Computational Biomechanics

 

Finite Element Analysis

Most of the simulations that I have performed are related to solid mechanics. The basic idea of FEA or stress analysis is to use the shape of an object and create smaller pieces from it (elements). 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 Stress 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.

Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) are simply flow simulations that are based on Mathematical equations. I am not claiming to be an expert in the Navier-Stokes governing equations.  I took several courses that discussed the derivations (with different assumptions) and what each component means.  It is interesting because the NS equation were not adequately solveable until the 'computer' age.  My Cardiovascular Fluid Dynamics, Professor K.B. Chandran pointed out the intricacies/difficulties of derivation (including some painful derivations on exams).

The components of a 3D flow simulation involve a surface mesh (2D), a volumetric mesh (3D) and boundary conditions (wall, velocity-inlet and pressure outlets and a whole host of other parameters).  We aren't just after pretty pictures and animations, but what the 'numbers' mean.  

Post-Processing of various indices is the most important step in interpreting the results.  Are we looking for flow drops, turbulence, wall-shear stress, pressure drops, vortices, flow re-circulation?  There is a whole suite of output variables that we have access to in ANSYS FLUENT.  

With that said, I have enjoyed implementing simulations that have 'real-world' implications.  I don't claim to be a master at CFD, but I try my best to ensure that the assumptions we make are acceptable.  This has opened the door to projects that I would never have been involved with.

Neonatal Hypoplastic Arch

This is a cardiovascular disease found in infants that affects the blood flow by a severe narrowing in the aortic arch.  The current repair method is shown (from the Oxford Journal).  Here is a brief description of the procedure:

A - Preoperative geometry.  The narrowing of the aortic arch is evident.

B - Cardio-thoracic surgeon will cut on the dotted lines.  

C - F:  The descending aorta is free to move in its new location closer to the ascending aorta.  The surgeon will suture the two pieces together.  The new geometry of the ascending aorta/descending aorta is shown in 'F'.  The arch resembles a gothic arch.  

Problems arise due to the gothic arch.  Fibrosis and clotting occurs in the arch region as the patient continues to grow.  This project was trying to assess alternative methods for this repair (and to see if it was 'better').  

TETRALOGY OF FALLOT

We had a pediatric cardiology 3rd year Fellow by the name of Dr. Govinda Paudel who has now finished his 4th year at the Mayo Clinic.  While he was researching in our lab, he came up with an idea to investigate a congenital disease known as the Tetrology of Fallot (TOF) using computational models.  

TOF is a heart defect that features four problems (AHA)

Often times a surgeon will elect to repair a stenosis (a narrowing of the blood vessel) in the left or right pulmonary artery (LPA and RPA).  However, the treatment may not alleviate the blood flow problem due to a high lung resistance.  The blood flow will start to flow backwards or start to 'regurgitate' in either the LPA or RPA if this is the case.

The 'big' idea was to create an idealized computational fluid dynamics simulation that investigates the relationship between stenosis and vascular resistance.  I helped put a computational model together that had physiological vascular lung resistance simulated by using porous media. We tweaked the stenosis (0%, 25%, 50% and 75%) while adjusting the vascular resistance (1x, 2x, 3x, 4x, and 5x normal vascular resistance).

We are hoping to put together a chart that a physician could use to determine if it is more likely that the poor blood flow is due to the stenosis or a high vascular resistance.  

As of now we have a paper in the word work and couple of abstracts, I'll update this page as we continue to be updated on our progress.  There is more left to do!