A validation of the biexponential model in diffusion MRI signal attenuation using diffusion Monte Carlo simulator

Transcription

1 A validation of the biexponential model in diffusion MRI signal attenuation using diffusion Monte Carlo simulator Poster No.: C-0331 Congress: ECR 2014 Type: Scientific Exhibit Authors: D. Nishigake, S. Kumazawa, H. Yabuuchi, F. Toyofuku; Fukuoka/ JP Keywords: MR physics, Computer applications, MR-Diffusion/Perfusion, Computer Applications-General, Physics, Tissue characterisation DOI: /ecr2014/C-0331 Any information contained in this pdf file is automatically generated from digital material submitted to EPOS by third parties in the form of scientific presentations. References to any names, marks, products, or services of third parties or hypertext links to thirdparty sites or information are provided solely as a convenience to you and do not in any way constitute or imply ECR's endorsement, sponsorship or recommendation of the third party, information, product or service. ECR is not responsible for the content of these pages and does not make any representations regarding the content or accuracy of material in this file. As per copyright regulations, any unauthorised use of the material or parts thereof as well as commercial reproduction or multiple distribution by any traditional or electronically based reproduction/publication method ist strictly prohibited. You agree to defend, indemnify, and hold ECR harmless from and against any and all claims, damages, costs, and expenses, including attorneys' fees, arising from or related to your use of these pages. Please note: Links to movies, ppt slideshows and any other multimedia files are not available in the pdf version of presentations. Page 1 of 17

2 Aims and objectives Diffusion-weighted imaging (DWI) is a primary magnetic resonance imaging (MRI) tool for noninvasive investigation of tissue microstructure in vivo and plays important roles in clinical diagnosis. Recently, the measured signal attenuation curves in DWI are analyzed by using biexponential model. Although it is reported that it is feasible to model the intra- and extra-cellular fractions as two components using biexponential model, the estimated volume fractions are clearly different from the actual component fractions [1]. This discrepancy has been investigated by many researchers in terms of permeability or restriction of cell membrane [2], difference of relaxation time of intra- and extracellular spaces [3], and other factors [4-5]. However, the discrepancy between the actual component fractions of intra- and extra-cellular spaces and the estimated volume fractions is unclear. In order to investigate the behavior of water molecules in vivo, the simulation of the diffusive motion of water molecules has been used for simple geometry and shape of tissue model [6]. The purpose of this study was to investigate the validation of the biexponential model using tissue composition model and Monte Carlo simulation of the diffusive motion of water molecules. Methods and materials We generated the signal of DWI in restricted diffusion environment reflecting the tissue structures using Monte Carlo simulation. The different patterns of DWI signal attenuations were simulated by changing the volume fractions of the tissue components within a voxel. We applied the biexponential model analysis to the simulated DWI signal attenuations which have the known volume fractions of the tissue components within a voxel. Monte Carlo Simulator and tissue composition model Diffusion phenomenon in vivo is described by free diffusion and restricted diffusion. In free diffusion, it is well known that the displacement at Brownian motion is described by Gaussian probability distribution. In our simulation, we generated the random numbers with Gaussian distribution by using Monte Carlo method, and used the generated random numbers on displacements to simulate Brownian motion. The displacement is according to zero mean and standard deviation which is given by Page 2 of 17

3 Fig. 4 where D is diffusion coefficient, # and # are the gradient duration and interval time, respectively. The phase change of the spin was calculated based on the displacement generated by Brownian motion. The phase change of the spin is given by Fig. 5 where # is the phase change of the particle, # is the gyromagnetic ratio, T is the time factor, G and r are the gradient and position vectors, respectively. Since signal attenuations in DWI based on the phase change were computed for each proton, the collective magnetization of the sample, as a vector, was computed adding the individual magnetization vectors of all spins. Signal attenuation in DWI is given by Fig. 6 Page 3 of 17

4 where S and S0 denote the signals in the presence of diffusion sensitization and the signal in the absence of diffusion sensitization, respectively, #i is the phase change for ith proton and M is the number of protons. In restricted diffusion environment, diffusion area of spins is restricted by many factors such as cell membranes. Therefore, we simulated restricted diffusion using tissue composition model which was assumed total reflection on boundary area. In our simulation, we treated the DWI signal attenuations from a single voxel. As shown in Fig.1 (a), the voxel consisted of the sub-voxel which was described by two types of tissue components (Fig.1 (b)). The tissue composition was changed by changing the volume fraction f of the tissue component. As shown in Fig.1 (c) and (d) restricted by two walls whose distances were 10[µm] and 30[µm], respectively. The diffusion coefficients D1 and -3 2 D2 calculated from DWI signal attenuations in these components were [mm / -3 2 s] and [mm /s], respectively. Page 4 of 17

5 Fig. 1: Tissue component model in our single voxel simulation. (a) a voxel consisting of sub-voxel, (b) sub-voxel described by two types of tissue components, and the tissue components restricted by two walls whose distances were (c) 10[µm] and (d) 30[µm], respectively. (e) The DWI signal attenuations in these components. The diffusion coefficients D1 = [mm2/s] and D2= [mm2/s] calculated from DWI signal attenuations in components (c) and (d), respectively. Simulation and data analysis Page 5 of 17

6 In our simulation, tissue composition model was changed by changing the volume fraction in tissue component model. The volume fraction f denotes the fraction of tissue component with diffusion coefficient D1. We simulated Brownian motion at each spin based on the condition which the initial position of spin was uniform in diffusion area, and calculated the signal in DWI. The detailed condition of simulation is shown in Table 1. In this study, we changed the b-value by changing only the diffusion encoding gradient magnitude. The obtained signal attenuation curves in DWI were fitted by biexponential model, and biexponential model is given by Fig. 7 where f1 is the volume fraction, and D1 and D2 denote diffusion coefficients in each component model, respectively. The volume fraction in biexponential model was estimated by minimizing root-mean-square error (RMSE) between simulated signal attenuations and biexponential-curves based on fixed D1 and D2. The RMSE is given by Fig. 8 where Si and Sbiexp denote the simulated DWI signal and estimated signal in biexponential model, respectively, and n is the number of data points. The minimization process was performed using downhill simplex method. Page 6 of 17

7 Table 1: The detailed condition in our simulation. Experiment using Monte Carlo simulator and tissue composition model We generated three different patterns of the volume fractions of tissue components within a voxel, i.e., f : (1-f) = 0.3:0.7, 0.4:0.6, and 0.5:0.5, respectively, and simulated the DWI Page 7 of 17

8 signal at each volume fraction of tissue component within a voxel using b-value ranging from 0 [s/mm ] to 8000 [s/mm ] with interval of 200 [s/mm ]. We applied the biexponential model analysis to the obtained signal attenuation curve in DWI, and estimated the volume fraction. We compared the estimated volume fraction using biexponential model analysis with the volume fraction used in simulation. Images for this section: Page 8 of 17

9 Fig. 1: Tissue component model in our single voxel simulation. (a) a voxel consisting of sub-voxel, (b) sub-voxel described by two types of tissue components, and the tissue components restricted by two walls whose distances were (c) 10[µm] and (d) 30[µm], respectively. (e) The DWI signal attenuations in these components. The diffusion coefficients D1 = [mm2/s] and D2= [mm2/s] calculated from DWI signal attenuations in components (c) and (d), respectively. Page 9 of 17

10 Table 1: The detailed condition in our simulation. Fig. 4 Fig. 5 Fig. 6 Fig. 7 Page 10 of 17

11 Fig. 8 Page 11 of 17

12 Results Figure 2 shows the DWI signal attenuation curves in our simulation and the signal curves estimated by biexponential model. Table 2 shows the estimated volume fraction using biexponential model analysis and the RMSE value at each volume fraction in tissue composition model. In case of f=0.5, the signal curve estimated by biexponential model analysis was in good agreement with the simulated DWI signal attenuation curve, and the RMSE value was relatively low. However, in cases of f=0.3 and 0.4, the signal curves estimated by biexponential model analysis were not in agreement with the simulated DWI signal attenuation curves, and the RMSE increased with decreasing the volume fraction in tissue composition model. Figure 3 shows the simulated DWI curve with volume fraction (f=0.3) in tissue component model, and the signal curve described by equation (4) with true volume fraction (f1=0.3). The biexponential curve with the true volume fraction was different from the simulated DWI curve with same volume fraction. This result demonstrates that the biexpoenntial curve might not be in agreement with the DWI signal attenuation curves, even if the parameters in this model are set as the true values. It seems that the estimation performance of the biexponential model analysis might be dependent on the volume fraction in tissue composition model. Page 12 of 17

13 Page 13 of 17

14 Fig. 2: The DWI signal attenuation curves in our simulation and the estimated signal curves using biexponential model. (a), (b) and (c) corresponding to the results for volume fractions f=0.3, 0.4, and 0.5, respectively. Table 2: The estimated volume fraction using biexponential model analysis and RMSE value at each volume fraction in tissue composition model. Fig. 3: The simulated DWI curve with volume fraction (f=0.3) in tissue component model, and the signal curve described by equation (4) with true volume fraction (f1=0.3). Page 14 of 17

15 Images for this section: Page 15 of 17

16 Fig. 2: The DWI signal attenuation curves in our simulation and the estimated signal curves using biexponential model. (a), (b) and (c) corresponding to the results for volume fractions f=0.3, 0.4, and 0.5, respectively. Table 2: The estimated volume fraction using biexponential model analysis and RMSE value at each volume fraction in tissue composition model. Fig. 3: The simulated DWI curve with volume fraction (f=0.3) in tissue component model, and the signal curve described by equation (4) with true volume fraction (f1=0.3). Page 16 of 17

17 Conclusion We have validated the biexponential model using diffusion Monte Carlo simulator with a simple tissue composition model. Our results suggested that the biexpoenntial model might fail to estimate the tissue composition. Personal information D. Nishigake, S. Kumazawa, H. Yabuuchi, F. Toyofuku. Department of Health Sciences, Graduate School of Medical Sciences, Kyushu University, Japan. mail to: gake1109@gmail.com References 1. Niendorf T, Dijkhuizen RM, Norris DG, et al., Biexponential Diffusion Attenuation in Various States of Brain Tissue: Implications for Diffusion-Weighted Imaging. Magn Reson Med 1996; 36: Schwarcz A, Bogner P, Meric P, et al., The existence of biexponential signal decay in magnetic resonance diffusion-weighted imaging appears to be independent of compartmentalization. Magn Reson Med 2004; 51: Vestergaard-Poulsen P, Hansen B, Ostergaard L, et al., Microstuctural Changes in Ischemic Cortical Gray Matter Predicted by a Model of Diffusion-Weighted MRI. J Magn Reson Imaging 2007; 26: Kiselev VG, Il'yasov KA, Is the "Biexponential Diffusion" Biexponential? Magn Reson Med 2007; 57: Le Bihan D, Breton E, Lallemand D, et al., Separation of diffusion and perfusion in intravoxel incoherent motion MR imaging. Radiology 1988; 168: Pérez-Sánchez JM, Rodrígue I, Ruiz-Cabello J. Random walk simulation of the MRI apparent diffusion coefficient in a geometrical model of the acinar tree. Biophys J 2009; 97: Page 17 of 17