Modified Gompertz model

Li J, J-D Gu, L Pan (2005) Transformation of dimethyl phthalate, dimethyl isophthalate, and dimethyltere-phthalate by Rhodococcus rubber Sa and modeling the process using the modified Gompertz model. Int Biodet Biodeg 55 223-232. 

It was found that is a function of temperature but the model was found to give a better fit than analytical expressions like the Avrami model or the modified Gompertz model (Kloek, Walstra and Van Vliet 2000). The main advantage of this model is that as it is formulated as a differential equation, it can be used to predict isothermal as well as dynamic crystallization. However, this model does not consider the polymorphism of the material which is a critical point in the crystallization of cocoa butter. Another contribution is the model of Fessas et al. (Fessas, Signorelli and Schiraldi 2005) which considers all the transitions possible between each... 

Table 3.2 Residual analysis for each sugar attenuation modelled using the modified Gompertz, IBF and 5P logistic models...

Figure 3.4 Modelled maltose attenuation data (MG, modified Gompertz IBF, incomplete 3-function 5P, five-parameter logistic). The residuals for each model are depicted on the right.

Because this class of functions has been used extensively to model cell growth kinetics, these functions can be modified to describe subpopulations of cells. The equations below describe a Gompertz growth model that has been modified to allow cells to oscillate between a therapeutically sensitive state (Rs) and a resistant state (Rr). The same modification can also be made to the simple growth model (28). 

FIGURE 21.13 Example profile of simple Gompertz growth model with disease modifying drug action. 

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