 Okay, so we'll continue the program, and now it's my pleasure to announce Pablo Lamata, who is working in cardiac modeling and image analysis, image processing, integrating all these things for many, many, many years, and who's currently working at King's College. So Pablo, please. Thank you, Brad. First words, of course, acknowledge and thanks to the people making this summer school possible and for inviting me to talk. And I'm coming from London. We sit in a hospital as a department of biomedical engineering, and that gives us some interesting opportunities to get a good understanding of the problems that we are facing. So the top I'm gonna give today is quite less technical compared to the previous one, but I'm gonna be using those technologies of numerical methods and computational simulations and what we're gonna try, and what I'm gonna try is to focus on a specific problem. It's a problem on how to identify when a cardiac valve is faulty or it's not working well, and that decision process of when is the best time to make a surgical intervention. So this is now overview of what I'm gonna be covering, the introduction of a general motivation of what is the value of mechanistic models. We have Christi yesterday talking also about mechanistic versus statistical or machine learning methods, and I will make a couple of claims of what mechanistic models brings as an additional value when we use them, and then I will go into the clinical motivation and how we can make this model-based data interpretation finishing on our current story of how we are making a clinical translation of these techniques. So these mechanistic models, what do I mean by mechanistic model is our representation in the computer of our understanding of the physics or of the physiology of how the heart works, how the pipe works in case of an artery. And the idea is that currently we do have a wealth of clinical data. Images are probably the most visual and appealing part of it that tells us about the clinical status of the patient, and that is the information of this guidance therapy. And in general, the models are a step in this loop between the data and the decision that is gonna help to provide additional information or a twist of the gear to get more accurate information or an additional piece of information by relating to in-connect bits of data. The compromise here is between data and models. Data is always gonna be observational and is gonna be based in specific of course, and we're gonna have objective metrics. And models are our understanding of the knowledge of the anatomy of the physiology of the physics, and they can also be used to make predictions as we had in the previous talk. But we also need to be aware of the limitations of these two big items. The data is always gonna be biased, it's gonna be always noisy in a bit or in a large amount, and it's gonna also face issues of reproducibility. Things that from the mechanistic models, we don't really, we don't always remember. We take the data and we take that from granted. But clinicians are very used to realize that that very robust metric of an ejection fraction that we have heard through the summer school can have a variation of a 5% to 10%, and it's not a big deal at all. And that's a big difference in terms of talking about the models. And when we talk about models, we think that we might be inclined to think that this is the absolute truth, but it's an absolute truth given a set of assumptions. And also we need to understand that when we make these models, there are bits of the modeling that we are quite sure that represent the reality of these patients, but there are gonna be always parameters or boundary conditions that we're not gonna be able to really control, and we need to test what is the sensitivity of our conclusions given those missing bits of the big picture in terms of the modeling. So in general, all my research life is about finding the best compromise between the data and the models. And if there's a take home message in general of this value of computational modeling is that they allow us to do two things. And I'm gonna draw the analogy of weather forecast. In weather forecast, you can more or less now understand that it's really easy to interpret why we have rains because there was high pressures here, low pressures there. And we can explain really well why this tsunami happened, blah, blah, blah. So that's the explanatory value of the model. And also we can use then the models to draw what is gonna be the prediction. So my kind of motivation as researcher is to focus much more on the first stage of providing the explanatory values between that data and that model to improve the clinical decisions and not to claim that we are able so eagerly that it's really attractive, but not to rush too much into prove the value of the predictive aspect of the models. General introduction finished and now I'm gonna focus on one specific clinical problem that is the estimation of what the pressure drop is through, for example, an aortic valve. Healthy and aortic stenosed valve and basically it's a gate that opens and close and if it's really well, if it's working well, it's gonna open widely. There's gonna be a lot of space for the blood to flow and there's not gonna be any problem. But if the valve is calcified or for other problems, the gates are not gonna open well. It's gonna be a narrow area to go through and that is gonna be an obstruction to the blood flow that is gonna translate into more forces needed to push the blood through the narrow gate and those forces can be assessed and are accepted as the biomarker to stratify what is the progression of the disease. So the focus here is the pressure drop before and after the valve. I will discuss a bit later where is before and where is after and what is the distinction between the peak and the net drop of pressure. But now also bring in a little bit of a wider motivation. This is a problem that is generally in other conditions. For example, when we have a co-actation and narrowing of the aorta, that's gonna be another construction to the flow, another source of this pressure drop that is gonna be diagnostic. That is gonna have a diagnostic value to take decisions there or in causes of chronic uneasiness or dissections. Now how do clinicians now measure the pressure drop? The most accurate method that is understood, that is accepted to be the ground truth is to use a catheterized pressure wire, go into the chamber in case of the valve and measure the pressure before the valve and after the valve and with that get the pressure drop. You can imagine that this is not so easy to do in everyday practice. It's gonna have some costs and it's gonna have some health risks for the patients. In the case of the hard valves, although that's considered to be the ground truth, it is not done anywhere almost because it has a 5% of risk of severe complications for those patients that already have that stenose valve. Sometimes could even be the death. So what is the 99% of the clinical practice today is to use a non-invasive imaging, Doppler ultrasound to capture velocity which is the physical, let's say, phenomenon of the blood and to use some basic physics to translate the information between velocity and the pressure drop. And the rest of the talk today is gonna be about this, about how to translate velocity into a pressure drop and trying to improve what is currently done in the clinic. In the clinic, there's gonna be a heavy simplification of the physics and it's gonna end up in a very simple formula. A formula that is four times that peak velocity squared that's driven through our newly principle and you can easily assess that oriented new probe into the jet of blood flow through the construction and capturing those events of peak velocity limitations. As always in imaging acquisition is inter-observerability, inter-observerability and in this case, you also need to pretty well align your probe in the direction of the jet and that sometimes is not so obvious because you're gonna do it. Then the line physical principles that enable us to acquire this non-invasive pressure drop measurement is the Doppler effect as we always experience the change of the pitch of the ambulance going forward and going towards you or going away from you and that is the principle used by the ultrasound waves to capture the velocity and the other one that I already mentioned is the Bernoulli's principle that I can quickly explain intuitively into what is the force that you need to go from a wide pipe where you have a slow flow and transit into a much smaller pipe where you have a much smaller area and if you want to get the same net flow you need to spatially accelerate your liquid in order to get the same net flow through a much smaller area. So it is like the push you need to make to your liquid to go from a low velocity profile to a high velocity profile due to a smaller cross section. So that is what is accounted for in current clinical practice. I also want to drive to briefly touch on basic concepts regarding pressure, blood pressure because we always understand that, well, I would say that a very nice analogy of pressure in a fluid is the concept of height in a river. So if we have a mountain and we have a valley, the blood is going to be accelerated from the mountain towards the valley. But the point is that we need to understand that, well, and with that analogy, the heart is going to be the elevator that is going to increase the pressure, is going to take the blood particles into the mountain so that they can go down the valley. But we need to understand that the heart flow is pulsatile. And in the central circulatory system, we're going to go through those cycles of positive and negative pressure and that's going to translate, and this is not so intuitive, that sometimes the pressure down the aorta is going to be higher than in the heart. And I will come back to that afterwards. But just keep the picture of that transition of between the mountain of the valley and that we have some pulsatile behavior. So the other key concept is that when we talk about the pressure drop is not the absolute value of pressure. We're not going to be talking about those 100 or 120 meters of mercury of absolute pressure. We're going to be talking about the pressure of difference between two anatomical points and sometimes they're going to be between the ascending aorta and the ascending aorta or sometimes they're going to also be within the ventricle and just after the valve. And some of you might be familiar more with the pressure transients in time. So this is a very, this assuming in the area of interest related to this image and if we have the ventricular pressure, the elevator going up and down, that's the blue transient here and the pressure wave is going to hit better earlier in the ascending aorta than in the ascending and that's going to be the light blue curve. The green curve is going to be at the ascending aorta is going to be a bit later and a bit augmented and what we're going to be measuring here is the red difference between the light blue and the light green is the pressure difference between these two points. You can already see here sometimes the pressure green is going to be higher than the again and the ascending compared to the ascending. I will get back to that point later again. And the other key concept to remember and it's something we have really touched in the previous presentation and it's basically Newton's laws applied to physics. What do we account for when we want to translate the information from velocity to a pressure drop and we account for three main physical aspects. One is the temporal acceleration. So when we temporarily accelerate the blood as a pump we are pushing and pulling. So we are pushing to accelerate and pulling to the accelerate. But at the same time we also have that component of the effective force that I was describing before as the Bernoulli principle. So the Bernoulli principle is a very, is a simplification of the 3D objective into a 1D scenario and accounting for those changes of the velocity, the momentum of the velocity as it travels through the pipe. And finally, and that relates to the spatial acceleration of blood. And then finally we have a component of viscosity as a component of friction, a component of inefficiency of the flow of dissipation of heat. And that those are the three main terms that in the easiest or the simplest form of the Navier-Stokes equation talking about an Newtonian flow without turbulence is what is the physics that I'm gonna be discussing today about how to improve the estimation of the pressure drop. Right, so another important clarification is that I'm not gonna be talking about capturing the anatomy of the patient and then computing all the physical variables. I'm gonna be talking about capturing velocity of the blood and then computing pressure. So it's not gonna be a pure CFD simulation where we have the boundary conditions and gonna simulate the reality. It's an observation of the flow and translating the information between velocity and pressure. So it's a model-based data interpretation of the velocity. And it's, as I said before, more specific now is a synergy between capturing the right imaging that is gonna give us the optimal spatial temporal resolution for the problem of computing the pressure drop and the modeling. What is the set of our physical assumptions that I can really take here to answer this specific question of computing the pressure drop? And so summary, the problem obtained a pressure drop, the state of the art is either through catheters or through Bernoulli's principle using Doppler to capture the peak event of the peak velocity. And the hypothesis here is that we're gonna introduce a bit more of imaging, we're gonna introduce a bit more of modeling and we're gonna get more information, more accurate information of the pressure drop and some more information. So we're gonna even eventually produce comprehensive spatial temporal maps of the pressure drop in the pipes. And I will discuss later what the potential value of that is. And trying to provide an overview of what we're talking about here. On one end of the spectrum of the methodologies we can talk about as the current megal practice capturing the peak velocity event and applying Bernoulli's principle. At the other end of the spectrum is what I'm gonna be discussing the first line during the talk is to get to a quite intensive imaging modality that captures a very rich spatial temporal resolution of velocity and is using for the float that was discussed a couple of days ago in the summer school and in between there will be other formulations. So one is simplifying all the physics into just a convective force in a single streamline. The other is accounting for the complete 3D physics for the Navier-Stokes equations. And also you can even go into a fourth channel here relying much less in data and relying only on anatomy and relying on forward simulations. But a little bit, what I wanted to provide is the picture that there's a continuum between availability of data and mathematical assumptions. And they go hand by hand. And probably doesn't need to go into many details here. The modality I'm even discussing for the rest of the talk is face-contrast samurai that making four acquisitions, a reference and three velocity encoded corresponding to X, Y and Z directions we can estimate in, we can capture in about 15 minutes in with current protocols the spatial temporal resolution and distribution of how the blood is flowing through our central system. Resolutions are about two millimeters isotropic in the best case. So keep that figure in mind. And in general what's gonna happen is that from the face-contrast samurai we're gonna go into these pressure indexes. Many times it's gonna be the pressure drop but as I will discuss there could be many other things. And we're gonna go through pre-processing some solver that is gonna transform, convert the velocity into pressure and some post-processing in order to offer those pressure biomarkers that are gonna be of clinical interest. So that's a general overview. And what I'm gonna discuss is two strategies to transform the formation of velocity into pressure with strengths and weaknesses. One is using a finite element method another is using an integral formulation working with work and energies. So these are the dry boring slices on just basically saying that to do starting from the Navier-Stokes equation in the complete form we can go through several steps in this frame or these integral formulations and to get into a tractable problem with strengths and weaknesses as I will discuss. So starting from the full Navier-Stokes rearranging basically we have all the information of velocity into the right-hand side and basically we need to solve a problem of I have the gradient of the pressure field and I want to reconstruct the complete pressure field. So taking the divergence and into the weak formulation this problem can be reformulated into a finite element solution. And by the time we publish this the methods that were on the table were iterative methods. But basically what they do is that they get the gradient field and they try to build the scalar field through iterative processes. So details are in this publication that I want to talk about them but at this stage that we brought to the table is that for those iterative methods you needed to define what the wonder if the problem was in a regular grid we are over-coining those difficulties by masking what are the valid finite elements to make the computation and we were able to include the viscous effects that so far were neglected. With this solution we went into the data we had at hand and we proposed a new way of looking at the pressure field at the pressure data and as I said this is a big jump for the clinician who is kind of used to think on a pressure drop and here the change of gears is that we want to go into the special temporal description of how the pressure field happens within our time in this case. And the beauty here is that we can start thinking not in just the pressure drop we can start thinking in those three physical processes these three physical forces that drive the blood flow independently because they're gonna tell us some complementary aspects of what are those forces independent aspects of the pump action or how the blood is being transmitted through that pipe. I will come to that in the next slides. First a methodological slide here what we get is the 40 flow sequence so it's a 3D plus time sequence we assemble as I described before the finite element method and we solve for the total and only accounting in the right hand side for the additive terms of the only the temporal acceleration only the spatial acceleration and only the viscous dissipation. So we have the total pressure drop the composing three components and the transient is gonna tell us something about the temporal acceleration and so it's gonna tell us something about the inotropic state of the heart how hard the heart is pushing and how synchronous of the synchronous it is to provide to produce a smooth transition between acceleration of the acceleration or how early or how late acceleration is happening. Convective is gonna tell us about the tortuosity whether there are constrictions or not and whether it's tapering or not changes in that diameter or changing in the tortuosity and viscous the viscous component is gonna tell us about the inefficiency of the system and as you can start thinking those are correlated aspects but not they are telling us independent aspects of the physiology of the pipe. So for this analysis we did we divided the order in six anatomical regions that as described here the signs of a salva where in between the valve and the end of the signals they are standing in the first part and second part separated by where the pulmonary artery crosses here the arc they're standing out the one and two and three with respect to the point of the end of the signs of a salva. And an overview of how it looks like things look like so blood is accelerated and accelerated so the transient effect the temporal acceleration is gonna have a big positive gradient and then it's gonna have a negative gradient and this is the picture of how the pressure is greater here with respect to the ascending order. The convective forces are gonna account for the fact that we're going from the ventricle into a narrow valve and then we'll cover a bit and when we drop some of momentum due to the blood going out and the curvature of the arc and the viscous is gonna be dissipation due to friction. I'm gonna enter into those components a bit deeper but I'm gonna offer you a more compact illustration of what those pressure maps are. So I'm gonna go from the aorta in this axis in zero down into the descending aorta and these two thick lines are the ones that go from the, let me remember here. So those are the between planes three and six so those thick lines are gonna be the middle of the ascending understanding, all right? So this is how the anatomy is divided in the vertical axis and this we have time. So the total pressure drop is gonna be the addition of the transient, the convective and the viscous effect each with its own color code. And as you can see in a healthy aorta this example, most of the total pressure drop is driven just by the acceleration and the acceleration. Acceleration is, systole will go from zero to 400 in this case and systole will go through the rest of the cycle. So there are hardly any pressure drops in diastole and you can see that the timing of these events are different in early systole. There's the maximum positive difference of pressure. Then we have the maximum negative pressure difference in a second part of systole when the block flow is decelerating and in contrast the convective and viscous events are picking in between those two events are picking when the block flow velocity is maximum. So coming into a more intuitive part of picture I'm gonna be comparing what happens in the ascending aorta and the descending aorta at the beginning of the cycle we have a positive gradient that is accelerating the blood in time but in the second part of the cycle we have a negative gradient that is decelerating the block flow. So if we go into a plot where we have the pressure difference versus the distance in at the beginning of systole we have a strong acceleration at peak velocity when the blood is at the maximum velocity there's hardly any acceleration and then at peak deceleration there's a peak negative gradient and where you have here is the error bars of nine health subjects. And this translates linking to what we show in the temporal transients of pressure wire recording we have time here and pressure amplitude here the blue corresponds to the positive pressure drop at the LFA of systole the green corresponds to the crossing between the pressure transient at the ascending understanding and the red transient corresponds to the temporal deceleration. And if we compare that we did in this patient so the healthy profiles to nine individual patients with nine aortic conditions one is a bicospic aortic valve that is going to have a narrow aortic opening another one that had an aortic dissection and was repaired so it had a stand on and a Marfan syndrome that they usually have a more tortuous anatomy if we go and compare the transient component of the pressure drop we saw that in general these three disease subjects they had a weaker pump action they had in general throughout all the regions a smaller pressure gradient and that can be also a reflection of a stiffer wall so if you link how familiar you are with the pressure waves traveling if those pressure waves travel really fast it means that the difference between point A and point B is going to be smaller so it's going to be a smaller pressure drop between in corresponding to the transient effect in terms of the convective effects I already touched on them before but this is one of the example of the healthy subject if we start from this point of zero at the point of the valve we're going to see a drop of pressure from more redder to a more yellowish pressures here and after that we're going to see a little bit of a recovery so in this early phase from zero to that point we see a bit of a recovery of pressure that is the opposite of what I described before of the Bernoulli principle you have a white pipe into a narrow pipe and now we're going to get back into a wider pipe so we see that the pressure is recovered a little bit in the early extending we then see a drop between that point and that point due to some momentum loss due to the bifurcations and the curvature and then we have a small net effect of maybe some tappering so the pipe was a bit wider here and a bit narrower here and probably some small, what do you call it? the small arteries going on the side of the descending heart when we compared that healthy profile to the three selected disease cases we ended up identifying salient features of related to the anatomy related to the fact that the pipe is not a smooth pipe it's sometimes a tortuous pipe so this was a dilated ascending order of the bicospecographic valve probably because the jet was hitting in this part of the wall and was causing that remodeling and that translated in a quite distinct very high pressure drop at the sinus of basalva which is the drop that is used to characterize the narrowing in the clinical valve in the clinical practice I mean we also were able to identify a drop under recovery through the vortex and we also were able to characterize this pseudo-coarctation so it's a kink at the end of the aorta and we were able to give a number of the severity of that kink in the case of the aortic dissection that had the stent and you need to believe me that the stent was starting that point again we were able to identify the point of the entry of the graft and to characterize what was the dysfunction of that graft so basically there was still a bit of a dilated part of the aorta and a narrow part of the graft and that was characterized by that pressure drop and in case of the Marathon syndrome velocities were weaker we already saw that the pump action of this patient was smaller but we also identify again and characterize the impact of the vortex by that pressure drop and recovery so this convective effect if we are able to produce this spatial temporal maps of pressure it's going to be able to help us to quantify the impact of this narrow end this vortices and this tortuosity of the flow basically and finally the component of the viscous effect is a component of inefficiency is friction and under the assumptions that we are throwing in here which is a laminar friction only this friction is going to be higher as we have higher velocities so it's going to pick a peak velocity and that peak at the green but we also saw that in the healthy subject peak escalation was already picking that and the other thing that we can see is that now the error bars are much wider so it's much nicer compared to the others and here's where we got a bit of distract we saw that we were expecting that this is conditions are going to be more inefficient but we saw that the healthy guys were more inefficient or were wasting more energy into friction the explanation is that the healthy guys had a more vigorous hard reaction and that was the main factor that was captured by this viscous component but we need to be aware that the assumptions we're throwing here are not really accounting for this phenomenon so it has been quantified that with the spatial temporal resolution of very face contrast samurai we can estimate like a 10 or 15% of the real attenuation that is going on through laminar assumptions by no means we are counting for two grand effects so we need to be aware of what we are actually measuring and what are we not capturing let me check the timing so I'm gonna jump now after going into one specific kind of solver that is the fem solver that allows us to provide all this rich description of the spatial temporal maps I'm gonna go into another solver that is gonna help us to provide a much better accuracy and precision of the total drop sacrificing not knowing what is going on in between those two points that I want to focus on and that's an integral way of solving the Navier-Stokes equation so again, the picture is that I have gradient of pressure equals a right hand side so what do I do to make the pressure difference between IMB if you take that initial Navier-Stokes equation you multiply by the velocity field and you make an integral of that initial equation you end up with a balance of work and energy and that balance of work of energy is that the delta P between two points is the addition of three energies the rate of change of kinetic energy the abective energy and the viscous energy divided by the net flow so what we're doing computationally is that from the MRI image after segmentation we're gonna define points inlet and outlet and we're gonna make an integral of how much kinetic energy in frame I is we're gonna compute how much kinetic energy is in the next frame and we're gonna make the difference as a finite difference and we are gonna estimate then the rate of change of the kinetic energy we then gonna compute how much abective energy is entering and leaving the domain and we're gonna integrate how much viscous energy is dissipated the key pros here is that instead of needing to make a meshing step and solving an expensive FEM step this is easily solved in a couple of seconds there is no need of that computational mesh and one important detail that is a bit subtle is that when you define that computational domain you need to have enough data points to build a valid element and when we were doing this FEM computation there was a big controversy of you have a regular grid, a square grid but your domain is gonna be curved so to define valid computational elements you were sacrificing quite a bit of data to define that kind of coarse grid compared to the data grid so if we were starting by a two by two by two and isotropic resolution on MRI we were ending up in a six by six by six or an eight by eight valid computational element and we were losing quite a bit of data there so there were some tricks to account for that boundary of elements that have valid data and have void data but that was a bit of a challenge and all those challenges were overcome by this and we don't need, we only need to make some they might look a bit cumbersome here but they are really easy integrals it's basically adding boxes by boxes information and most importantly compared to the previous method is that instead of needing to compute second order spatial derivatives for the viscous components so the viscous friction is all about how quickly your blood goes in this streamline corresponding to the other one and how much they have friction against each other if you do it through this way you only need to make the first order spatial derivative instead of the second order and that brings also numerical advantages and precision so with that we were, we did propose this improve method and we verified through an in silico workbench a CFD simulation where we had the perfect pressure drop and the perfect velocity field that we polluted with different sources of noise we compared to the simplified the different formulations and to the FEM PPE that I described before and we verified that we got increased accuracy and increased robustness and specifically to that factor of how you segment your data so in the previous step as we all know segmenting domains can be sometimes a bit of a bit challenging and it was quite good to see that in this integral way we were much more robust to definition of the mesh as I said and we were more and the contribution of adding that extra box along the boundary or not to the total integral that you do through this formulation was much, much less important than missing the complete element of the FEM PPE with this methodology, with this toolkit we went again to evaluate how clicker decisions are made so we made, we went to evaluate, re-evaluate this assumption that has been taken for 30 years now and of using the Bernoulli principle to estimate a pressure drop and I'm gonna go through the series of assumptions that I've taken in this principle to be used but before, as I said at the beginning I'm gonna focus a bit more of what is the difference between the peak pressure drop and the net pressure drop so what we're facing is the problem of characterizing this functional cardiac valve we want to give a number that tells how wide and how narrow that valve is and how that affects the performance of the heart we're trying to characterize what is the additional burden that we're bringing to the heart to pump the blood through that valve so there's a demand of the body and it's not only the geometry but to meet that demand of the body you need a pressure drop to go through that gate and there are two ways of thinking about this problem one is, so I have a chamber here and I want to characterize what's the pressure drop between before the valve and the point of maximum construction the point of maximum impairment due to the valve that's one way of thinking of it and that's a peak drop and the other way of thinking of it is no, I want to know what the burden is accounting for that and accounting for how the block flow or the jet is evolving down the pipe and that's a net pressure drop catheters are only able to characterize the net drop you cannot place a catheter in the point of maximum construction it's not going to be stable you can never place it there the Bernoulli's principle and Doppler echocardiography is measuring only the peak pressure drop and only the convective component and with a series of simplifications going to discuss regardless of those very striking fundamental differences catheters only able to measure the net drop and not the instantaneous drop by that time average and Doppler being able to measure only the peak drop and only the convective and with a series of assumptions clinical guidelines recommend the use of them indistinctly and with the same dress holds and that's very striking and it's basically telling us that although it was telling me that there's a huge opportunity here to make a difference because they are measuring things that are completely different but there's a very, very, very small distinction to be made there has been a lot of controversy and at the end of the day clinical decisions are based on what it's able to do you are able to do and as I said at the beginning a catheter is going to be really expensive or much more expensive and much more risky so at the end you need to base your decisions on what is available and that's the Doppler but I want to set a bit of that controversy that as an engineer you detect when physical numbers are used to take legal decisions and it's quite important to be aware of them so jumping to the specific role I'm going to focus on the peak pressure drop that is the one assessed by the Doppler Bernoulli's approach and the conceptual picture is that I am somewhere in the off-road track within the ventricle and I want to jump into that point of maximum construction and I want to know what's the pressure drop between those two points and basically I have two ways of computing that computing that accounting for the complete physics using the work energy relative pressure principle that I have described you before that accounts for the complete nervous talks or do it as it can be done in the clinical practice in the best way, best alignment of your probe with no inter-observable ability that's a simplified Bernoulli I'm going to visit now the assumptions that are taken to go from this formulation and this amount of data into that formulation so we did this using real data of 32 subjects and the assumption was that instead of capturing phase contrast MRI and Doppler we were synthesizing the best Doppler data that I said is simply sampling the peak velocity event at the point of maximum construction and the first assumption that we visited was is among these three components kinetic, affective and viscous is affective really the one that rules and we can neglect the rest of them and the reality was that yes, we can neglect it so both in esthetic patients that it was in group two that had the average drop currently computed us in the simplified Bernoulli methodology and group one of controls both in the blue controls and in the red esthetic the kinetic was much smaller than the affective and the viscous was much smaller than the affective note here that there's a change of the scale one speak here, 40 speak here, 40, 40, 40 so that first assumption verified with real data is true when the blood goes from the ventricle to the point of maximum construction those forces that are especially accelerating the blood rules, they rule that you can neglect the physics of the temporal acceleration and the physics of the viscous dissipation now one of the beauties of the WERP approach is that when you want to compute this affective pressure drop at the end of the day, you want to compute how much linear momentum is entering the domain and how much linear momentum is leaving the domain and through the Gauss divergence theorem we can then simplify our data acquisition problem into only requiring assuming that we have no loss of linear momentum through the walls so that the walls are not that origin but the change of linear momentum in the direction perpendicular to the walls is nominal and that is easy to verify that is essentially all hypothesis then we can simplify the need of data through from needing the whole volume to only need how much linear momentum is entering at the inlet of the pipe and how much linear momentum is leaving at the outlet of the pipe and there's a mathematical proof but basically it's all about the point of that how much as I said, what was the situation in the wide pipe and what's the situation at the point of the narrow pipe and you just need to compare those two so the other hypothesis that the other assumption that is taken in clinical practice is that there's a pressure drop the pressure drop between the point of maximum construction and before the construction but the point of way before the construction where do you actually fix the point? Is it at the apex of the ventricle in the middle of the ventricle just two centimeters before the valve that's also easy to fix and it's not so easy to measure so in clinical practice basically they neglect they assume that there's an acceleration from zero to the point of maximum construction and I believe these are very sensible hypotheses but still we visited with the data and we verify that if you compare what is the objective pressure drop accounting for what's the velocity profile 2.3 millimeters we took in this study before the valve or before the point of maximum construction and assuming that velocity here was zero this is how those two pressure drops relate yes you're losing a little bit so the no loss will be the real light the black line so you're estimating something slightly bigger because instead of having a zero here instead of so you're dropping this part of the inlet momentum so you are the acceleration from here to here is always slightly bigger than the acceleration from here to there is a slightly smaller but you can assume that or it's an acceptable loss and that simplifies again a lot the clinical practice and it's a valid assumption so yes it's valid assumption to only rely on an objective drop and yes it's a valid assumption to neglect the proximal velocity but what about now that simplification of considering the complete velocity profile or only considering a peak event a single velocity value and that's where things started to go away crazy so basically clinical practice is driven by a single velocity value but that velocity value is not a good representation of the shape of the velocity profile at that point of maximum construction and that's introducing an uncontrolled factor of the accuracy of the pressure drop that we can account much better by capturing a bit more of information and taking the right formulation and in a nutshell what is going on is that this is an in silico easy verification that when you have a blunt velocity profile at that point of maximum construction also a velocity profile that is almost flat Bernoulli principles hold and it's basically telling you that that point of maximum velocity is common throughout the velocity profile and is a good approximation of how much momentum is going through the valve but when you see some velocity profile that for example here is parabolic the error that you incur is that you are doubling your pressure drop analytic so if you estimate the pressure drop through Bernoulli's principle on a parabolic velocity file you are doubling the real pressure drop that happens due to the convective effects and that's what we verify and basically these are two of the experimental data we have this is the velocity profile of one of the controls and this is the velocity profile of one of the stenotic patients not the stenotic, yes stenotic patients sorry and the difference is in shape so this is not a perfect parabolic this is not a perfect blunt profile but you can see that the error here is going to be much smaller than the error here and as the severity of your this increases the shape of the velocity profile is expected we have not really verified that but is expected to start changing more from the blunt profile so you have a variable source of information, of errors and basically the scatter of these lines here on the horizontal line is a metric that we have already of that variability due to the fact that you're not accounting for the velocity profile so in summer here a more accurate and pressure drop is possible the cost is that instead of just needing a single peak velocity we need more information at that point of the profile and the future that I'm working on now is to make this happen on echocardiography so I know that this information is available on magnet but that's a modality that's not widely available and how to best compute that spatial temporal resolution of the pressure drop is not so obvious from echocardiography and the claim is that all this detail, all this rich information that we can retrieve from phase contrast hemorrhoi is slowly going to convince the clinical community and they will accept that instead of measuring directly the pressure making an accurate enough measurement of velocity is gonna tell us the information of pressure we need and so this will replace catheters and be considered the ground truth for a pressure estimation and those are the main values the non-invasively compared to catheters the higher accuracy and reproducibility and the additional insights not all of those claims are proved yet and that's what I'm working on this is my advertising slide we were given the news of a European project funded we are looking for 15 PhD students to start next September, October, November I know that you're already on your PhD or on your postdoc but if you have and you know people that are eager to work in Spain, France, UK, Norway, et cetera we are looking for, recruit an excellent batch of students and these are gonna be students really well treated by European Commission and having an excellent training program that we have designed for them through this Mariek reaction and the last slide that is also really important is to acknowledge the people that I work with and in my case, as I said, I'm quite privileged to have really nice technological guides that help me to make this technological push but also key clinicians that help me to understand the clinical pool whatever needs that really need to happen and funding bodies and thanks for your attention thanks to you, of course thank you very much for this very interesting talk maybe your first question is like you start from an observation that in clinical practice they use the pressure drop over the valve in order to make clinical decisions and then you say like, okay let's find a better way to estimate this which is I think a very good way of doing some research but on the other hand it's also like the clinicians use this pressure drop because they used to it but maybe it's not clinically the most important because what's likely the case is that you don't care about what the valve looks like as long as your ventricle can cope with it so possibly rather than the spatial gradient of the pressure the combination of spatial temporal relations might be more interesting so do you think you can get more information out of there and should we also drive it from the engineering side and say like, look maybe this might also be interesting rather than trying to reproduce what clinicians are using at the moment Yeah, quite good point the decision is not only driven by what's that additional burden that the valve brings is also related to how well the ventricles able to cope with that additional burden and this is not the complete answer to or is not the only number needed to take the decision of the for example when to make an implant of a valve so it is the energy or the drive here is basically to improve that number and it's basically as we have been discussing yesterday specifically talking with the regulator to the FDA the best way to improve clinical practice and to have an approved protocol is to replace something with something better so from that perspective I know is I want to think that it's a simple approach but I know this is not the only one piece of the picture to take into account to take that clinical decision and accounting for how well the heart copes I'm not so sure whether that acute picture that instantaneous picture of how the heart pump is functioning is gonna give you that information and probably you need some longitudinal data and then accounting for some longitudinal data maybe on the remodeling of the heart how the heart is changing is that complementary picture or that complementary information Any other questions? Just wait for the microphone please I used to think that the golden standard for pressure drop is the catheterization but you say it's not right but clinician I think they only think that the best way to measure pressure drop is catheterization so have you ever tried to validate your model with this measurement? So the answer is not simple and the answer is related to that extinction between the peak and the net drop I was trying to be clear and there's also the distinction between the absolute and relative pressure and it's related to the abuse of some nomenclature that it always happens so for example the clinical guidance referred to a pressure gradient a gradient is a drop of pressure versus distance but the measurement is the drop is not the gradient so there are many confounding factors here but in the natural is what is the golden standard? Well sorry what is the ground truth here? And the ground truth they accept more is the physical reality of the wire but even the pressure wire has many limitations of stability and you need to fight with not only with the abuse I would say objective reality but you also need to fight with the accepted reality let's say so exposing these limitations we have published also how when you insert a measurement device in a narrow anatomy you're gonna distort your measurement you're gonna introduce artifacts there so I don't have an obvious answer but yes I have dealt with the obvious questions of how do you validate these numbers and when we are publishing this in circuit imaging we were asked about these details and basically bringing the evidence that no matter what the actual pressure drop is the evidence we are bringing on the table is that we have these experimental velocity profiles and with these experimental velocity profiles if you account with this formulation and you account better for the physics you get the bias so that was the evidence that was enough to convince that something's going on here now the additional evidence in real patients with aortic stenosis with a pressure wire is not gonna happen and if it happened it was not gonna answer the question because we were missing two physical different things one is the peak drop and the other one is the time integrated systolic peak drop and the other one is the time integrated net drop accounting for different physics we will never be able to prove this without pressure sensor in the real patient so that's why we're planning to do phantom barrier verification where we have the measurement system part of the actual let's say narrowing in a way that it's not changing the physics with and without the measurement but when you translate in a clinical field you I think it's one other thing you have to do because it's the measure the pressure drop with the catheterization then they say okay we're gonna intervene in this and that so I think it's one of the best that you can do be in mind that 99% is a Doppler effect catheters are gonna be used in very small locations catheters are gonna be used yes as a ground truth but the community is now widely accepting that they don't need to account for all these physical details and they can see heavily simplified into that and the claim here is that simplify a bit less account a bit better for the physics and you do get a better number so that claim is not so different from what they're doing now okay thank you very much I think we have to move on