 So we started in the second session of presentations and I'm very pleased to welcome so Bindi Brooks who is coming from the University of Nottingham and Center for Mathematical Medicine and Biology. So Bindi has been working since many years on on airways so mechanobiology of of airways focusing on asthma and coupling so mechanics to all systems biology of of the cells in order to predict the fate of of the airways so in this in this disease and she recently got an important grant from the Medical Research Council in the UK and which she'll also then doing this Beautiful piece of work that she will be presenting now Thank you very much for the invitation to this To this summer school. I'm in particular to this beautiful city. I really do like being here very much. So thank you So I should start off by telling you something about asthma. It's a really prevalent disease lung disease Most people know roughly somebody somebody who has it if they don't have it themselves 300 million sufferers worldwide and although mortality rates may not be as the same as those associated with cardiovascular disease the severe cases of asthma require frequent hospitalizations they get exacerbations at any point and they're very hard to predict when they're going to come and so the quality of life type issues are are fairly significant and therefore a fairly big burden on national health services So what about the disease itself? It's As I already mentioned it's a lung disease. It's a chronic lung disease. It's characterized by essentially three things inflammation so you breathe in an allergen and your body mounts an immune response lots of white blood cells of different types come into the airway Hyperresponsiveness and what I mean by that is the smooth muscle cells that line the airway they contract in response to a cascade of stuff after having inflammation and in as in asthmatics that contraction happens really fast and to much lower doses of a contractile agonist than it does in normal people and every remodeling and this is associated with repeated episodes of asthmatic attacks and What happens there is in you then get overtime increases in smooth muscle Which so here I'm showing a picture of a histology slide So you've got on this side as a normal Slice through an airway. What we see and what we see is increased smooth muscle in the asthmatic airway an increased or thickened basement membrane which is which is essentially collagen and increased epithelial Number increased numbers of epithelial cells. So a thickening of the entire airway And this in turn can make the disease appear even worse because your airway contract even more in response to the inflammation and the contractile agonist The these three characteristics seem to be connected in some way but people aren't really clear on what that connection is and Whether one is a consequence or a cause of the disease So does remodeling happen first and does hyper responsiveness follow or is it all driven entirely by inflammation? so these are all sort of underlying questions that That people are still trying to grapple with one of the The things about all of one of the main thing about all of this is it's an inherently multi-scale problem So a clinician will observe things at the lung scale trouble with breathing wheezing all of those sorts of things and essentially it it is a result of If you go all the way down to the subcellular scale, it's a result of these Actomycin interactions that go on inside the smooth muscle cell that caused the smooth muscle to contract that causes narrowing off the airway that reduces Resistance to flow and therefore the stuff that's observed at the organ scale I'm going to focus most of my talk on the multi-scale problem associated with subcellular to cell to tissue level interactions and But then of course you can think about how this then has consequences further up the scale So one of the biggest mysteries about asthmatic airways is that Compared to non asthmatic airways is that if you take a deep breath if you slightly broncho constricted You've breathed in a bit of dust or pollen or something you get a bit of broncho constriction If you haven't if you're normal you take a deep breath your airways become quite Relaxed and everything's fine if you're an asthmatic on the other hand You take a deep breath and what might happen is you actually might get a little bit of a relief But then very quickly you broncho constrict again And you're back to your broncho constricted state and people haven't really understood why there is this big difference So a number of studies experimental studies have been focusing on understanding how tidal breathing and deep inspirations affect smooth muscle Response so what this involves typically is taking out an airway like this Taking a cutting off part of it part of it and then cutting it into a strip So that your smooth muscle is lined up along the length of the strip in this way And then what happens is you they mount the strip And they hold the length of the strip constant They apply a contractile agonist and what that does is if you hold the strip at some fixed length is you get this Increase in contractile force. So along here. I'm plotting force along here We've got time and what you get is this increase in contractile force and then which then plateaus to a maximum If at a particular point in time instead of keeping your length fixed you start applying length oscillations this is to mimic tidal breathing what you get is oscillations in the force and if you make your If you make the amplitude of those oscillations larger you get a decrease in the mean contractile force that seems to be proportional to that amplitude of oscillation On this side, we're just plotting the force as a function of the length So as you're cycling through the length oscillations, you see this sort of change in the force length behavior so essentially this sort of This sort of observation led people to think well clearly if you do a big deep inspiration Then you're going to make enough of a change to your cell level contractile stuff that's going on And that's why you get this reduction in force and the bigger your the bigger your excursion The bigger your drop in force however people have done Instead of taking a tissue strip another set another group of people have done experiments where you actually take out the airway the whole airway and Oops going backwards here Extract the whole airway And then applied two different protocols one is where they apply increasing Agonist concentration, but keep the amplitude of the pressure oscillations fixed and a second protocol in which they keep the agonist concentration Remember the agonist is the thing that's causing contraction of the smooth muscle if you keep the agonist concentration fixed But increase the amplitude of the pressure of the transmural pressure oscillations Then that's a little bit like increasing the length oscillation amplitude Okay, so the idea being that this is a little bit more like what might be happening in vivo rather than what you do to a tissue strip and what they found was That so if you look at these so the main panels to look at Are this of the radius what's happening to the radius and the thickness What they found is that in the top protocol where you just kept your Amplitude of oscillation fixed but increased contractile agonist There was not much difference between the static case a case where you had tidal breathing and a case where you had tidal breathing interspersed with deep inspirations So that was that was the one of those protocols the second protocol where you have Fixed agonist, but increasing amplitude pressure transmural pressure oscillations They found only a significant difference when the transmural pressure was really very large and which they believe was not necessarily What was happening in the tissue strip you were getting changes with the tissue strip even at much smaller strains So the question was Why weren't the results from the cell and tissue level Recapitulated at the level of the intact airway and we started getting interested in this question Because we felt that maybe by developing a mathematical model of these things that we might be able to answer these questions So this is essentially the then our multi-scale model I'm going to go into quite a lot of detail here So if you have any questions at any point in time, please stop me and ask I don't mind not getting through my all my slides. So So essentially what we're doing is we're starting off by saying we have an airway wall That's embedded in some parenchyma the surrounding the tissue that surrounds the airway which is essentially consisting of lots of alveoli and Within the airway we have these fibers that are arranged in a helical pattern around the airway And these fibers have both smooth muscle and extracellular matrix essentially collagen contained within them So then if you then look if you then look into those fibers what we then Imagine as that they they consist of lots and lots of these smooth muscle cells and within those smooth muscle cells You have these actin myosin contractile machinery and I'll go into some detail describing this in a minute I'm just I just want to give you an overview for now. Okay, so a Little bit of detail of how we model the airway wall in terms of sort of cardiovascular mechanics. It's relatively simple But it's for the it's being done for the first time in airways, which is slightly surprising It seems like airway mechanics is about 50 years behind cardiovascular mechanics, but here we go So essentially we're going to assume that my airway is in underplane strange it's being held fixed with no Axial deformation and we're going to assume that everything stays axisymmetric again That's a simplification because we've seen that there's quite a lot of buckling of the epithelial layer going on But for now, it's simpler to think of everything staying axisymmetric And then so you can write down these deformation gradient tensors for those of you familiar with solid mechanics It's all very straightforward. Those of you aren't you can just ignore this bit, but So then what you then? have to apply boundary conditions and the two main boundary conditions are that you're applying an internal when you're breathing you're applying a Transmitted pressure difference across your airway. So you've got a pressure Acting on the inside of the airway a pressure acting on the outside of the airway And then at the interface of the two materials the airway wall and the parenchema you have continuity of stress Radial stress and radial displacement Then we assume that we've got these helical fibers embedded in the airway wall two sets of them to ensure that everything stays axisymmetric even during deformation and Then these there's two functions imparted to these fibers first of all the extracellular matrix That's contained within the fibers strange stiffen. So as you stretch you you Stiffen the material and that the cells within those fibers are congenerating a contractile force And again, that's all happening in the direction of these fibers So again, you can write down the directions of these things in terms of the undeformed coordinates and the and the deformed ones and then you can and then we write down All of our constitutive laws in the following way So first of all, we assume our parenchema is homogenous Isotropic and compressible so a little bit like what Bob was talking about earlier today Although the material the making up the parenchema itself isn't compressible the air spaces in them get squeezed when you breathe in Breathe out rather and so you can think of the entire material as being compressible The airway wall we model as the the underlying matrix being homogeneous isotropic, but incompressible And then we write down a strain energy function the neo-hickian part of it for the parenchema it contains the compressibility J not equal to 1 And in the case of the airway wall, we just have the J is equal to 1 So you just have the the part associated with the first invariant and we then think about how we then associate passive and active properties to the helical fibers so this is done through writing down an expression for the passive properties which depend on these additional invariants and They're characterized by two parameters essentially this C1 which is related to the density of the fibers in the airway wall and This parameter C2 which tells you how quickly you get an increase in stiffness of of the Extracellular matrix as you're stretching it And then finally oh and finally we write down something associated with the active part of the strain energy function And here what we're saying is that it it's depends on this contractile force I'm calling a star and that's going to come from my cell model Which I'm going to talk about in a minute But it's only in it's indirectly associated with stretch not directly so we can Decouple the stretches from the contractile force and again Yeah, I can explain that in a bit more detail detail as we go So the total strain energy function then is made up of the neo-hickian part the passive part Associated with the fibers and the active part associated with the fibers So this contractile force a star is what we then need to Figure out and I'll come to that in a minute But essentially all of the stuff I've talked about goes into the Cauchy stress tensor which then Assuming conservation of momentum at each time step, so we're going to do a time dependent problem But at each time point we're going to assume that this is true So there's a Cauchy static equilibrium and what we end up with is a relationship between transmural pressure and the unknown Radius internal radius of the airway, so you apply a transmural pressure and we want to know what how the internal radius of the airway responds and Within that you have this contractile force generated by the by the cells So in case you missed it I should have pointed out that the capital R's are all the undiformed Coordinates and the small R's are the deformed coordinates and in this expression the only thing that you don't know is the little R a Which is the internal radius of the airway So at every time point what I want to do is solve this equation for our a Subject to what's happening to the contractile force in the cells Okay, so here's what the contractile force where the contractile force comes in So I've got a model here that not that looks at the cross bridge dynamics Internal to the cell and is real in relies on this idea that you've got this thick myosin filament That has got cross bridges coming off it and a thin actin filament that has got binding sites on it and that over When you have the right calcium and stuff in the cell then you get Foss-frolation of these myosin of these cross bridges They can attach to these binding sites and what and as a result they can pull the actin filament relative to the myosin filament Generating a velocity a shortening velocity and Therefore shortening of the cell So it's based on this Huxley sliding model Combined with a high Murphy kinetic scheme where we assume that the myosin cross bridges initially exists in an unfoss-frolated and Unattached form they get phosphorylated through calcium within the cell and When they've phosphorylated they're more ready to bind to actin binding sites which become these this This actin myosin complex and they can cycle between these two quite rapidly That's the thing that allows rapid movement of the actin myosin filaments relative to each other and the important thing about this is that they depend on the Local variable X which is how far away your nearest binding site is from yet the unstressed position of the cross bridge So a Quick thing about the defos-frolation of these complexes They then turn into something that cycle more slowly and they're called latch bridges in the literature Which then can become defos-frolated and return to the to the myosin Cross the unfoss-frolated unattached myosin cross bridge now all of this stuff Is governed by this equation here, so n is a vector that tells us what the fraction of How the cross bridges are distributed between these species So you've got all of these species in this vector n that n evolves in time as a result of being either Contractile agonist causing shortening of the smooth muscle or if you pull on the smooth muscle then you're cause you're you're Modifying the velocity accordingly and so n evolves according to this this sort of advection equation and the Reactions are all contained within this matrix t which contains these rate functions That I've specified here the g the the attachment and detachment of these cycling cross bridges are Governed by something that looks like this the details don't really matter at this point But the point is that there's space there's dependent on this variable x which indirectly depends on how How you're pulling your smooth muscle which will come into play when we're applying Oscillations to the to the tissue And then the thing about all of this is that when you know what when you if you solve this equation for n You can then figure out what the contractile force being generated is because the cross bridges that are attached these two species here cause our Modelled as lit linear springs, so if you then integrate over all of the all of the Cross bridges that are attached And multiply them by the extension then you've got a total contractile force As as and that's where our a star in the previous stuff comes in Okay Quite a little just a quick thing about this velocity here All of this all of n all of these ends here are variables at the cell or filament Scale, so you've got this local variable x telling you how each of these ends are distributed But this velocity here is essentially a macro scale Property because you at the tissue scale you're applying this velocity so So the all of the variables in here are essentially parameterized by this macro length scale are and I Should give you a quick idea of what I mean by these distributions of n So what at any time t you imagine you've got lots and lots of these cross bridges They're distributed in lots of different they're distributed such that they are attached in lots of different configurations So if I was to pick a Configuration where my cross bridges have a large and negative extension and I did a frequency I plotted the frequency of it then I would get something like this if I then picked out all of the cross bridges that had a slightly smaller but smaller negative extension it would look something like this and so on and what you end up with is a probability density function describing how n is distributed So at any point in time you've got a distribution that looks like this you apply some kind of stretch or or some you apply an agonist and things change and that change may then drive a redistribution of how n of how n is How n goes and so this might be how it then Changes so you can imagine that if you've got lots of length oscillation going on that those distributions are going to change with time and Here is an example of how those distributions change for a particular Example just taking a single cell and applying a a length oscillation So you then have these kinds of changes in your distributions Okay, so we've put all of this together what what that means is that I need to solve this equation and my pressure radius Equation at every point in time during my length oscillation so I've put all of this together into my airway model and Simulating what happens in in that context, but I just need to describe these figures a little bit more carefully So what I've got here is I'm applying a transmural pressure to the airway To mimic the experiment I talked about and I'm then Outputting the radius that you get as a result of that Transmural pressure. So if I do it very slowly I get these curves that I'm that I'm thinking of as a quasi static pressure radius curve and the black line at the top there is For a situation in which there is no contractile agonist and all you're doing is you're passively Inflating your airway and as you inflate your airway your radius is responding in the following way So you can see that to begin with you've essentially got what your your neo-hooking behavior But then the strange stiffening bits Comes in because collagen fibers are being recruited Getting stiff and therefore you now have very small change in radius in response to this larger increase in transmural pressure And that fits nicely, so we fit that passive response to some Pressure to some pressure radius data from this particular From the study that did those transmural pressure oscillations And then be after that we then say well, okay What happens if you now increase the amount if you actually apply some contractile agonist to this situation? And you do quasi static pressure radius curves in that case And so you then we then have these predictions of what happens to our pressure radius curves in the presence of increasing agonist And then on top of that we then may make the experimental Protocol where we keep the transmural pressure fixed but Sorry that the the amplitude of the oscillations fixed, but we increase the contractile agonist concentration. So what we see here is that when you Apply the transmural pressure Oscillations in the situation where you have this this green level of agonist you get this loop here If you apply if you then increase the amount of agonist you get this blue loop It's a loop, but you can't really see it. It's a very narrow one And then similarly if you do the same thing for a higher agonist level you get this sort of thing so what we found is that you get these You get a little bit of Bronco dilation Compared to so if you think about what your quasi static pressure curve looks like Applying that oscillation has caused a little bit of a Bronco dilation because your radius is now slightly higher But it's not it's not very big and very Surprisingly the one in which you actually had higher contractile agonist You actually got greater contract greater Bronco dilation Which is somewhat surprising most people assume that you've got if you have a Contracted airway, you've got a stiffer airway and therefore you're just you're going to be able to dilate it a lot less But we found that actually you can dilate it better, but it seems to depend on Where you might be on this pressure radius curve And that's because when you take the slope of those pressure radius curves and plot them as a function of transmural pressure Then what we actually see is that the very non-linear nature of these means that at the transmural pressure that we're applying the oscillations we have What we have is that the blue one Is that is that a much? When you apply the transmural pressures on that blue curve at that transmural pressure. It's at a much More compliant state than the other two so you would it you would So as a result what's happening is that when you're applying these transmural pressure oscillations You are applying far more. You're able to transmit far more of the strain to the contractile machinery Which is then causing a reduction in this Contractile force which is then allowing the airway to dilate more So we've actually been able to So there's a relationship here between how The the the amount of bronchodilation that you get Relative to the effective stiffness of the airway at the place in the pressure radius curve You're at when you're applying this bronchodilation so in some sense we would try to reckon we feel like we've reconciled the the discrepancy that we've seen between the Intact airway experiments and the tissue strip experiments because what's happening with the intact airway experiments is that they're not They hadn't really taken into account the effective stiffness at which they were applying the transmural pressure oscillations So it may be that What before I go on to that it may be that Pressing all kinds of buttons here Ah Here we go It may be that what we really need to do to improve bronchodilation in a bronchodilated in a bronchoconstricted Person is to find somehow find where their airways are at their most compliant And then to try and apply a deep inspiration at that point. It may be that the reason the asthmatic Person is not able to bronchodilate their airways Is that they're somewhere at this very stiff part of the curve and so So any kind of deep inspiration isn't transmitting the strains needed to perturb the the contractile machinery in the airway So perhaps what we need to do is take a deep breath out before we take a deep breath in So that we're moving our lungs to a more compliant airway a compliant part of our pressure In in the case of a whole lung it would be more like a pressure volume curve So that's just a hypothesis something that we need to test but what we did do is go back to the group that performed these experiments and asked them to to Repeat the experiment at a trans at a different transmural pressure And indeed they showed that by doing that that they were able to generate a much bigger Bronchodilation depending on where on the pressure radius curve they were Okay So if you now look at so if you just think about what you've got you've got an airway You've applied a transmural pressure to it You've got a response in terms of how there how how much bronchodilation you've got in terms of the radius Of course, you've got internal stresses in the airway wall and again We come back to stuff that Bart was talking about and and one of the main things that I want to point out about all that is that if you look at the circumferential stress, which is the The stresses that the the predominant stresses that the smooth muscle will be under within the airway wall What we find is that for as you as you first of all just for any Level of contractile agonist and even in the passive case that you've got this heterogeneity of circumferential stress as you go from the lumen to the outer part of the airway wall And if you increase that contractile agonist that heterogeneity changes And the other thing which I've not shown here is that if you've got a remodeled airway So you've got a thicker airway wall then that heterogeneity is exaggerated even further And what I've shown here is first of all stress so the circumferential stress plotted as a function of radius Both at the outer wall and at the lumen and first of all straight away you see that the That there's qualitatively the shapes although the shapes are similar Quantitatively they're quite different, but in particular what you can then do is look at how these stress strain curves vary with agonist and with transmural pressure And so that's kind of what I've done in this picture So it's essentially it would be a 3d surface if I was to plot it as Radius circumferential stress and transmural pressure into the slide But what I've simply what I've done to make it easier to visualize is simply connected up the points that Are essentially isopressure lines So so for zero transmural pressure as my contractile agonist increases I would follow this curve here, but at a higher transmural pressure I would follow this red curve up here for example and the difference between what's happening at the outer wall and what's happening at the lumen is Significant and we think may have some implications for how the smooth muscle then responds as a result So that's kind of That's kind of where I want to stop here for this part of my talk and But I Carry on and go on to describe some further work We've been doing as a result of what we've learned here, but I just want to give us sort of a part-way summary So first of all, I just want to say that in doing this We've ended up developing a fairly comprehensive Biomechanical model of the airway that combines both the dynamic Subcellular contractile force generation with the non-linear tissue level Mechanics of the airway Again, like I say, this is Relatively simple compared to a lot of the cardiovascular models Especially the kinds of things Bart was telling us about this morning But if this is essentially the first time that anybody's really looked at it in this way And we've learned to quite a lot. We feel by doing it The the thing that's come out of it is that we wonder if Perhaps we've been looking at this whole deep inspiration thing a little bit wrong Maybe we need to think about it in terms of where Where can we take a deep breath to maximize the benefit of taking that deep breath? And maybe it is associated with this non-linear pressure volume relationship that we know Probably exists at least pressure radius relationship at the level of a single airway And then we need to think about how that translates to pressure volume relationships at the level of the whole lung and then finally these stress heterogeneities that seem to exist and get modified as a result of Both the dynamics of breathing as well as the geometry of the airway itself Means that the smooth muscle and all the other cells in the airway are being subjected to quite different Micro-mechanical environments depending on where they are in the airway wall and we wonder whether this has some effect or some These things are responding to these stress heterogeneities To give rise to airway remodeling in a particular way So we know that mechanical cues play a big role in how smooth how cells in general respond And so we then went on to think about how these heterogeneities might play a role in airway remodeling Which essentially brings me to the second part of my talk But before I do does anybody have any questions about what I've already said I feel like I've gone through in quite a lot of detail. So Okay, so as I said right at the start We don't really know how these three characteristics are How they interact in asthma as a disease and in its progression So what we've done is we've kind of built on the on the airway model that I've already described But in but started to think about all these other aspects and how they might link to the mechanics of the airway and then we've In parallel, we're running some experiments in a mouse model of asthma And it's it's a very very well established mouse model that we know causes remodeling through challenging with an inflammatory agent and that is this overalbumin And essentially what we're trying to do with this study is to test a hypothesis Which is that although airway remodeling may indeed be initiated by inflammatory Mediators or inflammatory factors. We feel that it it is being perpetuated by mechanical Factors, so we're so we're developing a model and experiment that that is essentially trying to test this hypothesis Okay, so I'll just give you an overview of of What sort of things we're incorporating into this? First of all, we imagine that our Information the information that your airway sees is a result of challenges to your airway because of things you breathe in on a day-to-day basis, so it could be some allergen like a like Polyn or something or it could be pollution Etc. So so we have some notion of some challenges that occur as a function of time In our in our particular Mouse model we actually have an we actually know when that's happening in humans Of course, it's completely random in the mouse model. We know exactly when we're challenging So we've got a really good handle on the input into that That challenge causes a rise in what we call an inflammatory factor mu So it's it lumps together a whole bunch of things that's happening in the airway which includes the influx of inflammatory Cells like aacinophils neutrophils all white essentially white blood cells that migrate from the circulatory system into the airway and that in turn causes activation of Things like histamine within the airway wall, which is a contractile agonist so there's this link between inflammation and Contraction because of this of this process here within the mouse model We can also challenge with directly with contractile agonist and that would then enable us to test a hypothesis that that looks at remodeling that comes purely as a result of bronchoconstriction independent of information So each of those things then have a consequence the the inflammation we imagine Causes a phenotype switching between what we think of as essentially contractile smooth muscle and Proliferative smooth muscle so this is essentially key to our model our remod our model of remodeling If all ourselves proliferated at the rate at which we know they do in vitro For example, then our airways would just close within six days a rough back of the envelope calculation would tell you that so what we imagine is that most of our cells are in a quiescent or Essentially just a purely contractile state But that every now and then they get there's a switch to a more proliferative phenotype But that it doesn't last very long in that phenotype And goes and returns to this contractile one So we think that the inflammatory factor this mu the level of that drives phenotype switching So it affects this rate here and And it can also have an effect on extracellular matrix production or degradation So we also have a part of our model looking at that aspect We then imagine that the contractile agonist that's being Generated in exactly the same way as I described in the model previously Generates an active contractile tone So the that gives rise to these tissue stresses that I described and that in turn may affect phenotype switching in the way that That mu does it may affect the proliferative the rate at which proliferative cells divide And equally we know that there is some sort of mechanic transduction effects that also then cause further contractile agonist to be released so one of those one of those hypotheses involve activation of tdf beta from Latent stores in the extracellular matrix another hypothesis involves compressive stresses of the epithelial cells Causing release of endothelial in one. So all of these things can act as either contractile agonist or Pro-proliferative factors, so we are incorporating these within our modeling and then we also Incorporate the notion that these proliferative cells Lay down their own extracellular matrix and again There's a hypothesis or a thought that these the new extracellular matrix that's being laid down in these Airways is potentially of a different type and potentially Proliferative in some sense. So all of these things we kind of incorporate in this in this sort of large model Which we will then test in different ways So the nice thing about having a parallel mouse model study going on at the same time is that we know exactly When we're challenging the mice with this with this of algorithm, but also we have control mice as well and we sacrifice mice Control mice early on to Get an idea of how much smooth muscle is within an airway and how much extracellular matrix is within the airway To to fit in with the soap model with with our model that we're in court that requires these measures So that tells us what our control airway geometry should look like these things input feed into this frequency of event type input and Then we also sacrifice mice at different time points following challenge So we've been challenging a certain with a certain protocol and then we take time Then we sacrifice mice at these different time points and again We're able to measure for those mice exactly the amount of smooth muscle amount of collagen or extracellular matrix Which then enables us to come out with a remodeled airway geometry Both in the mouse model and in our simulated model and this then allows us to validate The and or figure out what sort of mechanisms are important and are underlying the remodeling process So Just a brief overview then of what goes into the Model of remodels all of those things are the dynamics the way in which the constituents may change but of course Those constituents are are within a geometry that is undergoing That has mechanical stresses associated with them So this is the sort of overview of how we in corporate those that the increases in smooth muscle And extracellular matrix and so on so first of all we imagine we have this undeformed radius or undeformed geometry Which I'll call a reference configuration so all the capital R is like in my previous model and then it the the Dynamics then tell us how Increases in smooth muscle and extracellular matrix then gives us a grown configuration according to the equations underlying that and I may just show you them briefly So that but that's a stress-free configuration and what we know of course is that There's air the airway is always under some kind of transmittal pressure and there is some contractile forces there and that gives a then we then have like in the previous model a An elastic deformation F that then tells us what our final configuration at any point in time is But the thing about all of this is that at this grown configuration This this process here from reference to grown configuration or this configuration to the next one is is Informed to some extent by what the mechanical stresses in the airway wall are as well So it's this highly coupled situation where this grown configuration depends on the stresses Or the mechanical state from the previous time point and so on and so forth Okay, so That's our that's our idea. That's how we're setting it all up The volumetric growth as I just mentioned is governed by the dynamics and stress feedback and the elastic deformation depends on the transmittal pressure and the fiber stress that I Talked about in the previous part Okay, so I think what I'll do at this point is just to say that this is very much work In progress If anybody's interested in the details of what goes into our into into this Into this part of the model, then I'm happy to Discuss at any at a later point, but I'm gonna I'm gonna run out of time here. So I'm gonna stop there essentially we're Trying to couple the both the mechanical and Biochemical processes that are going on inside the airway wall to understand how remodeling may happen And we've been able to identify a in a preliminary way. So maybe if I just skip forward to to that in a preliminary way how Different parameters within the model affect What's going on? So first of all here. I'm just showing what happens if you If you Compare what goes on with with changing inflammation magnitude and how quickly that inflammation resolves and what we find is that there's a That you can you can do a parameter exploration that tells us how the contract how the how the Airway remodels over time. So this is showing you the diameter the internal diameter of the airway Some five days after challenges have finished and So we can see so we can so along here is the amplitude of the Inflammation magnitude and along here is the how quickly that Inflammation resolves and you can see that if it resolves very slowly and you have large amplitude Then you get really rapid growth of the airway wall But the other the thing that's kind of important here is what also how quickly the contractile agonist So you end up with this kind of positive feedback loop, which where you have this contraction it causes further contractile agonist to be released and that then gives a Positive feedback loop that means that it takes a long time for the agonist to clear off even after challenges have finished And here what we've done is quantified the number of days the agonist hangs around for post-challenge so for the same set of parameters you can see that The agonist hangs around for quite a long period of time in this part of the For these this parameter choice here, but clears more rapidly for this parameter choice. So it's so what we find is that The there's a potential for an increased contractile tone Depending on how how the inflammation The inflammatory challenges that might be that you might Encounter Similarly, and then what you can do is look at how the radius So what I'm plotting here is the the radius of the airway as a function of time And what we're seeing here is what that contractile agonist is doing and how the circumferential stress is responding Within the airway wall and what we see here is that you still even after challenges have finished at day 50 You're still getting us increased in in the airway wall thickening of the airway wall even though Challenges are finished. So there's this sort of period in which things are still going on Even in the absence of challenges So these are all the sorts of things that we can look at with this model and in combination with the mouse model experiment We might be able to identify the sort of underlying mechanisms that might be driving What's going on? So that's the sort of idea of this work, which is very much in progress and these are very preliminary results So I don't want to I don't want to Speculate too much on what's going on at the moment. So I'll just I'll just skip to my acknowledgments and say that This is essentially work The first part of the talk was essentially all work by Jonathan Hiance was a student at the time The the second part of my talk is all is work essentially by Andrew and Andrew Billok and Michael Hill and then I've got other collaborators in both mathematical sciences and all of the respiratory medicine people running the over mouse model and then my funding There as well. So I'll just stop there because I think Okay, Bindi. Thank you very much for this very comprehensive description and So I think that's that's a that's a very nice example and how you cope with indeed complexity and rationalizing it and then further then couple it with with evidences and then use the model so as a not as a predictive much much more as an exploration as an explorative tool and which has And in hand with was experimentalist and medical doctors. So it's it's very nice example of that So other questions Hi In your model The agent that triggers the inflammatory status is always considered something external or there might be like an endogenous state In yes, we think it's always External most of the evidence associated with asthma is that it is external Driven usually by things like I mean the biggest thing these days seems to be things like pollution But at the same time if you're allergic if you have allergic asthma, it'll be things like Things like pollen that sort of stuff, but yes, it's extrinsic Yeah Thank you very much for the really interesting talk And I also very much like the fact that you're trying to couple these two temporal scales It's where you see like the acute effect and what it has on the Longer scale for remodeling which is I think something we should try to do much much more because that's relevant in the clinic in the end I was just wondering it's like one of the things that you said is like while you presented in a way as 2d Simulations, but you said that your fiber Distribution is a little bit like spiral like within the airways So I was wondering if there's like a differential change in in the radial versus longitudinal Forces remodeling and things like that and then partially related to that It's like when you say like a deep breath might be important whether a diaphragmatic versus a thoracic deep breath Might make a difference on whether you can see these differences Yeah, that's actually a really good point the so Yes, I've presented it as a 1d thing everything is is purely a function of radius, but we do see changes in longitudinal stresses definitely because it's in plane strain But you're totally right when we do a deep breath for instance. We've got on a different project. We've got some CT images for the start of a breath and the end of a breath and we've reconstructed the the airways and what we find is sure enough you get a lengthening of course of the airways along with dilation of the airway and We're just in the process of trying to understand how this model responds when you have lengthening of the airway at the same time And but the the the the complicating factor is that the lengthening And the dilation are related to the transmittal pressure. So so So whereas most most models of this kind you specify in advance what your axial stress stretches and then see a well what here's what happens But here it's all it's all connected through that transmittal pressure or transpulmonary pressure, of course so yeah, so we're still in very early stages of looking at that and What we've I'm trying to think what we found so far is that That lengthening Affects the bronchodilation as well To and in some counter-intuitive ways, and we're not a hundred percent sure how much of that is is actually Physiological yet, so and how much do you think there would be the influence of the vasculature with regard to the airways Can you model them totally separately or do you need to model them coupled? So I guess it depends on the question you're asking so of course for gas transfer that do things are intimately related, but in terms of purely thinking about the how the smooth muscle in the airways working and the bronchodilation they're somewhat separate, but that There is one aspect of it in terms of remodeling, so it seems that during remodeling you also get increased Vasculature around the airways as well So obviously that's going to have an effect then on how much inflammatory mediator comes through as well So so there is obviously connections there But I think that's maybe more of the longer term stuff And also when you look at the vasculature probably on the smallest level the pressure Gradient over the airways will be determined by the vasculature But it's probably then mainly the larger airways which are the most determined No, or I'm not completely sure so do the small airways also contract in a similar like the alveola. Oh, right No, no, no, so the only independent so the alveola I tend to have no smooth muscle in them any way So that's all that's all of the transmittal pressure Transparmory pressure goes into expanding most of the alveola. So, yeah, yeah, there's not much smooth muscle beyond the Yeah, the actual terminal just lost small question How much influence is there from the shear stresses that come from the air kind of circulation? So so the actual so the shear stresses are really really small because it's air rather than blood so but So far nobody's really looked at whether even those small shear stresses might be having some effect It may be that's that the epithelium are tuned epithelial cells are tuned to those small shear stresses So far they've been completely neglected in on in looking at this. It's all essentially been normal normal stresses Well, I do have a couple of couple of questions If I understood correctly then in the first part of the talk So the way the way you relate so the active force part of the cell Scale to the to the tissue scale is mostly probabilistic, right? Because do you have these are which is probabilistic so distribution of the different activation of myosin heads So in a sense if you had very few of them then you can think of it in a probabilistic way But when you then have lots and lots of them we can then write down the deterministic equation that I should the partial differential equation that I showed you So it does become deterministic At the level that I'm looking at it If you if you think of tissue damage for example where you would have fiber tick Fiber tick event and loss of capacity of contractility So you you might become even more probabilistic and then you you might Be explained you must be able to explain through the model so So maybe a large diversity of results between different Patient with disease right so so I guess I should have made clear that here of course I'm just assuming all my cells are identical and they're all going to respond in exactly the same way But you're right if I was to go to the level of modeling Individual cells With with some fiber fiber tick change it making fibrosis making changes to some parts of the cells or some Parts of the tissue I should say then yes, you're right. You you would get yeah Exactly as you say yeah That's another thing that I find very nice in those kinds of model is that so of course you're developing the models So according to specific research targets that you have but I think along the way you're treating tools that can be that can be reused for Much more to test much more hypothesis and that's I think that's great strengths of this kind of approaches And another question that I had is that and then second person remodeling part so if you look at if you look at the the chart of interactions that you have so at It's characteristic of complex systems and right in one box. You have much more than Three and three interactions at a time so How are you coping with the resolution of this is that Boolean network? Do you have stochastic distribution of results? so so what we're going to have in terms of The mouse so from the mouse data, we're going to end up having quite a large set of results so for a per mouse something like Of the order of 50 to 60 airways and of course we have n will have n equals 5 mice per Per time point. So the way we're planning to do it is to sample from do a sort of a fit a distribution to those to the input data sample from those and Then generate a set of a set of distribution a set of results Which we also will have some kind of distribution associated with them But all of the underlying stuff is driven by deterministic ODE's So we'll be also run. We'll also look at doing some Monte Carlo simulations where we're randomly Drawing from distributions of parameters as well and in the longer term We're looking at using Bayesian inference type techniques to try and Try and do some parameter inference as well, but that's sort of a sort of longer term So maybe if there is no physical question then we can move on So thank you again