the handbook of food engineering practice crc press chapter 10 ...

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semi-empirical kinetic/mathematical model that effectively represents the experimental data. Preferably the model would still have the general form of the quality function of eq.(14), where Q(A) can obtain any form other than the typical ones of Table 1. The steps for building such a model are described by Saguy and Karel (1980). Multivariable linear models, polynomial equations or nonlinear models can be defined and their fit to the data can be tested with computer aided multiple linear, polynomial or nonlinear regressions. Empirical equations modeling the effect of different composition or process parameters can be derived from statistical experimental designs, like the surface response methods (Thompson, 1983). A special category of reactions, the enzymatic reactions, important in foods are usually modeled by the Michaelis-Menten equation. This is a reaction rate function based on the steady-state enzyme kinetics approach (Engel, 1981). For an enzymatic system, with no inhibition, the rate equation has the form: r A = k [A] K m + [A] (16) where A is the substrate, k=k o [e] is proportional to the enzyme (e) concentration (k is usually called v max in biochemical terminology) and K m is a constant (r A = 0.5 k for [A] = K m ). When [A]>>K m , the equation reduces to a zero order reaction, r A =k. This is often the case in foods with uniformly distributed substrate in excess and small amounts of enzyme, e.g., lipolysis of milk fat. When K m >>[A], the equation reduces to first order, r A =(k/K m ) [A]. This occurs in foods where the enzymes are highly compartmentalized and have limited access to the substrate or where generally the substrate limits the reaction, e.g., browning of fruit and vegetable tissue due to polyphenolase activity. Thus, a large portion of enzymatic reactions in foods can be handled as zero or first order systems. 16
When a Michaelis-Menten rate equation has to be used, the Lineweaver-Burk transformation is used that allows the estimation of the parameters by linear regression 1 r A = K m k 1 [A] + 1 k (17) The described initial rate measurement differential method is usually applied for the kinetic analysis of enzymatic reactions. When one of the quality deterioration models previously described is used its applicability usually is limited to the particular food system that was studied. Since the model often does not correspond to the true mechanism of the reaction, a compositional change in the system may have an effect in the rate of loss of the quality parameter that cannot be predicted by it. Thus, any extrapolation of kinetic results to similar systems should be done very cautiously. In certain cases, an in depth kinetic study of specific reactions important to food quality is desirable, so that the effect of compositional changes can be studied. In these cases the actual mechanism of the reactions is sought to be revealed if possible. Such studies are usually done in model systems, rather than in actual foods, so that the composition and the relative concentrations of the components are closely controlled and monitored. They are particularly useful in cases where the toxicological or nutritional impact of the accumulation of breakdown products, including intermediate or side step reactions, is examined. Examples of such studies are the multistep breakdown of the sweetener aspartame (Stamp, 1990) and the two step reversible isomerization of β- carotene (Pecek et al, 1990). In the first case a complex statistical analysis using a nonlinear multiresponse method was employed where all the reaction steps for the true reaction mechanism are expressed in the form of a linear system of differential equations. With this method, all the experimental data is utilized simultaneously to determine the kinetic parameters for each degradation step by a multidimensional nonlinear regression 17
Page 1 and 2: THE HANDBOOK OF FOOD ENGINEERING PR
Page 3 and 4: It is a working definition for the
Page 5 and 6: 10.2 KINETICS OF FOOD DETERIORATION
Page 7 and 8: very small, allowing us to treat it
Page 9 and 10: Data can be fitted to these equatio
Page 11 and 12: criterion. The value of the R 2 , f
Page 13 and 14: of reaction systems involved in foo
Page 15: Lund, 1985). The standarized residu
Page 19 and 20: ∂ ln K eq ∂ (1/T) = - ∆Eo R (
Page 21 and 22: are available, the confidence range
Page 23 and 24: kinetic data is compared. Its main
Page 25 and 26: plot will give a relatively straigh
Page 27 and 28: temperatures (Fennema et al., 1973)
Page 29 and 30: Glass transition phenomena are also
Page 31 and 32: i.e. if T ∞ is chosen correctly,
Page 33 and 34: A number of recent publications deb
Page 35 and 36: The study of the temperature depend
Page 37 and 38: and bakery goods, upon losing moist
Page 39 and 40: ambient temperatures (e.g loss of c
Page 41 and 42: temperature and is an area of curre
Page 43 and 44: and variable temperature conditions
Page 45 and 46: Figure 8. Characteristic fluctuatin
Page 47 and 48: 10.3 APPLICATION OF FOOD KINETICS I
Page 49 and 50: time at each selected temperature.
Page 51 and 52: TTI can be used to monitor the temp
Page 53 and 54: 10.4 EXAMPLES OF APPLICATION OF KIN
Page 55 and 56: Figure 10. Thiamin retention of a m
Page 57 and 58: S = SS {1+ N p n-Np F[N p, n-N p ,
Page 59 and 60: 10.4.2. Examples of shelf life mode
Page 61 and 62: In Fig. 12a aspartame concentration
Page 63 and 64: the approach to follow to increase
Page 65 and 66: REFERENCES Arabshashi, A. (1982). E
Page 67 and 68:
Fennema, O., Powrie, W. D., Marth,
Page 69 and 70:
Labuza, T. P. (1975) Oxidative chan
Page 71 and 72:
Mohr, P. W., Krawiec, S. (1980) Tem
Page 73 and 74:
Sapru, V., and T.P. Labuza (1992) G
Page 75:
Yoshioka, S., Aso, Y., Uchiyama, M.
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