Hans Dierckx' Research Page

About me

Mon, 12 Jan 2026 00:00:00 +0000

This is the research page of Dr. Hans Dierckx.

Our team members:

Arstanbek Okenov

Tue, 16 Dec 2025 00:00:00 +0000

Publication in Chaos

Tue, 02 Dec 2025 00:00:00 +0000

When electrical waves do not propagate coherently through the heart, a dangerous arrhythmia can form.

Due to the apparent complexity of these patterns, it is challenging to see what is going on, and to devise appropriate intervention. Especially the chaotic phase during which wave breaks form and either vanish or organise into spirals, is hard to grasp.

Recently, we found that in complex excitation patterns, special points exist: heads (end points of fronts), tails (end points of wave backs) and pivots (end points of conduction blocks). We showed that these points persist over time and space as they possess topological charge.

In our paper in Chaos, resulting from the Master’s thesis of Aaron Gobeyn, we design and implement fast algorithms for the detection of head and tail quasiparticles.

Figure reprinted from Gobeyn et al., Chaos 35, 123105 (2025), licensed under a Creative Commons Attribution (CC BY) license

Outreach story in LUMC newsletter

Tue, 21 Oct 2025 00:00:00 +0000

Following our recent publication in Physical Review Letters, the LUMC press office translated the results into an accessible story, which you can read here.

Publication in Physical Review Letters

Thu, 18 Sep 2025 00:00:00 +0000

There are many open questions on how the patterns of electrical activity are organized inside the cardiac wall. Our paper in Physical Review Letters sheds new light on this: the conduction blocks that create and sustain arrhythmia can be quite general surfaces, with handles and side branches. The special points (quasi-particles, cardions) that we identified in surface recordings, now become three types of closed curves.

We also got two mathematical bonuses: the twiston seen in simulations by Fenton and Karma (Chaos, 1998) is a cardion of co-dimension 3, and one can create an untwisted scroll wave that rotates around a M"obius strip!

In view of future applications, we present a mathematically consistent way to classify and analyse three-dimensional patterns in excitable media.

Desmond defends his PhD

Tue, 10 Jun 2025 00:00:00 +0000

After four years of intense research, Desmond Kabus received his dual PhD degree from KU Leuven and Leiden University Medical Centre. Congratulations on behalf of your promoters Hans Dierckx and Daniel Pijnappels!

Lecture on digital innovation in healthcare

Thu, 22 May 2025 00:00:00 +0000

I was invited by colleague Dr. Edris Mahtab to give a talk about digital innovation for the Innovation Day of the Cardiothoracic Surgeons from the University Medical Centers of Amsterdam and Leiden.

Debora Hoogendijk

Fri, 07 Feb 2025 00:00:00 +0000

Promotors: Hans Dierckx, Vivi Rottschäfer
Supervisors: Tim De Coster
Subject: Spiral wave interaction
Studied Mathematics
Year 2024-2025

Bram Schalkwijk

Sat, 01 Feb 2025 00:00:00 +0000

Promotors: Edris Mahtab, Hans Dierckx
Supervisors: Samuel Max, Laurent Coopmans
Subject: Development of a VR Application for ECMO Training with Dynamic Patient Physiology Modelling
Studied Technical Medicine
Year 2024-2025

Moving to LUMC

Thu, 16 Jan 2025 00:00:00 +0000

Here I am even closer to experimental data and clinicians. I am part of the Experimental Cardiology Laboratory, working closely with Prof. Daniel Pijnappels, Dr. Twan de Vries and Dr. Vincent Portero.

Feynman-like diagrams in the heart!

Fri, 22 Nov 2024 00:00:00 +0000

Electrical patterns in the heart drive its mechanical contraction and therefore the pumping of blood. Since the cardiac muscle cells can transmit the electrical signal themselves, this pattern can go wild, leading to dangerous arrhythmias.

To understand and control complexity of excitation patterns is still challenging. In our paper, we asked ourselves: “What are the most fundamental building blocks of such a pattern, as seen on the heart’s surface?”

We started by considering that elementary (topological) building blocks are the regions of excited and unexcited tissue and the borders between them. Additionally, there are conduction blocks, i.e. zones where the next wave cannot yet propagate. Now, if one colors the medium in according to these 3 regions (excited, unexcited, local block), there are special points where these regions meet: heads (end points of wave fronts) and tails (end points of wave backs). These points should always be pairwise created or annihilated (with opposite chirality). Also, if one supposes that conduction blocks are thin, its end points should also appear in pairs.

The three sets of points are therefore akin to elementary particles in physics (say the 3 flavours of quarks). We propose to call these cardions, in analogy to baryons, fermions, twistons etc.

To our own surprise, we found that during ’normal’ evolution of patterns, the cardions bind together into `core particles’, which could explain why they were not observed before. During more ‘violent’ events, such as arrhythmia formation and termination, the cardions recombine.

To keep track of the topological changes during arrhythmia formation, we propose a diagrammatic way, see above. Presently, this is a schematic drawing reminiscent of the famous Feynman diagrams in physics; however, in our case there is (not yet) a deeper meaning such as the path integrals or cross-section calculations in particle physics.

Nonetheless, we show that heads, tails and pivots all have their own topological charge ($\pm$ 1/2), which constrains the possible interactions.

We are currently developing automated pipelines for cardion detection and analysis, which will enable to perform statistical analysis and systematically investigate arrhythmia initiation mechanisms.

Figure adapted from Arno et al., Scientific Reports volume 14, 28962 (2024), licensed under a Creative Commons Attribution (CC BY) license

LUMC Fellowship awarded

Tue, 19 Nov 2024 00:00:00 +0000

I received the 2024 LUMC fellowship, a competitive grant that will enable me to build my own research line at the Leiden University Medical Center. The topic of this grant is Creation of predictive in silico models from cardiac tissues and patient recordings to unravel arrhythmia mechanisms.

Attending CINC and Cardiac Physiome Conferences

Fri, 13 Sep 2024 00:00:00 +0000

I traveled to Germany to speak at two consecutive conferences: Computing in Cardiology (CINC, Karlsruhe) and the Cardiac Physiome Meeting (Freiburg)

SIAM-UQ24 conference

Tue, 27 Feb 2024 00:00:00 +0000

Within the BICEPS project, we want to incorporate uncertainty quantification into cardiac modeling. This conference was a perfect opportunity to present our first results. Being part of a mini-symposium about …, two presentations uncovered our work on the project so far. Marie Cloet gave a talk about … . Maarten Volkaerts, member of the NUMA research team and also part of the BICEPS project, presented his results on … .

Open Source

Thu, 01 Feb 2024 00:00:00 +0000

Cover image generated by Dall-E 3.

Publications

Tue, 30 Jan 2024 00:00:00 +0000

See my profile on Orcid

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New publication by Kabus et al. 2024

Thu, 25 Jan 2024 00:00:00 +0000

They introduce a fast and efficient data-driven methodology for creating reliable mathematical models of cardiac excitation using recorded videos at the tissue level.

In a nutshell, the paper demonstrates that recorded movies at the tissue level can be used to swiftly generate reliable mathematical models for cardiac tissue excitation. By leveraging exponentially weighed moving averages and polynomial regression, a rapid and efficient pipeline for creating in-silico models is unlocked. This method takes just a few minutes!

Congratulations to Desmond and his co-authors from the Leiden University Medical Center, Tim De Coster, Antoine de Vries and Daniel Pijnappels.

The full paper can be found here:
https://doi.org/10.1016/j.compbiomed.2024.107949

Junior College 2024

Tue, 23 Jan 2024 00:00:00 +0000

Video from a previous edition:

Seminar talk by Dylan Vermoortele

Mon, 11 Dec 2023 00:00:00 +0000

In his talk he elucidated how Sudden Cardiac Death is a complex interplay of different systems. Dylan demonstrated the methods he developed to study these systems in an experimental setting.

Many thanks to Dylan for coming over to Kortrijk and to the physics group at Kulak, with specifically Dr. Wouter Deleersnyder for organizing this seminar.

New publication by Cloet et al. 2023

Fri, 17 Nov 2023 00:00:00 +0000

The general topic is excitable systems: Think of the spread of rumor, flow of information in the brain or electrical activation of cardiac tissue. These can all be modeled on a network, and by studying excitation patterns in the network, we can learn more about the behavior of news in social networks, brain cells and cardiac activation.

“Scroll Waves and Filaments in Excitable Media of Higher Spatial Dimension” is the result of research during Marie’s master’s thesis.

The published version can be consulted on the Physical Review Letters website:
https://doi.org/10.1103/PhysRevLett.131.208401

The paper is also available on arXiv:
https://doi.org/10.48550/arXiv.2304.14861

Cover image generated by Dall-E 3.

Aaron Gobeyn

Sun, 01 Oct 2023 00:00:00 +0000

Promotors: Prof. Hans Dierckx
Supervisors: Desmond Kabus
Subject: Detection and analysis of quasi-particles in excitable media
Studied Physics
Year 2023-2024

New publication by Li et al. 2023 including Hans Dierckx

Wed, 06 Sep 2023 00:00:00 +0000

Read the article here: https://doi.org/10.1103/PhysRevE.108.034218

Cover image generated by Dall-E 3.

New publication by Leenknegt et al. 2023

Mon, 10 Jul 2023 00:00:00 +0000

Read the article here: https://doi.org/10.3389/fphys.2023.1213218

Cover image generated by Dall-E 3.

Lecture of Hans Dierckx at the Bio Dynamics Days 2023

Wed, 21 Jun 2023 00:00:00 +0000

Are you doing research in mathematical biology? Here are five ideas that can be helpful along the way.

Analytical solutions are still valuable
Biology exhibits non-linear structures whose slow drift can be found via perturbation theory
Geometric principles are out there
Break free from old concepts if they don’t work
Can we spot overarching ideas?

Theory of rotors and arrhythmias

Thu, 01 Jun 2023 00:00:00 +0000

Fundamental building blocks

The contraction of our hearts is coordinated by a traveling non-linear wave of electrical depolarization, which locally triggers mechanical contraction of the cells. Hence, abnormal patterns lead to inefficient pumping of blood. Depending on the precise emergent pattern and where it takes place, this may lead to chronic fatigue, blood clot formation and stroke, or sudden cardiac death.

Remarkably, many of the precise patterns are still incompletely understood. The more complex patterns are a complicated interplay between wave fronts, wave backs and conduction blocks (when a front hits a wave back). Such conduction block may result in the formation of a spiral-shaped rotating pattern (also called scroll wave in 3D, or rotor by medical doctors) that sustains itself and was seen in tachycardia. However, experimentally observed rotors have shorter lifespan that those in simulations. In case of unstable rotors, they further break-up into an irregular pattern (fibrillation), of which chaotic behaviour is expected but not yet proven.

Previous fundamental achievements include: a geometric theory for wave fronts and rotor filaments; determining the minimal thickness below which no 3D instability will happen; extending the notion of filament tension to quasi-periodic cores as observed in experiments.

Ongoing research entails the elaboration of a new topological description that unifies the concepts of conduction block, quasi-periodic rotors and filaments via topological phase defects. Furthermore, these findings are combined with experimental data, for physics-based inversion and source reconstruction of cardiac signals.

Curved-space viewpoint on cardiac anisotropy

The cardiac muscle cells are organised in such a way that the conduction of the electrical waves through the heart go faster in one direction, called the fiber direction, than the other ones. This is comparable to the gps system that tells you, it will take 30 minutes to go from Kortrijk to Ghent when you take the highway instead of 50 minutes only using small roads. So we can redefine distance in terms of travelling time, instead of using the Euclidean distance.

In mathematics or physics terms, this comes down to endowing cardiac tissue with a metric tensor, and from geometric considerations, the heart then becomes a Riemannian manifold.

Using tensor calculus, geodesics and covariant derivatives, it is thereby possible to obtain general theoretical results on the time-evolution (drift and stability) of wave fronts and rotors in the heart. These efforts are laying the foundation for the field of “cardiac geometrodynamics”.

Your browser doesn't support HTML5 video. Here is a link to the video instead.

Application of mathematical physics concepts to cardiac excitation

Here is a non-exhaustive list of concepts from mathematical physics that are being used in our research:

Geodesics, metric tensors, curved space
Anisotropy of wave propagation can be handled elegantly using a curved-space formalism. A glimpse thereof was added to a famous cardiology textbook. \
Symmetry breaking
Wave fronts and rotors have less Euclidean symmetries than the reaction-diffusion equation, leading to critical eigenmodes of the linearized operator (Goldstone modes).
Bra-ket notation
In perturbation theory, we typically project onto the response functions, which can be written in Dirac’s notation: e.g. $\left<Y|PV\right>$. The use of quantum mechanical notation in biological context is sometimes confusing referees.
Particle-wave duality
In contrast to quantum mechanics, our operators are non-selfadjoint. As a result, the right-hand eigenfunctions are waves (spirals) while left-hand eigenfunctions are localized, like particles. This localization explains why it is so difficult to restore chaotic activity in the heart. See this great video.
Curved-space coordinate systems
In general relativity theory, it is customary to use nearly Euclidean coordinate systems, e.g. Gauss coordinates, Fermi coordinates or Riemann normal coordinates. We apply all of these in a biological context (and sometimes need to further extend them still).
Action principle
Part of the emerging rotor dynamics can be derived from an action principle.
Topological charge & defects
Cardiac rotors revolve around a rotor filament, which is a topological defect. We recently showed that the defect in 3D should be a phase defect surface.
String-like and brane-like dynamics
We previously showed that rotor filaments act as strings in a background space that is curved due to anisotropy. In the recent phase defect interpretation, filaments become brane-like objects that are phase defect surfaces. More topological constraints apply to the edges of those phase defect surfaces.
Green’s functions
Certain aspects can be dealt with classical superposition, e.g. forward calculation of electrograms and quantifying mechano-electrical feedback on rotor drift.
Branch cuts, complex analysis
Recent work shows that at the heart of a linear-core rotor, there is a phase discontinuity or phase defect.
Feynman-Hellman theorem
We use this theorem to calculate filament rigidity, which explains why in thin tissue slabs, full-fledged 3D instability cannot occur.
Pauli matrices and commutators
Even in three dimensions, rotation of scroll waves occurs in a plane, and the set of Pauli matrices is a suitable basis shape to calculate the shape of circular scroll wave cores, as well as the isotropic invariants of higher-order corrections.
Higher-dimensional embedding
We extended Wellner’s minimal principle for rotor filaments to inhomogeneous media by adding a fourth spatial dimension which restores homogeneity.
Schrödinger’s equation
The link between the diffusion and Schrödinger’s equation goes back a long time and has inspired the path integral formalism for quantum mechanics. Here, we explained paradoxical onset of ectopic (additional) heart beats using the analogy - in the other direction.

Building theory from experimental observations

To make the connection between theory and practice, we need to test our ideas on observations of excitation patterns in real hearts. However, these data are scarse, since it is not yet possible to view inside individual patients’ hearts.

An experimental method that can be used on explanted hearts is optical voltage mapping. Here, a voltage-sensitive dye is administered to cardiac tissue to visualize excitation patterns with high resolution. Our first analysis within the group of arrhythmia patterns provided by Prof. E. Tolkacheva (Minneapolis, USA) demonstrated that cardiac rotors in rabbit hearts are organised around extended phase defect lines, rather than point singularities, forcing us to rethink the classical topological approach to cardiac arrhythmia organisation. In the next paper, we also identified the phase defects in cell cultures of human immortalized atrial myocytes, grown in the Pijnappels lab (University of Leiden, the Netherlands).

In ongoing work, we are performing pattern analysis and reconstruction on intracardiac electrograms, as well as ultrasound recordings.

5th OpenCARP user meeting

Fri, 26 May 2023 00:00:00 +0000

Check out this event

SIAM-DS23 conference

Mon, 15 May 2023 00:00:00 +0000

Group photo in HeartKOR shirts

Tue, 02 May 2023 00:00:00 +0000

Visit of Thorrez' Lab

Fri, 28 Apr 2023 00:00:00 +0000

David Van Hee

Wed, 01 Mar 2023 00:00:00 +0000

Promotors: Hans Dierckx, Joeri van der Veken
Supervisors: Marie Cloet
Subject: Prediction of wave break locations in the heart from extrinsic curvature calculations
Studied Biophysics
Year 2022-2021

Junior College 2023

Tue, 10 Jan 2023 00:00:00 +0000

Video from last year’s edition:

Day of Science 2022

Sun, 27 Nov 2022 00:00:00 +0000

Saturday, 27th of November was a day attributed to science in Flanders. Here at kulak, many groups organised or workshop, show or exhibition to promote science and let the general public have a taste of the wonderful science that is done. HeartKOR was present as well with a presentation on the basics of the heart and cardiac arrhythmia, some posters and some interactive simulations both in 2D and 3D (By Fenton and Abouzar Kaboudian) so people could play with adding obstacles in a cardiac medium and generate electrical patterns in the heart connected to arrhythmia like spiral waves.

More info…

Look here as well…

Nathan Dermul

Tue, 01 Nov 2022 00:00:00 +0000

Contact details

📌 Office A342, Etienne Sabbelaan 53, 8500 Kortrijk
📧 Look up email address on KU Leuven Who’s Who
📚 Publications via Lirias
📑 Publications via ORCID
🌍 Profile on LinkedIn

Questions and answers

What did you study for you bachelor’s and master’s degree?

I got my bachelor’s and master’s degree in Physics and Astronomy from the University of Ghent. During these 5 years I got to explore a wide variety of elective subjects including biophysics, computational physics, machine learning and astrophysics. I always loved the great variety of the education and was happy to combine ML techniques and astronomy in my master thesis.

Why did you choose to do a PhD in this team?

This research is situated in a very wide research domain, combining different scientific fields, while also juggling the wildly different scales necessary to tackle the problems accurately. Such kind of endeavors can also be found in astrophysical settings and lay very close to my heart. Luckely some elective courses during my education introduced me to interesting biophysical questions and their massive impact on human health, so I was able to find this opportunity.

What would you say is your speciality within the research group?

Focusing on the inversion modelling of cardiac wave propagation both in the electrical and mechanical domain, I have to make sure to use as much of the physical and clinical information as possible in order to obtain a fast yet accurate model. So I would say finding the best parts of every field and facilitating them to be friends is key in my research.

What are your hobbies/after work activities?

I’m trying to learn some music theory and piano. In addition to annoying everyone around me with ears, I like to read, go to the gym, play video games or gather with as much people as possible and pull out some nice board games.

For about 23 years of my life I couldn’t stand realistic, bloody images, so fainting during the rabbit dissection was nothing new. However as I wanted to go into the cardiac scene, I was able to (almost) completely cure my blood phobia after a few weeks of exposing myself to bloody movies, how-to-draw-blood yt tutorials and emergency hospital shows.

Marie Cloet

Thu, 13 Oct 2022 00:00:00 +0000

Promotors: Giovanni Samaey, Piet Claus, Hans Dierckx
Subject: Uncertainty quantification in cardiac excitation models

Contact details

📌 Office A342, Etienne Sabbelaan 53, 8500 Kortrijk
📧 Look up email address on KU Leuven Who’s Who
📚 Publications via Lirias
📑 Publications via ORCID
🌍 Profile on LinkedIn

Questions and answers

What did you study for your bachelor’s and master’s degree?

I studied Mathematics at KU Leuven Campus Kortrijk in my bachelor’s and I completed my Master in Applied Mathematics, with research option, at KU Leuven.

Why did you start a PhD in this group?

Since my bachelor’s thesis on the computation of the ECG out of a Cellular Automaton model of the heart, I was sold for the research conducted here. It’s a perfect match between mathematical methods and a life-saving, relevant biological application.

What would you say is your speciality within the research group?

In my Master’s, I chose both courses in applied mathematics, such as engineering science, plasma astrophysics and theoretical physics, and courses in pure mathematics. I think the skill I want to deploy is translating abstract mathematical concepts to useful applications and vice versa, in a way that the methods are both practical and rigorously underpinned.

What is your favorite part of doing a PhD?

I have only started, but I would say the act of doing science together. At Kulak, there are many colleages with whom I can discuss my research and my educational tasks. It’s cool to reach further with the support of your peers.

What is your least favorite part?

To be honest, I have not done anything that I did not like thus far… Besides the administration to fulfill the bureaucratic formalities, that’s mostly quite a burden!

What are your hobbies/after work activities?

I play rugby in the women’s team of Rugby RSL, the Bullets. Furthermore, I am member of the running club Dapalo in my home town. During my studies, I have been active as a volunteer in the chiro, which is a youth movement. Now and then, I still help during their activities.

In my last year of high school, I went on an exchange to Denmark with AFS. Now, I still understand Danish and other related Scandinavian languages. Which is helpful, since those countries are my favorite destination.

Master thesis at KU Leuven Kortrijk

Promotor: Hans Dierckx
Supervisor: Louise Arno
Subject: Non-linear waves in excitable networks
Studied: (applied) Mathematics
Year 2021-2022

Research stay in Bordeaux

Thu, 13 Oct 2022 00:00:00 +0000

“An amazing experience and amazing people! Liryc is a place where modeling meets the clinic every day. Inspiring! I look forward to working with them on phase defects during arrhythmia.”

Louise

Scientist@School

Wed, 12 Oct 2022 00:00:00 +0000

In January, Lore went to Sint-Paulus College in Wevelgem to give a lecture about some of our research done here at HeartKOR! They learned how mathematics and physics can be used to help solve cardiac arrhythmias.

The fifth grade students of this high school, together with their teacher, Lore Seynhaeve, tried to recreate a spiral wave!

Not only the Sint-Paulus College will be able to enjoy our lectures. Lore is also going to the Broederschool in Roeselare, and Louise will present our research to the young minds of school Atheneum Bellevue Izegem . This is all part of the program Scientist@School, organized by KU Leuven. Pictures of these event can be found in the foto album.

Louise went to Atheneum Bellevue in Izegem to give the same lecture about some of our research done here at HeartKOR! They learned how mathematics and physics can be used to help solve cardiac arrhythmias.

Another group photo at the KULAK orchard

Mon, 10 Oct 2022 00:00:00 +0000

Mathematics exhibition "Imaginary"

Fri, 07 Oct 2022 00:00:00 +0000

More info

New publication by Kabus et al. 2022

Tue, 12 Jul 2022 00:00:00 +0000

Desmond Kabus has published this paper with Louise Arno, Lore Leenknegt, Alexander Panfilov, and Hans Dierckx.

The full paper can be found here:
https://doi.org/10.1371/journal.pone.0271351

Cover image generated by Dall-E 3.

Summer School in Bordeaux

Sun, 03 Jul 2022 00:00:00 +0000

Info for students

Tue, 21 Jun 2022 00:00:00 +0000

Despite huge advances in the prevention and therapy of cardiac arrhythmias, they are still an important cause of death worldwide.

When heart rhythm disorders affect the lower cardiac chambers (ventricles), which pump blood to the body, the normal pumping of blood is suppressed. This makes ventrical arrhythmias often lethal.

Cardiac arrhythmias that occur in the upper chambers (atria), which pump blood to the ventricles, are not immediately lethal. Still, they cause blood clot formation; it is thought that that cardiac arrhythmias are responsible for at least a third of stroke cases.

Since the heartbeat originates from biochemical processes at the cell scale, understanding and managing cardiac arrhythmias requires an interdisciplinary collaboration: from fundamental science (biochemistry, math, physics, electrophysiology) to the patients’ bedside (engineering, data analysis, cardiology).

An important challenge is the multiscale nature of the problem: how can we relate fast biophysical processes in the cell membrane to large-scale electrical pattern formation in the heart? A first step is the creation of mathematical models, which has been performed over the past 50 years and has lead to better understanding of the electrical phenomena in the heart. To integrate information from the cellular to the organ level can be done not only using numerical simulations, but also with analytical methods.

Join us!

If you are a master student and want to write a master’s thesis on our topics, feel free to contact us.

In particular, bachelor, master and PhD thesis topics are available in several subdomains (and their intersection).

Depending on the candidate, the project can be oriented more towards theory or applied science:

theoretical/mathematical: differential geometry in the heart, topology of emerging patterns, curvature-driven dynamics, asymptotic solutions to partial differential equations, particle-like analysis using Feynman diagrams, analogies with string and brane theory.
computational: forward and inverse solutions of non-linear wave propagation in a cardiac geometry, physical models for the generation of electrical signals inside the heart.
applied: finding phase defects in movies of cardiac activation, estimate cardiac activity from deformation images, uncovering the physical laws governing phase evolution from data, machine learning, uncertainty quantification using Bayes’ rule.

Previous thesis topics

Check out previous master thesis topics via the tag: Master thesis
BSc:
- Interaction laws between spiral waves: Debora Hoogendijk (2025, Mathematics)
- Determining the dimension of the attractor in the heart: Maxime Devos (2022, Mathematics)
- Monodomain simulations of the ventricles during sinus rhythm: Phebe Coussens (2022, Mathematics)
- Chaos and Brownian motion in the heart: Lore Zwaenepoel, Ine Malfait and Jade Pauwelyn (2021-2022, Physics)
- Counting cell nuclei using machine learning: Quentin De Rore, Ibrahim El Kaddouri, Emiel Vanspranghels, Henri Vermeersch (2021, Engineering)
- Numerical detection of phase defects in optical mapping data: Jan Quan, Maarten Vanmarcke and Nhan T. Nguyen (2020, Engineering)
- Imposing transmural differences in action potential duration via Laplace’s equation: Dieter Debrauwer, Joren Matthys (2020, Mathematics)
- A cellullar automaton for cardiac excitation: Niels Bertier, Nika Pountouchachvili, Xander Fransen (2020, Mathematics)
- Calculating the ECG from a cellular automaton: Marie Cloet, Emiel Raveschot (2020, Mathematics)
- Stimulating the heart from the Purkinje fibres: Aldo Doggen (2020-2021, Mathematics)

Miscellaneous research topics

Tue, 21 Jun 2022 00:00:00 +0000

Geometry-driven dynamics in reaction-diffusion systems

The cardiac monodomain equations can be formulated as a set of parabolic differential equations of the reaction-diffusion type. Most of our theoretical results apply to the wide class of reaction-diffusion equations, only the existence of stable traveling waves or vortices needs to be assumed.

Therefore, our findings also apply to other reaction-diffusion systems, such as active diffusion of substances across the cell membrane, pattern formation on animal furs, signaling waves at the cellular of multicellular level, oxidation waves, and oscillating chemical reactions (e.g. the Belousov-Zhabotinsky (BZ) reaction).

One of our theoretical predictions on the drift of scroll waves in a medium of stepwise thickness, inspired by a cardiac application, was shortly thereafter experimentally verified in the BZ reaction by Steinbock et al:

H. Ke, Z. Zhang, and O. Steinbock, “Scroll Wave Drift Along Steps, Troughs, and Corners”, Chaos 25, 064303, 1-7, 2015 pdf

Spiral wave chimeras

Spiral wave chimeras are emergent structures in oscillatory media, with spatial coexistance of synchronized and asynchronized regions. The first chimeras were found in non-locally coupled media (i.e. with action-at-a-distance), but in collaboration with B.W. Li, we showed that also a classical reaction-diffusion system can generate spiral wave chimeras.

Cover image generated by Dall-E 3.

Data analysis and inversion

Fri, 17 Jun 2022 00:00:00 +0000

Ultrasound imaging of arrhythmias

Even though various heart rhythm disorders can be recognized by electrocardiograms, the exact three-dimensional spatio-temporal pattern of the cardiac activation sequence throughout the cardiac wall is not well understood during rhythm disorders. Imaging these complex wave patterns can be done directly by plunging needle electrodes or needle catheters into the heart, however in human patients this is impossible to do and indirect inverse electrocardiographic techniques are being developed in order to infer the whole image from surface measurements. The best known example is the electrocardiogram (ECG), but to find the precise activation pattern from body-surface measurements is an incompletely solved inverse problem.

A pilot study from 2018 [1] showed that mechanical deformation of the heart, which can be estimated by ultrasound data, is closely linked to the electrical phenomena during cardiac arrhythmias. This idea opens up new ways of gaining insight into the complex, inherently 3D, electrical patterns in a fast and non-invasive manner. Recent studies have shown that imaging the electromechanical activation sequence with ultrasound data can be helpfull in certain situations (see for example in silico [2], in vivo experiments [3]).

In the ICARUS project, we set out to expand upon this technique and bring it to a clinically feasible tool, working in close collaboration the University Hospital UZ Leuven (Gasthuisberg). This collaboration involves the Cardiovascular Imaging and Dynamics group of Prof. Jan Dhooge and the group of Prof. Joris Ector, head of ablation therapies at the hospital. By combining expertise in mathematical modelling, echocardiography and clinical experience, we will advance our understanding of the three-dimensional electrical patterns and improve diagnosis and localization of cardiac arrhythmias.

[1] Christoph, J., Chebbok, M., Richter, C., Schröder-Schetelig, J., Bittihn, P., Stein, S., … Luther, S. (2018). Electromechanical vortex filaments during cardiac fibrillation, Nature, 555(7698), 667–672. https://doi.org/10.1038/nature26001

[2] Lebert, J., & Christoph, J. (2019). Synchronization-based reconstruction of electromechanical wave dynamics in elastic excitable media. Chaos, 29(9), https://doi.org/10.1063/1.5101041

[3] Grubb, C. S., Melki, L., Wang, D. Y., Peacock, J., Dizon, J., Iyer, V., … Wan, E. Y. (2020). Noninvasive localization of cardiac arrhythmias using electromechanical wave imaging. Science Translational Medicine, 12(536). https://doi.org/10.1126/scitranslmed.aax6111

Inversion of cardiac electrograms

When cardiac myocytes activate or deactivate, they act as electrical dipole sources, generating a potential field in the torso. This extracellular potential is recorded on the cardiac surface during surgery, or on the body surface, where it is known as the electrocardiogram (ECG). While the ECG is routinely used to diagnose and classify arrhythmias, it is still not possible to accurately reconstruct the arrhythmia sources in the heart from body-surface recordings.

As a step-up to ECG reconstruction, we aim to first solve the inverse problem for intracardiac electrograms (iEGM). From measurements with electrodes on the inner cardiac surface (endocardium), we seek to infer the 4D wave pattern inside the myocardial wall using physics-based inversion methods.

Cover image source: Griffin Health

Towards a digital twin of the heart

Fri, 17 Jun 2022 00:00:00 +0000

Numerical modeling of arrhythmias

We have our own written C++-OpenMPI software, called Ithildin, to perform cardiac simulations using different geometries for the heart tissue. For electrogram simulations, we use the open cardiac electrophysiology simulator for in-silico experiments openCARP[1].

With these tools, we can perform a large variety of simulations to study different aspects of cardiac arrhythmias. In forward modeling, we seek quantitative predictions of pattern evolution and electrogram shapes.

[1] Plank, G., Loewe A., Neic. A et al. (2021). The openCARP simulation environment for cardiac electrophysiology. Computer Methods and Programs in Biomedicine 2021;208:106223. doi:10.1016/j.cmpb.2021.106223 *[2] Kabus D, Cloet M, Zemlin C, Bernus O, Dierckx H (2024). The Ithildin library for efficient numerical solution of anisotropic reaction-diffusion problems in excitable media. PLoS ONE 19(9): e0303674. [https://doi.org/10.1371/journal.pone.0303674] (https://doi.org/10.1371/journal.pone.0303674)

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Modeling the cardiac electrogram

Despite its widespread use, there are still fundamental insights lacking on how substrate parameters affect intracardiac electrograms, and which information can be inferred from electrogram recordings. For this, we are collaborating with A.P. Panfilov (Ghent University) and K. Zeppenfeld (University of Leiden) and P. Claus (KU Leuven).

Creation of individual models from machine learning

Mathematical models of heart function have been historically derived from detailed measurements of currents across the cell membrane. When applying the resulting model to a patient, it is silently assumed that the original model describes also the excitation properties of that person. As an alternative, we use machine learning methods to mimic this entire process and directly learn from recordings taken at the tissue scale in a specific heart.

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Experiments in the Gasthuisberg hospital

Wed, 01 Jun 2022 00:00:00 +0000

Lab visit in Leiden

Thu, 07 Apr 2022 00:00:00 +0000

Desmond is doing a joint PhD with LUMC in Leiden. Louise joined him for two days and visited the lab there! There, she could see the very thin slab of cardiac cell cultures and how they are contracting while electrical pulses were passing through them. A very exciting and interesting visit! We hope to go there soon to visit Desmond and the lab there with the entire team!

EHRA conference 2022

Tue, 05 Apr 2022 00:00:00 +0000

Desmond Kabus and Lore Leenknegt have presented e-posters at the EHRA conference in Copenhagen in April!

Desmond showed how to reliably detect phase defect lines in the centres of spiral waves. These lines can be used to get additional information about the electrical properties of heart muscle tissue. Lore presented on the effect of the wall thickness on the properties of the electrogram signal and how this can be analytically approximated.

Luckily, Nathan and Louise joined them at the conference, making it a very interesting, educational and fun experience!

DAE meets HeartKOR and KULAK

Thu, 31 Mar 2022 00:00:00 +0000

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Project by Judith Verdonck

The electrical waves controlling the heart beat behave much like forest fires, just on completely different time scales. Video by Judith Verdonck for her graduation project at Digital Arts and Entertainment:

Project by Robbe Casier

If trees would regrow faster, forest fires could travel in never-ending spiral waves. Terrifying! This is much like spiral waves that form in the heart during cardiac arrhythmias. Video by Robbe Casier for his graduation project at Digital Arts and Entertainment:

Junior College 2022

Thu, 03 Mar 2022 00:00:00 +0000

This month, the online lectures of junior college are published! Prof. Hans Dierckx, teamleader of heartKOR gave a lecture on cardiac arrhythmias and how this very hot and relevant research area needs mathematics and physics! Check out this lecture here.

This is an initiative that allows students in third grade to check out different subjects and get acquainted with scientific research and teaching style.

Brecht Vandenborre

Tue, 01 Mar 2022 00:00:00 +0000

Promotors: Hans Dierckx, Piet Claus
Supervisors: Lore Leenknegt, Dylan Vermoortele
Subject: The inverse problem of the electrogram
Studied Biophysics
Year 2021-2022

Group photo at the KULAK orchard

Wed, 02 Feb 2022 00:00:00 +0000

Group photo at the Kortrijk Christmas market

Thu, 20 Jan 2022 00:00:00 +0000

Children's university

Wed, 03 Nov 2021 00:00:00 +0000

Tell me more…

Group photo before the University Trail

Thu, 14 Oct 2021 00:00:00 +0000

Group photo at the staff party 2021

Tue, 28 Sep 2021 00:00:00 +0000

Research Day

Wed, 15 Sep 2021 00:00:00 +0000

More about this event…

Can we solve heart problems with math?

Wed, 03 Mar 2021 00:00:00 +0000

Link to Article

Desmond Kabus

Mon, 01 Feb 2021 00:00:00 +0000

Contact Details

📌 Office A330, Etienne Sabbelaan 53, 8500 Kortrijk
📧 Look up email address on KU Leuven Who’s Who
📚 Publications via Lirias
📑 Publications via ORCID
🌍 Personal website
🌍 Profile on LinkedIn

Questions and answers

What did you study for your bachelor’s and master’s degree?

For my B.Sc. and M.Sc. degrees, I studied theoretical physics at the Institute for Computational Plasma Physics at Ruhr-Universität Bochum, Germany. In terms of equations, modelling a plasma and the electrical patterns in the heart have a surprising amount of similarity! Lots of methods that can therefore transferred between those two subjects. My research for my master’s thesis was focused on a simplified version of the inverse problem of electrocardiography. In simpler terms, I used mathematics to find where certain conduction defects are located in idealised heart muscle tissue from electrical measurements inside the heart chambers. For this, I used optimisation strategies from both machine learning and the more classical mathematical approaches, such as the adjoint state method.

Why did you choose to do a PhD in this group?

Since I already got to know and love cardiology in my previous studies, it was a natural next step to look for PhD positions in the field. When I then saw the vacancy and figured out that I had already quoted some of the people involved in this project back in my Bachelor’s thesis, I knew that I found the group where I fit in perfectly.

What would you say is your speciality within the research group?

The technical nitty-gritty: algorithms, machine learning, and programming with C, C++, Python, etc. on GNU/Linux. All of this of course applied to the heart! To me it is exciting see how close I can push a computer to its limits for solving the challenging problems popping up everywhere in cardiology.

What is your favorite part of doing a PhD?

I love that I get to on the one hand explore the mathematics of cardiac electrophysiology with Hans Dierckx’ group at KU Leuven and on the other hand get to experience the cutting edge of its experimental side at the Laboratory of Cardiology with Daniël Pijnappels at Leiden University Medical Center in the Netherlands.

What is your least favorite part?

Checking your simulation that already ran for hours, realising that it failed, and therefore having to start from scratch...

What are your hobbies/after work activities?

I like many things such as travelling, video games and water sports. I especially love sailing in all places; lakes, canals and of course the sea! In my spare time, I sometimes even work as a sailing instructor. I like to combine the work trips for my doctorate research with exploring the places they take me.

At the moment when I decided that I want to do a PhD, I was picking blueberries in New Zealand’s Far North.

Lore Leenknegt

Sat, 01 Aug 2020 00:00:00 +0000

Contact details

Questions and answers

What did you study for your bachelor’s and master’s degree?

First I obtained a bachelor in Physics, after which I started a master in Biophysics. I realized I really like combining the theoretical concepts of physics and computational methods with a more applied area like biology, biochemistry, biotechnology, medicine, …

Why did you choose to do a PhD in this group?

As said before, my interests and studies lie within the broad field of biophysics. With the research topics in this group, knowledge and skills from different disciplines are combined. This variability is something I greatly enjoy, as well as the opportunity to use computational skills in scientific research. I also very much like the fact that in an indirect way, my research could end up helping people suffer less.

What would you say is your speciality within the research group?

The study of cardiac electrograms. How the tissue properties and catheter orientations affect the shape and size of these signals.

What is your favorite part of doing a PhD?

The variation. It is very non-repetitive and I really enjoy the enthusiasm rush I get from closing in on a nice scientific result.

What is your least favorite part?

Scanning literature…

What are your hobbies/after work activities?

One of my favorite activities is dancing. More specifically hiphop and couples dancing. Besides that, I love taking care of my pets (especially training my very young dog) and having quality time with special people in my life.

I talk a lot and pretty fast and use absurd humor in situations where I am uncomfortable.

Louise Arno

Mon, 01 Jun 2020 00:00:00 +0000

Contact details

Questions and answers

What did you study for your bachelor’s and master’s degree?

I studied mathematics at Ghent University. During my masters, I focussed on differential geometry and the application of this research onto theoretical physics. My favourite courses were quantum field theory, differential geometry 2 and writing my master thesis.

Why did you choose to do a PhD in this group?

When I was 18 years old, I doubted a lot what to study next. ‘Should I go for medicine, engineering or mathematics?’ was a question I have asked a million people! My passion for mathematics made the decision for me. But to be honest, at the end of my master degree, I was on the verge of starting med school. Being of social value is important to me. But then…this team came across my path. It was THE perfect opportunity to combine my studies with my interest in medicine.

What would you say is your speciality within the research group?

I have always been intrigued by the somehow creative process a mathematician tries to tackle a difficult problem. This way of problem solving is the most important skill my degree has given me and is, I would say, my speciality. ‘Analytical thinking’ is a process: translating a universal problem, like cardiac arrhythmias, to mathematics, (partially) solving the problem by using different techniques, to then translate the solution, like the theory of PDs, back to the ‘real’ world. Being able to practice this skill on one of the largest causes of death worldwide makes me a happy person.

What is your favorite part of doing a PhD?

For my day-to-day life, I would say: diversity! Of course, we do research every day, but we also have to teach, follow courses (also transferable skills) and communicate our research via conferences or events like day of science or children’s day at the uni.

Overall? The fact you learn so much about so many things (including yourself) is priceless.

What is your least favorite part?

A colleague once told me ‘A PhD is a marathon, not a sprint!’. Since I am a long-distance runner, it is quite ironic how hard this long-term process can be. Yes, I do believe a PhD is a long-term process, with lots of long-term management, sometimes with no results. Since I am a result-based person, a PhD is not only a process and marathon, it can also be a rollercoaster.

What are your hobbies/after work activities?

Besides long-distance running, I love to eat! Gourmet dining with friends, and colleagues of course, is one of my favourite activities. My friends also call me a professional conversation maker.

My eyes have a different colour (see picture).

Hans Dierckx

Wed, 01 Jan 2020 00:00:00 +0000

Welcome to my group page!

Since 2006 I am researching non-linear waves and emergent phenomena using techniques from mathematical physics. The main motivation for this comes from cardiac arrhythmias, where self-organizing vortices underly rhythm disorders. This is a major health challenge, see this chart of the World Health Organization.

From 2019-2024 I worked as Assistant Professor at KU Leuven at the Kortrijk Campus.

Since 2025 I am Associate professor at the Leiden University Medical Center. Our mission is to help cardiologists to better understand and visualize the complex spatiotemporal activation patterns in the heart.

We have different methods in our toolkit, ranging from theory (topology, differential geometry, perturbation theory) over numerical methods (forward and inverse modeling) to recent work on clinical data analysis and machine learning. But the most exciting is to combine all of these, enabling the creation of a physics-based cardiac digital twin!

Feel free to contact me, we are open to collaboration.

Contact details

📌 LUMC, Albinusdreef 2, ZA 2333 Leiden. Office D4-26G.
📧 Official LUMC webpage #- 📚 Publications via Lirias
📑 Publications via ORCID #- 🧑‍🏫 Link educational tasks
🌍 Profile on LinkedIn

Questions and answers

What did you study for you bachelor's and master's degree?

I have a Bachelor's and Master's degree in Applied Physics Engineering (NL: burgerlijk natuurkundig ingenieur) and a Bachelor's degree in Mathematics.

What was your PhD about?

Applying elements of string theory to the heart, in order to derive the laws of motion of rotor filaments in the anisotropic cardiac wall. A pdf version of my thesis is available here.

What would you say is your speciality research wise?

Geometric thinking on emergent patterns in the heart.

Why did you choose to become a Professor?

My research is my way to make a difference for science and for society. I deliberately chose a topic with implicit benefits for the public (patients).

What is your favourite part about being a research team leader?

To have my ideas multiplied among my students, and the work divided. To have the aha experience with every little or larger scientific discovery. To spread the word that math and physics are much wider applicable than is usually assumed.

What is your least favourite part about being a research team leader?

Having to choose between a myriad of possibilities to do interesting science.

What are your hobbies/after work activities?

Spending time with my wife and three wonderful kids.

No, you'll have to meet me in person for that.

Search

Wed, 01 Jan 2020 00:00:00 +0000

Hans Dierckx' Research Page

About me

Arstanbek Okenov

Publication in Chaos

Outreach story in LUMC newsletter

Publication in Physical Review Letters

Desmond defends his PhD

Lecture on digital innovation in healthcare

Debora Hoogendijk

Bram Schalkwijk

Moving to LUMC

Feynman-like diagrams in the heart!

LUMC Fellowship awarded

Attending CINC and Cardiac Physiome Conferences

SIAM-UQ24 conference

Open Source

Publications

New publication by Kabus et al. 2024

Junior College 2024

Seminar talk by Dylan Vermoortele

New publication by Cloet et al. 2023

Aaron Gobeyn

New publication by Li et al. 2023 including Hans Dierckx

New publication by Leenknegt et al. 2023

Lecture of Hans Dierckx at the Bio Dynamics Days 2023

Theory of rotors and arrhythmias

Fundamental building blocks

Curved-space viewpoint on cardiac anisotropy

Application of mathematical physics concepts to cardiac excitation

Building theory from experimental observations

5th OpenCARP user meeting

SIAM-DS23 conference

Group photo in HeartKOR shirts

Visit of Thorrez' Lab

Popular science article about digital twins

David Van Hee

Junior College 2023

Day of Science 2022

Nathan Dermul

Contact details

Questions and answers

What did you study for you bachelor’s and master’s degree?

Why did you choose to do a PhD in this team?

What would you say is your speciality within the research group?

What are your hobbies/after work activities?

Do you have a fun fact about yourself that you want to share?

Marie Cloet

Contact details

Questions and answers

What did you study for your bachelor’s and master’s degree?

Why did you start a PhD in this group?

What would you say is your speciality within the research group?

What is your favorite part of doing a PhD?

What is your least favorite part?

What are your hobbies/after work activities?

Do you have a fun fact about yourself that you want to share?

Master thesis at KU Leuven Kortrijk

Research stay in Bordeaux

Scientist@School

Another group photo at the KULAK orchard

Mathematics exhibition "Imaginary"

New publication by Kabus et al. 2022

Summer School in Bordeaux

Info for students

Join us!

Previous thesis topics

Miscellaneous research topics

Geometry-driven dynamics in reaction-diffusion systems

Spiral wave chimeras

Data analysis and inversion

Ultrasound imaging of arrhythmias

Inversion of cardiac electrograms

Towards a digital twin of the heart

Numerical modeling of arrhythmias

Modeling the cardiac electrogram

Creation of individual models from machine learning

Experiments in the Gasthuisberg hospital

Lab visit in Leiden

EHRA conference 2022

DAE meets HeartKOR and KULAK