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“Man cannot discover new oceans unless he has the courage to lose sight of the shore.”
~Andre Gide~

A brief explanation of z-ratio

 

Z-ratio can be helpful in ushering in a new era of Sleep/Wake Medicine, Sleep/Wake Research and Sleep/Wake Quantification for the masses.

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The first step in explaining z-ratio more fully is to offer the bibliography of publications relating to z-ratio http://www.sleep-wake.com/Z-ratio.pdf. Here is where you can download a z-ratio PowerPoint presentation I gave at the Initial World Sleep Association meeting in Berlin in 2005.  Please note that  I have depicted z-ratio with "-" on top (faster power more pronounced) and "+" on bottom (slower power more pronounced). This also mimics how a polygraph is configured with negative up and positive down, while also mimicking the hypnogram, showing wake UP and sleep down, deepening as the values go down, respectively.

 

In short, z-ratio is not “staging” sleep, as staging is somewhat subjective and capricious by its very nature. NB: The usage of MAJORITY in the z-ratio SLEEP journal paper was only to help z-ratio be accepted and fit it into the field's pre-ordained sleep staging/categorization mindset. It was also convenient since 2 Sec FFTs is what we had to work with at the time (1991.) Using our sleep system from CNS Inc, their FFT allowed us to configure majority(8)/minority(7) schema per 30sec epoch.  We knew that a short 2sec FFT meant a loss of resultant power bin size, but for z-ratio that does not matter as the bin size is huge (.5 - 7Hz for slow, and 7-25Hz for fast.) There is nothing sacrosanct about 30 second epochs. So, if we disregard the arbitrary pattern based staging classifications and forego the 30 sec epoch mandate, we end up with the possibility to investigate a fluid way to depict sleep...this was the genesis of my inventing z-ratio.

 

It all started back in 1988 when I started working with the CNS, Inc. sleep system which was using FFT for their Average Frequency Value (AFV), so I asked CNS to use their FFT data differently.  I used my hemisphereality analysis training which looked at LEFT versus RIGHT EEG power to emotional stimuli, and I just plugged FAST (FFT summed power 7-25Hz) and SLOW (FFT summed power .5-7Hz) into the formula.  L-R/L+R was replaced with S-F/S+F. This fluidly depicts Sleep/Wake in 2 sec increments. We have corroborated z-ratio in 1 sec increments on Maclab and in other sleep systems. Rembrandt and Compumedics have each written z-ratio add-ins for their systems, and from what I understand Somnostar actually includes it in their system by default, as an adjunct analysis. EDFBrowser (open sourced) by Teunis van Beelen has also written Z-EEG into his EDF viewer (see attached graphic of the channel options button for Z-EEG "EDFBrowser.jpg") http://www.teuniz.net/edfbrowser

 

All other sleep depiction issues relate to moment by moment sleep/wake determination. Vizual staging forces the scorer to choose which seconds of the recording are "sleep" or "wake" on any given page. So, in effect we are performing fluid second by second visual pattern recognitions, which is very cumbersome and we gloss over and do not account for the most important part of the PSG, the "non-sleep" time. Arousals are 3+ seconds of "waking" with 10 seconds of "sleep" preceding. The need for automated, sec by sec fluid sleep depiction is evident, just only few have put forth methods to do it in this short a time frame. Typical, automated methods look for ways to simulate the staging process with the computer making similar "judgments" as to stage. That is no longer needed. We now have a metric of sleep/wake. We can still utilize the stage scoring paradigm, but now we would have a quantified per second metric to gauge the sleep/wake ness of each second. This is exactly that we do when visually scoring. 

 

The algorithm calculates the relative contribution of fast (sleep) activity versus slow (sleep) activity in the period being analyzed (time series) via FFT. [NB:I will add that z-ratio is impervious to which analysis routine is being used for EEG power per frequency (FFT, Wavelet, PASS, etc.) as long as there is no apriori weighting of any portion of the spectrum being analyzed.] z-ratio is in effect just an algorithm of simple comparison. The beauty of the formula lies in its confinement between -1 and +1. It has always bothered me to see publications performing ratios of slow frequencies to alpha in a straight sf/α which had no boundaries to plot the data usefully to see subtleties.

 

The issue with FFT is that it does not determine WHERE in the time series the activity in question is located. Meaning, if you have a time series of say 4 seconds, and the FFT says you have a peak of 3 cps activity, the question remains WHERE in the 4 seconds is that 3 cps activity? Is it a burst, or diffuse? This is why I tried to take as short as possible time series for my FFT, and getting down to the core sampling time of 1 sec time series allowed using the FFT as a new source for further analysis. At the time of my first publication I only had access to our sleep system which  performed 2 second FFTs. This was OK, but still left doubt as to which second the activity was located in. This is also why I feel FFT should only be done on a per second basis, since the measurement of any power analysis derives to the power of "frequency per second." So, why would one want to have a time series of 30 seconds and perform a single FFT on the whole epoch if they are looking for sleep/wake transitions?

 

Z-ratio does not score sleep. It depicts the relative contribution of the fast to slow activity in single seconds. It yields a unified, objective, reproducible metric per channel. Z-ratio can be used in combination among derivations, since sleep detection per second is basically “fast is wake”, “slow is sleep” visual pattern recognition which is then arbitrarily categorized into "stages." Z-ratio could be used on each EEG derivation and logic sets could prevail to re-categorize standard staging rules based on the three standard derivations (EEG, EOG, EMG) down to per second "staging." But using z-ratio to only create 30-second staging categorizations would be a sin.  I would epxect that new findings in sleep could be found as z-ratio is adopted. Brain mapping of sleep/wake could be performed using this metric. I envision red and blue colors depicting the z-ratio scale (red = wake, blue= sleep) and gradiations of colorings per z-ratio interval per EEG derivation. It would be so amazing to see the mapping of sleep/wake across multiple derivations in real time. Similar to how we visualize "sleep" happening in Frontal and Central EEG derivations BEFORE Occipital; this would now allow the mapping of the micro-fluctuations of sleep/wake. Think possible insomnia feedback. The possibilities are endless.

 

When we let go of the artificial, static 30 second snapshots of sleep (two 30 second frames per minute) and think in fluid "60 frames per minute", we see a true movie of sleep versus the old fashioned flip book artificial "moving images."

 

As the world moves toward more and more artificial intelligence, these technologies require quality data as a source. Z-ratio provides high-quality, objective, reproducible per-second data streams. This treasure-trove of per-second data is AI ambrosia. 

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In the presentation I depict how a simple regression line through all of the z-ratios, from Lights Out to Lights On, can yield a set of two values (slope and intercept) depicting all of sleep/wake across the recorded period, or more correctly, analysis period as z-ratio also functions within wake EEG to detect microsleeps. It functions on EEG period. There is also the advancement of Sleep by using mathematically sound calculations and graphing on this new mathematically sound metric of weighting sleep/wake. I have been interested in phenotyping sleep based on the slope and intercept of the overnight z-ratio per second for over two decades [see slides 34-38] attached here.

 

There is also the, still to be sorted out, finding we made of an unrecognized 5-7 sec undulation of z-ratio across leads during sleep and wake [slides 43-49]. This is different from other power fluctuations as in Ronald Chervin's respiratory coupled fluctuations (RCREC) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2603494/ . I need to get my hands on some 24 hour EDF studies to prove that this brain z-ratio rhythmic activity is also seen throughout the wake period, which I predict it will be, as it has for the short wake episodes recorded in sleep studies. I speak of this in the Berlin presentation. This is probably some form of a thalamo-cortico loop activity, https://en.wikipedia.org/wiki/Recurrent_thalamo-cortical_resonance possibly the constant tension between inhibition and dis-inhibition.

 

Welcome to Z-EEG: When you absolutely, positively, have to have an objective, reproducible, independent algorithm to quickly and easily depict sleep/wake from a single channel of EEG.

 

Thank you for your interest in z-ratio.

 

"Simplicity is the ultimate form of sophistication"

~Leonardo Da Vinci~