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Okay. Good morning, everyone. Um, can you see my shared screen? Yes. Yeah, right stuff. Okay, So what I'm gonna do, um, here. I'm going to, uh, send everyone a link to the, uh, upper limb trauma. So just bear with me. I'm going to put it into the chat. And, Abdullah, would you be kind enough to continue to put the link in as new people arrive? Of course not a problem. Yeah. Great stuff. Okay, So what I've done is I've shared this link with you, and the link is called peripheral trauma. Humorous shoulder girdle, thrusted cage. Okay, so, uh, I want to go to number 16, and I want somebody to tell me what What's going on here? Okay, so we've got a patient who's fallen on the outstretched. Um, what do people think? Uh, clavicle Just still clavicle fracture? No, that is still part. So here's the acromioclavicular joint. There's the core record process. There's the glenoid. Now, normally, the glenoid and the humerus are superimposed, okay? And the humeral head is parallel to the cortex of the glenoid. Okay, But in this particular case, it's wider at the top than it is at the bottom, and the humeral head is sharing a liable prepare ins. So here's the scapula y projection, and it's called a scapula y projection. Because, uh uh, doctor, just to stop you, uh, we can't actually hear you. I think you're having, uh, interrupted Internet because your your zoom is quite interrupted. That's great. So? So this patient had a fall on the outstretched hand, and you can see that the distance between the glenoid and the humerus green greater at the top than it is at the bottom. Oh, yeah. Sorry about that. Thank you. Right. I think we're back in business. Okay, so apologies is about that. I think I had a temporary internet outage. Um, so apologies. So what we've got here is we've got widening of the clean out humoral distance at the top compared to the bottom, and the humeral head exhibits the lightbulb appearance. Here's the glenoid. Here's the acro me in, and there's the core record process, and it forms like a y pattern. And it's called the scapula y projection. And this should be superimposed over the glean oId. But it's not. It's either posterior or anterior. What do you think? Any thoughts. It doesn't matter guys, if you get this wrong, because I'll teach you so that you'll never forget. And and Syria and Syria, it's post area, it's posterior. And I'll tell you the reason why Every time you have an anterior dislocation, the humiral head always goes below the court record process. Okay, so it goes down and below the core record process, whereas this one, it looks as if it might still be in joint. But there are some clues that tell me that this is a posterior dislocation. And the first clue is that the course got a line of the glenoid is no longer parallel to the articular surface of the humerus. And the second one is that it looks a bit like a light bulb. Okay, the light so called light bulb sign now on its own, the frontal view is not enough To make this diagnosis, you need to ask for a lateral view or a scapula wide projection, and this is the scapula wide projection, and you can see the humiral head lies posterior to the bleed oId. And this is a posterior dislocation of the shoulder, which is much more serious. Does anyone know why? Um, it's it's more damaging to the capsule, and it's also, uh, more difficult to to pick up because it's easily overlooked. Okay, so everyone can pick up an anterior dislocation, and I'll show you an example shortly. But a posterior dislocation is very difficult to pick up. Steve just got to understand were the different, uh, markers are that to tell you that this is a posterior dislocation? So in the same light, I'm going to show you this one. So number 17 and you can see that this one has gone underneath the coracoid. So there's the core record process. It's gone underneath, and not only have we had an anterior dislocation of the shoulder, but we've got a comminuted fracture of the Greater Tuberosity. So that's been both a dislocation and a fracture at the same time. And that's not uncommon. And that's just another view. There's the scapula y projection. There's the chromium. There's the core record. There's the blade to the scapula, and you can see that the humiral head is now anterior to the glenoid. So the glenoid should be here, and it's now anterior to that glenoid. So the telltale signs are anterior dislocations occur below the court record process. Now, one of the other things that you need to look at when you're looking at any shoulder X ray is what is going on in the lungs. Okay, because the patient could have a rib fracture with a pneumothorax or they could even have for malignancy. So as well as picking up the trauma. Certainly the radiologists job is to pick up, uh, other pathology which may or may not be related to the trauma. OK, is everyone clear on that number? 18. So this patient has fallen on the shoulder directly on the shoulder. Anyone know what the diagnosis is Here? Clavicle fracture again? Yeah. Uh, it's a scapula fracture which occurs at the level of the chromium. You sit here so there's the scapula. There's the chromium, and it's occurred at the junction. Yeah, well done. Now that's a very unusual injury. And that sort of injury would be a direct impact injury to that particular area of scapula, which you can see that and you will see these images by going through the the scans. Yeah, great stuff. Okay. It's another patient who has fallen on the outstretched hand. Any thoughts? Anterior distribution is a fracture. You can see that the glenoid and the humerus are parallel. See that? So it's in joint. And in fact, if you do the lateral, it's in joint. There's the glenoid. There's the chromium. There's the core record process. There's the glue annoyed here, and it's articulating with the humerus. Is there a fracture on the head? Yeah. And what anatomical position is that? Oh, graded and wooden. Well, the Greater Tuberosity. Okay, so the greater tuberosity of the humerus has been fractured. Okay, but there's no dislocation. It's just a fracture of that Greater tuberosity. But it still needs to be immobilized. And what what happens is these patient's tend to go into a broad arm sling and this will heal up without any further intervention. OK, number 20 Uh, this is a patient who, uh, is a little old lady who has fallen over in the supermarket. So she's had a very, very minor fall. Have a look at that x ray and tell me what you think is going on. So there's definite fracture there, But is the fracture through normal bone or abnormal bone abnormal bone So in what ways? The bone abnormal. Yeah. So she's got a lytic lesion here. So the bone is osteopenic because she's an elderly lady and we've got an area of license, that bone destruction and the distal humerus. And there's a comminuted fracture through that pathological bone so it could be multiple myeloma. Could it be anything else Osteoporosis lost. The process tends to be generalist rather than focal. Um, so osteoporosis is certainly cause a fracture, but this is a focal lytic lesion. So along with myeloma, we need to think about metastases. Now what conditions? Matassa stars to bone, lung cancer. Anything else in a female breast? Yeah, thyroid and kidney. So the top four lytic metastases are from breast bronchus, thyroid and kidney. Okay. What do you think the most likely cause in this patient is? Rest. Okay? Any any other suggestions? Are there some lung lesions? We can say? Yes. What's this here? That's a lung cancer. So the patient's got a Latin cancer which has caused a metastasis to the bone, which is, of course, a pathological fracture. So the radiologist, because we are able to look at things in a systematic, orderly manner we can work out that Not only is this a pathological fracture, but the source of the metastatic deposit has come from a carcinoma of the lung Just here. Okay. All happy about that? OK, number 21 this is a patient to has fallen on the, um What do you think? Now, this is an election on spur, okay? And in itself is not an indication of any, uh, significant pathology. Okay, um, so there is a bone fragment there, and it may be that, uh, in the past, the spur has fractured. But this does not a new fracture, because see how it's well, corticated. It's a nicely, well, corticated spur. And so I would not regard that as an acute fracture. And the other thing about acute fractures, they tend to be associated with soft tissue swelling over here. But that's not swollen, so I don't think that's a fracture, but what do you think about the humerus? Very difficult to see the fat pad on here, actually. Yeah, There's humerus fracture. Can you see it here? Yes, sir. And the only hint that you've got a humerus fracture is perhaps that break there and a slight anterior angulations. Okay, but it's only slight. This is where you're going to pick up the fracture. Now, what structure is prone to getting damaged with a fracture just above the epicondyles the nose Read the little nerve that's used chip at higher up. Um, it's actually the brachial artery. Okay, because the brachial artery ruins in this vicinity. And it's particularly important in Children, because if it goes undetected, you can get an injury to the brachial artery, which leads to ischemia of the forearm. And that leads to a condition called Volkman Owns ischemic contracture. Okay. Volkman owns ischemic contracture. Um, and I'll show you an example of that. So if you look at number 22 uh, now it comes a bit later. Let's go to number 22. Anyway. Um, so this is the same patient I shared you earlier. Sorry. Wrong. Wrong. Well, that's in twice. For some reason. Uh, it's the other 20. I put it in twice. Called it 22. It's the second one that's called 22 and have a look at this one. So we've got patient. How old do you think that patient it is? Two child, isn't it? because we've got emphasis. Okay, so the first step, if ASUs to come, is the capitellum. Okay? And you can actually see the fat pad just here being of a lower density just visible there. And instead of the cortex going this way is being pushed back. And this is a superconductor fracture in a child. And the problem with this is is that it can be very difficult to pick up, because in Children you may not actually see the fracture. Okay, but if you suspect the fracture clinically, you should have the capital. Um, and the end of the humiral metaphysis this in line. And this has just gone backwards. Okay, so this is a super candle, a fracture in a child. And if if you don't treat that, that will lead to Volkmann. Skm it contracture. OK, number 23. What have we got here? Is it all one patient or seven? It's an adult patient. Yeah. So what if we go? So yeah, oblique fracture of the humerus. You can just see it on the edge of that film. You can just see it here, and you can sit here and this is the type of fracture that is prone to causing radial nerve damage. Okay. And you can see here how the humorist goes a little bit anteriorly. That's normal. Okay, so humorous goes down, and then it goes anteriorly in a supracondylar fracture. Um, this one here, see how it's gone, posteriorly Because the fracture is here, even though you can't see the fracture, so it's quite subtle. So going down the humerus, the capital talam and the trochlear are slightly more anterior in the anterior cortex. Okay. What boat? In this one, it has gone posteriorly. Yeah, and this is a superconductor fracture. OK, number 24. What sort of a fracture is that? There's a fracture of head, and these scapula's will the lateral train at the lateral side. So we've got a fracture here, and we've clearly got a fracture here as well. Yeah. How would you describe that fracture item? It's a surgical neck fracture. Okay, so it's a fracture of the surgical neck of the humerus, and, uh, there's a, um there's no dislocation as such, but whenever you get a fracture, you always get some migration of the human head. Now that looks like a fracture, but it's actually a pseudo fracture. So what's a pseudo fracture? A fake fracture? That's a great, uh, a great description. So what's the pseudo fracture? Well, pseudo fracture is something that looks like a fracture but is not a fracture. So that's a proper fracture. Because the two ends, the bones have come apart and separated. But this past the bone and this past the bone are still joined. And it's just that this bit of bone here, it doesn't have any calcified osteoid. So simply said Osteo Malaysia, that's absolutely spot on Correct. This is a case of osteo Malaysia. Okay, now it's a pseudo fracture because you can just see the sclerotic edges of that pseudo fracture. Okay, just here. And this is a typical site for a pseudo fracture in Osteo Malaysia. No osteo Malaysia is a condition of the bone in adults due to a lowering of vitamin D. Okay, so vitamin D allows calcium deposition in the bones, and so a low level of vitamin D causes the bones to become thin. Okay, and, uh, there are several causes of vitamin D deficiency. It could be in your diet. It could be a lack of sunlight it could be kidney disease or liver disease. Or it could be good disease where you don't absorb the vitamin d. Okay, but it always leads to low calcium. And the body tries to restore the calcium by taking it out of the bone and putting it into the blood. And that's why the bones become very thin. Whenever you see a pseudo fracture, either in the scapula or the ribs or sometimes in the pubic, remind the pelvis. These are very typical of pseudo fractures, and this is a patient with our stimulation. Now, the whole point of showing you this is that osteo Malaysia can also give you proper fractures because the bone is thin. Okay, so we've got two types of fracture on the same film. Uh, this is a pseudo fracture, and this is a proper fracture. Okay, right. I'm gonna go to, um just bear with me. I'll show you some more stiff now that where I'm still here. So what? Okay, so I'm going to show you some some cases here. I'll give you the I'll give you the, uh, listen to the chat. Okay. So given you another, uh, collection of cases and have a look at this one. I'll tell you what the answers are, uh, at the end. And you can relate this to, uh, the answers on the, uh, database that I've given you. So this patient has been involved in, um, uh, an episode of hospital admission whereby they've got accused abdominal pain. But the first thing I want to do is I want to show you the hand. X ray all looks fairly normal, but I just want to draw your attention to this and this and this and this, and then I'm going to show you the chest X ray, and I want to draw your attention to the scoliosis of the spine and these areas here, these areas here It's another chest X ray. Lots of nodules on the patient's skin. There's the scoliosis. And then the reason why the patient came in was abdominal pain. And I just want to show you what's going on. Can you see those nodules on the skin? Skin nodules? Okay, I'll come back to that in a second. So the patient's got writerly at fossa for pain. And can you see the difference intensity between the fat here and the fat here. Can you see those bubbles of gas? Yes. So what? What structure lies in the right iliac fossa, which can commonly become inflamed. The appendix? Yeah, and the fact that we've got gas there and we've got increased density implies we've got an inflammatory reaction, uh, of the region of the appendix with syrup chur. Now, ordinarily, we would then look for, uh, the appendix. So sometimes you need to look at the Corona als and the statue. Tal's to see the appendix. And if it is very, very inflamed, you may not see the appendix, but I can see the appendix just here, and it's ruptured just at the base of the appendix before it joins the cecum. So that patient has got appendicitis. So CT can be very useful at confirming the diagnosis. So if you wanted to take that patient to theater, you could do a CT scan, and that would confirm the diagnosis of appendicitis. Uh, some surgeons are happy to just make that diagnosis clinically, but more and more a lot of surgeons Well, um, ask for a CT scan so that, um they feel more confident about opening up the patient Okay. Now, what's the cause of all these nodules on the patient's skin? Not melanomas that neurofibromas. And the patient has got neurofibromatosis, type one. Okay, so they just happen to have dual pathology. And if you go back to the hand X ray, can you see these nodule is here. This is no jewels, uh, skin nodules. So it's just a nice demonstration of neurofibromatosis in a patient who just happens to have an appendicitis, which is ruptured. Okay, the other thing we need to do is radiologists is we need to put it onto lung windows. We can do that by you going down here. Sorry, not that one. So you need to click on that one. And they're good at lung windows, and we need to look very carefully for free gas in the abdomen. Okay. There's a really quite large skin nodule, just the But there's no free gas apart from in the vicinity of the perforated appendix. And we call that a localized appendiceal perforation. Okay. It's a localized appendix perforation. Okay, so the next one I'll show you is, um, again, it's on that. It's on that list of cases I've given you. How's that down start again. So my Internet is slow today, unfortunately, Okay, it's crashed. So, uh, I'm going to have to start again, So just bear with me. Go back up now, so that's fine. So I'll show you this one. This is the patient has got right upper quadrant pain, and I'm going to go straight for the CT. I'm going to go for the third one down, and I want you to tell me what you can see. Assist and gasses. So here's the liver. There's the left level low. I'm going to go through a bit of anatomy for you. There's the left liver lobe. There's the cord eight lobe. There's the inferior vena cava. There's the aorta. There's the slip of the diaphragm. Here's the stomach. Here's the spleen. Here is the right level lobe. That muscle is called serrated is anterior. That's called Latissimus Dorsi. And as I scrolled down, here's the pancreas. Where's the pancreas? Here? And this is the gallbladder. Now the gallbladder is normally full of fluid, but this particular goal, but it has got gas and fluid in it, and it's got gas in the wall of the gallbladder. Okay, so I'm just going to put that on linguine. Those there's the gas in the wall of the cold weather. There's the gas in the wall of the goal. But there's the fluid, and as we come more anteriorly, you can see gas and fluid. Okay, so that's bile and gas. And if I just revert back to the soft tissue windows, can you see that the mesenteric fat, which is black over here, has become gray around the gallbladder? So that tells me the patient has got can miss cystitis and because it's got gas in it and gas in the wall. It's called Emphysematous Cholecystitis Okay and Emphysematous. Colecystitis is a very, very serious condition affecting diabetics, and it's usually caused by a bacteria called E. Coli. And these patient's are often very sick. So I'll just show you what it looks like on the Corona reconstruction. This looks a bit more like a gold bladder you can see here, and you can see this fluid around the gallbladder, and there's inflammation, the fat around the gallbladder, and then we've got gas in the wall of the gallbladder. So this is emphysematous, coolest cystitis and fluid. Just here in Morrison's pouch, which is the Hepatorenal fossa. OK, bit more anatomy for you. Uh, this is the, uh, there's the adrenal plans, which has seen here look a bit like a wishbone. Those the the adrenal gland on the left hand side. So there's the adrenal gland here. There's the left kidney. There's the right kidney. That's the crux of the diaphragm cross of the diaphragm service muscle. So it's muscle. There's the ivc. There's the common iliac veins on the left. There's the commonality vein on the right, and there's a bladder with a balloon catheter in situ. Okay, so a little bit of anatomy for you. And, um, when you see this, um, condition emphysematous coalish cystitis, you'll know that the patient is very, very unwell. Okay, look at this one. Uh, it's crashed again. Sorry about this. It's not my computer that's crushed. It's, um it's the pack spin software. That's one of the troubles of of using this type of software. Okay, have a look at this one. This is a patient who is complaining of left, idea of foster pain, and they are elderly. It's crushed again. This is, um, slight problem with my software never mind. Let's try again. It doesn't like this at all. It's not, Uh, it's not opening very well, so I'm gonna have to close it down and start again. It's working fine now. I think there's a slight problem with this particular software, so just bear with me. So this patient is, um, complaining of left early at foster pain. And I'm just going to go straight for the abdomen. Actual views. Bit of anatomy for you. There's the left. A trio. There's the right atrium. There's the right ventricle. There's the aorta. A sending aortic root. There's the descending aorta. Left ventricle, right ventricle. Suffo Ghous, aorta. A circus fain hemizygous Fine. Sorry to Santeria latticed. Um, ast Dorsey Trapezius interventricular septum. What have we got in the liver? They could be cysts. Yeah, that certainly could be a cyst. But some of these have got some rim enhancement, a bit of enhancement around the periphery of that one. And there's the left liver lobe. There's the core date lobe. There's the right liver lobe. There's the stomach. There's the spleen. There's the aorta. There's the ivc as the portal vein. There's the right kidney left kidney Ivc left Renal vein superior Mesenteric Artery Superior Mesenteric vein. There's the head of the pancreas. There's the neck of the pancreas. I'm going up again. There's the body of the pancreas. There's the tail of the pancreas. That looks okay. There's the transverse colon. This is all small bell. There is the descending colon. And what we've got here is we've got an abscess of the descending colon. So it's called the para colic abscess. And can you see little pockets of gas Adherent the wall of the sigmoid colon. They're called diverticular, so anyone know what the diagnosis is. Grants diverticula OSIs. Yeah, so we got done particular OSIs. And it's complicated by a diverticular abscess. Can you see how this abscess is enhancing around? It's wall and it's stuck to the dome of the bladder. So there's a diverticular abscess. This is the diverticular disease. Can you see that the fat is slightly infiltrated around this point? And so if this is an abscess, what are these things here? Uh, diarrhea. So they are liver abscess. Ear's. Okay, So liver abscess is because the drainage of the sigmoid colon is via the mesenteric veins. The mesenteric veins drain into the superior mesenteric vein here, so I'll just show you the drainage. There's the muse. Enteric veins goes into the superior Mesenteric vein, which goes into the portal vein. Just, uh, and all that infection drains into the liver to full liver abscess. Ear's. So this patient's got liver abscesses from a diverticular abscess, and this can all be picked up by the radiologist. Okay, so that's a diverticular abscess, uh, forming liver abscesses. Okay, let's have a look. See what's going on here. Okay, this is a patient who's complaining of severe abdominal pain just from the scout film. You can see what is going on in the chest. What's this thing here? The costophrenic angles are no longer sharp. They're blunted. Why is that? Pleural effusion is excellent. Okay, so I'm going to go straight for the abdomen. Um, so that's the one. And I will put, uh, this one side by side. There you can see the pleural effusions. So there's the left atrium. There's the right atrium. There's the right ventricle. There's the left ventricle. There's the aorta. Yeah, route. There's the N G tube in the stomach. There's the Atticus vein. There's the Hemi Atticus vein. There's the descending aorta. The plural effusions are causing a little bit of partial collapse of both lower lobes. And as we go down, you can see the portal vein nicely here. There's obviously some inflammatory process going on here. There's the stomach. There's the PC. There's the plastic veins converging on the ivc. There's the nasogastric tube. There's the pancreas, which we saw earlier on. But instead of it being the same attenuation as muscle, it's a very low attenuation. And we've got some changes of the fat here. Pancreatitis, yeah, pancreatitis. This is a very severe pancreatitis, and of course, pancreatitis can be associated with plural effusions, which we can see here, usually on the left side. But this patient's got bilateral pleural effusions, and this is a pretty severe pancreatitis. And one of the features of pancreatitis, which is fairly constant, is that it causes thickening of the anterior Arenal fascia, which is this structure here in front of the perinephric fat. And it's also known as Garastas fascia. And I'll put that in the chat, and I'll spell it for you. So it's called Kurata Garastas fascia, and this is very, uh, indicative of a retro personnel inflammatory process. Uh, in this case caused by pancreatitis and this patient have also got a little bit of thrombus at the base of the portal vein. Just see the little bit of thrombus. But this is a very, very inflamed appendix. There's a little bit of free fluid in the abdomen. Okay, Um, but the vast majority of this inflammatory change is in the retroperitoneum. So pancreatitis. Very, very important. Uh, and very difficult to treat a condition. Now, whenever I see pancreatitis, I always try and look at the gallbladder, See if they're any stones now. I can't see any stones. Does that mean there aren't any stones? Anyone know why? Why does CT not exclude gallstones? They can be small. Yeah. What else? They could have been drinking. Yeah, there can be non radiopaque. Okay, So what's the best investigation for gallstones? Ultrasound. Thank you. It's an ultrasound. Yeah. So you need to do an ultrasound if you want to confirm or exclude gallstones. Now, you may see the gallstones on CT, in which case you confirm them on CT. But if you don't see them, the patient's still need to have an ultrasound scan because gallstones are often implicated in pancreatitis. Anyone know any of the coils of pancreatitis? Alcohol? Yeah. Alcohol. Yeah. Anything else? I'm like, uh, different things. Retro flow of the food. Um, yeah. Trauma from ERCP. Yeah, well done. Uh, trauma from a blow to the pancreas can give you traumatic pancreatitis. Uh, cystic fibrosis. What? We'll use this as soon. Yeah. Yeah, you've got it. So the main causes are gonna be gallstones and alcohol. Okay, They're gonna comprise almost 90% of the causes of pancreatitis. But you can see how easy it is to pick it up on C E. T. Now there are various clinical Santa pancreatitis. You can get a bruising over skin here, but really, if those signs are absent, it's quite difficult to pick it up clinically. Obviously, do a serum amylase. But the imaging is is really quite exquisite. And it shows you the pancreas, uh, is just full of fluid. There's a few areas of normal looking pancreas, but the vast majority has just turned 22 fluid. Okay, um, I think that's me. Done. I do apologize about my internet problem. My packs been problem. Um, and I can now appreciate what you must be going through in Ukraine with all these Internet troubles. Um, I've given you the link to that. Hacks been collection called medical students, all of which have got the diagnosis. So the ones I showed you in that particular, uh, section were pancreatitis, emphysematous, curly cystitis, neurofibromatosis with a perforated appendix and the diverticular abscess and liver abscess. Okay, so thank you very much indeed. If anyone's got any questions at all, I'll be very happy to answer. Um, if you've if you've not got another lecture to go to, um, I can stay on and answer some questions if you wish. Thank you so much for your time, Doctor. It's a very, very good lecture. Um, I've included the feedback form in the chat. The next lecture is starting in a few minutes. But if you do have a question for the doctor, you can on mute if you'd like to. Just to remind you, please do fulfill the feedback form before I put the certificate in the chat. Thank you. Why do emphysematous cholecystitis in diabetic patient's? Um, that's a very, very good question. It's to do with, um, uh, immune deficiency. But also there's an element of ischemia small vessel disease. So the gall blood is it is more prone to the effects of ischemia. So two combination of those, uh, those two things. And then, of course, um, you've got E. Coli. And that's because diabetics are more prone to infection due to immune deficiency. So it's multifactorial. But there's certainly a small vessel, um, problem. But also, uh, there is, uh, the the the case of, um, infection in an immunocompromised individual. Does that answer your question? And and actually, diabetics can also get emphysematous cystitis and emphasis immitis, uh, pylon arthritis. So that get emphysema in the bladder, but also emphysema in the kidney itself. And, um, this is, uh this is all due to the combination of, um, infection and, uh, small vessel disease. Okay. Thanks very much, guys. For your attention, I do apologize about the internet problems I've had, uh, and I just hope it will correct next time. One of the problems about pack spin, by the way, um, it is dependent on verse server as well as my internet. And I think we had a bit of a server problem today. Um, so It's a great way to teach, but we are sometimes at the mercy of the, um of the server from pack spin. Thanks very much. And see you next time. Thank you so much for your time, Doctor. Um, okay. My pleasure. Thank you. See you soon. Um, guys, I've put the certificate in the chat. The next lecture has now started. Just give a few minutes for you to download the, uh, certificate. Just bear in mind if you're using a phone or a tablet, you might not see the certificate in the chat. If that's the case, I'll put an email in the chat, send them the lecture date and time and your full name, and they'll provide you with the certificate also. So I'm just going to close up now. Um, we'll see you soon for the next lecture, which has already started. I've put the link in the chat. I'll send it again just once more