Phantom design for the validation of diffusion magnetic resonance imaging in brain white matter Els Fieremans Supervisor(s): Yves De Deene, Ignace Lemahieu Abstract—Diffusion magnetic resonance imaging is a non-invasive imaging technique that can measure the self-diffusion of water molecules in all directions. This imaging modality enables the visualization of brain white matter, which consists of neuronal fibers and is responsible for the regulation of the human nerve system. To determine the accuracy and precision of diffusion magnetic resonance in vivo, a hardware fiber phantom has been designed. The diffusion behavior inside the fiber phantoms has been modeled by means of Monte Carlo simulations of diffusion inside a packing of parallel cylinders. The simulations were verified using theoretical models for diffusion in porous media. Simulation results were compared to the experimental results and in agreement. Hence, the fiber phantoms are useful for the quantitative calibration of diffusion magnetic resonance imaging. Keywords—MRI, brain, nerve system, diffusion, Monte Carlo
I. I NTRODUCTION Magnetic resonance is the quantum mechanical phenomenon that arises when an object -or a patient- is exposed to a strong magnetic field. An important application of this phenomenon is magnetic resonance imaging (MRI), an imaging technique used primarily in medical settings to produce high quality images of the inside of the human body. Within this technique, diffusion weighted MRI (DW-MRI) is taking an increasingly important place. DW-MRI is a non-invasive imaging method that can measure the motion of water molecules in all directions. In tissues containing a large number of fibers, like skeletal muscles and brain white matter, water tends to diffuse mainly along the direction of those fibers. This way, DW-MRI has access to the organization in space of tissue micro structural components. An interesting application in this domain is the study of the human nerve system. The white matter of the brain consists of bundles of more or less myelinated axonal fibers running in parallel, which are responsible for the conductance of neural signals. Diffusion anisotropy is present because the diffusion in the directions of the fibers is faster than in the perpendicular direction. Assuming that the direction of the fastest diffusion would indicate the overall orientation of the fibers, a method to map out the orientation in space of the white matter tracks in the brain is available. The measurement of the diffusion signal with MRI and fiber tracking (Fig.1) enable a visualization of the three-dimensional structure of brain white matter tracts and have plenty of applications: surgical planning by treatment of epilepsy and brain tumors, investigation (Alzheimer, MS), connectivity of the brain, etc. To determine the accuracy and precision of DW-MRI a validation is necessary which requires a phantom with a well-known structure and diffusion behavior similar to those observed in E. Fieremans is with the Department of Electronics and Information Systems (ELIS) Medisip-IBiTech-IBBT, Ghent University (UGent), Gent, Belgium. Email:
[email protected] .
Fig. 1. Reconstruction of the neural fiber architecture of the brain.
brain white matter. This study presents flexible hardware phantoms of parallel fibers tightly held together by a shrinking tube. The diffusion in the interstitial space of a fiber phantom is modeled using Monte Carlo simulations. II. M ATERIALS AND
METHODS
A. Phantom manufacturing The diffusion fiber phantoms in this study were fabricated R by holding Dyneema fibers tightly together with a flexible, Poly-olefin low-temperature shrinking tube (see figure 2) [1]. R The Dyneema wires were untwisted, uncoated and consisted each of 780 parallel aligned fiber filaments with a diameter of 20 µm 1 . The fiber filaments, made from Ultra-high-molecularweight-Polyethylene (UHMWPE), are impermeable to water molecules and highly hydrophobic. To evaluate the effect of the fiber packing density on the diffusion properties experimentally, 54 straight fiber bundles with varying fiber density were fabricated by holding a varying number of fiber filaments together by a shrinking tube with an inside diameter of 9.5 mm. The fiber phantoms were fixed to a Plexiglas raster and placed in a cylindrical container to minimize the influence of motion and flow during the MR-measurements. B. MR measurements All experiments were performed on a Siemens Trio scanner (3T) equipped with an 8-element head coil at 20◦ C. Diffusion weighted imaging (DWI) was performed in 60 directions with an echo-planar spin echo sequence.A total of 20 slices was acquired in a repetition time of 8 s and with an echo time of 93 ms and a diffusion time ∆ of 36 ms. The resolution was 2 mm x 2 mm x 2 mm. The diffusion weighted images were used to compute the fractional anisotropy (FA) values, expressing the dependency of diffusion on direction. fiber tracking was performed using an Euler line integration algorithm [2]. Proton density (PD) measurements were carried out using a multiple spin echo sequence with 32 contrasts with 1 data
provided by manufacturer
Fig. 2. Photograph of a fiber phantom
Fig. 3. fiber tracking result 0,9
C. Monte Carlo simulations Random water molecule displacement was simulated in Matlab via three-dimensional Monte Carlo simulation of random walkers. For each simulation, 100.000 particles were initialized in a cubic raster (1 mm x 1 mm x 1mm) filled with impermeable cylinders (diameter 20 µm) parallel aligned along the z-axis. The trajectory of one spin particle was generated by moving the particle during each time step ∆ of 0.227 ms over √ a distance of 6D∆ (with D the diffusion coefficient of water in a free medium) in a randomly chosen direction. The particles were allowed to bounce elastically with the cylinders. → The apparent diffusion in a direction n is defined by coefficient → → → 2 1 n. s where s is the net displacement Dapp (∆) = 2∆ of a particle during the time period ∆. Simulations are performed for a hexagonal, square and random packing of parallel cylinders at a temperature of√20◦ C (D = 1.98.10−3 mm2 /s) for a free diffusion length, ld = D∆, of 40 µm and varying fiber densities. The simulated apparent diffusion coefficients Dapp in the three orthogonal directions, x, y and z with the z-direction parallel to the cylinders are used to calculate the fractional anisotropy (FA) according to the following formula: √ FA =
(DappX −DappY )2 +(DappX −DappZ )2 +(DappY −DappZ )2 √ √ 2 2 2 2 DappX +DappY +DappZ
The FA is a measure for anisotropy: FA = 0 means the diffusion is the same in all directions (isotropic), FA > 0 means the diffusion is preferential in one or more directions (anisotropic). III. R ESULT An example of a fiber tracking result after DW-MRI of a fiber phantom is displayed in figure 3. There is a good agreement between the actual fiber direction and the direction of the reconstructed fibers. Figure 4 shows the measured FA-values as a function of the measured PD-values. The error bars of the experimental data show the standard deviation over the chosen ROI’s within the fiber phantoms (containing 297 ± 45 voxels for the PDmeasurements and 96 ± 41 voxels for the FA-measurements). The experimental FA-data are compared to the simulated FAvalues for a hexagonal and a random packing geometry in the long time diffusion limit and for ld = 8.4 µm (corresponding with ∆ = 36 ms).
FA fiber phantoms simulation of FA (random,D ? 36ms) simulation of FA (random, long time) simulation of FA (hex, long time)
0,8
fractional anisotropy
∆TE = 40 ms, a TR of 10 s and a BW of 130 Hz/Px. The resolution was 0.9 mm x 0.9 mm x 2mm. The fiber density (FD) was obtained by 1-PD.
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0
0,2
0,4 0,6 proton density
0,8
1
Fig. 4. Comparison between the FA-measurements of the fiber phantoms and the simulated FA-values
IV. D ISCUSSION
AND CONCLUSION
The diffusion inside anisotropic fiber phantoms is modeled using Monte Carlo simulations of random walk. The simulation results for the regular packing geometries confirm the theory of diffusion in porous media [3]. The simulations revealed the time-dependence of the diffusion coefficient and the dependency of the fiber packing geometry. They may also serve as a useful tool to model the diffusion in vivo. A good agreement was found between the experimental FAdata and the simulations for random packing geometries with the corresponding packing densities. The random geometry is caused by the fabrication method of the phantoms which does not allow for controlling the average distance between fibers. The constructed anisotropic hardware diffusion phantoms have a well-known micro structure and diffusion behavior. R fiber phantoms are appropriate to testHence, the Dyneema ing DW-MRI sequences and validating of diffusion parameters on clinical MRI-scanners quantitatively. R EFERENCES [1] E. Fieremans, S. Delputte, K. Deblaere, Y. De Deene, Truyens B., D’Asseler Y., I. Lemahieu, and R. Van de Walle, “A flexible hardware phantom for validation of diffusion imaging sequences.,” in Proceedings ISMRM, Miami, 2005, p. 1301. [2] P.J. Basser and D.K. Jones, “Diffusion-tensor MRI: theory, experimental design and data analysis - a technical review,” NMR Biomed, vol. 15, pp. 456–467, 2002. [3] P. N. Sen and P. J. Basser, “A model for diffusion in white matter in the brain.,” Biophys J, vol. 89, no. 5, pp. 2927–2938, November 2005.
