Longitudinal Changes in Aortic Mechanical Properties from Angiotensin-II Infused Mice Obtained by an Inverse Finite Element Method

Introduction: Aortic aneurysms have a 90% mortality rate when they rupture [1]. Mice infused with Angiotensin-II (AngII), are often used as surrogate models of aortic aneurysm development. Following infusion of AngII, vascular inflammation and elevated blood pressure cause the aortic walls to remodel to be thicker and dilated with focal areas of degradation [2]. Given the large variation in the ruptured aorta’s mechanical properties [3] and the extent of vascular remodeling that aortic aneurysm undergoes, analyzing the growth and remodeling of aortic aneurysm in a subject-specific application could be important to decide when surgery should be done.
To achieve mouse-specific characterization of the growth and remodeling process, non-invasive means to track changes in aneurysm material properties over time is required. In this study, we used inverse modeling of high frequency ultrasound images to track the changes in in-vivo-estimated material properties of the murine thoracic aorta over time. We infused wild-type mice with AngII for 28 days, a period over which the aorta was expected to grow and remodel [2]. Changes in material properties from 0 to 28 days of AngII infusion were tracked via inverse finite element (FE) method. After 28 days, the same aortas were harvested and tested in a biaxial stretch-inflation test [4] to assess accuracy of the inverse FE method used.
[1] Melo, G.E.R. et al., Semin Thorac Cardiovasc Surg, 34(1):1-16,2022.
[2] Weiss, D., et al., Arteriolscl Throm Vas, 42(8),973-986,2022.
[3] Luo, Y., et al, Acta Biomaterialia, 42:286-295,2016.
[4] Ferruzzi, J., et al., Ann Biomed Eng, 41:1311-1330,2013.

Materials and

Methods: We obtained ultrasound images from ten 16-week-old C57Bl/6J mice, including three saline-infused controls and seven infused with 1000ng/kg/min AngII for 28 days. 4D ultrasound image of thoracic aorta at day 0 and 28 of infusion were obtained (25-55 MHz, Vevo3100, FUJIFILM VisualSonics), resulting in 0.03x0.03x0.1mm3 voxel resolution and 40 frames per cardiac cycle. The ascending and proximal descending thoracic aorta were segmented and tracked over the cardiac cycle to inform an inverse FE analysis of the aortic wall. Material properties of a four-fiber-family material model [5] in the FE model were adjusted until FE-obtained radial deformation matched ultrasound image tracked radius.
The finite element model (Fig 1a) was defined with Robin boundary conditions at the outer wall to model the surrounding tissue’s stiffness and deformation at the inlet and outlets are prescribed from the tracked ultrasound images. Pressure exerted on the geometry was based on a lumped parameter model of blood flow, with resistor-capacitor-resistor boundary, calibrated to Pulsed-Wave-Doppler measured velocities and tail-cuff measured blood pressures. The FE models were axially pre-stretched such that the predicted axial force is constant across diastole-to-systole [6] and circumferentially until the predicted diastolic aortic diameter matched the tracked ultrasound images. Inverse FE analysis results after 28 days of infusion were validated against findings from ex vivo biaxial testing of the same samples.
[5] Gasser, T. C., et al. J.R.Soc. Interface, 3(6), 15-35, 2006.
[6] Weizsäcker, H.W., et al., J.Biomech., 16(9): 703-715, 1983.

Results, Conclusions, and Discussions: Results
A comparison of the equibiaxial stress-strain relationships obtained from inverse FE modeling and from ex vivo biaxial testing at day 28 of infusion is shown in Fig 1b, with an average r2 of 0.92±0.14 (mean±sd). Material stiffness was generally underestimated by the inverse-FE method. The difference between inverse FE and ultrasound tracked radius, normalized by ultrasound tracked diastole-to-systole radius change, was 13.9±3.9%.
There is a trend towards reduction in axial fiber stiffness of AngII mice at 28 days of infusion (p=0.097; Fig 2a,b). However, no significant changes in the axial and circumferential tangential stiffness during systole (p=0.16, 0.22; Fig 2c,d), as the less stiff axial fibers were supported by stiffening of diagonal fibers (p=0.84; Fig 2a,b). We also observed a slight, but not statistically significant decrease in systolic axial and circumferential stretches (p= 0.16, 0.21; Fig 2e,f).

Discussion
The inverse FE method showed good agreement with ex vivo mechanical characterization (Fig. 1b). In addition, we observed a decrease in axial fiber stiffness and unchanged circumferential stiffness at day 28 post AngII infusion (Fig. 2b), both of which are similar to previous reports [7].
Despite the promising results, our study pointed to limitations in the inverse FE approach. The amount of information provided from the image is limited, unlike the large amount of deformation space that can be explored in ex vivo biaxial testing. These issues highlight the need for validation of inverse FE against ground truth ex vivo testing, an important part of this study, which is rarely found in literature [8]. The combination of methodological uncertainty and large variability of the AngII response [7, 9] made it difficult to obtain statistically significant observations. While, the study draws attention to a potential challenge when using image-based inverse methods that affect the sensitivity of the inverse FE method, it also showed potential of the inverse FE method to obtain longitudinal material properties non-invasively.
[7] Bersi, M.R., et al., Hypertension, 67(6): 890-896, 2016.
[8] Wang, L., et al., J. Funct. Biomater., 13: 147, 2022.
[9] Zhou, Y., et al., Am J Physiol Heart Circ Physiol, 285(6): 2797-2803, 2003.

Acknowledgements (Optional): This work was supported by: U01-HL139471, R01 HL164800, AHA Postdoctoral Fellowship (HW), AHA Career Development Award (MRB), the Indiana University School of Medicine (SQC), and computational resources of the Minnesota Supercomputing Institute.