Využití jazyka Modelica pro modelování ve fyziologii. Modely s rozprostřenými parametery, Tvorba výukových simulátorů.

Šilar, Jan

Mathematical models in physiology are useful to formulate and verify hypotheses, to make predictions, to estimate hidden parameters and in education. This thesis deals with modelling in physiology using the Modelica language. New methods for model implementation and simulator production were developed. Modelica is an open standard equation-based object-oriented language for modelling complex systems. It is highly convenient in physiology modelling due to its ability to describe extensive models in a lucid hierarchical way. The models are described by algebraic, ordinary differential and discrete equations. Partial differential equations are not supported by the Modelica standard yet. The thesis focuses on two main topics: 1) modelling of systems described by partial differential equations in Modelica 2) production of web-based e-learning simulators driven by models implemented in Modelica. A Modelica language extension called PDEModelica1 for 1-dimensional partial differential equations was designed (based on a previous extension). The OpenModelica modelling tool was extended to support PDEModelica1 using the method of lines. A model of countercurrent heat exchange between the artery and vein in a leg of a bird standing in water was implemented using PDEModelica1 to prove its usability. The...

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