Detecting Aortic Valve Anomaly From Induced Murmurs: Insights From Computational Hemodynamic Models

FIGURE 1. Three-dimensional models labeling important parts and dimensions for (A) the ascending aorta and (B) aortic valve employed in this study.

FIGURE 2. (A) Idealized valve model with circular cross-section with leaflet centerline highlighted using a black line, (B) snapshots of leaflet centerline at several instances during valve opening and (C) leaflet centerline at maximally opened and closed configurations, indicating the local range-of-motion vector, b→(x→).

FIGURE 3. Examples of leaflet kinematic features which can be obtained by tuning the mapping function, ξ: commonly observed opening mode shapes can be obtained using simple mathemtical dependencies such as (A) linear and (B) power relations between the mapping function and lumped displacement.

FIGURE 4. Comparison of valve configuration at three instances during leaflet opening using (top) high-speed imaging of in vitro experiments using bioprosthetic valves and (bottom) present simulations.

FIGURE 5. (A) A realistic human thorax model comprising of an adult male torso, thoracic skeletal structures (white) and a patient-specific left ventricle (LV) and thoracic aorta (red), showing the auscultation “post” for the aortic valve (blue) at the sternum, near the right second intercostal space. The torso and skeletal anatomy were sourced from the Visible Human Project (An anatomical data set developed under a contract from the National Library of Medicine by the Departments of Cellular and Structural Biology, and Radiology, University of Colorado School of Medicine https://www.nlm.nih.gov/research/visible/visible_human.html, while the LV and aorta model were segmented from a de-identified patient-specific thoracic CT scan. (B) Schematic showing the corresponding idealized aorta + thorax model employed for computational hemoacoustic modeling.

FIGURE 6. (A) Schematic showing simulation setup and (B) instantaneous upper and lower bounds on projected valve open area (PVOA) in the training dataset, indicated by the blue shaded region, with three baseline simulations, indicated using solid, dashed and dashed-dot black lines. These simulations correspond to cases 7, 13, and 20, respectively, from Supplementary Table 1 in Appendix A. Additionally, the secondary y-axis describes the instantaneous flow-rate profile used to drive simulations.

FIGURE 7. Illustration of flow physics and aortic jet dynamics in (A) Healthy, (B) RLM1, and (C) RLM2 cases. In each case, the left panel shows contours of axial velocity in five axial planes: 1.5, 3.0, 4.5, 6.0, and 7.5 cm from the aortic annulus and the right panel shows iso-surfaces of Q-criterion (Q = 104 m/s2) colored by axial velocity. Red colors indicate antegrade flow and blue colors indicate retrograde flow. Large regions of forward flow in a section plane can be used to identify aortic jet shape in that plane.

FIGURE 8. (left) Peak systolic valve configuration and (right) systolic surface acceleration measurement at the monitor point in the representative (A) Healthy, (B) RLM1, and (C) RLM2 cases. The colored dashed lines show instantaneous displacement of the three leaflets in each case and the vertical dashed black line denotes the instant of peak systole. Key instances of systolic heart sounds are also indicated: EC- ejection click, S2- “dub”/second heart sound, shaded triangles are used to mark the crescendo/decrescendo of the stenotic valve murmur.

FIGURE 9. (A) Simulated surface acceleration recorded on the thorax and the (B) corresponding centered and normalized acceleration for the 29 simulations and 15 synthesized healthy signals.

FIGURE 10. Histogram plots showing classification results, computed as LDA projection values of individual simulations from the training (cyan, red) and test (blue, orange) sets, relative to the threshold value (dashed black line).

FIGURE 11. (A) Scree plot indicating the cumulative explained variance ratio for the singular value spectrum. The five most important modes for LDA projection are colored using red circles. (B) Two-dimensional illustration of LDA projection for a sample dataset using the optimal projection vector w→. (C) LDA projection weights for the first 20 PCA modes and the five most important LDA modes colored in red.

FIGURE 12. Five most important PCA modes for LDA-based classification, shown with each mode shape (gray) and its corresponding contribution to the development dataset. Blue and red plots represent healthy and stenotic valves, respectively. Vertical dashed black lines at t/T=0.12and0.35 indicate the ends of acceleration and deceleration phases of systolic ejection, respectively. For each mode, energy ratio is listed in the bottom-right corner of the corresponding panel.