Generational-Based Constrained Mixture Model Captures Changes in Aortic Geometry and Material Properties in an AngiotensinII-Infused Mouse

Introduction: : Aortic aneurysms affect 17,000 Americans annually and have a 90% mortality rate when the aneurysm ruptures [1]. Mice infused with angiotensin II (AngII), are often used as animal models of aortic aneurysm development [2]. Following AngII infusion, blood pressure increases, and the aortic wall experiences extensive changes in its geometry and material properties [3]. Given the large variation in the ruptured aorta’s mechanical properties and the extent of remodeling that aortic aneurysm undergoes [4], analyzing the subject-specific growth and remodeling (G&R) of aortic aneurysm is important.
In this study, we proposed a generational constrained-mixture growth model that captures changes in mouse aortic geometry and material properties over the first few weeks post AngII infusion. We infused wild-type C57Bl/6J mice with AngII for 4 weeks, a period over which the aorta was expected to grow and remodel [2]. Changes in material properties were tracked via an inverse finite element (FE) method, and changes in the geometry were obtained using 4D ultrasound. The model was developed to be informed by non-invasive data only (ultrasound and pressure cuff), so that longitudinal changes in the aortic shape and material properties can be predicted. The G&R model is calibrated from weeks 0-3 post AngII infusion and extrapolated to week 4 for comparison to noninvasive imaging data.
[1] Melo, G.E.R. et al., Semin Thorac Cardiovasc Surg, 34(1):1-16, 2022. [2] Gadanec, L.K., et. al, Mol. Cell. Biochem,1-10 ,2023. [3] Bersi, M.R., et al., Hypertension, 67(6): 890-896, 2016. [4] Bojan, I.B., et al., Diagnostics, 13(2), 253, 2023.

Materials and

Methods: : As a proof-of-concept, we obtained ultrasound images from a representative 16-week-old C57Bl/6J mouse infused with 1000ng/kg/min AngII for 4 weeks. 4D ultrasound images of the thoracic aorta were obtained weekly at 0.03x0.03x0.1mm3 resolution and 40 frames per cardiac cycle. The ascending thoracic aorta was segmented and material properties were obtained from an inverse FE method.
A discrete generational model was used, in which the G&R of each constrained mixture constituent (i) occurred over discrete generations (γ). Elastin was modelled as neo-Hookean, and collagen as a four-fiber family model. The strain energy density of the material (W_(i,γ)) is related to the constituent masses (M_(i,γ)), which underwent a net process of decay and deposition at a rate of M ̇_(i,γ). Initial mass was normalized such that M_(i,0)=1, and W_(i,0) was obtained from inverse FE at week 0. Elastin was assumed to remain unchanged [1].
M ̇_(i,τ_γ ) is determined by target-stress homeostasis [1]. Values of steady-state mass deposition, fiber deposition stretches, and target stresses were calibrated by assuming the mouse reached adulthood (i.e., no more somatic growth) before AngII infusion. Volumetric growth rate was assumed to be isometric to maintain constant mass density. Subject-specific values of mass gain were estimated using the Nelder-Mead simplex algorithm, which minimized differences in aortic radius, thickness and axial length obtained from ultrasound and simulation at 1-3 weeks of infusion. The G&R model was then extrapolated to 4 weeks and compared to ultrasound scans and inverse-FE-obtained material properties obtained at the 4th week.[1] Wagenseil, J.E. BMMB,10:671-687, 2011.

Results, Conclusions, and Discussions:: The ultrasound-based geometry and the growth model are compared in Figure 1 for the geometry parameterized by radius, thickness, and axial length over 50 aortic segments. While the growth model captured the changes in radius from AngII infusion, it did not capture the changes in thickness and axial length as accurately.
Material properties obtained from the inverse FE method and the growth model are compared in Figure 2a, and the corresponding constituent mass production is shown in Figure 2b. There is an increase in both circumferential and diagonal stiffnesses at the expense of axial stiffness. This change comes from the re-distribution of the fibers, where the fibers found on the diagonals are reinforced and the axial fibers are degraded.
Discussion
The generational constrained mixture growth model can sufficiently capture changes in aortic geometry and material properties. Geometrically, the model captured the asymmetric growth, wherein thickness changed more than radius (as normalized to dimensions at t_0) with AngII infusion [1]. The growth model also produced trends consistent with those observed in prior studies. Namely, a decrease in axial fiber stiffness with increasing circumferential stiffness [2] and changes in the preferential fiber alignment, with AngII infused mice showing preferential alignment fiber to the diagonals with consistent loss of axial fibers [3].
Past studies applied a constrained mixture model to aortic growth in hypertension using simplified geometries to reduce computational complexity [4]. In this study, complexity was managed by discretizing time points into generations so we could maintain geometrical complexity. The effect of vessel curvature manifested in asymmetrical development of the diagonal fibers. Although the fibers were initialized identically, one family grew stiffer than others as it experienced more stress. Incorporation of mouse-specific measurements into computational models allows for the prediction of growth patterns specific to each animal, ultimately improving our ability to capture changes in aortic geometry and material properties.
[1] Wang, H., et al. AJP-Heart Physiol, 327.3: 642-659, 2024. [2] Cavinato, C., et al. J. Roy. Soc. Int., 21.217: 20240110, 2024. [3] Haskett, D., et al. JBME, 45.5:772-779, 2012. [4] Humphrey, J. D. Jour. of Elast., 145.1: 49-75, 2021.

Acknowledgements and/or References (Optional):: We thank Sydney Q. Clark at Purdue for the collection of US imaging data. Work supported by NIH grants U01-HL139471 and R01-HL164800, AHA Postdoc Fellowship (HW), AHA Career Development Award (MRB), and the Minnesota Supercomputing Institute.