From history Napoleon Bonaparte has 47 beats per minute, but no heart problems and had a great amount of victories, following this fact everything is relative

Claudia,

many years ago I was following patients after heterotopic heart transplantation, where the damaged heart remained in situ and the transplanted heart was "bagbacked" on the first. The damaged heart was autonomic innervated while the transplanted heart was denervated. The damaged heart was almoust silent from HRV with pNN50% of less than 1% and the noninervated heart had a pNN50% of 46%, with almost the same heart rate. In collaboration with the instutute of physiology we were measuring different parameters to get an idea about reaction of both hearts. Finally we used a chaotic model according to Layapunov. At least this index gave a global estimate of the HRV and the cardiovascular control.

Maybe this helps.........

Best

Being a non-physician, my comment is from someone who is an outsider. I hope that advanced statistical methodologies will be more effective in future years to contribute some useful answers to such questions. For example, images of a beating heart can be transformed to wavelet functions, which in turn can create hundreds of thousands of data values on the heart. Such data could be used to create a profile of the heart, and then we could compare many samples from different hearts to test for differences in profiles. Think BIG data analysis. I once worked with others on a book chapter about Glaucoma where we used such a methodology many years before wavelet functions became popular in medical research. Using process control procedures on such data we can identify sudden or gradual changes in "the process", and we can separate changes in the mean versus changes in variability (in the functioning of the heart), along with digital imaging.

 Dear Claudia,

I believe that nobody can answer your question with an absolutely true response. Assumptions and interpretations in Science are always biased by the way of scientific thinking and also by the accumulated evidence which not always are generated under the best conditions. During my thesis project I recorded the EEG activity and calculated the "network properties" of the resting brain. Unfortunately, I  interpreted in the wrong way these measures because I assumed that each node of the network (region of the electrode placement) corresponded to a brain area. Two possible solutions would have been the use of inverse solution approach or the application of fMRI technique instead of EEG method. Both of them record indirectly the activity of a brain region and, from this activity might be right (more close to the true) to calculate the network properties. Even with these solutions the analysis of the results would still having an associated error which depends on the correspondence between the nature of the measures and the nature of the physiological phenomenon under analysis. Thus, in my opinion, you should apply the more direct approach(es) which lead you to get information directly about the physiological mechanism. Otherwise, you should critically analyze the nature of both, the measures you are calculating and the physiological mechanism under study and then, arrive at your own conclusions.

Not necessarily irregularity implies complexity, it can be just an indication of in what amount a system is fed by white noise. Analysis of noise free realizations of auto-regressive models may help to avoid that inconvenience.

In my opinion the complexity approach requires a more global interpretation than in this case just the influence of the cardiovascular control. It should consider the inter-action between multiple sub-systems also between top-down and bottom-up levels on each of them.

My pesimistic answer to the question is based on the fact that any empirical estimate are based on ideal models, and real data rarely  convey to theoretical models. You squeeze a pice of paper, and you can asune that the obtained paper ball is a sphere, and you can measure its perimeter with a thread and then write a paper on the observed result that the perimeter of a paperbal is not constant. But the big problem is that the paperball is not a sphere. Others say that the paperball is a fractal, and try to measure the fractal dimendion of that paperball, and in reality the paperball is a mere paperball that sometimes conveys to a sphere and some times to a factal, but attempting to go deeper based on the perimetral variability of the paperbal is a nonsense.

Anyway, I recommend the use of recursive plot analysis to study heart rate variability, perhaps something interesting can come out.

Dear colleagues,

Thank you very much for sharing these interesting experiences and for all the advices. They have been helpful!

All the best,

Claudia

I think the question is formulated incorrectly. As a physiologist I could not understand what the "physiologic complexity" means. And moreover how it can vary?

Dear Dr. Valery Nikolaevitch Mukhin,

Thank you for your comment. As our colleague Prof. Marianne Levon Shahsuvaryan has stressed above, "everything is relative". I have just started learning the interesting aspects of this field of research which my question relates to. However, as far as I know it is common knowledge that physiologic systems are very complex. Complexity arises from the interplay of their different components, which interactions are associated with multiple spatiotemporal scales and occur in a nonlinear (and also nonstationary) manner. These interrelations make possible the adaptation of the system to a wide range of environmental perturbations. The degree of complexity of a biological system can be quantified by examining the fluctuations of its dynamics. For example, the complexity of the cardiac autonomic regulation may be quantified by analyzing the dynamic changes of the heart rate, a result of the chronotropic regulation exerted mainly by cholinergic parasympathetic and noradrenergic sympatethetic autonomic branches at the sinoatrial level. A reduced complexity of the physiologic system would mean a break down of the relations between its components (maybe because of degeneration of the structures), which so far it is believed to occur with ageing and diseases. At any rate, I expect to deepen in these aspects and gain more clarity in the future.

Kind regards,

Claudia

Dear Claudia,

Sorry for posting into your topic belatedly. However, this is a quite interesting topic and I am also looking for deepen the understanding. Here is my humble opinion.

The theory of physiologic complexity, as you stated, is supported by the idea that healthy systems will always be the most complex ones, because the multilevel interactions (crosstalks) and regulating mechanisms are at best performance in such organisms/systems. Any breakdown or function loss in one or more of these regulatory mechanisms causes a decrease in the complexity. Therefore, diseases and aging is associated to complexity loss.

Some studies revealed that entropy can either increase or decrease in pathological situations. Considering the idea of physiologic complexity, entropy cannot be assumed as a complexity index. Moreover, surrogate data tends to increase entropy (compared to original signal) but the original signal is considered more complex than its surrogate, as it contains the information which was destroyed in surrogate data.

So, why some authors still associate entropy to complexity? Because complexity can be interpreted in different ways. If you consider that the complexity of the system can be solely characterized by the signal dynamics you are analyzing, and not by the system itself, you may assume that the higher unpredictable the signal, the higher the complexity. In this case, entropy can be considered a measure of complexity. This is often called "dynamical complexity".

If we refer to proper books and papers, we will find that "complexity" does not have an universal definition. Instead, people describe what properties the complex systems usually show, which basically are:

1) Many interdependent elements, interacting each other through nonlinear rules;

2) Structures over several scales;

3) Emergent behavior;

When we expand it to living organisms, this is clear that our systems (humans, animals) fit as complex systems. But, how could we detect this complexity from time series? From the many measurements proposed to extract information from those time series, e.g. asymmetry, fractals, entropies. And how many and which information are necessary to characterize complexity in time series? I think this is a very good question!

The final point is: can only heart rate variability reflect the system complexity? Although powerful, this is a single variable taken to characterize a very complex organism. It is more or less the same of reducing the dimension used to characterize some object in space. Information will be lost. Multivariate analysis may be more powerful, taking into account more than one variable concomitantly to assess the dynamics of the system. For example, one can record respiration, arterial pressure, ECG and EEG, simultaneously, and use some methodology to characterize the complexity. However, due to several limitations, in many situations it is not possible to collect more than the ECG, from which we can calculate heart rate variability.

The study by A. Porta et al, J. Appl. Physiol. 113, 1810-1820, 2012 suggests that complexity analysis of heart rate and arterial pressure variabilities provides complementary information probably by focusing on different aspects of the cardiovascular control.

Dear Luiz Eduardo,

Thank you very much for the comprehensive explanation you have provided for this question. The way you have addressed your answer has gave me a lot of elements for understanding these facts and has clarified me many aspects on this matter. Thanks for taking time to reply this topic.

Best wishes,

Claudia

Dear Prof. Alberto Porta,

I am very interested in the analysis of HRV complexity for assessing cardiovascular dysautonomia in PD and related disorders. The results of this research you referenced and other works of your team in this topic are very interesting in showing how complexity analysis of cardiovascular dynamics is capable of detecting early impairments of cardiovascular control in PD. Also remarkably is the finding of an increased complexity of cardiovascular control in these patients, at least for the arterial pressure regulation even at rest. It would be really interesting to further analyze the progression of the structural and functional changes of the cardiovascular autonomic nervous system with relation to this rise of complexity of its dynamics in early and advanced PD. Thank you very much for your comment.

Best wishes,

Claudia

dear Claudia,

I am very interested in all pathological conditions determining, against the common belief, a raise of some aspect of the cardiovascular control complexity instead of its breakdown.

Yes Prof. Porta, this is very interesting indeed, although I have only heard of these results for PD (since increase of entropy measures in other pathological conditions are known not to mean an increase of complexity, but just of the irregularity because of occurrence of random dynamics, such as in the case of atrial fibrilation, as far as I know).

Although very revolutionary, this new concept is rather challenging. It is kind of puzzling to leave behind our traditional understanding of complexity, for realizing that even when it is recognized that there may be sympathetic cardiac denervation and/or dysfunction in one or both cardiovascular autonomic branches in PD, we still can expect an increase of the complexity of the cardiovascular regulatory mechanisms. So it is certainly a very attractive area of research.

I don't know if Prof. Porta agrees with me, I believe that it is still a matter of definition of what we understand by complexity. Diseases, such as PD, are characterized by some types of system dysfunction. From Goldberger's point of view, diseases will always represent complexity loss, due to the reasons previously discussed. However, we could think that the remaining mechanisms will adapt to the new situation (disease) and, from the point of view of those adapted systems, complexity could increase.

In anycase, we have to remember that the evaluation of complexity is performed on a system output (time series) and information about the mechanisms are usually mixed up. Heart rate variability (HRV) is affected by several diseases, including non cardiac ones. Thus, HRV is a rich source of information, but has the limitation of being a single variable.

Finally, there is the problem of what features are necessary to characterize complexity in time series. Entropy at several scales are usually accepted as a marker of complexity, but one could consider that entropy at scale one (sample entropy, for example) is sufficient.