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1. Why do we need Ag/AgCl electrodes?

In order to transfer a charge from an electrode in a solution, you have to switch from electronic current (in the metal) to an ionic current in the solution (or vice versa). Problem is, that the solution tries to "shield" the charged metal surface by (depending on the detailed look) at least the Helmholtz-Double layer of ions. That means, a metal in solution not only forms a an electrical half-cell, but a capacitor as well. Now, usually one could life with that issue, since the surrogate circuit only acts like a filter for signals, but depending on the "noble-ness" (the half-cell potential) of the metal, it is prone to corrosion, too. That means, with less noble metals, you are depositing metal ions in the body, which is not acceptable. Electrodes forming the capacitance by Helmholtz-Layer are called "polarizable".
A Ag/AgCl electrode transfers the charge across its boundaries by a reversible Redox-Reaction. It is thus not forming a double layer and has thus "no" filter properties.... It is called non-polarizable electrode.

2. How are similar electrodes rated? Is one "better" than another? More stable for instance?

Electrodes don’t have a current rating system because the decision of which electrode depends on budget, patient demographics, and, most of all, a simple issue of personal preference in most situations. If you compare electrodes, you have a few differences, such as different types of metal. Electrode options include gold, silver or silver/chloride, tin, platinum and more. Now these metal types are often just on the outside of the electrodes--for example a Gold Cup is typically an electrode made of silver with a plating of gold on top of the silver base. Many folks think a gold electrode is 100% gold and this is not the case. The purpose of the metal is to conduct, and each lab may decide which metal produces the best data for their service. Gold is usually preferred for PSG because it has been shown to enhance the slower frequencies better which is important for PSG labs. EEG and Epilepsy labs have a preference for silver metals because they accentuate the faster frequencies. I will admit that I have used many different types of metals and I have difficulty telling the difference in data results.
Beyond the metal, there are differences in the way the “cup” shape is made. A “stamped” style electrode typically has a bigger cup capacity and is a thinner thickness versus the “casted” style which is a thicker metal cup with a smaller cup capacity in some cases. Both collect data and it’s a preference as to which is preferred.Some casted styles have a thinner “rim” that touches the patient than a stamped, so some folks prefer a casted for skin integrity issues.
Other differences are the way lead wires are made. Some are made of copper, some of tinsel and other materials. That is what makes different lead wires “feel” different between manufacturers. Different strategies are used due to cost and artifact management.
And, then you have the transition to the use of fully disposable EEG electrodes which are electrodes made of a base of plastic and covered by silver, silver/silver chloride, or other materials. So, the summary to the above answer is that is up to each individual as data can support the advantages of each different type of lead, but whether that benefit translates to a usable benefit for your lab is a question only you can answer. To compare, I would recommend calling manufacturers and asking for samples for comparison purposes and do your own head to head comparison. Because remember, you can use different leads from different manufacturers, however, I would avoid mixing metals on the same patient or differing types of conductive paste. But, the same metal type with the same past or gel will be a solid comparison.

3. What are the best electrodes for signal?

You would assume this would be a fairly easy question to answer, but it’s not. It’s all dependent on what signals you are recording. For example epilepsy and EEG folks look for high amplitude fast frequencies and that is not the same data that a PSG technologists would be looking to obtain. And, the above question of type of signal could be handled by scientific data analysis of metal type and manufacturing styles; but even more importantly, what your preference for the tangible “feel” of the electrode. It’s a very subjective answer. And there is no concrete and definitive answer to your question. But, with that said, there are a few statements that have been widely acceptable for decades. I'm not saying each point is completely correct but arguably the below statements have been generally accepted. --Casted cup electrodes are more durable than stamped.
--But, stamped electrodes have larger “domes” for holding conductive paste than casted styles.
--Casted are more expensive than stamped.
--Gold electrodes record better PSG data than silver because they accentuate the slower frequencies.
--Silver leads are better for EEG and epilepsy studies for the reason mentioned above.
--Chlorided silver electrodes record EEG data even better than unchlorided silver electrodes
--ECG pads are better for recording peripheral data like legs than cup electrodes
Now, you add all the new products of flat electrodes, disposable EEG cups, and more, and your question gets even harder to answer. My recommendation: call around and ask for samples of gold, silver, silver chloride, stamped versions, casted versions , flat versions, disposable cups, and any other electrode type you want to consider. Then, I recommend you apply a few electrodes of each type to the same patient. Make up a montage and record the data and see how it looks. This will help you decide which electrode is the best for what part of the patient’s body and for your application technique. So the answer really is that all electrodes regardless of manufacturing style (stamped or casted) or metal type (gold, silver, silver/silver chloride) conduct the electrical signals from our patients in the form of EEG, EMG and other data. So which is best, truly is answered per each individual’s preference until a day arrives when one electrode type can prove its dominance over the rest. and lastly, the lead wire attached to the electrode is whole other conversation--same argument regarding which lead wire is best.

4. What is the advantage of using gold cup EEG electrodes instead of silver EEG electrodes?

Also, why is gold plating preferred on the EEG electrodes? What is the function or the role of gold on the electrode?
The answer to all of these questions has some historical background.
If we rolled the clock back 20 years these questions would have been more critical because our amplifier technology wasn’t as advanced as it is now and consequently the metal type of the electrode made a bigger difference. For example, with older equipment, it was important in PSG to use a gold or gold-plated electrode because the metal type would help to enhance slower frequencies, which was very helpful in applications such as PSG but not so helpful in applications such as EEG where the faster frequencies are of greater interest.
So, historically EEGers would want to use a silver or silver-silver chloride (Ag or Ag-AgCl) electrode to assist with enhancing the faster frequencies for epilepsy and the PSG community wanted to use a gold or gold-plated electrode to enhance the slower frequencies of sleep.
But, the reality is today’s amplifier technology is so good you will be very hard pressed to see a difference, as the amplifiers can show both ends of the spectrum very well and this allows you to filter in and out with greater confidence. Test it for yourself with your equipment; get samples of both types and do a side by side.
By the way, nearly all reusable EEG electrodes are made of a silver base (not actual gold) and then a layer of gold plate is applied or a layer of coating with silver-silver chloride was applied to the silver base underneath. This is the same concept with disposable EEG electrodes as they are made from a ABS plastic base and then plated or coated with either gold or silver. The characteristics of the metal types still exist but advancements in our equipment have enabled either choice to be equally appropriate. But, test it out with your specific equipment and judge for yourself.

5. What is the best electrode to be used with a PSG? Is it gold cup or silver chloride electrodes, and why?

Given the technology available today with high-end sleep systems, this question has become more subjective than ever. Historically, the gold cup electrode has been preferred because the gold did a better job of accentuating the slower frequencies than silver or silver chloride electrodes. This characteristic was a benefit for PSG as those frequencies were, in general, of greater interest than the faster frequencies. But, fast forward many years and the equipment manufacturers have made such advancements with the amplifier technology and the ability to re-montage and re-display digital data that our electrode metal choice has become less of a concern.
To really answer this question for your lab or service, you must do a comparison test. Use a volunteer and connect a small set of gold electrodes and run a short study. Then, remove those electrodes and repeat on the same volunteer. This head-to-head comparison will show you and your staff if any differences are present between the electrodes types and your particular equipment. In most cases I would bet no noticeable differences are evident but depending on the age of your equipment and the manufacturer, filters, etc., some slight differences may exist and you may find you have a preference. And this test can be done any time you are testing out options and want to verify if data quality will be affected negatively (or positively).
But, I want to warn you of one more difference that should be documented: the type of lead wire being used on the electrodes. Whether you prefer gold or silver chloride electrodes the type of lead wire can affect artifacts and data quality, so don’t ignore that piece of your electrode. To accurately test as mentioned above, ensure both electrode types have the same lead wire type attached.