Finite Element Analysis (FEA)

Most of the simulations that I have performed were related to solid mechanics.  The basic idea of FEA is to use a base geometry and decimate the shape in to finite elements (smaller shapes that make up the larger geometry) <- way to use the word in the definition.  The interaction between these finite elements and an external load can be calculated using numerical integration.  However, there is a little more to performing simulations.

Every simulation needs:

  • Geometry that represents object of interest (in my case, AAA geometries from 13 aneurysms).  Geometries can be 1D, 2D or 3D.
  • Element Type:  There has been significant work to develop and create element types for various applications.  When decimating geometries element type/choice is important as well as what type of problem that is being solved.  
  • Material Model, how does the material of the object interact when subject to loads?  Most of these material models come from experimental tests that can be curve-fitted or assumed to behave linearly.  There is an entire field dedicated to developing material models for various types of materials and biological soft tissues.  The idea is that the better the material model represents the material behavior, the better the simulation.  
  • Boundary Conditions generally describes how the problem/simulation is set up.  Boundary conditions include any force/loading scenario and any constraints that are needed to hold the geometry in place.  For example, I constrained the top and bottom (distal/proximal) points of each AAA model so that they couldn't move (constrained both rotation and translation).  If you don't constrain the geometry, the problem is not solvable. The AAA geometry was subject to a pressure load of 120 mmHg.  

AAA Finite Element Analysis

Here is an example of an abdominal aortic aneurysm under ideal systolic pressure (120 mmHg).  This model has different thicknesses and material properties at each point (which is special in itself, I claim:)).  This model can only be produced if we have post-mortem measurements of wall thicknesses and material properties.  CT and MRI scanners do not have high enough resolution to capture accurate wall thickness heterogeneity.  

Max Principal Stress in an unruptured AAA