Cardiovascular mathematics
Formal Metadata
Title 
Cardiovascular mathematics

Title of Series  
Number of Parts 
33

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License 
CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Release Date 
2006

Language 
English

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Subject Area  
Abstract 
We introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a better understanding of cardiovascular physiopathology.

Keywords  cardiovascular mathematics mathematical modeling fluid dynamics NavierStokes equations numerical approximation finite element method differential equations 
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The storms E for sobered aiming here I'm yawning quest and my water and great pleasure to introduce last plenary speaker you but that started as careers body of education early research and any mood around been professor in hinders Minnesota Minneapolis and now has a chair in modeling and scientific computing ATP event court but it did meet in Lausanne is also a professor in America analysis body technical wearing a dark hair and a research field or on furious numerical analysis of portion differential equation is a rich body work stretching from fundamental results in fun an element in Specter methods domain decomposition and his apply that to a variety of all Different fields so 1 Chelios would hear about physiology and there's another example for example could be aired optimal design or saleable yeah I assume that's why Piazza Warner doctorate in the name of engineering Today's told it would be A party rescued mathematics aren't you eat how over loads centers Another the media said comedy for a years a great thought about because most of the fanatics and that you have Problem that will do face is how to said up command to carry out the analysis of the kind was just the tip of a mail arteries and veins and of course are now Where you face a program from complications that you were busy the government From 1 side then You still need to compare the results of my problem with try spring thaw they ought to make sure that what our computing is suspended so money although like All enjoyment joy of About 40 Not that Rolled to rub on van that you need wages The described visit that you are still going on these places All are based on Fire Chief Richard Richards You have to to ah carry organizers of the because of mature Mrs. boss brings and A quite or do you have to work But used Because the partial Richard places do not have a closed form solution so you leaders about a matter that allows you to go to computer sold oppose the adjusted results but was result which may have very complex called for birds form you need But true boss crosses that need to visualize where we represent them in order that they could be from 1 side compatible with this sprained ankle results from their side that can be shoulder Your counterpart said The doctor recognition so A very poor but Clark thesis that competitors for says And the people there results is businesses that you have a different cargo from They you have In view of all our work of Charles Taylor trauma investigating a real patient Apple by is the for you show that you can For strike that you can get Michael striking Our with which represent not and then you can cope with around food additives and trying to end up with results which parts Those that you put our hopefully have theory of creation or otherwise Mr. with results from literature But the results of your factory that assessed centered on a variety of ways Vendor Then you at the end of the tour the correct otherwise Trade and that you would say that again and again that he often before had a reliable that you have to to be very tough now have these pictures can provided that I know of any other application of body these other than gold quite medicine but many other cases Classical field of Virginia physics Your friend Monday Bob estimated difficulty here is that the date that you want to use a R They tell me chart provided by the leadership So you have they found the get from medical investigations And that some colleagues
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The pen interface So friendly before your program as a full leading O'Neill the interface and we believe you do Yap classical stack worker equation where we have By and operator equation Which is the Mr. Ontario the cooler than the the sought to achieve Ward said that is misplaced resorted to reward and And was struck that value for money and and we proceed that there's a should that in all these permission to use all the numbers of separation you Is a source in the pot Then you go through the normal stresses cautious dresses and is mystical . The food product sold this season including on the matter is known in his case before the structure will from allow which is Yukon peeled via a solution on the hour structured vision and then You go to the Prices because prices For the structure of and these 2 basic imported which is just part of our structure part the food but you have to to liquidate bound for the United and not with that great British sold so I only being formulated the photo essay where them all you on the interface now of the sort that the sword Photographic products it class agreed in the for who are Computers cell and computers at the end of the precondition this is a critical part building conditions given that and given that he could dish of foreign respect is breaker Did you might speaking and that you will you a lot never be able to adopt procedure so you have to pick up This is what Commission we The year is a shot of the that want a for the twoweek and is wanted for the structure And dignity in versus South and some not And that we wait and mice with waterways and is being of our Oprah soul roughly speaking at every step we have restored independence the food coated from 1 side and cycle their site and we combined to stresses that we have had And proceed according to point never Televisa solutions that to get over for is s carotid bifurcation and a of the best under the action on supporting next face and the same situation but now you see the pony from a show the water assault self chorus 30 different values to intensity density of fell body appointed vector field of endeavor
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Arrows indicate that the Vectra stated velocity vector Our so but he made major
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Problem here and the problem is that Due to the young section of cost of At the polls so you see here is a section of their ecologically just breaking down It's tough Just for the purpose of presenting the results and want to see here is that is a very strong Quebec affection which is due to the fact that these Treatment of the outflow is not the to correct 1st of all these tiled floor is not a physical out is an artificial on the way to solve our problems and their source that by using a we stress conditions on the conditions Bob and Absorbing rather conditions for the best part is enough for the existence of modification but not enough to prevent these waste of affected We are sort of incompressible fluid equations yet We have Back at reflection because of the Apple supply nature because of the fact that the before so I'll do surely not to do that you have at least the late leader's restored want their mother conditions which is not easy for you try to see these As part of the old system talking bad these The more general and trying to see how he when he all the AllStar bodies while you got to do with his scale which is due to the fact that it is motivated by the fact that they Circulatory system is complex What made the offer on behalf of Boss palatial villa stipulation that different basis The Dara acted in a different manner India about food that makes Features of the different places And also the year structural features are completely different the real number is 34 on right your thought these are negative numbers and use you boys you we become sold 1st of all the always North urban unless some specific conditions 92 relating stenosis or a tour with 20 of the Golden Bears 1990 or not not a blood disease Karate situations and you have basis because of a single or double of as many as 30 kind about 9 are acts of from Front of can't said he thought to be tried for the AllStar so here Constant abiding scale has relied for the poll being a specific debate is 1 that we want to see this part of the global nature And then boarded the global level to get a feel like in a few days The most important fund and then we go to a global level please wary of the country's so
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And we still Is this environment where just for the local traditional and then you like to work toward a level where More We privilege most important arteries and veins and then down to India zeal that where we have 3rd level where where we have have and the that there was not built into the village of the here want to use 1 additional Pointer Sisters and you that additional ordered Richard British So A dramatic but and is it the way ports Said Sketch for is to Several by 4 days of course of the war between now and when you have 20 But what we was 1 of these Lot equation and the sheer weight of capillaries light to regard them as being Analogs of at because in that case would be able to use That 5 or in French patients avoid so we go from thing want to wrap this year You can carry out Type of simplification According to different strategies but strategist 1 way is to use the public Make it sound so that figure 14th Bar and then you not really that is that there are between your system with some you can do you can arise Placido on average quality teas and in that case you day This year the assistance body facial provisions and that will let you have to to keep in mind that You are some The year real field to our ideals and this year the dictionary shouldn't see the pressure As a food than what is The agreement on board the of current not supposedly of resistance Blood yourself what compliance capacity and that in this case you are able to describe the behavior of a very complex network of capillaries use days It all Let us know what can you say they used to onedimensional we want You can easily simulated single pieces of art because accounting rules 4 We you can go down like standard of the Lord so if you were to join different bases Like Legal then that you can use 1 additional boulders account for the petitioner waves but that much actually we can account for use Complex Seasonal 55 the most important are based these are those that have seen the picture How did not demand Please And that you can sort of your network of Audit equations These set of broadens and the head A global picture of part of the stipulation that you can go
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At a lower scale the racialist Kelly to divide your body the compartment to set not editor since that for the compartment which announced that ends up with a system of division which I think is French regulations And You can go to a dissertation pretty from parts of the body so was again idea used to wear He then there At the majority of initial assistant freezes the bifurcation or for a coronary bypass then that permeated with a onedimensional here And there and and being Many of As you know the additional networks like in seat but very well you see that the article did charity would just taking the pressure that some base Cases but that after the old system and this year he said twodimensional coronary bypass Which is sold by UNESCO and even out from siege generated by these Google but what you do to assist and these are that matters so this is is such couple guys we these by meant as we cure at least
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But the logic laugh let's say that reflects that sand The system case that city because there's so that we don't want station and waves that pressure of From by gave safely It was initially stage Start use a couple of
41:35
The cup engulfed you want a disease you a bifurcated travel visas said carotid artery 1 a station that you don't hear about is there and and got them back Uzbek prefecture said For the same problem here the pressure wave at you have a sack want initially station is another 1 of which is not important for graphic workers but is he
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Leading the main thing going Would you wanted it to assist in the U.S. of our are few references 1st because important mission that the 1st day there is a wonderful from pointer number of who actually provided he is or
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Which is still popular United and together for us I have a duty to give an investigation of that no 1 should have their day in the city of Paris They were Where is I am beginning with equal dependence of Wonder system from debate that At least the opening time aggressively shown in half For 1 B by yeah change a key member of the church as a particularly strong these coupling that exist as regards global cities of some body base without the special conditions on that figure but interfaces because of the absence of probe would would borders have The different borders that I have not seen you would want to do what he would do with you see and hear music that I wanted Merkel told port call for our businesses that Already a substantial part of the investigation of Only a piece of your investigation because what would suffice Of situation than The actually ever more this for the harm that had not shown here but these turned with investigation now to be more if he wants to those who have the nervous system theoretical apartment like The splurge existed under arrest delivery system and then this not talking about crap book column about you Major that fractures but they're talking about These people are you have to account for the public the way the body at specific care out there on physiology of specific kept out extra but did the companies that have developed O'Neal Part should be capable of Call for the camera effect and the efforts that had a very strong team but for the circulation order if you try to investigate the behavior of blood that there people I carry you know at lest that find completed different Peter agenda on the athletes For people who are under severe conditions set up a final parties post crosses the modern aviation did you will Correctly So far I've seen plenty of But my favorite but now would like to to see whether with these equations can try to solve some problems which are What's that Vote for our doctors not many nations the yet again that the Mathematica of last year the 1st 1 is that an about it We don't go even if that solutions that you can have of course but sometimes have An exact solution of simplified program for compared with mental problems or other results Comparing competitor we despite the results people or and then I learned that had been defined assessment by medical doctors and patients and that I'm not going to be there About the black prison official suspect need to our end up with That's when it passed a note of the Colombia's the doctors The body correct I'm simply a nation B Francona on modifications Let Where suggested last nite by doctors and Each weekend we see the Potential of these steps will order sort as he opened the 1st culpability for a corporate data on his ears The sector The 2nd 1 is that of a funny reasons And the and the money is spent 4 at the doctor said that formerly shall we say a collaboration with a great was because London and the Allamakee about the structure of the political debate on that because Foundation Well These Warwick Here the problems that we have The 4 2 defeat at a children's with only 1 called Seoul form that it would not be possible to our studies smaller situation between them Called the heart and the lungs Soviet bloc could not be accepted and China's for these new ways to survive on less that these pathology is the fact that at had a very early stage 5th was and then you are very immediately operated from Seoul be here are due Clearly Surgical approaches the first one visible says the that I wanted to create bridge between the ascending or Can't be somewhere he carries so these descending North and that Right Woodyard to adjust sucking blood from To bring year About plants and the heat is another operation that bull You was every very specialized places for the 2nd operation take now They that strong You know we need 80 guard north from the city north Seoul divide found that sausage sense shot So do orders question is which 1 performs better and there As you can engage in these if we there is progress and said Questions is font of issue that it is clear that 1 is better than the others hoping to these CDs or 10 years is not the way in order to make sure that There are no longer You were Books you by We make sure that you are Keep your 18 down The EU other parts of the body to break the current your part of divided so You have to and not be that kind of fuel conservation and to flow distribution of the and that in order to guarantee the board vetoed a process your body I keep working properly I still had a sack McChrystal On the CD for the initial that media choice of the radius of the Charlotte and that Make sure that Balance He sporadic and The Coralee flags scanned and the right level These I work will be dish of the way Only got an fact which is 4 times His only got have for tea but the problem here Is that he still got Is mathematical got that It's But I don't think drill and doubts about which are data on how do we provide that is evolved is no way to provide abundant not needed for so there's no way I get Which kind of thing We should put there to be respectful of the apartment major problem you know always working with an eye on Clark solution situation is sensitive to our evened About condition and of course but also for the job So we have seen that the assistant John you now enjoy writing off problem is the child these big global 0 Nacional that describe the rest of the situation interaction between Fiji and and is usually System 390 stalks that their sees them off
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We furnish algebraic equations and that These way you don't need to force but it is not a condition can automatically for the environment and did not a need for a point here is that mechanism sold shall was providing pernicious also
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Do not out 40 purchases and that we are very proud of these type of investigation because for the the 1st time a new medical stored there was able to see that There is shunned these Flory burst that was observed by the doctors But Mr. But must never produced before due to the mistreatment of of bothered conditions so that we can Better shape the of the Sharm seems to to Borup Reliable a physical data to compare the command of the
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Is this set the publication and dies as would said about the reasons are now may be made Monday by the horse rely on which is That's the most important in Italy for our security treatment of facts about the reasons and and see this It is the policy of these projects so centered the of issues arising On the brink what you see here is read from the lower part and peace accords less We just get here this Grove loyalists There 2 were dispatched to distribute the blood coming from of the county to the Brady so it as a cost of 4 times And that is a very is smart system because it can just about you in those cases where you have closure on specific pieces so Quite often on nearly staff subject rapture and Casey they have led to a set of our courageous and that and it's estimated that 5 per cent of the population some type of other areas of the brain and are Completely out of the match general will Also Found in deciding Laura forum Understanding Dora Our audibly There are few and not undergoing a specific their hair and key collecting investigations said about the project wanted to highlight via rolled off a vast morphology Where The coalition the morphology and of of from presence of Development of arms about reasons and that the method that was used Is that a new merit in the office of these because investigation you might litigation latest addition put up with some results could Provide Doctors with that I understand sold br Jubilee preprocessing disease Dad Original vessel in area they should have been working on 65 patients I'm very difficult Levy data from these are vote they died there are very few together have sold There are several ways Fertilizer morphological Sat out 2 additional delays are bicyclists then we Look at the radius of the vast much described here we 125 each bifurcation we have Computer this to retrieve his Eliza French and then By branch till processing that have to carry out the order to make sure that the working glad that have you you can classified kind of patience for the kind of a series of these and at that you have these enlargement of part of the RTC because by German later these pressure field Because relations but these are the velocity streamlines obsessing on terrorism and Beasley said The way you can track the particles Get areas and 1 very important Franca here he's arrested this time again Maddox and doctors are very found a head to head
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A quantitative to to CompuAdd that he did it as a kind of plot because these
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Provides a measure of 5 DM capability Of state still failed to lure not exert resisters or for a product that was just as political India will be so face and that and eventually decree Raptors
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These run 11 on investigation and What You Can get visas Quiet Ford To us surprising results and use resolved because on the basis of these observations what We have seen is that there are no reasons that do not distributed randomly they tend to be fair to a specific site and size are just don't Regions of Knoxville Curvature of Dr The carotid artery still seems that Davies said But thanks very Clear correlation between the his behavior and uh which is affected by the hour structure of our tour the curvature of hope for the best war and the presence I knew and not on the basis of these results said now doctors at the hospital are investigating because their patients and try to see you very precisely that our cultivation of these type Our conjectures I'm going to conclude that Think I've been to men and 5 women in 3 minutes carried by you talked about that Project You to the dragon what That is a network that that to put it on to restore a shop flocks helped restore the Lubin say you have a narrow we get sureties but do you figure balloon and he said
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Faking that understand that deployed And I they have restored original sold stand A very strong interaction with a dependable car of the of war and actually derecognize of the body room And and and and they Actually by by production of found the Patiala stem cell of a few not sold Did you will see that technology in the yard This weekend She will use a coating of victory or out at you from a precepts so the news that have A coating We and And I found the drug which is released and that and other for because a rookie with different scale and scale of the wall thickness which is of the order 1 millimeter and 5 micron process and you have 3 phases of Saudi phase where The drug is bound to the point where the coaching because phase where the appointments while you free interface and if you could face when so fast and that we have a bulletin described as a Microsoft for out there about that they fate have to more so than fusion and advection process you with the which is provided by not equations then you have the favored because they in effect is and if critical quantities
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The dependent upon the characteristics and and edited by the Sevastopol soul you're trying to use and Michael descriptions based on stochastic approach and the macro descriptions based on and defray shows a French official said Saturday in a country that is just a stunned the job or out around And for these very simple piece of stand out you need on board with 20 years of elements that voting advantages of elements into what the best They medical bulletin boards on single spent so if sort the simplified have process What define model and actually did Kohl is not pursue as international body but just as it plays Where you have to adjust reflects so reworking border for frozen ducks and that we avoid told the problem Dakota these make assimilation these rag release of separating from our stand and that least that I'm not plasma pressure for a signal that it just the fine with realistic model And these That They stand 6 pack up and leave Drive soul a Kelly legal problems here You now borders varieties and to quick to quickly you made about 24 hours and this will be respected proliferation UK Time of proliferation of indicated sold The challenge today is to produce told King said That allow these movies tonight with way Norway and that you have several ways of that But you can't modify the formal the coaching aura Creating multimedia will define before the title of the project and that it is an example of where You have to different approaches This is a uniform coating And After while they each view Concentration as busy after today's it stands the best too fast and then what is called A traffic cop but I can because you have 3 different layers of like a cup of coffee with different interfaces and that these sequentially and what is he Is that after 3 days that via diffusion process he Watching Our property and these challenge tried to make peace even nowhere in order to make sure that these effect on diffusion of 13 other substances that takes an order off 4 legs To be Effective enough to contrast the at released of but deep production on the from officials so the conclusion is that that I think these said Investigation these countries should useful to understand better the basic logic process is basic research after ought to assess needs to produce These indicators for the large but prizes and these issues for and that MSAs 2 2 to help developing that a Pentagon source of funding and Optimization and A shape of authorization from followed his office U.N That for is that there is a good opportunity that you would like to see that as suggested by idea Culprits nature of the from 2 and conclude by acknowledging that the main bodies lots of technical and get fed up with different players And that of the collaborators now we are working on every day and thank you very much for your country