Myocardium and the Holzapfel equation

[JHoward_UNT]

Hello ,I was wondering if anyone could help clear up some of my confusion on this. I'm trying to create an accurate representation of the myocardium using correct material definitions and parameters of the myocardium, and the myocardium is often described as anisotropic hyperelastic which is why I choose to use the Holzapfel equation. In Abaqus, the Holzapfel equation is defined using variables such as c10,k1,k2, kappa and D. However, everywhere else the Holzapfel equation is defined with variables such as afs,bfs,as,bs,a,b,af and bf and this is the area of my confusion, because their both defined as the strain energy formula for the Holzapfel equation but their variables are different as well as their variable definitions. Thank you.

 

[Mustaine3]

The definition that Abaqus uses is described in the documentation. In there you can see the parameters you have to provide.

Compare this to the definitions you find in other publications.

 

[FEA way]

Abaqus often uses different symbols for coefficients in material models. But the documentation chapters "Anisotropic hyperelastic behavior" (Materials Guide) and "Anisotropic hyperelastic material behavior" (Theory Guide) should let you clear this up. Apart from that check the benchmark problem "Anisotropic hyperelastic modeling of arterial layers".

Also, there are some scientific articles that use Holzapfel model in Abaqus for human cardiac tissue modelling and keep the same symbol convention. For example these two:
- "On the AIC‑based model reduction for the general Holzapfel–Ogden myocardial constitutive law" D. Guan et al.
- "Parameter estimation in a Holzapfel–Ogden law for healthy myocardium" H. Gao et al.

 

[IceBreakerSours]

Look at the citation in the Abaqus manuals - they must be citing the article from 2006. The myocardial constants you are running into in the academic literature are based off of Holzapfel and Ogden's publications after 2009, which generalize the 2006 formulation a bit. You could either take the v/uanisohyper code from old manuals for HGO2006, edit it to extend it to 2009/2015.. or use FEBio. Either way, it is going to be a non-trivial undertaking if you have no background in anisotropic hyperelasticity but the FEBio path might be easier because you only have to familiarize yourself with the user interface.

The bigger question for you is - do you know why you *need* the degree of anisotropy? If you are modeling the myocardium to ultimately compare with pressure-volume loops, I bet even a simple hyperelastic model will do just fine.

*********************************************************
Are you new to this forum? If so, please read these FAQs:

http://www.eng-tips.com/faqs.cfm?fid=376

http://www.eng-tips.com/faqs.cfm?fid=1083