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

Abstract

Purpose: Ultrasound imaging is key in the management of patients with an abdominal aortic aneurysm (AAA). It was recently shown that the cyclic diameter variations between diastole and systole, which can be quantified with US imaging, increase significantly with the strength of the applied probe pressure on the patient's abdomen. The goal of this study is to investigate this effect more thoroughly.

Methods: With finite-element modeling, pulsatile blood pressure and probe pressure are simulated in three patient-specific geometries. Two distinct models for the aortic wall were simulated: a nonlinear hyperelastic and a linear elastic model. In addition, varying stiffness was considered for the surrounding tissues. The effect of light, moderate, and firm probe pressure was quantified on the stresses and strains in the aortic wall, and on two in vivo stiffness measures. In addition, the Elasticity Loss Index was proposed to quantify the change in stiffness due to probe pressure.

Results: Firm probe pressure decreased the measured aortic stiffness, and material stiffness was affected only when the wall was modeled as nonlinear, suggesting a shift in the stress-strain curve. In addition, stiffer surrounding tissues and a more elongated aneurysm sac decreased the responsiveness to the probe pressure.

Conclusion: The effect of probe pressure on the AAA wall stiffness was clarified. In particular, the AAA wall nonlinear behavior was found to be of primary importance in determining the probe pressure response. Thus, further work will intend to make use of this novel finding in a clinical context.

Keywords: Abdominal aortic aneurysm; Finite-element method; Noninvasive mechanical characterization; Ultrasound probe pressure.

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

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 ${\lambda }_{\text{circ}}$ is obtained as either the relative diameter or the relative circumference change. In addition, it is also assumed the circumferential stress ${\sigma }_{\text{circ}}$ results from the combination of blood pressure and probe pressure. The corresponding material models are specified.

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

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.

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 (${\sigma }_{\text{circ}}$, top), and strains (${\epsilon }_{\text{circ}}$, bottom) around the scanning plane. ${\sigma }_{\text{circ}}$ result from diastolic blood pressure and probe pressure combined. ${\epsilon }_{\text{circ}}$ result from the transition from diastolic to systolic blood pressure, at constant probe pressure. Light (LPP) and firm (FPP) probe pressure results are presented. The scales are reported on the left hand side for each case. The spine contours are delineated (shaded black lines).

Fig. 6

The effect of the probe pressure on the wall circumferential stresses (${\sigma }_{\text{circ}}$, A, B) and circumferential strains (${\epsilon }_{\text{circ}}$, 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 ${\sigma }_{\text{circ}}$ 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. 5. C and D box plots summarize ${\epsilon }_{\text{circ}}$ in the same area due to the transition from diastolic to systolic blood pressure, at constant probe pressure. Growing external probe pressure values are considered: light (LPP), moderate (MPP), and firm (FPP). Surrounding tissues (ST) are assumed soft (red), medium (blue), or stiff (green). Significance (t test, p < 0.05) is indicated.

Fig. 7

Stiffness indexes ${\beta }_{\text{diam}}$ (top) and ${\beta }_{\text{circ}}$ (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 ${\beta }_{\text{circ}}$ with linear model.

Fig. 8

Diameter and circumference elasticity loss indexes (${\mathit{ELI}}_{\text{diam}}$, ${\mathit{ELI}}_{\text{circ}}$) 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). Horizontal red axis indicates where the ELIs are equal to 1. The ELI is positive and decreases with increased ST stiffness in all cases except when a linear model is assumed for the aortic wall and ${\mathit{ELI}}_{\text{circ}}$ is measured.