# Machine learning for biophysical heart modelling in high dimension parameter spaces

The heart is a complex, dynamic organ consisting of billions of individual cells working electro-mechanically in concert. Key to this is that these cells that are excitable, able to generate an electrical action potential, which in turn triggers contraction and ultimately pumping of blood to the rest of the body. These are incredibly well studies systems, and the electrical behavior of individual cells can be accurately modeled using systems of ordinary differential equations (ODEs) describing the flow of keys ions through the cell and its surroundings.

A promising new technology known as “heart on chip” systems opens up the possibility to study these heart cells in an environment that is similar to the environment inside the body. Using these systems, consisting of microfluidically controlled cardiac cells derived from human induced pluripotent stem cells (hIPSCs), we are able to measure properties that can be used to fit biophysical mathematical models. These models can then be used to ask questions like “how would these cells behave when exposed to a drug”, key questions for the development of safe and effective drugs.

One way to fit the mathematical model to the data, is to select some control parameters in the model and minimize a cost function that represent the mismatch between data and model. However, such optimization problems might have several optimal solutions, and furthermore, the dimensionality of these systems means that an adequate search of the space is outside modern computational capabilities. It is therefore of interest to look into more data-driven methods, such as neural networks to create classifiers that can be used to determine models based on some input data.

We will generate a training data set using simulated data as well as experimental traces to train a machine learning model that can be used as a fast an accurate predictor of cell behavior that will be used to both better understand these cells as well as accurately find heterogeneous effects from noisy data.

### Goal

The goal of the project is to investigate different machine learning methods for fitting cardiac cell models to experimental measurements of intracellular calcium and transmembrane potential signals to infer knowledge based biophysical relationships.

The first step will be to learn how to solve the governing biophysical models and investigate how the output of the model changes with respect to changes in the input parameters. We can then choose parameters to vary, and generate simulated data based on different input parameter sets. Machine learning algorithms can then be trained on these simulated data sets to see how they can classify or regress changes in the underlying model. We will also look at how these algorithms behave in presence of noise.

### Learning outcome

The student will learn about how we can model cardiac cells using system of ODEs and thereby gain basic knowledge of cardiac electrophysiology. The student will also learn different machine learning techniques for creating models based on simulated data.

A major part of the project will be to implement these models in python using some machine learning library (e.g PyTorch, Keras or Tensorflow), so the student will also be exposed to software of high importance in industry and research today.

### Qualifications

Basic understanding of ordinary differential equations

Basic programming skills in python

Interested in machine learning and computing

### Supervisors

- Simon Funke
- Sebastian Mitusch
- Henrik Nicolay Finsberg
- Samuel Wall

### Collaboration partners

UC Berkeley