 So we move on, so it's the second talk of this morning. So it's my pleasure to welcome Miguel Angel Martinez. So he's a food professor at the University of Saragossa. And he has a very long track record in modeling of soft tissues, including multi-physics composition effects and mechanobiological events. And so now he will explain us, so the transfer of this knowledge, so it's a problem of atherosclerosis and so using modeling in order to identify the most important features that contribute to the development of this disease. So thank you, Miguel Angel. Thank you, Guillermo, for this nice interaction. Well, the detail of this talk is, you can see in the slides, is a mechanobiology and mathematical modeling of atheromplac initiation and development. Logically, it's a work that has been developed by different people, and some parts of this talk correspond to some pieces of doctoral thesis, and I will present the people that has participated in this work at the end of the talk. So this is the outline I'm going to follow in the presentation. I will begin with a brief motivation about atherosclerosis. I will continue with the presentation of the modeling of atheromplac formation and development. Also, the tasks and objectives of this work I'm presenting here, the governing equation and some numerical example and some numerical results of these models. And I will finish the first part of the talk with some conclusions about this modeling of atheromplac initiation and progression. And the second part of the talk, I will present some possible further lines of research. Well, it is clear that atherosclerosis is one of the most fatal cardiovascular diseases. It has atherosclerosis, it's a disease with a high prevalence in the population, in the developed world, and it can be considered as a chronic disease with a relatively slow progression. But under some circumstances, what happens is it can be presented at Q events with can be, can have dramatic consequences. As the picture shows, atherosclerosis is the process in which plagues, consisting of deposit of cholesterol and other lipids, macrophages and calcium are built up in the arterial walls. And there are some primary effects that are basically the narrowing of the arteries that is known, usually known as stenosis, the heartening of the arteries, the loss of elasticity, and the reduction of back flow. However, the fatal vein occurs when the plaque ruptures and relays in its contents and causing the formation of blood clots, which travel around the cardiovascular system and can produce, for example, in the coronary arteries, can produce the heart attack or in the, or also strokes or ischemia, for example, in the arteries of the legs. Well, nowadays, there are important clinical problems relating with the detection of the vulnerability of atherosclerosis. Clinical staff has some difficulties in the diagnosis and this vulnerability of atherosclerosis. Because the available screening and diagnostic methods currently are insufficient to predict the event before it occurs. A second point, very important, from the clinical perspective, is the initiation and progression of the atherosclerosis and the causes that provoke this progression. So many efforts are being applied, but they are mainly focused on biomedical, biological, or genetic point of view. However, as we will see during this presentation, there are also important mechanical factors that have a direct influence in the progression on the atheroplague. Therefore, I consider that a multidisciplinary approach is necessary and the mixed research groups are necessary in order to bridge the gap between the medical and the engineering perspective of this problem. Well, as I said before, there are different time scales in the progression of the atherosclerosis. It should be considered as a cascade of different events that finally can provoke the plague rupture. So the atherosclerosis or atherogenesis is a very complex problem with a lot of cellular and molecular processes, including, for example, many growing factors, protein, signaling germs. So we are going to focus on the mechanical perspective of the progression of the atheroplague, and which are the main mechanical factors that provokes this progression. Observing the different processes of the atherone progression, there are two great families. The family of lipid accumulation, the process is related with lipid accumulation that is a slow process that appears during decades and are related with the increased fibrosis test. And the other family are the inflammation or inflammatory processes that are produced during years and are related with the increase in the extracellular matrix degradation and also with the decrease of the matrix synthesis. So the combination of these different processes can finally provoke the plague rupture. So one of the problems is the weakening of the fibrosis cap of the atheroplague. So if we observe this figure here, we can observe two different parts. This part here that is lipid accumulation that is in the inner part of the artery and this part here that is known as fibrosis cap that is composed mainly of extracellular matrix. What happens if the extracellular matrix weaken or lose its mechanical properties, what happened is that the probability of rupture increases. So it is well known that there are many factors that contribute to the black progression. Observing for example the biological factor, it is clear that there exists genetic factor, the LDL, low density lipoprotein concentration in the blood flow, diabetes or endocelial dysfunction. Another factors are environmental factors, for example the smoke and diet. But as I said before, we are going to focus on the biomechanical factors. It is clear that the mechanical factors seriously affect the progression of the atheroplague. Why? Because if we observe experimental evidences, we can observe that atherosclerotic place are located at predilection site, such as site branches, curved segment or bifurcation, which are known to disturb serial properties in the blood velocity flow. So the mechanical effect of the blood flow affects seriously the progression of the plaque. So several lines of research indicate that biomedical factors play an essential role in the progression of plagues. For example in the plague size and also in the plague composition. In the composition of the different parts of the atheroplague. Another important factor from a geometrical point of view are for example the bell cell curvature, also the bell cell compliance, pulsating blood flow or the heart motion. Well, between the all the biomechanical factors, they are one that is generally accepted that has an important effect in the initiation and progression of atheroplague. That is the friction that the blood flow is applied over the endothelium of the artery layer, of the arterial layer. So this friction fault is known as wall CR stress and seriously affect the permeability of the endothelium. It is proof, experimental proof that for very low wall CR stress, the permeability of the endothelium is increased. So there are some substances that are in the blood flow, for example the LDL, that pass through the endothelium towards the internal layers of the artery and appears at the position of lipid contents in the arterial part of the artery. So another important factor is the oscillatory CR effect of the blood flow over the endothelium. If the wall CR stress changes its direction or changes the sign of this wall CR stress, what is now the oscillatory CR index? So for high oscillatory CR index, the permeability of the endothelium is increased again. So these two factors, wall CR stress and the oscillatory effect of this wall CR stress seriously affect the progression of the disease, of the atheromplex. So there are special sites in which the flow is perturbed. So there are some points in which the wall CR stress decreases and the oscillatory CR stress increases. So these are known as atheropram sites. Well concerning the vulnerability of the plaque, well they are important factors that affect this vulnerability of the plaque. So the clinical stuff what's observed, what examines for consider if a plaque is vulnerable or not in many three parameters that are. The size of the lipid core we can observe here. The thickness of the fibrous gap, this is a extracellular matrix, so these three next and also the degree of stenosis of the artery. Based on these three characteristics they apply different techniques. For example, standing or balloon or applying a bypass surgery. So what happened is that there are many other parameters that can also affect the vulnerability of the atheromplex. For example, if we observe the geometrical parameters there are other parameters. For example, not only this thickness but also the length and the width of the plaque are for example, the stenosis ratio or the angle of this one. So another important parameter from a mechanical point of view is the residual stress that are inherent in the artery. More parameters where we made computational studies some years ago observing or trying to analyze the influence of the microcalcification. Microcalcification a small deposit of calcium that appears in the atheromplex. And there is a controversy between different authors. Some authors say that this microcalcification provoke an increase in the vulnerability risk of the plaque. So another authors say that, okay, this microcalcification has a very little or almost new effect on the vulnerability. What we obtained in this study was that it depends on two main parameters that was the stiffness of the microcalcification. So if we have various stiff microcalcification the risk is increased and also the location of the microcalcification. If this microcalcification is located in the shoulder of the atheromplex, the increase, the risk is also increased. So it depends on these two main factors. And another mechanical parameter that should be taken into account in order to examine the microcalcification, sorry, to examine the vulnerability of the plaque was the positive or remodeling of the atheromplex. This figure here show a positive remodeling is a growth of the plaque outwards and negative correspond to an inwards growth. Well, we compare both models of remodeling, conserving all the geometry, all the material parameters, all the variables except the positive or negative remodeling. And in all the cases we analyzed we observed that the vulnerability is increased for the case of positive remodeling. And this is an important case because this positive remodeling correspond to the initial stages of atherosclerosis and usually is asymptomatic. Well, let's return to the model of initiation of atheromplex. So from my point of view there are two great families for these models that are the continuum models are the agent-based models. I'm going to present some features of the different models. The continuum-based, sorry, continuum models are based on reaction, convection, diffusion equation. They consider the wall as a continuum. It's easy to model the transport phenomena of the different substances through the arterial wall. And also it is easy to couple with mechanics. These are the main advantages or features of this continuum model. But there are some important disadvantages that are they are phenomenological models, pure phenomenological models. They are deterministic. There is no statistical data in these models and it's difficult to validate with experimental data. And finally they present some numerical repulse. For example, numerical problems. For example, concerning the convection of the equation of the modeling of the volumetric growth. We are using finite element mesh and in the case of distortion of this finite element mesh we have numerical problem. On the contrary, the agent-based model are based on statistical rules. Consider the wall as a lattice, as a discrete lattice. So in each point of the space we can have a cell or a substance. So the different cells or substance interact each other. So they are based on cell population behavior. We can obtain probabilistic solution and usually they do not present numerical problems. The main drawbacks of this family of methods are that they are difficult to couple with mechanics. It's more difficult to model the transport phenomena and finally again they are difficult to validate with experimental data. This is a problem common to the two family of methods. Well, let's go with the first approach and the model I'm going to present here corresponds to the first approach. So the main objective of this presentation of this work is to present a numerical model based on reaction convection diffusion equation that includes the main processes, for example the blood flow dynamics and also the mass transfer of the different cells and substances in the inner part of the arterial wall in order to better, to main objectives that is to better understand the atherosclerosis growth process and a final and a far objective that is try to guide the future therapeutic strategies. So I'm going to present here the basics of this model after reading many literature on this topic and several meetings with biologists, physiologists and identify several species. We focus on the species I'm presented in this slide. We have five different type of cells. We have monocytes, macrophages. We have also foam cells and contractile and synthetic smoke muscle cells, five type of cells and four concentration of different substances that are LDL, oxidized LDL, cytokines and collion. So the process initiates, I put the video here. Okay, it goes on. The process initiate when the permeability of the endothelium is modified. So several substances or cell that are in the lumen basically the monocytes and LDL pass through the endothelium. When they pass the monocytes change to macrophages. Macrophages try to eat the LDL. So finally they die and for the big cell that is known as foam cells, the macrophages segregate different substances, mainly the cytokines. The cytokines is a signaling system that provokes the chains of the phenotype of contracted and smoke muscle cells that are in the outer part of the media. So they change the phenotype. They convert into synthetic smoke muscle cells. They proliferate to the inner part of the artery and finally synthetic smoke muscle cells segregate collion. So in this part here there is a concentration on three different substances. That are foam cell, lipid content on the plague, the synthetic smoke muscle cell and also different extracellular matrix that we are representing here with the collion. So there are different parts here and we have observed before that the plaque have separated parts. Well one of the problem we will see after of this model that we are not able to separate the different parts of the plaque. We have a continuum, concentration of the different substances. We have a continuum proportion of foam cell, smoke muscle cell or collion but no differentiation into the different part of the plaque. I will say. About the equations, the converting equation. It is clear we have a fluid dynamic. It is necessary to model the fluid dynamics of the problem. In this case we are going to consider a steady incompressible laminar and Newtonian blood flow. It's very simple from the fluid approximation. We use a standard Navier-Stokes and continue to equation. And after that it is necessary to model the path of the different substances from the blood flow towards the arterial walls. So what happened is that the endothelium changed the permeability. This permeability depends on mainly three different junction. It is known as three pore model. And this model, the permeability of, especially the leaky junction, the three pores are leaky junction, normal junction and vesicular pathway. Well, this junction here, the junction is very dependent on the wall shear stress level. So if the wall shear stress decrease or increase the oscillatory wall shear stress, what happened? That permeability increased. So if this permeability increased, the total transmolar volume flux increased. So there is increase in the flow from the blood flow towards the arterial layer to the intima or to the media. So an important part is also the Darcy's law. The Darcy's law, what give us is that give us the velocity of the plasma through the arterial layer. So the Darcy's law give the velocity and this velocity is proportional, is linearly proportional to the pressure drop. The pressure drop between the interior part of the vessel in the lumen and the exterior part that is the adventitia. Okay, the equations about solute dynamics. Well, we are going to consider two parts. The first step is a stationary step in which we are trying to achieve the permanent condition of the blood flow. So it is a standard Navier-Stoke equation and in the Navier-Stoke equation, we incorporate this equation with a diffusion and a convection term for two main substances that are in the blood flow that are LDL and monocyte. And we are going to consider two differing concentrations of LDL. We will consider the anormal concentration and a very high concentration to observe the differences of this parameter of the model. And the second part of the model, the second step is a transient part, is a time-dependent diffusion and convection equation along the arterial wall. So for example, for the case of LDL and monocyte, what happened is that this two, this substance and this cell pass through the endothelium and the pass depend on the transmural flow I presented in the previous slide. And this transmural flow depends highly on the wall shear stress. So this flow of LDL and monocyte depend directly on this variable. The equation of the difference substances for this case here in presenting the equation for LDL, oxidized LDL, cytokines and collagen. Well, the structure of the equation are very similar for all of them. We have a variation of the concentration, a variation with time. We have a diffusion term in blue. We have a convection term due to the velocity of the plasma, of the transmural plasma. We have two reaction terms. We can have production. We can have degradation. For example, for the case of LDL, we consider this temporal variation. We have diffusion, the convection. And in this case here, we have no production. We have only degradation. Why? Because the LDL is degradated to oxidized LDL. So this term is the same that this term here. We have a minus signum. We have here a positive contribution. So these are source term. These are sin term. Well, similar for the rest of the equation. For the equation for the different cell population. We have different parts, diffusion, convection, differentiation of the different cells. And we can have death or chemotaxid term. So there are similar equations for all the terms here. What about the parameters of these equations? Well, we have a total of 34 model parameters and there are different set of parameters. For example, there are some related with the blood diffusion. We have plasma diffusion coefficient. These parameters are very important. For example, the diffusion of the different substances through the arterial wall. Also different rates that affect the reaction terms. How these reaction terms vary or with time. Some geometrical parameters. Some threshold affecting the reaction terms. For example, the concentration of LDL has a upper threshold. And some other parameters related, for example, with material parameters or material features. For example, blood density, plasma density, collage intensity or intimate porosity. So one of the problem of this model is how we extract the different parameters. In this case, you can observe each parameter has its reference. What happens is that each parameter is obtained in different conditions. There are some parameters that have been gotten by in vitro studies, sonata in vivo studies, x vivo studies. From the in vivo study, there are some parameters from the human data or from experimental animals data. For example, mice or rabbit. So it is very difficult, it's almost impossible to get the parameters from the same source. So finally, this model, one of the problems or limitation of this model is the final validation because the parameters of the model has very different characteristics. Well, about the volume growth of the model. Well, it is necessary to consider an open system from the biological point of view is an open system because we have an incorporation of external energy. So this external energy which provokes is the growth of the biological system or the volume of the biological system. So it is possible to consider this volumetric growth observing the modification of the densities on the concentration and we can establish this growth with a string gradient tensor. So observing this tensor, we can pass to a velocity of the material points of the finite element mesh and this material points is dependent on each integration point and is modified in each time integration of the process. So in this case, we are going to consider that the volume change mainly due to three different contribution. The contribution of the form cell that we will consider as spherical, the smoke muscle cell, synthetic smoke muscle cell, we consider ellipsoid and the colline concentrations. So we took data from literature and they are the contribution to the volume growth. I present here the finite element mesh. You can observe that we consider an axis symmetrical, an axis of axis symmetry. So we can model as a two-dimensional problem. We have the inlet in the left part of the model and we have the outlet in the right part. This part here is an artificial stenosis. The objective of this stenosis is to provoke an artificial change in the world's air stress. So what we will observe, very low wall shear stress is caused in this part here. So you can observe the mesh. It's important to have a very fine mesh in order to compute very accurately the wall shear stress and also to compute the flux between the blood flow and the arterial wall. So we are going to consider three different scenarios. The first scenario is 10 years of height cholesterol. The second one, 10 years of normal cholesterol level. At the third scenario is a combination of both. Five years of height and five years of normal cholesterol level. So some results, observing the hemodynamical parameters of the model, the hemodynamical result, you can observe here that the stenosis causes an acceleration of the flow that is typical and a recirculation area. This recirculation zone, what at the end of this recirculation zone, which provokes is an increase, sorry, a decrease of the wall shear stress level. Observing the pressure, we observe a pressure drop just in the stenosis of the model. And what is more important is the wall shear stress. We, in this case, we have a stationary case, but we have a modification of the wall shear stress level. The normal wall shear stress level is about 1, 1.2 Pascal, in this case here, which is provoked here is just in this stenosis area. A cute increase of the wall shear stress, more than 10 Pascal appears, and about 10 centimeters downstream this stenosis, a cute decrease of the wall shear stenosis appears. And almost zero. So this area here, or this area here, is an athero-prone area. It is usually an area in which the athero-plague progresses. Well, observing the different concentration at the end of the time model that is 10 years for the third case. This case corresponds to five years high cholesterol and five years low cholesterol level. So we can observe the concentration for two different zones in the critical area. The first zone in red is very close to the endothelium, and the second in blue is in the inner part of the arterial wall. We can observe several conclusion, or we can obtain several conclusion. For example, the LDL in this point, it is observed that this important appears an important drop due to the change in the cholesterol level. So the cholesterol level in the blood flow pass directly to the cholesterol level, or the LDL concentration level in the artery. We can observe also that in the oxidized LDL, we have this drop also for five years, and we have an important initial increase in the oxidized LDL, and after that, tend to a stationary state. Also the monocyte, and what is important is also, for example, the concentration of a small muscle cell. What happened here is that the contractile small muscle cell that is the usual state of the cells is modified. So they change the phenotype and appear synthetic small muscle cells. So the contractile phenotype decreases, and the synthetic phenotype increases towards a maximum in this part here. Observing, for example, the concentration of the different substances and cells in the model, we can observe two different trends. For example, observing LDL and monocyte, we can observe that LDL and monocyte are concentrated in the inner part of the arterial wall, in the part that we have interface with the endothelium. What happened is that LDL is immediately oxidized, so chains to this one, so it's oxidized and the oxidized LDL appears in all the thickness of the artery, similar to the monocyte. And we can observe different diffusion of the distinct parameters or concentration, for example, for the small muscle cell, or for example, for the cytokines. The shape, the final shape of the artery will depend mainly on two effects, on the convection or on the diffusion of the different terms. If we have a hiker convection, we have a distribution in the radial direction. If the diffusion terms are predominant, we have dispersion in the longitudinal direction of the artery. I present here a qualitative modeling of the growing. I said before that it's very difficult to establish an experimental validation, but the levels of the growth are similar to the levels we can get in the literature. We can observe the different growth for the three scenarios, and it is important also to observe, but even for normal cholesterol level, the changes in the world's interest causes the apparition of a small atheroplake. One of the possibilities of this kind of model is to establish, to analyze, which is the importance of the different parameters that appear in the model. For example, what happened with the diffusion parameters? Well, we can analyze the influence of this diffusion parameter in the final results of the model. And these parameters are important because, for example, it depends on the microstructure of the tissue. So if you know how the arterial tissue is structured, it appears a lamina of a lasten that is oriented in a circumferential direction. So the diffusion of the different substances in the artery is easier in the longitudinal direction than in the radial direction because in the radial direction, you have to pass through the different lamellas. You have to pass through the different lasten lamina. So it is important to observe the differences between the diffusion coefficients. The results I have presented before correspond to an isotropic diffusion model, the same diffusion parameter for the radial and longitudinal direction. So the parameter gamma is the radian between the logint to the radial and diffusion coefficient. I think that it's more logical to establish, to fix a gamma parameter higher than one, for example, this case here, three, because it established that the facility of diffusion in the longitudinal direction is higher than in the radial direction. But we analyze different possibilities for the gamma parameter. It's a parametric study. And these are the results for this variation. If we compare, for example, the relative LDL concentration in the arterial wall, well, we can observe the 11 different models with different parameters and also compare some with experimental data. We can observe, okay, there is a good correlation between numerical and experimental results. And in this case, the influence of the diffusion is very low. The results are very similar. What happens with that? Well, we can observe here with the LDL. What happened is that the LDL trespass passed through the endotelium, but just after processing changed into oxidized LDL. So the diffusion of the LDL is very small. So the LDL concentration is not affected by the diffusion coefficients. But this coefficient seriously affect to the rest of the substances and cells of the model. For example, to the foam cell, mainly to the foam cell, but also to the vascular small cells or to the colline. It's important the effect of the foam cell that they highly depend on the diffusion. It's very dependent of this diffusion coefficient. And we can observe the differentiation between the high longitudinal diffusion, or in this case, more radial diffusion coefficient. Another important effect is the arterial pressure. So it seriously affect to the transmural plasma flow through the endothelium and through the arterial layer. This is the Darcy's equation. So we observe this is the plasma velocity that it depends on the pressure drop. Usually the pressure in the external layer of the artery in the adventitia is more or less constant. What changes is the pressure in the internal part of the artery, in the lumen. So if we change this internal pressure, what we are changing is the pressure drop increasing the velocity of the plasma and also affected to the convection terms. So if we increase the internal pressure, we have a more convection effect in the continuity equation of the different concentrations. So for example, for this case, we analyze three different possibilities, three different scenarios that are low diastolic arterial pressure, normal pressure, and hypertension conditions. So we can observe here the influence. In green, we have the normal pressure that are the base case. We have present before. And for the case of the low pressure, what happened is we have, the convection is less important than the diffusion. We have a shape of the atherotic atheroma plague more spread in the longitudinal direction. On the contrary, for the hypertension condition here, we have a predominant effect of the convection. So we have a shape of the atheroma plague much more acute as we can observe in this figure. So the diffusion coefficient and the internal pressure modify the influence of the two of the main aspect of the model, that is the diffusion and convection terms of the model. And similarly to the rest of the substances and cells of the model. So as main conclusions of this first part of the talk concerning the modeling of atheroma plague using continuum approach, a continuum equation, we can say that, well, a qualitative growth model is able to simulate from a global perspective the plague initiation and progression process. So this model should be considered as a preliminary step, as a first step to the understanding of the mechanical effects on these pathology projects. So it's important also to remark the limitation of this model. There are a lot of limitations. One is that it is necessary to include other biological processes. For example, the mechanotaxis. The mechanotaxis, we have only one term for mechanotaxis and it has a height important in the modeling of this disease. And also another limitation is that you can observe that we have a continuing distribution of the different cell population and substances. When in a real plaque, we have different parts. So this model are not able, these kind of models are not able to separate the different parts of the layer. If we want to separate the different parts of the atheron plaque, we have to use a agent-based model or a combination of both approaches. And another important limitation is the experimental validation. That is very difficult and it's not easy to validate these results. So another conclusion is the importance of the diffusion and convection coefficient and the importance of depending on the arterial pressure and on the diffusion coefficient. So how can we improve this kind of model focusing of a mechanical point of view from a mechanical perspective? Which aspect we can include in this model to improve the characteristic of this model from a mechanical point of view? There are several factors. For example, I am presenting here five different factors and I'll present after the influence of some of them. For example, the inclusion of mechanical stress is clear that the mechanical stress has also to affect the progression of atheron plaque. For example, the coupling between the mechanical and a modinamical effect. So the possibility of doing fluid structure interaction simulation. Or for example, also modeling the endothelial remodeling. So how the wall shear stress is modifying the morphology on the endothelial cell. This is another possible future line of research. And well, finally, how can we apply these techniques or this model to the clinical practice? How can we translate these techniques? Well, it should be necessary to apply this model to clinical image-based studies. So studies coming from patient-specific geometry and also one of the main problems of this model is a high computational cost. So another alternative is the use of some kind of machine learning techniques in order to apply this model to the clinical practice. So I'm going to very briefly present some of this point of continuation of this model. For example, the role of mechanical stresses in the artery in order to better simulate the atherosclerosis progression. Well, this is a study we did some years ago in collaboration with a French team lead by Professor Jacques Wayon of the university, Joseph Fourier of Grenoble. And the idea, the objective was to study the role of mechanical factors such as heart motion or the combination with internal pressure in the appearance of atheroplague in patient-specific coronary bifurcation. We took eight different patient-specific geometries of the coronary bifurcation. We've had the left anterior descendant coronary artery and also the circumflex. In this bifurcation here, we have to observe how the mechanical stress or mechanical stiffening can affect the appearance of atheroplague. Well, in order to include the motion of the heart, we took from this, we took patient-specific data. We have three types of data. For example, the radial expansion of the heart. We have also the twist, the twist angle of the heart. And very important also, the axial contraction of the heart. And this axial contraction is important. It's almost 14% in axial deformation, negative deformation. We took a hyper-elastic anisotropic model and parameters taken from the literature. We did finite element mesh, standard finite element meshes with exciteral elements. With the, it's a fiber tissue. It is necessary to include an estimation of the orientation of the fibers, mainly collagen fibers and small muscle cells. And also to apply the different parameters of the heart motion, that are the axial contraction, radial expansion and the twist angle. So we have different images in different parts of the cycle. So we are able to apply the different motion of the heart. And also, combine with the internal pressure in the artery. We can observe here the axial contraction of the artery and the vertical displacement is important. It's a real motion without magnification. Well, real is a finite element motion without magnification. Well, the parameter we took as comparison parameter was the luminal wall stiff net that is defined as a radio between the stress and stretch level in the different points of the solid meshes. So we can observe here some qualitative comparison between the higher stiffness in the wall and different zones of appearance of atheron plague in city images from each specific, passion specific geometry. So we can observe that there's this thank correlation between high stiffness and appearance of blacks. We can observe here also for passion number two and passion number five. And there is specific zones, a specific place with high wall stiffness and some correlation with these points here. It's important to observe that this correlation appears when we take into account the combined effect of the internal pressure and the heart motion. If we observe only the internal pressure, we have great areas of high stiffness and there is no correlation with the experimental evidences. Well, we did a statistical study trying to correlate the stiffness with the higher stiffness with the appearance of flakes. We observe here that for higher stiffness, we have a higher possibility of finding atheron flakes for the descending artery for the circumflex for the combination of this arteries. And also it can be established a relationship between two parameters that are the stiffness, the peak luminal stiffness and the luminal stretch. So these points, red points are the position on atheron places and the values of the stiffness and stretching. And we can observe that blacks appear always for higher stiffness, stiffness higher than 300 kilopascals and for stretching higher than 30%. So there is a correlation between some mechanical factor and the appearance of black. So this correlation appears in the spatial distribution. So it is important in order to identify the height rig zone for the appearance of atherosclerotic. And the idea is to try to incorporate these evidences into the continuum model for the growth of atheron plague. So a combination of a modemical factor plus some kind of solid factor, for example, luminal wall stiffness, I consider it could better represent the mechanical stimulus that promotes the initiation and progression of blacks. How can we combine both this effect? The first alternative, the first approach could be using fluid structure interaction analysis. What happen if we do this analysis, combination between fluid and solid in the same analysis? Well, in this case here, well, this is another study we did. And the objective was not to identify height rig zone for the appearance of black, but try to identify risk of vulnerability plagues, of vulnerable plagues, to start the vulnerability of different plagues. So we did a parametric model with different geometrical parameters. In this case here, we have four different parameters. For example, the cap thickness, this parameter here, the stenosis radio, the lipid core length in this direction and the lipid core width in this direction. The size of the lipid core. We establish a base case, this case here, and we modify each parameter in an individual way. So we modify, for example, the fever scap thickness, we modify in different four variation. So at the end, we have one base case, four times four, we have 16 variation of the base case, a total of 16 models. Well, the boundary condition for the freeze-solid interaction is, I know it, sorry, okay. The boundary condition, okay, it is well known that we have imposed time condition on the solid, in this case, restricting the displacement in the ends of the model, and also applying mixed velocity pressure boundary condition, our simple condition, but we apply a cardiac wave, both for the pressure and for the volume velocity. The pressure applied at the end of the model and the velocity applied at the inlet of the model. Analyzing the different variables of this combined model, for example, respecting, concerning the solid variables, we can observe that the maximum appears, well, each curve corresponds to each different model, geometrical model. The shape of the curves, I am representing here the maximal principal stress versus the time. So we can observe that the maximum appear always at the same time, and this time corresponds to the maximum pressure, and the shape is very similar to the shape of the pressure wave. So there is a direct correspondence between the pressure and the maximal principal stress. Well, even if we compare this fluid structure interaction analysis with a pure solid model, we can observe that in the central section, the results are more or less the same, are very, very similar. What happened in this case is that the presence of a pleic, fibrotic part of the plate, what happened is that this section is very, very stiff. So the inclusion of the internal pressure do not modify or don't modify the geometry of this part. So the displacements are negligible, so the results are the same. In this case, it could be better to apply only solid model, not fluid structure interaction. Analyzing the fluid variables, we can observe a typical case that corresponds to the high stenosis and acceleration, and here are some zones of disturbance of the flow. If we observe the wall shear stress, we can see here a higher wall shear stress in the stenosis zone, a lower wall shear stress in this part here. The lower wall shear stress affect or can affect to the pleic growth, and the wall shear stress, in this case here for higher stenosis, we have higher wall shear stress, higher than 40 Pascal. So this high wall shear stress can affect to the final possible rupture of the pleic, to the remodeling of the endosalial cells in this part here. Okay, we can observe here again the recirculation and very, very low wall shear stress zones here. So on this conclusion, if we try to combine the fluid analysis with the solid analysis in the same simulation, what happened for this model is that finally the solid results are similar to the solid analysis. So it is necessary to apply a combined analysis for this case. And for the case of the fluid analysis, it's more or less the same. It could be necessary to apply a pure fluid analysis. So in this case here for this plaque and to study the vulnerability of the plaque with separate analysis, solid or fluid analysis could be better and cheaper for an computational point of view. How to apply this to, for example, fashion-specific geometries? How it is possible to apply this model to the fashion-specific analysis or to realistic geometry? Well, the response is, the answer is just, what happened is that the computational cost is very high. So this is a first step in which we analyze not the whole model, studying the plaque growth, but only the modification on the permeability on the endothelium. I mean, we try to analyze how the modinamical and solid variables affect the endothelial cells morphology due to these factors. So we took in this case a coronary bifurcation. We applied the impedance method in order to extract velocity and pressure waveforms, waveforms. We can observe here the streamlines and we can observe that the solid is modified. So in this case, the fluid structure interaction analysis has a higher influence than in the previous case. And we can observe here different zones. We can observe here two different type of zone. For example, mark with two, with number two. We observe this zone here that corresponds to Heiger-Walscher stress. It corresponds to laminar flow, Heiger-Walscher stress, and the Walscher stress is always in the same direction. There is no changes in the direction of the Walscher stress. Well, these zones are known as athero-protective places and the endothelial cells, the morphology of the cell is more or less aligned with the direction of the flow. On the contrary, there are another zones mark, denote with one, this part here and this part here, when the sun recirculation, sun disturbance of the flow is presented. So in this case here, the Walscher stress is low, for example, in these zones here, and there is a change in the direction of the flow. So the oscillatory effect is higher. For example, this is the Walscher stress and the morphology on the endothelial cells is more rounded, aleatory, dispersed. So the permeability of this morphology and this morphology are very different. So how can we establish or modify or try to predict the morphology of the cells? Well, this possible, for example, in this case I'm presented considering that the cells are formed by different fibres. So we use, in this case, orientation density function to predict which is the orientation of the individual fibres in the cytoskeleton of the cell. So each fibrel can reorient, depending on the two main parameters, that is the average Walscher stress and also the oscillatory shear index. So it is possible to modify with these two parameters. We reorient the individual fibres. We have, at the end, the global shape of the endothelial cells and we can measure the shape with this parameter here, that is the shape index. So for example, for shape index close to one, we have a round shape of the cell and close to zero, we have a very aligned endothelial cells. These are experimental data that analyze study the influence on the Walscher stress level on the shape index. We can observe that for higher Walscher stress, the shape index is very lowest. The endothelial cell is aligned with the flow. This case corresponds to this part here. So we can also include not only the Walscher stress, but the effect of the oscillatory shear index and to try to establish which is the final shape of the endothelial cells. And we can apply this model to the passion-specific geometry. So we can analyze which is the oscillatory shear index, for example, in this realistic geometry and also the wall shear stress. So we can observe that the critical zones in this case are more or less the same. There is a controversy in which is the amodinamical parameter that better reproduce the growing of atheroplane. In this case, both parameters present similar results. We can apply this model of reorientation and finally obtain the global shape index in the different parts of the passion-specific geometry. We have this part here with these four that are atheroplane places. And in this part here, here, or here, we have this shape of the endothelial set that are known as atheroprotective shapes. So, well, I'm going to, I think it's more or less the hour. So I pass through this last application that is an interaction of how to apply machine learning techniques, but I pass through there and I go to the final acknowledgement. OK. So, well, these are the results, the main conclusion. But, well, I would like to thank to the people that have contributed to this work, and there are many persons that have participated. And I would like to thank to Miriam Celia, Stephanie Apeña, Mauro Malve, Alberto Garcia, and Paulo Zad. And also to the financial support of this research. And thank you all of you for your kind attention. OK. Thank you very much, Miel Angel. So, questions? Thank you very much for this very nice presentation. A simple question. In your own expert opinion, how about validation? I think if someone works in such an area, what should he or she do to validate theoretical models? You are referring to the first model or to the models I presented at the end of the presentation? I'm referring for the first model for the stenosis of the arteries due to macrophages or any other. It is very difficult to validate with experimental data, with experimental data, the global model. It is possible to validate individual parts of the model by using, for example, it is better to validate with in vitro models. So it is possible to use some part of the global model and validate with experimental model. It is very difficult to validate with the global model because there is a multifactorial model. So the influence of the different parameters is very complex to validate. So the final validation we have done is only from a qualitative point of view. So the shape of the plaque is similar to the plaque that clinicians have found in his experience, in their experience, but only from a qualitative point of view. Or quantitative in the degree of stenosis is the validation. So the final concentration, for example, of macrophages or monocytes is taken from the literature. The problem is that in the literature, you have a very, very broad range of the different parameters. So it is easier to validate because surely your model is inside of the lower and upper levels of this range. Just as I said, the opportunity to intervene here, I think that this is indeed an extremely relevant question, but it's an extremely relevant question in a specific optic of models. So as one of the speakers on Monday recalls, so models can be used, can have two different applications. So one is the prognosis, or predictive application, and another one would be explorative application. So for the second application, then maybe here validation is not as critical as choosing the right parameters in order to generate virtually the right hypothesis so as to suggest experiments that would have never been created otherwise. So I don't know Miguel Angel if you can comment on this capacity of the model. Why not the problem of the model is that we have a continued distribution of the different systems. So in correlating with evidences, if you take a plaque, for example, in the echo to the sign image of the plaque, is this one here. OK, let's go this plaque here. We can observe that we have different sounds. So it is difficult to validate this model because, well, if you observe the concentration of the different parts, probably the global concentration of our model correspond to the global concentration of this plaque. But it is not possible to detect the different borders, the different boundary layers of the different constituents of the plaque is one of the limitations of this model, of continuing model. For example, if you use agent's model, there are a lot of papers about agent's models, but they are more applied to inestimial restenosis, for example, than to atheron plaque. And you can separate the different parts of the plaque. So in this case, this model are not able to predict this experimental evidence. Thanks for your talk. In the last part of your presentation, you were proposing an equation that relates the shape of the endothelial cells with OSI and Walsh's test. How do you find out this? It's the benefit curve of your data. How do you find out that equation? OK, the equation of the shape index, or the, sorry, I'm going to put the slides. Yeah, it's the equation of the shape of the endothelial cells. Yeah, and here, OK. In the meantime, which Walsh's test is used to, in that equation, is the maximum time average value? Here, in this equation, OK. OK, in this case here. So what we did, I went very quickly through the formulation. What we have is a probability-orientation density function of the individual fibers. So what we did is to modify the individual orientation of each fibril. So its orientation is modified by two special parameters that are the Walsh's stress, the time average Walsh's stress, beta, this parameter here, and also the oscillatory shear index. And these parameters are included in this part here. And this is an exponential term that is the rotation of the individual fiber. So the rotation is affected by these two parameters. These parameters here is the Walsh's stress, an effect here. And this parameter is considered depending on the oscillatory shear index, an effect here. So each individual fiber is modified. And we took data from the literature. There are many papers considering the orientation of individual fibers. And finally, it is possible to validate. This is possible to validate with experimental data, with in vitro experimental data. Because you have the control on the Walsh's stress, on the flow features of the experimental data. And you have, by microscopy, you can also capture the shape of the endoscelial cell. So it is possible to modify it. And also you can observe each individual cell, which are the main components of the C2 skeleton and how they are distributed in this space. So it is possible to validate. Final question is, before you said in the previous study when you do idolized geometries, that you can separate flow dynamics and then solid mechanics, not necessarily FSI, in these patient-specific anatomies, that has an influence. Could you comment on, well, the results that you found out using patient-specific data and how the effect of not using FSI could impact on the shape of the endothelial cells, for example? Yeah. For this case, for the endothelial cell remodeling model, we use only a modeminal factors. We have the stress level, the solid stress level. But at this level, we didn't find the influence of the solid stress on the cell. So we neglect it. And we consider only the modeminal factors. We have the information about the solid stress, but this is not incorporated in this model at this moment. Question there? Thanks, Milán, for the presentation. I would like to know your opinion about just one topic, about coronaries. That is the hypothesis of just considering rigid ball is correct, for example, if you want to compute the pressure, according to your experience, does it affect the radial displacement and the longitudinal displacement of the wall? That is correct, just to consider just only for fluid dynamics. Yeah, I think it's an important limitation. It's an important simplification, mainly for the coronary arteries. For example, for other arteries, it could be OK. For example, for carotid or for fer-moral. But for the coronary, the coronary is moving, always moving, because it is linked to the heart. Probably the motion we are considering here is not so real, because what happened is that the coronary artery has a lot of chains in the direction, and probably the contraction what affect is not a pure contraction in the actual direction. But they probably affect to the flexion, to the bending on some part of the coronary artery. So I think it is important to consider what happened. It is much more complex, because I think it's only a fluid analysis that not also including the motion of the fluid mesh. So I think there are some people working on that, but it's not very, very easy. But do you think that it's important changing the pressure inside the, for example, if you want to compute the pressure drop between the stenosis, this movement of the coronary in the just in the. In the pressure. In the pressure. The pressure level. The pressure level. No, I think the effect of the pressure level can be included in a fluid analysis, pure fluid analysis. I think that the solid part is affected mainly by the heart motion, but not by the pressure. Thanks. I think indeed that this is so. And what you were saying, when you look at patients with coronary artery disease, they become very torturous. So there's really something going on. So I want to thank you again, and especially for mentioning machine learning, but very quickly scaling over machine learning.