EEG

[geo]

dear All,

I am interested in application of cross recurrence plots in EEG brain dynamics data analysis. Suppose we have two data sets: one EEG channel captured with scalp electrodes (in reality we have nine chanels) and one by depth electrodes from thalamus or subthalamic structures (we have 3 times 3 channels for left and right). Can both data sets be described in the same embedding dimension (I have not yet tried this out as my data are not yet in a suitable format). Probably the optimal embedding dimension could be different. How to proceed in such a case in CRP ?

Sincerely,

Dr. G. Otte (georges)

PS I am not a mathematician so please excuse me should this be a silly question. )

[Norbert]

i would suppose that CRPs are not appropriate for the comparison of the both data sets. but it is also a question what you are interested on. is the focus on the variation of the time scales or on the synchronisation of the data? maybe joint recurrence plots are more suitable.

best regards
norbert

[geo]

i would suppose that CRPs are not appropriate for the comparison of the both data sets. but it is also a question what you are interested on. is the focus on the variation of the time scales or on the synchronisation of the data? maybe joint recurrence plots are more suitable.

best regards
norbert

Dear Norbert,

Thanks for the reply. CRP was indeed what I had in mind (thanks to Your work). But what about the problem if both signals do not have the same embedding dimension ? Can You still use CRP ?

My signals: one source of signal is surface EEG (9 channels) the other is depth recording form basal ganglia in the brain (6 channels) simultaneously recorded for 48 H at 200 Hz sampling freq. A rather "large" data set.

Best regards,

Georges

[Norbert]

But what about the problem if both signals do not have the same embedding dimension ? Can You still use CRP ?

This is exactly the problem. The purpose of CRPs is to compare the states of two processes, what means that the states represent the same physical process, i.e. the data should have the same unit and the phase space reconstruction must be the same. It doesn't make sense to compare fully different phase space reconstructions, e.g. one from blood pressure and the other one from solar cycle. However, it could be interesting to look for a dependence between such kind of different processes. For such purpose it is more suitable to compare their recurrences, i.e. whether the recurrences of states in both systems separately occur at the same times. This is what the joint recurrence plot is doing. It is simply the element-wise product of the separate recurrence plots. Look at this article of Romano et al, 2005:
http://www.recurrence-plot.tk/bibliography.php?label=romano2005

Best regards,
Norbert

[geo]

But what about the problem if both signals do not have the same embedding dimension ? Can You still use CRP ?

This is exactly the problem. The purpose of CRPs is to compare the states of two processes, what means that the states represent the same physical process, i.e. the data should have the same unit and the phase space reconstruction must be the same. It doesn't make sense to compare fully different phase space reconstructions, e.g. one from blood pressure and the other one from solar cycle. However, it could be interesting to look for a dependence between such kind of different processes. For such purpose it is more suitable to compare their recurrences, i.e. whether the recurrences of states in both systems separately occur at the same times. This is what the joint recurrence plot is doing. It is simply the element-wise product of the separate recurrence plots. Look at this article of Romano et al, 2005:
http://www.recurrence-plot.tk/bibliography.php?label=romano2005

Best regards,
Norbert

Dear Norbert,

I agree completely. Essentially both type of signals are scalar times series reflecting the same" complex proces of "movement regulation" a neurological assembly involving motor cortex, basal ganglia and relying and reverberating frontostriatal loops and feed back mechanisms that regulate motor activity. Defects in these pathways can give raise to increased (fi chorea
and dyskinesia) or reduced motor output (parkinson) to the anterior motor neurones in the spinal cord. Essentially both signals should be measuring the same (complex) process dynamics but the granularity differs. Its is not that we compare unrelated signal sources but the first ones are superficial scalp EEG that pick up a lot of other activity from non motor neurological superficial cortical and deep neuronal processes and where signals are filtered by skin scalp, skull and meninges while the depth electrodes are directly in de subthalamic effector nucleus (picking up the direct motor signal to the thalamus) and not influenced by skull and membrane filters. I could bge that the signals will be modelled in diferent embedding dimensions. I recon that it would be best to measure this first before continuing these speculative questions (:=))) but anyhow even if the embedding dimension for the model should differ could chose the one of the most direct signal as "primairy" . Would that be allowed ?
Otherwise apart from synchrony how could i find out which signal drives which ?

I will do the analysis on the signals first and report back later with the results.

Best regards,

Georges

[Norbert]

I could bge that the signals will be modelled in diferent embedding dimensions. I recon that it would be best to measure this first before continuing these speculative questions (:=))) but anyhow even if the embedding dimension for the model should differ could chose the one of the most direct signal as "primairy" . Would that be allowed ?
Otherwise apart from synchrony how could i find out which signal drives which ?

In order to not under-embed one system, the embedding dimension should be chosen from the system with the higher dimension. On the other hand, you should also visually inspect the CRP, in order to check the structures. The optimal CRP should have many diagonal lines and less single dots. The diagonal lines should not be sharply interrupted. Sometimes it is neccessary to change the embedding parameters in order to get better CRPs.

In order to find out which system drives the other, I will suggest an approach as a new topic in quantification.

Best regards,
Norbert

[sultornsanee]

Did it work? ... I tried to use JRQA for multi channels but it doesn't work well. Could you give me an example for CRP Toolbox in Matlab?

[Norbert]

Have a look here: viewtopic.php?f=12&t=191

RQA of JRPs? How you would interpret the results?

[sultornsanee]

Thank You

[hoda1395]

Hello,

I am trying to use CPR to find the phase synchronization between electrodes of an EEG segment. well I should calculate the RP of each electrode for this purpose. I am using the mutual information and false nearest neighbor method to calculate the delay and embedding dimension and I am getting different values for each electrode. My question is for an EEG segment,should I use different parameters for embedding or it is better to use one delay and dimension for all electrodes? I know that if I use different embedding dimension for electrodes, comparing them and calculating CPR of pair wise electrodes are not meaningful but since I am getting various embedding dimension for each electrode, how can I choose the best embedding dimension?

[Norbert]

I would be careful when using embedding. Do not overembed because it will cause artefacts (spurious correlations in the RP and artificially many long lines). Therefore, I would probably use a low embedding dimension and delay for all channels (e.g., m=3, tau = 2). Final values depend on the data. It would also be helpful to check how the results change when slightly modifying the embedding parameters.

[hoda1395]

I would be careful when using embedding. Do not overembed because it will cause artefacts (spurious correlations in the RP and artificially many long lines). Therefore, I would probably use a low embedding dimension and delay for all channels (e.g., m=3, tau = 2). Final values depend on the data. It would also be helpful to check how the results change when slightly modifying the embedding parameters.

Thank you for your reply and the advice. In fact my final result would be the CPR value which varies (within limits) by changing the parameters. Is there any criteria to find out what combination of parameters are best to choose? Can I use statistical methods ( for this purpose? or by using surrogate data testing...I mean choosing the parameters that gives significant CPR matrix by surrogate data testing.

(Just as additional information, By CPR I mean Correlation based on Probability of Recurrence which is an estimate of phase synchrony of two time series which is proposed in http://link.springer.com/article/10.100 ... 006-1957-x)