MODELING OF CIRCULATION DYNAMICS WITH ACAUSAL MODELING TOOLS

Summary

This paper presents an innovative approach to modeling and simulation using acausal modeling tools, which is representative of the modeling language Modelica. This language allows the description of the modeled relationships directly with the equations. Advantages of this approach are demonstrated on the model circulation dynamics by Guyton, Coleman and Grange of the 1972, which is one of the first models of integrated physiological systems of the organism and opened the domain, which is now engaged in the integrative physiology. The introduction of acausal approach and its comparison to previous methods is the scientific contribution of this paper.

Keywords:
Modelica, Guyton, modeling, biomedicine, Dymola

Introduction

This paper aims to introduce an innovative approach to modeling and simulations using the so called acausal modeling tools. These tools, which is representative of the modeling language Modelica, allow to describe the relationships of model directly in tool using equations (we describe the equation and not the solution). Modelica language is now increasingly used in industry. Use in biological applications is still infrequent. Advantages of this approach are demonstrated by the model of circulation dynamics from Guyton, Coleman and Granger of the 1972 [1]. The original article contained as attachment accompanying diagram (see Figure 1), which graphically represents the model equation. 

The model describes the regulation of the circulatory system, including all its connection to other physiological systems of the organism, such as oxygen transport, the volume dynamics, body fluids osmolarity, lymph flow, plasma protein circulation, potassium and sodium homeostasis, kidney model, etc. The model considers the autonomic nervous regulation including the regulation of thirst and drinking, hormonal regulation of angiotensin, aldosterone and ADH. Model represents the broader context of the circulatory system and allows the body to simulate the behavior of normal, during physical activity and in a number of pathological conditions. He was one of the first models of integrated physiological systems of the organism and opened the domain, which is now engaged in the integrative physiology.

Methods

Guyton's chart that was part of the publication is a complex network of interconnected computing elements. The authors originally implemented the model in Fortran. Five years ago in our laboratory was the model implemented in block-oriented tool Simulink. Interconnection in this implementation accurately corresponds to the graphical diagram of the original publication (after correction of some errors in the original graphic diagram) [2]. An implementation where outputs of one block are connected to inputs of other blocks is called causal.

In Simulink, was published, another, more advanced version of Guyton's model (originally implemented in Fortran or C++) - Guyton's model of the 1986, including extensive descriptions can be found at http://physiome.cz/Guyton and Simulink version of Guyton's model 1992 published in 2011 Mangourova et al. [3]. The same model in causal language cellML [4] is not yet fully functional.

New language Modelica [5] allows the implementation of a causal model, where individual elements are connected and visually the same form as the original Guyton's model [6], and also such an implementation, where the behavior of the model expressed by equations. Approach where we focus exclusively on the model equations, are called acausal [7]. Comparison of causal and acausal approach is scientific contribution of this paper.

Let's bring these approaches to calculating the total lung resistance. Yellow highlighted in Figure 2 shows the sequence of individual computing blocks. This sequence graphically expresses the procedure to calculate of total lung resistance (RPT). It was therefore a causal approach. Now let us show an acausal approach. Figure 3 is an icon that represents the total lung resistance. Against the background of this image (Figure 4) are equations whose solution is left on your computer. Acausal modeling leaves the attention of equations and not the solution algorithm, as in causal modeling.

Results

According to Guyton's original diagram created three implementations - two causal (in the languages Simulink and Modelica) and an acausal (in the language Modelica - Figure 5). Causal implementation in Modelica was using our labs technology translated into code that is executable in the web browser. The model, which captures the Figure 6 is through a web browser freely available to all Internet users (http://patfbiokyb. lf1.cuni.cz/~tomkro/GuytonModel1972/) without the need to own development environment (Dymola). Causal and acausal model implementation show the same behavior and results.

Discussion

Modelica is a particularly useful tool for creating complex models [8, 9], where the clarity and readability of the most apparent. The current version of the model from Guyton's colleagues and students, under the name HumMod (http://hummod.org) is probably the largest comprehensive model of integrated physiological system of the body. Modelica version of HumMod, which in collaboration with American colleagues engaged in our laboratory (http://physiome.cz/hummod) allows a clear and understandable formalized the expression of complex relationships between the subsystems of the organism. Models of physiological systems, among other things, can serve as a basis for the production of teaching medical simulator. The aim of our work is just making these simulators and their use in teaching physicians [10, 11].

Conclusion

A causal approach focuses on the algorithm calculation and modeling of reality beneath it very often lost. An acausal approach is focused on the model equations and their solution (algorithm) leaves your computer. Figures 7 and 8 demonstrate that the causal structure of the model describes the implementation of the method of calculation rather than the structure of the modeled reality, while acausal approach represented better the modeled reality. 

Acausal modeling is a way to create understandable physiological models, where it is very important interdisciplinary cooperation of physiologists, technicians and in case of educational applications as well as artists. Acausal modeling using object-oriented and component-based approach, and significantly shortens the development cycle of the model. Acausal implementations of Guyton model of the 1972 (Figure 5) represents an innovative approach to creating of complex models. Individual components of this model include equations and are represented by icons on the outside. This property is one of the benefits acausal modeling - tto express the semantic meaning of each component.

Acknowledgement

This paper describes the outcome of research that has been accomplished as part of research program funded by the grant PRVOUK-P24/LF1/3 and by the grant FR—TI3/869.

Ing. Tomáš Kroček

Department of Pathological Physiology

First Faculty of Medicine Charles University in Prague

U nemocnice 5, CZ-120 00 Praha

E-mail: tomas.krocek@lf1.cuni.cz

tel: +420 224 965 912