Multi-parameter models

Two main methods, parametric and nonparametric, have been developed for this deconvolution. The parametric method involves development of a multi-parameter model for obtaining the value of reactivity distribution... 

Sensitivity analysis thus provides a method by which the structural stability of multi-parameter models can be assessed and described in more detail. We can say for the reference solution studied here that the Lotka-Volterra oscillator is structurally unstable to variations in I<4 and I<5 but not to variations in k, k2 and I<3. These properties of the Lotka-Volterra oscillator are, of course, well-known. The success of sensitivity analysis in unambiguously (and quantitatively) verifying these facts suggests that it will be a useful tool for the study of models which are not so well-understood. 

Cukier, R.I., Levine, H.B., Shuler, K.E. Nonlinear sensitivity analysis of multi-parameter model systems. J. Comput. Phys. 26, 1-42 (1978)... 

The most widely-accepted dose response model at the present time is the multi-stage model, which has great flexibility in curve-fitting, and also has a strong physiological justification. Although it is difficult to implement, there are already computer codes in existence that estimate the model parameters (13). The two most widely-used models, until recently, were the one-hit model and the log-probit model. They are both easy to implement, and represent opposite extremes in terms of shape - the former represents the linear non-threshold assumption, whereas the latter has a steep threshold-like curvature. In numerous applications with different substances it has been found that these three... 

Another possible advantage with MolSurf descriptors (and also other multi parameter descriptors) is the fact that they describe the investigated compounds not only with a single value, as in the case of PSA and log P descriptors, but in a multivariate way. This approach provides a more balanced description of the requirements that a structure must have in order to be well absorbed and may, in turn, provide additional insight on how to develop compounds having favorable absorption properties. However, as will be described in Section 16.4.10, simpler -i.e., less computationally demanding - parameters carrying similar information content with equal interpretability may be used to derive models for intestinal absorption at the same level of statistical quality. 

Mathematical optimization models that explicitly consider such a multi-stage structure belong to the class of multi-stage stochastic programs. A deterministic optimization model with uncertain parameters is extended to a multi-stage model by three measures ... 

Johansson F, Patterson R, Arvidsson PO, Moore V, Grant I, Backman P (2005) Prediction of human oral absorption using multi-parameter in silico models. AAPS J. 17 Abstract Ml 158. 

In summary while conceptually appealing, the application of complex multi-solute models for Sr sorption to zeolite is in the early stages of development. While preliminary results are encouraging, additional work is required to develop more efficient computational methods and develop an improved database for parameter estimation. The remainder of this section focuses on the simpler retardation factor approach. 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

As emphasized in the previous section, it is critical for the multi-scale integration to develop mathematically simple (with few parameters) yet physically realistic models with nanoscopic information. For the description of the multi-scale framework of HDI, we provide a bot-tom-up approach as given below to sketch multi-scale modeling as described in Figures 24 and 25 (Jhon et al., 2011). 

From a purely pragmatic standpoint, even two-dimensional models require too much computer time to be really practicable for optimization purposes. In addition, multi-dimensional models require values for parameters that are difficult or impossible either to estimate with sufficient accuracy, or to measure. 

Fig. 5 Chargeability factor A/can be predicted by a Fig. 6 Permeability prediction from electrical multi-linear model composed by different behaviour and structures parameters of porous parameters formation factor F, water porosity O, solids, k Katz and Thompson model Hg-specific surface Asp and water permeability k for kjsc Johnson, Schwartz and co-workers different textures. model.

Chargeability factor M depends on the brine/gas saturation of porous solids. Figure 3 gives the relationship between the chargeability and brine saturation for two samples. We noted that the M decreases hardly with the decrease of the brine saturation. The presence of vugs and karsts pore types (sample 9-LS8) seems to speed up the decrease of the M Chargeability factor M can be explained by a multi-linear model composed of different structures parameters such as the formation resistivity factor, water porosity, Hg-specific surface area and water permeability, e.g.. Fig. 5. 

The equivalent sink constraint is illustrated in Figure 8.8. In Figure 8.8A, the constraint holds and hence the parameters estimated from either the noncompartmental model (left) or the multicompart-mental model (right) will be equal. If the multi-compartmental model is a model of the system, then, of course, the information about the drug s disposition will be much richer, since many more specific parameters can be estimated to describe each compartment. 

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