FEM Simluations of Shear Waves in the Heart Wall
With knowledge of the stiffness of the heart wall, medical personnel can diagnose patients' heart condition. The stiffness of the heart can be altered, e.g. due to a heart attack. New ultrasound technology allows for in vivo observation of shear waves that propagate in the heart wall due to aortic-valve closure. Our main objective was to simulate this shear wave propagation along the heart wall with the help of the finite element method (FEM). We wanted to investigate whether we could obtain an estimate of the stiffness, based on measured shear wave speeds, in a heart wall modeled with a transversely isotropic material. To achieve this objective, we first made the following FEM models that we validated with plane wave theory:
- Plane Wave Model - A simple two-dimensional model with the transversely isotropic material implemented, which simulates plane wave propagation. The results agreed excellently with theory (less than 2% discrepancy).
- Finite-sized Wave Model - A two-dimensional transversely isotropic model that has a finite-sized source. We observed that plane wave theory gave satisfactory predictions for waves that propagate from the source (less than 6% discrepancy).
Then models that can simulate wave propagation down the heart wall were made:
- Curved Model - A three-dimensional model, which can represent a part of the heart wall. The model is made for investigation of the effect of curvature on wave speed, and we found that change in curvature only slightly affects the wave speed for both an isotropic and the transversely isotropic material.
- Truncated Ellipsoid Model - A three-dimensional model, which is a simple representation of the left ventricle. It was observed that the shear wave speed varied (plus/minus 5% from an average value) through the thickness of the model because of the transversely isotropic material implemented. We argue that current ultrasound technology is probably not able to capture this variation due to relatively high measuring uncertainty. Furthermore, we suggest that an assumption of isotropy can be acceptable even when the transversely isotropic material is implemented. This allows us to make an estimate of the stiffness of the model.
Other important results:
- We present novel analytical expressions for the material displacement vectors for plane waves that propagate in transversely isotropic media.
- A new type of characteristic surfaces that describe the relation between shear wave speed, propagation direction and stiffness is presented.
In conclusion, we show how we can investigate details of the wave propagation with the aid of the finite element method.
Place, publisher, year, edition, pages
Institutt for konstruksjonsteknikk , 2013. , 143 p.
IdentifiersURN: urn:nbn:no:ntnu:diva-22507Local ID: ntnudaim:8800OAI: oai:DiVA.org:ntnu-22507DiVA: diva2:649751
Hellevik, Leif Rune, ProfessorProt, Victorien