During the research phase of modelling crowds I developed a complexity analysis system using strange non-chaotic attractors. These are coupled non-linear oscillators and out of curiosity I tested, under scientific blind conditions, some patient data.
The heartbeat is far from constant - it varies as we exercise and rest. The dynamics of that variability has been speculated to indicate the "general" health of the heart. It is a large scale interactive system - waves of energy pass across the surface of the heart - each cell triggering the cells around it. In 1996 I speculated that the dynamic fractal analysis tools developed for large scale interactive systems could be used to determine the underlying structure of the heart rate variability. The question was could it distinguishing healthy heart rates from the unhealthy ones? The results were significant.
Cellular Automata models of the heart beat
A cellular automata mapping process is similar to a wave of excitable energy passing across the surface of the heart. Below an illustration of a shockwave passing through an excitable media
Cellular Automata model of a surface with a pulse.
Cellular Automata model of a surface defect with a pulse.
Wave front passing across the 3D surface of the heart
XenoFractal Analysis of the Heart Rate Variability of a patient with sleep apnoea
The Xenofractal Approach
The XenoFractal algorithm was used to analyse the heart rate variability of 18 blind data sets from sleep apnoea patients. The process involves taking the data and passing it through a coupled non-linear oscillator - similar to the analysis process for ForEx analysis. In short - the algorithm detects the underlying attractors and hence can determine whether the system has chaotic signatures. Chaos in the heart is a positive attribute - the the ForEx markets it's a negative attribute (you can't predict chaos).
The initial results were statistically significant (98%) so a second test was run on a further 21 patients (again blind) those results were also statistically significant (99%). Furthermore the Apneoa Scale was calculated from 3 hours of daytime HRV data.
These results were obtained by transforming the data through symplectic geometries via a dynamic, self-adaptive algorithm. As you can see the results were reasonable enough to warrant further testing. Although there were seven wrong results, the scaling process has a variable offset and when that test was recalibrated the results were better - but no longer a blind test therefore not shown here.
The second blind test results were considerable better - furthermore there were four other samples (not shown) which were non-apnoea sufferers but had "sick" hearts (two periodic limb movement syndrome, one abnormal lung function and one previous myocardial infarction). The analysis correctly identified these as "Sick" though not "Apnoea Sick". I have excluded those results from the table above.
Statistical Analysis from the Heart Rate Variability analysis of Sleep Apnoea.
The data was provided by Mike Hilton (now at Harvard Medical School - Boston)
Primary Research Questions
- Can we predict the early onset of atrial fibrillation?
- Is this chaotic analysis useful as a diagnostic tool?
- Can we classify the atrial fibrillation using this technique?
"In the United States, sleep apnoea affects an estimated 18 to 25 million persons, with less than 1 million being aware of their problem. For victims, daytime sleepiness can be so profound that it affects business and social life. Sometimes sufferers fall asleep at the wheel, causing motor vehicle accidents. The costs to society from loss of productivity, industrial and personal accidents, plus medical bills, is estimated to be over $60 billion per year. Once detected, sleep apnoea can be treated with continuous positive airway pressure (CPAP), as well as other therapies."
"Disorders of heart rhythm can be difficult to detect. They may be there briefly and then disappear as quickly as they appeared. It's a question of being there when it's happening." Melanie Raddon, a cardiac nurse for the British Heart Foundation - quoted from the Daily Mail on a report of an inquest on the death of a six year old child of cardiac dysrythmia which went undetected. August 1st, 2001
Nader Rifai, Ph.D., Associate Professor of Pathology, Harvard Medical School, and Director of Clinical Chemistry, Children's Hospital of Boston, one of the nation's leading clinical chemists believes that current clinical tests that measure traditional risk factors for coronary heart disease--such as high cholesterol, high blood pressure, and smoking--fail to identify nearly 50 percent of Americans who will eventually have a heart attack. August 3rd, 2001.