Welcome to the Dr. Tulsiobh Wailani Memorial Oration and this is to commemorate the wonderful person that Dr. Tulsiobh Wailani was and always supportive of all endeavours of either Maharashtra state radiology or of Indian radiologist and the person who's been the wonderful person who is going to be giving this oration is Dr. Nitin Chobal. Now, again, we always start with Dr. Nitin Chobal saying he needs no introduction, but I'm going to say a few things very briefly, more personal things. We all know he's a consultant at Jaisalok Hospital since many years. We also know that he runs the wonderful Thane Ultrasound Center since years, which is one of the premium institutes in the entire region and should I say Maharashtra. But I would also like to say that whenever any organizing committee sits down to chalk a scientific program in ultrasound, be it fetal ultrasound, MSK, be it abdominal, be it Doppler. And the first name that's written on that list is that of Dr. Nitin Chobal. Because we know that he can give any lecture any time. That's the key actually. I remember also during UltraFest, I think it was 2011 when Dr. Anil Ahuja was unwell and we just called Dr. Chobal and said, please come and give a lecture. And he just left his clinic and came, you know, I mean, I don't know how he prepared that lecture, but he did it. So, and this has been going on for years. It's not just a one-off thing. Even during the pandemic, when it started in 2020, I think Dr. Chobal gave, I think 100 lectures, sir. I don't remember more than 100 lectures. So, it's a great tribute to Dr. Chobal also. And we are very happy that he's agreed to give this oration for Dr. Tulsio Gwalani. And it's over to you, Dr. Chobal, sir. Yeah. Thank you, Sanjeev. So, you can see my screen, all of you. Okay, fine. So, thank you, Sanjeev and the team Sonobas. Thank you all of you for joining on a Sunday morning. I know Sunday morning is a little early for all this. And I have to really thank the Sonobas team because to give me this honor of giving the first Tulsi Gwalani Memorial Oration. Now, I distinctly remember the day when I first met Tulsi. I was a lecturer in Sion Hospital. And I don't know how many of you know Tulsi Manik. Tulsi Manik was in the Sion department, the Don or sort of, I would say Godfather. He always meant good for everyone, but he had his own style of working. So, he came to me. I remember I was in the, you know, the passage and he brought Tulsi Gwalani to me and he said in his own, you know, he had his own way of putting things. Chobal, he's my son. You'll see him from today. That was his word. I remember that, you know, that day typically. And then from that day onward, Tulsi has been under me, I would say. I was very lucky to have him as my student. And he considered me as his mentor, as his guide, as his teacher, not only in radiology, but also in other things in life. Sometimes I used to fire him for, you know, some things he did, which he was always grateful. So that is the first time I met Tulsi. But over years, you know, our relationship grew much beyond student and teacher relationship. It became more like friends and later on it became more like family friends as well. And I was very lucky to actually inaugurate and be the chief guest for all his machines. You know, when he started Sivileka, there was a time when he started his center with an Ultramark 4 machine, I think. And I was the chief guest in the evening. So typically all his inaugurations, you know, were in the evening. And they used to start with a lecture and then there was a lavish dinner and of course cocktails and all. So because it was Ullasnagar and because it was like an evening function, I mean, I used to go with zazik clothes like this. I was very young those days. So and we used to have a lovely time, you know, during the inauguration and after the inauguration. And as I said, I've inaugurated all his machines and all his center, be it Color Doppler, be it any new machine. And the last one we inaugurated with Dr. Tauri, who is again my teacher as well as his teacher, was his city scan. And that was some years back. And we had a wonderful evening.  And it was really, really fun. And I still remember that day as well. Tulsi was very lucky to have or is lucky to have Bhavisha with him all his life. She has been very supportive and I know Bhavisha personally. In fact, Bhavisha Tulsi, this couple, along with Jyoti and me have been abroad together on many occasions. We were together in Korea. We were together in AIM couple of AIMs. And I remember that he was with me when I gave my first AIM talk and he was there to encourage me sort of, you know, and then of course we were in Vienna with Kirit Shah. And so we have wonderful memories of this couple. And he's blessed with two wonderful daughters, Anisha and Viya. Now about Anisha, I would say that she is proving to be more than any son. You know, the way she has taken up his mantle, the way she runs the center and then of course now Riya is joining. She's just passed a radiology. And I mean, they're wonderful daughters and they are more than any son. And today, if Tulsi were to see this from wherever he is, he would be really, really happy his daughters are doing. And always they smile. This is a classical Tulsi Guarani smile. And if, you know, like Sajiv, if you were to have a photo competition and ask people to give a photo of Tulsi without a smile, it would be very difficult because it's not possible to have a photograph where he's not smiling. So I would say that Tulsi was a very sincere, simple, sober, studious, smiling student. And I was, as I said, I was, I was lucky to have him as my student and we had a wonderful relationship. So I would say as far as the family is concerned, Anisha, if you're listening and Babika, if you're listening that the Sonobas team, the entire radiology community is always with you.  Okay. So with this, I'll begin the oration and the topic which I've chosen for oration today is the fetal posterior fossa. So we know that the posterior fossa basically the brain itself is very small. But in this small brain, very often there is a confusion. And today what we are going to do is try and remove as much of this confusion as possible and try and make it simple so that we understand the posterior fossa and its region in a much, much better way. So we know that the cerebellum basically coordinates voluntary movements such as posture, balance, coordination, speech, which results in smooth and balanced muscular activity. It is involved in cardiovascular regulation during movements and posture. So if you suddenly change your posture, you know, what keeps you or what keeps the cardiovascular mechanism intact is the cerebellum. And we know very well what affects the cerebellum, this water layer, and we also know what happens after it gets affected as far as your posture is concerned. So we know it very well. But when it comes to the fetus and abnormality of the posterior fossa can be a hallmark or a marker of major problems in the fetus and therefore we need to pick it up. It can be sometimes a very minor problem but sometimes it can be a major problem. And typically we know that we always screen the fetal brain in three basic planes. That is the transventricular plane, the transthalamic plane and the posterior fossa view or in an axial plane. So typically here, of course, we look at the cerebellum, we look at the vermis, we look at the system of magna and of course we look at the nuclear fold. And typically in this view, if something is wrong, we become alert. So the common whistle blowers I would say for a posterior fossa abnormality are something like the posterior fossa are not well seen or the system of magna are getting obliterated. And this happens as we know in open neural tube defects which we are not going to talk about. The whistle blower could be with the fourth ventricle communicating with the system of magna or it could be in the form of a large cyst there. So sometimes the vermis, the cerebellum can be very small. You don't see the vermis. Sometimes you might see something very bright and ekojanic there or sometimes you might just see a large cyst but actually the cerebellum is normal. So these are some common whistle blowers which make you alert and then once you know that there's something is wrong, we need to extend our examination from the basic test to an extended neurosynogram. And we are very familiar with the fact that when we do an extended neurosynogram we take four coronal planes and we take three sagittal planes. And basically this is best done with the trans vaginal sonography. So with the trans vaginal sonography, we take a sweep in a sagittal plane from right to left or from left to right. And in the process we grow across the entire brain, including the midline structures, and in a coronal plane again we take a sweep from anterior to posterior or from posterior anterior, again going through all the major structures of the plane. So the posterior force is concerned, the most important views are going to be the midline sagittal view and the coronal view besides your axial view. So typically in the midline sagittal view when we see the corpus callosum, we will see the aqueduct, we will see the vermis, we will see the fourth ventricle a part of Blake's pouch. We also see the system of magna and the tentorium there. And when we take an axial view, this view, the fourth view in the coronal plane is often referred to as an owl eye view, owl's eye view, because the two occipital horns stand out like the eyes of an owl. And then we have the two cerebellum and the fourth ventricle there. So typically the most important structure or the landmark in the posterior force which we try and identify is the vermis. And how do we identify the vermis? In an axial plane of course it comes in the midline, but when we take a sagittal sweep from left to right, when we come in the midline, typically when we start seeing the corpus callosum, the area in the posterior force suddenly lights up like a bulb. And that is the vermis.  And we know from our basics of ultrasound that whenever any structure has multiple interfaces, that structure stands out. Like for example infantile polycystic kidney, why do they appear bright though there are cysts because of multiple interfaces. So typically we identify the vermis because it is bright. Number two, we always identify the fastidium. This is a very important landmark. And usually we see at least two fissures on ultrasound, which cover at least 50% of the depth of the vermis. But actually we know that the vermis has a lot of folia and cysts and it consists of multiple lobules. And today with excellent MRI machines, we are able to look at almost about 9 or 10 of these lobules. But even on a good ultrasound, we can see that the vermis has a typical lobular sort of morphology. We can see the important landmarks, which is very important when it comes to diagnosing body menoproplasia as we'll see later on. And then of course we look at other structures in the posterior fossa, like the cerebellar hemispheres themselves, like the system amygna. And of course, during that time we also look at the neutral fold. So as I said, for the posterior fossa, once you do a targeted or an extended neurosynogram, the best way is a transvaginal scan. And when we do a transvaginal scan, sometimes you might have to sort of give pressure, funding pressure or pressure on the lower abdomen. of the mother so that the head comes closer to your probe. And the best way to hit at this is through the posterior fontanelle. Because you are interested in the posterior fontanelle, we try and get good views through the posterior fontanelle. And in this way, we can get a beautiful angle between the brainstem and the vermis, which is a very important diagnostic point. But in case the fetus is beach, then what we need to do is look at it from above. And typically, one of the best ways to get a view through the posterior fossa is to do a semi decline. So you can just elevate the coach or give us some pillows, and then from look at the from top and you can see the vermis very very well. And now we have newer techniques like volume contrast imaging, where the contrast is so good the structures stand out very well. We have, of course, 3d and volumetric ultrasound. And the biggest advantage is that once you get an excel view, which we all of us are familiar with, we can get from the same in from a frame data, we can get a coronal view and a societal view. And today we'll highlight the importance of coronal view also. We can also do a surface rendering to look at the morphology of the vermis as well. So what are the things we look out for posterior fossa? We look at the vermis, of course. And in the vermis, we look out for the morphology of the vermis, whether the vestigium is seen, whether the lobulations are seen, whether the primary fissure is seen. We look at the biometrics. There are some measurements which are important, which I will just highlight. And then we look at the rest of the posterior fossa structures like the system of Agnes, Cerebellum, fourth ventricle, coroid plexus of the fourth ventricle, very important landmark, as we discussed today, the mid-brain and that. So amongst all the measurements of the vermis, the measurements which are very important are the perimeter of the vermis, the anterior posterior diameter of the vermis, which is also known as the anterior posterior diameter of the vermis and the craniocaudal diameter of the vermis, which is also referred to as a superior diameter. So for all practical purposes, perimeter, anterior posterior and cranial diameter of the vermis are very, very important. And of course, we have normograms now and charts. But remember that these charts could be different for 2D, these charts could be different for 3D and they could be different for MRI. So use the right chart to find out if the vermis is right size or not. Now, every time we look at any structure in the fetus, we always coordinate with the gestational age or we coordinate with some other structure. And for example, when it comes to vermis, we like to take the vermin area to BPD and this is turning out to be a very important ratio to pick up vermin apoplasia as Dario has put up in one of his papers. There are two important angles and why we measure these angles? Because as we'll see later on, there are some pathologies where the vermis rotates away from the midbrain. And the two important angles are the brainstem-vermus angle where we assume a line along the brainstem and along the anterior margin of the vermis and the brainstem-tentorium angle where we measure an angle from the brainstem to the tentorium. And we'll see the importance of both these angles as we go along. There's another very important measurement which very often we eyeball and that is the fourth ventricle index. This is the ratio between the lateral-lateral diameter of the vermis to the anterior-postural diameter of the vermis and this is typically one or little more than one. And typically when this is altered, that means the anterior-postural diameter of the fourth ventricle is larger. That is the time one should think of a vermin apoplasia. So this is known as a fourth ventricle index which is again proving to be very, very important. But there's a significant paradigm shift in the way we look at posterior-postural today as compared to what we did for so many years. And this is because we understand the embryology much better. So we understand that the brain as such goes on developing and the appearance of the brain, not only the posterior-postural but the entire brain, goes on changing drastically over a period of time, much opposite to heart where we know that the basic structures develop much at an early stage and remain the same as far as the outflows of the fourth chambers are concerned, your things change rapidly. And thanks to Prashant from Ahmedabad for this wonderful slide. And today, we are able to appreciate all these changes in the brain over a period of time with MRI. So Sheetal is another friend from Ahmedabad. She does wonderful work in fetal neurosynography in MR. And you won't believe, I told her, Sheetal, I want MRI pictures of different gestational age. And within a matter of few hours, she just collected everything, put it together and send it to me. So this is how you can really appreciate the changes which come up in the brain and posterior-postural. So today, we are going to focus over a period of time. Now, because the vermist is in the center sandwiched between the two cerebral hemispheres, one would assume that the vermist forms because of the fusion of cerebral hemispheres, but that is not true. We know that the vermist actually forms because from its own mesial primordium. And different parts of the vermist, in fact, develop from different parts of the mesial primordium. And therefore, we can get what is known as a segmental vermin abnormalities, as we will see later on in our talk. We also know that the hindbrain basically develops from the robin cephalon. And if you have a very high sensitive MR, today at 11 to 12 weeks of gestation, you can actually see the developing vermist. By 13 to 14 weeks, you can see the vestigial point and you can see the roof of the fourth ventricle. That is the time typically when you see a kink in the dorsal pontine flexure as well. So by 16 weeks, the vermist covers the fourth ventricle and by 18 weeks, the vermist usually is complete. And therefore, this 18 weeks is a very important figure in the development of posterior-postural structures, which we need to keep in mind as we will see later on in our talk. Now typically, this is your Raman cephalic vesicle from where the hindbrain is going to develop as I said. And in this, we see a transverse crease coming up. Now this transverse crease divides this Raman cephalic vesicle into two parts. One is the anterior membranous area and the second is the posterior membranous area. This is also known as cranial and caudal and this is also known as superior and inferior. Today, we are going to call this area as the anterior membranous, area membranous superior and this area as the area membranous inferior to make things very easy. Now, this transverse crease, which we talked about, eventually develops into a coroid plexus of the fourth ventricle. Now this anterior membranous or the area membranous superior has got basically has a potential to form basically vermus and cerebellum because it has got the right sort of structures to form the cerebellum and the vermus. So the cerebellum and the vermus come up from the area membranous superior. So as the cerebellum basically grows inferiorly, the area membranous inferior or the area membranous inferior, this area bulges out between the vermus and the nucleus bacillus to form the Blake's pouch. So this is a Blake's pouch, which actually happens normally. And typically this area is the subarachnoid space, which is going to form your cisterna magna. So as the Blake's pouch enlarges at some time, usually it is around 30 to 14 weeks, the Blake's pouch normally fenestrates and the neck of the Blake's pouch becomes the foramen of magendi. And then we have a communication between the fourth ventricle and the cisterna magna. So this we need to remember that Blake's pouch formation is a normal phenomena. The Blake's pouch actually represents, as I said, just an imagination of the anterior area membranous inferior. And typically when it perforates, we have the foramen of magendi coming up, which communicates with the cisterna magna. Now in case there is no perforation or there is a delayed perforation, then what we have here is a Blake's pouch cyst. Okay, so this we need to understand. Now another very important thing is we said that the crease, which we talked about develops into the coroid plexus. We said that the area above that is the anterior, is the area membranous superior. The area below that is the area membranous inferior. And this area is the area which is going to develop from which the vermis and the cerebellum are going to develop. This is the area from where the Blake's pouch is going to develop. And therefore, if there is a problem in this area, the superior area in the region of vermis and cerebellum where they are developing, for example, if there is a problem in the form of a cyst formation, like what we have in dandemococyst or what we have in vermina, then we would expect the coroid plexus to be inferior to that cyst. Whereas if we have a problem in the area membranous inferior, like the Blake's pouch cyst, which we are talking about, we expect the coroid plexus of the fourth ventricle to be superior to that cyst. So this we need to understand. And therefore, whenever there is a dandemocomal formation or a varimian apoplasia, the coroid plexus of the fourth ventricle typically is located inferior and lateral. Whereas in the Blake's pouch cyst, it is located superior and lateral. So I hope this is clear that just to repeat, this is the midline coroid plexus. All your anomalies like the dandemocomal formation of varimian apoplasia are a problem of area membranous superior. The Blake's pouch is a problem of area membranous inferior. The coroid plexus is here. Therefore, if you have a cyst because of this problem, the coroid plexus is going to be down or inferior. If you have a problem here, the coroid plexus is going to be superior. And this helps us. The position of the coroid plexus of the fourth ventricle helps us in differentiating between these pathologies. I hope I'm clear. So the same thing when you translate in the early pregnancy, the cyst in a dandemocomal formation, the position of the coroid plexus in dandemocomal formation or a varimian apoplasia is referred to as outside because it is inferior and lateral. Whereas the position of the coroid plexus of the fourth ventricle in a Blake's pouch is referred to as inside the cyst because it is superior and lateral. So these positions of the coroid plexus give us a clue about what type of malformation we are dealing with and we'll see examples of that as we go along. So today we understand the coroid plexus of fourth ventricle in a much better way. We know that it is not just that line, it is like two inverted L's. So this is your foramen of Majendi and these are the foramen of Lushkar. This is a beautiful article and editorial which Dario has written, I think, just a couple of months back. Why this is important to understand is because now we are doing anti-scans routinely and we are trying to pick up more and more anomalies in the first trimester. And therefore, definitely we would like to pick up posterior force abnormalities or I would say suspect posterior force abnormalities in the first trimester itself. Now, when we take our sagittal plane, if you look at the three sonorus and areas that is the brainstem, the fourth ventricle and the cystinomagna, these roughly have a ratio of 3s to 2s to 1. That is, this is larger, this is slightly less, smaller and this is smallest. This is important to remember because if this becomes prominent, that catches your attention. And today we look at the posterior force and not only in a sagittal plane but also in an axial plane. And we see the same landmarks, the brainstem, the fourth ventricle, which is also known as IT, the cystinomagna and the coroid plexus, which is the roof of the fourth ventricle. And the coroid plexus actually can be seen very well in an axial view. And if you just sort of tilt the probe, we can see a beautiful communication between the fourth ventricle and the Blake's pouch. And we can see the coroid plexus of the fourth ventricle very well. So routinely when we do an anti-scan, we always not only do we take a sagittal but we always take an axial view and that is a standard, at least in our center. Now, because of volume contrast imaging and because of very high resistion probes, even in a sagittal view in the first time, we can identify a lot of structures. The aqueduct of cereals stands out this time around this time because it's a very prominent structure. Here we have, of course, the vernis, which is developing. We have the coroid plexus. That's your fourth ventricle and this is your Blake's pouch. The same structures can be identified in a sagittal plane also. And the charm of volume ultrasound is that once you take one plane, that is, for example, the axial plane, we can reconstruct from that plane, the coronal plane, which is very important, as well as the sagittal plane for studying. Therefore, since we understand things now, since we understand the embryology better, since we have newer machines and newer techniques to show us the, I don't know, maybe better, we are looking out for newer and newer signs of posterior fossa abnormalities in the first trimester. One of the most important eye-catching signs of an abnormality or a potential abnormality of the posterior fossa in the first trimester is a very prominent fourth ventricle. The prominent fourth ventricle is an eye-catching thing, which is an important sign and we'll see examples of that. The aqueduct of cereals can be prominent or it can be small. Very often, instead of seeing three sonorescent areas, you might see only one sonorescent or two sonorescent areas. If you take a ratio of brainstem to brainstem occipital distance, this is decreased in potential or in posterior fossa abnormalities as compared to an increase in the size of the brainstem to brainstem occipital ratio to open neural tube defects. And very often, you can see that the pormidoburman angle is increased. We'll repeat all this later again. But these are some of the whistle blowers which we look out for in the first trimester to predict a posterior fossa abnormality. So typically at this point itself, we can see that typically in the first trimester, this aqueduct of cereals is very prominent and shows an increase in size in fita with blex pulses. And this is typically obliterated or small in size in fita with dandy wakamal formation. Even in the first trimester, we can appreciate that the position of the vermice is normal in blex pulses whereas the vermice is rotated in a dandy wakamal formation. So we are trying to make an attempt to come to a diagnosis in the first trimester, but we have to be careful as we'll see. And sometimes the porous flex of the fourth reticle may not be seen in the first trimester. So the whistle blowers of possible posterior, the word is possible, remember this, of possible posterior fossa abnormalities or evolving posterior fossa abnormalities, I will see. The whistle blowers, which are typically point out to this in the first trimester during the dandy scan are increased IT or the increased size of the fourth reticle, altered size of aqueduct of cereals either increased or decreased, altered position of the coroid flex of the fourth reticle. The coroid flex is not seen, brainstorm to brainstorm occipital ratio decrease, altered pontomormin angle and two anechoic spaces rather than three and we'll see examples of that. Here we see a very prominent in IT, we see a prominent aqueduct of cereals, therefore I will be on a lookout for evolving blex pouch. Here we see a very prominent IT, we see that instead of three soloscent areas I am seeing only one prominent soloscent area and if I take a ratio of brainstem to brainstem occipital distance, I see that this ratio is grossly smaller. And again, therefore, I will look out for evolving posterior fossa abnormalities, maybe even our main hyperplasia and here again in an axial view, we can see that the fourth reticle is very prominent. So how do I know that the fourth reticle is prominent in first trimester? Again, we have charts. So we have a wonderful chart published in 2019 of various measurements in the posterior fossa like the brainstem, brainstem occipital distance etc. The fourth reticular size, which we expect to see at the time of anti-scan. So let's see some examples. Here we see a very prominent IT and when we followed it up with 17 weeks, there is a sense, there is a communication of the fourth reticle which is very well seen. But remember, she's only 17 weeks and as I said, we need to wait, we need to wait till 18 or sometimes even 19, 20 weeks to make a definite diagnosis and therefore I'll wait and watch. Here we have another case, IT very prominent. We can see that the brainstem to brainstem occipital ratio is very low. It is only about 0.4. We are not seeing the other sonorescent areas very well and an axial view shows a very prominent IT, again very important. When we followed this up at 18 weeks, this was vermin hyperplasia, a very small vermin, a rotation of vermin which actually I mean at 18 weeks then we could make a little confident diagnosis. This is a beautiful case which Vaisakhi has sent and I always use this because the pictures are really beautiful. Here again at 12 weeks, there's a very prominent IT or the fourth reticle. At 16 weeks, we can see that there is a cyst forming in the posterior fossa. If you look at the position of the coroid plexus, it is inferior and lateral, therefore one would think whether it's an evolving vermin hyperplasia or even a dandy walker which we rightly saw at about 19 weeks. The size was very small. There was a mild rotation and she could make a very confident diagnosis of vermin hyperplasia. So it's very important to make or suspect these abnormalities in the first semester. Remember that an increased IT can also be a marker of chromosomal abnormalities. Here for example, along with an increased IT, we had an abdominal wall defect and that was a trisomy 18. An increased IT can also be a marker of other chromosomal abnormalities, typically triploidy. It is very well known that triploidies can manifest in the first semester with an increased intracranial transversal system. So that's a core tween again where we again see a very prominent IT and when we followed it up, there were multiple anomalies including vermin hyperplasia, there was cardiac anomaly, there was pleural effusion, pericardial effusion, etc. But be very careful. Here's an example, a prominent IT in a core tween. So we said, okay, let's wait and watch. But when we saw at 18, 19 weeks, everything normal. The vermin is normal, the anger is normal. So everything normal. Yet another example, what looks like a very prominent IT, borderline prominent IT, we said, okay, we'll follow it up and at 20, 21 weeks, everything normal. So the moral of the story is, as far as the first trimester is concerned, be on the lookout for markers of posterior fossa abnormalities. Suspect posterior fossa abnormalities is very important now to suspect. Maybe if you suspect strongly, you can do a CVS at that time and do a microarray or send it for even today for exam sequencing. But the important thing is, follow it up. Do not take a hurry decisions, give time for normal epidemiological development and make a decision by 18 weeks or even if you want to wait for 20 weeks, that is good enough and nowadays we can extend the follow up even later. So that is as far as the first trimester is concerned. So what are we worried about? We are worried about the posterior fossa. We are worried about the four big things. And the four big things are mega cisterna magna, blake spousers, warm in apoplasia and dandy worker. Why do we need to differentiate between them? We need to differentiate between them because these two have excellent prognosis, whereas these two, we can have a lot of problems, not only as far as the outcome is concerned, but also we now know that we can pick up a lot of variations on exam sequencing or copy number variants when we do a microarray. So it is very important to differentiate between the four. And in the couple of slides from here, we will see how to differentiate between these four entities, which is very important in practice. So what are we going to look at? Of course, we are going to look at whether the fourth medical is open or closed. We are going to look at wormian biometry, which we talked about. We are going to look at wormian morphology. We are going to find out whether the wormaceous is rotated. We are going to look at the midbrain size and structure. We are going to look at the position of the coroid plexus, the fourth ventricle, very important. We are going to look at the cerebellar hemispheres and of course the cisterna magna and then come to a diagnosis. So let's see how we go about it. Even the fourth ventricle is closed in all probability we are dealing with the mega cisterna magna. If the fourth ventricle is open, we could be dealing with dandy walker or wormian apopecia. And in Blake's pouch, we saw that the fourth ventricle apparently appears to be open but it is not actually open because we know that there is no fenestration which has occurred at this stage. So we will see examples and you will understand it better. For some years back, we gave a lot of importance to these angles, the brainstem wormaceous angle and there were figures which were quoted. But now we know that we cannot depend on these figures because we know that biological things never follow mathematical rules. So you cannot have hard and fast mathematical sort of cutoff figures. We know that there is a lot of overlap. We need to take these figures with a pinch of salt. Enough to say that in Blake's pouch, since the wormian rotation is mild, in wormian apopecia it is more and in dandy walker it is significant. That much even if you remember it's good enough. The figure, if at all, which is very important or diagnostic is the brainstem tentorium angle which gets altered in dandy walker malformation. So if you have an altered dandy brainstem tentorium angle, the diagnosis of dandy walker malformation is done. System of magna, mega system of magna, large system of magna typically above 10 millimeters. But what is important is that everything else is normal. We have a normal wormaceous size, shape, morphology, brainstem wormaceous angle normal, brainstem tentorium angle normal. This usually has a very good outcome and we can reassure the patient. But whenever we see one abnormality, we need to look out for other abnormalities. And for example in this fetus, we not only see a large system of magna, mega system of magna, we see limb abnormalities, we see facial abnormalities, we see cardiac abnormalities. And this was again at price only 18. So once you see something, we need to look at everything else. Blake's pouch, again, as I said, the whistle blower is a cyst in the posterior fossa or a communication of the fourth ventricle and the system of magna. Then we take an axial view, we realize that the size of the wormaceous is normal. The morphology of the wormaceous is normal. There is an upward rotation, but the rotation is mild. And there's of course a cyst communicating with the fourth ventricle. And when we take a coronal plane, we expect to see the corral plexus where superior and lateral in relation to the cyst. So here is a classical Blake's pouch cyst. You can see the walls of the Blake's pouch cyst. That's your system of magna. This is not yet perforated. And we can see the corral plexus of the fourth ventricle, which are superior lateral. And the wormaceous size is normal. The perimeter is normal. The brainstem wormaceous angle is normal. And of course, the brainstem temporal angle is normal. All classical Blake's pouch. Now, sometimes this fenestration can appear late. For example, this is a fetus we saw recently, 23 weeks, open fourth ventricle Blake's pouch is there. Again, wormaceous is quite normal. No significant, very mild rotation, not significant. We can wait and watch because sometimes this fenestration can happen late, typically even at 28, 29 weeks and sometimes even in a post-natal period. And in a Blake's pouch cyst, as I said earlier, the position of the corral plexus is superior lateral to the inlet of the cyst. And that helps us in differentiating. But again, when you see one thing on fetal ultrasound, look out for other things. And here we have ventricle migraine. So this is going to be quite different from other simple Blake's pouch cysts. Then we have wormaceous. Again, what is the whistleblower? Open fourth ventricle. Once you see that, we're going to take a societal view. And we see that the wormaceous is smaller, hypoplastic. Typically, the inferior or posterior portion of the wormaceous is very small. The shape of the wormaceous is altered. So this is one condition where the morphology of wormaceous plays a very, very important part as we see. There's an upward rotation of wormaceous, which is usually significant more than 30 degrees. And of course, we see a communicating cyst with the fourth ventricle. So that's a very classical example. What we see in a societal view is a very small wormaceous. If you look at this wormaceous, the normal morphology is not seen. We are just seeing the vestigeum, but not too great. We are not seeing any fissures at all. And of course, the wormaceous is rotated. And if you look at the position of the corral plexus in relation to the cyst, it is inferior lateral. Everything classical of wormane hyperplasia. Today, when we see wormane hyperplasia, or when we see dandy walker, we not only do carotapping, we in fact do microarray. And most of the times, we nowadays land up doing full-exam sequencing as well, because that has become cheaper and it gives us much more information. Another very important, I would say, whistleblower or eye-opener towards possible wormane hyperplasia, as I said earlier, is an altered fourth ventricle index. Here, you can see that the AP diameter of the fourth ventricle is much larger as compared to the lateral-lateral diameter, telling us that this index is less than one and we need to be suspicious. So this is one situation where not only the morphology of the wormaceous is altered or important to pick up, but perimeters and size become a very important issue. Again, look out for anomalies, typically cardiac anomalies or anything else in the brain, intracranial as well as extracranial anomalies, and whenever required, do an MR. And we'll see a couple of examples of MR later.  The cyst is very large. And of course, the diagnostic feature is an upward displacement of the tentorium, which usually goes above 70, 75 or even at 90 degrees. The wormaceous is very small. There's an anticlock rotation of the wormaceous and there's a large cyst in the posterior fossa. So usually a large cyst in the posterior fossa, wormaceous very small, that's an angle which is almost 92 degrees, all clinch a diagnosis of dandy walker malformation. Sometimes you might be able to see the wormaceous, but very often in dandy walker malformation, the wormaceous is very small, hardly seen, and this angle is of course diagnostic. But again, whenever you have dandy walker, look out for other anomalies here. We, for example, we have corpus callus and urgenus, we have limb anomalies, we have cytosome anomalies, we have facial abnormalities. Again, this was at price of 18. So dandy walker malformation and wormaceous hyperplasia, look out for other intracranial and extracranial anomalies. In fact, look out for intracranial extracranial anomalies in all the cities. Dandy walker malformation, the wormaceous is not too good. There can be so many problems post-natal motor delay, hypotenia, spasticity attacks here, poor coordination, etc., etc. Now this is a paper, there were two papers published in 2014 and 2016, which were systemic meta-analysis of the four entities, that is the mega system, magna, blake, spout, wormaceous, and hyperplasia. And as you can see that as you go from mega system of magna to dandy walker, the incidence of aneuploidy went on increasing. But today we don't stop doing only caretapping. We of course do microarray, look out for copy number variations and in fact do an exam sequences also in majority of the cases. Again, the incidence of intracranial and extracranial anomalies goes on increasing as we go from mega system of magna to dandy walker and the incidence of neurodevelopmental delay also goes on increasing as we go from mega system of magna to dandy walker. So where do we draw the red line? Typically in this area, these two have usually a very good prognosis and therefore counseling is very important. And these two usually one needs to be very careful and again counseling is extremely important for as far as the patients are concerned. So typically then we can have other abnormalities in the posterior fossa besides the common four ones. The four ones are the big ones as I said. We can have again a posterior fossa abnormality or dandy walker marmalation or a severe worm in hyperplasia associated with ventricular mingling and renal cystic areas, which is typical of a goldstone syndrome. We can have Joubert syndrome. Joubert syndrome as we know is a spectrum. It is not one syndrome as such. There are multiple sort of types of jubbers which have been described in some big spectrum. But typically what happens is there's an aplasia of the worm. We don't see the worm. What we see here is basically just a soft tissue. The hemispheres are very close to each other. The fourth ventricle is sort of a bat wing shape. And of course, because of the thickening and elongation of the superior pedangals, we get a typical molar tooth size. And most of them are abnormalities in the kidney in the form of cystic areas. So again, as I said, today we need not stop at even array. We need to do exon sequencing. And this particular fitness we did an exon sequencing. This was a Joubert syndrome type 5, at least 10 basic ones have been known. And we could identify the mutation, which is supposed to be one of the common mutations in Joubert syndrome. Now this one is from Dr. Ramu because he has an excellent collection of jubbers. So what we see is all the signs classical sign of jubbers. As we can see that the worm is not seen in the center. There's an abnormal fourth ventricle. We can see that the AP diameter is much more as compared to lateral diameter. We can see that the fourth ventricle is open. And we can see thickening of the superior cerebellar pedangals giving rise to a classical molar tooth appearance.  So Joubert syndrome is not a one entity. It's a group of disorders which are related to each other. This comes under autosomal resistive symbiopathy. These children have hypotonia, irregular neonatal breathing, their facial dysmorphism. They have problems with the eye movements, which is very typical. They have intellectual impairment as well. There are a lot of syndromes which have been associated with this, like the core syndrome, the cerebral ocular anal syndrome, etc. And today many mutations have been identified when we do a gene analysis. Then we have an entity where the cerebellum is very small. And both the cerebellar hemispheres appear to be fused. And this is rhombin encephalosynapsis. And if you look at the shape of the system of magna, it is a chrysanthic shape of the system of magna. And this is very commonly associated with other impractical analogies, typically holoprosyncephal. And here we have a classical example of rhombin encephalosynapsis. We have a fusion of the cerebellum, a small cerebellum as such totally. And we can see that there is an associated holoprosyncephal. There are abnormalities in the face and abnormalities in the limbs also. Here's another example of rhombin encephalosynapsis. Very small cerebellum, worm is not seen at all, ventricular legality. And this fetus did not have any extracranial anomalies as such. So rhombin encephalosynapsis, we have a missing cerebellar vermus. There's a fusion of the cerebral hemispheres. And of course, we have a lot of abnormalities, including bacterial abnormalities. We could have other syndromes like the gomislopis GLA syndrome. This shouldn't again have poor balance at the abnormal eye movements. So most of the posterior force abnormalities you can see have a balance problem at taxia and eye movements. Because as we said in the beginning, this is where all this is controlled. Now when we do our anomaly scan or even for that matter, whenever we do a follow-up scan, we always like to measure the cerebellar diameter. And we know that usually the cerebellar diameter in millimeters corresponds to the weeks. But what we see here is that the fever is 21 weeks and two days. But if you look at a cerebellum, it is only about 1.4 centimeters. So one would expect the cerebellum to be at least 20 millimeters in this fetus with 21 weeks of gestation. So this cerebellum is very small, but the shape of cerebellum is maintained. And again, the vermus is very small or hardly seen. And this is typical of cerebellar hypoplasia. Now to diagnose cerebellar hypoplasia, again, what is important is we need to correlate with the head circumference. So what we need to do is either we have charts of the diameter in relation to the head circumference or relation to the bilateral diameter. And only if this is less than 5 percentile, we should think of cerebellar hypoplasia. So this here, as the name suggests, the cerebellum is small. I think as I said, the shape is very often maintained. The system of magna may look very prominent. The fourth radical index may be altered. And there are usually associated intracranial and extracranial anomalies seen, and the outcome is usually poor. Now very rarely, you can have a unilateral cerebellar hypoplasia. That means one part of the cerebellum is grown very well, but one part is not grown well. And this typically happens because of an insult. And this insult is either in the form of human age or in the form of an ischemic insult, or it can be a combination of both. Now unilateral cerebellar hypoplasia, if the worm is developed well, can potentially still have a very good outcome. So this we need to remember. Not a very common thing to happen. The other condition where we very often see an asymmetric cerebellar hemispheres is when you have hemimegaloencephaly. So as a part of hemimegaloencephaly, where there is a symmetry in the rest of the brains, we can also get an asymmetry in the posterior cranial contents or in the cerebellar hemispheres. Then whenever we see that the cerebellum is small, always look at the mid-brain structures. Here for example, this is from Shekhar and I'll talk about Shekhar briefly. Now here we see that the wormace looks quite okay. We have a CSP, which is prominent. We have a system of magna, which is prominent. But when we look at the brainstem, the brainstem is hardly seen. It is extremely thin, the mid-brain and the pons. And if you were to do the measurements and put it in a chart, this would be 100% less than 5%. In fact, you don't have to measure in this particular case because it's extremely thin and hardly appreciated. So that is classical ponto cerebellar hypoplasia. These are beautiful pictures by another very close student of mine, Shekhar, whom again we lost a couple of years back. And he has given me a lot of his cases he used to share. And I usually try and keep at least one of his case in my talks so that we always remember Shekhar whenever I give talks. So ponto cerebellar hypoplasia is very rare and as I said, we have a small cerebellum and brainstem. They're usually associated with profound intellectual disability, delayed or absence psychometric milestone. It's a very often autism and recessive. And now several mutations have been identified. So Sheetal and a group again have presented a wonderful paper as an editorial in the White Journal about I think in 2021. I'm written here, but it's hidden here, which all of you should read wonderful paper, really beautiful paper and cases. So they identified two feti with ponto cerebellar hypoplasia and they identified two rare syndromes after genome sequencing. One is an Emanian syndrome. The other is an auditory neuropathy spectrum. But what is very interesting here is if you look at the ultrasound pictures, small cerebellum, small vermus, I'm sorry, small brainstem and pons. And the same thing is seen very well on an MRI. Again, small midbrain and a very small cerebellum and they went on to do gene analysis and came out with this diagnosis. And the fetus again, very small vermus, very small, very small cerebellum, very small brainstem, again correlating very well, excellent correlation between ultrasound pictures and MRI. And again, full genome sequencing was done and they came to this very rare diagnosis. And as I said, these two cases are published. And the reason why I kept these two cases is to show that how well you can correlate ultrasound with MR and most importantly, you should not stop there, but do an exam sequencing to come to a complete diagnosis. So again, congrats for these excellent cases. Then we can have a cyst in the posterior fossa, but the rest of the structures cerebellum, vermus everything is normal and the cyst is pushing all the structures. And that typically happens in an adrenoidal cyst. So adrenoidal cysts typically are retro cerebellar that deform the cerebral hemispheres. The cyst walls, you may not see because they're very thin and you can have an obstructive ventricle megalitis because ventricle megalitis is very common with posterior fossa adrenoidal cysts. Then you can have a situation where the vermus or the cerebellum becomes very bright. And there are two things we need to keep in mind. One is a very rare thing, which is fetal infection. This was a very rare case. The fetus had a lot of other signs of fetal infection. And of course, the cerebellum was very bright. But more commonly, when you see a very bright cerebellum, think of cerebellar hemorrhage, which is very common. And when you see cerebellar hemorrhage, and if there is no cause, you can find out attribute like maternal cause or any maternal hemorrhage disorders or mother taking any medicines, etc. Then think of an underlying vascular malformation in the cerebellum. And recently in the Uskon, Katina gave a wonderful talk where she showed a series of cases of vascular malformation malformations of the cerebellum, some of them giving rise to cerebellar hemorrhage. So this we need to keep in mind. So as I said that other visceral blower is an effacement of posterior fursal. That means you don't see the system and the entire thing is effaced. And that is associated with open neural tube defects. And as I said in the beginning, that we are not going to cover this today. And then again, occipital encephalosil, we are not going to cover this today because that's a part and parcel of open neural tube defects.  It does cause a lot of confusion, but I think over a period of time, we understand it better. And we are trying to decipher this confusion. And I hope that I have been able or I have been successful in clearing some of your confusions. And I hope that I have been able to also sort of, you know, too new to trying to pick up posterior fursal abnormalities in the first semester. But what is important is give time for normal and biological development. Be very logical in your approach. Genetic testing, very important. Nowadays, complete exam, it takes time, but it's easily available and the cost is also low. So you can always do a basic fish microarray and store the DNA for exam sequencing if time is the concern. Counseling is very important. And in fact, in our center, we have different specialists for different counseling. So we have a pediatric neurologist. I think we would come for one of the ultra fests. He was in one of the ultra fests and for sorobors, I don't remember. And so counseling has to be done properly with the genetics with us is and maybe a pediatric neurologist, because as we said, we have extremes. We have two things like, for example, the Blake's pouch and the mega system Magnum, which are very good to know is we don't want them to terminate on this week. We have problems like women, hyperplasia and of course, Dandy Walker, which can have problems. MR playing a very important role. There's no doubt about it. And whenever there is a doubt or whenever you want, always refer to an MR for an MR. So I have to thank all of you for your patient link sling. I have to thank Pooja. I forgot to mention her.  And whenever I have a talk and I want line diagrams, I just tell Pooja and she sends it. Next thing I have to thank my team from center. We have an excellent team on my fellows and whenever I will actually make them run around, take this, take that, you know, do this, do that. So I have to thank all of them and my shali and Jyoti and everything everyone else who helped me in putting up this. And of course, thanks to the Sonobas team for this wonderful opportunity and for giving this honor of giving the first Tulsi Memorial Oration. And as I said in the beginning that Tulsi and his family can always look upon the Sonobas team for any support they can look upon all of us, not only as meteorologists, but as family members. Thank you so much. Thank you, sir. That was really wonderful and the beginning also where you put forward your pictures with Dr. Tulsi was really wonderful. I just wish to say that those who missed the complete lecture or who came in midway, you can always follow this lecture once again on YouTube it will be on for a few days more right from the start. And we also have Dr. Hanisha Gwalani with us but before that we have Dr. Deepak Patkar here who is the integral part of Indian radiologist and he would like to say a few words to us. Dr. Patkar sir please. Dr. Patkar you are mute I think. Thank you Sanjeev and thank you Dr. Rinchaval for an outstanding presentation. I've been traveling with you from I think early 90s and you're getting better and better not older and older. Really good slides and extremely good presentation. Thank you for that. As far as Tulsi is concerned I have a lot of nice memories of Dr. Gwalani and not still yet it's me when I think of him. He's a friend from 1985. We have done our residency together at Nair. We have traveled together for conferences. He used to be there for most of the conferences within Bombay and around. Importantly we've had family holidays together. I have worked for one of his first centers in Kallan where I used to report the MRIs. He used to send the scans in sorry I'm on the phone so incoming calls are coming. So he used to send his scans physically from Kallan to Nanavati every afternoon evening. The previous scans I used to report them, get them typed, sign off and send. So that's the kind of memories I have. There used to be about 10 scans and used to take about 2 hours. A guy used to wait for 2 hours. I used to sign off the reports, take them back. I don't know what time they must be reaching. So a very very cool, composed, calm person and very very loving person.  As they have also turned out to be wonderful human beings. We at Indian Radiologist are indebted to him for what he's done for us and in the field of radiology as well. Moving on to the educational front, third wave has put all of us on the back foot. We will of course at Indian radiologist not stop learning and teaching. These activities will continue online. The online activities of general club, master classes and hybrid activities whenever possible will happen. We'll find our best way out of this. Master classes on onco imaging, breast imaging and conventional radiology will happen in January and March. So look out for their dates on our website and all social media platforms. Thank you all who attended this session and help us make it very very successful one. Of course, Dr. Chobhan is the most important person today. And also thank you all for remembering Dr. Galani. In the meanwhile, let us all stay safe, march yourself, take a booster dose which starts from tomorrow and have a good day. Thank you. Thank you, Dr. Patkar. And before we end, I'd like to also, we have Dr. Hanisha Gwalani with us and I'd like to remind everybody that Sonobhas is going to be held. Our next dates are 19th and 20th March, physical event at the Renaissance if and when the wave settles. So we'll hope and pray that it does. But right now it's over to you, Hanisha. Please, you can speak. Hello everybody. First of all, I would like to thank the entire team of Sonobhas, especially Dr. Jignesh Sir and Dr. Mani Sir, who came up with this idea of having a memorial oration for my father. And Dr. Nitin Sir, my heart felt gratitude to you for agreeing to do this and for all the kind words that you said. It's a matter of an absolute honor for my father because I knew how much he looked up to you as his guru. That is how he used to address you whenever he spoke about you. And he used to share a lot of teaching stories and a lot of wonderful memories he made with you. And I would also like to take this opportunity to thank everyone from this fraternity who reached out to me and my family, sent their prayers, words of courage, best wishes, kind thoughts. During that challenging and shocking time. Thank you. Thank you very much. It means a lot. It was my father's innate nature to be there for people. He was a people's person and he would often go out of his way to add value to the lives of all those who seek his guidance. And he was fondly addressed as Golu by most of his friends and colleagues and more often than not, I am introduced as Golu's daughter and I cannot be more proud about it. He was a strong pillar of our family, a true friend and a very ethical doctor and a gem of a person. And he knew how to celebrate life to the fullest. I thank everybody. I'm a very proud daughter and I feel really overwhelmed to see the amount of love and respect that he has gained from this fraternity. And I feel fortunate and rather humbled to receive all that love from this fraternity. On behalf of my family, I thank you all once again. Thank you very much.


We're now going to take a look at the equations that describe the hydrostatic forces on surfaces submerged below a surface. So we'll be looking at plain surfaces to begin with. And so what we're going to do now, we're going to go through a couple of sections on a derivation for the equations here. And first of all, we'll be looking for the resultant force on the plain surface. And then the second thing that we'll be doing is trying to determine where does that resultant force act. So this is a lot of fluid statics that we're doing. It's very similar to course and statics. But what I'll do, I'll begin by drawing out a diagram that we'll be referring to as we go through the analysis. Okay, so this is a schematic for the plate that we're going to be deriving the equations for. A couple of things to note on here. First of all, what we have done is we've defined our coordinate system with respect to the center of area on the plate, which is right at that location. And so CA will denote the center of area. We've said that the center of area is acting at a depth HCA below the surface. The z-coordinate goes perpendicular to the plate as shown here on this part of the diagram. And then the x and the y-coordinates are there. We look at a differential element on the plate, and we will be deriving the equations from that differential element. The last thing to say is that the hydrostatic pressure averaged over the entire plate acts at a location that we referred to as being the center of pressure, Cp. And that is denoted by this vector Fr here. So what we're going to do, let's continue on, we'll refer back to this diagram as we work through it. But one of the things that we can also say about the resultant force is that it acts normal to the plate, as we said for hydrostatic forces earlier. And so although that vector looks a little crooked, it's supposed to be normal. And that's due to the fact that the fluid is not moving for hydrostatic. So what we're going to do, we're going to do a derivation for the forces on one side of the plate. So let's continue on with that and see what we get. So what we can begin by doing is writing out the differential force that would exist on our differential element. So this is the differential element here. Let's take a look at what the differential force would be. And we can write Df as being the pressure at that location multiplied by the differential area. And of course, if we want to get the resultant force, then what we would need to do is we would need to integrate that across the entire plate itself. Now we know the pressure distribution from hydrostatic. So let's introduce that. So with the pressure distribution, what we can do is we can write out the force. So we get this relationship here. And notice I've been using PA and P atmosphere. That's referring to the same thing. So just be aware of that. Now with this, what we know is the atmospheric pressure is not a function of location on the plate. Atmospheric pressure is a constant. So we can pull that out and integrate that first term without a problem. For the second one, what we need to know is we need to know how H, that is the depth of fluid at a given location. Let's look back at our diagram. H is shown here as being the depth of the differential element. We need to know how that varies as we move around and look at different differential elements. So the one thing that we do know is that H is only a function of y. If you move across the plate in the x direction, the depth does not change. It's only if you move in y that the depth will change. So we know that. And what we can do for the resultant vector is we can, first of all, for the first term, it is just the atmospheric pressure times the area of the plate. We can pull out the density and the gravitational constant and the second integral. And then that is HDA. So what we need to do, we need to handle this integral here. And so in order to do that, we're going to take a look at the relationship between depth and the area. And we'll re-express that in terms of sine value, sine theta. So let's take a look at that now. And I'll begin by drawing out the plate again. So here's our plate. And let's say this is our center of area located right there. And recall, that is where our coordinate system begins from. We've defined the coordinate system there. And if I sketch up, we said that the angle of the plate was theta. So if we are at a location y, and remember, coordinate system begins at the center of area. So at a location y, at this location, the center of area, we know that we have HCA. That is the depth at the center of area. But if we're at some location y, like right there, I'm going to draw a little right angle triangle. I know that this angle here is theta. And consequently, we know that this distance here can be determined through trigonometry to be y sine theta. So what we can write at any location where we're looking at our differential element y, we can write out that H at a given y location is the depth at the center of area minus y sine theta. And if we go lower along the plate, then y would be negative and that would be HCA and it turned into a plus y sine theta because it would be minus minus y. But that gives us a relationship for the depth at a given location where our differential element is. So what we can do is we can take that and plug it back into the integral for the resultant force on the plate. So we have this. Now what I'm going to do, I'm going to expand the integral. So HCA is a constant. This is varying with y. So let's rewrite that. And I've been able to pull HCA out because HCA is a constant. It's not changing. The center of area is defined. And then we have a minus, a minus that turns into a plus. We get rho g sine theta. And that will be a double integral over the area. So we get that there. Now, this is an integral that is rather well known. And what that refers to is the center of area for the plate itself. So that would be the center of area. But remember, we've defined our coordinate system. Let's go back to our schematic. We define the coordinate system to be about the center of area itself. Consequently, what that means is that where our coordinate system is defined, this is actually zero. And that last term disappears from our equation. So what we are then left with, what we're left with is this equation here. So the resultant force on the plate is nothing more than the pressure at the center of area. And that's what this is showing. Pressure center of area multiplied by the area of the plate. And I've shown it in vector notation here because we need to preserve the vectors. However, we can simplify that a little bit if we note the following. So if we note the pressure as being an outward force, so let's draw our plate again. We had our free surface up here. And what we note is Fr is an outward vector. So if we just say that it's an outward force and it's acting normal onto the plate surface, we can then neglect the vector notation. The other thing, let's say, I said Pa is P atmosphere here. Let's assume that we have a scenario where we have liquid in here and we have air down here, atmospheric air. Consequently, we can say here is also P atmosphere. If you have that specific case, if you have the outside pressure being P atmosphere and if you have knowing that the pressure or the force is acting normal to the plate, what we can do is we can simplify or get rid of the vector notation. And what we end up with, the pressure at the center of axis is nothing more than rho G H C A. And then that is multiplied by the area of the plate. And so in some books, you'll find this as being the expression for the pressure at the center of, or sorry, for the force that acts on the plate. And remember, this force is not at the center of area, but at center of pressure, which is different from the center of area. And so consequently, here we've derived what the force is. What we need to do in the next segment is we need to figure out where that center of pressure is. So that is hydrostatic forces and pressure distribution on a submerged plane surface will continue on by trying to figure out where the force is located at the center of pressure.


Jerry of the circus see it's a nice day, isn't it? I just love this backyard on days like this the show going on just as regular and them didn't send them Guess I feel kind of sad you do why I've been over talking to Kelly Well, I don't know a jolly a man in the lap than Kelly. He's the best cheerer up for I know See that Irish menagerie man's got more animal stories than anyone else in the business. Yeah, I know come on Jerry snap out of it.  Oh, he wasn't telling any stories Well, then whatever's wrong. Did he hear about the new new what? No GNU. Oh You're talking about an animal. Yeah, the one that died. Oh Yeah, one of them died in Fordham. It seems like an awful lot happened in Fordham I'll say oh now Jerry, there's no reason for you to feel so upset, but they're pretty animals so gentle I knew about it when it happened, but you were so all fired busy. I guess I never thought of mentioning it Mr. Angle must feel pretty bad. Of course he does but after all when you're around so many animals all the time Things are bound to happen over a long period of time. Oh, I don't feel so bad about the one that died Well, I thought you said that Say what on earth is going on behind that funny little freckled face of yours Jerry?  What? Yeah You see he's left all alone and he's grieving some fears Kelly says that happens now and then animals just die when they lose another animal They like a lot. Yeah, I know that's true. Oh, well, that's really a shame Jerry Yes, that's why I'm feeling so sort of blue and yet. It's such a swell day. It's so good to be here Well, we'd better get going Jerry. Yes. I'll just sit here and wait for a you know He's probably over at the wagon now. Come on Jerry now. You can't help that new by worrying about it Yeah, I know but I sure wish there's something I could do she was a good house today. I never saw so many kids Yeah, they sure like your act. I didn't have any trouble hearing them applaud you and El Mundo Oh, he was going great today. He sure was in a good mood. Did you hear him squeal after he picked me up and put me on his head? I sure did look like you most lost your balance for a minute. I almost did I was so surprised. He never squeal like that before scared me for a minute. Just high spirits Jerry That was all it's funny how much I'm getting to like that. Oh, but I never was scared of them But now I well I can just hardly wait to work with them Well, that's the test of a real animal performer. How do you mean? Well an animal and his master have to like each other to do their best and if you really love your animal You can make him do lots more and I suppose that so oh Well, here we are Well, hello there brought your pay envelopes around oh say thanks and sign here. Here's an indelible Well, that's service. Thank you. Oh, that's okay too many folks in the midway Mr. Randall thought it better to have me deliver the envelope. Here you are. You can read my writing. Sure Well, so long Why do you read wasn't here? You'll kind of mean open and this pay without him being here. Oh, well, it's yours, too Yeah, it's good to have this makeup off. I wonder where Rags is guess I'll take a look around no wait a second I'll walk away with you. I want to see Mr. Randall a minute sure here. I'll hang up this stuff Where's my belt? Oh, they're under the chair. I'm gonna buy some special frags this week. Oh good. All right, let's go Well, what are you gonna get him? Oh, I don't know I'll think of something you know I think it's pretty nice the way you always buy rags a present every week Well money doesn't mean anything to him and I guess he earned some kind of a bonus sure it does Yeah, but most most folks wouldn't think of that bombs. Yeah now what look over there where coming from behind that bandwagon Well, well, I'll be it's right. It sure is but what she got in his mouth rags. Come here. You might what you got Jumping horse feathers. It's a cat cat. Hey, right put that down. Why you will hurt that here eggs Put that cat down.  Looks half-starred I'm gonna get a somebody you better get it to the doctor first Yeah, I guess I had he was over them and then every ten a while back trying to make that for a new e You know, it's tragic how animals will starve themselves to death on purpose Sounds like the majors on a rampage again poor major might be in a midget certainly makes him sensitive Thoughtless thoughtless. I appeal to you just a minute Jerry bumps I want you to hear this. What did you say if a big bully called you a dummy? Yes, sir I'm me you don't mean to say Velco said you were down. Well, not exactly that But he said I'd make a good dummy, you know for a ventriloquist.  I won't He thinks he's so smart, you know, some people just like to brag. That's probably what he was doing Hmm. Why do you know what he said? He said that that be fater said said that I was just a sample a sample Do you get that sample why sample of a man? But you think I'm gonna stand around and take that kind of talk from from a human crane Think she's wonderful cuz he can lift heavy weight. I'll just calm down major I'll talk to Belko and see that he's a little more careful of what he said, and that's not all you ought to hear the lies He tells why is sure a lot of nonsense about being able to drag a truck with his teeth and Swing a trunk around his head with his teeth.  Well, that's really going too far Say it is why why I was just speechless. That's what I was imagine throwing me through a basket I never heard of such no, and now don't you worry any more major? I'll see the Belko, but you go on tonight and no nonsense now. You hear me? All right, but I'm warning you I'll not stand to be belittled by a man made out of just muscle and bone My guess I prove before the brains are more important than brawn. It's all right major. I'll see Belko. Goodbye Guess I know when I'm right. Well. Goodbye folks. Oh, goodbye Boy major can sure work himself up into a stew can he certainly can He gets into a perfect lather, but as soon as he flies off the handle and gets it over where they feel it's better Well, Jerry, what have you got there? Rags just brought him. Isn't he cute poor cat? I looks half-star Seems as if it's hurting some way. Yeah when Rags brought it in it just later on the ground didn't get up On its feet or anything. Well, you better get us some food Jerry. Thanks, mr. Randall I will thought maybe I'd better let the doctor see it. Yeah, that's a good idea Jerry We can't take it with us, but we will do what we can for it. I yours to all mr. Randall Oh, couldn't we just whoa, it wouldn't be in the way or I'm sorry, Jerry But that's quite out of the question say uh bumps. I've been wondering mm-hmm. What about well You suppose Belko can do all the things that he claims he can't well Couldn't say offhand but there have been men with phenomenal teeth who did unusual stunts You know, I was thinking say that's a good idea Imagine really doing those stunts in the sideshow boy that oughta pack a man Well, I wasn't thinking of the sideshow Jerry You mean yeah, he really is good It might be worth featuring him under the main top say boy that it's your burn up the major Oh, no, no all he wants is to be the main attraction in his own tent He doesn't care what happens under the big dog But he certainly raises a rumpus if anyone steals his thunder in the sideshow He does what you're gonna do mr. Randall. Yeah, I'm not sure Jerry, but you might do an errand for me sure anything You say well run along and take care of your cat first and then look up Belko and send him to me in the office wagon I'm headed for there now sure I will oh say am I meant to ask you if I could get Lester over in the workshop to Rig me up some kind of a fake bull headgear for right I'm sure he can I know what has to be done. All right. All right, go ahead and tell us to you got my okay Well, I've got work to do. I'll be seeing you. I'm sorry about the cab Jerry But I guess you've got your hands full enough with rags. Goodbye Sam. Well, bye mr. Randall coming bumps Well, I guess I may as well got nothing special to do. I'm awful disappointed You don't know how I eat to leave this poor little kitten behind Maybe it'll be best in the long run Jerry never can tell if it's hurt bad to travel and mightn't be good for it Well, here's a menadry town. Hope the doctor is still here Mind holding the flat back and kind of got my hands full Come on right come on boy after all this is your Yeah, the doctor round no not now, but I expect him back any minute good. We'll wait here then Hello bumps. How's tricks? Oh good. Say what you got there Jerry? It's work for a little thing But maybe the doc could help sure thing. How's your patient? I don't know I can't seem to interest more than anything and it's breaking me heart poor mod. Look at her just laying in there Say she's looking at us. No You're right Jerry say that's more interest than she showed all day Oh, oh, there she is turning away again Yeah, that's the trouble sure if we can just keep her interested enough so she'd want to keep on living on yeah The rest would be easy because there's not a thing in the world wrong except. She's graven her heart out. Hey Kelly She's watching us again Say you don't think it's this cat do you know what she'd want would say wait a minute here Give me that kid careful now. Don't hurt it. I want I just want to see it Kelly I believe you've hit on something Hey, look mods watching Kelly she is yeah, I guess she thinks the catch more miserable than she is but look She's getting up. She's moving over Kelly wouldn't it be wonderful to be in a wait a minute folks Here comes the doctor. Maybe he'll know what to do


Tired of the everyday routine, ever dream of a life of romantic adventure, want to get away from it all? We offer you escape, escape, designed to free you from the four walls of today for a half hour of high adventure. Well, we are primers. Yeah, but we did not make contact until half an hour ago. Look, you have the ticket? Yes, I have it. That's all I could get. Well, that will do. Oh, no, Mr. Eric here. This is Mr. Calendar. He will take you to Hanover. How are you? Bruce, better not to get on the train? No, no. We'll wait for the whistle. Why? Here's the crowd for cover. Then Mr. Eric, turn your face to me. That's the ticket back to the train. Now, wait. All right now, Eric. See you back in a few days, Ernst. As the British's own terminus of the East German underground, I'd had my share of surprises, but none to match finding Watten-Herrick in my custody. This was the man who had disappeared behind the iron curtain nearly a year ago, voluntarily. Brilliant nuclear physicist and authority on thermonuclear reaction. He'd been swallowed up in the gigantic red moor of Eastern Europe. The highest bidder for his brain. And now he was back. It was up to me to escort him safely to Hanover through British intelligence. And as we rode, I speculated on why he had come back. I suppose you're wondering why I came back. Why did you? Simple. I finally realized I'd picked the wrong side. So I took the whole show and came home. Just like that, as you say. Just like that. You sound pretty casual. How else should I be? I don't know. It was my conscience you're concerned with. Don't bother. I got more from them than they got from me. Oh. Yes, I know. Every installation they've set up, what the questionable material output is per day and what their potential is for producing the hydrogen-bombing quantity. Uh-huh. Where are your records? Notes. That sort of thing. I memorized. Paper and pencil were too risky. I had a security guard with me constantly. How did you get away? He walked out of Magdeburg. What about the guard? I imagine they'll bury him with full military honors. Yes, I imagine they'll loathe. Yes. But we're here now and I'm safe and that's all that really matters, isn't it? Well, I won't feel safe until we get past Tullis, Leibniz. When's that? Oh, about two hours. Do we stop there? That's for a few minutes. Hey, mind if I take a nap? Suit yourself. Wake me up, Tullis, Leibniz, will you? Right. So he went to sleep. And I thought about how easy his escape had been. Too easy. This was no ordinary defection to the camp of the free world. This man was important. Important enough that his safe arrival could cause considerable embarrassment to those from whom he escaped. We wheezed into Tullis, Leibniz. A few passengers got out. One came aboard. And we started off again. Did you sleep well? Very. Where are we? Leaving Tullis, Leibniz. You slept? No, I... Yes? Who is it? Conductor, sir. Well, come in. Bruce, now will you please tell this stupid... One moment if you please. But there is no time for... Go ahead, identify me, but hurry. It's all right, Conductor, I know. What about the spare, sir? Well, I'll take care of it later now, if you please. Of course, sir, forgive me, but my job... And I have a wife and yes, yes, we know all that. Now will you go, please? Yes, sir. Bruce, now we are in trouble. They know what's the matter. They know where we are. What? They have an agent aboard this train. When did he get on? Just now, at Tullis, Leibniz. Oh, we just left Tullis, Leibniz.   No, that is the problem. We won't get to Hanover. Why? There is a bomb on board. The time is to destroy the train with me, get on the Oak River Bridge. Well, then we'll stop the train. No, I thought of that, and that's no good. Because whoever it is has orders to explode it if the train stops for any reason before we reach the river. When did you learn this? An hour after you left. I received a message from the man in Marguerite. They found a body of that guard. Soon after, Herrick left. They missed you in Erbetsfelde, and they arranged this tireless labor interception. But how did you... I drove, and when I got here, the train was pulling out of the station jut.  It's too late for that now. Yes. We've got to find the bomb. It's for the agent, a man or a woman. No, I don't know, Bruce. How soon before we reach the Oak River? But from now about an hour and a half. An hour and a half. Well, between the three of us, we should be... No, Herrick, you stay here. But at least I should... Herrick. Yes? We know nothing of atomic reactions. That is your field. This is ours. Just do as you're told. Will you please... I'm sorry. All right. Ernst? Yes? Get the conductor. Yes, and Herrick. But why? We are not at war. Why should they want to do this to me? It's not you. It's us. They're doing it, too. But what can I do? Where shall I look? We'll do the looking. All we want from you is cooperation. Of course, I will cooperate. What else is there for me to do? Not much. Now, first, do you have a list of the passengers that got on a tour? Yes. That's good. Second, can we get into the baggage car while the train is in motion? On this train, you can. Some of the first and second passengers... All right. That's enough as long as we can get on this one. No, wait. What about the baggage? Did we take much aboard at electricity? Only the baggage clerk knows that. You'll go with me when I go to the baggage car. Yes, sir. Ernst? Yeah?   Yes, yes. Match up every bag with an owner. All right. Mark the location of any objects that you may find. You may have put it on one of the baggage shelves and left the train. Where will you be? Baggage car. Yes. But after that... Back here. It's a calendar. Yes, Eric. It won't be easy staying here. You didn't expect it to be, did you? I suppose not. Well, nothing. Good luck. But if he's not a policeman and not a soldier, why should I let him in? This baggage car is... Carl, do not argue with us. There's no time. But why should I... Here, here. Let me, let me. Carl, this is an emergency. I must be permitted inside to check the baggage. But where is your permit? Badge, credentials, anything that I may locate. Jobs are hard to get. My wife and children will... All right, all right, then I'll tell you. Someone has planted a bomb on board that's going to go off. I'm bombed? Yes, I'm bombed. And if I don't find it in... Well, let me see. In an hour and 15 minutes, none of us will be able to hold a job anymore. Now, may we come in? Yes. Come in, come in. All right. What do you want to know? How many pieces of baggage came aboard at Salisleven? Two. Not many. Five, two cases. A trunk is in that crate. The crate? What's in the crate? I don't know. It's Bluetooth to Hanover. All right, have you got a hammer? But I have no story. Get me a hammer. All right, thank you. Okay, careful, please. Careful, oh no. Oh my God. It's furniture. Okay, now the suitcases. Over here. Yeah. Have you a sharp knife? Yes, but why? I must cut the bags open. Cut? But the owners will... I'll take the responsibility. Now get the knife. It was the only thing to do. The bags had to be cut open and affected by hand. Opening a catch might set the bomb off, even if the detonator wasn't wide to it, which in all likelihood it was. As I cut into the first bag, I felt a hard knot forming in the center of my stomach. I reached inside the bag. Second case. Then we broke open the truck. I left the conductor and Carl and went back to the compartment. Nothing? No. Where's that? Still checking bags, I suppose. How much time do we have? Not quite an hour. Time enough? I don't know. You're sure the bomb is a book? Yes, I'm sure. That doesn't make mistakes. What do we do now? Well, you do just what you've been doing. Stay here. I'm going out and check the passengers that came aboard at Tullesleben. Anything you want me to tell Ernst when he gets back? Yes, if he gets back before... We're doomed, I tell you. What's the matter, Dietrich? The engineer is going to stop the train. Stop? What do you mean stop? He can't. I told you what would happen if we stopped before we reached the open. Nevertheless, the engineer is going to stop. Why? He says he has a bad coupling on the coal tender. Did you tell him why we couldn't stop? He says he can see the bad coupling on the coal tender. The bomb he cannot see. Oh, no. Therefore, the bad coupling must take precedence. He's going to stop the train. Dietrich, the conductor, had just informed me that due to a defective coupling, the engineer was about to stop the train. And under these circumstances, it was a horrifying shock. Because we knew that the train was to be blown up if it stopped for any reason. Before we reached the open river. Well, I thought you would still be in the... What's the matter? The engineer is going to stop the train. No, he can't. I told you what would happen. Yes, I know, I know. Dietrich told him. What more can I do? It's out of my hands. Well, there's one thing more you can do. What, Mr. Cullen? Go back to the engineer. Tell him we want 15 minutes. And tell him that if he refuses, I'll personally kill him. But the coupling, what about the coupling? I don't care about the coupling. If it breaks, we're dead anyway. Let's at least try to find the bomb. Yes, Mr. Cullen, I'll tell him. Bruce, what shall we do if that engineer refuses? And I will kill him. Or at least get him out of the cabin. Let the fireman run on the train. You know, there is still the possibility that agents may have planted the bomb and himself then led the train. I might, but we don't know. No, that we don't. What about the baggage car? That's clean. The passengers' luggage? Oh, no, every piece matched up. Yeah. Now, where can we go now? Dietrich gave you a list of passengers that boarded the tower side, you know? Yes, yes. All right, give it to me. All right, here. But they are all Czech, Bruce. Except one couple in second class. What? One couple. Couple? Yes. Married couple newly wed. They could not possibly be the ones that would be very clever of them. Wouldn't it? Yes, very. Where are they? In this car. They come part in the third from the end. Have you a pistol? Yes. All right, give it to me. Here. Do you want me to come with you? No. Give me five minutes. All right. This was infinitely worse than fighting in the dark. Dark fighting terrified me. Here my enemy was unseen, unknown and out of reach, yet he was close enough to mark us all for death at a specific time. As I hurried along the corridor, I glanced at my watch. If the engineer gave us the 15 minutes I'd asked for, then we'd already used three of those precious minutes planning strategies. One thing I knew for certain was that the hand holding the gun in my pocket would not come out until I was completely satisfied as to the identity of the newly wed. What can I do for you? My name is Bruce Callender. There's been a bit of a stirrer board and, well, the conductor made me a kind of deputy to make an inquiry. May I come in? Of course. Thank you. I'm Lieutenant Carlson, well, neighbor. This is my wife, Gerda. Well, this is just, uh, uh, Callender. How do you do? How do you do? You're, uh, a manager, aren't you? Uh, no, no, uh, a Canadian. Oh, good show, good show. The habit of being with us, though, boy. Well, not right now, thank you. Oh, all right. Well, what's all the fuss about, Mr. Callender? Well, it seems that there was a jewel robbery in Salasleben. The thief was apprehended at the station, but not before he'd managed to stow the loot somewhere. The authorities believed that he may have put it in someone's baggage with the view toward recovering it sometime during the journey. Oh, then you'll, uh, want to inspect our baggage, is that it? Oh, no, no, no, no, I have no authority to do that, but if you will, see for yourself so that I can report it to the conductors. I doubt very much whether to give me an eye to my police or Gerda's. They haven't been out of our fights since we arrived at the station. But, uh, you won't mind making the inspection. No, no, not at all, my dear fellow. But I'm afraid you'll be wasting your time. Oh, look here, do you have a drink, won't you? Uh, no, thanks, anyway. Well, we're on our honeymoon, you know. Oh, really? Yes, I've been trying to get Gerda to marry me for a long time now. It wasn't until yesterday that she finally made up her mind. Oh, yesterday? That's right. I finally wore down the resistance, didn't I Gerda? Yes, my dear, of course. They, uh, bagged, if you'll please, Lieutenant. Oh, yes, yes, forgive me. Only two, mine and Gerda's. I'll get them done. Shirts, socks, eyes. Why, Mr. Carimba, there's nothing here. Ah, good. Uh, now, Mrs. Crafters. I'll do it, Gerda. No, no, you may not open this. Then, if you will open it yourself. I can't. Why not, Gerda? Don't ask me why. I can't do it. That's all. You have to have a reason. Please, leave me alone. This is no time to be stubborn. You will come to construct the law. I don't care about the law. My valise will not be opened. Yes, it will. I will not open it. Then I will. He snapped open the catchers of Gerda's valise. And then he saw it. A picture of a rosy cheek boy in a Luftwaffe uniform. Proud, arrogant, with a super-race. Lieutenant turned away.  I sat there for a moment. It isn't very pleasant to see a man's world disintegrated by a photograph. What happened? They're not the ones. Oh, no, what? I don't know. I do. I'm jumping off the train. What? Why? They're after me, not you. If I'm off, the train is safe.  How do you propose to let him know you've jumped when we can't even locate him? I can't even die nobly, can I? Wait here for me, Ernst. There you go. I define deep. Mr. Calendar, I was on my way to see you now. We need more time. The engineer must give us more time. But he won't. Well, he'll have to. Can the fireman run the train? Yes, but it's incomplete. Excuse me. What do you want? The cabin is closed. When will we get out of the train? Well, it's closed now. Have we waited long enough? Yes. Not more than an hour. Oh, my God. One moment. Mr. Calendar, the little woman at the end of the train has been locked towards the woman's house since we left the train. But, Dietrich, that's where it is. That's the only place that could be. We've looked everywhere else. Yes. Get rid of the woman. Go on, I'll get rid of her. She's here to watch you, madame. Oh, madame. For what? Let's see, madame. She will play. Let's see. Shall we force the door? No. He'll set the thing off before we crack it. But are you sure he's in there? I'm not sure he isn't in there. How will you find out? Well, I'm going to climb to the top of the car. Move down to the laboratory. Smash the window and shoot. And I hope I hit him and not the bomb. But if it is not he, then, he will have killed an innocent man. And if it is, and I don't shoot over a hundred innocent people, we'll be dead in five minutes. I don't know if I should permit it. After all, I'm the chief conductor. We've got five minutes, Dietrich. Don't try to stop me. The responsibility is yours. I will do what I can to help. All right. Now get on. Tell him what I'm going to do. Tell him as soon as he hears the shots to have you open the door. He'll disarm the bomb. Now is that clear? Yes, Mr. Collins. All right, then hurry. We only have four minutes. As we land on the corridor, I turned and went to the door leading to the outside of the train. And there I took off my shoes and checked if this the learns had given me. At any moment I expected the train to start slowing down, which I knew must be followed by the blast. Until I got to the roof of the car, I didn't quite know how I was going to reach down and break the glass. But when I got there, I saw that this time the brakes had come my way. This was an old relic that had the light standard for each end of the car. Carefully, so as not to betray any movement to the man beneath me, I hooked one leg around the standard and let myself ease down. But I hung there for a second. I thought the man inside was the man I saw. This is my last chance to have to be. Then suddenly there was a shift of wind and I was almost blinded to the cinders pouring out of the entrance. I saw an imperceptible shadow go through the train as the brakes were applied. The time was now. I raised my gun and... Hello, Dietrich. Everything cleaned up. Yes, Mr. Kaleme. The passengers are still a little excited. No doubt. You shoot very straight, Mr. Kaleme. The body will be turned over to the authority to hand over. I'll adjust a minute, Dietrich. I'll be right back. Uh, pardon me, Adam. Oui? The door is open now. Je comprends pas. Oh, forgive me. La porte est ouvert. Oh, enfin. Merci. You're quite welcome, I assure you. Would you like to win a brand new 1954 high-style Plymouth convertible? Well, and be sure to enter the big Plymouth contest that starts this Thursday. $25,000 in prizes, including six new 54 Plymouths and hundreds of cash prizes. Your Plymouth dealer can give you an entry blank next Thursday. You'll see it contains a complete list of the prizes and the easy rules. But don't put it off because the contest closes midnight, Monday, October 19th. So how about a big red circle on the calendar around this coming Thursday? That's the day to see the new 54 Plymouths and enter the big contest. Is it a date? The special music for Escape was composed and conducted by Rex Corey. This is Roy Rowan speaking. Escape Transcribe was brought to you by Plymouth, along with a reminder that you visit your Plymouth dealer on Thursday, enter the $25,000 contest, and see the big, bright, beautiful new 54 Plymouth Thursday. This is the CBS Radio Network.