It is well known that in Heart Rate Variability - HRV analysis the use of linear and non linear methodologies is suggested. Sometimes, some methods also enable us to evaluate fractal features. Does anyone have any indications of what it means to find fractal dimension whose counterpart is a) white noise, b) time-dependent at all scales, c) statistically self-similar behaviour? What about clinical implications?
DFA is well known to me. I asked another thing. I asked , not for DFA but in general, What could means time dependence at all scales ,statistically self-similar behaviour and white noise in a fractal analysis of a given R-R time series
Good morning gentleman,
although I have no direct answer for your brilliant question, maybe my findings may a help a little. I have found, that fractal dimension of in-vivo heart (1.49±0.03) is almost the same as in ex-vivo heart (1.45±0.14), indicating that the fractal features of HRV are probably predominantly affected by intrinsic behaviour of heart, not by sympathetic/parasympathetic branches of nervous system. For that reason I suppose, that answer should comes from analysis of intrinsic heart behaviour.
(The 5 minutes long records of (a) five rabbits (b) five isolated rabbit hearts perfused in Langendorff mode have been used, and fractal dimension has been computed by box-count algorithm).
Oto what do you expect by box counting method. We are speaking here of dynamical time dependence , a signal as time series. My question of course was a) about white noise, b) about time dependence at all scales c) statistically self-similar behaviour.
In my reserach group we have used a non-linear chaotic analysis of several biosignals, such as ECG, HRV, EMG. The name of the technique is Recurrence Quantification Analysis (see, for example, Norbert Marwan, M. Carmen Romano, Marco Thiel, Jürgen Kurths"recurrence plots for the analysis of complex systems" Physics reports, 2007, 438, 237-239 available at www.sciencedirect.com ) and a good parameter we have investigated and widely used is the percentage of determinism (%DET)
Scaling in HR time series can be uncovered by many techniques (already mentioned in several answers). The meaning has to do, in my opinion, with self-similarity as it shows that (a) the cardiac system has memory, i.e. it responds not only to current influences but to past stimuli as well, and (b) the complexity of the HR output emerges from the interaction of elements that operate at different time scales (e.g. the two branches of the autonomous nervous system). Bruce West provides brilliant explanations in his excellent book "Where medicine went wrong". I would recommend specifically section 7.2. "Heart failure and fractal loss", but chapters 5 (fractal physiology) and 6 (Complexity) are essential readings in this field.
I recommend the review article by Bravi and Seely:
http://www.biomedcentral.com/content/pdf/1475-925X-10-90.pdf
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