62.7. Results and Discussion

The deformed shape of the abdominal aorta model after the first load step is the zero-pressure geometry:

Figure 62.6: Total Deformation (USUM) After Inverse Solving (First Load Step)

Total Deformation (USUM) After Inverse Solving (First Load Step)

In addition to the zero-pressure geometry, the inverse-solving load step also gives the stress/strain results of the input geometry at end-diastolic pressure (80 mm Hg):

Figure 62.7: Maximum Principal Stress After Inverse Solving (First Load Step)

Maximum Principal Stress After Inverse Solving (First Load Step)

Figure 62.8: Maximum Principal Strain After Inverse Solving (First Load Step)

Maximum Principal Strain After Inverse Solving (First Load Step)

In the second load step, the analysis is continued via forward solving (INVOPT,OFF) and the pressure load is increased until it reaches end-systolic pressure (120 mm Hg):

Figure 62.9: Total Deformation (USUM) After Forward Solving (Second Load Step)

Total Deformation (USUM) After Forward Solving (Second Load Step)

Figure 62.10: Maximum Principal Stress After Forward Solving (Second Load Step)

Maximum Principal Stress After Forward Solving (Second Load Step)

Figure 62.11: Maximum Principal Strain Plot of the Abdominal Aorta Model at End-Systolic Pressure (120 mm Hg)

Maximum Principal Strain Plot of the Abdominal Aorta Model at End-Systolic Pressure (120 mm Hg)

For comparison purposes only, the following figure shows one of the cross-sections in the proximal abdominal aorta at zero-pressure, end-diastolic pressure, and end-systolic pressure conditions:

Figure 62.12: Deformation of Cross-Section at the Proximal Abdominal Aorta Location for Various Pressure Conditions

Deformation of Cross-Section at the Proximal Abdominal Aorta Location for Various Pressure Conditions

The input geometry is considered at end-diastolic pressure (80 mm Hg), the deformed geometry after the first load step (inverse solving) is at zero-pressure, and the deformed geometry after the second load step is at end-systolic pressure (120 mm Hg). The outer diameters of the cross-section in deformed states are approximately calculated by creating a local cylindrical coordinate system at the approximate center of the deformed cross-section.

The following figures highlight the results accuracy of this simulation using inverse solving vs. a simulation solved for the same model without accounting for the prestressed effect. In a comparison case, the input geometry is assumed to be the zero-pressure geometry, and a forward-solving analysis is performed with end-systolic pressure (120 mm Hg) in only one load step:

Figure 62.13: Comparison of Total Deformation (USUM) at End-Systolic Pressure (120 mm Hg)

Comparison of Total Deformation (USUM) at End-Systolic Pressure (120 mm Hg)

Figure 62.14: Comparison of Maximum Principal Stress at End-Systolic Pressure (120 mm Hg)

Comparison of Maximum Principal Stress at End-Systolic Pressure (120 mm Hg)

In the comparison case, the maximum total deformation at one of the junctions is higher than that of the simulation using inverse solving.

When using the inverse-solving method to account for the input geometry at end-diastolic pressure (80 mm Hg) and prestress effects, the actual maximum total deformation is much lower.