Average wall stress in an aneurysm

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SUMMARY

The discussion focuses on calculating the average wall stress in a closed spherical aneurysm, emphasizing the relationship between wall thickness (h) and inner radius (r_i). Participants suggest that the stress is influenced by the blood pressure and the wall thickness, with an equation likely relating these variables inversely. A method to approach the problem involves determining the cross-sectional area of the aneurysm wall and integrating the forces acting on it to derive the stress. The conversation highlights the complexity of the problem, particularly in understanding the forces within the aneurysm walls.

PREREQUISITES
  • Understanding of arterial aneurysms and their mechanics
  • Familiarity with free body diagrams in physics
  • Knowledge of stress and pressure calculations
  • Basic calculus for integration of forces
NEXT STEPS
  • Study the mechanics of arterial aneurysms and their stability
  • Learn how to construct and analyze free body diagrams
  • Explore the relationship between pressure and stress in materials
  • Practice integration techniques for calculating forces in spherical geometries
USEFUL FOR

Medical researchers, biomedical engineers, and students studying vascular mechanics or materials science will benefit from this discussion, particularly those focused on aneurysm analysis and related stress calculations.

tandoorichicken
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Hints, please?

"An arterial aneurysm is a life threatening condition associated with a balloon like expansion of a local segment of an artery. Using a free body diagram determine the average wall stresses in a closed spherical aneurysm with wall thickness h and inner radius [itex]r_i[/itex].
Ignore blood flow for this purpose."

Intuitively, it makes sense that an increased stress would decrease the wall thickness h, making for a more unstable aneurysm. I would imagine an equation relating the normal wall stress and wall thickness as inversely proportional quantities, but once again as usual I'm having trouble squeezing the actual mathematical statements out of the info given.:confused:

A head-start maybe?
 
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Without knowing the context of your problem, I might be off base here, but it seems to me there are two possible interpretations of this problem. One is that the stress is just the force per unit area on the inside of the sphere, but that is just the pressure of the blood contained and has nothing to do with the thickness of the walls. I'm guessing your problem is a more difficult problem related to the stress within the walls tending to rip it apart. That will depend on the wall thickness and on the blood pressure.

My guess is the place to start is to find the area of a cross section of the wall of the sphere along a plane cutting the sphere in half. The cross section would be a ring or "washer" with an inner radius r and an outer radius r+h. Then for a given blood pressure you would need to integrate over the wall of a hemisphere to find the total force acting on that hemisphere. That force is counteracted by the forces holding the two hemispheres together, and that force is distributed over the area of the ring. The ratio of the force to the area would be the stress.

Not sure about this, but absent any additional context and information, it's the way I interpret it.
 

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