4D Flow Patterns and Relative Pressure Distribution in a Left Ventricle Model by Shake-the-Box and Proper Orthogonal Decomposition Analysis

Abstract

Purpose Intraventricular blood flow dynamics are associated with cardiac function. Accurate, noninvasive, and easy assessments of hemodynamic quantities (such as velocity, vortex, and pressure) could be an important addition to the clinical diagnosis and treatment of heart diseases. However, the complex time-varying flow brings many challenges to the existing noninvasive image-based hemodynamic assessments. The development of reliable techniques and analysis tools is essential for the application of hemodynamic biomarkers in clinical practice. Methods In this study, a time-resolved particle tracking method, Shake-the-Box, was applied to reconstruct the flow in a realistic left ventricle (LV) silicone model with biological valves. Based on the obtained velocity, 4D pressure field was calculated using a Poisson equation-based pressure solver. Furthermore, flow analysis by proper orthogonal decomposition (POD) of the 4D velocity field has been performed. Results As a result of the Shake-the-Box algorithm, we have extracted: (i) particle positions, (ii) particle tracks, and finally, (iii) 4D velocity fields. From the latter, the temporal evolution of the 3D pressure field during the full cardiac cycle was obtained. The obtained maximal pressure difference extracted along the base-to-apex was about 2.7 mmHg, which is in good agreement with those reported in vivo. The POD analysis results showed a clear picture of different scale of vortices in the pulsatile LV flow, together with their time-varying information and corresponding kinetic energy content. To reconstruct 95% of the kinetic energy of the LV flow, only the first six POD modes would be required, leading to significant data reduction. Conclusions This work demonstrated Shake-the-Box is a promising technique to accurately reconstruct the left ventricle flow field in vitro. The good spatial and temporal resolutions of the velocity measurements enabled a 4D reconstruction of the pressure field in the left ventricle. The application of POD analysis showed its potential in reducing the complexity of the high-resolution left ventricle flow measurements. For future work, image analysis, multi-modality flow assessments, and the development of new flow-derived biomarkers can benefit from fast and data-reducing POD analysis.

Lagrangian particle tracking in the presence of obstructing objects

“…Over the last years volumetric Lagrangian particle tracking (LPT) techniques have matured enough to be applicable for a wide variety of different flow cases. They have been utilized to study the flow within models of the human ventricle [1], to characterize the transport of aerosols [2] at a cubic meter scale, to assess the aerodynamic performance of cyclists [3] or to determine the wake of a ducted propeller [4], among many other applications. Here, the measured flow fields are strongly * Author to whom any correspondence should be addressed.…”

“…But the object's geometrical properties (shape, location, orientation) are still neglected during the flow reconstruction. Despite the presence of the object, the reconstruction is possible in these cases since the model is either transparent and does not obstruct the views of the cameras [1], the model is placed just outside of the measurement volume [4] to not interfere with the reconstruction algorithm, or the full flow field is reconstructed by combining several sub-volumes, each recorded with a different location of the multi-camera system mounted on a robot arm, to overcome the optical blockage [3].…”