Simulation of the Magneto-Hemodynamic Effect for Aortic Flow Esra Neufeld1*, Dominik Szczerba1, Stefan Benkler1, Adamos Kyriakou1, Josh Guag2, Wolfgang Kainz2, Victor Krauthamer2, Howard Bassen2, Sebastian Kozerke3, and Niels Kuster1 1 Foundation for Research on Information Technologies in Society (IT’IS), Zurich, Switzerland, 2Center for Devices and Radiological Health, FDA, Silver Spring, MD, USA, 3Institute for Biomedical Engineering, ETH, Zurich, Switzerland * Corresponding author e-mail:
[email protected]
INTRODUCTION The objective is to develop a method to non-invasively characterize cardiac blood-flow, including stroke volume and cardiac output along with spatial resolution of flow characteristics. The developed techniques should be able to gather information about blood flow that can supplement present non-invasive ultrasound techniques for blood flow measurements to evaluate heart failure conditions. This additional blood flow information is based on a physiological marker called the magneto-hemodynamic (MHD) signal. The MHD signal can be recorded as a distortion of the Electrocardiogram (ECG) signal while the patient is exposed to a strong static magnetic field [1]. This ECG signal distortion is caused by induced electrical currents in the blood flow. Modeling can be used to identify suitable ECG measurement locations and to study how the recorded signal can be interpreted. The modeling is done for the Virtual Family male [2] – a detailed MRI based anatomical model. MATERIALS AND METHODS MRI measurements: High quality flow measurements have been obtained for the original virtual family male volunteer using a 3T MR scanner. The flow speed has been measured (with 25 fps time resolution) in multiple planes to obtain the flow distributions in the aorta and vena cava at different cross-sections. This data is essential to determine the boundary conditions for the flow simulations. A time resolved volume scan (4D) of the aortic arch has been recorded as well for validation purposes. Furthermore, images have been acquired to ascertain that the aorta of the subject has not significantly changed since the virtual family male model was segmented. ECG: An ECG was recorded for gating purposes during the scans using the scanners ECG sensing ability. While the MHD effect could clearly be seen in the 3T magnet, it was not possible to measure the ECG signal outside of the magnet due to limitations imposed by the scanner software. Therefore, ECG measurements will have to be performed separately at a later time. Model Generation: The virtual family male model has been constructed by segmenting MR images into more than 200 tissue classes and extracting CAD models from them. For the flow simulations, the original aorta segmentation has been used to generate a high quality second order tetrahedron mesh at several resolutions for the sensitivity analysis. Flow Simulations: To solve the incompressible flow equations a fully implicit finite element formulation of the Navier Stokes equations using a Schur complement preconditioner has been used [3,4]. Three heart cycles have been simulated with a temporal
resolution of 1ms. The inflow profile into the ascending aorta as well as the volume rates into the arch branchings have been taken from the measurement to constrain the flow simulations. EM Simulations: In the second step we compute the electromagnetic (EM) field using a Finite Element (FEM) code. The electromagnetic field follows flow changes fast enough to be considered instantaneous. Due to the relatively low blood flow velocities the magnetic field produced by the induced currents in the blood do not significantly alter the overall magnetic field. Because of the weak coupling between the flow and the EM problem we are able to calculate the solutions for both independently but still accurately. The following quasi-static equation is solved on a three dimensional non-uniform rectilinear grid: divσ gradφ divσ v B
(1) where σ is the electrical conductivity (based on Gabriel tissue parameters [5]), v is the blood velocity field and B is the constant external magnetic field. The solver is embedded in the simulation platform SEMCAD X. Solver Validation: The simulation approach (flow and EM) has been validated experimentally in a simple setup (plastic pipe with flowing saline solution). RESULTS The simple validation setup produced agreement between simulation and experiment within 2%. The flow in the aortic arch has been found to be highly intricate, with retrograde velocities, multiple recirculation zones and chaotic behavior in the diastolic phase. It was found that high resolution (>70’000’000 voxels) is needed to converge to a grid independent EM solution and that the resolution of the flow simulation affects the finer details of the MHD signal. The extraction of the MHD signal at the ECG electrode locations described in [6] resulted in a similar MHD time curve within the inter-subject variability. The MHD signal varies sensitively with the ECG electrode location. CONCLUSIONS Transient flow and EM simulations have been performed for a volunteer using detailed MRI based geometric models and flow boundary conditions using experimentally validated software. The calculated surface field permits the extraction of an MHD signal that appears consistent with those observed for real subjects. The next steps include measuring the MHD signal for the virtual family volunteer at optimized positions and comparing it with the simulation results as well as studying the impact of specific flow aspects on the MHD signal. REFERENCES [1] T. S. Tenforde, Magnetically induced electric fields and currents in the circulatory system, Prog. Biophys. Mol. Biol., 87: 279–288, 2008. [2] Christ A et al. The Virtual Family - Development of Anatomical CAD Models of two Adults and two Children for Dosimetric Simulations, Phys. Med. Biol. 2009 [3] T. Gohil et al. Simulation of oscillatory flow in an aortic bifurcation using FVM and FEM: a comparative study of implementation strategie. Int. J. Num. Meth. Fluids, 2010. [4] K. Burckhardt et al. Fast Implicit Simulation of Oscillatory Flow in Human Abdominal Bifurcation Using a Schur Complement Preconditioner. Euro-Par 2009 Parallel Processing, 747–759, 2009. [5] S. Gabriel et al. The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Phys. Med. Biol., 41: 2271–2293, 1996. [6] G. M. Nijm et al. Extraction of the magnetohydrodynamic blood flow potential from the surface electrocardiogram in magnetic resonance imaging. Med. Biol. Eng. Comp., 46 (7): 729–733, 2008.
