Finite-element-method (FEM) model generation of time-resolved 3D echocardiographic geometry data for mitral-valve volumetry

INTRODUCTION: Mitral Valve (MV) 3D structural data can be easily obtained using standard transesophageal echocardiography (TEE) devices but quantitative pre- and intraoperative volume analysis of the MV is presently not feasible in the cardiac operation room (OR). Finite element method (FEM) modelling is necessary to carry out precise and individual volume analysis and in the future will form the basis for simulation of cardiac interventions. METHOD: With the present retrospective pilot study we describe a method to transfer MV geometric data to 3D Slicer 2 software, an open-source medical visualization and analysis software package. A newly developed software program (ROIExtract) allowed selection of a region-of-interest (ROI) from the TEE data and data transformation for use in 3D Slicer. FEM models for quantitative volumetric studies were generated. RESULTS: ROI selection permitted the visualization and calculations required to create a sequence of volume rendered models of the MV allowing time-based visualization of regional deformation. Quantitation of tissue volume, especially important in myxomatous degeneration can be carried out. Rendered volumes are shown in 3D as well as in time-resolved 4D animations. CONCLUSION: The visualization of the segmented MV may significantly enhance clinical interpretation. This method provides an infrastructure for the study of image guided assessment of clinical findings and surgical planning. For complete pre- and intraoperative 3D MV FEM analysis, three input elements are necessary: 1. time-gated, reality-based structural information, 2. continuous MV pressure and 3. instantaneous tissue elastance. The present process makes the first of these elements available. Volume defect analysis is essential to fully understand functional and geometrical dysfunction of but not limited to the valve. 3D Slicer was used for semi-automatic valve border detection and volume-rendering of clinical 3D echocardiographic data. FEM based models were also calculated. METHOD: A Philips/HP Sonos 5500 ultrasound device stores volume data as time-resolved 4D volume data sets. Data sets for three subjects were used. Since 3D Slicer does not process time-resolved data sets, we employed a standard movie maker to animate the individual time-based models and visualizations. Calculation time and model size were minimized. Pressures were also easily available. We speculate that calculation of instantaneous elastance may be possible using instantaneous pressure values and tissue deformation data derived from the animated FEM

Output feedback boundary control of heterodirectional semilinear hyperbolic systems

We solve the problem of stabilizing a general class of 1-d semilinear hyperbolic systems with an arbitrary number of states convecting in each direction and with the actuation and sensing restricted to one boundary. The control design is based on the dynamics on the characteristic lines along which the inputs propagate through the domain and the predictability of states in the interior of the domain up to the time they are affected by the inputs. In the context of broad solutions, the state-feedback controller drives systems with globally Lipschitz nonlinearities from an arbitrary initial condition to the origin in minimum time. Alternatively, it is possible to satisfy a tracking objective at the uncontrolled boundary or, for systems with C1-coefficients and initial conditions, to design the control inputs to obtain classical C1-solutions that also reach the origin in finite time. Further, we design an observer that estimates the distributed state from boundary measurements only. The observer combined with the state-feedback controller solves the output-feedback control problem

Reduced‐order modeling of flow and concentration polarization in membrane systems with permeation

Modeling of concentration polarization (CP) is important to ensure a successful membrane system design. Although computational fluid dynamics (CFD) remains a common approach to study CP, it usually requires a long computational time to investigate a short simulated time in membrane systems. In this work, we proposed a reduced‐order model to predict CP in membrane systems with permeation. We modify Berman's velocity profile and incorporated it to the reduced‐order model of the mass‐transfer equation. The proposed model shows excellent agreement with CFD results, while offering a reduction of two orders of magnitude in computational time. We also validate the model with published experimental data and demonstrate that the model can predict permeate flux in close proximity under various operating conditions. The proposed model offers an attractive alternative to solving the full Navier–Stokes and mass‐transfer equations, and opens the possibility to further investigate various approaches to reduce concentration polarization