Modeling and Simulation of the Human Cardiovascular System in Dymola/Modelica by Means of Bond Graphs

Methodology

To maximize the maintainability of the models, it is useful to graphically model down as far as possible, i.e., to postpone the transition from the graphical to equation-based models for as long as possible. Bond graphs [2] are particularly well suited for the modeling of complex physical processes, because they represent the most primitive graphical modeling methodology that is still fully object-oiented. The transition from the bond graph layer to the equation layer is trivial and so generic that it can be programmed out once and for all times. Consequently, the user of a bond graph library should hardly ever face the need to model any physical phenomena using equations.

Status Quo

In [4,5], the hemodynamic submodel was reprogrammed in the simulation language ACSL to improve the readability and maintainability of the code. The central nervous control functions were reprogrammed from scratch making use of the Fuzzy Inductive Reasoning (FIR) Methodology [6]. It was shown that FIR is considerably better suited than NARMAX for the replication of the measured control characteristics.

In [7], the hemodynamic submodel was reprogrammed in Dymola by making use of its bond graph library [2]. The new version of the model is fully graphical. For the first time, we have available a mathematical description of the hemodynamics that can be understood not only by programmers, but also by medical personnel.

In [8], also the central nervous control submodel was ported to the Dymola modeling environment, which enables us to model and simulate the cardiovascular system in high resolution using Dymola/Modelica.

Tasks to be tackled

How can the simulation results be interpreted? How can characteristics of particular heart diseases be determined from the simulation results? How can parameter values be better grouped so that they can be more easily manipulated by medical personnel? These are some of the questions that are to be investigated in this project.

How can the model of the heart be better isolated? Is it possible to remove the model of the heart from the overall model of the cardiovascular system and replace it by a model of a heart-lung machine? Is it possible to add to the overall model a model of a pace maker that strengthens the function of the human heart? These are further questions that shall be investigated in this poject.

When rebuilding the model of the hemodynamics in Dymola using bond graphs, it was discovered that a few of the resistors in the model assume negative values. This is not physically meaningful. This project should therefore investigate where these negative resistor values come from and how the model can be reinterpreted in a physically more meaningful fashion.

References

1. Brück, D., H. Elmqvist, H. Olsson, S.E. Mattsson (2002), Dymola for Multi-Engineering Modeling and Simulation, Proc. 2^nd International Modelica Conference, Oberpfaffenhofen, Germany, pp. 55:1-55:8.

2. Cellier, F.E. and A. Nebot (2005), The Modelica Bond Graph Library, Proc. 4^th International Modelica Conference, Hamburg, Germany, Vol.1, pp. 57-65.

3. Vallverdú, M. (1993), Modelado y Simulación del Sistema de Control Cardiovascular en Pacientes con Lesiones Coronarias, Doktorarbeit, Institut de Cibernètica, Universitat Politècnica de Catalunya, Barcelona, Spain.

4. Nebot, A. (1994), Qualitative Modeling and Simulation of Biomedical Systems Using Fuzzy Inductive Reasoning, Doktorarbeit, Institut de Cibernètica, Universitat Politècnica de Catalunya, Barcelona, Spain.

5. Nebot, À., F.E. Cellier, and M. Vallverdú (1998), Mixed Quantitative/Qualitative Modeling and Simulation of the Cardiovascular System, Computer Methods and Programs in Biomedicine, 55(2), pp.127-155.

6. Cellier, F.E., À. Nebot, F. Mugica and Á. de Albornoz (1996), Combined Qualitative/Quantitative Simulation Models of Continuous-Time Processes Using Fuzzy Inductive Reasoning Techniques, Intl. J. General Systems, 24(1-2), pp.95-116.

7. Cellier, F.E. and A. Nebot (2005), Object-oriented Modeling in the Service of Medicine, Proc. 6^th Asia Simulation Conference, Beijing, China, Vol.1, pp. 33-40.

8. Cellier, F.E. and V. Sanz (2009), Mixed Quantitative and Qualitative Simulation in Modelica, Proc. 7^th International Modelica Conference, Como, Italy, pp. 86-95.