Hands on Lumped Parameter Models with Workshop | JuliaCon 2023

The lumped-parameter model (also called lumped-element model) simplifies the description of the behavior of spatially distributed physical systems, such as electrical circuits, into a topology consisting of discrete entities that approximate the behavior of the distributed system under certain assumptions. It is useful in electrical systems (including electronics), mechanical multi-body systems, heat transfer, acoustics and circulatory mechanics. Our focus in this workshop will will be on the dynamics of the circulatory system, or cardio-vascular system. Within the realm of circulatory system mechanics, lumped parameter (0D) modelling offers the unique ability to examine both cardiac function and global hemodynamics within the context of a single model. Due to the interconnected nature of the cardiovascular system, being able to quantify both is crucial for the effective prediction and diagnosis of cardiovascular diseases. Lumped parameter modelling derives one of its main strengths from the minimal computation time required to solve ODEs and algebraic equations. Furthermore, the relatively simple structure of the model allows most personalized simulations to be automated. Meaning the ability to embed these lumped parameter models into a clinical workflow could one day become trivial. is an acausal modelling library, built on top of and the SciML ecosystem. This tight integration means that once the model is set up, global optimization, sensitivity analysis, uncertainty analysis, ..., are just a few lines of code away. And due to the speed of Julia, even high-dimensional parameter models become feasible for a high-abstraction level modeling system. In this workshop we will introduce in a hands on fashion. We will walk users through the fundamentals of acausal modelling, and will then demonstrate how we can build up complex cardio-vascular network from simple elements in a “if you can draw it, you can model it paradigm“ by simply connecting the individual components. We will then use the power of , , and other packagers in the SciML ecosystem to show how the created models can be fed into the wider analysis framework. We will demonstrate how new models/elements can be implemented. We will then take the user through the event handling feature within ModelingToolkit to demonstrate how we can recreate complex physiological components which open a new era of modelling which other platforms can’t support. In the second half of the workshop we will focus on model analysis and demonstrate how our pre-built circulation models can be used within relevant research. The participants will leave with a clear understanding of how to use the Julia package ecosystem to efficiently handle these difficult circulation models, and will have a new perspective for understanding the model analysis advances made by Julia in recent years.