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Estimation of cardiovascular system parameter from real data

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in English book of this is very different public so it's about kind of ostracism along the heart is that of some of the smaller what commissions lies all of this is we use you know what our diseases of the ecological systems of different kind of
diseases 0 information on the basis of this forcing organizers not to the right shape so that the way that the doctors operators that there's some biomarkers we some criteria to define when the this this no danger or not and they can operate in this this case cases the promise that these biomarkers can only be assistance this there a total on pressure to assess if the person is to be pretty so there is that the main goal of the mother mother mother and if it is a tried to assistance markers so this parameter from measurements that they're not interested in this model goal in mind the model shows very small
example have so it is be part of the book the 1st 5 bodies about to modernize the model of blood flow and there is a simple model the 2nd part is about the most promise all glistening Department of the model and there's some very recent it's up to those those desire 1 of the
artifacts so that you know I can model the blogosphere incompressible fluid using the resource questions in 3 D as you will know that you know what analysis questions you want to this in a very so in the two-dimensional way you a measure of the the model can be more on find depend on the Europe Goals you can assign mentors to to solve the blood flow and try to calculate the velocity and pressure at this point of the image this is very nice if you have enough they don't give enough power to this is very nice approach but it's very spaces of picks on time they want to talk about their identity which is cheaper somehow as as one-dimensional model this year
eulogises have the flow around the one-dimensional manifolds convinced that this will be a one-dimensional model of the treaty but and increases are some of the interaction of those cells on each cross section so this a very short description no other variables are the item section because it can change time is the flow rate along the since line in the use of pressure on along the line that you had to read the pressure with the change of our so it's a kind of a simplified model of the interaction between the pressure in the vessel walls the so this form right here means you have pressure change due to changes in our plus nuclear missile system you can make this also is more complicated so this a variables are so flow and pressure so multiple one-dimensional lines so this is it's not even mathematically complicated this model many different ways you to add additional the questions from the the lines meets the sodium of so this not easy mathematically but this is a condition that can solve this much faster and you can have arbitrary complex geometries so let's say you you must also be which falls the so we use it so if it if I were limited so you can just imagine says history of our ASR techniques which is set of variables bitch point of view of the network and the update is every time depending on the operator and the states of interesting so this was a talk about so it's not really the always think about few seconds to solve this kind of model or not it is very important because you want to know in this problem you to solve this there are times when you needed to do this very thousand times and it's important to take 10 seconds on them and maybe but it is still the this point at the end I want to solve assume now you have simple description of my a one-dimensional model which is this 1 here from my state x depends on the state at the time before and some parameters and they have a set of observations which sets and they are from so is a observation operator or the State space age of 7 system plus some noise the main goal of this so I have this model and they want to have a better model which fits from all my observation so as a and B of very commonly known use least-squares OK want all this is my the view of the results and want to find the different peaks at which minimizes cost function so I want minimize In some along the distance between my major and my observations they also want to have them to be close to my results in want of 1 of the difference I want to have also known all the difference between my correct state and my so what users so that the called common filter which is the property of solving this probably the most rational means at each iteration I correct the make my state and my parameter depending on there isn't so side solved the problem but incorrect my state and parameter using some is this course filter because we fit of the model results according to the and submission very does just
that so library on his work so here the counterfeiters that particle because we don't need so many abundant operator to find the name and the way that the feet finds the optimal way so status similar the users of the models list lightning modifies the of 1 time point in time I have my state and my parameter for the for the gasses generated different assessors of model with different parameter values but i propagates this slide by my operator to each of them and then take the results of last 60 error they get from different that so difficult particles and according to this 1 can those statistics and find the optimal correction to they feel federal action for a new state environment of so in the very good points that you if you want to estimate the parameters to only the plus 1 grunts of it's very efficient and do you think Buddhism bias so you can start to each the particle on different processes basically processes 2 of this filter the thing is so this right so he fell on our model for the for a problem and you can use this as a MacBook the figure out what the before and after the 1 that's what it is that modern there since the fifty-second users was of for complex problems so this is all we did is new couple of
examples is the data much of of mind but within the people below are cynical tubes model of the human affairs system and different the to the pub different measurements putting the model so this rule arrows application where they have measured the blood flow and the name of the blood flow and the pressure thus provide the parameters for the model so we could have the geometry and all the physical parameters from the literature and those that have received we can this amazing we don't know and then the parameters describing the the oracle which will be sent to the State party so we start from a very different matter the it is the result so this is this this slightly this parameter in the in the paper and is ratio over time of our submission associated this start from quite different so they also almost 3 times bigger than the beginning and eventually they are very close to the the reference frame so different prevented they given the purposes would not all of them so there are some parameters but this was estimated this because the promise but not upholstered is unique solution to that fundamental manulife is and was so the running with the want to achieve but what we had to take his if the error with respect to the measurement is there's a lot to know this picture shows the blue points are the error we fuse the initial rate of and the red triangles and there after we no for according to however filtering and they're always better and the yellow starts is error user parameters in the paper so you get even that evidence the 1 user provided they provide the purposes of the future works so just minimize the error respect that is a very easy case because there is a the mother was control of is that for all the geometry of the physics is published web if you want to loosen real cases that's
oriented dialogs all nice in time you know geometry money on parameters so what we start to do is to do this but environment the space which all my mother iteration is just so I I have to run a mistake for a time t this is the mystacial be done the set for another patent an observation is just ordered a freighter from of my mn measure will be there are lots of right image this is more robust goes to you can also not something than 5 sample measurements and also because principle if you think about application you want to estimate the document to the pressure the difference between peak and candidates must size or amount to the application as a result of ongoing topic I want to show you some this is results so we had In the case some date of patients in different locations but pressure at different locations that we use this model which is about 120 messes of course you can resist the right model whether views known and also open question but was it which parameters we fix we cannot estimate on PAMI descriptive exams and practice to make things so this all well let's see what we
can do so this is the 1st example so my mother inflow boundary commission which is this the shape and this Parliament try so I can say how much it is the flow rates which are involves of the heart this how long is my youthful my incoming flow with my flow and tried to the broadest parameters is the results so this feature saves 1 parameter so decrease the 1 is increased and what you see in the beside the picture is that so the bias of the primitive worms the strive means that it is not good estimates for the figure pros on estimate of how would be estimated by the blue 1 is is more relevant and is the error with respect to the measure of the times to see decreases for a while but then stays Morris for the
guys this so I tried to make 1 diameter of the inflow and then the success of the so it is not so easy to other the red 1 is this parameter here is this increase before and now syphilis so as to increase the that is what I get the error decreased this course and then the last picture so you can save you if you're not convinced I wish I what is happening with the data so this is all the the yellow all core is the instrument of that we had before and the rule 1 is the data if distinguishes us without using any figure and the red 1 is the summation result after I use my response question is it just with 2 parameters modification of that I get much better reminds us so there it's provides a with the the global to go and for iteration 5 4 can match this even better for you what if I for differences so you can see it's very very the the Senate so reduce the size the the speaker but doesn't get this there's no free press broad because this is higher it more 1 measurement the so we can reduce average of the measure which is the the 1st harmonic so the artist is features that capture the point is if you have you missed many few measurements difficult to assess the front and so that's all of so thank you for
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Metadata

Formal Metadata

Title Estimation of cardiovascular system parameter from real data
Title of Series The Leibniz "Mathematical Modeling and Simulation" (MMS) Days 2017
Author Caiazzo, Alfonso
Contributors Gottfried Wilhelm Leibniz Universität Hannover (LUH)
FIZ Karlsruhe (zbMATH)
License CC Attribution - NonCommercial - NoDerivatives 3.0 Germany:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/21902
Publisher Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
Release Date 2017
Language English
Production Year 2017
Production Place Hannover

Content Metadata

Subject Area Mathematics
Abstract This talks shows preliminary results for the estimation of some parameters regarding the cardiovascular system (e.g., vessel mechanical properties, vasculature resistance) using real patient data. The mathematical model is based on efficient one-dimensional network for the blood flow simulation and on the unscented Kalman filtering for the parameter estimation.

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