Elastic Foundations as Heterogeneous Adventitial Boundary Condition for the Assessment of Aortic Wall and Peri-Aortic Stiffness from Dense-MRI Data Using Inverse FEM Approach

Background: The establishment of in vivo, patient-specific, and regionally resolved techniques to quantify aortic properties is key for improving risk assessment in clinical practice and scientific understanding of cardiovascular growth and remodeling. Many in vivo studies quantify vascular stiffness using Pulse Wave Velocity. This method provides an averaged measure of stiffness for the entire aorta, ignoring variations in wall stiffness and boundary conditions. Previous studies using Displacement Encoding with Stimulated Echoes Magnetic Resonance Imaging (DENSE-MRI) suggested that the infrarenal abdominal aorta (IAA) deforms heterogeneously throughout the cardiac cycle. Method: Herein, we hypothesize that the aortic wall strain heterogeneity is driven in healthy aortas by adventitial tethering to perivascular tissues that can be modeled with elastic foundation boundary conditions (EFBC) using a collection of linear-springs with a circumferential distribution of stiffness. Nine healthy-human IAAs were modeled using patient-specific imaging and displacement fields from SSFP and DENSE MRI, followed by assessment of aortic wall properties and heterogeneous EFBC parameters using inverse Finite Element Method (FEM). Results: In contrast to traction-free boundary condition, prescription of EFBC reduced the nodal displacement error by 60% and reproduced the DENSE-derived strain distribution. Estimated aortic stiffness was in agreement with previously reported experimental test data. The distribution of normalized EFBC stiffness was consistent among all patients and spatially correlated to standard peri-aortic anatomical features. Conclusion: Results suggest that EFBCs can be generalized for human adults with normal anatomy. This approach is computationally inexpensive, making it ideal for large-population clinical research and incorporation into computational cardiovascular fluid-structure analyses.https://scholarscompass.vcu.edu/gradposters/1113/thumbnail.jp

Chaos and a Resonance Mechanism for Structure Formation in Inflationary Models

We exhibit a resonance mechanism of amplification of density perturbations in inflationary mo-dels, using a minimal set of ingredients (an effective cosmological constant, a scalar field minimally coupled to the gravitational field and matter), common to most models in the literature of inflation. This mechanism is based on the structure of homoclinic cylinders, emanating from an unstable periodic orbit in the neighborhood of a saddle-center critical point, present in the phase space of the model. The cylindrical structure induces oscillatory motions of the scales of the universe whenever the orbit visits the neighborhood of the saddle-center, before the universe enters a period of exponential expansion. The oscillations of the scale functions produce, by a resonance mechanism, the amplification of a selected wave number spectrum of density perturbations, and can explain the hierarchy of scales observed in the actual universe. The transversal crossings of the homoclinic cylinders induce chaos in the dynamics of the model, a fact intimately connected to the resonance mechanism occuring immediately before the exit to inflation.Comment: 4 pages. This essay received an Honorable Mention from the Gravity Research Foundation, 1998-Ed. To appear in Mod. Phys. Lett.

Combining exclusive semi-leptonic and hadronic B decays to measure |V_ub|

The Cabibbo-Kobayashi-Maskawa matrix element |V_ub| can be extracted from the rate for the semi-leptonic decay B -> pi + l + antineutrino_l, with little theoretical uncertainty, provided the hadronic form factor for the B -> pi transition can be measured from some other B decay. In here, we suggest using the decay B -> pi J\psi. This is a color suppressed decay, and it cannot be properly described within the usual factorization approximation; we use instead a simple and very general phenomenological model for the b d J\psi vertex. In order to relate the hadronic form factors in the B -> pi J\psi and B -> pi + l + antineutrino_l decays, we use form factor relations that hold for heavy-to-light transitions at large recoil.Comment: Latex, 7 pages, no figure