3.4 Fractal Dynamics in HRV: DFA

• So to address these limitations, CK Peng who is a good friend and mentor of mine and also a scientific adviser for Labfront, published this in 1994. And this was the first study that looked into something called detrended fluctuation analysis. This is something that CK had developed, it's based off of a Hearst exponent, Hearst exponent is a marker of memory and persistence. And unlike the one over f power law relationship is a time domain based analysis. The power law is a frequency based analysis, the DFA is a time domain based analysis. And this DFA is amenable to non stationary data. And it is quite computationally simple. 
• Tp explain how the DFA is done, you, for instance, take this heart rate data or in this case, interpeak interval, as you do it by Vt number here, you take it and you integrate the mean center data to create much more of this graph, which tends to be a little smoother. And you divide this data into epochs, the F Fox are based on scale. So if you had a scale that was F 10, the each epoch would be divided into 10 points. If you had an F scale of 100, then these, each box would be 100 data points in size. And for each epoch, you d trend it and you calculate the root mean squared. In other words, you find out the fluctuations that occur around this linear fix. And then you average all the root mean squared across all the epochs. And then you do the same thing repeats two through four for different scales, and you get this relationship where you get the fluctuation versus the scale and you get this linear relationship. And what's considered healthy, a healthy DFA relationship is an alpha of 1.0. Whereas a unhealthy or in other words, something that has significant white noise, which they simulated by randomizing the data, the alpha is point five.
• This graph shows the relationship here in terms of pink noise, brown noise and white noise. And the pink noise has again a slope of one similar to the power law relationship. However, white noise has a smaller slope, Brownian motion has a higher slope. And this is a comparison between the two and you could clearly see that there is a difference between the two. In terms of the directionality. However, the pink noise, or alpha of one is a balance between these two extremes. And the reason there's a difference in the directionality in this direction of the slope, is that DFA has the the lower frequency represented by the higher scales, where's the power loss slope of lower frequencies occupies left of this graph. So if you take a look at Brownian motion, which is dominated predominantly by low frequencies, you can see that this has a higher slope in the positive direction, whereas in parallel, it has a negative slope. Here. There is a mathematical relationship between these two, where beta is one minus two of alpha two here.
• When CK Peng applied DFA to normal and congestive heart failure patients, he found interesting observation here. This is again the DFA graph which maps fluctuation with respect to scale. This is a normal individuals graph versus the congestive heart failure individuals. But you see here something which he termed the crossover phenomenon, where you have a change in the slope. And this occurred in both the healthy individual as well as the congestive heart failure patients, but it occurred in a different way for each. But I think it's good to note that this crossover phenomenon occurred pretty much in the same region, where we have this change from linearity to not linear relationship in the parallel whatever f graph and the question is, what this the significance of this particular frequency, which is around point oh, 3.03 hertz or so. The physiological significance of this crossover phenomenon is unclear.
• But there must be something that's happening at the point O, three hertz region, approximately, which leads to this different relationship and this crossover phenomenon and I think that's something that's worth exploring for sure. Because there's different relationships different slot CK Peng divided DFA into two parts alpha one for the higher frequencies and alpha two for the lower frequencies. And for the healthy individual, it's interesting that the slope is close to one so it resembles pink noise. Whereas what's considered healthy is of slope greater than one or even on more so on the Brownian region, whereas those the congestive heart failure patients tend to have white noise like alpha one, whereas the alpha two is much more Brownian.
• So this is a summary forest plot put out by sent in 2018. Again, looking at DFA alpha one specifically in regards to mortality across multiple conditions, myocardial infarction, LV dysfunction, non cardiac conditions, and you could see that alpha one in the deceased tends to have be lower compared to the alpha one in those who were remained alive. And this relationship this comparison between those deceased versus live remains quite statistically significant across all these studies, none of which crossover for equivalency for any of these studies.
• To summarize our Riveros fractal measures, I would say that fractal measures have prognostic implications even in free running conditions. Again, just like I had talked about in this previous epidemiological studies, the heart rate was collected using 24 hour Holter monitoring. And again, this was done in free running conditions without any restrictions about what the participants can or cannot do.
• Or variability is applicable to the general population not limited to specific cardiovascular conditions, and a power law whatever app in DFA Alpha One frequently outperformed traditional Heart Rate Variability measures and predicting mortality. I didn't really go into too much details, but it seems that this was specifically consistent across multiple studies and more so in the era of beta blockers, which tended to affect the traditional Heart Rate Variability measures more.
• The other interesting thing is that power law one of F tend to correlate more with all cause mortality, whereas DFA Alpha One correlated more with cardiac mortality. And this is an example of this. This was a study by Maka Kalia in 2001. It was a study that involved 325 elderly individuals in Finland 24 hours of continuous ECG with a follow up of 10 years and they evaluated DFA alpha one power one of F nsdn N. And the first thing to note is you could see this table which again categorized in all different kinds of mortality, all cause cardiac death, sudden cardiac death, cerebrovascular mortality and non cardiovascular mortality. And you can see the first thing is that the SDNs when entered in a model associated with these other power fractal or fractal measures, it tends to be all non significant indicating that these fractal measurements may have more of a predictive power than standard traditional measures. And then the other thing to note is that when it comes to non cardiac mortality, and since all cause or cerebrovascular or non cardiovascular mortality, the power law slope tended to do a better job compared to DFA alpha one, whereas DFA Alpha One did better overall in terms of cardiovascular prediction, and this includes cardiac death in sudden cardiac death.
• But in regards to DFA, it is more related to LF HF ratio and this is shown in Makkah collio published in 2001, and JCC. These are three examples, this is a healthy individual, for instance, this healthy individual had an Alpha was close to one which is close to pink noise. And the reason this this individual had essentially high long term variability and normal short term variability, which is expected of pink noise. On the other hand, this individual had more of a Browning feature with more lower frequency power compared to the higher frequencies. And this is an individual that has more of a white noise picture where you have frequencies that are much more distributed uniformly across all the frequency ranges. But the relationship can be clear when you see where the lower frequency is represented in the DFA graph, the lower frequencies is occupied here and the higher frequencies is in this region here. So if you have a predominance of lower frequency, then you would anticipate having a higher frequency as you do in this example here and the converse is true here, where you basically have more of a higher short term variability which is represented here. So again DFA is correlated with LF over HF ratio. However, that does not maintain its relationship in free running conditions. Simply because DFA is more attuned for nonstationary data compared to 40 transforms, which is used for low frequency and high frequency ratios. So DFA alpha one still remains more advantageous for that reason, particularly if you're going to apply it in real world practical situations.
• In nearly all the studies dysrhythmias afib, frequent ectopic beats were excluded in these studies, just like the epidemiological studies. And so, again, expect to exclude a number of individuals, if you are going to implement fractal measures in your studies. But it is also worth including some of these individuals to see how a fib does affect these fractal measures, because these fractal measures are essentially based on the idea of balance between order and disorder. And a fit is a disordered state. So I can't see why we cannot include these individuals in your study.
• Just like the epidemiological studies, nearly all the studies acquired only a snapshot of heart rate variability. These were obtained on a single day, which was then carried over to figure out the mortality which lasted for years. And wondering, dynamic cases and heart rate variability are potentially helpful but understudied. And an example of the utilization of dynamic changes in fractal correlations can be seen from this more recent application of the FAA alpha to exercise. This was published by Bruce Rogers in 2021, in frontiers in physiology, and in this case, there was a ramp up and exercise given over time to the point where you reach a lactate threshold, the first threshold, and you can see that around the same time this lactate threshold is reached, the DFA starts to decrease. And according to Bruce Rogers, there is a cut off of point seven, five, which correlates to Lt one, or in other words, the thresholds of electric build up. This is, you know, not established. Certainly this group has published a number of other studies, but this is, you know, probably needs to be validated.
• Finally, we're in an era of wearables and large public and private datasets. An example of large public datasets include all of us, which is the precision medicine initiative by the NIH is a Million Veteran Program within the VA administration or the VA programs. And then you certainly have private datasets such as Epic and Cerner. And many of these are considering incorporating wearable devices in their datasets. And this dataset will also include other information, not only clinical conditions, but also genetic information and a lot of blood and biochemical biomarkers. So we're entering in an era where these wearable related variables such as heart rate variability, will be found simultaneously with other measures related to health. I think we're entering a golden age of understanding a lot of the heart rate variability relationships with medical conditions, and also overall health. So I think we're entering a very exciting time for this reason. And heart rate variability, which is dynamic, which is shown to be associated with mortality and numerous conditions will probably regain a lot of attention and some of the attention will be directed towards the things that have been neglected before. That includes the very low frequencies, the ultra low frequencies, the fractal measures, for instance, or the dynamic modulations of these variables in across the course of the day, the weeks, months and the year. So I think this is the good this is a great time to enter Heart Rate Variability research, given these large scale developments that we're seeing overall in research

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