of the emmetropic IOL power, a reduction of 40%, 35%, 30%, 25%, 20%, 15%, 10% and 5% was applied to children 0-3, 3-6, 6-12, 12-18, 18-24, 24-30, 30-36, 36-48 months, respectively. The following data were collected: follow-up, age at surgery, uni- or bilaterality, implanted IOL power and final refraction. During this period, 81 children (125 eyes) met the inclusion criteria with a median follow-up of 60 months (36-97). The median age at surgery was 6.61 months (0.76-48). We included 52 children with bilateral cataract (96 eyes) and 29 children with unilateral cataract (29 eyes). The mean implanted IOL power was 23.3 ± 4.6 diopters (D). The mean spherical equivalent at last follow-up was 0.07 ± 3.5 D. Our undercorrection formula for IOL implantation after congenital cataract surgery leads to long-term refractive results globally close to emmetropia.

Laser circumferential scanning photoelectric detection model and analysis of terminal‐sensitive projectile

AbstractThe intersection status of terminal‐sensitive projectile and target is uncertain, which leads to the problem that it is difficult to accurately calculate the laser echo power. This paper studies a new calculation method of laser echo power based on laser circumferential scanning detection mechanism and establishes the mathematical model of laser dynamic scanning by the spatial geometric relationship between terminal‐sensitive projectile and ground target. Combining the characteristics of reflected laser echo power of ground target, we derive the laser echo power calculation function with temporal and spatial distribution characteristics. According to the detection requirements, we configure the parameters of the system and carry out quantitative simulation experiments, the results show when the emitting frequency and scanning speed of pulsed laser were matched, the detection probability is the greatest. With the increase of intersection distance, the reflected laser echo power will decrease, which is basically consistent with the simulation results.

Myopic outcome after intraocular lens implantation in a patient who previously had small-incision lenticule extraction

Introduction: This is a report of cataract surgery in a post–small-incision lenticule extraction (SMILE) patient with low myopia. Patient and clinical findings: A 49-year-old man underwent bilateral SMILE 18 months previously, and the visual acuity of both eyes recovered to 20/20. The patient noticed a gradual reduction in visual acuity in his left eye and blurring for 3 months. The corrected distance visual acuity (CDVA) was 20/67 in his left eye. Diagnosis, intervention, and outcomes: The slitlamp examination revealed an anterior subcapsular cataract. The intraocular lens (IOL) power was calculated by using a multiformula averaging method. A standard femtosecond laser–assisted phacoemulsification cataract surgery was performed and a trifocal IOL implanted. 2 months after IOL implantation, the uncorrected distance visual acuity of the left eye was 20/33, the autorefraction values were −1.37 −0.25 × 146, and the CDVA was 20/20. Conclusions: This case report showed that current postrefractive IOL power calculation formulas or methods may lead to myopic outcomes in patients who previously received SMILE. A standard IOL calculation may be more suitable for such patients. Additional case studies are needed to accurately calculate IOL power after SMILE similar to laser in situ keratomileusis.

Power analysis for stepped wedge trials with multiple interventions.

Stepped wedge design (SWD) trials are cluster randomized trials that feature staggered, unidirectional cross-over between treatment conditions. Existing literature on power for SWDs focuses primarily on designs with two conditions, typically a control and an intervention condition. However, SWDs with more than one treatment condition are being proposed and conducted. We present a linear mixed model for SWDs with two or more interventions, including both multiarm and factorial designs. We derive standard errors of the intervention effect coefficients, and present power calculation methods. We consider both repeated cross-sectional and cohort designs. Design features, with a focus on treatment allocations, are examined to determine their impact on power.

Alternative method of intraocular lens power calculation in eyes with short axial length

To develop an alternative method of intraocular lens (IOL) power calculation in eyes with mature cataract and axial length (AL) of less than 22.0 mm using modern formulas Barrett Universal II and Hill RBF. The study enrolled 41 patients (41 eyes) who underwent phacoemulsification (PE). Ultrasound biometry (Tomey Biometer Al-100) and keratometry (Topcon-8800) were used for IOL power calculation by SRK/T and Haigis formulas. To calculate IOL power by Barrett Universal II and Hill RBF formulas, 0.2 mm were added to AL measured with ultrasonography (retinal thickness). One month after PE, spherical equivalent of refraction was compared with target refraction (calculated by the formulas listed above), and based on that a conclusion was made on the accuracy of calculations. Haigis formula was found to be the least accurate (IOL calculation error -0.39±0.79 D). The calculation error in SRK/T (0.04±0.79 D), Barrett Universal II (0.02±0.79 D) and Hill RBF (-0.05±0.73 D) formulas was much lower. However, among them Hill RBF had the lowest spread of the mean absolute IOL calculation error. Pairwise comparison revealed significant difference of mean IOL calculation error by Haigis formula versus the others. There was no significant difference in the following pairs: SRK/T - Barrett Universal II (p=0.855), and SRK/T - Hill RBF (p=0.167), but there was a significant difference (p=0.043) in the Barrett Universal II - Hill RBF pairdue to the tendency for slight hypermetropic calculation error in the former and the inherent slight myopic shift in the latter.. The proposed alternative method of IOL power calculation in eyes with mature cataract and short AL using modern formulas (Barrett Universal II and Hill RBF) shows higher accuracy compared to the formulas embedded in ultrasound biometer (SRK/T and Haigis), and can be recommended for use in everyday practice.

An Approach for Power Quantification Based on Stockwell Transform and CPC Power Theory

This article presents a power calculation method for non-sinusoidal signals with non-stationary characteristics based on currents’ physical components (CPC) power theory and the discrete Stockwell transform (DST). The DST independently localizes the real and imaginary components of the spectrum at any given time interval, being suitable for analyzing non-stationary waveforms. The proposed method allows for an instantaneous tracking of the power components defined in CPC power theory based on a time–frequency analysis provided by the DST. Thus, the proposed method is able to identify alterations in the harmonic content, and consequently track variations on the powers, in all time instants. The proposed method is validated using non-stationary signals, including a scenario with frequency deviation, presenting rather promising results when compared to the Fourier-based approach. Additionally, the proposed method is also assessed in noisy environments by inserting an additive Gaussian noise, based on real oscillographic records, presenting a good performance, which attests its suitability for power quality (PQ) analysis and power calculation.

Intraocular lens power calculation in eyes with previous corneal refractive surgery.

Intraocular lens (IOL) power calculation after corneal refractive surgery (CRS) becomes an expanding challenge for ophthalmologists as more and more cataract surgeries after CRS are required. These patients typically also have high expectations as to visual performance. Conventional IOL power calculation schemes frequently provide inaccurate results in these cases. This review aims to summarize and recommend currently available IOL power calculation methods for eyes with the most common CRS methods: radial keratotomy (RK), photorefractive keratectomy (PRK), laser in situ keratomileusis (LASIK), and small incision lenticule extraction (SMILE). To this end, biometry measuring methods and IOL formulas will be explained and combinations of both are proposed. In synopsis, it is evident that the latest generation of vergence formulas exhibit favorable IOL power prediction accuracy in post-CRS eyes, even though the predictive precision of methods in eyes without CRS is not attained. Ray tracing computation, intraoperative aberrometry, and machine learning–based formulas hold potential to further improve refractive outcomes in post-CRS eyes.

Estimation of multivariate treatment effects in contaminated clinical trials.

The paper addresses estimating and testing treatment effects with multivariate outcomes in clinical trials where imperfect diagnostic devices are used to assign subjects to treatment groups. The paper focuses on the pre-post design and proposes two novel methods for estimating and testing treatment effects. In addition, methods for sample size and power calculations are developed. The methods are compared with each other and with a traditional method in a simulation study. The new methods show significant advantages in terms of power, coverage probability, and required sample size. The application of the methods is illustrated with data from electroencephalogram (EEG) recordings of alcoholic and control subjects.

Power considerations for generalized estimating equations analyses of four-level cluster randomized trials.

In this article, we develop methods for sample size and power calculations in four-level intervention studies when intervention assignment is carried out at any level, with a particular focus on cluster randomized trials (CRTs). CRTs involving four levels are becoming popular in healthcare research, where the effects are measured, for example, from evaluations (level 1) within participants (level 2) in divisions (level 3) that are nested in clusters (level 4). In such multilevel CRTs, we consider three types of intraclass correlations between different evaluations to account for such clustering: that of the same participant, that of different participants from the same division, and that of different participants from different divisions in the same cluster. Assuming arbitrary link and variance functions, with the proposed correlation structure as the true correlation structure, closed-form sample size formulas for randomization carried out at any level (including individually randomized trials within a four-level clustered structure) are derived based on the generalized estimating equations approach using the model-based variance and using the sandwich variance with an independence working correlation matrix. We demonstrate that empirical power corresponds well with that predicted by the proposed method for as few as eight clusters, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator, under both balanced and unbalanceddesigns.

Allowing for stratification in sample size planning of two-arm trials with continuous or binary outcome: Overview and tutorial.

More often than not, clinical trials and even nonclinical medical experiments have to be run with observational units sampled from populations to be assumed heterogeneous with respect to covariates associated with the outcome. Relevant covariates which are known prior to randomization are usually categorical in type, and the corresponding subpopulations are called strata. In contrast to randomization which in most cases is performed in a way ensuring approximately constant sample size ratios across the strata, sample size planning is rarely done taking stratification into account. This holds true although the statistical literature provides a reasonably rich repertoire of testing procedures for stratified comparisons between two treatments in a parallel group design. For all of them, at least approximate methods of power calculation are available from which algorithms or even closed-form formulae for required sample sizes can be derived. The objective of this tutorial is to give a systematic review of the most frequently applicable of these methods and to compare them in terms of their efficiency under standard settings. Based on the results, recommendations for the sample size planning of stratified two-arm trials are given.

Free Switching Control Strategy for Multi-Operation Modes of Multi-Port Energy Router in Distribution Area

For the distribution area with a high penetration rate of new energy, the traditional power supply system has some problems, such as a single form of power supply and low utilization of new energy. Because the multi-port energy router can realize the interconnection and complementation of multiple energy forms, it has become the key piece of equipment in the hybrid AC/DC distribution area. Nevertheless, restricted by the existing control strategy, the performance of the energy router in complex operation mode switching and coordinated control still needs to be further improved. To address this issue, the free switching control strategy is proposed in this paper. Firstly, the topology and model of the multi-port energy router are designed and established. Secondly, the operation mode of the system is analyzed, and the control strategy of each port is designed. Then, a reference power calculation method suitable for multi-mode operation is derived. Based on this, the control strategy does not need to be changed when operation modes are switched. Furthermore, the extended state observer is introduced to track and compensate for the new energy disturbance, which can improve the power quality of the system. Finally, the simulation and experimental results show that the proposed control strategy of the multi-port energy router can realize flexible and controllable power transmission among various modules in the distribution area and the free switching of multi-operation modes without changing the control strategy.

Swdpwr: A SAS macro and an R package for power calculations in stepped wedge cluster randomized trials

Background and objective:The stepped wedge cluster randomized trial is a study design increasingly used in a wide variety of settings, including public health intervention evaluations, clinical and health service research. Previous studies presenting power calculation methods for stepped wedge designs have focused on continuous outcomes and relied on normal approximations for binary outcomes. These approximations for binary outcomes may or may not be accurate, depending on whether or not the normal approximation to the binomial distribution is reasonable. Although not always accurate, such approximation methods have been widely used for binary outcomes. To improve the approximations for binary outcomes, two new methods for stepped wedge designs (SWDs) of binary outcomes have recently been published. However, these new methods have not been implemented in publicly available software. The objective of this paper is to present power calculation software for SWDs in various settings for both continuous and binary outcomes. Methods: We have developed a SAS macro %swdpwr, an R package swdpwr and a Shiny app for power calculations in SWDs. Different scenarios including cross-sectional and cohort designs, binary and continuous outcomes, marginal and conditional models, three link functions, with and without time effects under exchangeable, nested exchangeable and block exchangeable correlation structures are accommodated in this software. Unequal numbers of clusters per sequence are also allowed. Power calculations for a closed cohort employ a block exchangeable within-cluster correlation structure that accounts for three intracluster (intraclass) correlations: the within-period, between-period, and within-individual correlations. Cross-sectional cohorts allow for nested exchangeable or exchangeable correlation structures defined by the within-period and the between-period intracluster correlations only. Our software assumes a complete design and equal cluster-period sizes. While the methods accommodate correlation structures of constant within-period intracluster correlation coefficient (ICC) as well as a different within- and between-period ICC, it does not allow the between-period ICC to decay. Results:swdpwr provides an efficient tool to support investigators in the design and analysis of stepped wedge cluster randomized trials. swdpwr addresses the implementation gap between newly proposed methodology and their application to obtain more accurate power calculations in SWDs. Conclusions: In an effort to make computationally efficient (and non-simulation-based) power methods under both the cross-sectional and closed-cohort designs for continuous and binary outcomes more accessible, we have developed this user-friendly software. swdpwr is implemented under two platforms: SAS and R, satisfying the needs of investigators from various backgrounds. Additionally, the Shiny app enables users who are not able to use SAS or R to implement these methods online straightforwardly.

Comparison and analysis of several instantaneous reactive power calculation methods

Briefly describes several more common algorithm of reactive power when the input signal is a sine signal and research all kinds of reactive power calculation method, through matlab using the theory of monte carlo random multiple sets of random number them as the amplitude and phase Angle of voltage, current, the different calculation method of the size of the instantaneous reactive power, To get the best calculation method. Multiple groups of random numbers can avoid the error caused by using only one set of data for testing in existing papers.

COMPARISON OF OPTICAL BIOMETRY AND A SCAN FOR CALCULATION OF INTRAOCULAR LENS POWER IN AGE RELATED NUCLEAR CATARACT AT TERTIARY CARE EYE HOSPITAL

Objective: To compare optical biometry and A-scan for calculating intraocular lens power in patients with nuclear cataract at tertiary care eye hospital.
 Study Design: Cross sectional comparative study.
 Place and Duration of Study: Armed Forces Institute of Ophthalmology, Pak Emirates Military Hospital, Rawalpindi, from Jul to Dec 2018.
 Methodology: In this study 70 eyes of 70 patients planned for cataract surgery by phacoemulsification underwent both optical biometry with intraocular lens master and ultrasound biometry applanation by A scan after informed consent. Intraocular lens power calculated by these two methods of biometry was compared. Phacoemulsification surgery was performed through a 2.3 mm superior temporal clear corneal incision. All patients underwent in the bag implantation of the same intraocular lens type.
 Results: The mean age of the patients was 62.89 ± 6.69 years. A significant (p-value<0.001) difference in intraocular lens power calculation was noted (20.96 ± 1.76 vs. 22.03 ± 1.61) with optical biometry and A-scan respectively. Association on the basis of age groups showed a significant (p-value<0.001) difference in both strata that was among patients having age ≤65 years and patients having age >65 years.
 Conclusion: Optical biometry was found efficient and safe method for calculation of intraocular lens power. Optical biometry is noncontact method having very less chance of infection and suitable for most of the eye types.

Power calculation for analyses of cross-sectional stepped-wedge cluster randomized trials with binary outcomes via generalized estimating equations.

Power calculation for stepped-wedge cluster randomized trials (SW-CRTs) presents unique challenges, beyond those of standard parallel cluster randomized trials, due to the need to consider temporal within cluster correlations and background period effects. To date, power calculation methods specific to SW-CRTs have primarily been developed under a linear model. When the outcome is binary, the use of a linear model corresponds to assessing a prevalence difference; yet trial analysis often employs a nonlinear link function. We propose power calculation methods for cross-sectional SW-CRTs under a logistic model fitted by generalized estimating equations. Firstly, under an exchangeable correlation structure, we show the power based on a logistic model is lower than that from assuming a linear model in the absence of period effects. We then evaluate the impact of background prevalence changes over time on power. To allow the correlation among outcomes in the same cluster to change over time and with treatment status, we generalize the methods to more complex correlation structures. Our simulation studies demonstrate that the proposed power calculation methods perform well with the model-based variance under the true correlation structure and reveal that a working independence structure can result in substantial efficiency loss, while a working exchangeable structure performs well even when the underlying correlation structure deviates from exchangeable. An extension to our methods accounts for variable cluster sizes and reveals that unequal cluster sizes have a modest impact on power. We illustrate the approaches by application to a quality of care improvement trial for acute coronary syndrome.

Rational design justification of the tunnel boring shield executive body for the conditions of the mines of Saint Petersburg Metrostroy

The article discusses the features of running tunnels in difficult mining and geological conditions of the Saint Petersburg Metrostroy using modern tunnel boring shields of Herrenknecht company with hybrid executive bodies equipped with a incisors and rock cutters. The work of a hybrid executive body is analyzed when driving along a heterogeneous bottomhole massif consisting of Cambrian clay with limestone interlayers. Theoretical and experimental studies of vibroactive cones, a graphical representation of the dependence of the depth of their penetration on the axial force and axial force together with the applied shock load (the dependences of the penetration depth are interpreted as a linear dependence) have been carried out. An increase in the intensity of destruction of a heterogeneous bottomhole massif consisting of Cambrian clay and limestone interlayers using vibroactive rock-cutting tools (spiked roller) was theoretically and experimentally confirmed, while the growth of the penetration rate is determined depending on the number of their parameters. The design is considered, the principle of operation and the method of power calculation of a rotary executive body equipped with vibroactive cutters are described, on the basis of which a nomogram of the dependence of the torque and performance of the tunnel boring shield on the feed rate of the executive body to the bottom is built.

Corneal power values for use with keratoprostheses and intraocular lenses

AbstractPurposeTo specify a keratoprosthesis (KPro) power value for use with an intraocular lens (IOL).MethodsRaytracing software was used to determine the imaging properties of both the natural cornea and conceptual KPro designs, and IOL power calculation methods were reviewed. Traditional calculations use ‘thick lens’ models for the overall eye, while also using ‘thin lens’ approximations for the cornea and IOL. The power of the natural cornea acts approximately at the apex, although this is unlikely to be the case for a KPro. The IOL location is determined using an empirical adjustment that is calculated from clinical results for natural eyes.ResultsThe use of a KPro has a similar optical effect to corneal refractive surgery, where the cornea no longer matches the original eye. A modification of the ‘double‐K’ calculation method can be used by specifying the KPro effective power at the original corneal apex, but still estimating the postoperative IOL location using the original corneal power. The KPro power is measured by assembling the KPro with fluid and a window to simulate the way it is used, recording the best focus power at room temperature with a 3 mm diameter aperture, rescaling to the in situ power at 35°C using refractive index changes, and then rescaling again to the power expected relative to the original corneal apex. When expressed as a K value, a keratometer refractive index of 1.332 is proposed. If necessary, clinical results may be used later to make empirical adjustments to the calculation method.ConclusionsA KPro power can be specified relative to the expected location of the original corneal apex using a keratometer index of 1.332. A double‐K calculation can then be used to determine the correct KPro and IOL power values for a pseudophakic eye.

Calculation Method of DC Limit Power Considering Influence of New-generation Synchronous Condensers

Because the new-generation synchronous condenser has strong excitation ability and leading power factor operation ability, the DC transmission power value will be effectively improved. In this paper, the reactive power limit value models of the new-generation synchronous condensers under phase-in and phase-lag operation conditions were established. Then, the correlation model between AC and DC systems considering the effects of new-generation synchronous condensers is established. Based on this, the commutation angle of DC and the parameters related to the inverter side are calculated under rated conditions. Moreover, the AC system equations is combined to solve the potential of the equivalent AC system and the power angle of DC bus voltage. Then, using DC current as an independent variable to find the maximum DC power considering the reactive power limit value of the new-generation synchronous condensers. Therefore, the initial reactive power output of new-generation synchronous condensers and the maximum power of DC transmission can be calculated.The results of this paper provide a theoretical basis for improving DC transmission power in power system analysis, and have an important role in promoting the consumption of renewable energy at the DC-fed AC grid.

Comparison of Axis Determination With Different Toric Intraocular Lens Power Calculation Methods.

To compare the axis position of the measured total corneal astigmatism (TCA) with the axis of the anterior keratometry and the calculated axis position of different toric intraocular lens (IOL) calculators. A total of 163 astigmatic eyes of 163 patients were retrospectively analyzed. The axis of the actual TCA, measured with anterior segment optical coherence tomography, was compared to the anterior keratometric value (Group I) and three different methods of TCA calculation for toric IOL power determination: Abulafia-Koch regression formula (Group II), Barrett Toric Calculator V2.0 (Group III), and Barrett Toric Calculator V2.0 including measured posterior keratometric value (Group IV). Eyes were assigned to three subgroups: with-the-rule, against-the-rule, and oblique astigmatism. The mean deviation calculated from measured TCA was +0.56° (Group I), -0.32° (Group II), -0.37° (Group III), and -1.00° (Group IV). For with-the-rule astigmatism, the TCA axis agreed most with Group I (6.5% outliers > 5° deviation). For against-the-rule astigmatism, Group IV and Group II were closest to the measured TCA axis (1.5% and 3% outliers with > 5° deviation). The means of the calculated axis were similar to the measured TCA, but the proportion of outliers with an axis deviation of greater than 5° showed remarkable differences. Isolated anterior keratometric value measurements showed the fewest outliers in with-the-rule astigmatism. In against-the-rule astigmatism, Abulafia-Koch calculation should be used for axis determination. [J Refract Surg. 2021;37(9):642-647.].

Comparisons of intraocular lens power calculation methods for eyes with previous myopic laser refractive surgery: Bayesian network meta-analysis.

To compare the accuracy of the methods for calculation of intraocular lens (IOL) power in eyes with previous myopic laser refractive surgery. EENT Hospital of Fudan University, Shanghai, China. Network meta-analysis. A literature search of MEDLINE and Cochrane Library from January 2000 to July 2019 was conducted for studies that evaluated methods of calculating IOL power in eyes with previous myopic laser refractive surgery. Outcomes measurements were the percentages of prediction error within ±0.50 diopters (D) and ±1.00 D of the target refraction (% ±0.50 D and % ±1.00 D). Traditional and network meta-analysis were conducted. Nineteen prospective or retrospective clinical studies, including 1217 eyes and 13 calculation methods, were identified. A traditional meta-analysis showed that compared with the widely used Haigis-L method, the Barrett True-K formula, optical coherence tomography (OCT), and Masket methods showed significantly higher % ±0.50 D, whereas no difference was found in the % ±1.00 D. A network meta-analysis revealed that compared with the Haigis-L method, the OCT, Barrett True-K formula, and optiwave refractive analysis (ORA) methods performed better on the % ±0.50 D, whereas the Barrett True-K formula and ORA methods performed better on the % ±1.00 D. Based on the performances of both outcomes, the Barrett True-K formula, OCT, and ORA methods showed highest probability to rank the top 3 among the 13 methods. The Barrett True-K formula, OCT, and ORA methods seemed to offer greater accuracy than others in calculating the IOL power for postrefractive surgery eyes.