Elucidating a Complex Rhythm with a Simple Model

Posted by on Jan 16, 2015 in Complexity Science | 0 comments

Burning the heart can cure it from beating abnormally, however, the right bit of heart tissue needs to be destroyed. Atrial fibrillation (AF) is the most common abnormal heart rhythm, affecting 1% of the population, and can cause stroke. Clinicians find it much more difficult to treat AF by burning despite it being the most common abnormal heart rhythm. This is because it is not clear which part of the heart is responsible for the disease. My supervisors, Kim Christensen and Nicholas Peters, and I have recently developed and studied a mathematical model (published in Physical Review Letters) which provides insight into where clinicians should burn and why the disease is difficult to treat.

Normally, the heart beats in synchrony so that the upper chambers pump blood into the lower chambers first and then the lower chambers pump the blood out of the heart. Pacemaker cells (found in the upper chambers) rhythmically send out electrical signals to neighbouring muscle cells, telling them to contract. This electrical wave travels across heart muscle cells from the upper chambers to the lower chambers like a smooth Mexican wave (see this video). An abnormal heart rhythm is when these waves travel abnormally, which removes the synchrony of the pumping action.

As we age we all develop fibrosis, which is connective tissue in the heart that disrupts connections between muscle cells and as a result can disrupt the electrical waves. Our risk of AF also increases with age, but the mechanism of this is not fully understood. The increase in fibrosis with age is a potential explanation as to why the risk of AF also increases with age.

We developed a mathematical model that represents how cells are organised and connected within heart muscle tissue and how that changes with age. As the amount of fibrosis increased to a critical point the electrical waves would spontaneously re-organise into circular and spiral patterns, mirroring atrial fibrillation (see video below). We found that “burning” particular regions in the model where the cells were structured in a certain way could stop the fibrillation, however, when there was too much fibrosis the burning was unsuccessful.

The model was able to reproduce features of AF observed in patients, namely, that an increase in fibrosis was related to an increase in the prevalence of AF and that destroying specific regions of tissue could sometimes stop the abnormal rhythm. In addition to this the model also reflects how the disease develops in time: AF initially occurs for short periods and gradually gets longer as the condition progresses. However, medical imaging is unable to identify the structure of tissue at this scale in patients undergoing treatment.

The mathematical model highlights where future research could be targeted. A lot of work and caution is required to translate results from a mathematical model to biological and clinical studies. Furthermore, the study is an interesting example of how simple models can reproduce features of real complex systems.


K. Christensen, K. A. Manani, N.S. Peters. Simple Model For Identifying Critical Regions in Atrial Fibrillation, 2015. Physical Review Letters 114:028104. DOI: http://dx.doi.org/10.1103/PhysRevLett.114.028104 (open access)

U. Schotten, S. Verheule, P. Kirchhof, A. Goette. Pathophysiological mechanisms of atrial fibrillation: a translational appraisal, 2011. Physiological Reviews, 91(1), 265-325.

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About Kishan Manani

Kishan Manani is a PhD Student at the Center for Complexity Science and British Heart Foundation Centre of Research Excellence at Imperial College London. His research interests are in modelling cardiac dynamics, excitable media, atrial fibrillation and machine learning in medicine. The focus of his PhD is the development and study of simple models of cardiac dynamics to study the effects of tissue structure in atrial fibrillation. He also uses machine learning tools with a recently developed signals processing engine to data mine clinical electrograms, electrical signals from electrodes in contact with the atrial surface during catheter ablation therapy.

He obtained an MSci Physics degree at Imperial College London in 2012 where he was awarded the Callendar Prize for all round excellence in physics: his master’s thesis focused on developing cellular automata models and applying techniques from non-linear dynamics to investigate atrial fibrillation. Kishan actively engages in STEM outreach by giving talks and demonstrations in various London schools.

Kishan’s academic webpage