double-K Method Research Articles

Application of Bilinear Softening Laws and Fracture Toughness of Foamed Concrete

This study examined the fracture and failed performance of foamed concrete materials by testing normalized notched beams under three-point bending via three methods: inverse analysis, digital image correlation (DIC), and finite element modeling (FEM). It also discussed both experimental and FEM characteristics. However, inverse analysis is only applicable for specimens with a notch height of 30 mm. Bilinear softening of the tested beams was estimated to identify the fracture energy (GF), critical crack length (ac), and elastic modulus (E). Additionally, the fracture toughness was calculated by adopting the double-K method (initiation fracture, unstable fracture, and cohesive fracture). Two-dimensional FEA modeling of the fracture was conducted using the traction-separation law (TSL), incorporating the extended finite element method (XFEM) and cohesive zone (CZM) techniques. A finite element sensitivity for the XFEM and CZM was performed, with the global mesh size of 2 and the damage stabilization cohesion of 1 × 10−5 showed good convergence and were used in other models. Further comparison of the DIC experiment findings with those from the FEM demonstrated good agreement in terms of crack propagation simulation.

Reply to Cione et al. Comment on "Iida et al. Development of a New Method for Calculating Intraocular Lens Power after Myopic Laser In Situ Keratomileusis by Combining the Anterior-Posterior Ratio of the Corneal Radius of the Curvature with the Double-K Method. J. Clin. Med. 2022, 11, 522".

We appreciate the insightful comments [...].

Comment on Iida et al. Development of a New Method for Calculating Intraocular Lens Power after Myopic Laser In Situ Keratomileusis by Combining the Anterior-Posterior Ratio of the Corneal Radius of the Curvature with the Double-K Method. J. Clin. Med. 2022, 11, 522.

We read with great interest the article by Iida et al. [...].

Development of a New Method for Calculating Intraocular Lens Power after Myopic Laser In Situ Keratomileusis by Combining the Anterior-Posterior Ratio of the Corneal Radius of the Curvature with the Double-K Method.

Background: A new method, the Iida–Shimizu–Shoji (ISS) method, is proposed for calculating intraocular lens (IOL) power that combines the anterior–posterior ratio of the corneal radius of the curvature after laser in situ keratomileusis (LASIK) and to compare the predictability of the method with that of other IOL formulas after LASIK. Methods: The estimated corneal power before LASIK (Kpre) in the double-K method was 43.86 D according to the American Society of Cataract and Refractive Surgery calculator, and the K readings of the IOL master were used as the K values after LASIK (Kpost). The factor for correcting the target refractive value (correcting factor [C-factor]) was calculated from the correlation between the anterior–posterior ratio of the corneal radius of the curvature and the refractive error obtained using this method for 30 eyes of 30 patients. Results: Fifty-nine eyes of 59 patients were included. The mean values of the numerical and absolute prediction errors obtained using the ISS method were −0.02 ± 0.45 diopter (D) and 0.35 ± 0.27 D, respectively. The prediction errors using the ISS method were within ±0.25, ±0.50, and ±1.00 D in 49.2%, 76.3%, and 96.6% of the eyes, respectively. The predictability of the ISS method was comparable to or better than some of the other formulas. Conclusions: The ISS method is useful for calculating the IOL power in eyes treated with cataract surgery after LASIK.

Comparison of intraocular lens calculation methods after myopic laser-assisted in situ keratomileusis and radial keratotomy without prior refractive data

AimTo compare intraocular lens (IOL) calculation methods not requiring refraction data prior to myopic laser-assisted in situ keratomileusis (LASIK) and radial keratotomy (RK).MethodsIn post-LASIK eyes, the methods not requiring prior...

Size effect on double-K fracture parameters of concrete based on fracture extreme theory

Based on fracture extreme theory (FET), the size effect on initial fracture toughness $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and unstable fracture toughness $$K_{\mathrm{I}}^{\mathrm{un}}$$ of concrete for three-point bending beam was investigated. Nine groups of geometrically similar specimen were simulated to obtain peak load and critical crack mouth opening displacement, of which specimen depth was from 200 to 1000 mm and initial crack length-to-depth ratios were from 0.1 to 0.6. The $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ were calculated by FET and double-K method, in which FET adopted the linear, bilinear, and trilinear cohesive stress distribution assumptions and double-K method only used the linear cohesive stress distribution assumption. With linear cohesive stress distribution assumption, $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ determined by FET and double- K method were compared. Then, the influence of specimen depth on $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ was discussed. In addition, $$K_{\mathrm{I}}^{\mathrm{ini}}/K_{\mathrm{I}}^{\mathrm{un}}$$ calculated via FET using different cohesive stress distribution assumptions were analyzed.

Intraocular Lens power calculation after laser refractive surgery: A Meta-Analysis

There are an increasing number of people who have had refractive surgery now developing cataract. To compare the accuracy of different intraocular lens (IOL) power calculation formulas after laser refractive surgery (photorefractive keratectomy or laser in situ keratomileusis), a comprehensive literature search of PubMed and EMBASE was conducted to identify comparative cohort studies and case series comparing different formulas: Haigis-L, Shammas-PL, SRK/T, Holladay 1 and Hoffer Q. Seven cohort studies and three observational studies including 260 eyes were identified. There were significant differences when Hoffer Q formula compared with SRK/T, Holladay 1. Holladay 1 formula produced less prediction error than SRK/T formula in double-K method. Hoffer Q formula performed best among SRK/T and Holladay 1 formulas in total and single-K method. In eyes with previous data, it is recommended to choose double-K formula except SRK/T formula. In eyes with no previous data, Haigis-L formula is recommended if available, if the fourth formula is unavailable, single-k Hoffer Q is a good choice.

Calculation of Unknown Preoperative K Readings in Postrefractive Surgery Patients

Purpose To determine the unknown preoperative K readings (Kpre) to be used in history-based methods, for intraocular lens (IOL) power calculation in patients who have undergone myopic photorefractive keratectomy (PRK). Methods A regression formula generated from the left eyes of 174 patients who had undergone PRK for myopia or for myopic astigmatism was compared with other methods in 168 right eyes. The Pearson index and paired t-test were utilized for statistical analysis. Results The differences between Kpre and those obtained with the other methods were as follows: 0.61 ± 0.94 D (range: −3.94 to 2.05 D, p < 0.01) subtracting the effective treatment, 0.01 ± 0.86 D (range: −2.61 to 2.34 D, p = 0.82) with Rosa's formula, −0.02 ± 1.31 D (range: −3.43 to 3.68 D, p = 0.82) with the current study formula, and −0.43 ± 1.40 D (range: −3.98 to 3.12 D, p < 0.01) utilizing a mean K (Km) of 43.5 D. Conclusions These formulas may permit the utilization of history-based methods, that is, the double-K method in calculating the IOL power following PRK when Kpre are unknown.

Determining initial fracture toughness of concrete for split-tension specimens based on the extreme theory

A theoretical method to determine the initial fracture toughness KIini of concrete for central-notched split-tension specimens was developed based on the extreme theory. In this method, the KIini, critical crack tip opening displacement CTODc, and half critical effective crack extension Δɑc could be obtained by the experimental peak load of a single specimen. The measurement of critical crack mouth opening displacement CMODc was unnecessary in this method. The fracture parameters were calculated using the cube and cylinder split-tension specimens. Results showed that the values of KIini obtained by the proposed method were slightly smaller than those obtained by the double-K method, and the difference between them generally decreases with the loading rates. And the values of CTODc and Δɑc obtained by the proposed method were more stable compared with those obtained by the double-K method.

Potential Impacts of Climate Change on Phosphorus and DO in Yuqiao Reservoir

The climate indicators and water quality parameters, e.g. total phosphorus (TP) and dissolved oxygen (DO) in a period of 20 years (1992-2011) were analyzed to explore potential impacts of climate change on nutrients and DO. Firstly, the study period was divided into two decades: 1992-2001 cool decade and 2002-2011 warm decade for the Mann Kendall statistical test and the accumulative anomaly test. Secondly, the significance of climate parameters in seasonal variations was analyzed by comparing the nonlinear trends of parameters using non-parametric regression in two decades respectively. Finally, comparing the relationship between climate indicators and water quality parameters for two decades, the potential impacts were investigated by double-k method. The results showed that the higher temperature potentially decreased TP concentrations in winter and spring and DO concentration in autumn. However, the increases in air temperature in winter and spring increased DO concentration. The increase in wind speed was most likely to increase TP and DO concentrations in all four seasons. A positive correlation between precipitation and TP concentration was found in all four seasons. The DO concentration declined when rainfall decreased in summer. The difference in temporal trends between inflow P loading and concentrations in reservoir indicated the potential impacts of climate change on TP concentration. The field data in TP and macrophytes biomass in spring was the evidence supporting that TP in spring was likely to decline when the air temperature increased. The study provides a reference for the impacts and mechanisms of climate change on water quality in Yuqiao reservoir.

Evaluation of Orbscan II plus non-history double-K method in intraocular lens power calculation for patients after refractive surgery

To explore the accuracy of intraocular lens (IOL) power calculation with non-history method using the keratometric value derived from one zone of Orbscan II topography after laser in situ keratomileusis (LASIK). For this retrospective study, 20 eyes from 20 patients undergoing myopic LASIK were included from August 2008 to November 2011. Posterior corneal curvature in peripheral 7 to 10 mm fitting zone of postoperative cornea was measured with Orbscan II topography. The ratio between anterior cornea and posterior cornea was used to calculate the preoperative total corneal power of each eye. The predicted postoperative spherical equivalent was calculated by the calculated preoperative total corneal power, power of implanted IOL, refractive error before cataract surgery and eye length from IOL-Master into the double-K method for SRK-T formula. The predicted postoperative spherical equivalent was also calculated by double-K method for SRK-T formula with clinical history. The mean difference between actual and predicted postoperative spherical equivalent, i.e. mean absolute error (MAE), were compared. (1) Non-history method: MAE of 11 eyes was within ± 0.5 D (55%), MAE of 15 eyes within ± 1.0 D (75%) and MAE of all eyes within ± 2.0 D. (2) Clinical-history method: MAE of 10 eyes was within ± 0.5 D (50%), MAE of 14 eyes within ± 1.0 D (70%) and MAE of all eyes within ± 2.0 D. (3) Comparison of non-history and clinical-history methods: The MAE of non-history method was (0.61 ± 0.59) D and the MAE of clinical-history method (0.68 ± 0.55) D. Paired t-test showed no statistically significant difference between two methods (t = -1.248, P = 0.227). The non-history method using the keratometric value derived from one zone of Orbscan II topography after LASIK provides an accurate calculation of IOL power and it can be used as a substitute for incomplete clinical data.

Modified double-K method for intraocular lens power calculation after excimer laser corneal refractive surgery

To propose the new anterior-posterior method (A-P method) that does not require historical data to calculate intraocular lens (IOL) power after laser in situ keratomileusis (LASIK) and to compare the accuracy of the method with other IOL formulas after LASIK. Keio University Hospital, Tokyo, Japan. Case series. Eyes having phacoemulsification and IOL implantation after myopic LASIK were analyzed retrospectively. The A-P method is a modification of the double-K method using the SRK/T formula in which the estimated pre-LASIK keratometry (K) power calculated from the post-LASIK posterior sagittal power in the 6.0 mm zone is used for the preoperative K value in the double-K method and the post-LASIK anterior sagittal power is used for the postoperative K value. The accuracy of the A-P method was compared with that of other formulas that do not require preoperative data and with formulas that require preoperative data. The median values of the arithmetic and absolute prediction errors using the A-P method were 0.16 diopter (D) and 0.54 D, respectively. The prediction errors using the A-P method were within ± 0.50 D in 46.4% of eyes and within ± 1.00 D in 75.0%. The percentage of eyes within ± 1.00 D of the prediction errors with the A-P method was highest with the no-history methods. The A-P method may be a good option for calculating IOL power in eyes having cataract surgery after LASIK when preoperative LASIK data are unavailable.

A theoretical method for determining initiation toughness based on experimental peak load

A theoretical method for determining the initiation toughness was proposed using input conditions of the peak load and the tensile softening curve. In this method, the cohesive stress is considered to calculate the values of critical effective crack length, crack tip opening displacement, and the initiation toughness. The calculated results using the proposed method were compared with those by the double-K method+. The comparison showed that the values obtained by the proposed method were slightly greater than those by the double-K method. Moreover, the calculation results of initiation toughness by the proposed method were verified to be independent of the specimen size and not sensitive to the tensile softening curve.

A new central–peripheral corneal curvature method for intraocular lens power calculation after excimer laser refractive surgery

To propose the central-peripheral (C-P) method, which requires no data history to calculate intraocular lens (IOL) powers for eyes that underwent laser in situ keratomileusis (LASIK), and compare the accuracy of the C-P method with other IOL formulas for eyes after LASIK. Sixteen patients with cataract (25 eyes) who underwent myopic LASIK were analysed retrospectively. The C-P method is a modified double-K method using the SRK/T formula, in which the estimated pre-LASIK keratometric power calculated from the post-LASIK peripheral anterior sagittal power (also called the axial power) is used for the Kpre in the double-K method using the SRK/T formula, and the post-LASIK anterior sagittal power is used for the Kpost. We compared the accuracy of the C-P method with other popular IOL calculation formulas for use in eyes after LASIK. The median values of the arithmetic and absolute prediction errors with the C-P method were 0.11 diopter (D) (range, -1.67 to 1.97 D) and 0.55 D (range, 0.02-1.97 D), respectively. The prediction error using the C-P method was within ±0.5 D in 48% of eyes, within -1.0 to +0.5 D in 60% of eyes, and within ±1.0 D in 68% of eyes. The C-P method resulted in a significantly higher percentage of eyes within ±0.5 D than the BESSt formula, Shammas-PL formula, true net power method, double-K method using 43.5 D for Kpre, and Feiz-Mannis method. The C-P method may be a good option for calculating IOL powers in eyes undergoing cataract surgery after LASIK when the preoperative LASIK data are unavailable.

Evaluation of Fracture Parameters by Double-G, Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (4), unstable fracture toughness (K-Ic(c)), unstable fracture toughness (K-Ic(un)) and initiation fracture toughness (K-Ic(ini)) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K-Ic(un) of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.

Orbscan II and double-K method for IOL calculation after refractive surgery

Precise IOL calculation in post-refractive surgery patients is still a challenge for the cataract surgeon. The purpose of this study is to test whether adding Orbscan II values into the double-K method improves IOL calculation in this group of patients. A prospective study with 43 eyes previously submitted to refractive surgery that underwent cataract extraction. IOL calculation was performed with double-K method. Post-K value was derived from Orbscan total-mean power map. The average corneal curvature of the general population (43.8D) was used as the pre-K value. Refraction results 30 days after surgery were compared with refraction that would be obtained if we used: (1) post-K values from keratometry, (2) post-K values from topography, and (3) pre-K values from Orbscan total-mean power. Anterior chamber depth measures obtained with the IOL Master and Orbscan II were compared. Mean postoperative spherical equivalent (SE) was -0.25 ± 1.10 D in eyes submitted to radial keratotomy , -1.04 ± 1.42 D in eyes previously submitted to myopic Lasik, and +0.05 ± 1.76 D in those submitted to hyperopic surgeries. Had we inputted post-K values derived from keratometer and from topography, we would have obtained significantly higher postoperative refractive errors in eyes previously submitted to myopic refractive surgery (p < 0.05). Refractions using pre-K derived from the central 8 mm Orbscan instead of 43.8 D were similar in all studied groups (p > 0.05). Anterior chamber depth measured with IOL Master or Orbscan were similar. Orbscan measurements used as the post-K values into the double-K method provide a precise IOL calculation, especially in post myopic refractive surgery patients.

El cálculo de la lente intraocular tras cirugía foto-refractiva corneal: Revisión de la literatura

Revision of methods for estimating corneal power (Kpost) and effective lens position (ELP) for cataract surgery after corneal refractive surgery. Review of medical literature. To calculate the intraocular lens that achieves emetropia after corneal refractive surgery it is necessary to correct the Kpost and to estimate the effective lens position again correcting it. There are different formulae depending on the available information. Ideally, we need pre (Kpre) and post-treatment keratometry record (Kpost) and pre (Rpre) and post (Rpost) refraction. In this way, we can use the Aramberri's double-K method in the formula for calculating intraocular lens power. Previously to keratorefractive procedure is advisable to have pre-treatment refraction and keratometry (K and method) registered: Kpre value is critical to calculate the ELP.

Intraocular Lens Power Calculation After Automated Lamellar Keratoplasty for High Myopia

To report intraocular lens (IOL) power calculation in 2 eyes that were highly undercorrected by previous myopic automated lamellar keratoplasty (ALK). A 35-year-old man underwent bilateral myopic ALK, which caused high residual myopia (-9.0 -4.0 x 171 and -9.5 -4.5 x 74). The patient then underwent cataract surgery with IOL implantation for cataract development. The double-K clinical history method was utilized, and satisfactory IOL power prediction results were obtained. Two no-history IOL power calculation methods (Rosa correcting factor method and Ferrara theoretical variable refractive index method), which involved axial length-dependent modification of the keratometer-measured corneal radius, and 1 no-history IOL power calculation method (Shammas' method), which involved axial length-independent modification of the keratometer-measured corneal power, were tested on these 2 eyes. In both eyes, the double-K SRK-T clinical history method gave small IOL prediction errors (-0.66 and -0.81 D). The Shammas' no-history method gave a slightly higher IOL prediction error in the right eye (-1.67 D) and a small IOL prediction error in the left eye (-0.74 D). Unacceptable IOL power prediction errors would have resulted if Rosa's correcting factor method (-8.07 and -8.35 D) or Ferrara's theoretical variable refractive index method (-17.56 and -18.51 D) had been applied. When we utilized Rosa's method for the IOL power calculation by assuming that the previous ALK had fully corrected the refractive error, the predicted IOL powers were very close to the benchmark IOL powers (IOL power prediction errors: 1.16 and 0.37 D). When we utilized Ferrara's method with the same assumption, the IOL power prediction errors remained high (-6.32 and -7.16 D). For patients who have had previous myopic ALK (and whose eyes are highly undercorrected) and who require cataract surgery and for whom the pre-ALK history is available, the double-K method appears to yield excellent predictive results. However, if the pre-ALK history is not available, the Shammas' no-history method appears to yield better results than the Rosa's or the Ferrara's method. High undercorrection by the previous ALK might have been one of the major reasons why Rosa's method resulted in a high IOL prediction error in these 2 eyes. The cause for the marked IOL prediction error by Ferrara's method in this case, however, remains to be determined.

A Comparative Analysis of Intraocular Lens Power Calculation Methods After Myopic Excimer Laser Surgery

To compare the accuracy and predictability of different intraocular lens (IOL) power calculation methods in eyes after myopic excimer laser surgery. Phacoemulsification and IOL implantation outcomes in 37 eyes of 37 patients with prior LASIK or photorefractive keratectomy were documented (amount of correction=-6.92+/-3.12 diopters (D), range: -2.00 to -13.00 D). The theoretical IOL power that would have resulted in emmetropia was calculated (IOLemme). Using the clinical history keratometry and biometry, the IOL power was calculated using the following methods: Sanders, Retzlaff, Kraff (SRK)-T, SRK-T Double-K (DK), Holladay 1 DK, Hoffer Q DK, Holladay 2 DK, Feiz-Mannis, and Ladas-Stark corneal bypass. The calculated IOL power was compared to IOLemme and used to determine the mean error and mean absolute error of refractive outcome for each eye. The calculated IOL power using the SRK-T, Feiz-Mannis, and Holladay 1 DK methods were significantly different from IOLemme. The lowest mean absolute error was achieved using the Hoffer Q DK method (0.75+/-0.52 D), Holladay 2 DK (0.75+/-0.62 D), SRK-T DK (0.76+/-0.60 D), and Ladas-Stark (0.83+/-63 D). With the SRK-T DK method, 51.4% of eyes were within +/-0.50 D of emmetropia and 67.6% of eyes were within +/-1.00 D. The Holladay 2 DK method had the highest percentage (81.1%) of eyes within +/-1.00 D and 45.9% within +/-0.50 D. The refractive results of IOL implantation using the same biometry data in eyes after LASIK can vary markedly. The SRK-T DK, Hoffer Q DK, and Holladay 2 DK methods resulted in the highest accuracy.

Calculation of intraocular lens power after corneal refractive surgery

Underestimation of required intraocular lens (IOL) power with resultant hyperopia is common in post-corneal refractive surgery eyes. A number of methods to minimize error have been proposed but most studies have been small and theoretical. We retrospectively reviewed 34 eyes that had undergone routine phacoemulsification and IOL implantation after photorefractive keratectomy or laser in situ keratomileusis. Sixteen eyes were included in the final analysis. Using known pre- and postoperative data, four methods were used to obtain keratometric values combined with three common IOL formulae (Holladay 2, SRK/T and Hoffer Q) and Koch's published Double-K nomogram. The Double-K method was also used in conjunction with the Holladay 2 formula. Target refractions were calculated and then compared to actual postoperative results. The Clinical History method at the spectacle plane produced the lowest mean K-values. Shammas adjustment formula combined with the Holladay 2 and Hoffer Q produced results closest to emmetropia. The Double-K methods produced the least number of hyperopic results. Overall, all methods would have resulted in unacceptably high rates of hyperopia and deviation from target refraction. No method produces acceptably consistent results because modern IOL formulae were designed for presurgical eyes. Accuracy will only be improved when new IOL formulae based on the anatomy of postrefractive eyes become available. Shammas adjustment formula and regression formulae are viable alternatives especially when there is a lack of preoperative data. The Double-K methods are best suited to avoiding a hyperopic surprise.