Modelica in physiological modelling : Models with spatially distributed parameters, Authoring educational simulators
Abstract
Mathematics has been used in physiology for quite a long time (e.g. the work by Michaelis and Menten (Menten & Michaelis, 1913). The advantage of using computers to solve more complicated models started intensive research in this area since approximately the 1960s.
The development of a physiological model requires a multi-disciplinary team including at least a physiologist, a mathematician and a software developer. They also have to cooperate with experimenters on verification of the model by a comparison to real data.
Models provide a formalised quantitative description of the system under consideration by mathematical relations. Models are used in physiology in several different ways.
Models are often developed for scientific purposes. Hypotheses regarding behaviour of physiological systems may be formulated in a form of a mathematical model.
The model may be evaluated, the results may be compared to experimental data and thus the hypotheses may be tested this way. Models generally help us to understand the relations of many complex systems.
Models may sometimes replace real experiments. Such in silico experiments are used e.g. in pharmacology for preliminary testing effects of new drugs.
Models allow to predict future evolution. This is useful in decision making in clinical practice such as choosing an optimal dose of medication (commonly used e.g. in anesthesiology).
Models may help to estimate the value of physiological parameters that can not be easily measured directly. For example, measurement of pulse wave velocity is used to estimate stiffness of arteries.
Simulation applications based on models are used in education. They conveniently supplement the traditional lecture format with an active learning element.
We focus on physiological model development and our models serve mostly for either scientific or educational purposes. In the case of the education, the models do not necessarily have to be completely accurate as the students should rather learn trends and relations between variables than their precise values.
Educational simulators may be based on smaller models describing just the isolated system under study (Jiří Kofránek, Vu, Snaselova, Kerekes, & Velan, 2001). The other related systems that interact with this studied system may be omitted.
The behaviour is more understandable without the possibly complicated feedback loops through the related systems. This method is called Ceteris paribus (all other things being equal).
When the particular systems are explained enough, more complicated simulators may be used to explain interactions and relations between several systems. In the applications where the reality should be mimicked closely more complex integrative models are needed.
Even though we might be interested in the behaviour of a single body MODELICA IN PHYSIOLOGICAL MODELLING ING. JAN ŠILAR 14 organ, the model is usually composed of many different systems as this organ interacts directly or indirectly with the other systems and the effect of these feedback loops can not be neglected in this case.
Model by Arthur Guyton et al. published in 1972 (Guyton, Coleman, & Granger, 1972) was one of the first integrative models. The model has been continuously developed, the current version is called HumMod (Hester et al., 2011) and has more than 10 000 variables.
Such complexity requires proper modelling languages and tools in order to keep the model uncluttered. HumMod version 1.6.1 was reimplemented by Marek Matejak (Matejak & Kofranek, 2015) using Modelica modelling language and Physiolibrary (Mateják et al., 2014) which significantly contributed to its clarity.
For instance a phenomenon that needs an integrative modelling is hypertension as it requires modelling of the cardiovascular and respiratory systems, the kidney, the water, osmotic and electrolyte balance, the oxygen and carbon dioxide transport, and the neural and hormonal regulations. We have participated in a project discussing several integrative models applied on simulation of high-salt diet induced hypertension (Kurtz et al., 2018).
This paper is attached as Appendix 2. Guyton's classic 1972 model (Guyton et al., 1972) and its 2 evolved derivatives Quantitative Cardiovascular Physiology-2005 and HumMod-3.0.4 (Hester et al., 2011) were compared to experimental data.
None of the models accurately predicts the changes in sodium balance, cardiac output and systemic vascular resistance in response to the increased salt diet. As the source code of the original Guyton 1972 model was not available, we had to reimplement it according to the NASA report (White, 1973).
The implementation was tested using some Guyton's original protocols, whose results are available. Then a new protocol for the testing purposes were implemented and simulated.