A visualization-based analysis method for multiparameter models of capillary tissue-exchange

Abstract

In order to successfully use a model for parameter identification, it must be carefully analyzed. Current analysis methods, however, are ad hoc and provide only partial information. We extended these methods through the application of stacked dimensions, a scientific visualization method. The end result of our extensions are multi-dimensional parametric model-images. These images depict a model as a function of all its parameters in a single graphic. We applied parametric model-images to model verification (behavioral analysis), sensitivity analysis, and identifiability analysis. We applied our methodology to the evaluation of pulmonary vascular capillary-transport models. Results have shown that the visualization-based method provides a more complete view of a model's behavior and its other characteristics. Furthermore, our method has also proven to be more computationally efficient than the traditional approaches.

Transient transcapillary exchange of water driven by osmotic forces in the heart

“…Relative sensitivities [(‫ץ‬W/W)/(‫ץ‬P/P) or ‫ץ‬ ln W/‫ץ‬ ln P] rather than absolute sensitivities (‫ץ‬W/‫ץ‬P) were used to provide dimensionless sensitivity functions. Because the sensitivity functions are dependent on the parameter values (8), sensitivity analysis was performed after an initial manual fit to a small number of preliminary data sets. The sensitivity curves shown in RESULTS were generated with the mean parameter values obtained from optimization against the full data set but do not differ significantly from the preliminary results used for experimental design.…”

Visualization-Based Analysis of Multiparameter Models Using Environment for N-Dimensional Model Analysis

“…Visualization-based behavior analysis is the simplest of all the methods. It involves studying the model behavior (or output) as a function of its parameters (13). The N-dimensional image (behavioral image) needed to accomplish this is the same image described in the previous hypothetical example-lines of f (t) now become model output-time curves.…”

“…For this we will be using the method of stacked-dimensions. This method has been described in great detail elsewhere (13,15). We will provide a brief summary of it here.…”

“…This is known as the absolute sensitivity function. To carry out a visualization-based extension of this analysis, n sensitivity images, one for each parameter P i in › , need to be generated (13). Each image shows the range of variation of the partial derivative of the model with respect to one parameter as a function of all the model parameters.…”

“…All of these, however, suffer from incompleteness of analysis, as well as a lack of a systematic approach. New methodology which extends the analytical methods described in the literature through the addition of N-dimensional visualization has been described by us previously as a way of addressing these problems (13). In this paper, we present additional improvements to the visualization-based analysis methods.…”