Ultrasound Probe Pressure Affects Aortic Wall Stiffness: A Patient-Specific Computational Study in Abdominal Aortic Aneurysms

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  Fig. 1. Overview of the simulation workflow. First we segmented patient-specific CT scans (A), then defined 3D solid parts (B), and generated the finite-element meshes (C). Afterwards, we prescribed the pressures (P) and boundary conditions (BC) (D), where the pressures were applied to the surfaces depicted in light blue. Specifically, we assigned the pulsed blood pressure inside the aorta, and the probe pressure onto the external surface of the abdomen. The boundary conditions were applied to the surfaces depicted in red. Displacement and rotations were blocked on the spine, while out-of-plane transverse displacements were fixed at both the aortic inlet and outlet

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  Fig. 2. Interpretation of the Elasticity Loss Index (ELI). The ratio between the two tangent stiffness indexes measured at firm (FPP) and light probe pressures (LPP). It is assumed that the circumferential stretch ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _\text{circ}$$\end{document}λcirc is obtained as either the relative diameter or the relative circumference change. In addition, it is also assumed the circumferential stress \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _\text{circ}$$\end{document}σcirc results from the combination of blood pressure and probe pressure. The corresponding material models are specified.

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  Fig. 3. Patient-specific AAA geometries segmented from CT scans. The top row shows the anterior views for Patients 1, 2 and 3. The corresponding lateral views are in the bottom row, together with a delineation of the vertebral spine. The maximum diameter sections are shown in yellow

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  Fig. 4. Simulation results plotted at the maximum diameter cross section for each patient-specific geometry. The diastolic (dotted line) and systolic (solid line) geometries are shown together. Color maps of total displacement from diastole to systole are displayed. Probe pressure increases from left to right. Results are shown for linear (top) and nonlinear HGO (bottom) AAA material assumptions. Color scales are reported below each patient. The spine contours are delineated (shaded black lines), as well as the probe pressure direction (white arrows). The wall thickness is depicted for visualization purposes.

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  Fig. 5. Simulation results are shown for Patient 1, with a linear (left) or a nonlinear (right) aortic material model, and soft surrounding tissues. The displayed color maps represent the circumferential stresses (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _\text{circ}$$\end{document}σcirc, top), and strains (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _\text{circ}$$\end{document}εcirc, bottom) around the scanning plane. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _\text{circ}$$\end{document}σcirc result from diastolic blood pressure and probe pressure combined. \documentclass[12pt]{minimal} \usepackage{amsmath}…

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  Fig. 6. The effect of the probe pressure on the wall circumferential stresses (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _\text{circ}$$\end{document}σcirc, A, B) and circumferential strains (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _\text{circ}$$\end{document}εcirc, C, D) is shown, assuming either a linear (A, C) or a nonlinear (B, D) aortic model. A and B box plots report the stresses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _\text{circ}$$\end{document}σcirc resulting from the combined effects of blood pressure and probe pressure in the elements (n=82±4) within the maximum cross section, as shown in Fig.…

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  Fig. 7. Stiffness indexes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _\text{diam}$$\end{document}βdiam (top) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _\text{circ}$$\end{document}βcirc (bottom). Each color represents one patient (P1, P2, P3). The values of stiffness are reported for each probe pressure condition: light (LPP), moderate (LPP), and firm probe pressure (FPP). Results are reported for soft surrounding tissues. Results were obtained using a linear aortic material model (left) and a nonlinear aortic material model (right). A decrease in measured stiffness with probe pressure can be observed consistently in all cases except for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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  Fig. 8. Diameter and circumference elasticity loss indexes (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ELI}_\text{diam}$$\end{document}ELIdiam, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ELI}_\text{circ}$$\end{document}ELIcirc) calculated as the ratio of the (A) relative diameter changes or (B) relative circumference changes, measured for firm and light probe pressure conditions, plotted against the surrounding tissues (ST) shear moduli: 5 kPa, 10 kPa, and 20 kPa corresponding to soft, medium, and stiff ST, respectively. Each line refers to a different patient-specific geometry: solid, yellow line for Patient 1 (P1), dashed, cyan line for Patient 2 (P2), and dotted, magenta line for Patient 3 (P3). Results are reported for a linearized material model (filled circle) and a nonlinear material model (empty circle).…