Okay, beautiful. Hello, everyone. Good afternoon and welcome to another episode of Dr. Jill Live. If you missed any previous episodes, you can find us on YouTube channel under my name. There's over 100 podcast interviews with experts like our expert today who I'm super excited to introduce. And we just got to know each other briefly now and we're introduced by friend, but I'm super excited to dive deeper today. Dr. Prodromus is an international leader in the use of stem cell and platelet rich plasma PRP treatment. He's performed more than 3000 stem cell and platelet rich plasma treatments for arthritis, tendon injuries, and related disorders as part of a prospective study that is the largest study by an orthopedic surgeon in existence to our knowledge. So super excited that you're doing the research as well. Dr. Prodromus received his bachelor's degree with honors from Princeton University and his medical doctorate degree from John Hopkins Medical School. He served his surgical internship at the University of Chicago. We're both from Illinois at some point there with medical training and his orthopedic surgical residency at Rush University and his fellowship in orthopedics and sports medicine at the Harvard Medical School and Mass General Hospital. He's board certified in orthopedic surgery and is the editor of a major textbook for orthopedic surgeons on the ACL. He's a founding member of the American College of Regenerative Medicine and chairman of its institutional review board. He served as an assistant professor of orthopedic surgery at Rush University for 27 years before stepping back to focus on foundation and stem cell work. Dr. Prodromus, it's an honor and delight to get to know you here and thanks for joining me today. Yeah, thanks so much for doing this. It's so great that you work to get useful information out. You're welcome. And you know, we were just talking before how passionate we are about really like root cause, functional, integrative, and why I don't want to go deep into this, but our system, many people have felt this is not great at getting to root cause. And I don't want a bad mouth because we've both been trained in some of the best institutes of the United States in medicine. But the truth is we often are trained with get a label, get an ICD-10, and then we stop there and we give a medicine for that ill or we prescribe a surgery all totally appropriate. But the deeper stuff that we're doing that I want to interview on is really getting to the root cause and actually solving the problem versus just putting a band-aid on it. I want to hear, though, first, your journey. Where did you grow up and how did you get into medicine? Tell us a little bit about how did you get this? I grew up in the Chicago Burbs and I just I liked science when I was a kid and nothing more to it than that. I just thought it'd be interesting. Cool. And what a career. And then orthopedics, how did that intrigue your interest as far as the? Well, it's kind of interesting because when I was at Hopkins and deciding what I wanted to do, I, I liked the idea of being a physician as well as a surgeon and orthopedics appealed to me because you're a surgeon, but you don't just have to operate on people. And it's kind of ironic because the field in the 38 years that I've been doing it has gotten much more surgical than it was. And so one of the reasons that PRP and stem cell work appeals to me is it's a way to get people better without surgery. So it's just, you know, it was an opportunity to take a huge area of medicine and try to know everything about it. Amazing. And what many people who listen maybe don't know, but we in medicine do know is it's a highly competitive field. So that means you were obviously very academically astute. And in the realm of you were, you know, an exceller, stellar student to get into orthopedics, especially in the institutions that you did. So when did you really shift from just surgery kind of the typical orthopedic practice into the more anti-aging and stem cell and some of this kinds of stuff? How long have you been doing that? So I was a sports medicine guy after my fellowship at Harvard and was heavily into that, had a narrow practice doing knee and shoulder surgery, editor of the textbook on the ACL for orthopedic surgeons. So I spent most of my career doing that. And in 2009, I read about the late Kobe Bryant getting an injection of play, the rich plasma, and seemed to get better. And so we researched it. And I established a 501c3 non-profit foundation in 2003. And I published extensively and hired researchers so we could, you know, I was just always interested in evidence based medicine. So I charged one of my research people and I said, why don't we learn about this? And she did. And it sounded interesting. So I started doing it first one in December of 2010. And there's, you know, most musculoskeletal problems don't need surgery, but we're surgeons, right? So sometimes we operate maybe even when we shouldn't. So, so I injected a few people with some knee problems and they got remarkably better. And I thought, wow, this is amazing. So I started doing more and more of it. We started, we're up to 5000 patients now, a prospective huge study. And people just did well. So I was doing that. And I was publishing. And actually, then I was solicited by a guy who was one of the pioneers of stem cell work in orthopedics in the country who people wanted to franchise him. And he said, you're an academic guy, why don't you join me? So he kind of introduced me to it. And I became interested in stem cell work and started reading about it. And it's the same kind of thing. It's a way to try to heal things without surgery. And then as time went on, I just started doing more and more of both, excuse me, and, and just, and just became fascinated by it. Wow. And again, I've got a quite a bit of experience with patients having that. I would say I don't do that in clinic at all and leave it to you guys, the experts, but tell us more about first PRP and then stem cells. I know they're similar. What actually happens with the immune system when you inject your own platelets? So, so when you inject your platelets, they have growth factors and anti-inflammatory cytokines. So there's no drug that has growth factors that helps you heal. And the anti-inflammatory cytokines, quiet inflammation and joints in a beneficial way, unlike cortisone, for example, which kills cartilage. And stem cells work sort of similarly. And I should tell you too, my journey was originally PRP, orthopedic problem, stem cell, orthopedic problems, and then like arthritis and osteoarthritis and then stem cells for inflammatory arthritis, like rheumatoid arthritis, which is an autoimmune disease. And then other autoimmune diseases to the point now where most of the stem cell work that I do really isn't orthopedic. We have great success with back problems and joints, but do are involved in some things that are just amazing with, you know, with MS with spinal cord injury with autism, other things. So, but the short answer is that's what they do. They help heal disorders, which no drug does, and which no, you know, I mean, surgery, we can put joints back together. We can't make it heal. Yeah, gosh, and it makes sense because we're using our own immune system, doing what it's supposed to do, just, you know, accentuate it at the site. What would you, why would you choose PRP over stem cell or stem cell over PRP in a certain situation, like give us some examples of uses when a patient might. So, so none of this, none of this fits the pharma model of medicine, which kind of dominates everything. And so, so none of it's reimbursed. So we do a PRP injection and charge about $750 for an injection. That's a lot of money, but we have great success, even with single injections stem cell treatments are on the order of 20,000. So I get people calling me from all over the country, all over the world, actually, and they read about our stem cell work. And I got featured by Tony Robinson, his book for our work on stem cells. And so, you know, when I can, I like to treat people with PRP because it's a heck of a lot cheaper. I treat a lot of professional athletes, NFL athletes, in particular, and a lot of times, a lot of times, a bigger factor than the PRP or the stem cells is how you handle the joint.  I've got, again, some high profile NFL people who were doing knee exercises that were aggravating the joint that, you know, shouldn't have been or Achilles exercises. And I just say, just don't beat the joint up, let it heal and they get better. So, so I do PRP when I can for orthopedic problems because it's so much cheaper and it's easier. And then in cases where, and for most musculoskeletal problems, it's good enough, you know, but where it isn't, then we can use stem cells. Amazing. My experiences might make you laugh, but in micro-needling on the face is great for the skin and collagen production. And you can add PRP to the micro-needling. And the healing for me was like a third or a half the time after a procedure like that for increasing collagen. And I was really impressed. One thing then the next step with those, again, this is different from orthopedics, but I'm curious because now the, the derm, the estheticians are often using exosomes. Have you done any work with exosomes at all in this realm or? So I'll be careful what I say here, but exosomes are not like allowed in the US. You may or may not know this, but they're not. And so we don't do anything that doesn't have to be approved. We go offshore. We have a stem cell center in Antigua. We have one in Monterey, Mexico, and we operate a full licensure there. So, so have I used exosomes? No. And, and so, so, so amniotic fluid is allowed. But it's not really exosomes, really stem cells. And sometimes people play fast and loose a little bit with terminology. So from my perspective, if I could use exosomes in the US, I would do it, but I can't. And if I'm going to bring people offshore to do it anyway, I'd rather use stem cells. And I'd say an interesting thing. So we're very evidence-based. We publish extensively in good journals. So there are only two studies. If you look in PubMed under exosomes, there's only two studies that exist. One was in long COVID where it didn't do any good. So the thing, the problem I have with exosomes is one, they're not allowed. And two, there's no evidence that they do any good. Now, I'm not saying they don't. And I'm talking legit exosomes, but there's lots of literature on stem cells. So we do those. And sometimes exosomes are kind of like stem cell light. You see, exosomes kind of fit the pharma model, which dominates everything.  The thing with stem cells is, and so, see, real exosomes are probably useful, but exosomes, in my opinion, are just a more expensive PRP. So we do PRP for $750. It's kind of a lot of money. But the usual exosome model is you buy a bottle of these things a doctor does for 1500 bucks from somebody, and then you sell it to a patient for 3000 bucks. And maybe it works, but it's a lot more expensive. And there's no data anywhere that indicates that it works even as well as PRP. Maybe it does, as opposed to stem cells where there's lots of data. So I think the push for exosomes is dominated more by economic reasons than other things. And when and if there's data showing that it really works, and then it's cost effective, and when it's legal, I'll use it. But in the meantime, I don't. That makes so much sense. I actually love that you clarified, even for me, because I love the evidence-based foundation that you're on. So tell us a little about the studies around PRP and stem cells and what kind of outcomes they've seen. So we get, so taking all commerce, we get people, and I'll tell you something, you mentioned drugs that are useful or indicated in surgery that's useful. But I'll tell you, most of the prescriptions that are out there, at least in my field, are not only not useful, they're bad for people. And a tremendous amount of orthopedic surgery, in my opinion, is sort of unnecessary now. And I'm not the only one who feels that way. So just a few examples. So I spent, made my living fixing ACLs and fixing rotator cuffs. If a rotator cuff is completely torn, it detaches, it retracts, you have to reattach it. So no stem cells can help that. Right. Although there are people using stem cells for that, but it doesn't help. But most rotator cuff disorders are 90 plus percent are not completely tears or partial tears. So we published a paper, 65 or 70 patients, minimum two-year follow-up using PRP, and none of the patients wound up needing surgery, minimum two-year follow-up, and none of them completed the tear. So a lot of those people are operated on by colleagues of mind. Why? I mean, they mean well and they want to help people. But if the only tool you have is a hammer, everything looks like a nail. So if what you're doing is surgery, you operated people. But the fact is that partial tears of the rotator cuff, which is most of them, surgery doesn't help. Studies have shown this, and I just didn't do it for that reason. So shoulder problems. Most of them rotator cuff would do well. Arthritis. So we just had a study that was presented at the International Carpenter's Repair Society in Berlin last June, just published in a good journal. 568 needs, three to seven-year follow-up. It's a huge study, the lack of which hardly anybody does. And so what we found was that taking all comers, and these were all total joint replacement candidates, 80 percent of the people out of not needing joint replacements, minimum three-year follow-up, even, and we stratified our results by how many millimeters of joint space there were, even the bone-on-bone people. So you think, and a lot of people think, right, it adds bone-on-bone, ballgame's over, I need surgery, right? Not so. So 65 percent of the people, bone-on-bone, minimum three-year follow-up did not need joint replacements. If they had just two millimeters of joint space, the number went up to 80 percent. If they had four millimeters or more of joint space, which is a noticeably abnormal x-ray, but not real severe, 100 percent of them did pretty well. So we get people from all over coming to us, or people have told them they need joint replacements, and they don't, and they do well. And we do, usually without substance, usually it's PRP. There are a number of nutritional supplements that help in the knee. We use hyaluronic acid. The one place where we even bone-on-bone, terrible shoulders, terrible knees, bone-on-bone, hips don't do well with traditional PRP. We're actually starting a protocol, which is only available now to people for the Department of Defense. It's a verencing protocol using lymphocytes to break down scar tissue. We're doing our first two patients in Monterey, Mexico in about a month, where even bad hips we expect to respond. So the short answer is tendon problems, arthritis, most people don't need surgery. And I'll say another interesting fact. So I'm independent. When I started 38 years ago, everybody was independent pretty much. Now, very few people are. So if you're an orthopedic surgeon and you're working for a corporation, I wouldn't say most of them, but a lot of the people that I know are not allowed to do PRP, at least around here. So they're told that they're there to operate. And if they want PRP or something else non-surgical, they've got to send it off to somebody else. So this puts people in kind of a difficult situation. I have a luxury of people don't need surgery. I'll send the therapy, I'll do PRP, I'll do other things. But it's increasingly difficult for orthopedic surgeons today to embrace non-surgical treatment just kind of for economic reasons. Yeah. You know, I want to just comment on that, because for those listening, we in medicine, when you say that, I get it because I'm the same way. And if you go to an HMO, I won't mention any names, an HMO or some of these organizations, those docs, they might have very good intentions and even know there's better options than just a prescription or surgical referral, but they're not allowed within that system to do that. And for you and I, I don't work for the insurance company. I don't work for any of those people. I get to decide with the patient in front of me, what's the best thing for you? And what can you afford? And how can we make this happen?  And there's no other person in every other hospitals, you know, these groups, what you're saying, and what I'm seeing as well as there are a lot of other factors that sadly influence even the well-meaning position. And I like that you say that because that's the truth, because a lot of people are, why didn't they offer me, you know, Vaswellia or curcumin or something natural? Like, well, they either didn't know it or they couldn't talk about it in that system. It's, it's got, it's or well, the young. So people, one of the main purposes of VMR, which people don't realize is it allows administrators and higher ups to monitor every phone call you make, every prescription you do. And doctors now, I have a friend who had a patient with a total cholesterol of 203, which by itself means almost nothing. And she didn't, she's actually a functional doctor now working for a hospital corporation. She didn't offer a statin and she got dinged. They said, well, dear doctor, shouldn't you have offered something? It's terrible. I'll tell you an interesting anecdote, which shows how bad it's gotten. So we have success with stem cells, with retinal disease, back in the generation, amazing stuff. So we need a retinal scan for people. So we had a patient with Kaiser from California who consulted us and we needed this retinal scan. So the, the doctor, it had been refused by the powers that be. So I told the patient. So the patient went and made an appointment with the ophthalmologist. You know why? Because they didn't want to have a phone call and they didn't want to have an email or a text because he could be monitored. So they behind closed doors told the doctor why they wanted the doctor made up a rationale and prescribed it, but they were afraid to do it through normal channels because they would have gotten dinged and maybe even gotten in trouble. Oh, that's so sad. And you're like, this is why again, doctors are frustrated because as we know better and know more, we're still in an old antiquated system that doesn't allow for this free thinking. Now you mentioned, I know I do functionalists. I do a lot of integrative herbs and things that I know are inflammatory. Talk a little bit about NSAIDs, narcotics, the kinds of things we do for pain and why they're maybe not healthy. And then what are some things that you use as alternatives? Yeah. So there are no prescription dogs that are good for orthopedics, none. So we get people off of NSAIDs always NSAIDs do three things that are bad. They mask pain and we see people, and I could show you some interesting videos, people come in and chronic pain on NSAIDs and the people that are really red hot are the people that are taking those because they mask pain, they hurt themselves and they don't know it. We stop those drugs and they get better. So number one, they mask pain. Number two, they interfere with healing in a significant way. There was a study that showed that if you gave people celibrex after rotator cuff repair, their re-tear rate went from 3% to 37% at one year. These are potent anti-healing drugs. The third thing is they're incredibly toxic and estimated 16,000 deaths every year in the U.S. from the New England Journal of Medicine article on the side effects of these drugs. So we get everybody off and we never use it. So supplements. So we did a deep type of research people four years ago or so into supplements and we looked for PubMed indexed journals, good journals, articles, clinical trials, not animals of supplements against placebo control studies to see what was helpful. So it turns out there are 12 supplements that have shown some efficacy for arthritis. So we ranked the 12 in declining order of efficacy. So we prescribe part of our algorithm of people with knee arthritis. We use hyaluronic acid, which is happily paid for and has been shown in studies to help with the need and other joints. We do PRP and we do supplements. So the ones that we use in declining orders, the ones that have shown most to least data, glucosamine to control is number one, boswellic acid in one form or another is number two, made from frankincense. Number three is curcumin. Number four is pycnogenol. Number five is type two collagen, not type one, but type two. And then there's some others. So we prescribe these for everybody. And doing that algorithm, we have great success. But I'll say something else that is just horrific antidepressants. So 100 million antidepressant prescriptions written in the U.S. last year.  Antidepressants, people are often scared of taking these things because they say, well, you know, you're depressed and maybe they'll hurt yourself for your loved ones themselves. So there's a black box warning on all these antidepressants. They say for people 25 and under, but I think it's everybody that antidepressants increase the incidence of suicidal ideation. And there's a recent study out of Sweden showing you it isn't just an ideation. There are actually more suicides among them. Right? So, so people on short-term studies would seem to indicate that these things have pain-killing properties. And in my opinion, they don't. So we get people off of these things. They're addictive. Once you're on them, you're hooked. It's like an opiate. It's horrible, my opinion. And then opiates, we never use opiates. We don't use any prescription drugs. There are none that are good for musculoskeletal problems. Wow. I love that. I love that you're so clear because again, I see that in my practice. And often I'm having the same discussions with patients on these meds, because they do. They have downstream effects. There's no one who's born with a serotonin deficiency. This is not, and the science has come out since then, since the pharmaceuticals have sold us this bill, as far as the reality of neurotransmitters.  Well, as you allude to. So the serotonin reuptake inhibitors, SSRIs, you probably know about it a year ago. They find out it doesn't even do that. Yes. And it's nuts. What it does do is cause changes in your brain. We work a lot. We do stem cell treatments. We've got a couple of NFL quarterbacks, for example. And one of the things it does is it helps their focus. It helps their sleep. And we work with Tim Royer, who works with a lot of professional athletes, great sleep person. And all drugs, all drugs, all drugs that influence sleep, they induce sleep, induce artificial sleep. And he doesn't use them at all. Right? So I don't think anybody should use them, but it's like an easy way out. And in particular, in particular, these antidepressants. Yeah. And in the sad thing you alluded to, too, as you talk about our medical colleagues and stuff that are stuck in these systems, one of the things that often happened is that Doc has someone who feels sad or anxious or can't sleep or depressed or symptoms, or maybe just pain or inflammation. They don't know what to do. They're not looking for root cause like you and I are doing. So their default is, oh, well, maybe you need an antidepressant because we don't know, we call it functional, not functional medicine, but functional disorders, which are actually just, we don't know, idiopathic. We don't know what's happening. Now you and I know there's root cause, but the average doc maybe who doesn't have that answer will just say, well, let's try an antidepressant. And they're put into a box because as you probably know, doctors now working for corporations get fired, terminated for low productivity, right? And it's been shown that the way to see people faster is to give them drugs. So you get them in, you say, hey, you know, this is the drug. See you later to actually take time to talk about lifestyle, which is vastly more important is time consuming and it doesn't fit in to the modern model of corporate medicine. So these docs a lot of times are put into a box of almost having to do this. Couldn't agree more. So future of medicine, you're obviously on the forefront and seeing some of these things. Where do you think is, where is the research headed? Where are things headed with your field and what you're doing? So let me talk to you about themselves a little bit. So we, I'll tell you some of the things we're doing and some of the things we found in every patient we treat is part of a prospective study. Every patient is followed up by your research team. We do tests before and after. So autism, we have nine patients so far in the clinical trial for autism. They all got better. One regressed after a matter of weeks, but the others have gotten better and stayed better.  So we have great success with autism. It's a very simple thing. It's just infuse, a simple IV infusion, very well tolerated. People we have as old as 27, as young as four. So autism has been fantastic. Autism is an immune mediated disorder, which is, you know, kind of explains why stem cells work. Back pain. We've got a clinical trial of 39 patients so far with at least a couple of months follow-up. 80% plus have had great success. These are people who have failed surgery, people with terrible problems. So we do stem cells in the facet joints, in the epidural space, occasionally into the disc. Back surgery is, you know, there are times when you're really needed, but has a tremendous failure rate. And when back surgery fails, it tends to fail spectacularly. A lot of drug-addicted people, right? So we've had great success doing that. We do peripheral joints, knees and shoulders, but most of the time we don't need to because PRP works well. We have great success with autoimmune disorders. I work with a doctor in Buenos Aires, Argentina, and Monterey, who's developed a vaccine for MS. 200 treated patients with more than 20-year follow-up, 80% plus. It's a vaccine made from your own T cells. So your T cells are removed by apheresis.  And 10 to 12 vaccine shots, it's completely safe. No serious adverse events. It goes away and it stays gone. He's got 20-year follow-up. It's just remarkable. Doesn't exactly fit the pharma model, right? You know, pharma is great. They help a lot of people, but they have no interest in this treatment because they can't monetize it and they can't patent it, right? So MS, spinal cord injured people. We have people, paraplegics, 80 paraplegics and quadriplegics treated. And we get people in whale chairs who get out of wheelchairs and walk. It's remarkable using stem cells. And again, if we had more time, the venue was different, I could show you videos of people. We've got people right now in Buenos Aires, Argentina, where we do this, one lady now from Seattle, well, to the lady who fell and couldn't stand up and is now standing after only a month. It takes six months to get people better. So spinal cord injury, eye disease, macular degeneration, retinal disease, other autoimmune disorders, scleroderma. We've got two scleroderma patients now. One had severe lung disease, which scleroderma patients can have. After four months of treatment, can't scan completely clear, breathing easier, idiopathic pulmonary fibrosis, horrible, universally fatable disease. You just suffocate to death. We've got a couple of patients in a protocol for that. One, it's stabilized. Another one was on six liters of oxygen, down to two liters of oxygen, breathing better. So you asked me for a title of this and I said, revolutionizing disease treatment. And you're thinking, wow, that sounds kind of stuck up, right? But it's really real. It's just amazing what this technology is capable of doing. Amazing, amazing. And it makes sense because a lot of the things you're describing are these overactive. Our innate immune system has gotten confused with all the signals outside, whether it's chemicals or toxins or infections. And so many of these diseases you're describing are an overactive T-cell population. And I'm assuming that stem cell comes in and really just re-regulates the immune signaling. There's three different things that are involved. The one is we can just inject the stem cells. And in the case of autism, that's good enough. I mean, and I'm sure people get a little better. We can inject stem cells for rheumatoid arthritis for MS a lot of them and they'll suppress it in many cases, but it tends to come back and it doesn't work in all cases. So we use T-cell vaccines and I'm using that more and more. It's more complicated. You get aphoresis. It takes about a week. You get aphoresis. You take these cells out. As I was just describing for MS, you can do it for inflammatory bowel disease, rheumatoid arthritis, polymyelodromatica, type 1 diabetes. And then a vaccine is made and it's put back, but you have to do it monthly for a while. And the last thing is what we call effector cells. So we'll take lymphocytes out, say for the central nervous system. So these lymphocytes are challenged with neural antigens. They're injected back. So what happens when you damage tissue that doesn't only heal, central nervous system or heart or retina or hair cells in the ear is for two weeks, it's in a phase of healing called TH1 where it can heal with the stem cells. After that, it modulates to TH2, T-helper 2, and scar tissue is laid down over and the stem cells can't get to it. So by injecting these lymphocytes, they seek out this area of inflammation with a scar tissue and they partially reverse it and get rid of some of the scar tissue. Then we co-culture those lymphocytes with stem cells from you that we've taken before and grown. So in 48 hours, these activated lymphocytes will partially differentiate your own adipose-derived stem cells into neural progenitor cells. They're like nerve cells. They're injected. They seek out these lymphocytes which have labeled this tissue, which enables them to cross the blood-brain barrier because some of the scar tissue has been whittled away. They're able to help heal it and people start to heal. So we do that a couple of days later. You go home, repeat this at intervals and we can get the spine to heal. We can get myocardium. We're just treating our first patients there to heal. I mean, it sounds like science fiction. I know, but it's real stuff and we have documentation and we publish things about it. Amazing. Amazing. And no, to me, it doesn't because I've been following this rule, but you're right. Some of our listeners, I'm sure this is just out there, but this is where the future is going. Root cause and really using the techniques and the technology that we have to optimize human performance, resilience, and healing. Let me talk about something else in that regard, too. So the obvious question is, well, gee, number one, if this is so great, why isn't everybody doing it? And number two, if it's so great, why isn't the FDA approved? So mesenchymal stem cells, these are non-embryonic. These are not fetal. These are not aborted. These are what we're called adult stem cells. So they're either from you as an adult or they could be from a newborn who's a medical court has donated. These are more or less discovered in 1976. And for decades, there was lots of research, good research, great success, very safe. It's not like people were dying from this. They weren't. 2005, the FDA decided in the EMA in Europe, they should regulate these. And why? Well, they said it could be unsafe and there are scams in one thing and another. So fine. And so when this happened, they imposed the same standard on stem cells that is imposed on pharmaceutical drugs, which are double-blind, randomized, placebo-controlled studies. So if you're talking to people from the FDA, and I love the FDA and they try to help people, but they would say, yeah, they're legal, but you have to do an IND, an investigational new drug protocol. The problem is these studies are $100 million studies. That money exists no place except pharma. Pharma's great, but pharma can't patent this, can't monetize it. And so they don't do these studies. So the bottom line is the studies don't get done. So you can do it illegally in the United States. I'm not interested in breaking any laws. So what's happened is it's been driven offshore. So we have a center in Antigua, we have a licensure to do it, we have one in Monterey, Mexico. There's other good ones in other places offshore. But this is completely safe. We have had zero serious adverse events. And we know, we follow up, our patients get annoyed with us sometimes because we call them, we say, how are you doing? And a lot of them want to know, some of them say, why are you bothering me? They say, well, this is the only way we know is if we find out what's going on. And I spend a lot of money on this foundation that isn't supported by anything else just so we can know what we're actually doing. So my point is this treatment is completely safe. Now, we have made it a point to study adverse events because there have been bad things that have happened to people with stem cells. What we have found in every case is that they come from one or two things, either bad doctors or bad cells. Bad doctors, doctors doing it that don't really understand the field or cells that are made from a tissue bank that is a substandard place. But this can happen not in stem cells. There was something like 30 patients died from fungal infections from cortisol from a compounding pharmacy. You probably know about this, right? From a dirty lab. So you can do anything badly and have problems. But properly done, stem cell treatment from a reputable lab is incredibly safe. Stem cells are what has evolved through time to help us heal ourselves.  Yeah, because they come from. Dr. Pardomis, this is amazing. And thank you. I just felt such gratitude for you for seeing the potential and then pouring your heart and mind and life into this because it really is leading the edge for all of us with the research. And I love your commitment to data and to collecting research because that's what's going to move this forward in our current system is continuing to collect the data. Where can people find you more information about your clinic or clinics?  But we have two things. I can give you a phone number and URL, but our phone number is<PHONE_NUMBER>. That gets you into the system. And if you call, if you call about stem cells or whatever, we've got, we've got a terrific team actually. And then our stem cell institute, we have a nonprofit too, but the stem cell institute is the thepsci.com. So it's the pro dromos stem cell institute.com. So thcepsci.com. If you go there, there's an email care at thepsci.com. So you get a real person, not a phone bank. Again, we've got a great team. We love answering questions. We evaluate people at no charge. Amazing. And I will link if you're listening to this audio or seeing us on video, you'll be able to find the links to these wherever you're listening. Thank you again. I want to say something else because you have a nonprofit. I know there's a lot of docs and other people that have means that would, I love the idea of supporting your work. Where could people get information about supporting your foundation? So the foundation, it's the forum. So it's the foundation for regenerative medicine. So it's the thcephorem.org. Perfect. And it has its own website. And you can make tax deductible donations to that that support our research or can be put into a fund to we deal with children with cerebral palsy and other things you don't have means into a fund that is used to help pay for treatment for people who can't afford it. I love that. Love, love, love that. Well, hopefully we'll have more conversations maybe next time we have you share some of the video that are pro dromos. This has been a delight and a joy and no listeners have enjoyed it as well. Thank you so much for your time. Jill, thank you for the opportunity and I commend you on doing what you're doing to spread good information. Thank you.


Hello, so let us continue with the discussion of Fourier transforms, in the last capsule we proved the Riemann-Lebesgue Lemma for Fourier series again, but gave Riemann's own argument for that. The argument we gave in the first lecture was quite different, but the second argument is very convenient to give the analog of Riemann-Lebesgue Lemma for Fourier transform. So what is the Riemann-Lebesgue Lemma for Fourier transform again, theorem 45 on the slide, if f is in l 1 of r, then the Fourier transform f hat of chi tends to 0 as chi tends to plus minus infinity. First let us imitate the same argument we gave before, to show that if a function f is continuous on minus a a, then integral from minus a to a f of x e to the power minus i x chi dx goes to 0 as x goes to plus minus infinity. Call the integral i and you set x equal to y plus pi upon chi and proceed exactly as we did before. Now use Lousen's theorem as indicated in the last capsule to extend it from continuous functions from minus a a to l 1 functions on minus a a. Now let us assume that f is in l 1 of r. Remember that if a function is Lebesgue integrable, then given any epsilon greater than 0, you can take a large interval minus a a such that outside the large interval the contribution of the integral is terribly small. So, the integral mod f x dx outside the interval minus a a is less than epsilon by 2. So, now we need to only worry about the closed interval minus a a. So, let us see how to deal with the closed interval minus a a.  In other words, I am trying to estimate the Fourier transform f hat of chi. So, mod f hat of chi is what you see on the left hand side. Break this integral into two integrals from minus a to a that is the second piece and the first piece is integral from r minus minus a a. The first piece take the absolute value inside the integral use triangle inequality e to the power minus i x chi is a unit complex number and you get that that contribution is less than epsilon by 2. Now, take the second integral mod integral minus a to a f of x e to the power minus i x chi d chi and we know that that piece goes to 0 as chi tends to plus or minus infinity. So, there is a chi not bigger than 0 such that for mod chi bigger than chi not that absolute value integral minus a to a f of x e to the power minus i x chi dx is less than epsilon by 2 and accordingly we conclude that mod f hat of chi less than epsilon when mod chi bigger than chi not that was pretty easy because we did the detailed analysis for the Riemann-Lebesgue Lemma for Fourier series and a large part of the argument simply carried forward over here and that completes the proof of the Riemann-Lebesgue Lemma. Now, we want to estimate the Fourier transform in L2 norm. We could take a function f in the Schwarz class and we want the estimate for the Fourier transform in L2 norm. Why do we want the estimate in L2 norm because of the pleasant feature that L2 of r is a Hilbert space and so hopefully Hilbert space techniques can be brought into play. However, the argument is not so straightforward. We need a certain result known as the Plancherel's theorem or the Parseval's formula for Fourier transform. We have the Parseval formula for Fourier series and we have a Parseval formula for Fourier transforms. Suppose f and g are in the Schwarz class S then equation 4.11 in the display that is the Parseval's formula or Plancherel's theorem integral minus infinity to infinity f of t gt bar dt equal to 1 upon 2 pi integral over the real line f hat of chi g hat of chi bar d chi where the bar signifies the complex conjugation. Again we need to employ the e to the power minus epsilon chi square trick. So, let us try first why this has to be done. Let us try the naive approach. So, take the right hand side of 4.11 and let us put in the definition of Fourier transform f hat of chi is integral over the real line f of x e to the power minus i chi x g hat of chi is integral over the real line gy e to the power minus i chi y dy, but since I am taking the complex conjugation it will become e to the power plus i chi y dy. So, these 2 integrals over the real line combine to give me an integral over the plane namely integral over r squared f of x gy bar e to the power minus i chi x minus y dx dy. Now I want to switch the order of integration. So, the integral over r 2 will be done later and the integration with respect to the chi variable will be done first and I get the integral over the real line e to the power minus i chi into x minus y d chi. Again we ran into the same oscillatory integral for which we need to introduce the x minus epsilon chi square trick. We have now gained sufficient experience how to do this. Well we need the Fourier transform of the Gaussian along the way. So, the right hand side can be written as limit as epsilon goes to 0 1 upon 2 pi integral minus infinity to infinity f hat of chi g hat of chi bar e to the power minus epsilon chi squared. The limit was inside the integral I can pull it outside the integral because f hat and g hat are in the schwar space they decay very rapidly. Now that the limit has come outside the integral I will put in the definition of f hat and g hat as I described while I was doing the previous slide I get f of x gy bar dx dy it will be a integral over r 2 and what I will get is x p of minus i chi into x minus y and now I have the e to the power minus epsilon chi squared d chi. And so the inner integral now can be computed it is a Fourier transform of the Gaussian what you see here is a Fourier transform of the Gaussian that is another Gaussian and the epsilon will come in the denominator and there will be a root pi by root epsilon 1 root pi cancelled out and 1 upon 2 root pi epsilon times. Now the usual change of variables x minus y equal to root 4 epsilon z this simplifies to e to the power minus z squared dy will be 2 root epsilon dz and the 2 root epsilon cancels out a root pi remains the denominator and I will get e to the power minus s squared d s take the limit inside the integral and you will get simply g x bar and you get simply integral e to the power minus z squared dz which is the root pi the root pi and the root pi cancels out you get f x g x bar dx and to take the limit inside and outside the integral you need to appeal to the dominated convergence theorem from the theory of Lebesgue integrals that is a standard argument. So that is how you prove the Plancherel's theorem or the Parseval formula in the Parseval formula we must take f equal to g if I take f equal to g then this says that integral minus infinity to infinity mod f t squared dt equals 1 upon 2 pi integral minus infinity to infinity mod f hat chi the whole squared d chi. So 4.11 simplifies when g equal to f to the following formula 4.12. So 4.12 follows immediately from 4.11 taking f equal to g. So theorem 47 is the important link that we wanted to extend the Fourier transform as an operator on L2 of r how does it how does this estimate 4.12 help us to achieve this. So let me first record the thing as theorem 48. So the Fourier transform extends as a bounded linear operator on L2 of r further it is a linear isomorphism on to L2 of r in the earlier case from L1 it was into L infinity but here in the context of L2 the Fourier transform maps L2 on to L2 so it is surjective in this case. Now we shall use the fact that the Schwarz space s is dense in L2 of r the Schwarz space is dense in L1 it is dense in L2 in fact it is dense in Lp for any p between 1 and infinity 1 included in infinity excluded. We shall not prove this theorem that the Schwarz space is dense in L2 it is a version of the Luzin's theorem if you like. So now that we established 4.12 let us denote by script f the mapping from s to s given by the Fourier transform. Now the Fourier transform maps s on to s thanks to the inversion theorem. So this f if you restrict it to the Schwarz space I get a mapping from s on to itself. Now I want to extend this map to a operator on L2 on to L2 for that we observe that being linear norm of the Fourier transform of f minus Fourier transform of g is less than or equal to root 2 pi norm of f minus g and f and g are in the Schwarz class. When I say norm I mean L2 norm in this particular context and thanks to the inversion theorem we also have the inverse Fourier transform of f minus inverse Fourier transform of g less than or equal to 1 upon root 2 pi the L2 norm of f minus g and which shows that both the Fourier transform and its inverse as a map from s to s are uniformly continuous with respect to the L2 metric. So what we have here is we got a metric space capital X which is L2 metric which is L2 of the real line and we got a subspace y which is dense in x what is the subspace the Schwarz class s. So now we are in the following situation we have a complete metric space x and we are going to dense subspace y and we have a mapping from y to y which is uniformly continuous then t extends continuously as a map from x to x. I repeat that in our context x is L2 of the real line and y is the Schwarz class and this transformation t is the Fourier transform operator and we know that the Fourier transform maps s onto s and it is continuous with respect to the L2 topology is uniformly continuous with respect to the L2 norm. So we want to prove lemma 4.9 once we prove lemma 4.9 then we would have established theorem 48 and this equality 4.12 will continue to hold by the density argument by the density of s in L2. So let us prove the lemma. So we need to define t as a map from x to x. So take an element little x in capital X because y is dense in x I can select a sequence y n in capital Y converging to x. Now look at the sequence ty n. Now ty n is going to be a Cauchy sequence because t is uniformly continuous because ty n minus ty m or the distance between ty n and ty m is less than or equal to epsilon for all n m greater than or equal to n naught because of uniform continuity of. So because ty n is Cauchy and the metric space x is complete remember L2 of r is a Hilbert space it is complete. So ty n converges to some point let us call that point tx and we want to say that that tx is the image point that we are looking for but there is one small problem that we need to address and the problem is the following. It may happen in fact it will happen that there are several sequences converging to x. Say I take two sequences y n converging to x and z n converging to x and y n and z n are sequences in y. Correspondingly ty n is a Cauchy sequence t z n is also a Cauchy sequence question is will ty n and t z n converge to the same limit the answer is yes then this assignment tx to x is a well-defined assignment and we get a well-defined mapping. If ty n and t z n converge to different limits then we are going to be in serious problem now we shall show that that does not happen indeed ty n and t z n will both converge to the same limit to do this we use an interlacing argument which is very frequently used in analysis. So, y n converges to x and z n converges to x we know that. So, let us interlace the sequences y n and z n as follows first put y 1 and then z 1 and then y 2 and then z 2 and y 3 and z 3 we interlaced the two sequences y n and z n the interlaced sequence again converges to x correct because y n and z n individually converge to x. So, ty 1 t z 1 ty 2 t z 2 etcetera is a Cauchy sequence and so it converges as as above. So, both the subsequences ty 1 t y 2 t y 3 and t z 1 t z 2 t z 3 they must converge to the same limit. So, the limit t x is independent of the choice of the sequence y n. So, this assignment of t x to this domain point x is a well defined assignment and we get a well defined map from x to x and this extension is also denoted by the same letter t now we have to show that this extension is also continuous that part I am leaving it as an exercise for you. So, now with this lemma out of the way we can see that the Fourier transform is now extended as a continuous linear map from L 2 onto itself and the estimate 4.13 holds because it holds for the Schwartz class and so it continues to hold for L 2 of r. Now, the next item that we need to discuss is the notion of convolution of two functions and we want to prove the convolution theorem for Fourier transform. The convolution theorem roughly says that if I take two functions f and g the Fourier transform of f star g is a product of the Fourier transforms f hat into g hat. So, let us describe what is the convolution of two functions. Let us begin by taking two absolutely integrable functions f and g on the real line.  Check that f star g equal to g star f and check that the convolution is also absolutely integrable. So, the next theorem says that if f and g are both in the Schwartz class and the convolution f star g is also in the Schwartz class and further f star g hat is f hat into g hat equation 4.14 in the slide. We shall not prove the first part of the theorem. We shall not prove that f star g is again in the Schwartz class. The proof is not difficult. It just gets involved and the proof follows routine arguments. By way of analogy, you may have seen the convolution theorem for Laplace transforms in undergraduate courses in ODE's. There is only one small piece of warning that I would like to give you that in undergraduate courses on ordinary differential equations, the definition of convolution that you see in the context of Laplace transforms is slightly different because when you compute Laplace transforms, you are ignoring the function on the left hand side and the Laplace's integral is an integral from 0 to infinity. So, what happens is that the convolution theorem for Laplace's transform should be written as the Laplace transform of the heavy side function u times f star u times g will be Laplace of f into Laplace of g. That is how the Laplace transform convolution theorem ought to be stated. Okay, let us get to the proof of the convolution theorem. So, let us start with the Fourier transform of f star g. Fourier transform of f star g is what put in the integral. Integral over r e to the power minus i x chi f star g x dx. Next step is obvious, no prizes for guessing. It is going to be the definition of the convolution integral over r f of y g of x minus y dy and I am going to switch the order of integration. I am going to get integral f of y dy integral g of x minus y e to the power minus x chi.  So, here e to the power minus i y chi comes out of the integral and that is simply the product of the two Fourier transforms. And so, the proof of the convolution theorem is complete. Let us use the convolution theorem to discuss some solutions of partial differential equations. The heat equation. We already discussed the heat equation in the context of Fourier series in the first part of the course. We return back to the heat equation in the context of Fourier transforms. We solve the initial value problem for the heat equation ut minus u xx equal to 0 and the initial distribution of heat is u of x comma 0 equal to f of x. Now, what we will do is that we will take the Fourier transform and we shall obtain an ODE for the Fourier transform. We will solve the ODE and we will use the inversion theorem to get the integral representation for the solution of the heat equation. The advantage of this over the previous method is that in the previous method we used Fourier series and there we needed the fact that f of x is a periodic function. So, in the previous discussion the heat equation was solved for periodic initial conditions and the solution sought was also periodic. Here we do not have periodicity the initial condition need not be periodic. We shall discuss the wave equation also utt minus u xx equal to 0. We shall discuss the wave equation in one space dimension. We shall discuss the conservation of energy for the wave equation. We shall discuss the principle of equipartitioning of energy in the context of wave equation in one space dimension using Parseval formula. So, I think with this let me close this capsule here and we will take up in the next capsule the solutions of initial value problems for these classical PDEs. Thank you very much.