 Okay, then we can continue with talking about the models. Now we go back to the musculoskeletal part instead of the cardiac part, but as you saw already in the previous days, a lot of the things are very, very similar, although it's a different problem, maybe biological, medical, but he approaches and the way of doing things are very, very similar. And it's my pleasure to introduce Jérôme Noyye, who is working here at the university, and he's doing mainly modeling of the musculoskeletal system. But again, in this integrated approach where you go from data, experimental models, like in vivo and vitro models, and then to computational models and try to iterate through it in order to answer specific questions. Jérôme? Okay, I think. Okay, so thank you very much, Bart, for the introduction. So the talk I will present, I try to paste together so a lot of pieces of work that we have accumulated in spine modeling so along the years in order to build a consistent story. And so as I hope you remember the talk of Karine Wurst on Monday where she was mentioning nutrition as a possible important factor in intervertebral disc degeneration. And because intervertebral disc is avascular, it has few cells, a lot of extracellular matrix, and the maintenance of this matrix so it depends on the capacity of those few cells to have anabolic activity, and of course, in turn, depends on the availability of nutrients to these cells. And the availability of the nutrients, so as Karine already mentioned, basically comes mostly from the peripheral vasculature that on the top and bottom of the intervertebral disc through these interfaces that we call the end plate. And then you need to have diffusion of the solids. So typically oxygen and glucose through the disc. And this diffusion should allow solids achieving the center of the disc in order to feed the cells here. And at the same time, so the cells make glycolytic respiration and then they produce acylactic that contributes to lower pH and this acylactic should also be eliminated. So diffusion via these end plates. So some people also have cultured cells in vitro and what they have seen is that, so here you have a reference of one millimeter of glucose. And when they provoke partial or total glucose deprivation, what they see is that the cells of the center of the disc start to lose their ability to express important cellular matrix proteins such as protaglycansin, collagen type 2, which are the main component of the center of the intervertebral disc that ensures the proper function of the disc and also a proper physical environment for the cells of the disc. Moreover, so concentration of 0.5 millimolar of glucose has been identified as critical. So below 0.5 millimolar, basically you have this decrease in expression so no specific difference between complete deprivation and dispersal deprivation and it has also been shown that below this critical concentration the cells start to die along the time because they are just starving. So of course this problem of nutrition is also affected by mechanical loads. So the cell of the intervertebral disc, like any cell of the musculoskeletal system are indeed highly responsive to mechanical loads. So you have two direct ways of response. So there is a direct mechanotransduction which involves so the signaling through the integrins that are attached to the matrix and then remodeling of the cytoskeleton that sends signal to the nucleus so in the end we come to biosynthesis. And then there is another pathway that has been called indirect mechanotransduction and this indirect mechanotransduction basically involves nutrition. So imagine the solutes that diffuse through the intervertebral disc matrix which is a sponge so it has pores and these pores are filled with fluid and then the solutes have to make their way through this pores. So when you compress the intervertebral disc this is a sponge so what you're doing is that you're contributing to collapse the pores and so the water flow out. So basically you have less medium to allow the solutes to diffuse through the tissue and then to come to the cells. Then of course the ability of the disc to deform or the degree to which you will deform under specific external loads depends on the tissue properties. Typically the permeability, the fluid content, the porosity, the fixed charge density so the amount of protoglycans that controls the osmotic pressure and all those parameters depend on the interplay between three major components which are the protoglycans, the collagen type 2 and the water. And once we have basically altered the tissue properties we have altered the nutrition, we follow this path. We have a remodeling of the matrix and then of course this remodeling of the matrix so further alter the tissue properties and we enter basically or we expect to enter in a catabolic loop that might be particularly relevant to this pathogenesis. So the nutrition is known to be limited in the intervertebral disc and the ingredients have been assessed. However, whether this indirect mechanotransduction is really important to the intervertebral disc pathogenesis, it's mostly an educated guess. There are no specific strong evidences about this especially in vivo. So there have been a lot of in vitro studies in cultures and organ cultures more recently that brought some evidences however in order to extrapolate all these evidences to the in vivo situation then we have to interpolate those evidences which is particularly difficult. And so here comes basically the strengths of numerical modelling. So you're generating equations that allows you to explain different evidences they come from here, from there, and then from this interpretation then you hope to establish so an educated guess about the relationship between those evidences and one you have this educated guess so you have all the tools in order to try to produce new evidences through new experiments. So with this in mind the specific question that we have been tackling is so whether nutrition can contribute to this generation and whether this generation can alter nutrition and of course the mechanisms through which we can have this feedback loop. So here in terms of modelling we are tackling three major challenges. So one challenge is to have this tissue model that can capture the degenerative changes when you have degenerative changes. So you have changes in protoglycan contents, in water contents you also have damage, so here you can see for example cracks in the matrix then we need to couple this composition and biomechanical aspects so the analysis of the solute transport through the disk and then of course everything should be in the end related to cell biophysics and cell activity so in order to make a stronger link with biological evidences. So I will start with a kind of model set we've been using in order to have tissue models able to capture degenerative changes so we base the modelling approach on pyrohyperelasticity so in the center we have the gel-like part of the disk which is mainly collagen type 2 and protoglycans and so on the periphery you have fiber reinforced structures so basically the function of the disk is shaped by the ability to develop strong hydrostatic pressures when the disk is loaded externally here and this hydrostatic pressure put on attractions these fibers and then you achieve a very strong mechanical strength at the same time you can have a very controlled flexibility because the water is able to flow out if you have slow movements or static positions etc. So these are the mechanical features we need to capture so we basically have simulate a solid matrix and we derive the stress of solid matrix from this potential with elasticity coefficients and to the stress that we derive from here so we add pore pressure stress which represents the mechanical contribution of the water that depends so on the pore pressure within capillaries that is related to the permeability or the hydraulic conductivity of the tissue and the ability of water to flow out when you load the disk and it also depends on the osmotic pressure so which is mostly due to the presence of protoglycans and with their fixed charge density that can attract water and then this water that is attracted through the osmotic effect also contributes to the mechanical disk mechanics so in the annulus fibrosis we have a similar approach but we also take into account the fibers through these additional terms so this is state-of-the-art constitutive equation this general framework is also completely state-of-the-art and basically through this reinforcement so what we will see that what is important to capture is the interaction, is the local interactions that we will have between the two tissues and we will comment on this later so based on these theories here and more so what we customized it a little bit because we have seen that those equations would be valid for non-damage and healthy tissue as soon as you start to have cracks within the tissue so you affect in a different way the stiffness of the resistance of the tissue to volumetric deformations and to changes of shape so based on micro-mechanics theoretical explorations reported by Dormin and Kondo years ago so we could derive these damaged and stiffness parameters so shear modulus and bulk modulus in function of damage parameter which is related to typical crack density and crack shape so we can also relate these damage parameters so basically to the porosity so you have cracks in a specific shape that can open and then water can also flow in so through these damage parameters we basically establish a link between tissue damage so elastic parameters and also pro-mechanical parameters so in order to assess whether this new model was reasonable so what we have done is that we went into specimen-specific modeling so we got degenerated calivary spine specimens that were tested in vitro and they were so imaged so from the clinical images we rebuilt models and we got an interpretable disc of different shapes and different degeneration grades so this is a Pierman degeneration grade so here you have almost healthy, moderately degenerated and with advanced degeneration and then we looked how our model parameters were evolving with degeneration so as to be able to reproduce mechanical behavior of the specimen and here we got a very good surprise so we assessed our undamaged stiffness we see that our undamaged stiffness is so basically we're generally increasing with degeneration and indeed when you have degeneration which you have in intents to reproduce a tissue you have production of collagen type 1 which is called fibrosis so that generally stiffens the tissue however at the same time we also know that the change of integrative disc stiffness with degeneration has always been a debate there are some people that say that the disc softens with degeneration and other people that say that the disc stiffens with degeneration and what is happening when you look a little bit closer into the literature is that you see that from almost healthy to moderately degenerated you tend to have a stiffening of the interpretable disc but when you pass from healthy to advanced degeneration you tend indeed to have a softer interpretable disc and this is basically what we were able to capture through the accumulation of damage we can see that the accumulation of damage was not too high so for grade 2 and grade 3 but we had a dramatically jump up to for grade 4 so in order to reproduce not to reproduce mechanical experiments and then of course at the same time we predicted a drop in the swelling pressure in the fissure density where we got a result that were nicely aligned with the literature and we got a drop of porosity with degenerated porosity of around a bit more than 70% of water which is also commonly reported in the literature so through independent experiments we validated our model so within a full lumbar spine model we simulated forward flexion and then we had our several discs that had degeneration-specific mechanical properties and then we have been able to validate the deformation of each disc so in function of the level and the degeneration grade so of course we have done this before we had this model but this is the story of the presentation go in disorder then when we have this kind of disc model so what we have to do is to basically couple to the diffusion of the solutes of the nutrients and then to the reactions that would produce at the cell level that would also contribute to the local and current concentration of the solutes so here we have basically a reaction diffusion equation so we have the diffusion term so we can basically couple the diffusion term to the current porosity of the tissue so when you mechanically deform the tissue so you change the porosity and then you change the diffusion coefficient so of the different solutes and for the reactions so basically we have those empirical laws that come from experimental literature where people have tracked so basically the consumption of oxygen, of glucose and the production of lactate so in function of the pH the current oxygen concentration and of the porosity and of the cell density so this is the overall scheme that we follow to couple the mechanics then to this equation this is a weak coupling so we first solve so our perm-mechanical analysis so extract the current porosities we also extract the displacement fields in order to capture the change in diffusion distances and we enter basically in this loop so we solve the equation for oxygen and for lactate then for glucose we also update the pH and once we have solved those equations so basically what we can do so based on experimental evidences we can infer on the probabilities that cells have to die in function of the current glucose level, pH level and time so here we have a rather complex model and as I said it's very difficult to validate this integrated mechanotransport model of the intervitable disk because it's very difficult to get to obtain controlled evidences so the thing that you usually do in modeling when you can actually assess what you have is sensitivity analysis so you do sensitivity analysis you check what are the parameters that most influence your predictions and then you try to focus basically on those parameters so to link more mechanistically those parameters to your system and this is what we've done we've seen that basically the porosity and the swelling pressure mostly affect the distribution of solutes into the disk when you do mechanical, you apply mechanical loads and as well as the cell density so the next step was basically to further refine the osmoporohyperelastic model and through the Dolan theory we were basically able to relate the osmotic pressure to the fixed charge density of the protoglycans and this fixed charge density of the protoglycans also through empirical equations so it can be related directly to the contents of the protoglycans through this theory you also split the total water content into water contents that is affected by the osmotic pressure which is called extrafibrillar water and through the water content that contributes that is driven by capillarity movements so by Darcy's law which would be the intrafibrillar water content that depends on the collagen content so here we basically have an updated model that were important parameters that we can directly calibrate from biochemical measurements and this is what we have done for healthy discs and for moderately degenerated interval discs and then we used this model so to simulate seven days of typical physical activity and we of course coupled our nutrition model and then we assessed through the design of experiments sensitivity analysis so we assessed which were the biochemical components that mostly affected the nutrition of the local nutrition of the disc cells that mostly affected the local nutrition of the disc cells when this component was switched from grade one to grade three so from healthy to moderately degenerated so in general our glucose concentrations were always higher than the currently non-treasurer for cell death we didn't have any cell death however when any of the parameters were switched from grade one to grade three so we were always reducing our glucose concentrations and here came the interesting aspect if you were looking and what was happening in the anterior annulus fibrosis and more specifically at the interface indeed you were seeing that the water content of the nucleus pulposus was dramatically affecting the glucose availability to the cells in those areas independently on the protoglycan contents so this was very interesting because in general when you assess this degeneration or when you say that you start to have this degeneration you accept that you already had a depletion of the protoglycans which is one of the first biochemical signs of degeneration but here basically this reduction of availability of glucose to the cells within the central part is independent of the depletion of the protoglycans it's only the water so it basically brought us I will come back to this later it basically brought us into a question that what can provoke this degeneration of the center of the disk independently on the protoglycan depletion so when you're physically active during the day you're expelling water you have almost 16 hour of activities if you're healthy you sleep about 8 hours per day and during these 8 hours you're basically recovering the fluid so all the fluid exchanges that mostly take place through these end plates so basically what we've done is that we also wanted to be able to simulate the degeneration of this end plate and specifically there is very seen cartilage layer here the importance of which has been often overlooked because this is not a tissue that can be easily assessed chemically or histochemically because it's very seen and but we can use modeling to do that so we basically further expanded so the model so by having a composition dependence of the permeability of this tissue and so what we found so we could validate the model we could see basically that basically we had permeability increase when we had depletion of protoglycans and collagen which agreed with literature and when we imposed the mean composition we were also able to predict the mean permeability according to values that have been measured in the literature so now we have our composition dependence of the center of the disk of the periphery of the disk and of this seen cartilage layer so we can take biochemical measurements in the literature in order to play with the relative composition of each component and we assess the effect on the overall water content calculated in the center of the disk that we have found that mostly affects the nutrition of the cells in those areas and here big surprise so we've seen that this is a healthy case this is one we have basically all the tissues degenerated so of course you lose water but if you only simulate the degeneration of this layer of water exchange you're basically dropping making the water content drop so at a very similar level to the fully degenerated to the fully degenerated case so which basically suggests that we should have a very closer look at to this and if you look then what happens in terms of glucose concentration at the interface so basically you see that when you're simulating the degeneration of this tissue you're around 1 millimolar of glucose little bit below you don't achieve 0.5 but when you have all tissues degenerated so including the cell then basically you're starting to you're starting to provoke cell death into your organ so really highlighting so the dramatic importance of this thin tissue no of course here we are not taking into account aging we're just simulating so degeneration and we don't care whether it's aging whether it's accelerated degeneration but we try to infer on accelerated degeneration so we could use this model in order to in order to target a little bit in order to target more aging process if you remember the talk of Karin Karin was making the difference between what was normal aging so we're all degenerating but that's within the normality and you can have accelerated degeneration so so here we found some we found evidences in the literature that depending on the oxygen level so the production of the protoglycans was basically lowered okay so this is what we've did we've done so we have our fixed charge density which is a parameter of the pro-mechanical model and then we've started to make this fixed charge density depending on the time so depending on the depletion due to the half life of the molecules of the protoglycans and and function of the production of the protoglycans by the cells so we have a production rate so we assume that in a healthy conditions and with a nice nutritional environment basically we should have a homostatic preservation of the fixed charge density and then we can calculate this full production and then based on those evidences so we make the production so switch from one value to 80% of this value so when we have low oxygen low oxygen contents so we put everything into the mechanotransport disk model and we basically simulate 28 years of big physical activity and what we see is that in the center of the disk we're starting to lose protoglycans and if we look what happens after a little bit more than 21 years we start to find a fixed charge density or protoglycan contents that corresponds to what is being measured in grade 3 in tavertebral disc in the normal population not in the population that is considered as pathologic I mean normal aging and if we consider that our time zero is a fully maturing tavertebral disk so you have a fully maturing tavertebral disk around the age of between 25 years old plus minus some years so basically it brings you to an age of around 45 50 years old and indeed there are clinical evidences that this is the age at which you have most prevalence of grade 3 in tavertebral disk however when you have this kind of this kind of degeneration so basically you don't have cell death you're not expecting dramatic acceleration of this at least based on this kind of modeling so of course here what we have so we're predicting the nutritional environment in function of the mechanics and we say there is partial there is no deprivation or there is partial deprivation and then we can infer whether we will have cell death or no cell death but between the dramatic event of cell death and healthy condition many biological things can happen so if the cells are stressed because of the nutrition or because of the combination of nutrition and the loads through direct mechanotransduction through direct stimulation they can also start to produce inflammatory factors proteases that will enter into the loop of degeneration so basically through the approach that I've shown formerly we can infer on the importance of some tissues but it's very difficult to see whether we are not underestimating or overestimating what could happen and also to link the results to evidences biological evidences so here what we did is that we developed a lower scale level which is an agent-based model so I don't know if you are familiar with the agents but basically the agents so you take an entity which is an agent and the agents act as a single solver as an independent solver so you put rules into these agents so the solver resolves these rules you can have different agents that have different rules and then you leave the agent interacting between each other so cooperating and the rules of one agent will start to affect basically the solving of the other agent etc and you start to generate a stochastic and emergent system which is more proper of the biological of the biological reality and through these rules you can also input a lot of different parameters much more easily than through finite element simulations where you should start to generate strong couplings so basically we have our agent and then we made our agent sensitive to glucose, to oxygen, to lactate to the hydrostatic pressure and to the porosity and through these environmental parameters so the agent regulates its simulated biological activity so this would be basically the agent so within the agent we have different models to shape the biological activity so we have an immunopositivity model which is based on the Markov chain and it basically relates the probability to have the secretion of inflammatory factors in function of the intracellular production of inflammatory factors and the same for the growth factors then we have a cell viability model so basically the probability of cell viability before it was only shaped by the contents of glucose or the pH so here it will so depend on the inflammatory cytokines that will stimulate it so the production of energy due to respiration for example to the growth factor will inhibit the probability of cells factors of course so inhibit and you also have so ritual alimentation so cell death activates cell death which is something known in apoptosis for the nutrition so we gave up the we gave up the phenomenological the phenomenological equations that we had for the reaction in order to build a full Michaelis Menten model where you take into account so those intracellular glucose transporters and for the effect of loads we have so basically the load into different descriptors so magnitude frequency and amplitude and through the network based on gated channels so we are able to make the difference between the relative effects of each load descriptor and then we have a sub model which is the integration sub model within the agent where we make everything interacting with everything so black arrows are activation red arrows are inhibition so the way we generate the network is based on what is commonly known from the literature so it's qualitative and to make it quantitative so we use a kind of Boolean integrated Boolean model and the whole the entire integration of the Boolean model so it generates like a continuous model of activations and inhibitions and the good thing of this model so we've set all the activation inhibition coefficients to mean natural values somehow we didn't calibrate the model because the good thing of this model that has been developed for general purposes is that the qualitative behavior of the network depends on the connectivity that you have put into the network so we can directly assess whether our connectivity is reasonable or not in relation to what is known in the literature and the final result of this network is basically the expression of matrix proteins collagen type 1 type 2, protocol icons matrix metalloproteases that basically depend on inflammatory cytokines and growth factors and energy stores on the nutrition so we've changed, we've taken the model we've taken so the agents with all the intra-cellular models and then through the immunopositivity models the agents release produce and uptake so inflammatory cytokines and so growth factors they also modify their nutritional environments through the respiration and then you start to have so agent corporations so we have about 5000 agents collaborating and we changed environmental pH and glucose and we check the effect that it has on the relative expression of the protocol icons and collagen type 2 and compare it to cell culture experiments and through this we've been able to basically validate so our model qualitatively because this is a relative expression and so we've been able to validate so the connectivity of the network that we have in order to have the sensitivity of the cells to a nutritional environment by integrating us so very important biological components so there is something very interesting that we've seen is that so in the indirect mechanotranslution models that have shown before so we had repeatedly when we were altering the model we had repeatedly this concentration of 1 millimolar of glucose but it was very difficult to achieve 0.5 millimolar in glucose unless you apply very extreme loads that generate extreme dehydration of the tissue but then when we ran the systems biology model we've seen that when we achieved this 1 millimolar of glucose these are completely independent simulations we basically started to trigger some catabolic some catabolic events so this is basically a very good reason to go back into the experimental biology and do a better screening of the glucose concentration effect because glucose concentrations around these concentrations so between 1 and 5 it has never been assessed before and this is what I've said this is just an illustration that basically we're always doing around 1 millimolar when we simulate aging so tissue degradation so for example only the degeneration of this so this was through indirect mechanotransliction so now back to the systems biology model another level of assessment since we are able to take into account the effect of the mechanical loads so based on do you remember that Karin mentioned the study where the surgeon agreed to have a pressure sensor into his intervascular disc so we retook basically the result of this study and we imposed to the model so the intradiscal pressure associated to the different activities that the surgeon was doing and here we also got something that we are very happy is that so these basically bars is no load so we can take it as a control with respect to this control when we simulate walking we're basically we're basically favoring the production of extracellular matrix we are limiting the production of catabolic factors we're increasing the production of gross factors and there are some spine surgeons in the room and indeed walking is one of the physical activity that is generally recommended for person that have low back disorders but have to keep being active so these are the conclusions that we had based on all these results so basically deformation induced local dehydration basically it seems critical to disc nutrition so for standard disc sizes nutrition controlled protoglycan depression so it seems to control a natural aging process but this is different from accelerated degeneration this is what Marl says and the early degeneration of the cartilage end plate so because of this is seems to have a very dramatic effect and can really contribute to accelerated degeneration and this needs to be to be looked experimentally and then of course we've seen so the poor of systems biology modeling so in order to basically couple the scales what would happen at the organ tissue level and then at the lower level where you can very established tight relationships with biological evidences so based on cell cultures that are otherwise very difficult to interpret in terms of what happens into the organ organ or in people and this is another thing that we are speaking about patient specificity so this is some slide that I did during a Blanca Blanca stock so patient specificity and here there is something that the eternal question does size matter so as answer is yes size matters ok so so the specimen specimen specific simulation that we've done so we found out that we had intravatibral disc with a heist of around 10 millimeters that would be the standard disc heist in the standard population and but we have some disc with that were very thick with a heist of about 15 millimeter and by coupling the nutrition model to the mechanical model so independently on the nutrition grade that is being simulated we've seen that in the center of the disc because lack of nutrition so basically we can already alter the cell viability so we can have up to 40 percent of cell death so which mean that there are some patients that we don't know why but they have spontaneous dehydration of the disc patients that can be very young around 20 30 years old and here so one additional clue that model can bring that whether it would be correlated with the heist of the disc whether patient with very large intravatibral disc wouldn't be prone to accelerated degeneration because of high diffusion high diffusion distances so thank you for your attention I would like to particularly thank so these collaborators who have respectfully contributed to many aspects of what I have shown to the funding entities and to all the external collaborators that we had and happy to take questions thank you very much for this interesting overview and a very very elaborative model maybe one thing is like you regularly said like you do your model you get from your variables or parameters from experiments and what is your opinion these things can you find it in the literature do you have to find collaborators that can do your experiments do you need to organize the experiments yourself how do you see it as like a modeling researcher what's good approaches mm-hmm so it depends on what you're looking at for us for all what are the mechanical parameters there is there is a lot of things already in the literature and by playing with sensitivity analysis you can you can basically assess the effect of the variability of your on your prediction so basically you can you can target the kind of prediction that is less affected by this variability or the kind of prediction is most affected by this variability and then you will go more in detail into some specific parameters so if you go more in detail into the specific parameters you can be lucky you can find a narrower literature that targets those parameters or you have to develop collaboration so here we've been lucky we have developed a collaboration with with Professor Keita Ito at the end of an University of Technology who were working basically on composition dependent disk modeling as for the systems biology model and and the relationship with individual experiments or again cultural experiments it's a little bit tricky because there is a very strong variability in the literature between the conditions of of cell cultures so the origin of the cells in general you have already degenerated cells that are senescent so we're assumed that our cells initially are healthy so when you have healthy cells basically in general which you have bovine or ovine cells you have an animal model not a human model so here it becomes a little bit more tricky to do it yourself because of regulation and and also to find out collaborations so for in for healthy cells so as far as we know there are very few persons who do that outside Europe you have to go to Canada and so we have established contact already with those persons but then of course everything starts to depend on funding because you have to start to pay things to do that. Any other questions? Ok