Investigation of dynamic quality changes and optimization of drying parameters of carrots (Daucus carota var. laguna)

Funding information Bundesministerium für Ernährung und Landwirtschaft, Grant/Award Number: BLE 2817OE005; European Commission, Grant/ Award Number: Core Organic Cofund; Institut Penyelidikan dan Kemajuan Pertanian Malaysia Abstract The effect of air temperature and sample thickness on the color changes and total carotenoids content of carrot slices was investigated. Temperature, exposure time, and moisture levels significantly affected the dynamic changes of total carotenoids and color. A slow and linear decrease in total carotenoids was observed at higher moisture content until reaching an inflection point at around 0.45 gw/gdm for all temperatures studied. Thereafter, the retention in total carotenoids decreased rapidly. The highest retention for a final product was 66.2% when drying at 60 C while retention was between 42.2 and 51.1% when drying at 50 and 70 C. These changes occurred alongside a noticeable change in color at moisture contents below the inflection point of 0.45 gw/gdm for all drying temperatures. Design of experiment based optimization of the drying process resulted in an ideal temperature of 59.8 C and 3.5 mm slice thickness with the predicted values for La*b*; ΔE of 62.18 ± 5.12, 22.46 ± 1.98, 40.35 ± 6.64, 6.31 ± 4.74; rehydration ratio of 0.48 ± 0.07; and total carotenoids of 163.83 ± 17.38 μg/g or 67.38%, respectively, all at a 95% prediction interval.


Practical applications
Convective drying is the most widely used drying technique for food preservation due to its easy application and readily available technology. However, the quality of the end product is currently lower than it would be achievable due to a lack of direct integration of quality characteristics into process design. Monitoring the quality changes as a function of moisture content throughout the drying process is essential to developing advanced process parameters with a view to increasing final product quality. This study describes the experimentally determined dynamic quality changes of carrots throughout the drying process in order to identify the critical points at which the process settings should be changed to increase the retention of valuable components and sensory quality attributes, and thus, to provide consumers with higher quality products.

| INTRODUCTION
Carrots are globally the second most consumed vegetable and have been identified as one of the healthiest vegetables due to their abundance of phytochemical constituents such as beta-carotene, vitamin C, and minerals (Anon, 2011). These nutrients provide significant health benefits to humans in terms of antioxidant capability, anticancer, anti-inflammatory, and many other properties (Da Silva Dias, 2014). Fresh carrots are used in many dishes around the world such as stews, soups, curries, and salads, as well as in baked goods such as cakes and bread. The crop can also be processed into many nutritious goods such as puree, juice, oil, dried products, and baby food (Nguyen & Nguyen, 2015;Saidel et al., 2015).
In freshly harvested crops, such as carrot, the presence of water accelerates phytochemical degradation due to enzymatic and nonenzymatic processes. Thus, reducing the water content through drying is imperative. By doing so, the material becomes easier to handle and less prone to microbial degradation (Pittia & Antonello, 2016). Drying can also result in a loss of bioactive compound and flavors. Thus, the drying process must be carried out as quickly and evenly as possible (Chin, Siew, & Soon, 2015). Inadequate drying gives rise to microbial infection, whereas overdrying or unfavorable process settings result in drastic loss of quality.
Drying at low temperatures between 30 and 50 C is recommended to preserve heat-sensitive active ingredients in medicinal plant or herbs (Müller & Heindl, 2006). However, different crops require different drying temperatures depending on their desired quality attributes and nutrient content. The most commonly applied temperatures for preserving food materials using convective air drying were reported to be in the range of 50 to 90 C (Krokida & Maroulis, 2000).
Minimizing quality changes of carrots after drying is imperative for quality assurance and final evaluation of the finished product. Many studies (Table 1) have analyzed convective drying of different varieties of carrots with diverse processing conditions, which have resulted in a variation of findings because different varieties of carrot respond differently to the drying process (Markowski et al., 2006). Drying behavior of different cultivars of the same crop may also vary due to the characteristics of the different varieties (Aboltins, Rubina, Palabinskis, & Jotautiene, 2016;Oke & Workneh, 2014). Furthermore, the experimental setup also impacts on the product response in terms of product quality. Therefore, more drying trials need to be undertaken for different varieties of carrots because the inadequacy of drying information related to the product quality of specific varieties of carrots generates quality-related problems for the industry, such as consumer and market acceptability. In light of this, there is a need to develop specific and innovative drying strategies that simultaneously minimize the quality degradation of carrots, while maximizing the production efficiency under optimum operating conditions. Furthermore, drying is a nonlinear, dynamic, unsteady, and complex process that needs to be monitored with care because the process leads to different levels of quality degradation depending on factors such as properties of wet material, chemical composition, shapes, dimensions, and process parameters (Moscetti et al., 2017). Thus, monitoring the product quality throughout the entire drying process is crucial because it will influence the decision-making in selecting and developing proper drying strategies for carrots, as well as the information is needed for the development of noninvasive quality measurements for intelligent drying systems. Most of the previous research either reported on the quality of the product at the end of the drying period or described the quality degradation as a function of drying time rather than evaluating the influence of moisture content on quality changes throughout the drying process. This leads to a poor understanding of how the quality reacts to changes in moisture content and exposure time. Therefore, an intelligent approach needs to be explored, which optimizes the parameters throughout the entire drying process, in order to identify potential critical control points for parameter settings to realize the highest retention of the nutrients through optimized process control. Therefore, the aim of this study was to investigate the impact of drying settings and the influence of moisture content on drying behaviors and dynamic quality changes, such as color and total carotenoids content, throughout the entire drying process of carrots, as well as the optimization of the process parameters using response surface methodology (RSM). The results obtained will be fundamental in the designing of a quality-oriented innovative drying strategy for the improvement of the whole drying process in the future.

| Raw materials
Organic carrots (var. laguna) at optimum maturity of 3.5 months after planting were obtained from the University of Kassel's farm in  Mulet, Berna, and Rossello (1989) Nantes Hot air dryer Shrinkage, total carotenoids, total polyphenols, and antioxidant activity Eim et al. (2013) Frankenhausen, Kassel, Germany. The roots were stored in a lowtemperature refrigerator at the commercially practiced storage temperature for carrots of 1 C ± 1 (Liew & Prange, 1994). Prior to drying, the roots were washed with distilled water, peeled, and sliced to two different thicknesses (3 and 6 mm) using a food slicer (model E21EU, Graef, GmbH, Germany). The maximum thickness of 6 mm was chosen because severe browning occurs at greater thicknesses as a result of the longer drying time (Sra, Sandhu, & Ahluwalia, 2011 (Correia, Loro, Zanatta, Spoto, & Vieira, 2015;Rawson, Tiwari, Tuohy, O'Donnell, & Brunton, 2011). Before each drying run, the dryer was started 1 hr in advance to attain steady-state conditions.
The initial moisture content of the carrots was determined according to the AOAC method (Association Official Analytical Chemists, 2019) by drying the sample in an oven at 105 C for 24 hr (ULM 400, Mermert GmbH, Germany). The initial moisture content was recorded to be around 7.02 g w /g dm . The weight of the samples prior to moisture content determination was recorded in 30 min intervals during drying by weighing the samples manually using an electronic balance (model E2000D, Sartorius, Göttingen, Germany, readability 0.001 g) until the samples reached a final moisture content of 0.14 ± 0.02 g w /g dm . It was decided to dry at this level because drying below 0.11 g w /g dm (10% wet basis) accelerates the Maillard reaction causing brown discoloration in carrots (Eichner, Laible, & Wolf, 1985). Moreover, final moisture contents between 0.11 and 0.14 g w /g dm are common in the industrial drying of carrots (Kowalski, Szadzi nska, & Łechta nska, 2013). Water activity was measured at the end of the drying process using a water activity meter (Novasina, LabSwift model, Novasina AG, Switzerland) in order to ensure that the moisture content of the final product was safe for subsequent storage. For quality analysis, a total of four slices from four roots were withdrawn from the dryer at every measurement point of 30 min in order to ensure the consistency and traceability of the total carotenoid content throughout the drying period. A total of 12 slices from 12 roots were used for each setting in this experiment. All slices were vacuum packed, sealed, and kept at −30 C for further chemical analysis. All the drying experiments were performed in triplicate and around 1,000 slices of carrot were chemically analyzed for total carotenoids content to ensure the accuracy of the results obtained.

| Total carotenoids
Total carotenoids content was determined according to the method reported by Moscetti et al. (2017), with minor modification, by extracting 100 mg of carrot tissue in 10 mL of solvent mixture of hexane, acetone, and ethanol (2:1:1). The solution mixture was homogenized for 2 min at 8000 rpm using a laboratory homogenizer (Model T25, IKA, Staufen, Germany) and incubated inside a refrigerator for 1 hr at 4 C, until the sample turned completely white, in order to ensure all the total carotenoids were fully extracted. Then, 5 ml of distilled water was added to the extracted sample to allow phase separation. The upper layer was separated from the aqueous phase and consequently subjected to assessment for total carotenoids by measuring the absorbance at a wavelength of 450 nm using a UV/Vis spectrophotometer (model Genesys™ 10 series, Thermo Electron Co). The total carotenoids content was determined using Equation (1).
where A is the absorbance reading of the sample, V 1 is the dilution factor, A 1% is the extinction coefficient of the 1% solution (i.e., 2500 AU), and C 1% is the concentration of the 1% solution (10 mg/ml). The total carotenoids content was converted to mg/g dm based on dry matter content, and the concentration was expressed as a percent retention in this study.

| Degradation kinetics of total carotenoids
The degradation of total carotenoids during drying at 50, 60, and 70 C was modeled by applying Equations (2) and (3) for zero-and first-order reaction, respectively (Fratianni et al., 2013): where C is the concentration (%) at time t; C 0 is the concentration (%) at time zero; K 0 is the zero-order rate constant (hr −1 ); K 1 is the firstorder rate constant (hr −1 ); t is the drying time (hr). The efficiency of the fitted model was determined by the highest correlation coefficient (R 2 ) and the lowest root mean square error (RMSE). The reaction rate constant (K) for both models can be obtained from the slope of the linear Equations (2) and (3).
The activation energy (E a ) for total carotenoids degradation was calculated using the Arrhenius equation (Equation 5).
where R is the universal gas constant (8.3142 kJ/mol), T is the absolute drying temperature in kelvin, and k o is the frequency factor or the Arrhenius constant (time −1 ). The activation energy, E a , can be obtained from the slope of ln K versus 1/T, where K was obtained from Equations (2) and (3) for both zero-and first-order models.

| Calculation of the moisture ratio
The following equation was used to determine the moisture ratio (MR) of the carrot slices during the drying process (Botelho et al., 2011): where M (g w /g dm) is the moisture content at any given time t, M o is the initial moisture content, and M e is the equilibrium moisture content. The MR was simplified to M t /M 0 as in Equation (7)

| Calculation of effective moisture diffusivity and activation energy
The effective moisture diffusivity and activation energy are critical parameters for modeling and simulation of drying processes, and greatly depend on temperature and moisture content of the material (Darvishi, Farhudi, & Behroozi-Khazaei, 2017 A plot of ln MR versus time gives a straight line with a slope of π 2 D eff /4L 2 where L is half the thickness of the slab in meters. The diffusivity coefficient can be obtained from the slope of Equation (8).
The activation energy (E a ), which is the function of temperature, was calculated using the Arrhenius equation as in Equation (9), and the value can be obtained from the slope of lnD eff versus 1/T as in Equation (10) (Doymaz & Özdemir, 2014):

| Measurement of color
Color measurements were performed using a Minolta chroma meter (model CR-400, Minolta Camera Co. Ltd. Osaka, Japan). The chroma meter was calibrated against a standard white reference tile prior to sample measurements. The color was measured on four slices from four roots at each measurement point for each replicate. Measurements were taken two times for each slice, and the values were averaged over the slice. The color measurements were performed based on the 3D color space of CIE La*b* scales where L represents the brightness of the color, a* is the redness, and b* is the yellowness (de Mendonça et al., 2017). From the color values, the total color change of ΔE was calculated using Equation (11), which is based on changes in color parameters of L, a*, and b* during the drying process.
where subscript "0" refers to the color reading of fresh carrot slices.
Fresh carrots were used as a reference and a larger ΔE denotes a greater color change from the reference material (Akoy, 2014).

| Rehydration ratio
Dried samples from the same roots, which were used in the chemical analyses, were soaked in a water bath at 95 C for 10 min, removed from the water bath, and drained on a metal sieve for 5 min. Then, the excess water was carefully removed by blotting on filter paper for 2 min to ensure that all remaining water was fully drained before weighing. The weight of the drained carrots was recorded and the rehydration ratio was calculated as in Equation (12), which is based on the differences of the weight of the rehydrated sample (W r ) to the weight of the fresh samples before drying (W 0 ) (Lewicki, 1998): 2.9 | Statistical analysis for optimization of process parameter A general multilevel factorial design with two continuous independent factors and several dependent responses was statistically analyzed using the RSM (Design-Expert ® Software Version 9 [DX9], Stat-Ease, Inc., MN). The drying temperature was set at three levels of 50, 60, and 70 C, and the sample thickness was set at two levels of thicknesses, 3 and 6 mm. The same experimental design was reported by Ogolla et al. (2019) for spray drying of camel milk. To obtain the regression coefficients, the experimental data were fitted to a secondorder polynomial model indicated by Equation (13), with the general linear model approach: where β 0 , β i , β ii , and β ij are the regression coefficients for the intercept and the linear, quadratic, and interaction terms, respectively, while y is the response, x i and x j are the independent variables, and ε is the non-  (Bruns, Scarminio, & de Barros Neto, 2006). The interactions between drying air temperatures, slice thickness, and the responses were derived from the regression models and visualized using 3D response surface plots. The coefficient estimates are shown for coded factors. The actual factor levels are standardized in a range from −1 for the lowest actual level to +1 for the highest actual level of a certain factor ( Table 7). As the second step, the multiresponse goal con-

| RESULTS AND DISCUSSION
3.1 | The effect of drying temperature and thickness on drying time and drying rate The results from Figures 1 and 2 indicate that the drying time to achieve the desired level of moisture content as in Table 2 is greatly dependent on slice thickness and temperature. These are commonly known facts that have been reported by other researchers for carrot drying and many other products, with results depending on shape, dimension, drying methods, and parameter settings (Zielinska & Markowski, 2012;Eim et al., 2013;Koca et al., 2007). However, these previous works were based on different varieties of carrots that were sourced from different locations across the world. Markowski et al. (2006) reported that different varieties of carrots with the same dimensions responded differently during drying treatments causing a variation in drying characteristics. The differences are due to divergence in the varieties, food matrix, structure, tissue, and chemical composition within the crop as explained further by Capuano, Oliviero, and van Boekel (2017). The authors explained in detail that all the variations will generate different levels of chemical reactions within the food matrix when subjected to thermal treatments, such as drying, which consequently may influence the drying behavior due to changes in thermal properties. Water activity of the final product was also measured at the end of drying experiments in order to ensure a safe level of water activity for subsequent storage. The values of water activity were between 0.342 and 0.361 (Table 3), which is a recommended level for storage stability of carrots (Lavelli, Zanoni, & Zaniboni, 2007 previously published study on sorption isotherms, which show that moisture content of 0.14 g w /g dm results in a water activity of >0.6 (Kaya, Aydın, & Demirtaş, 2009). The present study, however, shows decidedly lower water activity at these moisture contents. This can be explained by the fact that water activity is a function of chemical components, physicochemical state, porosity, temperature, and surface tension (Rahman and Labuza, 2007). Therefore, the same level of moisture content at the same temperature will result in different levels of water activity due to differences in varieties and/or chemical composition within one variety caused by different growing conditions (Bajaj, Kaur, & Sukhija, 1980;Brunsgaard, Kidmose, Sørensen, Kaack, & Eggum, 1994).
Drying characteristics of carrots can be obtained from the drying curves as displayed in Figures 1 and 2. When drying at 50, 60, and 70 C, the time taken to reach the desired moisture content for 3 mm slice thickness was 420, 360, and 300 min, respectively. The required time is significantly increased for 6 mm slice thickness with total drying times of 540, 480, and 420 min. The increment of 2 hr drying time for all temperatures studied, when the thickness is doubled from 3 to 6 mm, was similar to those reported by Sonmete, Mengeş, Ertekin, and Özcan (2017). The authors observed that the increment in total drying time for 6 mm thickness, as compared with 3 mm thickness, was not higher than 2 hr when drying at 55, 65, and 75 C with an airflow of 2.0 m/s. The authors reported total drying times of approximately 4.3, 3.3, and 2 hr for 3 mm thickness when dried at 55, 65, and 75 C with an airflow of 2.0 m/s and around 6, 4, and 3 hr when drying under the same conditions for 6 mm.
The increase in drying time with an increase in slice thickness must be due to the lower surface area-to-volume ratio, and the longer distance for the moisture to travel from the inside of the material to the surface (Kek, Chin, & Yusof, 2014). In other words, the drying rate will increase as the temperature increases, and the slice thickness decreases due to shorter transport distance and an increased relative of heat and mass transfer ( Figure 3). Furthermore, the thermal gradient between drying air and drying material increases with increasing temperatures, causing an increase in heat transfer and drying rates (Sturm et al., 2012). The differences in energy consumption for heat and mass transfer cause thicker samples to require more energy to evaporate internal moisture to the surface as explained by Wang and Xi (2005). This reflects the longer drying time for thicker samples with lower drying rates when compared with high drying rates in thinner samples. Thicker samples also have a higher level of dry solid than thinner samples leading to longer drying times because, according to Geankoplis
The activation energy, which is temperature dependent, can be obtained from the slope of the straight line of the Arrhenius equation as displayed in Figure 5. The activation energy for carrots calculated from this study is 16.386 and 20.292 kJ/mol for 3 and 6 mm thickness, respectively. Higher activation energy values were observed in thicker samples due to longer distances for moisture transport, causing higher energy requirements for heat transfer. The range of F I G U R E 4 Coefficient of effective diffusivity, D eff (m 2 /s), obtained for the drying of carrot F I G U R E 5 The Arrhenius representation of the natural logarithmic coefficient of diffusivity as a function of drying temperature of carrot F I G U R E 3 Effect of drying temperature on drying rate for 3 and 6 mm of slice thicknesses activation energy for agricultural produce was reported to be from 12.7 to 110 kJ/mol (Zogzas, Maroulis, & Marinos-Kouris, 1996). Thus, the results obtained in this study were still within the acceptable range of documented data.

| Color characteristics
Color characteristics are the most common parameter measured in dried food products as they are one of the first quality attributes that could be visualized by a consumer (Chua, Mujumdar, Chou, Hawlader, & Ho, 2000). The dynamic changes in color throughout the drying process could be observed by total color changes of ΔE.
The results from the experiment showed that minimal ΔE ( The changes in ΔE values were more noticeable at reduced moisture content of less than 0.45 g w /g dm for a thicker sample of 6 mm when dried at 50 and 60 C and also for a thinner sample of 3 mm when dried at 70 C ( Figure 6). The trends were apparent for all process settings, especially when drying at 50 and 60 C where the changes were slow and almost linear at a higher moisture content until it reaches the inflection point at the lower moisture content of 0.45 g w /g dm. The greater changes in color are due to the increase in absolute values of L with a decrease in values of a* due to longer drying times or higher drying temperature. The results indicate that the orange color of the final product gets lighter, or decreases in brightness, due to longer drying times for thicker samples. The degradation of color in terms of L, a*, and b* in carrots might correspond to the degradation of thermolabile components of carotenoids, which will be discussed in the next section on dynamic changes of total carotenoids. The degradation is very likely due to autoxidation of total carotenoids under the influence of rigorous operating conditions (Zielinska & Markowski, 2012). Additionally, the oxidation of carotenoids causes losses in color and flavors due to formation of colorless lower molecular weight reaction products such as ß-ionone and ß-damascenon, which leads to pigment degradation in carrots (Sturm & Hensel, 2017). Samples dried at 50 and 70 C for both thicknesses showed lower color retention while drying at 60 C resulted in minimal color degradation (Figure 8). The results confirm that drying temperature significantly (p < .05) affected the color parameters L, a*, and ΔE values of carrots, while the b* value was affected by both drying temperature and thickness, as shown in Table 6.
Many studies with different results reported on the effect of drying temperature and thicknesses on color changes of agricultural crops. It was observed that color retention of the dried product greatly depends on cultivars, preprocessing treatments, and process parameters as reported by Onwude, Hashim, and Chen (2016)  The obtained results from this experiment confirm that both temperature and duration of exposure time during drying greatly affect the color retention of sliced carrots and can be correlated with chemical instability of total carotenoids as influenced by moisture content and process parameters. This will be discussed further in the next section on dynamic changes of total carotenoids during drying. The findings are similar to those of Zielinska and Markowski (2012) Karabulut, Topcu, Duran, Turan, and Ozturk (2007). Moreover, thermal damage of carotenoids occurs at elevated temperature due to severe cellular destruction that could speed up the losses via oxidation (Kaimainen, 2014;Schwartz, Elbe, & Giusti, 2008). According to Zielinska and Markowski (2012), carotenoid degradation can be caused by lipid peroxidation, which may affect the color due to nonenzymatic browning.
Nonenzymatic browning occurs due to the reactions of food components such as amines with carbonyl groups of reducing sugars (aldehydes and ketones), which participate in the chain of Maillard reactions and lead to the formation of brown pigments or colored polymers such as melanoidins resulting in the loss of carotenoids (Potes, Lim, & Roos, 2017). Carbonylic compounds are a chemically organic functional group of a carbon atom double bonded to an oxygen atom formed through oxidation, which leads to degradation of total carotenoids (Boon, McClements, Weiss, & Decker, 2010). The results from Figures 9 and 10 also show that linear degradation of total carotenoids could be observed at higher moisture contents of more than 0.45 g w /g dm , which demonstrates slow degradation of total carotenoids at the early stage of drying for samples dried at 50 and 60 C. At this point, the membrane integrity of the tissue was still intact and consequently reduced degradation of nutrients, such as total carotenoids, from thermal damage, which has been explained further by Karim and Adebowale (2009) and Kaimainen (2014). It is also possible that the endogenous water-soluble antioxidative components, such as ascorbic acid, amino acids, bioflavonoids, and other polyphenolic compounds, present in carrots protect the total carotenoids from thermal degradation at the initial stage of drying when the moisture content is still high (Arya, Natesan, Parihar, & Vijayaraghavan, 1979;Karim & Adebowale, 2009). However, rapid losses of total carotenoids were observed for samples dried at 70 C at the early stage of drying for both thicknesses. This is probably due to rapid heating at high temperature that could speed up the moisture losses on the surface and ultimately promote the degradation of total carotenoids as a result of exposure to hot air (Pan, Wu, Li, Mujumdar, & Kudra, 1997).
The results from this study have proven that total carotenoids, which are fat-soluble pro-vitamin A, are stable in high moisture system at optimum temperature of 60 C because the presence of sufficient water on the surface of sliced carrots at the early stage of drying provides maximum resistance from oxidation as described by Ramakrishnan and Francis (1979). However, drying at 70 C causes degradation of total carotenoids due to thermal damage at elevated temperature. It could be observed that a distinct reduction in retention occurred at lower moisture contents of 0.45 g w /g dm and less for all temperatures studied, showing that the critical degradation lies in this area at the point where appropriate process and parameters settings need to be employed. During this period, it could be assumed F I G U R E 1 0 Retention of total carotenoids in carrot at different temperatures as a function of moisture content for 6 mm thickness F I G U R E 9 Retention of total carotenoids in carrot at different temperatures as a function of moisture content for 3 mm thickness that the internal temperature of the slices increased as the drying proceeds, causing a reduction in moisture content that could possibly disrupt the cellular structure leading to rapid degradation of nutrients (Karim & Adebowale, 2009   ing, the knowledge on dynamic changes of total carotenoids as a function of moisture content along the drying process, which has been described in this study, is not mentioned in other studies. Therefore, from the results, it could be concluded that drying at 60 C leads to highest retention of carotenoids ( Figure 11).

| Degradation kinetics of total carotenoids
In general, the degradation kinetics of nutrients in food is influenced by moisture content and temperature in the food system. Since food products are exposed to a wide range of temperatures and different levels of moisture removal during drying, kinetic models are needed to predict the evolution of nutrients of interest with time (Karim & Adebowale, 2009). Degradation kinetics of total carotenoids in carrots, shown in Figures 12 and 13, were modeled using Equations (2) and (3) because quality degradation of food, as affected by thermal processes, normally followed zero-and first-order reaction kinetics (Maiti, Raju, & Bawa, 2012). The linear plots showed that degradation of total F I G U R E 1 2 Zero-order degradation kinetics of total carotenoids at different temperatures and thicknesses carotenoids for thinner samples (3 mm) followed first-order kinetics, and thicker samples (6 mm) were best represented using zero-order kinetics for all temperatures studied. The selection of the best model is based on the R 2 value and RMSE as in Table 5. The activation energy values for degradation of carotenoids for the first-order model were 35.61 kJ/mol for 6 mm and 40.60 kJ/mol for 3 mm. The higher activation energy for 3 mm thickness indicated that the degradation of total carotenoids is more temperature sensitive (Dutta, Dutta, Raychaudhuri, & Chakraborty, 2006) than at the higher thickness. The results demonstrated that the activation energy for degradation of carotenoids obtained from this experiment was adequate to cause discoloration of the product as stated by Lee and Kim (1989). The authors stated that the activation energy for degradation of carotenoids between 32.2 and 114.5 kJ/mol will most likely cause the discoloration of the product, which can be correlated with losses of color in carrots as explained in the previous section. Different levels of kinetics parameters for degradation of carotenoids particularly ß-carotene were documented in the literature (Pénicaud, Achir, Dhuique-Mayer, Dornier, & Bohuon, 2011). These variations may be due to different processing conditions, chemical composition of different crops, and the presence of acids, iron, free radicals, and metal catalysis, which influence the degradation kinetics (Boon et al., 2010). Modeling quality degradation along the drying process is important in order to predict the retention of total carotenoids at any given time of drying, so that better process control could be developed in order to improve the process efficiency and quality retention.

| Rehydration ratio
Rehydration ratio is one of the most important quality attributes in dried materials because most of the dehydrated products must be rehydrated for their final use (Akoy, 2014). The ratio indicates the capability of the material to restore to its original state by absorbing water after drying. The results obtained showed that drying at a high temperature of 70 C for 6 mm slice thickness reduced the rehydration ratio significantly (p < .05) when compared to drying at 50 and 60 C  Table 6). Drying at a lower temperature of 50 and 60 C had shown better rehydration capacity for 3 mm thickness of dried samples. This must be due to minimal cellular destruction and dislocation, which occur at lower temperatures, so that the material is capable of absorbing more water (Nour, Trandafir, & Ionica, 2011).
However, the rehydration capacity was decreased for thicker samples of 6 mm when drying at 70 C because the structural damage and shrinkage are more severe when dehydrated at high temperatures causing lower rehydration ratios for thicker samples. Furthermore, drying at 70 C causes higher drying rates at the initial stage, which might lead to case hardening of the product surface that results in the formation of dense structure (Krokida & Maroulis, 2000). This will limit the water migration from the solution into the dried samples due to decreased ability of the dried materials to absorb water. Additionally, substantial amounts of soluble solids might be leached into the external water during rehydration, hence affecting the nutritional quality of the products and, simultaneously, its ability to absorb water (Vega-Gálvez et al., 2015). It may be noted that a higher rehydration ratio indicates a better product. The results also proved that slice thickness greatly affected the rehydration ratio of carrots (Table 6).

| Optimization of process parameters
The optimum conditions for drying of organic carrots were determined from the following RSM in order to obtain optimal color parameters (La*b*) with minimal ΔE, a maximum rehydration ratio, and also the highest retention of total carotenoids. These target-dependent variables were categorized according to their importance (Table 7).
The most important was categorized as an importance of 5 while the independent variables were automatically categorized as an importance of 3. In the case of the color parameters L, a*, and b*, the target values were set to similar values of the fresh carrot. The settings for all goals for the best solutions of the optimization resulted in a desirability value of 0.781, as presented in Table 8. Gamboa-Santos et al. (2013) and Eim et al. (2013) also reported on the optimization of carrot drying using different setting parameters, shapes, dimensions, and quality attributes. However, those authors used different designs of experiment and processing software resulting in different desirability values for optimization.
The drying temperature of 59.8 C and slice thickness of 3.5 mm were found to be the most desirable solutions for the optimum parameters for drying of carrots when all response variables were set as important. Under optimized conditions (Table 8), the predicted values for L, a*, b*, ΔE, rehydration ratio, and total carotenoids at 95% prediction interval were 62.18 ± 5.12, 22.46 ± 1.98, 40.35 ± 6.64, 6.31 ± 4.74, 0.48 ± 0.07, and 163.83 ± 17.38 μg/g or 67.38%, respectively. All the quality parameters can be modeled mathematically using linear and polynomial functions as in Table 9.
The optimization results indicate that the drying temperature significantly influences the color parameters, total color changes (ΔE), rehydration ratio, and retention of total carotenoids (Table 6). It is also possible that the experimental setup during drying also influences the quality retention of dried materials. However, optimizing the quality of the final product in this study, which is based on the black box concept, can only predict the quality of the product at the end of the process without considering the quality transformation along the drying process. The optimization should include information of the quality changes as a function of moisture content, which can be advantageous for the industry because it could potentially be applied to online measurement that could provide more reliable and faster results when performing routine analysis for quality assurance than existing conventional laboratory methods, which are always laborious and time consuming. Therefore, this study demonstrates the importance of monitoring the quality changes of carrots throughout the drying process because it has a significant impact on the quality of the end product.

| CONCLUSION
The study has shown that the drying characteristics and final quality of dried organic carrot are highly dependent on process parameters. Notes: A is the drying temperature ( C), B is the slice thickness (mm), and AB is the interaction between temperature and thickness.
The effective diffusivity increased with an increase in drying temperature and decreased with a reduction in slice thickness. The values of effective diffusivity were in the range of 2.705 × 10 −10 to 4.011 × 10 −10 m 2 /s for 3 mm thickness and 5.409 × 10 −10 to 8.813 × 10 −10 m 2 /s for 6 mm thickness for all temperatures studied.
The activation energy of carrots was found to be 16.386 and 20.292 kJ/mol for 3 and 6 mm thickness, respectively. The outputs from RSM with regard to quality resulted in optimal operating conditions of 59.8 C with a slice thickness of 3.5 mm.
The results from this study proved that the dynamic changes of color and total carotenoids throughout the drying process are dependent on temperature, time, and moisture levels of the material.
Evaluating the changes in total carotenoids as a function of moisture content in this study provides a better understanding of stability of total carotenoids when subjected to different process conditions at varying exposure times, and this information is valuable for process design and optimization. This experiment showed that knowing the exact dynamics of moisture removal is critical for the process control and simulation of different drying strategies, particularly when attempting to correlate physicochemical and thermodynamic aspects. The study clearly indicates that monitoring the dynamic changes of quality degradation throughout the drying process is essential for the future development of real-time noninvasive quality measurements and, consequently, the development of smart drying technologies.
Future research needs to focus on maximizing the quality retention through smart drying techniques and minimizing the production cost of dried carrots so that premium quality products at an affordable price could be produced. The data from this experiment can be used as a reference and baseline for further research in developing novel drying techniques, as well as upgrading the existing technologies, so that suitable, energy saving, and cost-effective drying strategies can be developed.

ACKNOWLEDGMENTS
The authors gratefully acknowledge the University of Kassel, Malay-