MagnetoHemoDynamics in MRI devices

Transcription

1 MagnetoHemoDynamics in MRI devices Conference on Mathematics of Medical Imaging June -4, Jean-Frédéric Gerbeau INRIA Paris-Rocquencourt & Laboratoire J-L. Lions France Joint work with A. Drochon (UTC), O. Fokapu (UTC), V. Martin (UTC & INRIA)

2 MHD Artifact in MRI Philips MRI, 3 Teslas Permanent uniform magnetic field (typically.5 Teslas) Today: 3 Teslas (human), Teslas (animals) Tomorrow : Teslas (human), 7 Teslas (animals)

3 MHD Artifact in MRI Electrocardiograms (ECG): synchronize MRI sequences ( gating ) Several known artifacts. Among them : MHD T wave may be as large as the R wave : may result in triggering problems for MR image acquisition B = T B = 3T D. Abi Abdallah, A. Drochon, O. Fokapu(UTC) 3

4 MHD induced current R u ECG P T B j = σ(e + u B) Aorta Flow rate 4

5 MHD and blood flows: MHD and blood flows Kinouchi et al. (Bioelectromag., 996), Tenforde (Prog. Biophys. Mol. Biol., 5). Simplified D stationary computations : no fluid, no electrophysiology. Prediction Teslas: - ma/cm in aorta, 5 ma/cm in the heart - Normal cardiac current density - ma/cm - Flow rate reduction : 5 % In vivo observation Chakeres et al. (J. Mag. Res. Imag. 3): at 8 Teslas, no flow reduction, but consistent pressure increase MHD artifact Gupta et al. (IEEE Tr. Biomed Eng., 8) : analytical solution in a straight pipe + ECGSIM Nijm et al. (Comp. Card., 8), Kainz et al. (Phys Med Biol, ) 5

6 Roadmap Electrophysiology in the heart Electrostatic in the torso MHD in the aorta 6

7 Roadmap Electrophysiology in the heart Electrostatic in the torso MHD in the aorta 7

8 Cell scale Physiological models In F. Sachse Springer 4 : 8 models of cardiac cells! Noble 6, Luo Rudy 9 & 94,... Up to sixty state variables : very difficult to parametrize Phenomelogical models The purpose is to reproduce the shape of the action potential: Typically or 4 state variables FitzHugh 6, Nagumo et al. 6, Fenton-Carma 98, Mitchell-Schaeffer 3...

9 Tissue scale Bidomain equations : A m C m V m t + I ion (V m, g) div(σ i u i ) = A m I app, in Ω H Anisotropic conductivity div(σ e u e ) = div(σ i u i ), in Ω H g t + G(V m, g) =, in Ω H σ i u i n =, on Γ epi σ i,e (x) = σ t i,ei + (σ l i,e σ t i,e)a(x) a(x) If the anisotropy is the same in both media : mono-domain equations σ e u e n =, on Γ epi

10 Roadmap Electrophysiology in the heart Electrostatic in the torso MHD in the aorta

11 Heart-torso coupling Torso: passive conductor div(σt u T )=, in Ω T σ T u T n T =, on Γ ext Strong coupling conditions: u e = u T, on Γ epi σ e u e n = σ T u T n, on Γ epi Weak coupling conditions: u e = u T, on Γ epi σ e u e n =, on Γ epi (Krassowsca-Neu 94, Clements et al. 4, Pierre 5, Lines et. al 6,...)

12 Body surface potential Strong / Weak coupling with the torso Monodomain / Bidomain equations & fibers Mitchell-Schaeffer phenomenological model 3 different cells Careful initialization of the simulation extra-cellular potential body surface potential Boulakia, Fernández, Cazeau, JFG, Zemzemi, Annals Biomed Engng.

13 -lead ECG Simulated I ECG: III avl V V3 V II avr avf V V4 V Real ECG: Fernández, Boulakia, Cazeau, JFG, Zemzemi, Annals Biomed Engng. D D3 avl V V3 V5 D avr avf V V4 V6 (from

14 Example : Electro-mechanical coupling Healthy case Right bundle branch block Chapelle, Fernández, JFG, Moireau, Sainte-Marie, Zemzemi, FIMH 9 4

15 Example : infarct Example:Anterior infarct Anterior infarct : ST elevation Posterior infarct: ST depression Simulation : E. Schenone & M. Boulakia

16 Statistical classification Prometeo project (F. Ieva & AM Paganoni, Politecnino di Milano) Pilot analysis: database of - 5 normal ECG - LBBB - 3 RBBB Statistical clustering... Our normal, LBBB and RBBB ecg are correctly classified!

17 Roadmap Electrophysiology in the heart Electrostatic in the torso MHD in the aorta 7

18 MHD in blood flows Nondimensional parameters: u Magnetic Reynolds: Rm = µ σ U L 9 Hartman number: Ha = B L σ η. B Quasi-static approximation ( t B ): E = φ a Ohm law: j = σ(e + u B) =σ( φ a + u B) u t + u u u + p = Ha Re Re Φ a B + Ha Re div u =, σ σ div Φ a = div u B σ σ (u B) B, 8 σ blood.5s/m

19 Code verification Analytical solution of the full MHD equation (Bessel functions...) Gold (96), Abi-Abdallah et al. (9) 9

20 Code verification 3D test from a D benchmark proposed by Tenforde et al. 996 Excellent agreement with their results

21 Computational domain

22 Inlet BC: 5 Inflow 4 3 Inflow cm3/s time, ms Flow rate (about 5L/min): At the 4 Outlets: 3-element Windkessel R d Velocity field Potential R p C Aorta geometry: courtesy of C.A. Taylor

23 Coupling algorithm Weak coupling

24 Coupling algorithm Strong coupling (relaxed Dirichlet-Neumann)

25 MHD effect on the ECG Without Magnetic Field With Magnetic Field (B = 3T) I avr V V4 I avr V V II avl V V5 II avl V V III avf V3 V6 III avf V3 V B = T B = 3T 5

26 6

27 Conclusion Results: We do obtain a T-wave perturbation No significant flow perturbation (to be confirmed) No significant perturbation on the myocardium (to be confirmed) Possible future works: Improve the model: other vessels? FSI? Optimize the ECG lead locations to reduce the artifact Extract information from the perturbed signal 7