Abstract
Based on 247 growth data, the growth of S. aureus 2064 in dependence on temperatures (8-50°C) and aw values (0.999-0.83) was described. Optimal values of awat all studied temperatures were determined by using Gibson model. Its compatibility was confirmed by several statistical indices, e.g. root mean square errors (RMSE 0.003-0.138), standard errors of prediction (%SEP 0.6-17.5). Cardinal values for S. aureus growth (Tmin=7.7°C, Topt=40.6°C, Tmax=46.7°C, awmin=0.808, awopt=0.994, μopt=1.97 1/h) were determined by using CM model with indices RMSE=0.071, SEP=17.5%. Our findings can provide relevant growth information that can be used in S. aureus exposure assessment or in validation of other data regarding the growth of this opportunistic pathogen in foods.
Key words: Secondary growth model, Salt addition, Cardinal temperature
Introduction
In the traditional way of production of some cheese’s varieties, raw milk is used. Thanks to the ubiquitous presence of coagulase- positive staphylococci in raw milk, also Staphylococcus aureus may be present. Its growth and potential production of 23 different types of heat-stable enterotoxins (SEs) with respect to food matrices and environmental conditions represent a potential risk to public health resulting in foodborne staphylococcal outbreaks. Besides SEs, S. aureus also disposes of other pathogenic factors – surface associated factors, enzymes and toxins (Asperger and Zangerl, 2003) that all contribute to the remarkable potential of S. aureus as a pathogen of human and animals. Moreover, this potential is multiplied by frequent occurrence of S. aureus in environment. In primary production and dairy environments, animals, people and operational environments are the main sources of a product’s contamination by S. aureus. One third of human population is asymptomatic carrier of S. aureus, so this microorganism can contaminate foods through food handlers’ cross-contamination (infected wounds, skin lesions) or by coughing and sneezing (Baird-Parker, 2000). Following contamination of food matrices, further destiny of microorganisms is dependent on the actual environmental factors. The knowledge of their effects on the pathogens growth is crucial to control their behavior (McCann et al., 2003) and consecutively to ensure microbiological safety of foods. A scientific basis of the HACCP concept and quantitative microbial risk assessment provides predictive microbiology that is based on a mathematical relationship between microbial growth responses and environmental factors (Mellefont et al., 2003). Such a knowledge may help to estimate the growth of microorganisms i) in the context of food safety (Ingham et al., 2009) or e.g. Listeria monocytogenes (Cornu et el., 2011) or ii) in the context of food spoilage (Pin et al., 1999) and extended shelf-life (Gougouli et al., 2011).
The nutritional requirements of S. aureus are complex and vary from strain to strain (Asperger and Zangerl, 2003). A characteristic feature which distinguishes S. aureus from other pathogenic bacteria is its high tolerance to low water activity (aw) values and NaCl concentrations of up to 20%. Generally, minimal awrequired for S. aureus growth is 0.83-0.86 (Medveďová and Valík, 2012). Ability of S. aureus to grow at such high salt concentrations is related to its adaptive response to osmotic stress. This is due to the intracellular accumulation of compatible solutes, including proline, betaine, choline, taurine, or by their transport from a growth medium (O’Byrne and Booth, 2002). There is a variety of transport systems, activated/induced by NaCl, which are responsible for entry of osmoprotectants into the cell. Besides the accumulation of compatible solutes (e.g. proline, betaine, choline, taurine) to maintain intracellular turgor pressure in response to high osmolarity environments, S. aureus also responds to NaCl stress by altering specific gene and protein expression (Scybert et al., 2003).
Several S. aureus growth data determined in both artificial media and in foods are present in databases. However, the majority of them do not provide S. aureus growth parameters in the whole growth range of selected environmental factors or a combination of several environmental factors. Uniformity of specific growth rates (0.163±0.025 1/h) of 64 different S. aureus strains all isolated from raw milk cheeses was confirmed by coefficient of variance vc=15.5% in Medveďová et al. (2014) supposing uniformity of whole species responses to environmental factors. Also, the similarity of growth rates between isolate 2064 and enterotoxinogenic S. aureus 14733 isolated from milk vending machine biofilm was confirmed (Medveďová et al., 2017). Based on that, the main objective of this study was to provide additional data of S. aureus 2064 isolated from specific artisanal raw milk cheese that can be used in the validation of S. aureus growth already determined. The preliminary results of salt addition effect at only 15 and 18°C were published by Medveďová et al. (2009). So, the main objective of this work is to characterize the growth of S. aureus isolate in dependence on aw(adjusted by NaCl, as the main food preservative) and in whole temperature range, and subsequently to determine cardinal environmental factors. In this connection, these data may be taken into consideration in prediction of additional growth studies of various isolates from specific foods and food environment that may contribute to reliable assessing of the variability of S. aureus growth dynamic under specific conditions.
Materials and Methods
Microorganism
S. aureus 2064 isolate was selected for this study. It was isolated from ewes’ lump cheese by MVDr. Hanzélyová (State Veterinary and Food Institution, Prešov, Slovakia) in 2009 by using cultivation method on selective Baird-Parker agar according to EN ISO 6888-1. Its identity was confirmed by Medveďová et al. (2009), however the isolate does not produce enterotoxins.
Media
The isolate was maintained between experiments on Plate Count Agar slopes (PCA; Sigma-Aldrich, St. Louis, USA) at 6±1°C and stored for months at -40°C. A standard S. aureus 2064 inoculum (0.3 mL from 103 dilution of an 18h culture grown on PCA agar at 37°C) was inoculated aseptically into 300 mL of pre-tempered PCA broth (Difco; Le Pont de Claix, France) to reach initial S. aureus counts as close as possible to 103 CFU/mL. The samples were incubated in three parallels and repetitions at static aerobic conditions at 8, 10, 12, 15, 18, 21, 25, 30, 35, 37, 39, 43, 46 and 50°C±0.5°C in order to study S. aureus 2064 growth in dependence on temperature and aw.
The effect of water activity on S. aureus 2064 growth
The effect of awon S. aureus 2064 growth was studied in three parallels and repetitions of PCA broth with adjusted awvalue at temperatures from 8 to 50°C at static aerobic conditions. The awvalues of broth were set by the NaCl addition (Sigma- Aldrich, Buchs, Switzerland) and controlled by an aw-meter (Aw-Sprint TH500, Novasina, Lachen, Switzerland).
Counts of S. aureus 2064 in growth media
At chosen time intervals, depending on actual temperature, numbers of the isolate were determined according to ISO 4833-1:2013 on PCA agar.
Fitting the growth curves and primary modeling
S. aureus 2064 growth parameters were analyzed, fitted and calculated using DMFit Excel Add-in package version 3.5 (ComBase managed by United States Department of Agriculture-Agricultural Research Service, Washington, USA and University of Tasmania Food Safety Centre Hobart, Australia) that incorporates the mechanistic model of Baranyi and Roberts (1994). The actual counts were plotted against time and fitted to a model for the estimation of μ (specific growth rate), ΔN (S. aureus 2064 growth increase in stationary phase against initial density). Growth parameters from the individual parallel experiments were further analyzed by the secondary models using the Microsoft Office, version 2007 (Microsoft, Redmond, USA) and the Statistica data analysis software system, version 8.0 (Statsoft, Inc., Tulsa, USA).
Secondary modeling
The specific growth rate was firstly modeled as a function of awaccording to Gibson et al. (1994). Using the model described by the following formula
lnμ = C0 +C1bw+ C2b2w |
the optimum awvalue at each temperature for the maximum growth rate can be calculated as follows:
Indices C0, C1 and C2 where estimated by linear regression and awoptis the value of awat which the maximum specific growth rate equals its optimal value μopt. The parameter bwis calculated as:
Cardinal model CM was used to describe the cumulative influence of temperature and awon the microbial growth rate. The specific growth rate was subjected to secondary modelling in relation to the incubation temperature (Rosso et al., 1993). The combined effect of temperature and awwas determined according to the gamma concept (Zwietering et al., 1991), based on individual cardinal models (Rosso et al., 1993):
(1) |
where
(2) |
and
(3) |
where Toptis the temperature at which the maximum specific growth rate equals its optimal value μopt. The cardinal values of temperature and awwere subsequently defined by nonlinear regression as the equation parameters.
Validation of the growth parameters
To evaluate goodness of fit of the mathematical equations describing S. aureus responses to the various temperature and aw conditions, several mathematical and statistical indices were used. The regression coefficient (R2) and the root mean square error (RMSE; as the average deviation between observed and predicted values) was calculated according to Garcia et al. (2011), the per cent variance (%V; as a measure of the goodness of the model fit) was used as was given by Daughtry et al. (1997). Finally, the bias (Bf) and discrepancy (%Df) factors as defined by Baranyi et al. (1999) were used. The indices were calculated according equations:
(4) |
(5) |
(6) |
(7) |
where μobsand μpredare observed and predicted values of the specific growth rates, n is number of the data points, NTis number of model terms, Af is accuracy indices.
Results and Discussion
Study of aw and incubation temperature effect on S. aureus 2064 growth dynamic
The effect of the aw and incubation temperature (at gradually ranked temperatures from 8°C to 50°C) on the S. aureus 2064 growth dynamic was described in model media (PCA broth). The awvalues of the tested media were adjusted by NaCl, using its addition in the range from 0% up to 21%, and subsequently expressed as the actual aw value. The initial S. aureus 2064 concentration in all experiments (n=307) was 3.20±0.23 log CFU/mL with cv=7.35% − where coefficient of variance is dependent on standard deviation and average specific growth rate value as
– which was necessary for comparing the growth ability of the tested isolate under changing environmental conditions. On the other hand, the counts in stationary phase were strongly dependent on the incubation temperature and/or salt addition.
The growth parameters obtained from primary growth curves are summarized in Table 1. Generally, growth of isolate 2064 was faster as more optimal incubation temperature and aw values were reached. Also, by increasing the incubation temperature, S. aureus 2064 tolerated more drastic conditions as expressed by lower minimal aw values at which it grew. Since isolate 2064 was incubated at 8°C, it could not resist either the NaCl addition or the temperature of 8°C itself. These findings are in accordance with Normanno et al. (2005) who also did not observe growth of S. aureus at 8°C. However, according Valero et al. (2009), S. aureus grew at 8°C, aw=0.989 (2% of NaCl) and pH<6 in 50% of cases, while at awlevels below 0.983, its growth was only observed at pH values 6.0-7.0. Also, Valík and Görner (1993) reported that the ability of S. aureus to resist high salt concentration is strain dependent, since the minimal awvalue for growth in their experiments ranged from 0.93 to 0.86. At 10°C and 12°C, S. aureus 2064 was able to grow until the NaCl concentration of 5% (aw=0.968) and 8% (aw=0.951), in order. However, its dying at these temperatures was observed at NaCl additions higher than 8% (aw=0.951) or 10% (aw=0.928). Contrary, no growth at 10°C and aw=0.971 was reported by Castillejo-Rodríguez et al. (2002) and at 12°C and aw=0.950 as reported Buchanan et al. (1993). Also, Lee at al. (1977) observed that S. aureus did not grow at 12°C and aw=0.915 (13% of NaCl). As reported Valero et al. (2009), resistance of S. aureus to low awvalues at 19°C was shown, since the growth was detected at pH 7.0 and aw=0.867. In our case, S. aureus 2064 was not able to grow at 18°C if the NaCl addition was higher than 15% (aw=0.893).
Table 1.
T | aw | μ | ΔN | T | aw | μ | ΔN | T | aw | μ | ΔN |
---|---|---|---|---|---|---|---|---|---|---|---|
8 | 0.998 | -0.004* | -1.66* | 21 | 0.890 | 0.026 | 4.35 | 37 | 0.913 | 0.509 | 4.15 |
8 | 0.989 | -0.0004* | -0.24* | 21 | 0.871 | -0.023* | -1.62* | 37 | 0.894 | 0.427 | 3.60 |
8 | 0.972 | -0.003* | -0.77* | 25 | 0.988 | 0.737 | 5.67 | 37 | 0.880 | 0.224 | 3.76 |
10 | 0.997 | 0.044 | 4.27 | 25 | 0.977 | 0.622 | 5.27 | 37 | 0.860 | 0.152 | 3.71 |
10 | 0.989 | 0.029 | 3.46 | 25 | 0.955 | 0.547 | 5.16 | 37 | 0.855 | -0.025* | -2.15* |
10 | 0.968 | 0.035 | 5.04 | 25 | 0.941 | 0.534 | 4.26 | 39 | 0.998 | 1.867 | 5.75 |
10 | 0.951 | -0.002* | -0.98* | 25 | 0.917 | 0.319 | 3.77 | 39 | 0.994 | 1.863 | 5.75 |
12 | 0.992 | 0.064 | 4.33 | 25 | 0.894 | 0.138 | 4.75 | 39 | 0.966 | 1.502 | 5.24 |
12 | 0.988 | 0.092 | 4.59 | 25 | 0.879 | 0.092 | 4.20 | 39 | 0.947 | 1.132 | 4.97 |
12 | 0.969 | 0.063 | 4.50 | 25 | 0.865 | 0.037 | 3.79 | 39 | 0.930 | 1.014 | 4.68 |
12 | 0.955 | 0.048 | 5.02 | 25 | 0.859 | -0.261* | -2.19* | 39 | 0.909 | 0.627 | 4.24 |
12 | 0.928 | -0.005* | -0.95* | 30 | 0.987 | 0.968 | 5.00 | 39 | 0.894 | 0.554 | 3.75 |
12 | 0.909 | -0.006* | -1.28* | 30 | 0.983 | 1.062 | 4.89 | 39 | 0.862 | 0.223 | 3.63 |
15 | 0.998 | 0.155 | 5.76 | 30 | 0.969 | 0.923 | 5.15 | 39 | 0.842 | -0.003* | -1.48* |
15 | 0.992 | 0.162 | 5.79 | 30 | 0.953 | 0.732 | 5.04 | 43 | 0.997 | 1.744 | 5.38 |
15 | 0.966 | 0.114 | 5.09 | 30 | 0.930 | 0.510 | 4.73 | 43 | 0.985 | 1.801 | 5.07 |
15 | 0.945 | 0.073 | 5.13 | 30 | 0.896 | 0.221 | 4.74 | 43 | 0.965 | 1.274 | 4.49 |
15 | 0.923 | 0.052 | 4.37 | 30 | 0.883 | 0.219 | 4.14 | 43 | 0.945 | 1.114 | 3.80 |
15 | 0.904 | 0.012 | 4.10 | 30 | 0.868 | 0.087 | 3.82 | 43 | 0.925 | 0.714 | 3.68 |
15 | 0.888 | -0.005* | -0.84* | 30 | 0.856 | -0.004* | -2.19* | 43 | 0.913 | 0.521 | 3.19 |
15 | 0.865 | -0.005* | -0.87* | 35 | 0.993 | 1.632 | 5.58 | 43 | 0.889 | 0.449 | 2.98 |
18 | 0.988 | 0.304 | 4.69 | 35 | 0.997 | 1.602 | 5.11 | 43 | 0.860 | 0.089 | 2.92 |
18 | 0.983 | 0.280 | 4.87 | 35 | 0.966 | 1.236 | 5.05 | 43 | 0.840 | -0.020* | -2.02* |
18 | 0.964 | 0.206 | 4.97 | 35 | 0.947 | 0.965 | 4.02 | 46 | 0.997 | -0.831 | -2.32 |
18 | 0.944 | 0.161 | 5.21 | 35 | 0.927 | 0.965 | 4.47 | 46 | 0.991 | 0.770 | 2.56 |
18 | 0.930 | 0.083 | 4.76 | 35 | 0.913 | 0.601 | 3.96 | 46 | 0.972 | 0.668 | 3.26 |
18 | 0.913 | 0.061 | 4.00 | 35 | 0.886 | 0.325 | 4.35 | 46 | 0.954 | 0.395 | 2.90 |
18 | 0.893 | 0.007 | 4.12 | 35 | 0.870 | 0.226 | 4.08 | 46 | 0.929 | 0.170 | 2.76 |
18 | 0.869 | -0.007* | -0.84* | 35 | 0.863 | 0.059 | 3.30 | 46 | 0.909 | 0.088 | 2.20 |
21 | 0.992 | 0.423 | 4.65 | 35 | 0.855 | -0.228* | -2.25* | 46 | 0.891 | -0.055* | -2.06* |
21 | 0.979 | 0.431 | 4.42 | 37 | 0.993 | 1.796 | 5.38 | 50 | 0.998 | -1.013* | -2.96* |
21 | 0.959 | 0.374 | 5.22 | 37 | 0.988 | 1.784 | 5.05 | 50 | 0.989 | -0.873* | -2.42* |
21 | 0.943 | 0.237 | 4.97 | 37 | 0.964 | 1.558 | 4.83 | 50 | 0.971 | -0.486* | -1.70* |
21 | 0.926 | 0.162 | 5.37 | 37 | 0.947 | 1.117 | 4.88 | ||||
21 | 0.908 | 0.114 | 4.45 | 37 | 0.925 | 0.654 | 4.51 |
T - incubation temperature (°C), aw - actual aw value of media, – specific growth rate (1/h), ΔN – S. aureus 2064 growth increment in stationary phase against initial density (log CFU/mL)
*decreasing of counts
At higher temperatures (39 and 46°C) a similar effect of salt presence in the growth media on S. aureus growth was observed. The isolate confirmed its high salt tolerance even at these temperatures. The ability of bacteria to grow at high salt conditions is related to their adaptive response to osmotic stress by the intracellular accumulation of compatible solutes or by their transport from the growth medium. It was mentioned by Vaaomonde et al. (1984) that S. aureus cells died relatively rapidly in the presence of NaCl. However, a variety of transport systems, e.g. betaine (BPI and BPII) or proline (PutP) transport systems (O´Byrne and Booth (2002) are activated or induced by NaCl and are responsible for entry of osmoprotectants (betaine, proline etc.) into the cell. Besides that, S. aureus may also undergo an extensive program of gene and proteins expression in response to NaCl stress (Scybert et al., 2003) or temperature stress (Rigoulay et al., 2004). It was shown that HtrA proteins (heat shock-induced envelope- associated serine proteases) are essential for bacteria to survive at high temperatures (Lipinska et al., 1990) and that they are responsible for degradation of denatured proteins produced at high temperatures and or under osmotic stress (Rigoulay et al., 2004).
Interestingly, isolate 2064 was not able to grow at 46°C in media without NaCl. But 2% NaCl addition (aw=0.991) into PCA broth caused that S. aureus 2064 started to grow and it grew only till 5 log counts. The final NaCl concentration at which the microorganism was able to multiply at 46°C was 13% NaCl (aw=0.909). Studies have shown that in most cases a reduced awleads to an increase in thermotolerance (O´Byrne and Booth, 2002). Shebuski et al. (2000) observed the similar protective effect when S. aureus was heat treated in the presence of increasing salt concentrations. Santoro et al. (1992) reported that activation energy of water molecules is higher in presence of heat and so they have a potent ability to interact with proteins and accelerate their duration. O´Byrne and Booth (2002) have also found that increased proteins thermostability is frequently observed when the awvalue of the solvent is reduced, and that compatible solutes enhance thermostability. Cebrián et al. (2010) observed that 48°C was the last most protective heat-shock temperature for S. aureus in terms of developed thermotolerance. In our case, at 50°C no growth of S. aureus 2064 was detected at all.
Secondary modeling
Firstly, to describe the aweffect on S. aureus 2064 specific growth rate at each incubation temperature in PCA broth, the model of Gibson et al. (1994) was used. Equations for S. aureus 2064 growth dynamic responses as a function of awvalues at all incubation temperatures are summarized in Table 2 with graphical representations depicted in Figure 1. By using this model, the optimal awvalues for S. aureus 2064 in PCA broth at each single incubation temperature can be calculated as it is summarized in Table 2. The optimal awvalues were strongly dependent on the incubation temperature. It was also interesting that at extreme temperatures S. aureus required some NaCl in the media, as is expressed by the lower optimal awvalues in comparison to the almost optimal incubation temperature. It can be assumed that the halophilic character of S. aureus is manifested in the need for some NaCl amount in the media to initiate the metabolism under less favorable conditions. However, in such a condition the awrange allowing the staphylococcal growth is more limited, as it is expressed by the higher minimal awvalues in contrast to the higher or more optimal incubation temperature conditions.
Due the fact that the growth rate was simultaneously influenced by awand incubation temperature, we used the complete gamma concept. In this case, the gamma factors for studied environmental factors were calculated to establish the cardinal model (CM, Figure 2) that was adequate to describe the effect of incubation temperature and awon S. aureus 2064 specific growth rate. As one can see, with increases of the incubation temperature up to 40°C, the specific growth rate increased with a constant slope. At temperatures higher than 40°C, the growth of S. aureus slows down. Therefore, the curvature is observed in the optimal region, i.e. 35–40°C. According to CM model and combining a global fit, seven parameters of CM model, i.e., cardinal temperatures (Tmin=7.72±0.03°C, Topt=40.63±0.04°C, Tmax=46.73±0.02°C), cardinal awvalues (awmin=0.808±0.0023, awopt=0.994±0.0004, awmaxfixed to 1) and the optimal growth rate (μopt=1.97 1/h) were identified. The optimal temperature of Topt=40.63°C seems to be high, however, according to experimental data the isolate grew with the maximal specific growth rate at 39°C and the model only supported this observation. Also Sutherland et al. (1994) reported temperature about 40°C as optimal and Taub et al. (2003) published that S. aureus grew in bread with the highest specific growth rate also at 40°C. Knowing of cardinal values may increase the stability of products with increase S. aureus prevalence as they can help to set conditions during manufacture (heat treatment conditions), maximal allowed storage temperature ensuring no increase of S. aureus or maximal addition of salt leading to S. aureus growth inhibition. Further, the results can be also used in exposure assessment of S. aureus in raw milk cheeses manufactured traditionally in Slovakia as was earlier published by Ačai et al. (2014a) and Ačai et al. (2014b).
Validation
Several mathematical and statistical indices were used to validate mathematical equations describing S. aureus 2064 responses to environmental conditions (Table 2). In view of R2or more stringent term %V, the worst fit (%V<93%) of the Gibson model to the isolate growth rate at 10 and 12°C was achieved. This might be accounted for the worse S. aureus ability to adapt to the low incubation temperature, which was also noticed during the primary growth parameters analysis. However, it is worthy of note that %V of the CM model and of the majority of Gibson models, were higher than 98%. Taking into account that the smaller the RMSE, the better is the fit, the highest error is estimated by using the CM model. On the other hand, the lowest error of predictions (formulated as %SEP) was calculated for the Gibson model at 39°C although the highest error is expected at 46°C. Further, bias factor Bf<1 indicates slower predicted growth than the observed one, and Bf>1 indicates faster predicted growth than observed. In our case, faster growth in real media can be expected only if using Gibson model at 15°C and 18°C and in using CM model. Moreover, according to recommendation of Ross (1999) all models can be considered as acceptable since Bf is in range 0.90-1.05.
Table 2.
Equation | n | awopt | Bf | %Df | R2 | %V | RMSE | %SEP |
---|---|---|---|---|---|---|---|---|
lnμ10 = 53.972bw 2 − 14.087bw − 2.577 | 9 | 0.982 | 0.999 | 6.9 | 0.755 | 51.0 | 0.0025 | 7.2 |
lnμ12 = −93.792 + 24.711bw − 4.112 | 12 | 0.983 | 0.999 | 10.6 | 0.814 | 74.4 | 0.0077 | 12.2 |
lnμ15 = −53.802bw 2 + 11.471bw − 2.342 | 21 | 0.989 | 1.001 | 22.3 | 0.954 | 94.6 | 0.0105 | 14.8 |
lnμ18 = −32.829bw 2 + 4.961bw − 1.338 | 21 | 0.994 | 1.001 | 11.7 | 0.974 | 96.9 | 0.0142 | 9.2 |
lnμ21 = −59.491bw 2 + 16.983bw − 2.048 | 21 | 0.980 | 1.000 | 17.5 | 0.942 | 93.0 | 0.0252 | 12.8 |
lnμ25 = −53.522bw 2 + 16.387bw − 1.569 | 21 | 0.977 | 0.999 | 11.9 | 0.977 | 97.3 | 0.0616 | 11.5 |
lnμ30 = −49.647bw 2 + 14.186bw − 1.013 | 27 | 0.979 | 0.999 | 15.3 | 0.977 | 97.4 | 0.0422 | 6.8 |
lnμ35 = −30.633bw 2 + 6.652bw − 0.155 | 24 | 0.988 | 0.999 | 12.2 | 0.972 | 96.8 | 0.1113 | 11.5 |
lnμ37 = −35.936bw 2 + 8.010bw − 0.159 | 30 | 0.988 | 0.999 | 9.6 | 0.988 | 98.6 | 0.0538 | 8.2 |
lnμ39 = −29.074bw 2 + 6.191bw − 0.325 | 24 | 0.989 | 1.000 | 9.7 | 0.981 | 97.8 | 0.0067 | 0.6 |
lnμ43 = −42.346bw 2 + 10.144bw − 0.035 | 27 | 0.986 | 0.999 | 23.7 | 0.949 | 94.1 | 0.1381 | 12.7 |
lnμ46= −29.621b 2 + 1.486bw − 0.0025 | 21 | 0.999 | 0.931 | 22.1 | 0.976 | 96.9 | 0.0692 | 17.5 |
STA 2064: CM model | 27 | 0.0711 | 1.026 | 32.3 | 0.982 | 98.2 | 0.0711 | 17.5 |
Acknowledgements
We would like to thank Kevin Slavin for checking the English in the manuscript.
Funding Statement
Funding: This work was funded by grants VEGA No. 1/0532/18.
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