Inverse elastostatic stress analysis in pre-deformed biological structures: Demonstration using abdominal aortic...

Area of Science:

• Biomechanics
• Computational mechanics
• Medical imaging analysis

Background:

• Current stress analysis of biological membranes often assumes the in vivo deformed geometry is the stress-free state, which is inaccurate.
• This assumption can lead to significant errors in estimating biomechanical stresses within these structures.

Purpose of the Study:

• To present and validate an inverse elastostatic approach for determining the true initial stress-free geometry of elastic biological structures.
• To demonstrate the method's utility in patient-specific modeling and quantify errors in conventional approaches.

Main Methods:

• Developed an inverse elastostatic method to compute the initial geometry from a given deformed state.
• Applied the method to a patient-specific model of an abdominal aortic aneurysm.
• Analyzed the impact of material parameter variations on stress estimation accuracy.

Main Results:

• The inverse elastostatic approach successfully determines the initial stress-free geometry, removing the conventional limitation.
• Significant errors in stress estimation were identified in the conventional approach for the abdominal aortic aneurysm model.
• The scope of error was quantified within realistic variations of material properties.

Conclusions:

• The inverse elastostatic method provides a more accurate foundation for stress analysis in membrane-like biological structures.
• This approach is crucial for reliable biomechanical assessments, particularly in patient-specific medical applications like aneurysm analysis.
• Eliminating the assumption of stress-free deformed geometry enhances the precision of computational modeling in biology and medicine.