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I know there are a number of people here that work in the audio industry and others that just know a lot more about it than I do so I'm posting here.

It's for a future project I'm working on. I'm looking to build something that will create a pulsed electromagnetic field in discreet frequencies from 5Hz to 200Hz. The 200Hz is easy but the 5Hz is the problem. I found a "reference amp" that went down to DC but the price range was out of this world.

It needs to be 100W, preferably mono or stereo bridged. 2 or 4 ohms would probably be perfect.

Any suggestions? I'd like to also minimize the cost.

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I figure I could create the square wave input with a computer or Arduino board, feed it through the amp, and build a coil to create the electromagnetic field. I might need help with the coil too, but I figure I can wind a coil, buy or preferably rent a gaussmeter and do some experimentation.

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You might ask what I'm building? I want to build a PEMF (PEMFt) device (google that if interested).

Here is the back story:

My mother-in-law has Parkinson's disease. Brother-in-law Bill works to connect venture capitalists with people needing investments. Brother-in-law Kevin is a world famous doctor (lectures other doctors all over the world).

So Bill was trying to connect investors with a guy who is building PEMFt machines to be sold to the medical profession. PEMFt is approved for pain clinics, bone repair, and veterinary medicine in the USA and a lot of other uses in Europe, Australia and other countries. In some of those other countries PEMFt has shown to help a large percentage of Parkinson's patients. Kevin says it definitely won't hurt to use the machines and there is a chance it might help.

Parkinson's isn't curable and the medicines that treat the symptoms have less and less effect as time goes on, so anything that can slow the eventual decline and perhaps even show some slight improvement is a good thing.

I read a lot about PEMF/PEMFt and it seems like proverbial "snake oil" - too good to be true. But Kevin says it definitely won't hurt.

The guy building the machines that Bill is trying to connect to investors doesn't have FDA approval to sell them yet (it's a loooooooong process), but is letting people use them while he takes notes and evaluates the progress or lack of progress of the people that come in. He isn't allowed to charge money, so he has a tip jar to help pay for the electric consumption.

OK it's getting like a B movie, isn't it??? Waiting for the "Bride of Frankenstein" to appear at any moment (she was hot, wasn't she? -- and that hair-do -- wow!)

OK to get serious again...

So we figure, it won't hurt, and we bring mother-in-law down for a month's worth of treatment. The problem is that it's 2 hours each way in moderate traffic, and another hour for treatment - and at 5+ hours used up, the day for us is shot - as self-employed people that means no income generated. But mom is worth it. So we did it for a month.

Problem was complicated by mom needing surgery for arthritis in the neck and got a portable PEMF device to help the bones grow back. The portable device was programmed to die in 90 days.

While we were taking mom Leilani and I figured, it wouldn't hurt so why not spend the hour getting zapped instead of sitting in the waiting room. After a month I noticed much better eyesight. I'm farsighted and even when these glasses were new, I couldn't read tiny type. Now with my glasses I can read things I couldn't read with a magnifying glass and my glasses when they were new! I also noticed a little finger that I injured many years ago that gave me pain while playing guitar and certain notes on the saxophone doesn't hurt at all an more. Also a sharper and quicker mind. Leilani noticed improvements as well. So maybe it isn't snake-oil after all.

Well they sell home units, but (1) they are underpowered by comparison and (2) at least $4,000 each. The ones they use that are proper powered for pain clinics and race horses cost $20,000 and up. OUCH!

So I figure I can build something that creates an electromagnetic field, after all, that's what the voice coil in a speaker does. So I contact an engineering friend who gave me a few pointers, reassured me that my thinking is right, and I'm out to build a PEMFt machine that isn't 4 hours away. They won't have the automatic control for frequency and timing that the expensive units have, but I can set frequency with the signal generator and use an alarm clock for timing.

At least investigating if it is affordable. I figure I can produce the square wave. I've even seen old Heathkit devices for sale on eBay.

So the biggest problem now is an affordable power amp that can go down to 5Hz. Once I locate that, then I'll investigate the gaussmeter and coil construction.

Any help with the amp?

Thanks,
Notes
First thing to know is the Impedance of your coil...

The Impedance is important because any amplifier you find will have to be able to develop your required 100W into that impedance.

So what is the size of this coil, what is the gauge of presumably copper wire of this coil, does the coil have a ferrite or iron core in it or is it an air core?

For something as you describe, I'm thinking that a full on Audio amplifier may not be needed, although it is "off the shelf" -- what you describe likely does not need to be a High Fidelity amplifier. That could then make the entire process a lot less expensive. Could be as little as a couple or four FET outputs on a heatsink with a small driver board. (For pulsing a coil with sqarewaves from the given ~5hZ to 200KHz, a signal generator or waveform gen would be $$$ OVERKILL. A 'Triple Nickel' LM555 IC and a handful of components can be used as the generator. And FETs may not be the best route, either, I'd consider the lowly SCR (Silicon Controlled Rectifier) as the driver, definitely.)

Feel free to PM me, Bob.


--Mac
Square wave pulse? Sounds like good old CW to me.But faster.LOL. Find an old Crown DC300. They went down to DC.
I would think that portable Pain Management devices would be of interest to the Veteran's Administration (VA) or Disabled American Veterans (DAV) and they have $$$ to throw at it. I will help in any way possible, Bob. Another idea might be to contact medical schools and get the school involved, perhaps as a doctoral thesis project.

Addendum: I have one VA Dr friend who is a Psychiatrist and fellow musician who, if nothing else, could open some doors for you.
I have no intent on marketing this thing. FDA approval is both expensive and time consuming. There are already approved devices out there used in pain clinics in the USA and for other purposes in other civilized countries. Plus I don't want the responsibility for anyone else's health.

If you google PEMF and PEMFt you will find the applications for this to be widespread. Arthritis, vision problems, bone regeneration, nerve regeneration and tons of others including to relieve the symptoms of Parkinson's Disease. PD is a brain disease. Among other things it causes limb tremors, which the drugs mostly control, but also, PD patients fall a lot as the brain and the legs sometime don't coordinate. This is a severe problem as mom hurts herself when she falls. She lives alone and refuses to go into an assisted care facility.

So if I can build this thing, it will definitely continue to help my eyesight, finger injury, and brain quickness, and if it relieves mom from one fall, it's worth the money.

And I forgot to mention. I've had bursitis in my hip since I was a teenager. It's a family thing on my father's side (thanks Dad). All traces of it are gone. PEMFt is supposed to work for arthritis too.

I'd still be taking her to the already invented machine, if it were not a 5 or more hour day and a half tank of gas.

The Crown amp looks good, and there are a lot of them for sale. Thanks John.

I might go with the signal generator instead of the computer as then I could rack everything together.

All and all I want the field to be 20 - 30 Gauss. I haven't investigated which frequencies do which job yet. There is a lot of research to be done before I start, and I'm gigging a lot this time of year, so I don't expect to have it done next year.

And Mac, a PM is coming your way.

Thanks all.

Any more info is appreciated.

Bob
One more thing, I read that NASA uses PEMF for manned space flight as human life is depending on the natural PEMF of planet earth which is much weaker in orbit. The more I research PEMF the more amazed I am. Like I said, if I didn't have first hand experience with the benefits, I'd think this kind of thing to be akin to quackery.

It's Monday, no gig today, so I'll catch up on some Norton Music stuff. Birthday gig tomorrow and then more holiday parties. Life is good!

I think all I need now is the formulas or advice on winding the coils. The will be air core (or human body part core), big enough to fit a human head into, and 4 ohms impedance. I'm supposing the variables are wire gauge, number of windings, and diameter. The field should be 20 - 30 Gauss, and I need to find the formulas for that.

Notes
How about a rack mount analog synth set to square wave. Not sure if it'll go down to 5 Hz.
Notes, yes, the good old Crown DC300/DC350 series amps will go right down to DC.

Take a look at "function generators" rather than "signal" generators, too.


--Mac
Another thought I also have is this:Are you going to want and rectify the output so that the coil always sees the same polarity. I may not be saying this right but I think you know what I mean. If the output is actually AC even though square wave the magnetic field will also switch poles North/South based on this oscillation. Maybe what you really want is pulsating DC? AKA rectified AC but unfiltered.
Hmm, not sure. Rectified DC seems to make more sense and switchable N or S polarity.

Thanks again.
Quote:

Hmm, not sure. Rectified DC seems to make more sense and switchable N or S polarity.




I suspect this could be more important than it first appears... given that the human body seems to contain a balance of forces at pretty much every level (at least that I've read about) it may actually be important to balance the N's with the S's. (I have no desire to get into a metaphysical Yin/Yang type debate here, it's just an observation)

Might be worth checking the NASA patent if you can locate it as it will probably mention that aspect.
Just had a quick look - couldn't find a NASA patent but did find a trademark..?

This patent information did come up though - haven't read 'em so I don't know if they'll help:
http://www.google.com/patents/US6132362
http://www.google.com/patents/US5181902
http://www.google.com/patents/US5743844
http://www.google.com/patents/US6443883
Thanks Lawrie - this could be a gold mine.

I also found these:

http://patentscope.wipo.int/search/en/de...r=&maxRec=1

http://patft.uspto.gov/netacgi/nph-Parse...p;RS=PN/7335156
Found a book translated from German that says this cures tinnitus in a large percentage of cases. This might make this thread on topic, since many musicians suffer from tinnitus.

Notes
I think I'd REALLY like to see the details of what you eventually come up with...
I'll share, but of course, you accept full responsibility and use at your own risk.

Of course, if anyone wants to help with the research, we can make it a group project.

The possibility of reducing tinnitus, relieving arthritis, improving nerve conduction speed, regenerating nerves, better vision, and speedier brain functions are things that many musicians can benefit from.

Early gig today, so I don't have much time to google. My next step is to find out if it's really a square wave or pulsed on/off. Gigs straight through Sunday too. It's a great time of the year to be a musician in Florida.

Notes
Notes, there's an online square waveform generator here: save to .wav is part of the page. Burn to CD. Done.

http://www.audiocheck.net/audiofrequencysignalgenerator_squaretone.php

-Scott
Thanks Scott. They are of short duration, but I'm sure audacity can fix that after downloading.

Plus I'll have to make sure the CD player will go down to 5Hz

I also found a "Spectro Signal Generator" - shareware for about $10 - I could use a laptop if the USB to Audio interface has a wide enough bandwidth. I checked the manual for my Edirol units but bandwidth is not noted in the specs. I suppose I could go computer to computer and use Audacity for a check.

Right now I'm trying to find out if I really need a square wave or more of a pulsed wave (for lack of a better term: a square wave with no zero crossing).

But I've got a one-nighter gig every day until Christmas Eve so my googleing and/or testing will be limited until after Christmas.

Bob
Haven't had a lot of google time, but so far this is what I suspect:

The source is not really a square wave that goes from + to - but either from + to 0 or - to 0.

More googling next week. Early setup for another gig today.

Notes
Quote:

Haven't had a lot of google time, but so far this is what I suspect:

The source is not really a square wave that goes from + to - but either from + to 0 or - to 0.

More googling next week. Early setup for another gig today.

Notes



This really shouldn't matter if you are converting this through a coil I would think. Seems like you have more homework to do.
Quote:


This really shouldn't matter if you are converting this through a coil I would think. Seems like you have more homework to do.




Agreed.


--Mac
Quote:

Quote:

Haven't had a lot of google time, but so far this is what I suspect:

The source is not really a square wave that goes from + to - but either from + to 0 or - to 0.

More googling next week. Early setup for another gig today.

Notes



This really shouldn't matter if you are converting this through a coil I would think. Seems like you have more homework to do.



I think it does matter. It's not just a coil. It's a coil around a core.The North /South poles of the magnet will reverse.
Where did you find out that there is a core involved, John?

Even with an iron or ferrite core, I don't think polarity will be an issue, simply because if you tried to hit the coil with a DC pulse, the collapsing magnetic field of the core would then generate a back EMF in the coil, which would also generate a magnetic field of the opposite polarity for that part of the time, then the whole thing repeats again with each cycle.


--Mac
Yep, more homework is mandatory. Just got off an afternoon Christmas party gig, and am pooped, dinner to follow, then some fun with the wife. Date with google tomorrow AM.

Notes
OK, in my research, I found a PEMF unit that does what I want my home-built unit to do, for less than the price of a decent gaussmeter (which I would need to measure my results).

So I'm probably going to get that unit instead of building my own.

PEMF therapy is supposed to relive arthritis, reduce tinnitus, reduce 'senior moments', improve eyesight, and number of other things that might be of interest to musicians.

Is anyone interested in keeping this thread alive and reporting results?

If yes, say so, if not I'll let it die.

Insights and incites by Notes
Quote:


PEMF therapy is supposed to relive arthritis, reduce tinnitus, reduce 'senior moments', improve eyesight, and number of other things that might be of interest to musicians.




While I do wish you well with your experiments, I must state that whenever a single item, be it an herbal "cure" or a machine, touts long lists like the above listing all sorts of claims as to the ailments it supposedly has cured, to date every one of 'em has been the proverbial snake oil.

A hundred years ago or so, the big thing was Diathermy.

Today, the remaining pieces of Diathermy apparatus foisted off onto the public are the things of collectors and museums where people marvel over the gullibility of their grandparents.

Have Fun, Notes, but by all means please be skeptical here.


--Mac
Bob, I am interested enough to want to hear your progress and results. Thanks for letting us in.

Richard
Hmm, I thought I already answered this, but I must not have hit the "Send" button.

After extensive googling, I found that it does need to be a pulse, preferably zero to north polarity.

I also found a commercial unit, that does what I want and costs less than a decent gaussmeter that I would need to test my build. So I'll probably spring for the commercial product.

Now PEMF therapy is supposed to do a few things that might be of interest to musicians (1) relieve arthritis (2) reduce tinnitus (3) increase brain power - of course these things are not FDA approved, and not guaranteed to do any of the above. Also, one uses them at their own risk. But they are approved in Europe and other countries for these symptoms, and also approved by the FDA for bone healing after a fracture.

If anyone is interested in reports and/or progress let me know.

If not, I'll just let this thread die.

Notes
I read on the Internet that it can also make me lose 40 pounds and make me handsome and good looking, too.


--Mac
Enough likker in the other person can do that, too.
Tall, Dark and Handsome.

Hey, two outta three ain't bad...



--Mac
I'm interested in your results Notes, both positive and negative.
Quote:

While I do wish you well with your experiments, I must state that whenever a single item, be it an herbal "cure" or a machine, touts long lists like the above listing all sorts of claims as to the ailments it supposedly has cured, to date every one of 'em has been the proverbial snake oil.<...>




My feelings exactly. Especially when something claims to cure so many different diseases. If we couldn't have tried it so inexpensively, I would have shrugged it off as snake oil and not even drove to the 'clinic'. But mother-in-law wanted to try it.

When we took my mother-in-law down it was an act of desperation. Brother-in-law the surgeon said it wouldn't hurt and was probably worth a try as the PEMF machines are approved in Europe, Australia and many other countries plus here in the USA they use them for bone healing and in pain clinics ... and in addition they are used for veterinary medicine, especially to relieve arthritis in race horses.

But her current problems weren't Parkinson's related. She had a pinched spinal cord and needed surgery to relieve the pressure. So any PD improvements were masked by the pinched nerves.

So Leilani and I figured since it won't hurt, and since it was less boring than waiting in the waiting room, we could lay down on the lounge chair and get zapped ourselves.

So after a few weeks, I'm looking at my droid phone keyboard, and I can see the difference between the comma and the period. My glasses are old and I'm overdue for a new pair. Even when new, I couldn't read tiny type as the compromise between near and far objects put close focus at about relaxed arms length (book reading length). By the end of the month I could read tiny print anywhere, on the back of those pink sugar substitute packets in a restaurant, and everywhere else. I find myself looking for small print to read, and in decent light I can read anything (with my present glasses). Haven't been able to do that in 20 or more years.

I have an injured small finger on the left hand. Probably from the days when I played basketball. It's been bothering me a lot when playing guitar, playing G#s on the sax, and using the left Shift key on the computer. Pain was all gone. This was like magic because that joint has been bothering me for decades.

I have bursitis in my hip and have had that since high school. Runs in my dad's family. By eating an alkaline balanced diet I got rid of 90% of it. Since the PEMF I can jump up and down and it doesn't bother it a bit (I still eat the alkaline diet).

Leilani had eyesight improvement and increased joint comfort as well.

And as the months passed after the 'treatment' my eyesight started to revert and my finger got some slight discomfort back - but not the strong pain when playing the guitar like it did.

So I'm starting to think it isn't snake oil at all. Not that I believe all the claims about it, they just seem too good to be true. But for joint pain and eyesight it seems to work on us.

So I've done a lot of googling to find that NASA uses PEMF whenever humans go into space, including the space station. It seems the earth itself has a pulsed electromagnetic field of about 9.6Hz and the animals that evolved with it can't live without the magnetic field. The magnetic field gets weaker and weaker with distance, so the people who spend days or months in space need the pulsed field or their health will degenerate. NASA uses a square wave, north polarity, at 9.6Hz.

Also studies show that the earth's magnetic field has been steadily getting weaker, which is why some scientists are predicting another reversing of the poles. But this get beyond fact and into guesswork.

The medical profession in Europe has had remarkable results with the majority of Parkinson's Disease patients and a number of other diseases.

Pain clinics pay up to $60,000 to buy a clinical machine that does the entire body at once (like the ones we laid on at Ernie's "clinic").

According to what I've googled: It seems to work with calcium, which I found out is paramagnetic (magnets affect it but it doesn't stay magnetized like iron). According to the theory, calcium is constantly being replaced in the bones (this part is a fact) and the old calcium lodges itself in the joints and the nerves. The pulsed magnetic field shakes the loose calcium and if you drink enough liquids, it flushes out with your urine.

So I figure (1) it can't hurt and (2) it certainly helps my finger, hip and eyesight, and (3) if there is a chance it will help mother-in-law's PD, it's worth a try anyway.

So while I remain skeptical about the PD, if it helps her arthritis like it helped my finger and hip, that's good enough. If it helps the PD, it's even better.

So I've plunked down some bucks and I'll let everyone know what we are experiencing. Positive, negative or nothing at all.

So while it won't make you handsome Mac it might help a few of us with arthritis problems.

I won't know if I don't try it. I'll keep you all posted as long as anyone is interested. If not I'll just let the thread die.

Insights, incites, and some guarded hopefulness by Notes
For Mac and the other skeptics (myself included) there is a lot of very positive information about Pulsed Electromagnetic Fields on the U.S. National Library of Medicine - National Institute of Health web site.

1200 peer-reviewed published studies are listed here.

http://www.ncbi.nlm.nih.gov/pubmed?term=pulsed%20electrmagnetic%20field

The more I learn about this, the more I actually like it. Of course I'm hopeful, especially for my mother-in-law so that is bound to slant my view, but on the other hand, as a natural skeptic I am doing my best to keep my hopes and wishes out of the investigation.

Insights and incites by Notes
Here are the conclusions of other peer-reviewed scientific studies about PEMFT along with the name of the study if you want to read the abstract.
http://pulse4life.com/docs/Scientific_Studies_On_PEMF.pdf

And as for the effects on me:

My arthritis, and bursitis is gone - completely.

PLUS: My brain is sharper, my energy level is up, and my vision is much better. I'm farsighted, which means nothing is in focus, but far things are less out of focus than near things. The compromise in my glasses was near focus is sharp at comfortable distance and newspaper sized typeface. Now I can read the tiniest print and can focus on things about a foot away from my eyes (with my glasses).

Leilani has had similar results. Her arthritis is lessened but not gone yet, her vision better (she's nearsighted), her mind is sharper, but her energy level hasn't increased (but I don't think it needs it).

The $600 machine will pay for itself in the supplements I'm no longer taking. They offer a 90 return policy, but they aren't getting it back.

I've ordered another for my mother-in-law to see if it will help with her Parkinson's and never damage. Both conditions have peer-reviewed mostly positive papers published.

Of course, this isn't a scientific double-blind test, but merely my personal experience with the device. But I'm sold.

Notes
WOW, Bob ... that sounds pretty darn promising. Might have to look into this myself.

Thanks for the update and the link to the PDF. VERY interesting stuff!

Cheers,
Mike
This is very interesting and exciting news Bob. Would you happen to have a link or other info on the unit that you are using? Thanks.

Jeff
Hang in there. I'm in the process of setting up a web site to talk about PEMFT. Should be up today, I'll post here when it's done.

That will keep long OT posts off the music forum.

Notes
OK, I've started a website http://www.pemft.info that explains my journey into PEMFT (Pulsed Electromagnetic Field Therapy) from day one. Please read the home page. I gave the condensed version here when I was trying to build my more powerful PEMFT device, this page gives the whole story.
    In this site:
  • I plan to include all the science based information I found (and not the hype) from my hundreds of searches on the web. There is no place with all the information in one place - I'm going to try to correct that

  • It will be advertiser supported so that it can remain free

  • I'll include pros and cons

  • I plan to include comparisons of the various commercial devices with their waveforms, field strength, etc. - this information is difficult to find

  • I'll also include verified testimonials for different devices

  • Note: since you asked -- the top ad on the "where to buy" page is the link to the $600 device I'm currently using. If you plan to buy, please use that link - I'm hoping the ads will support the site.

So why the website? First of all, I have put thousands of hours googling this and it was frustrating. I like writing HTML code so it was fun to create the website. I found a good deal on a web host that the ads should pay for. I don't expect to get rich on the ads, but as long as the ads support the page I'll keep it up.

Most importantly, while I started out skeptical, I'm very enthusiastic about this technology. Because of the difficulty to find good information, I paid way too much for a much weaker machine before I found the better one. And I didn't want to be responsible for a health-care decision for anybody else but me, so I found peer-reviewed, scientific articles about PEMFT and included them on the site. That way if you want to do this yourself, you can make in informed decision.

Now I've recently started putting the magnet under a 4" "memory foam" topper and sleeping with it. Not in the "sleep mode" (I have no trouble sleeping) but in the more powerful "recover mode" (I would suggest trying the sleep mode first to get used to it, but I've been doing this for a few months now).

The arthritis in my little finger is completely gone, Leilani's arthritis is lessened considerably. I typed all day yesterday creating the website and neither the injured little finger nor the former "trigger finger" on my mouse hand have any sensation at all.

My mind is more alert and I have more physical energy. Leilani's mind is more alert but she always runs at maximum physical energy.

It's magic.

So I'll continue to give reports on my health experience, but for any more questions, please go to the http://www.pemft.info site.
Not just Magic, Notes ole bean, but since yer gettin' into technology, the terminology we like to use around here is to tell 'em its, "FM".

The M stands for Magic, be creative as to what that F stands for.

As in,

"How does that work?"

"Its FM."





--Mac
I recall my days as a CableTV Field Engineer and I remember FM very well along with the term we can't define on this forum RCH
We got one of these for my mother-in-law who has Parkinson's. It comes with a 90 day risk-free trial - if it doesn't work, send it back and get your money back. So we had nothing to lose but the shipping charge.

Every Tuesday afternoon mom comes out to listen to us perform. We are used to seeing her sit there with the "Frozen Parkinson's Face", with her eyes staring, mouth partly open and responding to but not initiating conversation with the other regulars at her table.

After only two nights with it, we saw her eyes alive and darting, her face lit up and smiling, and she was initiating conversation with the other regulars at her table. While we were packing up our gear, another of the regulars told Leilani that her mom was sure having a good day today. It was good to hear that from someone who didn't know we were doing anything new.

She said she is also walking better and is more alert. She's had it less than a week now, and already says it's a keeper and it's not going back.

------

From The U.S. Library of Medicine - National Institute of Health:
http://www.ncbi.nlm.nih.gov/pubmed/8496242?dopt=Abstract

Beneficial effects of electromagnetic fields
Bioelectric Research Center, Columbia University, Riverdale, New York 10463

Abstract

Selective control of cell function by applying specifically configured, weak, time-varying magnetic fields has added a new, exciting dimension to biology and medicine. Field parameters for therapeutic, pulsed electromagnetic field (PEMFs) were designed to induce voltages similar to those produced, normally, during dynamic mechanical deformation of connective tissues. As a result, a wide variety of challenging musculoskeletal disorders have been treated successfully over the past two decades. More than a quarter million patients with chronically ununited fractures have benefitted, worldwide, from this surgically non-invasive method, without risk, discomfort, or the high costs of operative repair. Many of the athermal bioresponses, at the cellular and subcellular levels, have been identified and found appropriate to correct or modify the pathologic processes for which PEMFs have been used. Not only is efficacy supported by these basic studies but by a number of double-blind trials. As understanding of mechanisms expands, specific requirements for field energetics are being defined and the range of treatable ills broadened. These include nerve regeneration, wound healing, graft behavior, diabetes, and myocardial and cerebral ischemia (heart attack and stroke), among other conditions. Preliminary data even suggest possible benefits in controlling malignancy.


The more I learn about this, the more like magic it becomes.

Notes
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