www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 77 (2006) 575–584

The firmness of stored tomatoes (cv. Tradiro). 1. Kinetic and nearinfrared models to describe firmness and moisture loss

C. Van Dijk *, C. Boeriu, F. Peter 1, T. Stolle-Smits 2, L.M.M. Tijskens

Agrotechnology and Food Innovations BV, P.O. Box 17, 6700AA Wageningen, The Netherlands

Received 21 October 2004; accepted 4 July 2005Available online 1 September 2005

Abstract

The aim of this research was to develop practical applicable models capable to describe and to predict the temperature dependentfirmness and moisture loss of tomatoes during storage. To gather the required information to develop these models batches of 20tomatoes (cv. Tradiro), each harvested at two maturity stages, were stored at four different temperatures (3, 12, 20 and 25 �C) up tofour weeks. One temperature (3 �C) is known to cause chilling injury to the product. During storage at these temperatures firmnessloss, moisture loss and near infrared spectra were measured on individual tomatoes at regular intervals. The decrease in firmness wasmeasured non-destructively by flat-plate compression, moisture loss was measured by weight loss. The information on firmness andmoisture loss was used to develop two types of models. The first type of model was based on fundamental laws of chemical kinetics,assuming plausible chemical reaction mechanisms. These reaction mechanisms describe the processes underlying either firmness, ormoisture loss. From these reaction mechanisms a set of differential equations was derived and solved at constant temperature. Forthese kinetic models, both for firmness, and moisture loss, two independent processes were assumed. One process is mainly expressedat low (<10 �C) temperatures and relates to chilling injury; its contribution increases at decreasing temperatures. The other processrelates to the normally observed fruit softening and moisture loss process during storage. Throughout the entire temperature rangeits contribution increases at increasing temperature. The second type of model was based on Partial Least Squares Regression anal-ysis, relating the data on firmness to the near infrared spectral data. Due to their difference in nature the kinetic models describe thefirmness change and moisture loss in time at constant external condition. The regression model describes the actual firmness of ahomogeneous batch of tomatoes.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Tomato; Firmness; Moisture loss; Modelling; Near infrared spectroscopy

1. Introduction

For fresh agricultural products firmness is a qualityattribute of prime importance. To understand, to de-

0260-8774/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jfoodeng.2005.07.029

* Corresponding author. Tel.: +31 317 475 012; fax: +31 317 475347.

E-mail address: cees.vandijk@wur.nl (C. Van Dijk).1 Present address: Laboratory of Organic Chemistry and Technol-

ogies, University ‘‘Politehnica’’ Timisoara, Romania Str. Bocsei nr. 6,1900 Timisoara, Romania.

2 Present address: Diosynth BV, P.O. Box 20, 5340 BH, Oss, TheNetherlands.

scribe and to quantify firmness and firmness behaviourof fresh fruits and vegetables, a substantial amount ofresearch has been addressed towards this issue. Manyunresolved questions still remain, however. For exam-ple, at the molecular level it is still unclear how the dif-ferent processes active in firmness decline, related to cellwall and membrane breakdown, enzyme activation andinactivation, etc., interact with one another. It is evenmore obscure how these effects at the molecular levelcan be translated to the product level. For the importantagricultural product tomatoes this situation is not differ-ent. During growth, ripening and senescence this fruit is,

Nomenclature

Variable

Ea activation energy (J mol�1)F force (N)FRM firmness (N m�1; slope, or m; distance)LV latent variableRMSEC root mean squares error of calibrationRMSEP root mean squares error of predictionT temperature (�C or K)k reaction rate constant (day�1)t time (day)

Indices

act actual temperature of the experimentC chilling-injury related processes

E enzyme catalysed processesf free; refers to water directly available to evap-

oratefix fixed firmness partFRM firmness loss related processesi anyML moisture loss related processesout moisture content in the environmentref at reference temperatures sink; refers to water not directly available to

evaporatevar variable firmness part0 initial

576 C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584

like all other plants, continuously subjected to enzymeorchestrated modifications (Stolle-Smits et al., 1999).During the pre-harvest period the expressions of thesemodifications reflect themselves in changes in fruit firm-ness, in its chemical composition and in its colour. Fortomatoes the maturity at harvest is, to a great extent, ex-pressed by its colour (Tijskens, 1994).

To bridge the time-gap between the moment of har-vest and consumption it is common practice to storetomatoes. Storage aims at keeping the product qualityas close to its optimal ‘‘fitness for use’’ (Kramer &Twigg, 1970; Steenkamp, 1989) as possible. To minimisethe biological activity of the product the environmentalconditions (for example, temperature, relative humidityand gas composition) are adapted in a product specificway. It is however long known that, if the storage tem-perature decreases below a certain temperature, the rateof product deterioration increases at decreasing temper-ature. This cold induced process, named chilling injury,can be observed for products from (sub) tropical origin,including tomatoes (Wang, Boyan, & Eanes, 1990). Fortomatoes a temperature of 12 �C is considered to be asafe storage temperature (Polderdijk, Tijskens, Robbers,& Van der Valk, 1993).

This study concerns the firmness decrease and mois-ture loss of tomatoes during storage. The role of cell wallmodifying enzymes, possibly involved in the softeningprocess, will be discussed elsewhere (Van Dijk, Boeriu,Stolle-Smits, & Tijskens, in press). To describe and quan-tify firmness decay as well as moisture loss a more funda-mental (Van Dijk & Tijskens, 2000) and a more empiricalapproach were addressed. For the more fundamentalapproach it is necessary to decompose the intricate pro-blem of the various modes of action of temperature onfirmness decay and on moisture loss into the constitutingprocesses. The type of temperature related action eitherrefers to chilling injury or normal senescence associated

firmness decline. To be able to unravel the temperaturerelated modes of action on firmness and on moisture loss,the tomatoes were stored at distinct temperatures. Themodels resulting from this approach should be struc-tured and built in such a way that they can be appliedthroughout the integral distribution chain.

The empirical approach relates the changes in firm-ness and moisture with changes in the non-destructivelymeasured near infrared spectra. Using multivariate dataanalysis statistical relations between the near infraredspectral information and the firmness decay were estab-lished. It has to be realised however, that the applicationareas of both models are different. The models, whichare based on assumed but plausible reaction mecha-nisms and kinetics, are suited to predict the productbehaviour in time. The statistical near infrared modelsare capable to estimate the actual status of a product,with respect to its firmness.

2. Material and methods

2.1. Tomato samples and harvesting

Tomatoes (Lycopersicon esculentum L., cv. Tradiro),grown in a greenhouse in Belgium, were harvested attwo stages of maturity, colour Stages 6 and 8, in April1998. Selection on colour was based on the colour cardsused by both the Dutch and the Belgian Growers Asso-ciations (OECD, 1988). Throughout the remainder ofthis study colour Stages 6 and 8 will be referred to asStages 6 and 8, respectively. After transportation tothe laboratory and storage overnight at ambient temper-ature and relative humidity, the samples were stored atfour different temperatures. The day the storage experi-ment started is defined as the beginning of the experi-ment (t = 0).

C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584 577

2.2. Storage experiments

Tomatoes were stored at 3 �C (chilling-injury temper-ature) and at 12 �C (optimal storage temperature) forabout three weeks and at 20 �C and 25 �C for about fourweeks, all at a relative humidity of about 90%. From thestart of the storage experiment samples were withdrawnat regular intervals during a period of 20 days (storagetemperatures of 20 �C and 25 �C) and of 29 days (storagetemperatures of 3 �C and 12 �C) respectively, for furtheranalysis. A sample consisted of 20 tomatoes, either Stage6, or 8, stored at one of the above mentioned tempera-tures. Prior to the non-destructive compression and nearinfrared measurements the tomatoes were equilibrated atroom temperature (19 ± 1 �C) for at least 2 h, to avoideffects of storage temperature on the measurements. Intotal 1400 individual tomatoes were analysed.

2.3. Non-destructive compression measurements of

tomatoes

Non-destructive compression measurements wereperformed using a Universal Testing Machine, Instron4301. Flat plate compression was applied at a speed of0.02 m min�1 to a maximal force of 3 N. Using this setup the distance (m), the slope (N m�1), as well as the to-mato diameter (m) were determined. Singular compres-sion measurements were performed on the equator ofthe tomato to avoid potential interference of consecutivecompression measurements on the results. The averagevalue obtained for both the slope and the distance ofeither 20 Stage 6, or 8 tomatoes, representing one tem-perature–time combination, was used as input valuefor further analysis.

2.4. Non-destructive near infrared (NIR) measurements

Spectra were recorded in the reflectance mode usingan InfraAlyzer 500 instrument (Bran and Luebbe,Germany) equipped with a PbS detector and a fibreoptic set up. Measurements were made in a wavelengthrange between 1100 and 2500 nm at 4-nm intervals atambient temperature (20 �C). The detected diffuse reflec-tances (R) were transformed into apparent absorbencies(log 1/R). Four reflection spectra were taken at equidis-tant points alongside the equator of the fruit. Aftertransformation into apparent absorbencies the averagevalue of the four measurements for each individual to-mato at each wavelength was calculated. The averagevalue for 20 tomatoes at each wavelength, representingone temperature–time combination, was used as inputvalue for further analysis. Due to the increase in sig-nal-to noise ratio, the spectral information above2200 nm was discarded. For the development of the purestatistical NIR models (see below), either the raw spec-tral data, or their derivative was used.

2.5. Determination of moisture loss of tomatoes

Batches of 20 tomatoes, either Stage 6 or 8, werestored for 30 days at temperatures of 3, 12, 20 and25 �C, respectively, all at a relative humidity of about90%. At the start of the experiment (t = 0) and at day1, 2, 7, 13, 21, and 30, the weight of individual tomatoeswithin a batch was determined. After weighing, thetomatoes were put back to their original storage condi-tions. The weight loss was calculated relative to theweight at day zero (t = 0), the start of the experiment.

Moisture loss was expressed as normalised percent-age weight loss:

%Weight loss ¼Weightðt¼0Þ �Weightðt¼tÞ

Weightðt¼0Þ� 100% ð1Þ

Weight(t=0) is the average weight of a batch of tomatoesat the start of the experiment and weight(t=t) is the aver-age weight of the same batch at t = t. The loss in weightwas attributed entirely to moisture loss, ignoring thecontribution of metabolic processes to the weight loss(not determined).

2.6. Development of models based on chemical kinetics,

and their statistical analysis

The models were developed using a system of prob-lem decomposition (Sloof, 2001). This system is orientedtowards modelling of the underlying processes thatcause the observed phenomena rather than modellingthe observed phenomena themselves. The models arebased on assumed but plausible kinetic mechanismsdescribing the particular process. Using the well-knownrules of chemical kinetics the models were developedfurther. The mathematical development and statisticalanalysis were carried out according to Tijskens, Hertog,and Van Dijk (1997). No transformations were appliedto the data to prevent the introduction of additional er-rors during estimation (Ross, 1990). The data were ana-lysed as one integral set using time and temperaturesimultaneously as explaining variables (Tijskens, 1994).

Experiments are mostly conducted at constant exter-nal conditions like, for example, temperature. To ana-lyse the experimental data, analytical solutions of themodel formulation at constant external conditions aretherefore required. These analytical solutions will be de-duced from the differential equations, but are only appli-cable at constant conditions. In practice constantconditions are very rare. The model formulations appli-cable at any time and temperature are, however, the dif-ferential equations. The formulation of the differentialequations is the core of the model rather than the result-ing analytical solutions. These analytical solutions are alogical consequence of the differential equations. Theexperimental set-up defines the boundary conditions

578 C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584

for the differential equations (Tijskens, Hertog, & VanDijk, 1999).

2.7. Development of NIR models

The NIR spectral data were analysed using the statis-tical program Unscrambler, version 6.1 (CAMO A/S,Norway). The statistical relation between the measuredfirmness data (Y-block) and the NIR spectral data (X-block) were studied by the method of partial leastsquares regression (PLSR) on so called latent variables(LVs). PLSR allows the simultaneous use of stronglyinterrelated X-variables by focusing the systematiccovariances in the X-block into a few latent variables(Johnson & Wichern, 1992). The models were validatedusing the ‘‘full cross-validation’’ technique to ensurepredictive validity, guarding against over-fitting. Fullcross-validation is a method in which as many modelsare made as objects. However, each time one of the ob-jects is left out which is only being used for testing. Thesquared difference between the predicted and real Y-value for each omitted sample is summed and averaged,giving the validation Y-variance. The predictive abilityof the calibration models is described by the root meansquares error of calibration (RMSEC; Geladi & Kowal-ski, 1986). PLSR models were made for slope, distanceand moisture loss including all tomato samples. Thesemodels were used to predict the actual slope and dis-tance for all samples.

To assess the predictive capability of the near infraredmethod, PLSR models were made for the slope and dis-tance using 50 randomly selected samples. The predic-tive capacity of this model was tested on the 20remaining samples and expressed as the root meansquares error of prediction (RMSEP).

3. Results and discussion

3.1. Development of models for firmness loss based on

chemical kinetics

3.1.1. Model development on firmness loss

The texture and firmness of fruits and vegetables arebased on the presence and interactions of different chem-ical components, like pectins in the middle lamellae andthe cellulose/hemi-cellulose matrix in the primary cellwall, and on physical aspects like archestructure andturgor (Van Dijk & Tijskens, 2000). During storagesome of these chemical components or physical aspectsare affected, some are not. Therefore it is assumed thatthe firmness (FRM; N m�1) of fruits and vegetables con-sists of two parts, a variable (FRMvar) and a fixed(FRMfix) part (Van Dijk & Tijskens, 2000):

FRM ¼ FRMfix þ FRMvar ð2Þ

Components adding to the fixed part of the firmness are,for example, the (chemically inert) cellulose/hemi-cellu-lose matrix. The turgor and part of pectin, susceptibleto enzymatic degradation, contribute to the variablepart of the firmness. The well-described enzymaticbreakdown of the pectin moiety within the tomato tissue(Hadfield & Bennett, 1998) by pectolytic enzymes inrelation to fruit softening is comprised in Eq. (3a).

Fruits of (sub) tropical origin are most often prone tochilling injury (Wang et al., 1990). The primary conse-quence of chilling injury is results into irreversible dam-age of the plant cell membranes. Chilling-temperaturescause phase transitions in the membranes (Raison,1986), thereby affecting the membrane fluidity (Murate& Los, 1997) resulting in membrane damage, causingelectrolyte leakage (Sharom, Willemot, & Thompson,1994). This altogether results in a cascade of secondaryreactions, which finally leads to an altered cellular struc-ture and, as a consequence, tissue softening. The tissuesoftening, only caused by chilling injury, is describedin Eq. (3b). The combined effect of damage caused bychilling injury and, as a consequence, altered enzymaticactivities affecting the cell wall integrity, thus the firm-ness, is represented in Eq. (3c). In this latter equationthe source of the softening is related to chilling injury,the effects are related to enzyme actions. This whole sit-uation can be summarised in the following reactionmechanism:

FRMvar;E !kFRMvar;E

Decay ð3aÞ

FRMvar;C !kFRMvar;C

Decay ð3bÞ

FRMvar;E !kFRMvar;C

Decay ð3cÞ

FRMvar,E and FRMvar,C represent the variable part ofthe firmness susceptible to enzymatic degradation(Eqs. (3a) and (3c)) and to chilling injury, respectively.‘‘Decay’’ are reaction products, which do not contributeto firmness and k (day�1) is the reaction rate constant.The indices ‘‘E’’ and ‘‘C’’ refer to enzyme and to chill-ing-injury related softening processes, respectively.

Based on the fundamental rules of chemical kinetics,the following set of differential equations can bededuced:

dFRMvar;E

dt¼ �ðkFRMvar;E

þ kFRMvar;CÞ � FRMvar;E ð4aÞ

dFRMvar;C

dt¼ �kFRMvar;C

� FRMvar;C ð4bÞ

At constant external conditions (like temperature inthese experimental series) an analytical solution can beobtained for both firmness aspects FRMvar,E andFRMvar,C by solving the set of differential equations,where t is time (days) and k the rate constant of a par-ticular process. By summing both firmness aspects

C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584 579

(FRMvar,E and FRMvar,C) and adding the fixed,unchangeable part of the firmness, (FRMfix) oneobtains:

FRMðtÞ¼ FRMfixþFRMvar;E;0 � expð�ðkFRMvar;E

þ kFRMvar;CÞ � tÞ

þFRMvar;C;0 � expð�kFRMvar;C� tÞ ð5Þ

In this latter equation, ‘‘t’’ refers to the storage time(days) and the indices ‘‘0’’ in FRMvar,E,0 and FRMvar,C,0

to the beginning of the experiment (t = 0). Eq. (5) de-scribes the change of the total firmness, FRM, at con-stant temperature in time. All rate constants ki areassumed to depend on temperature according to Arrhe-nius� law:

ki ¼ ki;ref � expEai

R� 1

T ref

� 1

T act

� �� �ð6Þ

In Eq. (6), Eai is the activation energy (J mol�1) of reac-tion ‘‘i’’, and Tref is the reference temperature and Tact

the actual temperature at which the experiment was per-formed (K). Tref was 20 �C in all analyses.

3.1.2. Raw data on firmness and relations

In the experimental set-up, both the slope (N m�1)and the compression distance (m) were measured. Thecompression-measuring graph can be approximated bya triangle. The height of this triangle is the predefinedend-force Fend (=3 N) and the base the compression dis-tance D (m). A linear correlation of the data for slopewith the reciprocal data for distance of either the indi-vidual tomatoes (n = 1400), or the average data for thebatches (n = 70), gives a value for R2 of 0.987 and0.996, respectively. This signifies that slope and distanceare indeed inversely related: D = Fend/slope.

Sensory firmness is, in general, related to tissuebreaking force. The slope of a compression measure-ment shows a high correlation with the breaking force.For this reason the slope was directly related to thedeveloped firmness model (Eq. (5)). The distance onthe other hand is related to the inverse of the same mod-el (Eq. (7)).

DðtÞ ¼ F end

FRMfix þ FRMvar;E;0 � expð�ðkFRMvar;Eþ kFRMvar;C

Þ � tÞ þ FRMvar;C;0 � expð�kFRMvar;C� tÞ ð7Þ

3.1.3. Statistical analysis and interpretation

The numerical values for slope range between 1.6 and7.3 (N m�1) and for distance between 0.45 and 2.1 m. Toavoid excessive importance of the high data values ofslope compared to distance, a weight factor was used.The individual values for slope (n = 70) and distance(n = 70) were divided by the average of all these valuesfor slope and distance, respectively. Based on the models

developed above, these normalised data (actual individ-ual slopes, or actual individual distances divided by themean slope respectively the mean distance) were statisti-cally analysed by multiple non-linear regression on slope(Eq. (5)) and compression distance (Eq. (7)) separately,and combined.

In Table 1 the results of the non-linear regressionanalyses of the weighed data, after correction for theircorresponding weight factor, are presented. Stage 6tomatoes have a higher total initial firmness, whichequals FRMfix + FRMvar,E,0 + FRMvar,C,0, than Stage8 tomatoes. This difference is caused by the value ofthe variable part of the firmness, FRMvar,E, susceptibleto enzymatic degradation, which is higher for Stage 6than Stage 8 tomatoes. The firmness part affected bychilling injury, FRMvar,C, is independent of the maturitystage at harvest. The fixed part of firmness (FRMfix),that part of the firmness that cannot be degraded, noteven by chilling-injury related processes, is the samefor both maturity stages at harvest.

In Fig. 1 the data for distance for Stage 6 tomatoes(Fig. 1A) and slope for Stage 8 tomatoes (Fig. 1B),stored at the different temperatures studied, are shown.The corresponding figures for the distance of Stage 8,respectively, the slope of Stage 6 tomatoes, are notshown, since they are similar. Included in these figuresare the simulations based on the kinetic models, as de-rived in Eqs. (3–6), using the numerical values presentedin Table 1.

The parameter values on the processes occurringexclusively during safe, ‘‘non-chilling injury’’ storage,kFRMvar;E;ref

and EFRMvar;E, are estimated in all three analy-

ses as the same (data not shown). This signifies that suf-ficient information is contained within the data toestimate the parameters involved (kFRMvar;E;ref

andEFRMvar;E

). At this point it should be noted that the acti-vation energy of the chilling-injury related processes isnegative. As a consequence, the contribution of the chill-ing-injury processes to the decrease in firmness vanishesat increasing temperature. Two measuring points seemto be outliers, the longest storage time at 3 �C for bothstages of maturity. This indicates that the model does

not completely cover all processes during chilling injury.This furthermore suggests that the reliability of theparameter estimates for the chilling-injury related pro-cess are lower than for the enzymatic processes relatedto fruit softening. This is not surprising, since only onechilling temperature was applied (3 �C) in contrast tothree safe temperatures (12, 20 and 25 �C). The completemodel has, however, sufficient descriptive and predictive

Table 1Results of statistical analyses, of the normalised data for slope,distance and ‘‘slope and distance’’ combined, to assess the values of thekinetic and batch parameters relevant to tomato firmness decrease

Parameter Estimate for

Slope Distance Combined

Kinetic parameter

kFRMvar;E1.29 · 10�1 1.30 · 10�1 1.40 · 10�1

EFRMvar;E 8.25 · 104 8.25 · 104 8.39 · 104

kFRMvar;C4.68 · 10�8 3.48 · 10�8 9.52 · 10�9

EFRMvar;C�5.30 · 105 �5.46 · 105 �5.97 · 105

Batch parameter

FRMfix 1.07 1.08 1.07FRMvar,E,0 (Stage 6) 4.63 4.63 4.76FRMvar,E,0 (Stage 8) 3.58 3.59 3.63FRMvar,C,0 1.12 1.12 1.18

Administrative information

R2adj ð%Þ 92 87 90

RMSEC 3.50 · 10�1 1.20 · 10�1 ndN 70 70 140Tref (�C) 20 20 20

Note: s.e. not available due to software limitations.

0.3

0.8

1.3

1.8

0 5 10 15 20 25 30

Storage time (days)

Com

pres

sion

dis

tanc

e x

103 (

m)

Storage time (days)

1.5

4.0

6.5

0 5 10 15 20 25 30

Com

pres

sion

slo

pe x

103 (N

.m-1

)

(A)

(B)

Fig. 1. Effect of storage time and temperature on the firmness ofStages 6 and 8 tomatoes measured as distance (Stage 6 tomatoes; 1 A)and slope (Stage 8 tomatoes; 1B). Measured values are at 3 �C; �,12 �C; m, 20 �C; d and 25 �C; j. NIR-predicted values are at 3 �C; �,12 �C; n, 20 �C; s and 25 �C; h. Predicted values according to Eq. (4)(slope) and Eq. (6) (distance) and the numerical information of Table 2are at: 3 �C; (——), 12 �C; (— — —), 20 �C; (. . .. . .. . .) and at 25 �C;(—-—-—).

580 C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584

power to be useful for practical applications. The three-dimensional behaviour of firmness of Stage 8 tomatoes,expressed as slope, based on the estimated parameters ofTable 1, is shown in Fig. 2. From this figure, an optimalstorage temperature for these tomatoes of 6 �C can bededuced. Below this temperature the effect of chilling in-jury on the rate in firmness decrease and on the endvalue are obvious.

Based on the numerical information presented inTable 1 the percentage contribution of the chilling-injury induced firmness decay to the overall firmnessdecay can be estimated at each time and temperature.In Table 2 the percentage contribution of the firmnessdecay caused by chilling injury to the variable part ofthe firmness at 5 and 15 days is presented. Five days rep-resents the average storage time of tomatoes in Europe.Fifteen days represents the storage period of shippedtomatoes (H.A.M. Boerrigter; A&F.BV; personal com-munication). From this table it can be concluded thata small part of the firmness decay at 6 �C is caused bychilling injury. At the commonly used storage tempera-ture of 12 �C the contribution of chilling injury is virtu-ally absent.

At infinite storage time the tomato firmness extrapo-lates to the fixed firmness part, FRMfix. The estimate ofFRMfix seems to be independent of the maturity of har-vest of the tomatoes (see Table 1). Chilling injury isassociated with membrane damage (Sharom et al.,1994). This membrane damage is represented byFRMvar,c, the cold susceptible part of FRMvar. The esti-mated value of FRMvar,c is the same for Stage 8 as forStage 6 tomatoes (see Table 1). This suggests that the

Fig. 2. Three-dimensional simulation of the effect of storage temper-ature and time on the firmness, expressed as slope, of Stage 8 tomatoes.

Table 2The calculated effect of storage time and temperature on the firmness (Fvar) and moisture (ML) loss and the contribution of the chilling injury to theselosses

Temperature (�C) Effect of storage time and temperature on firmnessloss and the % contribution of chilling injury to thisloss

Effect of storage time and temperature on moistureloss and the % contribution of chilling injury to thisloss

Firmness loss (%) Contribution ofchilling injury (%)

Moisture loss (%) Contribution ofchilling injury (%)

Storage duration (days)

5 15 5 15 5 15 5 15

0 87 100 86 100 0.45 1.6 24 483 20 48 15 37 0.48 1.4 12 306 10 26 1.3 3.8 0.55 1.4 5.6 169 12 31 0.1 0.3 0.65 1.5 2.7 7.812 17 40 0 0 0.77 1.7 1.2 3.615 23 50 0 0 0.91 1.9 0.6 1.620 36 65 0 0 1.2 2.6 0.2 0.425 52 74 0 0 1.7 3.7 0 0.1

Storage time (days)0 8 16 24 32

0

2

4

6

Moi

stur

e lo

ss (

%)

Fig. 3. Effect of storage time and temperature on the moisture loss ofStage 6 tomatoes. Measured values are at 3 �C; �, 12 �C; m, 20 �C; d

and 25 �C, j. Predicted values according to Eq. (9) and the numericalinformation of Table 3 are at: 3 �C, (——-); 12 �C ,(———); 20 �C,(. . .. . .. . .) and at 25 �C; (—-—-—).

C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584 581

main difference between Stages 8 and 6 tomatoes is asso-ciated with the variable part of the firmness. This is ex-pressed by the difference in values of FRMvar,E,0. It istentative to speculate that this difference in FRMvar,E,0

is caused by the difference in amount and compositionof cell wall polysaccharides, susceptible to enzymaticmodification and degradation processes.

3.2. Development of models for moisture loss based on

kinetic mechanisms

3.2.1. Raw data on moisture loss

As can be derived from the data (not shown), the ef-fect of harvest maturity on moisture loss is very smalland will be neglected in the further model developmentand data analyses. At first glance the behaviour of mois-ture loss in time is exponential towards an end-value: themaximum amount of water a tomato can lose. Thismaximum, potential moisture loss seems to depend ontemperature (see Fig. 3). Since the relative humidity(RH) during storage was roughly constant and the samefor all four temperatures, no effect of RH can bededuced. Therefore RH will not be considered in themodel development. It has however, to be realised thatthe vapour-pressure deficit, rather than the RH, is theactual driving force for evaporation. The consequenceis that the rate constant for moisture loss has to bestrongly related with the vapour-pressure deficit.

3.2.2. Model development on moisture loss

It seems reasonable to assume that in all livingorganisms two main sources of water can be distin-guished. The first source refers to free, unbound water(Wf), capable to migrate freely and available to evapo-rate (Eq. (8a)). The second source, which can be consid-ered as a sink, refers to water, associated with cellularmacromolecules, or confined to the cell interior due to

the presence of an intact cell membrane (Ws). Due tothese limitations it cannot migrate freely and evaporate.A dynamic equilibrium exists between these two sourcesof water. For example, pectolytic enzymes affect thecharge (demethylation of pectin by pectin methyl ester-ase), and the degree of polymerisation (degradation ofpectin by poly-galacturonase) (Hadfield & Bennett,1998) of pectin and, as a consequence, its water bindingcapacity. These and other cell wall modifying enzymaticreactions are represented in Eq. (8b), causing the above-described equilibrium to shift during storage. A directconsequence of chilling injury is membrane damage,causing electrolyte leakage (Sharom, Willemot &Thompson) also affecting the above-described equi-librium. This effect of chilling injury is described inEq. (8c).

This conceptual model was used to formulate a mech-anism to describe the overall process of moisture lossand is expressed in the following equations:

Table 3Results of statistical analysis of the data for moisture to assess thevalues of the kinetic and batch parameters relevant to tomato moistureloss

Parameter Estimate

Kinetic parameter

kML 9.60 · 10�2

EML 4.81 · 104

kE 1.01 · 10�2

EE 1.02 · 105

kC 1.07 · 10�4

EC �1.75 · 105

Batch parameter

Wf,0 3.40Ws,0 2.02 · 101

Wout,0 0

Administrative information

R2adj ð%Þ 99

RMSEC 1.91 · 10�1

N 56Tref (�C) 20

Note: s.e. not available due to software limitations.

Fig. 4. Three-dimensional simulation of the effect of storage temper-ature and time on the moisture loss of tomatoes.

582 C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584

W f !kML W out ð8aÞ

W s!kE W f ð8bÞ

W s!kC W f ð8cÞ

Wout is the moisture content in the environment, whichis in dynamic and continuous exchange with the free,unbound water, Wf. Indice ‘‘ML’’ refers to moisture lossby diffusion into the environment, ‘‘E’’ and ‘‘C’’ to theprocess in which a shift to free water occurs by enzy-matic and chilling-injury related processes, respectively.The following set of differential equations can be ob-tained from Eq. (8) using the fundamental rules ofchemical kinetics:

dW s

dt¼ ð�kE � kCÞ � W s ð9aÞ

dW f

dt¼ ðkE þ kCÞ � W s þ kML � ðW out � W fÞ ð9bÞ

dW out

dt¼ kML � ðW f � W outÞ ð9cÞ

At constant external conditions (like temperature andrelative humidity, as in the experimental series) an ana-lytical solution can be obtained for the moisture loss bysolving the set of differential equations:

W outðtÞ ¼ W f ;0 þðkE þ kCÞ � W s;0

�kML þ kE þ kC

� �

� ð1� expð�kML � tÞÞ þ W out;0

� ð1� expð�kE � t � kC � tÞÞ � kML � W s;0

�kML þ kE þ kC

� �

ð10Þ

In this latter equation, ‘‘t’’ refers to the storage time(days) and the indices ‘‘0’’ in Wf,0, Ws,0 and Wout,0 tothe beginning of the experiment (t = 0).

3.2.3. Statistical analysis and interpretation

The data on moisture loss were statistically analysedby multiple non-linear regression based on the modeldeveloped (Eqs. (8)–(10)). The results of the non-linearregression analyses are presented in Table 3. From thistable it is obvious that the second term in Eq. (10) iszero, since Wout,0 is put at zero. This can be explainedas follows. At the start of the experiment (t = 0), whichis rather arbitrarily chosen, the tomatoes were weighedand the weight loss was set at zero, thereby also settingWout,0 at zero.

In Fig. 3 the data for the moisture loss of Stage 6tomatoes, stored at four different temperatures areshown. Since moisture losses are identical for Stages 6and 8 tomatoes this information is not shown for Stage8 tomatoes. Included in this figure are the simulationsbased on the kinetic models, as derived in Eqs. (8)–(10), using the numerical values presented in Table 3.It is nicely shown that for the non-chilling temperatures,

the higher the storage temperature the greater the mois-ture loss. The opposite becomes true for tomatoes storedat 3 �C for about three weeks. After this period themoisture loss at 3 �C tends to become larger than at12 �C. Apparently the tissue damage caused by chillinginjury begins to prevail the tissue damage at physiolog-ical temperatures resulting in a situation were the ob-served water loss becomes higher at lowertemperatures. This behaviour becomes obvious in the3D representation (see Fig. 4) of moisture loss as func-tion of storage time and temperature. For this batch

Table 4Results of prediction of slope and distance of tomatoes stored at fourdifferent temperatures based on near infrared spectra using partial leastsquares regression analysis

Statistical information Variables

X-variables Near infrared spectraY-variable Slope (N m�1) Distance (mm)

Calibration-set

R2cal ð%Þ 97 95

RMSEC 2.29 · 10�1 7.60 · 10�2

Number of LVs 7 8N 70 70

Training-set

R2cal ð%Þ 98 97

RMSEC 2.07 · 10�1 7.00 · 10�2

Number of LVs 7 8N 50 50

Prediction-set

R2p ð%Þ 83 84

RMSEP 5.14 · 10�1 1.11 · 10�1

N 20 20

R2cal, R2

p correlation coefficient of calibration and prediction,respectively.

C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584 583

of tomatoes the calculated moisture loss is at minimumat 6 �C. This is the same temperature as the estimatedminimum for firmness loss.

As is the case for the firmness decay, the activationenergy of the chilling-injury process for moisture lossis negative. The consequence is that the contributionof chilling-injury process to the decrease in moisture lossdecreases at increasing temperature. Based on thenumerical information of Table 3 the calculated percent-age contribution of the moisture loss, caused by chillinginjury, during storage for 5 and 15 days is presented inTable 1. From this table it is obvious that the conse-quences of chilling injury are less severe for moistureloss than for firmness decay, however, the effects of chill-ing injury extents to higher temperatures for moistureloss in comparison with firmness loss.

As discussed above, the vapour-pressure deficit is theactual driving force for evaporation. At a RH of 100%the vapour pressure at 3, 12, 20 and 25 �C is 0.76,1.40, 2.33 and 3.17 kPa, respectively. The estimates forthe value of kML, describing the evaporation process atthese temperatures, are 28.4, 55.2, 96.0 and134 · 10�3 day�1, respectively. The correlation (R2) be-tween the values for the vapour-pressure deficit and esti-mates for kML is, for the temperatures analysed, 0.9998,suggesting a strong relation between the value of the def-icit and the value of the rate constant. Recently, an acti-vation energy at 25 �C of 48.0 kJ mol�1 was measuredfor the evaporation of water (Rushdi & Moroi, 2003).This latter value is almost the same as the value forthe activation energy estimated in this study(48.1 kJ mol�1), applying a complete different approach.This altogether suggests that the underlying assump-tions for the model development, presented in Eq. (8),to explain the data, represent a realistic approach.

3.3. Near infrared models on firmness loss

In the previous section emphasis was put on model-ling of assumed reaction mechanisms causing the ob-served changes in firmness (slope and distance). In thischapter, statistical relations between the near infraredspectra and the non-destructively measured propertiesslope and distance are established. Partial least squaresregression (PLSR) models were made for these two vari-ables. These models were optimised with regard to theminimal number of latent variables (LVs) and rootmean squares errors of calibration (RMSEC) and max-imal correlation. PLSR models were made using all to-mato samples (n = 70) as calibration set. The result ofthis analysis is given in Table 4. The near infrared pre-dicted values for distance and slope are shown inFig. 1A and B, respectively.

To test the actual predictive power of near infraredspectroscopy for slope and distance 50 tomato sampleswere randomly selected and used as training set to

develop the PLSR models. Their predictive power wastested on the remainder of the tomato samples (n = 20).The results of this analysis are presented in Table 4.

Applying the PLSR calibration models, based on to-mato batches, to the (1400) individual tomatoes showedthat these models could not predict the firmness of theindividual tomatoes (R2 < 0.3). Obviously, the varianceof the individual tomatoes per batch was such that itprecluded the use of the near infrared calibration curves,based on batches. Furthermore, no reliable PLSR mod-els could be made for slope and distance using the infor-mation of the individual tomatoes (results not shown).

4. Conclusions

Two types of models were developed. The first type ofmodel was based on fundamental laws of chemicalkinetics, assuming plausible reaction mechanisms. Thistype of model describes the firmness decay and moistureloss of tomatoes in time at constant external conditions.The second type of model was on partial least squaresregression analysis, relating the data on firmness lossto the near infrared spectral data. These regression mod-els describe the actual firmness loss of a homogeneousbatch of tomatoes.

Acknowledgement

This research was partly financed by the EuropeanCommission under contract number FAIR CT95-0302.

584 C. Van Dijk et al. / Journal of Food Engineering 77 (2006) 575–584

References

Geladi, P., & Kowalski, B. R. (1986). Partial least squares regression: atutorial. Analytica Chimica Acta, 185, 1–17.

Hadfield, K. A., & Bennett, A. B. (1998). Polygalacturonases: manygenes in search of a function. Plant Physiology, 117, 337–343.

Johnson, R. A., & Wichern, D. W. (1992). Principal componentanalysis, projection persuit and graphical procedures. In Applied

multivariate statistical analysis (pp. 356–395). New York: PrenticeHall.

Kramer, A., & Twigg, B. A. (1970). Quality control for the food

industry. Westport: AVI Pub. Co.Murate, N., & Los, D. A. (1997). Membrane fluidity and temperature

perception. Plant Physiology, 115, 875–879.OECD (1988). International standardisation of fruit and vegetables.

Tomatoes.Polderdijk, J. J., Tijskens, L. M. M., Robbers, J. E., & Van der Valk,

H. C. P. M. (1993). Predictive model of keeping quality oftomatoes. Postharvest Biology and Technology, 2, 179–185.

Raison, J. K. (1986). Phase transitions in liposomes formed from thepolar lipids of mitochondria from chilling-sensitive plants. Plant

Physiology, 81, 807–811.Ross, G. J. S. (1990). Nonlinear estimation. New York: Springer Verlag.Rushdi, M., & Moroi, Y. (2003). Evaporation rate measurements of

water and liquid 1-alkonols across air–liquid interface usingthermographimetry. Bulletin of the Chemical Society Japan, 76,919–926.

Sharom, M. S., Willemot, C., & Thompson, J. E. (1994). Chillinginjury induced lipid phase changes in membranes of tomato fruit.Plant Physiology, 105, 305–308.

Sloof, M. (2001). Problem decomposition. In L. M. M. Tijskens, M. L.A. T. M. Hertog, & B. M. Nicolaı (Eds.), Food process modelling

(pp. 19–34). Cambridge, UK: Woodhead Publishing.

Steenkamp, J. B. E. M. (1989). Product quality: an investigation into the

concept and how it is perceived by consumers. Ph.D. Thesis,Agricultural University Wageningen, The Netherlands.

Stolle-Smits, T., Beekhuizen, J. G., Kok, M. T. C., Pijnenburg, M.,Recourt, K., Derksen, J. W. M., et al. (1999). Changes in cell wallpolysaccharides of green bean pods during development. Plant

Physiology, 121, 363–372.Tijskens, L. M. M. (1994). Modelling colour of tomatoes. Advantage

of multiple nonlinear regression. In Proceedings COST94 workshop

post-harvest treatment of fruit and vegetables (pp. 175–185), 14–15September, Leuven, Belgium.

Tijskens, L. M. M., Hertog, M. L. A. T. M., & Van Dijk, C. (1997).Generic modelling and practical applications. In B. M. Nicolaı, B.M., & J. De Baerdemaeker (Eds.), Food quality modelling (pp. 145 –151). Cost Action 915.

Tijskens, L. M. M., Hertog, M. L. A. T. M., Van Dijk, C. (1999).GESSI: a generic enzyme system for stimulation and inactivationduring storage and processing. In: M. Hagg, R. Ahvenainen, A.M.Evers, K. Tiilikkala (Eds.), Proceedings Second International

Conference AGRI-FOOD QUALITY II (pp. 81–86), 22–25 April1998, Turku, Finland.

Van Dijk, C., Boeriu, C., Stolle-Smits, T., Tijskens, L. M. M. (inpress). The firmness of stored tomatoes (cv. Tradiro). 2. Kinetic andnear infrared models to describe pectin degrading enzymes andfirmness loss. Journal of Food Engineering, doi:10.1016/j.jfoodeng.2005.07.017.

Van Dijk, C., & Tijskens, L. M. M. (2000). Mathematical modeling ofenzymatic reactions as related to texture after storage and mildpreheat treatment. In S. M. Alzamora, M. S. Tapia, & A. Lopez-Malo (Eds.), Minimally processed fruits and vegetables

(pp. 127–152). Maryland, USA: Aspen Publishers.Wang, C. I., Boyan, B. D., & Eanes, E. D. (1990). In C. Y. Wang (Ed.),

Chilling injury of horticultural crops. CRC Press.