Displacement Encoding with Stimulated Echoes Magnetic Resonance Imaging (DENSE MRI) is a unique technique that has recently been developed to quantify non-invasive, patient-specific regional aortic wall kinematics [1]. Prior work with this technique revealed that deformation of the aorta in vivo is non-uniform, in contrast to reports from in vitro pressurization tests of excised aortas which result in uniform deformations that are maintained an approximately regular cylindrical geometry. Perivascular tethering and support is a key factor for this difference in vivo deformation throughout the cardiac cycle due to its constraint on the motion of large blood vessels, though there have only been scant research on quantifying its effects [2]. Most prior numerical and theoretical analyses of vascular mechanics have assumed uniform or traction-free boundary conditions at the external surface of the vascular wall, leading to non-physiologic deformation into idealized annular cross-sections. We propose a methodology to estimate patient-specific material properties of the aortic wall through the use of a heterogeneous Elastic Foundation Boundary Condition (EFBC) to model the effects of non-uniform tissues on the deformation of the descending thoracic and abdominal aorta [3]. The EFBC is implemented as a collection of linear springs attached radially on the adventitial surface of the aortic wall. The stiffness of each spring varies as a function of its angular position around the aortic circumference and the local spring density. The aortic wall is modeled as an orthotropic hyper-elastic material and is loaded with a time-dependent pulse pressure on its luminal surface. Patient-specific DENSE-derived displacement fields are utilized as the target for an inverse Finite Element Method (FEM) approach that iterates over the wall and perivascular tissue material properties until the simulated deformation matches the deformation observed in vivo. This approach successfully reproduces the patient-specific non-symmetric displacement fields measured by DENSE-MRI, and the resulting geometry generally agrees with standard steady-state free precession (SSFP) cine MRI imaging throughout the cardiac cycle. Calculated aortic wall material properties corroborate the reported differences in material stiffness between the thoracic and abdominal aorta, the latter being stiffer. Furthermore, our method reproduced the well-known stiffening effect of aging. Most remarkably, the resulting peri-aortic EFBC was found to be regionally consistent among all healthy individuals studied and the perivascular stiffness distribution agreed well with the existing anatomic features, (i.e., larger radial stiffness adjacent to the rigid vertebra, and softer into the peritoneal cavity at the abdomen, and into the lungs at the thorax). In summary, the combination of DENSE-MRI and inverse FEM is a powerful image-based patient-specific computational method for estimating regionally heterogeneous perivascular boundary conditions and healthy aortic wall material properties. 
References:
[1]	Wilson et al. 2019, ‚ÄúIn Vivo Quantification of Regional Circumferential Green Strain in the Thoracic and Abdominal Aorta by Two-Dimensional Spiral Cine DENSE MRI,‚Äù J. Biomech. Eng., 141(6), p. 060901.
[2]	Ferruzzi et al. 2018, ‚ÄúCombining in Vivo and in Vitro Biomechanical Data Reveals Key Roles of Perivascular Tethering in Central Artery Function.‚Äù PLoS ONE 13(9).
[3]	Bracamonte et al. 2020, ‚ÄúAssessing Patient-Specific Mechanical Properties of Aortic Wall and Peri-Aortic Structures from in Vivo Dense MR Imaging Using an Inverse Finite Element Method and Elastic Foundation Boundary Conditions,‚Äù J. Biomech. Eng. In press.


Modeling aortic perivascular support with heterogeneous elastic foundation boundary condition in an inverse FEM approach with patient-specific DENSE MRI

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