Image-based Biaxial Aortic Tissue Stiffness Estimation using Vascular Deformation Mapping

Introduction: Aortic stiffness is both heterogeneous (different values in different regions along the aorta) and anisotropic (distinct stiffness patterns in axial and circumferential directions), and it has been recognized as an important indicator of vascular health. Typically, older patients or those with aortic diseases, such as aortic dissection or Marfan’s syndrome, exhibit stiffer aortas. Numerous efforts have been made to estimate aortic stiffness. Some stiffness calibration efforts have relied on invasive approaches, whereby strips of aortic tissue from different regions are tested in both axial and circumferential directions. On the other hand, non-invasive, image-based approaches have been limited to characterizing the aortic tissue as isotropic and have thus been unable to discriminate stiffness between different spatial directions. In this work, we propose a workflow to assess biaxial aortic stiffness using routinely available dynamic computed tomography angiography (CTA) images. Our method measures the 3D displacements of the aorta from dynamic CTA images using a vascular deformation mapping (VDM) technique, and then computes axial and circumferential stretches. Assuming a non-linear and biaxial constitute model, stretches are calculated and compared with VDM-derived stretches over the entire aorta. This enables the determination of both axial and circumferential stiffness. Our technique successfully matches VDM-derived stretches with computed stretches, thereby calibrating heterogeneous and anisotropic aortic stiffness. However, validation of VDM-derived stretches over the cardiac cycle is still needed. In this work, we demonstrate both our biaxial aortic stiffness estimation technique and introduce a VDM calibration pipeline, which is used for validating VDM-derived stretches.

Materials and

Methods: Our technique calibrates biaxial aortic stiffness by minimizing the discrepancies between VDM-derived and computed aortic wall stretches. VDM uses a deformable image registration technique to quantify the 3D displacement between diastolic and systolic CTA images. VDM-derived stretches are calculated based on the resulting 3D displacement field. Computed stretches are calculated using a nonlinear rotation-free shell model in conjunction with a biaxial constitutive model. This model incorporates parameters that define the stiffness of elastin, which forms a ground matrix without a preferential spatial orientation, as well as the stiffness of the axial and circumferential collagen, which are oriented fibers. Blood pressure and aortic root motion are inputs for the nonlinear shell model. The elastin stiffness parameter is calibrated with literature values, given that elastin bears only a small fraction of the pressure load. The axial and circumferential collagen stiffness parameters are iteratively optimized, rendering spatially varying values that minimize the discrepancies between the VMD-derived and the computed stretches. Figure 1 summarizes our technique.
In this workflow, VDM-derived stretches are a key input and are considered as ground truth. The deformable image registration used in VDM incorporates several parameters designed to penalize non-physiological deformations. VDM-derived stretches and corresponding calibrated VDM parameters have not been validated yet. The principal challenge in calibrating VDM parameters is the absence of an established ground truth. To address this issue, we generated synthetic data for aortic motion which can be used for calibrating VDM.

Results, Conclusions, and Discussions: Figure 1 demonstrates our biaxial stiffness estimation technique in the thoracic aorta of a patient treated with a stent-graft. Our technique successfully matches axial and circumferential stretches with VDM-derived stretches after some iterations. Also, it successfully captures the larger stiffness of the aortic section covered by the endograft (see yellow arrows). Consistent with its smaller load bearing function, the elastin stiffness (~0.01 MPa) is much smaller than the collagen stiffness (~0.5 MPa).
However, the VDM-derived stretches must be validated against ground truth data (see Figure 2). To address this, we generated synthetic data on aortic motion to use as ground truth. A 3D systolic configuration was first obtained using the rotation-free shell formulation, the diastolic medical image, and its segmentation mask. A Neo-Hookean constitutive model was used with prescribed heterogeneous stiffness. Next, the diastolic aortic configuration was loaded with prescribed blood pressure pulse and aortic root motion in the axial direction. The 3D aortic displacement is then calculated from the diastolic and computed systolic configurations. The displacement field on the aortic surface was then interpolated into the 3D near-aortic space. Finally, the 3D displacement field was used to warp the diastolic medical image and its mask to generate a synthetic systolic medical image and corresponding mask. Lastly, VDM calculated 3D displacement from the reference diastolic and the synthetic systolic images and their masks. VDM-measure displacements are then compared against the computational ground truth, and the discrepancy is used to calibrate VDM deformable registration parameters.
The regularization terms of the deformable registration consist of 4 parameters. Three parameters contribute to a rigidity penalty term and the fourth sets a bending energy (BE). The rigidity penalty term consists of affine, orthonormality, and properness conditions (AC, OC, and PC, respectively). AC and BE contribute to maintaining smoothness. OC encourages the local rigidity. PC prevents improper rotational deformation. Figure 3 shows how these parameters affect the registration results in 2D examples. Currently, we are optimizing the calibration of these parameters using synthetic ground truth under different assumptions. Validated VDM results will be used to verify the accuracy of our biaxial aortic stiffness estimation technique.

Acknowledgements (Optional):