Calculated Growth Rates Research Articles

Clinical outcomes and rates of aortic growth and reoperation after 1-stage repair of extensive chronic thoracic aortic dissection

ObjectiveThe study objective was to analyze clinical outcomes, distal segmental aortic growth, and aortic reoperation rates after 1-stage open repair of extensive chronic thoracic aortic dissection via bilateral anterior thoracotomy. MethodsEighty patients underwent extensive 1-stage repair of chronic aortic dissection that included the ascending aorta, the entire aortic arch, and the varying lengths of the descending thoracic aorta. One half or more of the descending thoracic aorta was replaced in 62 (78%) of the 80 patients. Hospital mortality was 2.5% (2 patients). Stroke occurred in 1 patient (1.2%), spinal cord ischemic injury occurred in 1 patient (1.2%), and renal failure requiring long-term dialysis occurred in 2 patients (2.5%). Sixty-five of the 78 hospital survivors (83%) had serial imaging studies suitable for calculation of growth rates of the remaining dissected thoracic and abdominal aorta. Forty-seven patients were followed for more than 5 years, and 21 patients were followed for more than 10 years. ResultsThe mean annual growth rate for the distal contiguous aorta was 1.7 mm/y. Forty aortas increased in diameter, 16 aortas remained unchanged, and 9 aortas decreased in diameter. Five patients required reoperation on the contiguous thoracic or abdominal aorta 8, 27, 34, 51, and 174 months postoperatively for progressive enlargement. Actuarial freedom from reoperation on the contiguous aorta at 5 and 10 years was 95.4% and 93%, respectively. Actuarial freedom from any aortic reoperation at 5 and 10 years was 89.2% and 84.4%, respectively. Actuarial survival for the entire cohort at 5 and 10 years was 76.4% and 52.6%, respectively, and survival free of any aortic operation was 68.6% and 43.9%, respectively. No patient whose cause of death was known died of aortic rupture. ConclusionsOur extended experience with the 1-stage open procedure confirms its safety and durability for treatment of chronic aortic dissection with enlargement confined to the thoracic aorta. The procedure is associated with low operative risk and a low incidence of reoperation on the contiguous aorta. It represents a suitable alternative to the 2-stage, frozen elephant trunk, and hybrid procedures that are also used to treat this condition.

Diseases and vector: a 10 years view of scientific literature on Aedes aegypti

Transmission levels and severity of infections in Aedes aegypti-transmitted diseases have been currently intensified. This short communication is a bibliometric approach about research on this vector, which is responsible for more than 25,000 deaths annually. Current scientific research on A. aegypti is characterized, using Scopus as data source. A total of 5039 published articles during the period 2006–2015 were retrieved. Two time-slices to calculate growth rates by countries and subject areas were developed. Co-word analysis for research fronts identification was used. Scientific output was mainly concentrated in four Scopus subject areas: Medicine; Immunology and Microbiology; Agricultural and Biological Sciences; and Biochemistry, Genetics and Molecular Biology. Highest growth rate was observed in Pharmacology, Toxicology and Pharmaceutics. United States, Brazil and India were the most productive countries. Four research fronts were identified: epidemiology; gene expression and biological control; larvicidal and insecticidal effects; and reproduction and insecticide resistance. Literature on A. aegypti during the last 10 years showed an exponential growth. This growing was associated with the identification of mosquitos in new environments, as well as the appearance of outbreaks related to diseases transmitted by this vector.

Experimental study of fatigue crack growth in raw and annealed pure copper with considering cyclic plastic effects

Some material, such as copper indicates hardening behavior under cyclic loading. Linear elastic fracture mechanics can be applied for low loads that the plastic zone size is small in compare with specimen dimensions. However, the cyclic J integral depends on the cyclic plastic response, therefore in ductile materials, the elastic plastic fracture mechanics based on the cyclic J integral justify fracture parameters better than the linear elastic fracture mechanics in various loadings. In this paper, for the cyclic loading in various loading conditions, crack growth behavior of copper with 99.9% purity was studied. For evaluation and comparison of the cyclic plastic behavior effects on the fatigue crack growth, some specimens were annealed in thermal furnace under420 °C for 35 min. With symmetric strain-controlled loadings, hysteresis loops were obtained for annealed and raw specimens. For studying of the fatigue crack growth rates, two important parameters as ΔK (stress intensity range) and ΔJ (J-integral range) are evaluated. Crack growth parameters such as the fatigue life, crack growth rate and constants of Paris law and Dowling equation were investigated. Results revealed that in the same loading ranges, if growth rate is expressed versus ΔK, Paris law parameters are dependent to the load ratio, R while in representation versus ΔJ, these parameters are almost constant. Also, the fatigue crack growth rate calculations based on the ΔJ in materials such as annealed copper that has important hardening behavior, are more accurate.

Formation and growth of silica layer beneath environmental barrier coatings under water-vapor environment

Environmental barrier coatings (EBCs) have widely been employed as protective coatings for SiC-based ceramic matrix composites (CMC-SiCs) against combustion corrosion in advanced gas turbines. During service, a layer of oxides forms beneath EBCs, which plays key role in lifetime of coated CMC-SiC parts. In this study, the kinetics of thermally grown silica oxide (silica-TGO) were examined through rare earth disilicates coated CMC-SiC composites subjected to corrosion under 50%H2O-50%O2 gas flow environment. Results revealed that growth of silica-TGO followed parabolic behavior, indicating diffusion controlled process. Calculated growth rates and activation energies of silica-TGO suggested that oxygen ion was the main active oxidant involved at relatively low partial pressure of water vapor. Corrosion environments containing different H2O/O2 ratios were also investigated and the data indicated that water vapor was also involved in growth of silica-TGO. The role of EBCs in corrosion process was also analyzed and discussed.

The Role of logistics in the exploitation of crude oil from the seabed

The process of oil and natural gas extraction is one of the most technically complex processes in the modern industry. Offshore platforms, special drill ships and mobile oil plants are the only ways of extracting oil from the seabed. The paper will highlight the role of oil in the maritime economy and the importance of the logistic chain on the example of Norway. It will provide a theoretical overview of the role of oil exploration through the logistic system, oil stock analysis, export and import analysis of oil quantities through world regions by the model and calculation of direct growth rates of selected variables. In this paper, methods of analysis and synthesis, inductive and deductive methods, comparative methods and growth matrix methods have been used.

Non-plastidial expression of a synthetic insect geranyl pyrophosphate synthase effectively increases tobacco plant biomass

Designing effective synthetic genes of interest is a fundamental step in plant synthetic biology for biomass. Geranyl pyrophosphate (diphosphate) synthase (GPPS) catalyzes a bottleneck step toward terpenoid metabolism. We previously designed and synthesized a plant (Arabidopsis thaliana)-insect (Myzus persicae, Mp) GPPS- human influenza hemagglutinin (HA) cDNA, namely PTP-MpGPPS-HA (or PTP-sMpGPPS-HA, s: synthetic), to localize the protein in plastids and improve plant biomass. To better understand the effects of different subcellular localizations on plant performance, herein we report PTP-sMpGPPS-HA re-design to synthesize a new MpGPPS-HA cDNA, namely sMpGPPS-HA, to express a non-plastidial sMpGPPS-HA protein. The sMpGPPS-HA cDNA driven by a 2 × S 35S promoter was introduced into Nicotiana tabacum Xanthi. PTP-MpGPPS-HA and PMDC84 vector transgenic plants were also generated as positive and negative controls, respectively. Eighteen to twenty transgenic T0 lines were generated for each sMpGPPS-HA, PTP-sMpGPPS-HA, and PMDC84. Transcriptional genotyping analysis demonstrated the expression of sMpGPPS-HA in transgenic plants. Confocal microscopy analysis of transgenic progeny demonstrated the non-plastidial localization of sMpGPPS-HA. Growth of T1 transgenic and wild-type control plants showed that the expression of sMpGPPS-HA effectively increased plant height by 50–80%, leaf numbers and sizes, and dry biomass by 60–80%. Calculation of the vegetative growth rates showed that the expression of sMpGPPS-HA increased plant height each week. Moreover, sMpGPPS-HA expression promoted early flowering and reduced leaf carotenoid levels. In conclusion, non-plastidial expression of the novel sMpGPPS-HA was effective for improving tobacco growth and biomass. Our data indicate that research examining different subcellular localizations facilitates a better understanding of in planta functions of proteins encoded by synthetic cDNAs.

A new method for non-invasive biomass determination based on stereo photogrammetry.

A novel, non-destructive method for the biomass estimation of biological samples on culture dishes was developed. To achieve this, a photogrammetric system, which consists of a digital single-lens reflex camera (DSLR), an illuminated platform where the culture dishes are positioned and an Arduino board which controls the capturing process, was constructed. The camera was mounted on a holder which set the camera at different title angles and the platform rotated, to capture images from different directions. A software, based on stereo photogrammetry, was developed for the three-dimensional (3D) reconstruction of the samples. The proof-of-concept was demonstrated in a series of experiments with plant tissue cultures and specifically with calli cultures of Salvia fruticosa and Ocimum basilicum. For a period of 14days images of these cultures were acquired and 3D-reconstructions and volumetric data were obtained. The volumetric data correlated well with the experimental measurements and made the calculation of the specific growth rate, µ max, possible. The µ max value for S. fruticosa samples was 0.14day-1 and for O. basilicum 0.16day-1. The developed method demonstrated the high potential of this photogrammetric approach in the biological sciences.

Growth and Final Height Among Children With Phenylketonuria.

Growth is an important criterion to evaluate health in childhood and adolescence, especially in patients depending on special dietary treatment. Phenylketonuria (PKU) is the most common inherited disease of amino acid metabolism. Patients with PKU depend on a special phenylalanine-restricted diet, low in natural protein. The study aimed to evaluate growth, growth rate, and target height in 224 patients with PKU. Retrospective, longitudinal analysis of standardized, yearly measurements of height, weight, and calculated growth rate (SD score [SDS]) of patients with PKU aged 0 to 18 years were conducted by using the national computerized CrescNet database. Inclusion was restricted to patients carried to term with a confirmed diagnosis of PKU or mild hyperphenylalaninemia determined by newborn screening and early treatment initiation. From birth to adulthood, patients with PKU were significantly shorter than healthy German children (height SDS at 18 years: -0.882 ± 0.108, P < .001). They missed their target height by 3 cm by adulthood (women: P = .02) and 5 cm (men: P = .01). In patients receiving casein hydrolysate during childhood, this was more pronounced compared with patients receiving amino acid mixtures (P < .001). Growth rate was significantly reduced during their first 2 years of life and in puberty (growth rate SDS: -1.1 to -0.5 m/year, P < .001 and -0.5; P < .02). Early diagnosed, treated, and continuously monitored patients with PKU showed reduced height from birth onward. During the last 2 decades, this phenomenon attenuated, probably because of advances in PKU therapy related to protein supplements and special low-protein foods.

A contribution to the theory of the equatorial noise generation in the Earth’s magnetosphere

This work is devoted to the study of the generation of the equatorial noise—electromagnetic emission below the LHR frequency observed near the equatorial plane of the magnetosphere at distances of ~4RE. According to accepted views, the generation of the equatorial noise is related to the instability of ring current protons. In this work, a logarithmic distribution of energetic protons over the magnetic moment with an empty loss cone is proposed, and arguments for the formation of such a distribution are presented. The main result of the work is the calculation and analysis of the instability growth rate of waves forming the equatorial noise. The growth rate obtained in this work significantly differs from that encountered in the literature.

Economic Growth and Recovery in the United States: 1919-1941

This paper has two main sections and an appendix. The first provides an overview of what lay behind record productivity growth in the US economy between 1929 and 1941. The second considers the role of rigidities and other negative supply conditions in worsening the downturn and slowing recovery. While I argue consistently that the overarching explanation of the Great Depression will and should continue to emphasize a collapse and slow revival of the growth of aggregate demand, I spend relatively little time on what drives this, since the literature deals extensively with this elsewhere. The paper instead concentrates on the aggregate supply side - both the broad array of positive shocks that I argue propelled potential and, eventually, actual output forward, and the negative conditions which, in interaction with aggregate demand, may have increased the size of the output gap and prolonged its persistence. An appendix offers detail discussion and updated calculations of productivity growth rates for the critical period 1929 through 1941.

Velocity shear Kelvin-Helmholtz instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In this paper parallel flow velocity shear Kelvin-Helmholtz instability has been studied in two different extended regions of the inner magnetosphere of Saturn. The method of the characteristic solution and kinetic approach has been used in the mathematical calculation of dispersion relation and growth rate of K-H waves. Effect of magnetic field (B), inhomogeneity (P/a), velocity shear scale length (Ai), temperature anisotropy (T⊥/T||), electric field (E), ratio of electron to ion temperature (Te/Ti), density gradient (εnρi) and angle of propagation (θ) on the dimensionless growth rate of K-H waves in the inner magnetosphere of Saturn has been observed with respect to k⊥ρi. Calculations of this theoretical analysis have been done taking the data from the Cassini in the inner magnetosphere of Saturn in the two extended regions of Rs ∼4.60–4.01 and Rs ∼4.82–5.0. In our study velocity shear, temperature anisotropy and magnitude of the electric field are observed to be the major sources of free energy for the K-H instability in both the regions considered. The inhomogeneity of electric field, electron-ion temperature ratio, and density gradient have been observed playing stabilizing effect on K-H instability. This study also indicates the effect of the vicinity of icy moon Enceladus on the growth of K-H instability.

Statistical Package for Growth Rates Made Easy.

Growth rates are an important tool in microbiology because they provide high throughput fitness measurements. The release of GrowthRates, a program that uses the output of plate reader files to automatically calculate growth rates, has facilitated experimental procedures in many areas. However, many sources of variation within replicate growth rate data exist and can decrease data reliability. We have developed a new statistical package, CompareGrowthRates (CGR), to enhance the program GrowthRates and accurately measure variation in growth rate data sets. We define a metric, Variability-score (V-score), that can help determine if variation within a data set might result in false interpretations. CGR also uses the bootstrap method to determine the fraction of bootstrap replicates in which a strain will grow the fastest. We illustrate the usage of CGR with growth rate data sets similar to those in Mira, Meza, et al. (Adaptive landscapes of resistance genes change as antibiotic concentrations change. Mol Biol Evol. 32(10): 2707-2715). These statistical methods are compatible with the analytic methods described in Growth Rates Made Easy and can be used with any set of growth rate output from GrowthRates.

Electron cyclotron maser instability (ECMI) in strong magnetic guide field reconnection

Abstract. The ECMI model of electromagnetic radiation from electron holes is shown to be applicable to spontaneous magnetic reconnection. We apply it to reconnection in strong current-aligned magnetic guide fields. Such guide fields participate only passively in reconnection, which occurs in the antiparallel components to both sides of the guide-field-aligned current sheets with current carried by kinetic Alfvén waves. Reconnection generates long (the order of hundreds of electron inertial scales) electron exhaust regions at the reconnection site X point, which are extended perpendicular to the current and the guide fields. Exhausts contain a strongly density-depleted hot electron component and have properties similar to electron holes. Exhaust electron momentum space distributions are highly deformed, exhibiting steep gradients transverse to both the reconnecting and guide fields. Such properties suggest application of the ECMI mechanism with the fundamental ECMI X-mode emission beneath the nonrelativistic guide field cyclotron frequency in localized source regions. An outline of the mechanism and its prospects is given. Potential applications are the kilometric radiation (AKR) in auroral physics, solar radio emissions during flares, planetary emissions and astrophysical scenarios (radiation from stars and compact objects) involving the presence of strong magnetic fields and field-aligned currents. Drift of the exhausts along the guide field maps the local field and plasma properties. Escape of radiation from the exhaust and radiation source region still poses a problem. The mechanism can be studied in 2-D particle simulations of strong guide field reconnection which favours 2-D, mapping the deformation of the electron distribution perpendicular to the guide field, and using it in the numerical calculation of the ECMI growth rate. The mechanism suggests also that reconnection in general may become a source of the ECMI with or without guide fields. This is of particular interest in extended turbulent plasmas where reconnection serves as an integral dissipation mechanism of turbulent energy in myriads of small-scale current filaments.

Fresh and Dry Mass Estimates of Hermetia illucens (Linnaeus, 1758) (Diptera: Stratiomyidae) Larvae Associated with Swine Decomposition in Urban Area of Central Amazonia

Information on biomass is substantial for calculating growth rates and may be employed in the medicolegal and economic importance of Hermetia illucens (Linnaeus, 1758). Although biomass is essential to understanding many ecological processes, it is not easily measured. Biomass may be determined by directly weighing or indirectly through regression models of fresh/dry mass versus body dimensions. In this study, we evaluated the association between morphometry and fresh/dry mass of immature H. illucens using linear, exponential, and power regression models. We measured width and length of the cephalic capsule, overall body length, and width of the largest abdominal segment of 280 larvae. Overall body length and width of the largest abdominal segment were the best predictors for biomass. Exponential models best fitted body dimensions and biomass (both fresh and dry), followed by power and linear models. In all models, fresh and dry biomass were strongly correlated (>75%). Values estimated by the models did not differ from observed ones, and prediction power varied from 27 to 79%. Accordingly, the correspondence between biomass and body dimensions should facilitate and motivate the development of applied studies involving H. illucens in the Amazon region.

MAGenTA: a Galaxy implemented tool for complete Tn-Seq analysis and data visualization.

Transposon insertion sequencing (Tn-Seq) is a microbial systems-level tool, that can determine on a genome-wide scale and in high-throughput, whether a gene, or a specific genomic region, is important for fitness under a specific experimental condition. Here, we present MAGenTA, a suite of analysis tools which accurately calculate the growth rate for each disrupted gene in the genome to enable the discovery of: (i) new leads for gene function, (ii) non-coding RNAs; (iii) genes, pathways and ncRNAs that are involved in tolerating drugs or induce disease; (iv) higher order genome organization; and (v) host-factors that affect bacterial host susceptibility. MAGenTA is a complete Tn-Seq analysis pipeline making sensitive genome-wide fitness (i.e. growth rate) analysis available for most transposons and Tn-Seq associated approaches (e.g. TraDis, HiTS, IN-Seq) and includes fitness (growth rate) calculations, sliding window analysis, bottleneck calculations and corrections, statistics to compare experiments and strains and genome-wide fitness visualization. MAGenTA is available at the Galaxy public ToolShed repository and all source code can be found and are freely available at https://vanopijnenlab.github.io/MAGenTA/ . vanopijn@bc.edu. Supplementary data are available at Bioinformatics online.

Population structure of the sicklefin lemon shark Negaprion acutidens within the Curieuse Marine National Park, Seychelles

This study produced the first data on population parameters for sicklefin lemon shark Negaprion acutidens at the granitic Seychelles Islands, adding to a limited catalogue of species information. Juveniles at a site in the Curieuse Marine National Park were tagged over two periods, in 2014–2015 and 2015–2016, with measurements of length (precaudal, fork and total) and weight, sex, and state of the umbilical opening recorded. Recapture data were used to calculate growth rates and population size. Mean annual growth rate was 5.40 cm y–1. A mean size at birth of 62.5 cm TL is in line with previous assessments of the species. Population-size estimates were similar for the two sampling periods (comprising 311 and 255 individuals) and higher than anticipated. Movements to outside the lagoon were recorded for early ages, and this, combined with weight loss and a reduction in condition factor as displayed in several individuals, suggests that the study area alone could not support the large number of sharks pupped yearly.

Rise And Fall Of Ulips In Indian Life Insurance Market

Reforms in the insurance sector were introduced much later in fact almost a decade later with the enactment of the Insurance Regulatory and Development Authority Act 1999, which facilitated the liberalization and opening of the insurance sector. There were two options before the Government of India to privatize insurance sector viz. (a) selling of two public sector insurance companies (LIC and GIC) to private and (b) allowing private sector to enter into insurance market and compete with the LIC and GIC. The Government took the latter route to open the insurance sector in 2000 and LIC and GIC were left untouched. Indian private companies entered the market as joint ventures with some of world’s largest insurance companies. Coexistence of private and public companies heightened competition and Indian insurance sector witnessed several significant changes such as a large number of new innovative products, improved distribution channels and the introduction of world class regulatory and supervisory standards. The most significant product innovation in the life insurance segment is the introduction of unit linked products (ULIPs). Unit linked plans offer long term investment option plus life coverage. In fact ULIPs are combination of both investment and insurance.In this research paper an attempt is made (a) to examine the rise and fall of ULIPs across the private insurers and LIC in the Indian insurance market by analyzing the distribution of first year premium during 2003-14 . The materials in the form of data and information are gathered from the Annual Reports of IRDA and Reports of Economic Survey of India of various years. The data and information collected were processed presented and analyzed using SPSS version 20. Mann Whitney Test Z value (equivalent to Wilcoxon’s rank sum z test) is also used in addition to the calculation of growth rate and percentage contribution of ULIPs to the total premium.

Global equatorial plasma bubble growth rates using ionosphere data assimilation

AbstractFlux tube integrated Rayleigh‐Taylor instability growth rates computed by using the results of ionosphere data assimilation are used for the first time to investigate global plasma bubble occurrence. The study is carried out by assimilating total electron content measurements using ground‐based Global Positioning System (GPS) receivers into thermosphere ionosphere electrodynamic general circulation model, and the growth rates are calculated by using standalone model run without assimilation (control run) as well as using prior (or forecast) state output of the assimilation run. The growth rates are compared with the rate of change of total electron content index (ROTI), estimated from global network of GPS receivers, as well as all‐sky airglow observations carried out over Taiwan on the nights of 16 and 17 March 2015. In contrast to the growth rates using the control run, results using data assimilation show remarkable agreement with the ROTI. Further, the all‐sky images reveal intense plasma bubbles over Taiwan on the night of 16 March, when the corresponding assimilated growth rate is also pronounced. Similarly, the absence of plasma bubbles in the all‐sky images on the night of 17 March (St. Patrick's Day storm) is supported by smaller growth rates predicted by the assimilation model. Significant improvements in the calculated growth rates could be achieved because of the accurate updating of zonal electric field in the data assimilation forecast. The results suggest that realistic estimate or prediction of plasma bubble occurrence could be feasible by taking advantage of the data assimilation approach adopted in this work.

Waves in the innermost open boundary layer formed by dayside magnetopause reconnection

AbstractWe present two Time History of Events and Macroscale Interactions during Substorms observations of whistler mode and electrostatic wave events in the innermost open boundary layer (IOBL), formed by dayside magnetopause reconnection. The IOBL is identified by high‐speed electrons from the magnetosheath on the magnetospheric side of the ion outflow from the reconnection site. Quasi‐parallel whistler mode waves propagating toward the reconnection region are observed, along with a partial shortage of magnetospheric electrons moving away from the reconnection region. Calculation of wave linear growth rates shows that the waves can be excited by the perpendicular electron temperature anisotropy that develops due to the partial shortage of field‐aligned magnetospheric electrons. Electrostatic waves close to the lower hybrid resonance frequency are observed in the IOBL in the second event, which occurred during the main phase of a magnetospheric storm. Magnetospheric electrons are almost completely lost in the event, except at pitch angles close to 90°, yet whistler mode waves are not observed. An electron beam from the magnetosheath and counterstreaming cold electrons originating from the plasmaspheric plume are observed in association with the electrostatic waves. Growth rate calculations show that the waves are likely to be ion acoustic waves excited via couplings between the flowing cold electrons and background cold ions. We suggest that differences in solar wind conditions and magnetic reconnection characteristics may control the shapes of the electron velocity distribution functions and the resulting plasma wave properties in the IOBL.

An analytical model for predicting growth rate and departure diameter of a bubble in subcooled flow boiling

Bubble formation in flow boiling undergoes an ebullition cycle in which nucleation is followed by bubble growth, departure and a waiting period. Bubble growth rate plays an important role in bubble dynamics and also affects the whole ebullition cycle. It is difficult to make analytical calculation of bubble growth rate and departure diameter due to involvement of various forces and heat transfer processes on a nucleating bubble. In this paper, an analytical technique is proposed to calculate the growth rate and departure diameter of a nucleating bubble in subcooled flow boiling. Both force and energy balance approaches have been applied to calculate the growth and departure diameter of the bubble. Heat transfer contributions from evaporative microlayer beneath the bubble, superheated liquid surrounding the bubble and condensation from the bubble cap have been considered to calculate the bubble growth rate. In place of using a constant coefficient to represent the fraction of bubble in subcooled bulk liquid by existing analytical models, the present model correlates the coefficient with the operating parameters of flow boiling. An effort has also been made for accurate calculation of temperature distribution in heated surface and flowing liquid. Bubble growth rate and departure diameter have been calculated for different values of coolant mass flux, system pressure, applied heat flux, surface orientation angle and liquid subcooling. The heat transfer contribution from individual layer towards the growth rate of the bubble has been quantified and analyzed. The present analytical model has been validated with a wide range of experimental data and it produces better agreement with the experimental data compared to existing analytical models.