To estimate biogenic amines and changes in quality of rainbow trout (Oncorhynchus mykiss) fillets at different temperatures, we determined the sensory attributes, total volatile basic nitrogen (TVB-N), total viable counts (TVC), and biogenic amines (BAs) of samples that were untreated (CK) or dry cured with 1.8% salt (T). There was no significant difference between CK and T samples in terms of TVB-N, TVC, and BAs. TVB-N and TVC increased significantly (P < 0.05) with storage time at 3, 9, and 15°C. Putrescine (PUT) and cadaverine (CAD) increased significantly (P < 0.05) at −3, 3, 9, and 15°C during storage. Histamine formed more easily when storage temperatures were higher. The kinetic models of sensory scores for TVB-N, TVC, PUT, CAD, and the sum of PUT and CAD (PUT+CAD) in T samples versus storage time and temperature were developed based on the Arrhenius equation. High regression coefficients (R2 > 0.9) indicated the acceptability of the kinetic model for predicting changes in the quality of the rainbow trout fillets. Relative errors between predicted and experimental values of TVB-N, TVC, and PUT+CAD were all within 10% except for TVB-N on day 6. The prediction model based on TVB-N, TVC, and PUT+CAD can be applied to evaluate changes in quality of rainbow trout fillets from −3 to 15°C (270 to 288 K).

Rainbow trout (Oncorhynchus mykiss) is an important cold water fish that is native to North America but is now found throughout the world due to introduction by humans; it is named for the colorful stripe on the side of the body. Like other freshwater fishes, rainbow trout are perishable because of the high protein content, high moisture level, enzyme activity, and nearly neutral pH of muscle tissue. There have been few studies of rainbow trout under different storage conditions (21, 25). Controlling microorganisms in fish is the key to preservation. Common preservation methods include low temperatures (28), drying (9), modified atmosphere packaging (16), and additives (15).

Low-temperature storage is an important preservation method. Super chilling, chilling, and low temperatures can slow down the process of spoilage, maintain food quality, and prolong shelf life. Shi et al. (29) reported that low temperatures could control the quality of silver carp (Hypophthalmichthys molitrix) fillets by inhibiting the formation of biogenic amines. Ando et al. (2) reported that super chilling was an efficient way to prolong the storage period for squid and maintain higher quality. There is a long history of using salt to preserve food. Salt is capable of preserving fish and prolonging storage by decreasing water activity, suppressing microbial growth, and enhancing the functional properties of proteins (8). Zhang et al. (38) found that high salt concentrations extended the shelf life of common carp (Cyprinus carpio) compared with a low salt concentrations. However, too much salt is not conducive to maintaining good flavor, and salt increases certain health risks (15, 24). To provide good taste and extend the shelf life of fish, the concentration of salt is usually 1 to 2% (15, 38).

Biogenic amines (BAs) are the main indicators of freshness in fish. These low-molecular-weight organic compounds contain nitrogen and exhibit bioactivity. Tryptamine (TRM), 2-phenylethylamine (2-PHE), putrescine (PUT), cadaverine (CAD), histamine (HIM), tyramine (TYM), spermidine (SPD), and spermine (SPM) are the most common BAs found in foods. Except for SPD and SPM, the formation of BAs is related to the decarboxylation of corresponding free amino acids that are derived from proteins and peptides by spoilage bacteria (36). Consequently, BAs are always used as indicators to evaluate fish quality. According to Anli and Bayram (3) and Becker et al. (5), a high intake of biogenic amines such as HIM and TYM may pose a health risk to humans, causing numbness of the tongue, vomiting, diarrhea, and/or headaches. Therefore, research is needed on the effects of storage conditions on changes in BAs.

The kinetic model is applied widely to predict changes in the quality of fish. Many kinetic models based on the Arrhenius equation have been used successfully to model changes in quality in aquatic products such as silver carp (30), frozen shrimp (33), and brined bream (Megalobrama amblycephala) (34). Kinetic models offer a practical way to predict the quality of aquatic products during storage.

However, there are few studies on the effects of storage temperature and low salt concentration on rainbow trout, and no studies have included the use of prediction models for dry-cured rainbow trout with salt. In this study, we focused on changes in the quality and BAs of rainbow trout fillets treated with 1.8% salt and stored at −3, 3, 9, and 15°C (270, 276, 282, and 288 K). We evaluated the sensory attributes, total volatile basic nitrogen (TVB-N), total viable counts (TVC), and BAs and established predictive models for changes in the quality of brined rainbow trout. We hope that this work provides a reference for the preservation of rainbow trout fillets sold for human consumption.

Materials and pretreatment. Live rainbow trout (weight 788.73 ± 18.48 g; length 40.68 ± 0.89 cm) were purchased from an aquatic product wholesale market in Beijing, People's Republic of China in August 2015, transported to the laboratory, and oxygenated before slaughter; all fish were killed within 2 h. Fish were stunned, scaled, gutted, filleted, and rinsed with tap water. Fillets were divided into two groups: one that received no processing (CK) and one that was dry cured with 1.8% salt (T). All fillets were packed in polyvinyl chloride bags (commercial food-grade packaging bags) with normal pressure, and then each group was divided into four subgroups (n = 33, 18, 18, 12) that were stored at −3, 3, 9, and 15°C, respectively. We sampled white dorsal muscle from a whole fillet randomly for analysis of all the parameters every 3 days for samples at −3 and 3°C and every day for samples at 9 and 15°C. Each analysis was run in triplicate for three individual samples.

Sensory assessment. Sensory assessment (SA) was performed according to the method reported by Ojagh et al. (22). Fresh fish samples were evaluated by a panel of seven trained individuals (three men and four women). The color, odor, texture, and tone of raw fish muscle were rated by each evaluator. Each of the four attributes was scored on a 5-point scale, where 5 is the highest level and 1 is the lowest. The total SA was the mean of the total scores (4 to 20 points for each evaluator) given by the seven evaluators for the four attributes. A value of 12 was regarded as borderline for acceptability.

Determination of TVB-N. TVB-N was measured by the microtitration method based on the method of Song et al. (31) with some modifications. A 5-g sample of fish muscle was homogenized in 50 ml of distilled water and stirred for 30 min. This mixture was then centrifuged and filtered. After adding 5 ml of MgO (10 g/liter) to 5 ml of filtrate, the mixture was distilled through a Kjeldahl apparatus (KDY-9820, Tongrunyuan Ltd., Beijing, China). The distillate was absorbed by 20 ml of boric acid solution (20 g/liter) that contained a mixed indicator produced from dissolution of 0.1 g of methyl red and 0.1 g of methylene blue in 100 ml of ethanol. The boric acid solution was then titrated with 0.01 mol/liter hydrochloric acid solution. The TVB-N value was determined according to the consumption of hydrochloric acid.

Microbiological analysis. TVC were determined from agar plates using the pour plate method (29) with some modifications. A 5-g sample of fish muscle was added to 45 ml of sterile 0.9% physiological saline and homogenized. The homogenized samples (0.5 ml) were serially diluted in 4.5 ml of sterile 0.9% saline and incubated at 30°C for 72 h.

Determination of BAs. Preparation and derivatization of BAs for rainbow trout fillets followed the method of Li et al. (20) and Zhang et al. (38). Identification and quantification of BAs were performed using high-performance liquid chromatography (HPLC; LC-10AT series, Shimadzu, Kyoto, Japan) equipped with a SPD-10A (V) detector and COSMOSIL 5C18-PAQ column (4.6 mm inside diameter by 250 mm; NacalaiTesque, Inc., Kyoto, Japan). The mobile phases A and B were ammonium acetate (0.1 mol liter−1) and acetonitrile, respectively. The gradient elution program was as follows: 0 min, 50% B; 25 min, 90% B; 35 min, 90% B; 45 min, 50% B. The flow rate was 0.8 ml min−1, the temperature was 30°C, and the injection volume was 50 μl. The HPLC analysis produced a peak at 254 nm, and eight BAs (TRM, 2-PHE, PUT, CAD, HIM, TYM, SPD, and SPM) were detected.

Establishment and verification of predictive models of quality. Rainbow trout fillets in the experimental group were stored at −3, 3, 9, and 15°C and treated with 1.8% salt. The experimental data were calculated based on the Arrhenius model and integrated as described by Giannakourou and Taoukis (13). The data for sensory scores, TVB-N, TVC, and BAs of fillets stored at −3, 3, 9, and 15°C were used to build the predictive models, and the data at −3°C were used to validate the models using the statistical software Excel (2007; Microsoft, Redmond, WA).

Statistical analysis. All data were subjected to an analysis of variance, and results are reported as means ± standard deviations. The least significant difference procedure was used to test for differences between means at the 5% significance level using SPSS software (version 21.0, SPSS Inc., IBM, Armonk, NY).

SA. The sensory scores for CK and T samples decreased with storage time, and there was a significant difference (P < 0.05) between CK and T samples (Fig. 1a and 1b). The observed shelf life of rainbow trout stored at −3, 3, 9, and 15°C, as evaluated by panelists who claimed that the fish were not acceptable, was 19, 9, 3, and 1 day, respectively, for CK samples and 21, 10, 3, and 1 day, respectively, for T samples.

FIGURE 1.

Changes in sensory scores, TVB-N (total volatile base nitrogen) values, and TVC (total viable counts) of rainbow trout fillets stored at −3, 3, 9, and 15°C. CK, untreated; T, treated with 1.8% salt. (a) Sensory scores of CK samples; (b) sensory scores of T samples; (c) TVB-N of CK samples; (d) TVB-N of T samples; (e) TVC of CK samples; (f) TVC of T samples.

FIGURE 1.

Changes in sensory scores, TVB-N (total volatile base nitrogen) values, and TVC (total viable counts) of rainbow trout fillets stored at −3, 3, 9, and 15°C. CK, untreated; T, treated with 1.8% salt. (a) Sensory scores of CK samples; (b) sensory scores of T samples; (c) TVB-N of CK samples; (d) TVB-N of T samples; (e) TVC of CK samples; (f) TVC of T samples.

Close modal

TVB-N. Initially, the TVB-N value was 11.48 mg/100 g. Although there was a slight fluctuation, TVB-N values gradually increased with storage time (Fig. 1c and 1d). Except for the samples stored at −3°C, TVB-N values increased significantly (P < 0.05) with time during the final days of storage. However, there was no significant difference between CK and T samples.

TVC. The initial level of bacteria in rainbow trout fillets was 4.68 log CFU/g, indicating that the fish were of good quality. TVC increased slowly at the beginning and then increased significantly (P < 0.05) with storage time (Fig. 1e and 1f). TVC of samples stored at 3, 9, and 15°C had the same trend, but TVC of fillets stored at −3°C fluctuated. TVC at 3, 9, and 15°C were <6 log CFU/g on day 30 for both CK and T samples; however, TVC exceeded the acceptable level of 7 log CFU/g after 9, 3, and 2 days, respectively, for CK samples and after 12, 5, and 3 days for T samples, respectively. Nevertheless, there was no significant (P > 0.05) difference between CK and T samples at any of the storage temperatures.

BAs. The concentrations of eight BAs in rainbow trout fillets stored at −3, 3, 9, and 15°C are shown in Tables 1 and 2. The concentration of 2-PHE was 73.77 ± 0.00 mg/kg, and HIM was not detected at first. The initial concentrations of TRM, PUT, CAD, TYM, SPD, and SPM had low values of 0.17 ± 0.02, 0.07 ± 0.03, 0.40 ± 0.17, 0.90 ± 0.20, 0.37 ± 0.33, and 1.06 ± 0.28 mg/kg, respectively.

TABLE 1.

Concentrations of biogenic amines (BAs) in rainbow trout fillets stored at −3 and 3°C

Concentrations of biogenic amines (BAs) in rainbow trout fillets stored at −3 and 3°C
Concentrations of biogenic amines (BAs) in rainbow trout fillets stored at −3 and 3°C
TABLE 1.

Extended

Extended
Extended
TABLE 2.

Concentration of biogenic amines (BAs) in rainbow trout fillets stored at 9 and 15°C

Concentration of biogenic amines (BAs) in rainbow trout fillets stored at 9 and 15°C
Concentration of biogenic amines (BAs) in rainbow trout fillets stored at 9 and 15°C
TABLE 2.

Extended

Extended
Extended

The concentrations of TRM, 2-PHE, and TYM in all groups fluctuated during storage. However, changes in TRM and TYM were slight compared with those of other BAs, and concentrations became stable at later stages of storage, but 2-PHE was high and appeared to change drastically, which resulted in a dramatic fluctuation in the total concentration of BAs overall during storage. Generally, 2-PHE and TYM were the most abundant BAs.

There was hardly any HIM when samples were stored at −3 and 3°C. Although there was only a small increase in HIM for samples stored at 9 and 15°C, the concentrations remained low and there was no significant change over time. The concentrations of SPD and SPM were relatively stable, especially those of SPM, and mostly remained at 1.00 to 1.50 mg/kg.

PUT and CAD were major BAs. The PUT and CAD concentrations fluctuated in the early stages of storage when samples were stored at −3°C but increased significantly (P < 0.05) with storage time at both −3 and 3°C. For samples stored at 9°C, the PUT concentrations increased significantly (P < 0.05) in the final 2 days of storage for CK samples, although there was no significant change for T samples (i.e., from 0.07 ± 0.03 to 0.23 ± 0.09 mg/kg). The PUT and CAD concentrations increased significantly (P < 0.05) on the final day for CK samples at 15°C, but there was no significant change in PUT and CAD for T samples, which reached only 0.62 ± 0.47 and 0.54 ± 0.46 mg/kg, respectively. However, there was no significant difference between CK and T samples for any of the eight BAs.

Predictive models of quality. The sensory scores, TVB-N, TVC, PUT, CAD, and PUT+CAD values were fitted by a conventional first-order model:

formula

where C is the freshness indicator at a certain time, C0 is the initial value, and k is the rate constant (day−1) at a given temperature, which were calculated from the slope of the regression of ln(C/C0) versus time.

The Arrhenius equation used was

formula

where k0 is the preexponential factor, Ea is the activation energy (J mol−1), T is the absolute temperature (K), and R is the gas constant (8.3144 J[mol K]−1). k0 and Ea are all experience constants related to the nature of the response system. Substituting equation 2 into equation 1 gives the modified Arrhenius equation:

formula

The slope of the regression line (−Ea/R) was obtained from the plot of ln k versus the reciprocal of the thermodynamic temperature (T−1), after obtaining k at different temperatures. Ea was calculated, and k0 was obtained from the interception of the regression line.

For T samples, activation energies (Ea) of sensory scores, TVB-N, TVC, PUT, CAD, and PUT+CAD were 86.39, 143.47, 110.52, 78.51, 138.25, and 116.00 kJ mol−1, respectively, and the corresponding k0 were 1.60 × 1015, 1.65 ×1025, 2.29 ×1019, 1.06 ×1014, 1.77 ×1025, and 4.28 ×1020, respectively (Table 3). The corresponding R2 values were 0.8971, 0.9994, 0.9739, 0.9464, 0.9238, and 0.9485, respectively, based on the kinetic parameters of the Arrhenius model regression analysis. TVB-N, TVC, and BAs are traditional indicators to predict the quality of fish, and the R2 of TVB-N, TVC, and PUT+CAD were the highest of all the models (Table 3). Thus TVB-N, TVC, and PUT+CAD were chosen to be indicators to predict the changes in the quality of rainbow trout fillets.

TABLE 3.

Parameters of kinetics model for sensory scores, TVB-N, TVC, PUT, CAD, and PUT+CAD of rainbow trout treated with 1.8% salt at different temperaturesa

Parameters of kinetics model for sensory scores, TVB-N, TVC, PUT, CAD, and PUT+CAD of rainbow trout treated with 1.8% salt at different temperaturesa
Parameters of kinetics model for sensory scores, TVB-N, TVC, PUT, CAD, and PUT+CAD of rainbow trout treated with 1.8% salt at different temperaturesa

The predictive model of the quality of rainbow trout based on TVB-N was

formula

the predictive model of quality of rainbow trout based on TVC was

formula

and the predictive model of quality of rainbow trout based on PUT+CAD was

formula

where CTVB-N, CTVC, and CPUT+CAD are predictive values of TVB-N, TVC, and PUT+CAD of rainbow trout. CTVB−N0, CTVC0 and CPUT+CAD0 are the initial values of TVB-N, TVC, and PUT+CAD.

Validation of the predictive model of quality. The validation of the predictive model was measured by the changes in quality of the rainbow trout fillets stored at −3°C (270 K). The quality was determined by the values of TVB-N, TVC, and PUT−CAD. We compared predictive values and experimental values for days 6, 15, and 18 (Table 4). Except for TVB-N on day 6, the relative errors between predictive values and experimental values were all within 10%.

TABLE 4.

Predicted and experimental freshness indictor values of rainbow trout treated with 1.8% salt and stored at −3°C (270 K)

Predicted and experimental freshness indictor values of rainbow trout treated with 1.8% salt and stored at −3°C (270 K)
Predicted and experimental freshness indictor values of rainbow trout treated with 1.8% salt and stored at −3°C (270 K)

Sensory characteristics are important indicators that directly influence consumers' acceptance of food. In this study, sensory scores for rainbow trout fillets decreased significantly (P < 0.05) with storage time. Samples that were stored at lower temperatures received higher scores than did samples that were stored at higher temperatures. There was also a significant difference between CK and T samples stored at all temperatures. Thus, low storage temperature and a low concentration of salt seem to slow the sensory changes in rainbow trout fillets. Similar results have been reported by Hong et al. (15) and Zhang et al. (35).

The initial value of TVB-N (11.48 mg/100 g) was similar to that found by Shen et al. (28) (11.39 mg/100 g). The change in TVB-N was related to the metabolism of spoilage bacteria and the activity of endogenous enzymes (32). Temperature and water activity affect both bacteria and the activity of enzymes. TVB-N values of samples stored at −3°C increased slowly because the water in the fillets was partially frozen and the metabolism of the bacteria was suppressed. Compared with samples stored at −3 and 3°C, TVB-N values of those stored at 9 and 15°C increased sharply, especially in the final days of storage. For CK samples at 9 and 15°C, TVB-N values increased to 19.60 and 20.53 mg/100 g on days 5 and 3, respectively, but reached only 13.35 and 16.52 mg/100 g on days 27 and 15 during storage at −3 and 3°C, respectively. These results suggest that storage temperature had a major effect on changes in the quality of the fillets and that low temperatures helped to preserve the quality.

However, there was a slight decline in quality during the final days of storage in some samples, suggesting that volatile nitrogenous substances were decomposed by bacteria (7). Rezaei and Hosseini (25) reported that TVB-N in rainbow trout stored in ice was not stable. In the present study, the TVB-N in CK and T samples at all temperatures were not significantly different (P > 0.05). Because rainbow trout is a cold water species, the maintenance of quality may depend more on temperature than on the concentration of salt.

The initial microbial load in freshwater fish is affected by water conditions and temperature (6, 31), and this load ranges from 2 to 6 log CFU/g (1, 6, 12, 25, 27, 37). Hence, initial TVC differ even for the same species of fish. TVC of rainbow trout fillets stored at 3, 9, and 15°C increased significantly (P < 0.05) with storage time, but the growth rates of bacteria differed at different storage temperatures (Fig. 1e and 1f). TVC for CK samples increased to above the allowable limit on days 9, 3, and 1 at 3, 9, and 15°C, respectively, but were <7 log CFU/g at −3°C during the entire storage period. Low storage temperatures can prolong the shelf life of fish by inhibiting the metabolism and growth of bacteria (10, 35).

Although many studies have been conducted to evaluate the function of salt in food preservation (15, 38), there was no significant difference between CK and T samples in the present study. Salt likely enhances preservation at low temperatures through super chilling or chilling, but when storage temperatures are higher, a low concentration of salt may not prolong the shelf life of fish. The rates of physical and chemical reactions and bacterial growth increase nearly exponentially with higher temperatures. When fillets are stored at high temperatures such as 15°C, the effect of temperature can overpower a effect of a low salt concentration. The trend for TVC was similar to that for TVB-N values in this study; therefore, TVC could be a useful indicator to predict changes in the quality of rainbow trout fillets.

BAs are commonly found in fish, and their concentrations are related to the quality of fish (20, 23). BAs have been regarded as the standard by which to judge the quality and safety of fish for consumption. In the present study, the fluctuation of TRM, TYM, and particularly 2-PHE caused the concentration of the total BAs (eight) to fluctuate, as has been reported by others (19, 38). This may have resulted from the decomposition of some BAs, such as SPM (17). Zhang et al. (36) reported that the formation of BAs was related to decarboxylase-positive microorganisms. The change in microorganisms during storage might influence the activity of decarboxylase, which might cause the fluctuation in BAs. Further research is needed on this possibility.

PUT, CAD, and HIM are often used as indicators to predict changes in the quality of fish (17, 26) and are the most important BAs associated with the safety of fish for consumption; HIM is particularly important because of its toxicity. In this study, the concentrations of PUT and CAD increased significantly (P < 0.05) with storage time. But there was no significant change in PUT in T samples at 9 and 15°C or in CAD in T samples at 15°C, which only increased from 0.07 ± 0.03, 0.07 ± 0.03, and 0.40 ± 0.17 mg/kg to 0.23 ± 0.09, 0.62 ± 0.47, and 0.54 ± 0.46 mg/kg, respectively. Treatments with 1.8% salt may have affected the formation of PUT and CAD by inhibiting microbial growth (36), but no significant difference was observed between CK and T samples in terms of the change in BAs during storage. Combined with the change in TVB-N and TVC, the effect of storage temperature was greater than the effect of 1.8% salt on changes in quality and BAs of rainbow trout, which might be explained by changes in HIM. There was little HIM in samples stored at −3°C, but HIM was found at higher concentrations in samples that were stored at higher temperatures. Low storage temperature might decrease the activity of histidine decarboxylase and inhibit the growth of decarboxylase-positive microorganisms that produce histidine decarboxylase (37), leading to low concentrations of HIM. In contrast, high storage temperature promoted the activity of related bacteria and enzymes and accelerated the degradation of fish quality. The HIM concentrations in this study were much lower than those reported by some other researchers, but Krizek et al. (19) and Song et al. (31) found similar concentrations of HIM in rainbow trout and bream.

The concentrations of SPD and SPM in fillets were relatively constant, because these BAs are natural constituents of living cells (4). SPM has been reported as stable in black carp (Mylopharyngodon piceus) (11), bighead carp (Aristichthys nobilis) (14), and common carp (38). Although the concentrations of TRM, 2-PHE, and TYM fluctuated and there was little HIM, these four BAs plus SPD and SPM were not considered suitable as indicators to predict changes in the quality of rainbow trout. The values for PUT, CAD, PUT+CAD, SA, TVB-N, and TVC were more informative in rainbow trout during storage, especially at 3 and 9°C. Zhang et al. (38) reported a close correlation between PUT, CAD, PUT+CAD, SA, TVB-N, and TVC in common carp. Therefore, PUT, CAD, and PUT+CAD might be suitable for assessing and predicting the quality of rainbow trout during storage.

At higher storage temperatures, the rate constant k increased. TVB-N, TVC, and PUT+CAD values produced high R2 values using the Arrhenius equation. The established quality models based on TVB-N, TVC, and PUT+CAD predicted accurately the predictive values and the experimental values, almost all with relative errors within 10%. Thus, the established models can be used to predict the changes in rainbow trout that were stored from −3 to 15°C (270 to 288 K). The establishment of predictive models for fish quality can also reduce costs and improve the management of preservation (18).

Eight BAs were detected in rainbow trout in this study. The concentrations of TRM, 2-PHE, and TYM fluctuated during storage, but SPD and SPM concentrations were stable. The initial concentrations of PUT and CAD were low but increased significantly (P < 0.05) with time during the later stages of storage, with changes in SA, TVB-N, and TVC. This finding indicates that PUT and CAD are more suitable than other BAs for monitoring changes in quality of rainbow trout stored at low temperatures. The established models for T samples were suitable for predicting changes in TVB-N, TVC, and PUT+CAD of rainbow trout from −3 to 15°C (270 to 288 K). This study is the first time that PUT+CAD concentrations have been used to predict the quality of rainbow trout fillets. Dry curing with 1.8% salt improved the sensory qualities of the fillets but did not significantly affect TVB-N values, TVC, and BA concentrations during storage. The results suggest that temperature had a major influence on SA, TVB-N, TVC, and BAs in rainbow trout. The increase in the rate constant k with temperature also corroborated the effect of storage temperature on changes in quality. Storage at low temperatures was more effective than dry curing with 1.8% salt for preservation of rainbow trout fillets. Further studies should be conducted to investigate the detailed mechanism for the changes in the BAs at different temperatures in rainbow trout.

This study was supported by Beijing Natural Science Foundation (award 6152017), the National Science and Technology Ministry of China (awards 2015BAD17B03 and 2015BAD28B00), and the National Natural Science Foundation of China (award 31471683). We thank Thomas A. Gavin (Cornell University) for help with editing the English in this article.

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