Water loss in table grapes : model development and validation under dynamic storage conditions

Fresh produce continuously lose water during the post-harvest handling. Relatively small moisture losses are enough to cause shriveling, wilting and undesirable texture changes (Kader, 2002). On addition, percent loss of fresh weight is used to describe freshness of horticultural products, since the loss of water decreases their economic value by reducing the saleable weight (Hertog et al., 2015; Shibairo et al., 2002). Table grape (Vitis Vinifera L.) is a nonclimacteric fruit very sensitive to temperature and humidity levels. Hence, storage at low temperature, around 0 °C (Fourie, 2008), and high levels of relative humidity (RH), around 95% (Alferez et al., 2005), are recommended to maintain grapes in a good condition. The main table grapes post-harvest quality problems are decay caused by Botrytis cinerea, rachis desiccation and stem browning caused by water loss. Cumulative water losses also lead to berry shatter, wilting of the cluster and shriveling of the berries (Crisosto & Mitchell, 2002). On some table grapes varieties water losses of 2 to 3%, based on the initial weight, are sufficient to make stems show symptoms of browning (Crisosto et al., 1994). However, grape berries do not show symptoms of dehydration until the damage is quite evident in the stems. Losses in weight above 5% are necessary to wrinkles starts to appear in the berry skin (Nelson, 1978).


Introduction
Fresh produce continuously lose water during the post-harvest handling.Relatively small moisture losses are enough to cause shriveling, wilting and undesirable texture changes (Kader, 2002).On addition, percent loss of fresh weight is used to describe freshness of horticultural products, since the loss of water decreases their economic value by reducing the saleable weight (Hertog et al., 2015;Shibairo et al., 2002).Table grape (Vitis Vinifera L.) is a nonclimacteric fruit very sensitive to temperature and humidity levels.Hence, storage at low temperature, around 0 °C (Fourie, 2008), and high levels of relative humidity (RH), around 95% (Alferez et al., 2005), are recommended to maintain grapes in a good condition.The main table grapes post-harvest quality problems are decay caused by Botrytis cinerea, rachis desiccation and stem browning caused by water loss.Cumulative water losses also lead to berry shatter, wilting of the cluster and shriveling of the berries (Crisosto & Mitchell, 2002).On some table grapes varieties water losses of 2 to 3%, based on the initial weight, are sufficient to make stems show symptoms of browning (Crisosto et al., 1994).However, grape berries do not show symptoms of dehydration until the damage is quite evident in the stems.Losses in weight above 5% are necessary to wrinkles starts to appear in the berry skin (Nelson, 1978).
Liquid water moves across membranes of plant tissues and escapes to the air present in the intercellular spaces as water vapor.Ondeed, the chemical potential of water in cells compared with that in the adjacent air determines the direction for net water movement occurring at cell-air interface (Nobel, 2005;Shamaila, 2005).Subsequently, the plant releases this water vapor into the surrounding atmosphere through a moisture transport known as epidermal transpiration (Maguire et al., 2001;Veraverbeke et al., 2003).Plant transpiration is affected by both fruit characteristics (e.g.surface-to-volume ratio, ripening stage) and climatic conditions (e.g.temperature, RH).Transpiration rate was found to be better expressed in quantity of water loss per unit time per unit fresh weight (Leonardi et al., 1999).
Nevertheless, dealing with a homogeneous batch of particular specie the transpiration rate will be primarily controlled by the difference in water vapor pressure (WVP).Therefore, considering the air inside the plant material nearly saturated, the difference in WVP is determined solely by the temperature of the fruit, dry-bulb temperature and the humidity of the air (Thompson, 2002).Hence, the environmental conditions are essential in the water loss process.
Mathematical modelling has the ultimate goal of predicting future behavior of the products in any circumstances (Tijskens & Schouten, 2009).Hence, modelling techniques has been applied to describe changes in the quality attributes of many fresh products (Amodio et al., 2013(Amodio et al., , 2015;;Gwanpua et al., 2012Gwanpua et al., , 2013;;Hertog et al., 2004b, c;Schouten et al., 2007Schouten et al., , 2010)).On some of the reported works, the transpiration process was related to changes in texture attributes (Smedt et al., 2002) and visible wrinkling of the fruit skin (Hertog, 2002).However, even though the transpiration from fruit can be well described by the approach of steady state solution of Fick's first law, most of the publications on modelling this phenomenon consider constant temperature and RH during the storage time (Hertog et al., 2004a;Maguire et al., 1999;Mahajan et al., 2008).Nunes et al. (2009) demonstrated that variations in storage conditions are normally encountered in the cold chain and they have a huge effect on decreasing the quality and shelf life of grapes and other fresh products.However, some authors suggested that the weakest link of the cold chain is the domestic storage, while home refrigerators and freezers frequently present poor temperature control (James et al., 2008;Laguerre et al., 2002).A study performed by Gogou et al. (2015) for selected food products in Greece and France supports this argument, revealing that during the domestic storage temperatures may vary from ~ 4 °C to ~ 11 °C.On some cases the registered mean temperature was in a range of 8 °C to 10 °C.
On another relevant research, Lichter et al. (2011) found weight loss of gapes to be linear in constant conditions, but to our knowledge, there is no study about the weight loss profile of this fruit at home storage.Neither influence of dynamic storage conditions in its transpiration rate or validation of diffusional approach for variable scenarios was available yet.
According to the above literature review, no information is available about grapes transpiration rates and weight loss behavior under variable conditions of temperature and RH.So this study aimed proposing a methodology to develop a weight loss model for table grapes and validate its predictions in dynamic environment conditions of a common (domestic) refrigerator.Dnce cooling delays contribute in shortening the fruit market life (Crisosto et al., 2001;Johnston et al., 2005), the effect of waiting times was also studied by exposing fruit to cooling delays and comparing their transpiration rates to those of clusters stored under continuous refrigeration.

Material
Table grapes (Vitis Vinifera L. cv.Crimson Seedless) were harvested, prepared and packed from a farm in Petrolina (PE, Brazil) in September and Dctober 2016 on the commercial stage of maturity (17.8% and 20.5% in soluble solid content (SSC), respectively).On both seasons, only fruit without visible Botrytis infection and mechanical damage were packed in PET punnets (185 mm × 115 mm × 90 mm).The fruit were transported from the farm to the local supplier (Mape Frutas Agroindustrial, Jundiaí, SP, Brazil) in refrigerated truck.After the arrival at the local supplier, table grapes were purchased and transported to the laboratory at University of Campinas within 1 h.All the samples were weighed using a weighing scale (AM 5500, Marte Cientifica, São Paulo, Brazil, with an accuracy of 0.01 g) to get the initial mass (548.3 ± 14.2 g and 551.4 ± 3.9 g in the first and in the second seasons, respectively).

Experimental procedure
The punnets were divided into 4 controlled temperature environments, which were formed by four refrigerators equipped with temperature controllers (N323TR, Novus Automation Onc., Porto Alegre, Brazil).The experiment was repeated twice with two different batches of table grapes and triplicates were used in both repetitions.Air temperature and relative humidity were measured inside the four storage containers.Table 1 shows the average and standard deviation (SD) of temperature and relative humidity levels used in the experiments for model building.Air temperature was measured with thin film temperature sensor elements Pt100 (CRZ-2005, Novus Automation Onc., Porto Alegre, Brazil), and the air relative humidity (RH) was measured with relative humidity and temperature transmitters (RHT-WM, Novus Automation Onc., Porto Alegre, Brazil).
On order to evaluate the weight loss profile, the mass of each sample was measured every two days for twenty nine days of experiment.A similar experimental setup was employed for both repetitions (fruit from September and Dctober seasons).Cluster water loss was calculated as a percentage of its fresh (initial) weight.Subsequently, a transpiration model was used to fit the experimental data over time and to study the temperature and RH dependence of the transpiration rates.

Development of the transpiration rate model
The flow of water vapor through a fruit surface can be calculated according to the Fick's law of diffusion, which is proportional to the difference between humidity of fruit internal atmosphere and humidity of the surrounding air (Ben-Yehoshua, 1987).Equation 1developed for calculating the transpiration rate of mushrooms (Mahajan et al., 2008), was used to calculate the amount of water loss from the plant per unit weight per unit time.
( ) ( ) ( ) Where TR is the transpiration rate (g h -1 kg -1 ), expressed as a function of temperature and RH; k i is the mass transfer coefficient; aw i is the determined average water activity of the grapes (0.977 ± 0.0006); aw is the water activity of the container (RH/100); a is a coefficient constant; T is the temperature (°C).
Sousa-Gallagher et al. ( 2013) have combined Equation 1 with a technique reported by Leonardi et al. (1999), Equation 2, to evaluate transpiration rate related to weight loss, resulting in Equation 3.
where M and M i are the weight and the initial weight (g), respectively; t is the time (h).These rates were compared to those of fruit maintained in continuous refrigeration.Thus, this study determines the effect of cooling delays on subsequent transpiration rates.

Grapes transpiration rate
Figure 1 shows the weight loss of grapes during storage at approximately 50% RH in three different temperatures (SC1-R2, SC2-R2 and SC3-R2).Grapes mass decreased constantly with time at all combinations of temperature and RH.For similar relative humidity, fruit maintained at low temperature (2.3 °C) lost weight slower than those stored at higher one (10.1 °C).The transpiration rates of fruit in higher temperatures were accelerated by increasing the vapor pressure deficit and the respiration rates of the stems.This results support the ones reported by Lichter et al. (2011), which also found a linear profile for the mass decreasing in grapes of cultivars 'Thompson' and 'Superior' .This linear profile indicates a direct proportionality between the amount of mass loss and the storage time.Both temperature and humidity impact the transpiration rate in fruit, as have been seen for strawberries (Sousa-Gallagher et al., 2013) and mushrooms (Mahajan et al., 2008).On grape clusters, the most sensitive part to moisture diffusivity and dehydration is the stem.Ots respiration rate is multiple times higher than the berry respiration (Mencarelli et al., 2005).Subsequently, increasing temperature can increase the transpiration rate of the clusters by accelerating the metabolic respiration of the stems and shifting the vapor pressure difference between fruit surface and the air.
Fitting Equation 1 to experimental data for each experimental condition (Table 1), TR was accurately calculated.Values ranged from 0.104 to 0.201 g kg -1 h -1 over all the combinations of temperature and humidity tested.This small range was found due to the strict levels of RH (~ 50% -65%) and temperature tested (2-16 °C).As mentioned by Tijskens et al. (2010), since the water loss is a generic process, i.e., the same model formulation and the same rate constant for all the individuals, the variations Grapes transpiration data obtained for all the combinations of temperature and RH described in Table 1 was used to estimate the values of constants k i and a. Equation 2 was fitted by non-linear regression analysis using a Statistica software (Statsoft, 2007) to estimate the model parameters.

Dynamic conditions model
Total weight loss from a plant tissue is the integral of rates of weight loss at any particular time over the period following harvest (Maguire et al., 2001).As argued by Labuza (1982), given a historic of the storage conditions, it is possible to divide the whole period in small intervals (t j ) in which these storage conditions are considered constant.Meanwhile, a generic phenomenon depending on environmental conditions also occurs at constant rates.Similarly, provided the rates of weight loss for each stage of the historic of a fruit, it is possible to calculate the total weight loss as the summation of the constant rates.
Based in those aspects, the following model in Equation 4was proposed to predict the weight of grapes based on the fact that the initial weight is decreased by the sum of weight loss for each time interval.On those time intervals, measured temperature (T j ) and container water activity (aw j ) was considered constant.Additionally, the parameter ki and a were considered constant throughout the time intervals. ( )

Validation of the model
On order to evaluate the reliability of Equation 4for dynamic conditions, several relevant experiments were conducted in triplicate.The experimental setup was repeated twice in two different batches of table grapes cv.'Crimson Seedless' .Punnets containing the clusters were stored in common domestic refrigerator (CRM30, Whirlpool S.A., São Paulo, Brazil) undergoing fluctuating temperatures (mean temperature 8.2 ± 1.5 °C and 5.1 ± 2.9 °C, for first and second repetitions, respectively).A data logger system (Field Logger Register V2.2x B, Novus Automation Onc., Porto Alegre, Brazil) was employed to collect the measurements of the temperature and RH sensors, building the historic of these climatic conditions during the experiment period.Ontervals of 1 min between measurements were used to build the historic of both temperature and RH.Weight loss of the stored grapes was measured periodically for nineteen days and the experimental data compared with model predictions.

Cooling delay trials
Apart from the punnets stored under continuously refrigeration to estimate the model parameters, some samples were held for different time periods (24, 48, 72 h) at 25.1 ± 2 °C and 45.3 ± 8.9% RH to simulate environment conditions of temperature abuse during cooling delays.The experiments were conducted in triplicates for each waiting time period.After those periods, the samples were transferred to low temperatures (0.9-4.1 °C and ~ 45% RH).
During waiting time trials, the grape punnets were weighed daily to evaluate the transpiration rates (TR) by using Equation 2. here considers the whole cluster as homogeneous structure, setting a single constant value for the process.Therefore, this simplification made about the cluster structure appears to represent adequately the overall water loss process in dynamic temperature conditions.

Effect of cooling delays on subsequent transpiration rates
Figure 4 shows that transpiration rates (TR; g kg -1 h -1 ) estimated in subsequent continuous temperature treatment were not significantly influenced by prior exposure to environmental temperatures.The transpiration rates, calculated with Equation 1, for cooling delay treatments were similar to those of continuous refrigeration.Tukey test at a significance level of 0.05 indicates that does not exist significant difference among the transpiration rates of all treatments.Ot suggests that effects of temperature on transpiration rates are not dependent on prior events in the cold chain for this cultivar of grapes.However, delayed in the transpiration rates are attributed to the effect of the storage conditions.

Development of the transpiration model
Experimental data obtained at all combinations of constant temperature and RH reported in section 2.1 were used to estimate constant coefficients (k i and a) of the mathematical model (Equation 3).Their values were estimated using non-linear regression by Statistica software.Estimates and standard errors (SE) yielded by the regression are shown in Table 2. Figure 2a shows the relationship between the observed and predicted values of weight loss of grapes for all experimental data.Figure 2b shows the distribution of the residuals obtained from Equation 3and Figure 2c shows residuals versus predicted values of weight.Therefore, the model described the water loss process adequately as shown by the R 2 and by the good agreement between observed and predicted mass of grapes (Figure 2a).The normal distribution of the residuals (Figure 2b) was quantified by the Kolgomorov-Smirnov test (d = 0.086), indicating that the trend was not biased.The observed versus predicted plot (Figure 2c) indicates that the residuals are very close to the expected normal value.

Validation experiments
The model was validated by evaluating the model predictions for table grapes weight loss, as described in section Validation of the model.Figure 3 shows the good agreement between experimental and predicted values.Each point of the experimental data curve corresponds to the average of three samples.The weight loss of the grapes followed approximately a linear profile during the monitored period.However, the rate of the weight loss changed proportionally to the fluctuations of the refrigerator temperatures.On the first validation experiment (Figure 3a) temperature ranged from ~ 3 °C to ~ 17 °C, meanwhile in the second one (Figure 3b) temperature ranged from ~ -3 °C to ~ 18 °C.
The goodness of fit for each validation test was determined by calculation of the mean relative percentage deviation modulus (E) as proposed by McLaughlin and D'Beirne (1999).The E values were 0.28 and 1.10% for Figure 3a and Figure 3b, respectively.Larger amplitudes in the temperature fluctuation profile, as shown by Figure 3b, seem to increase the gap between model predictions and observed data (R 2 value was 0.995 and 0.577 for Figure 3a and Figure 3b, respectively).
The results above indicate that the developed model approach was adequate, confirming its predictive ability.Although previous publication has demonstrated that berries, the whole stem and grape stem parts have different dehydration kinetics (Ngcobo et al., 2013), the modelling approach presented Table 2.Estimated parameters of the mathematical model (Equation 3), where k i is the mass transfer coefficient (g h -1 kg -1 ) and a is the overall effect of temperature coefficient (°C -1 ), standard error (SE) of the estimation and determination coefficient (R 2 ).cooling significantly reduced the mass of the table grapes clusters in comparison with those maintained under continuous refrigeration.Consequently, the overall quality decay of grapes exposed to cooling delay was accelerated while its visual quality deteriorated rapidly, reinforcing the importance of stringent cold chain management for table grapes.
These presented results indicate that the modified equation Equation 4has potential to describe the influence of temperature perturbation during postharvest handling.Thus, this model can be used to estimate the weight loss as consequence of interruptions in the cold chain, as well as to minimize losses during the logistical operations.This study is, to the best of our knowledge, pioneer to measure weight loss curves for table grapes from cooling delay treatments.

Conclusion
Transpiration rates of table grapes packed in PET punnets were found to be in the range of 0.104 to 0.201 g kg -1 h -1 .A mathematical model developed on the basis of Fick's law of diffusion considering the effect of temperature and RH, yielded adequate description of mass loss of table grapes during storage at different combinations of temperature and RH.A modification in the model was proposed and tested for non-isothermal conditions situations.The results obtained in the validation experiments indicate that the model can provide satisfactory predictions for table grapes weight loss, and describe adequately the fruit behavior in variable temperature and RH conditions.A proposed study for the subsequent transpiration rates for table grapes submitted to cooling delays revealed that the temperature dependency of the weight loss was not associated to prior events in the cold chain, in this case the exposure to unfavorable temperatures.These results reinforce that the proposed model has the capacity to describe the influence of temperature perturbation during postharvest chain.Therefore, the model approach is useful to understand the evolution of water loss of table grapes with temperature, RH, and time.

Figure 1 .
Figure 1.Changes in weight of grapes (M) over time (h).The values were normalized with respect to the initial weight of grapes (Mi).Each point of the curve corresponds to the average of three samples.Standard deviations are shown in error bars.

Figure 2 .
Figure 2. Relationship between observed and predicted weight of grapes for all the experimental data obtained (a).Frequency distribution of the residual values (b).Predicted versus residual values (c).

Figure 3 .
Figure 3. Relationship between the model predictions (dotted line) and the experimental data (symbols) for changes in mass of table grapes stored at common refrigerators.The values (M) were normalized with respect to the initial weight of grapes (M i ).The non-isothermal temperature historic (continuous line) is registered in right side Y axis.First validation experiment with deviation modulus of 0.28% (a).Second validation experiment with deviation modulus of 1.10% (b).

Figure 4 .
Figure 4. Transpiration rates (TR; g h -1 kg -1 ) and normalized weight with respect to the initial weight (M/M i ) of table grapes exposed to cooling delays periods (24, 48 and 72 h) and continuous refrigeration (0 h).Each point of the curve (symbols) corresponds to the average of three samples.Standard deviations are shown in error bars.

Table 1 .
Average and standard deviation (± SD) of temperature and relative humidity levels used in the two repetitions (R) of the experiment for model building.