Mathematician Federica Caforio is developing methods for so-called cardiac digital twins: computational models of real hearts that integrate electrical signal transmission, tissue mechanics and blood flow. The starting point for her research was seed funding: the L’Oréal Fellowship for Women in Science, which Caforio received in 2023. This enabled her to develop a proof of concept – initially using synthetic data, i.e. experimental data generated entirely on a computer. The aim was to draw conclusions about the passive properties of heart tissue from information on displacement and strain. In other words: how stiff is the tissue? How does it react to stress?
Caforio is now taking things a step further. As part of a UFO (Unconventional Research) project funded by the Province of Styria, she is working on the active properties of the heart – specifically, the contraction that turns the organ into a pump. This is because heart tissue is not just soft and elastic. It also generates active ‘stress’, contracting and thereby driving the circulatory system. Every heart has its own characteristics.
Mathematically, this personalisation is highly complex. The model contains numerous parameters: some describe electrical processes, others mechanical deformations or the interaction with blood flow. The task of the researchers at the Institute of Mathematics is to adjust these parameters so that the simulation matches clinical measurement data as closely as possible. To complicate matters, different combinations of parameters can produce similar results.
Caforio’s approach therefore combines classical mathematical models with machine learning. At its heart are Physics-Informed Neural Networks, or PINNs for short. Unlike purely data-driven neural networks, they are designed not only to fit existing data but also to take physical laws into account. Put simply: the network does not learn a plausible form, but one that also obeys the underlying equations.
This is crucial for cardiac research. Whilst a predicted displacement field may, at first glance, match the measured data, it only becomes medically useful if it also makes physical sense. With PINNs, therefore, both factors are incorporated into the calculation: fidelity to the data and fidelity to physics, such as differential equations, boundary conditions and initial conditions.
International network
Since April 2026, Caforio has been leading a BioTechMed-Graz Young Researcher Group. The three-year project aims to expand the method and make it more robust: moving from individual mechanical problems to multiphysical models that consider electrophysiology and mechanics together. It is based on a strong international collaborative network with partners at MedUni Graz (Computational Cardiology Lab, Cardiology), Graz University of Technology, the IDea-Lab, and renowned research groups at the Politecnico di Milano, the University of Trento and the Pontificia Universidad Católica de Chile. The collaboration brings together expertise in cardiology, mathematical modelling, computational science and artificial intelligence.
The clinical aim is clear: to visualise tissue changes non-invasively. Scarring in the heart muscle is of particular interest. Such scar tissue can be stiffer than healthy tissue and lose its ability to contract. If a parameter estimation pipeline can detect such spatially varying properties, it could show doctors where scarring is located and how pronounced it is.
Currently, late gadolinium-enhanced MRI – an MRI technique using contrast agents – is often regarded as the gold standard for detecting such scarring. However, it is expensive, not suitable for all patients and can be problematic, particularly for those with kidney problems. Caforio’s long-term vision is therefore to develop an alternative: existing image and motion data could be used to create a virtual representation that visualises relevant tissue changes without the need for additional contrast agent.
A digital twin of the heart would then be more than just a pretty picture on a screen. It could be used to refine diagnoses and test potential treatments in advance. Instead of trying out several procedures or treatment options one after the other, doctors could in future first simulate on the virtual heart what is likely to happen inside the body.