It depends on your simulation, if the vessel undergoes very little strain (~2% or so) you can model them using elastic material itself. If its higher then you must use some non-linear material models like ogden or mooney rivlin

It depends on your simulation, if the vessel undergoes very little strain (~2% or so) you can model them using elastic material itself. If its higher then you must use some non-linear material models like ogden or mooney rivlin

Yes it depends on your simulation, the type of blood vessel etc. but more up to date non linear models account for anisotropic properties ( fibre reinforced tissue). i.e Holzapfel. Ansys 14. Otherwise Mooney-Rivlin & Ogden are good.

Thanks for both of you Govinda and Paul. I am working with abdominal aorta which having more strain due to energy from the main blood vessel flow in the body. The interrelation between fluid and solid are really big concern in choosing the right material properties.

I have some studies on rat aorta material properties (natural frequency, dynamic modulus of elasticity, coefficient of viscosity). These are dependent on the intraluminal pressure in the physiologically normal range.

Thank you Mariya for your sharing

You may wish to consider whether the intraluminal pressure should be modeled statically or dynamically. By dynamically I mean time varying pressure that simulates how pressure varied with pulse stages. Presumably maximum pressure would occur immediately post-diastole, and minimum pressure between two diastoles. The former would be considerably simpler to implement, while the latter would be substantially more accurate, particularly when modeling aorta properties and function. .

Ian: I planned to dynamically model the pressure based on actual pulse waveform which probably using pressure on two diastoles as you mentioned above. But in term of accuracy, how significant are they in determining aorta properties in overall?

Two good starting places for this and related information:

https://en.wikipedia.org/wiki/Blood_viscosity

https://en.wikipedia.org/wiki/Hemodynamics

both article cite a number of journal and book publications.

Abd Halim, Choice of the artery model need to be based on the type of simulation you are planning. Since you plan to work on abdominal / thoracic aorta, it would be appropriate to choose a nonlinear model. the deformation is likely to be larger than 2% and could end up as high as 15% in certain cases, especially when you are interested in aneurysm models. You may look at the following article. This gives a reasonable basis for the choice of the model.

http://lamp.tugraz.at/~karl/verlagspdf/sommer.pdf

Thanks Daniels and Muraleedharan for your interested resource links!

you can look for it in the literature... there are a lot of works about it...i can send you one review on that if you wish...Send me a request i will send you... ([email protected])

The mathematical models available for pressure gradient wave form in different arteries are not appropriate. I find the book "McDonald's Blood flow in arteries : Theoretical, Experimental and Clinical Principles" by Nicholas and Rourke (5th Edition, Oxford University Press, 2005) as an excellent resource of information. To be precise, most of the articles model the pressure gradient wave form as a constant term superimposed with the cosine wave form : Ao + A1 cos(omega * t ). But, McDonald and Womersley have categorically established during 1955-1960 that sufficient number of harmonics in the Fourier Series Expansion of pulsatile wave form of pressure gradient should be considered to get realistic results. In our recent work, we have taken pressure gradient wave from of Femoral, Brachial and Pulmonary Artery available in the literature and digitized the wave form and developed Fourier Series Expansion with nearly 50 to 60 Harmonics and analyzed the blood flow in the respective arteries. We have neglected, of course, the elastic nature of the arterial walls and considered them as rigid, to begin with, but considered the walls to be made of porous medium and employed Darcy Law to model the flow within the walls along with BJ interfacial conditions. The paper has been communicated and it is under review. Our results reflect that it is essential to consider to sufficient number of harmonics and the simple model stated above which is very widely used is incapable of capturing the pulsatile nature of blood flow. This is more so in calculating the WSS and OSI to analyze the possibility of formation of atherosclerosis. I will only be happy to know any good work on modeling the elastic nature of the walls (preferably a linear model).

The arterial wall is a multi-layer material, with each layer having different properties. In the most sofisticated aproaches, this complexity is handled by having a single constitutive law for all layers, and using different sets of parameters for each. In general this is a valid approach, because the behavior is essentially the same with chanes in the anisotropy direction, which is generally accepted to be governed by the collagen content (up to 95% in the adventitia, around 30-40% in the media, less than 50-60% in the intima --these are total values, not just type I).

So in order to characterize the material properly you need layer-wise properties, and (at least) 2 testing directions, usually tension tests in axial and circumferential directions, but could also be stretch-inflation tests with or without torsion.

Apart from the anisotropy (which must be included in the constitutive model if you want to have meaningful simulations), you need to count the nonlinearity of the material (strain stiffening, due to collagen fiber recruitment). There's also the well-known residual stress of the vessel, which is generally higher in elastic than in muscular vessels.

If you are lucky, you will find literature on your artery of interest, with the whole stress-strain curve, which you can use to fit the material model of interest. Other publications report a "typical" curve and the fit parameters for their samples, without really reporting the goodness-of-fit or making the actual data available. The best places to start are Holzapfel, Humphrey and Sacks (these are 3 separate groups), then follow the links leading to and from them.

As Cacho-Nerin explains the core problem is blood vessels are not materials, they are complex structures. Therefore they do not really have material properties. This is true in general for tissues--e.g. bone, ligament, cartilage. However, it can be convenient for research and design purposes to test tissue specimens and assume their structures are sufficiently homogenous to calculate material properties based on force/displacement data and specimen dimensions. Even then it is absolutely essential to recognize (at minimum) that the specimens are viscoelastic. Therefore, for example, they do not exhibit a Young's modulus. In general the stiffness and strength of tissue specimens is highly dependent on strain rate or cyclic displacement rate. There are lots of (mostly old) publications reporting e.g. Young's Modulus for tissues. That does NOT mean the tissue has this property. It just means the people doing the work (and the editors and reviewers for the journal) did not (at the time of publication) sufficiently understand tissue mechanics.

Gerhard Holzapfel (composite vessel wall models) and Charles Peskin (fiber model of arbitrary elastic material) done extensive research in this field. You also may look at my group's publications in 2012 dealing with elastic models implementation for 1D haemodynamics. All this can be easily found through Internet.