Information about presenter 2013-now Engineer R&D ithera Medical GmbH 2011-2013 M.Sc. in Biomedical Computing (TU München) Thesis title: A General Reconstruction Framework for Constrained Optimisation Problems in Hyperpolarised 13 C Metabolic MR Imaging Contents 1. Introduction 2. Problem and Objectives 3. Theory and Methods 4. Results 5. Conclusion 6. References 2006-2011 Diploma in Biomedical Engineering (National Research University of Electronic Technology) Thesis title: Numerical Modeling of Ultrasonic Data for Purposes of Acoustic Elastography 25.01.2015 1
1 H Introduction 13 C B 0 B 0 M Thermal Dynamic Nuclear Polarisation 10,000-fold M Hyper Non-proton chemical shift imaging (CSI) Quantification of metabolism in vivo Difficult measurement conditions: - Magnetization decay (in vivo ~30 s) - Limited pyruvate dose - 5-D acquired data Fast imaging sequences and reliable reconstruction required 1 H-MRI 13 C-MRSI. Lactate Reference Reference O O H 3 C-C- 13 C-OH Tumor Tumor 25.01.2015 2
Problem and Objectives Direct unregularized methods for the solution of least squares problem are fast but not accurate Iterative reconstruction with included regularization term The goal of the study is to enhance the quality of images by means of iterative reconstruction with included a priori knowledge in a form of additional constraints 25.01.2015 3
Theory and Methods Add prior knowledge Penalty term α is a weighting factor Numerical simulations Time series of 2D images representing maps of two metabolites whose pixel intensities were changing according to the two-site exchange model 1 Experiment x = arg min x A x s 2 2 + α R(x) 2 2 Data fidelity term s measured MR signal A = C F forward model matrix (spectral + spatial encoding) x unknown metabolite concentrations 3 T GE Signa Excite scanner, a dual-tuned rat coil, spiral trajectory (FOV=80 mm, nom. resolution 32x32) and 7 echo times (ΔTE=1.2 ms) 2 25.01.2015 4
Types of Regularization Terms Proton Image-based Mask 1. Active Contour Segmentation 4 R M x = α I βm f x where M mask derived from anatomical image f, β smoothing factor Tikhonov Regularisation 2. Histogram Thresholding R Tikh x = α I(x x ref ) 2 2 Total Variation R TV (x) = α x x + y x dxdy Total Generalised Variation 3 Ω R TGV (x) = min α 1 x v dr + α 0 v Ω Ω 1 2 ( v + vt ) dr 25.01.2015 5
RMSE RMSE Results (a) on Simulated Data True pyruvate True lactate Ringing artifacts and bleeding patterns in places of pyruvate distribution in case of conventional reconstruction by pseudoinverse (pinv). Interval of measurement before the end of injection is the most error-prone (t end = 8s). TGV regularization has equally good edge-preserving and denoising properties, and performs better than Tikhonov or TV regularization. pinv(a), RMSE=0.096 TV, RMSE=0.035 Tikhonov, RMSE=0.079 TGV, RMSE=0.039 pinv(a), RMSE=0.322 TV, RMSE=0.184 Tikhonov, RMSE=0.201 TGV, RMSE=0.069 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 Error for reconstructed pyruvate data k P L =0.08 s -1 pinv(a) Tikhonov penalty TV penalty TGV penalty 10 20 30 40 Time [s] 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Error for reconstructed lactate data k P L =0.08 s -1 pinv(a) Tikhonov penalty TV penalty TGV penalty 10 20 30 40 Time [s] 25.01.2015 6
Pyruvate Lactate Results (b) on in Vivo Data R reference; T - tumour; K - kidney Anatomy T R NUFFT TGV TGV+Mask NUFFT TGV TGV+Mask K Magnified ROI Overlay with proton image SNR = 46.9 SNR = 67.2 (43%) SNR = 15.2 SNR = 21.5 (41%) SNR improvement (mean SNR increase in 5 data sets: 26% (pyruvate), 32% (lactate), 21% (alanine), 26% (pyruvate hydrate)) and denoising properties demonstrated Rate constant of pyruvate-to-lactate conversion are comparable (0.029 s -1 (NUFFT), 0.024 s -1 (TGV)) Longer computational time (5.65 s (NUFFT), 519.85 s (TGV)) 25.01.2015 7
Conclusion MRS imaging with hyperpolarised 13C agents reveals a wealth of metabolic information (spatially and time-resolved) SNR limited due to rapid signal decay (polarisation replenishes) The simulation framework for 13C metabolic imaging with quantitative evaluation of reconstruction performance was presented Comparison of several penalty functions revealed the superiority of TGV constraint for iterative reconstruction with regularization then applied to in vivo data SNR improvement of up to 40%, better delineation of structure borders and denoising performance were achieved with TGV penalty 25.01.2015 8
References 1: Zierhut M. et al. Kinetic modelling of hyperpolarized 13C-pyruvate metabolism in normal rats and TRAMP mice, J Magn Reson, 202(1), 85-92 (2010) 2: Wiesinger F. et al. IDEAL spiral CSI for dynamic metabolic MR imaging of hyperpolarized [1-13C]pyruvate, Magn Reson Med., 68(1), 8-16 (2012) 3: Knoll F. et al. Second Order Total Generalized Variation (TGV) for MRI, Magn Reson Med., 65, 480 491 (2011) 4: Chan T. et al. Active contours without edges for vector-valued images. J Vis Communication, 11(2):130 141, 2000 (2012) Acknowledgements: Co-funding by BMBF grant #13EZ1114 25.01.2015 9