# Complexity Science

## 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. References 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. Press Releases http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/newssummary/news_22-12-2014-15-54-17...

## Matlab for cluster analysis

Posted by on Jun 27, 2013 in Complexity Science | 0 comments

In this post I shall describe some useful Matlab functions for detecting and analysing clusters in a 2-D matrix. If you have a matrix e.g.  $latex A = \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0 \end{array} \right) &s=-4$ and want to identify clusters, cluster size etc. then the following function will help: A = [ 1 1 1 ; 0 0 1 ; 1 1 0]; % Generates a matrix [LabeledClusters NumberOfClusters] = bwlabel(A,4); % Finds clusters The first line will produce the matrix shown above. This matrix is then used as an argument in the bwlabel function. The additional input of the number 4 is to specify how a cluster is defined. If the input is 4 then an element in the array will only check its north, south, east and west neighbours in constructing a cluster. The alternative input is 8 in which case an element in the array will check north-east, north-west, south-east and south-west neighbours also. The LabeledClusters matrix will be: $latex A = \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0 & 0 & 1 \\ 2 & 2 & 0 \end{array} \right) &s=-4$ and the NumberOfClusters will be a scalar. In this case NumberOfClusters is two as there are two clusters in the matrix A. To get a list (vector) of sizes of all the different clusters use the following: s = regionprops(LabeledClusterMatrix,'Area'); AreaOfEachCluster = cat(1,s.Area); The output AreaOfEachCluster is a list of the size of each cluster. The location in the list corresponds to the number of the cluster as given by the LabeledClusters matrix. From here it is easy to obtain a histogram of cluster sizes (using Matlab’s hist() function), average cluster size etc. To experiment you should try using bwlabel(A,8) instead of bwlabel(A,4) Here is the script: A = [ 1 1 1 ; 0 0 1 ; 1 1 0]; [LabeledClusters NumberOfClusters] = bwlabel(A,4); s = regionprops(LabeledClusterMatrix,'Area'); AreaOfEachCluster =...

## What is money?

Posted by on May 29, 2013 in Complexity Science | 0 comments

Money is really important to the economy, and us too. But what do we understand about money?

Well, to the majority of people, money merely a store of wealth and more importantly a medium for trade. How much you’ve earned equals how much worth of the object you can obtain. But the reality is that it could be quite complicated when one consider the money supply, which contributes to inflation or deflation.

## Emergence of Insight

Posted by on Apr 15, 2013 in Complexity Science | 0 comments

Insight is a profound experience which frequently appears unconsciously in a very short moment like light flashes in our mind. It is always interesting to understand how these moments could help us to solve complicated problems, which even intensive logical thinking cannot handle it.