In the present study, we describe the purification and biochemica

In the present study, we describe the purification and biochemical characterization of a new hemorrhagic metalloproteinase from Bothrops atrox snake venom. The proteinase was isolated by consecutive gel

filtration and anion exchange chromatography, which provided a high level of homogeneity as confirmed by reverse phase chromatography, SDS-PAGE, isoelectric focusing and N-terminal amino acid sequencing. The purification of PI-class SVMPs is commonly performed using two to three chromatographic steps that predominantly consist of gel filtration and ionic exchange techniques (Mandelbaum et al., 1982 and Muniz et al., 2008). The purified SVMPs include leucurolysin-A from Bothrops leucurus ( Gremski et al., 2007), bothropasin Vorinostat molecular weight from Bothrops jararaca ( Muniz et al., 2008), BaH4 from Bothrops asper ( Franceschi et al., 2000) and ammodytagin from Vipera ammodytes ammodytes ( Kurtović et al., 2011). BaH1 was isolated from Bothrops asper venom in three chromatographic steps using gel filtration, ion exchange and hydrophobic PD-0332991 cell line interaction methods ( Borkow et al., 1993). Other PI SVMPs were obtained by different procedures: atroxlysin-I from Bothrops atrox ( Sanchez et al., 2010) was isolated by two gel filtration steps, and B-mooMPα-I was isolated from Bothrops moojeni using a combination

of gel filtration, ionic exchange and affinity chromatography techniques ( Bernardes et al., 2008). Batroxase comprises approximately Ureohydrolase 1.2% (w/w) of the crude B. atrox snake venom, with a pI of 7.5 and a molecular mass of 22.9 kDa, as determined by mass spectrometry (data not shown), or ∼27 kDa, as determined by SDS-PAGE under reduced conditions ( Fig. 1B insert). PI-class SVMPs, which display a single proteolytic domain, have molecular masses from ∼20 to 30 kDa (Lopes et al., 2009), as represented by BnP1 from Bothrops neuwiedi ( Baldo et al., 2008) at 24 kDa, BlaH1 from Bothrops lanceolatus ( Stroka et al., 2005) at 28 kDa, leucurolysin-A from Bothrops leucurus ( Gremski et al., 2007) at

23 kDa and atroxlysin-I from Bothrops atrox ( Sanchez et al., 2010) at 23 kDa. Envenomation by Bothrops spp. venoms is characterized by local and systemic hemorrhage caused by the proteolytic digestion of extracellular matrix components ( Escalante et al., 2011). The contribution of Batroxase to the hemorrhagic process was initially evaluated in the dorsal skin of mice. Batroxase was found to have an MHD of 10 μg, which was similar to that of other SVMPs; for example, atrolysin C and D from Crotalus atrox have MHDs of 8 and 11 μg, respectively ( Bjarnason and Fox, 1994), BaP1 has an MHD of 20 μg ( Gutiérrez et al., 2005) and atroxlysin-I has an MHD of 19.9 μg ( Sanchez et al., 2010). These doses are relatively high compared with those of PII and PIII SVMPs, which have MHDs from 0.

In those with knee osteoarthritis specifically, 14% require assis

In those with knee osteoarthritis specifically, 14% require assistance with routine needs and 11% with personal care.74 A study21 based on NHIS data from 2007 to 2009 reported that 21.1 million, or 42% of the 49.9 million adults GSI-IX mw with physician-diagnosed arthritis, had arthritis-attributable activity limitations. Arthritis-attributable activity limitations were defined as any limitations in an individual’s usual activities as a result of arthritis or joint symptoms. Rheumatoid arthritis is estimated to be present in 1.3 million U.S. adults 18 years or older, representing 0.6% of the population, based on NHIS- and NHANES-derived

analyses from the National Arthritis Data Workgroup.29 In 2011, Jacobs et al30 reported higher estimates of 2% of adults selleck screening library in North America. The most recent estimate of the incidence of rheumatoid arthritis is 41 per 100,000 person-years based on the Rochester Epidemiology Project.32 Rheumatoid arthritis is also associated with significant disability. People with rheumatoid arthritis are 30% more likely to need help with personal care and are limited in daily activities at twice the rate of disease-free individuals.34 One study36 followed up employees with early-stage rheumatoid arthritis and found a 39% prevalence of work disability

after 10 years. The economic burden of all arthritis is significant. In 2007, the cost attributable to arthritis and other rheumatic conditions in the United States was estimated at $128 billion ($162 billion

in 2013 dollars).25 This estimate, derived from national Medical Expenditure Panel Survey data, was partitioned into $80.8 billion ($115 billion in 2013 dollars) in direct medical expenditures and $47.0 billion ($59.4 billion in 2013 dollars) in indirectly lost earnings. In 2010, Kotlarz et al26 used Medical Expenditure Panel Survey data from the same period and estimated that the costs caused by absenteeism from osteoarthritis alone are $10.3 billion per year ($11.6 billion in 2013 dollars) because of an estimated 3 lost workdays per year. The functional and work limitations of persons with Glutamate dehydrogenase rheumatoid arthritis contribute to an estimated $10.9 billion ($13.0 billion in 2013 dollars) in indirect costs from lost wages and costs to employers, based on 2005 administrative claims databases covering private and Medicare/Medicaid beneficiaries in the United States.33 On top of this figure, the group attributed an additional $10.3 billion ($12.3 billion in 2013 dollars) in intangible quality-of-life deterioration as estimated by legal system jury awards, as well as $9.6 billion lost ($11.4 billion in 2013 dollars) in lifetime earnings because of early mortality. Excess health care costs, in the form of copays and medications, amounted to $8.4 billion ($10.6 billion in 2013 dollars), for a total indirect cost of $39.2 billion per year ($46.7 billion in 2013 dollars). Stroke is a leading cause of serious long-term disability in the United States.

As larger platelets are more reactive in response to stimuli, sel

As larger platelets are more reactive in response to stimuli, selective consumption of larger platelets might occur.

Consequently, the MPV of circulating platelets would be decreased. Micro- and macro-thromboembolic events are one of the major complications for patients with advanced NSCLC and can be fatal [27], [28] and [29]. Therefore, this may be a possible explanation for the poor prognosis of patients with a low MPV/PC ratio. The MPV and PC were also significant prognostic factors for OS in univariate analyses (P = −0.0270 and P = 0.0124, respectively). However, multivariate analysis did not indicate the superiority of them against the MPV/PC ratio when considered independently (HR of a low MPV/PC ratio: 1.668 [P = 0.0008], HR of a low MPV: 1.381 [P = 0.0121], and HR of a high PC: 1.380 [P = 0.0114]). Therefore, we concluded that the MPV/PC ratio was a more reliable and accurate Pictilisib biomarker than the MPV or PC alone. Despite the retrospective nature and small size of the present study, our results clearly demonstrated that a low MPV/PC ratio at initial diagnosis was an independent unfavorable prognostic factor

for patients with advanced NSCLC. Further investigation should clarify the etiology by which the amount and volume of circulating platelets modulate mortality in patients with NSCLC. The authors have declared no conflict of interest. “
“Over the past Selleckchem E7080 Meloxicam two decades, the

mortality attributed to lung cancer has increased and it is now the leading cause of cancer deaths [1]. Late diagnosis is a fundamental obstacle to improving the outcomes of lung cancer, with more than 70% of new cases presenting too late for curative treatment to be attempted [2]. Owing to the development of new chemotherapeutic agents, the costs of care for inoperable lung cancer are growing rapidly [3]. Therefore, it is worth examining the lifetime utility difference for patients with operable and inoperable lung cancer, which emphasizes the importance of early diagnosis of lung cancer. For the assessment of lifetime utility difference, both survival and quality-of-life (QoL) should be taken into consideration, and thus, the quality-adjusted life year (QALY) unit is more suitable than estimating survival alone for comparison of various types of healthcare services [4]. Quality-adjusted life expectancy (QALE) can be estimated via adjusting the survival function with the mean QoL at each time point, t, using the following equation [5], [6] and [7]: QALE=∫E[QoL(t/x)]S(t/x)dtQALE=∫EQoLt/xSt/xdtE[QoL(t/x)] denotes the expected value of health state (QoL) for patients with condition x at time t and S(t/x) denotes the survival function for condition x at time t. Previous studies discussing the benefits of surgery mostly focused on survival alone, and usually did not take lead-time bias into consideration [8].

We assume a rather specific function for alpha not only with resp

We assume a rather specific function for alpha not only with respect to the type of cognitive processes but also with respect to physiology. selleck chemicals With respect to physiology one important

aspect is that alpha operates to inhibit task irrelevant neural structures and thereby helps to establish a more focused access to the KS. There may be different kinds of attentional processes comprising e.g., also those which rely on excitatory processes only. In addition, there may be different kinds of attention, related to different cognitive processing modes, such as a sustained focus on the encoding of new or alerting information. We consider alpha a specific kind of attention that is related to inhibitory control processes of the KS. The next section is a selective review about variables that typically modulate P1 amplitude and/or latency. The most important examples are (1) spatial attention, (2) reflexive attention, (3) object based attention, (4) target properties investigated in search paradigms, and (5) perceptual features. The aim of this brief review is to provide evidence for the

second assumption stating that the P1 amplitude reflects early categorization processes during access to the KS, which are based on the analysis of global stimulus properties. The spatial location of a relevant stimulus or object may be considered an important variable that influences early stages of visual processing and access to the KS. For the investigation of spatial attention, at least three types of paradigms can be distinguished. The first Fluorouracil order two investigate top–down controlled spatial selection processes. As illustrated in Fig. 1A, type 1 paradigms are designed to direct attention to a specific location – usually to the left or right hemifield – over a run (block) of trials simply by instructing subjects to do so. Type 2 paradigms use a cue to direct attention to a specific location on a trial per trial basis. Type 3 paradigms are used

to study Non-specific serine/threonine protein kinase reflexive attention, either using a cue or not. Convergent evidence from type 1 and 2 paradigms indicates that stimuli flashed at an attended location elicit a larger P1 than stimuli flashed at unattended locations (e.g., Heinze et al., 1994, Heinze and Mangun, 1995, Mangun et al., 1997 and Mangun and Buck, 1998 for reviews cf. Mangun, 2003, Hillyard et al., 1998 and Hillyard and Anllo-Vento, 1998). As a first example, let us consider the findings from a type 1 paradigm (attend left vs. right hemifield) used in a study by Mangun et al. (2001). Stimuli were gratings of vertically oriented black and white stripes and were presented for 100 ms. Targets were slightly shorter than standards and appeared in 25% of all trials. All stimuli were randomly presented to the left or right hemifield. Subjects were instructed to respond to a target in the attended hemifield only. The results for standard stimuli are depicted in Fig.

Under hydroponic conditions with diverse N deficiency levels, the

Under hydroponic conditions with diverse N deficiency levels, the root surface area and belowground biomass of switchgrass were reduced by deficient N (Table 2), so that WUE decreased as N decreased (Table 3). The rate of transpiration

is directly related to the degree of stomatal opening, and to the evaporative demand of the atmosphere surrounding the leaf. Deficiency of N can influence stomatal opening, and thus transpiration rate. There are contradictory conclusions in the literature about the influence of N deficiency on stomatal conductance. Lower rates of stomatal conductance in low-N-grown plants have been reported [28] and [29], Protease Inhibitor Library but the opposite or no effect of N application is also reported [26] and [30]. Possible reasons could lie in the choice of tested materials and experimental conditions. In the present study, under N deficiency stress, the stomatal GSK2118436 mouse conductance of switchgrass decreased considerably (Table 3). Given that the amount of transpiration by a plant

depends on the number and size of leaves, leaf areas, and plant roots, seedlings grown with nutrient solution lacking N showed a drop in transpiration rate (Table 3). Full-strength Hoagland’s nutrient solution treatment supported the highest value of transpiration because of the increased photosynthesis and stomata conduction. There is a linear correlation between photosynthesis and transpiration [31] and [32]. Thus, for hydroponically cultivated switchgrass, deficient N supply affected the chlorophyll content and stomatal opening

and thereby the leaf area and photosynthetic characteristics. This effect reduced the plant’s ability to manufacture carbohydrates by photosynthesis and consequently reduced its biomass. The results agree with Carnitine dehydrogenase the findings by Stroup et al. and Kering et al. [24] and [33]. All the traits showed obvious differences among the applied N deficiency stresses (Table 2 and Table 3), suggesting that switchgrass responds strongly to N. However, the tiller number showed no significant difference across cultivars and ecotypes and no cultivar-by-treatment and ecotype-by-treatment interactions (Table S1). One possible explanation would be that the six chosen switchgrass cultivars simply show no difference in tiller number. This could also explain why R:S showed no difference across ecotypes but showed highly significant differences across treatments. There is no current index for evaluating the tolerance of switchgrass to mineral nutrient deficiency conditions. According to previous indoor and field study experiments, combined with the physiological characteristics of switchgrass, total biomass, height, tiller number, leaf area, root surface area, net photosynthesis and chlorophyll content were chosen as evaluation indices for effectively measuring its performance.

For the years after 2007, the MACC emissions were scaled using th

For the years after 2007, the MACC emissions were scaled using the emission trends of each country from EMEP. For those emission groups missing from the MACC

inventory (natural, marine, volcanic and Iceland emissions) the EMEP emissions were used. For north-western Russia (the Kola Peninsula, Karelia and Leningrad Oblast) the FMI’s own inventory is still used, because the locations of the enterprises there are more exact; also there are some well-known sources, e.g. in Karelia, missing from the MACC inventory. For the Baltic Sea model we use the specific Baltic Sea ship emission inventory. This AIS-signal-based inventory was developed at the FMI in co-operation with researchers from Åbo Akademi University and Turku University and with the support of the Marine Administration, FMA, and the Finnish State Technical Research Centre, VTT (Stipa TSA HDAC concentration et al. 2007). Each ship over the 300 tons gross tonnage limit sailing the BS has to send AIS-transmitter safety signals at variable time intervals: these signals contain the unique IMO code of the ship and information on the ship’s movements, its load, destination and type. These signals are collected by AIS-receiver stations located on the coasts of the Baltic Sea. The FMA collects the AIS signals into a local database and sends this information, as do also the other maritime administration offices surrounding the BS, to the HELCOM database (DB).

FMI, having access to the HELCOM DB, decodes the AIS-signals selleck chemicals llc and, using the IMO code, retrieves information on the ship’s machinery from the Lloyds data base. The FMI model STEAM (Ship Traffic selleckchem Emission Assessment Model, Jalkanen et al. 2009) calculates an emission estimate for each individual ship as a function of the ship’s type, its engine load, fuel type, speed and emission control technology, using current weather and wave height information, and sums the emissions on a latitude-longitude grid with a selected resolution, then reporting on-line using a ∼ 450 s–1 h time-interval.

Emissions calculated with STEAM are available from 2006 onwards. That year the temporal coverage of the signals collected was about 93%, while around 16% of ships sailed without an IMO number (Jalkanen et al. 2012). For small pleasure boats and other vessels, we use the VTT emission inventory. When the AIS signal data are missing, the monthly average emission estimate has been used. The FMI, MACC and EMEP estimates of the BS international ship traffic emissions are compared in Table 1. Over the BS, North Sea and the English Channel the maximum allowable sulphur content of marine fuels decreased due to the EU directive (2005/33/EC) from 1.5 to 1% in July 2010, and to 0.1% in port areas in January 2010. From the year 2009 to 2011, the FMI-estimated ship emissions of SO2 decreased by 48 kt and the EMEP emissions by 40 kt SO2.

Among the proteins that are able to modify the cell permeability,

Among the proteins that are able to modify the cell permeability, are the hyaluronidases. Hyaluronidases are glycosidases (El-Safory et al., 2010) EPZ015666 price capable of hydrolysing the hyaluronic acid and, thus, digest partially the extracellular matrix (Hoffman, 2006), increasing the infiltration and, possibly, the action of other compounds of the venom on cellular structures. The hyaluronic acid is a polysaccharide of high molecular weight found in the extracellular matrix, especially in connective tissues. This

polysaccharide is known as a “lubricant” responsible for the viscoelastic properties of fluid tissues and as a stabilizing and moisturizing agent of connective tissues (El-Safory et al., 2010). According to Wahby et al. (2012), hyaluronidase increases the permeability of the cell membranes and causes a reduction in the viscosity of the fluids injected into the tissues. Another protein that can be related to the mutagenicity of the wasp venom is phospholipase. Phospholipases are proteins that also have action on the lipid bilayer of the cells, by disrupting the phospholipids of the biological membranes, since they can catalyse the hydrolysis of ester

bonds at specific positions of the 1,2-diacyl-3,sn-phosphoglyceride, BYL719 releasing fatty acids ( Santos et al., 2007). According to Aoki et al. (2007), some phospholipases A (phospholipase A1 – PLA1) can hydrolyse both phospholipids and triacylglycerols, as well as galactolipids. But there are

also some PLA1 that only hydrolyses phosphatidylserine and phosphatidic acid. Denaturation of the phospholipids leads to the formation of pores in the membrane, allowing an easier entrance of other compounds into the cells, leading to cell lysis, inflammation and tissue damages ( Dotimas and Hider, 1987). P. paulista presents phospholipase A1 that has direct haemolytic action in erythrocytes ( Santos et al., 2007). Mastoparans, the main components of the vespid venoms (Souza et al., 2009), seem to promote the formation very of ionic channels in the lipid membranes, leading to cell lysis (Li et al., 2000). These compounds also increase the permeability of the membrane to ions and small molecules, by forming pores when in high concentrations. According to Gusovsky et al. (1991), this action is due, probably, to the interaction of the mastoparans with the guanine nucleotide binding protein, so that there is a collapse of phosphoinositol. Furthermore, mastoparans can stimulate the activity of phospholipase A2 and C (Perianin and Snyderman, 1989), mobilization of Ca2+ from the sarcoplasmic reticulum (Hirata et al., 2000 and Hirata et al., 2003), induce the mitochondrial permeability transition (Pfeiffer et al., 1995) and cell death by necrosis and apoptosis (Perianin and Snyderman, 1989).

At 1 home, staff members remarked that they were surprised by how

At 1 home, staff members remarked that they were surprised by how few direct care staff attended care conferences. Findings on care conference attendance can lead to an exploration of ways to improve participation within individual NHs, and present an opportunity for benchmarking across homes nationwide. The phase 1 and phase 3 data collection took place with a convenience sample of NHs, and therefore the findings cannot be considered to represent homes overall. However, professional and paraprofessional

staffing at the phase 3 pilot sites was remarkably similar to national levels. Pilot sites generally were high performing (4–5 stars) and some already had participated in QI initiatives. This group may be more likely than the norm to adopt PCC measurement tools and methods. NHs with a low rating BTK inhibitor datasheet are more likely to focus on basic quality

of care than PCC improvement. Also, in phase 3, most sites chose to interview NH residents who were cognitively capable and able to speak. Although the phase 1 validation study tested the concept of preference congruence with residents with some degree of cognitive impairment, the AE phase 3 pilot did not focus on this population. A further limitation is that the phase 3 pilot study reflected a 2-week timeframe. More data are needed over a longer period to see click here whether staff engage in interviews and use PCC information to improve daily care practices consistently. One pilot community intends to use positive feedback from the toolkit to reinforce staff efforts, celebrate successes, and motivate further engagement in QI. Reverse transcriptase In terms of timing, the PCC toolkit recommends interviewing residents upon admission and before care conferences as a way to keep up with changes in preferences over time. An additional limitation is that the pilot study did not measure resident satisfaction with preference fulfillment prior to implementing preference congruence interviews. A future study will begin with this step in order to gain insight on pre- and postsatisfaction

levels. The AE PCC project is the first initiative to collect data from NHs nationwide regarding resident-centered care planning and resident satisfaction with 16 elements of PCC. Over time, the project expects to develop a rich database that can be used for benchmarking on these key indicators. However, PCC is a broad concept that encompasses many more dimensions of NH life that could also become the focus for benchmarking. These include the presence of a homelike environment; choice and self-determination for residents; flexible schedules for residents; meaningful activity and socialization opportunities; high quality interaction with staff; and workforce policies that support PCC (eg, staff training in PCC practices, consistent staffing assignments) as well as other indicators.

Fluorescence in situ hybridization (FISH) is the primary method t

Fluorescence in situ hybridization (FISH) is the primary method to detect ALK, ROS1 and RET fusions in NSCLC [14], [25] and [26]. However, it is not wildly used in China due to its high spent, time consuming and also check details the interpretation of results. Immunohistochemistry (IHC) is another method to detect ALK fusion, but there is no standard procedure for all the labs and the same result could be explained differently by different pathologists. Soda showed us in his study

that different technologies should apply to different samples, and multiplex RT-PCR was applicable for the fluid samples [27]. Here, we use a reverse-transcript polymerase chain reaction (RT-PCR) method-ARMS-to detect ALK, ROS1 and RET fusions in 50 CB samples. Wu [12] used RT-PCR and FISH to detect ALK fusion and they found a concordance rate of 85%, but they did not check cell block samples that were ALK fusion positive using FISH. Soda [27] reported in their research that PCR-based detection of EML4-ALK should have a higher analytic sensitivity compared with

IHC or FISH. In this study, although we did not use FISH to conform the PCR results, we used DNA sequencing as a substitute. All the positive results using the PCR method were all conformed by DNA sequencing. We believe that the cell block samples could detect the three fusion genes using both RT-PCR and DNA sequencing. We tested the quality of cell block samples from the points of malignant cell ratio and PCR selleck chemical controls, finding that they were qualified to do the gene detection. The fusion positive results were all validated by DNA sequencing and the specific variants were also given. The results indicate that cell block samples preserved at least 10 months

could be used to detect fusion genes. EML4-ALK fusion gene detection using plural effusions had been reported by Wu et al [12]. They used RT-PCR and direct sequencing methods and found a 34% presence in EGFR wild type lung adenocarcinoma patients. Shaw et al. [19] got a 33% prevalence in never/light smokers in EGFR wild type lung adenocarcinoma patients using FISH method. Although Cai et.al [28] used 19 cell block samples and 35 fine-needle aspirates to detect EGFR, KRAS and ALK genes in primary and metastatic ASK1 lung adenocarcinomas, they did not show whether the CB samples be used for ALK detection or not. As far as we know, there is no study that reports the three fusion genes detected specially using CB samples. In the 50 EGFR wild type lung adenocarcinoma patients, EML4-ALK had a prevalence of 28%, which was a little lower than the former data [11] and [12]. Nonetheless, considering the small number of cases in our study, this slight difference should be reasonable. We had also examined ROS1 and RET fusion genes in the 50 samples.

When the electric current is zero, the frequency

of the N

When the electric current is zero, the frequency

of the NMR signal is almost the same as the frequency of the oscillator adjusted at the static magnetic field of the magnet H0. The waveforms after the NMR signal was detected at a frequency of ω0 only vary slightly, as shown in Fig. 6a. We refer to this as being “on resonance”. On the other hand, when the PEFC generates electric power and electric current flows through the MEA, the frequency of the NMR signal shifts. In this case, the waveforms detected at a frequency of ω0 oscillate violently, as shown in Fig. 6b. The frequency shift of the NMR signal, Δω, can be calculated from the speed which the phase angle of the waveform, θ, rotates. The phase angle θ is calculable from the arctangent of the waveform (SI, SQ) [16]. The phase angle was calculated in the time period “A” illustrated in Fig. 6a, and is shown in Fig. 7a. The frequency shift selleck compound click here ΔωNo-curr in the case when the current was zero was calculated by approximating the change of the phase angle as a straight line. Fig. 7b shows the phase angle calculated similarly when the PEFS was generating electricity. Because the phase angle rotates between −π to +π, the phase angle θ shown in Fig.

7b was corrected by additions of multiples of π so that the phase angle was continuous. The frequency shift ΔωCurr when the PEFC was generating electricity was calculated from the slope of the phase angle. A substantial frequency shift Δω was obtained from the difference (ΔωCurr − ΔωNo-curr). The spatial distribution of the frequency shift, Δωexp(y) measured in an experiment when the PEFC had just started electrical power generation at t = 0 s, is shown in Fig. 8. The shape of the spatial distribution is almost a straight line with a constant slope. The frequency shift, Δωexp(y), at the position y = 0 is not zero as shown in the figure. The gap from zero was caused by another additional magnetic field formed by current flowing into the electric wire which connected the PEFC to

the electric load. On the other hand, if a spatial distribution of the local electric current density, check i(y), generated within the PEFC is assumed, the additional magnetic field formed by the current, Hi,th(y), can be analyzed theoretically using the Biot-Savart law [17]. In this analysis, it was assumed that the electric current had a spatial distribution only in the y direction, which is the direction of the gas inlet and outlet, and that it was uniformly distributed in the x direction. The justification for this assumption is that the differences of gas concentration and water content in the PEM are large in the gas flow direction and are very small in the x direction. The additional magnetic field, Hi,th(y), can be replaced by the frequency shift, Δωth(y) using Eq. (2).