Christian Graff PhD Candidate Applied Mathematics GIDP International Society for Magnetic Resonance in Medicine (ISMRM) 16th Annual Meeting Toronto, Canada May 3-9, 2008   “Computer-Generated Abdominal Phantom for Evaluation of MR Estimation Techniques”

Computer-generated phantoms provide a convenient way to generate large numbers of sample data sets, and have been used in a variety of contexts in MR imaging [1,2]. However, care must be taken in interpreting the results of computer-phantom studies since a computer simulation is always a simplification of the real imaging process. For example, compressed-sensing reconstruction techniques have recently become popular in MR [3]. These techniques have been shown to be extremely accurate for objects of low total-variation, like the Shepp-Logan phantom and most types of physical phantoms used in MR. In contrast, the human body contains much more variability, and thus results from phantom studies may not accurately predict performance with in vivo data.

Quantitative evaluation in MR imaging typically involves measuring a signal-to-noise ratio (SNR), contrast-to noise ratio (CNR), or using a group of radiologists to rank images. With the increasing interest in non-Cartesian imaging and parameter map estimation, the linearity assumptions that justify the use of SNR and CNR as a measure of image quality are no longer always valid. Using radiologists to rank images can be costly and time consuming, and may not be a relevant measure of reconstruction quality if the images or parameter maps are to be used for computerized diagnosis. Evaluating methods for reconstructing parameter maps can be problematic in vivo because of the lack of a gold-standard measurement and the difficultly in obtaining sufficient numbers of patients.

To overcome these problems, we have developed a computer-generated phantom for the evaluation of MR-parameter estimation techniques in the abdomen. In our phantom, a variety of practical effects, such as tissue texture and variability, along with coil sensitivities and fat suppression have been modeled to produce data sets which are as close as possible to in vivo data.

Methods: The procedure used to randomly generate a k-space data set is shown in Fig 1. The model for the abdomen’s anatomical structure is derived from high-resolution photographic images obtained from the Visible Human Project [4]. These images are segmented into 15 different tissue types as shown in Fig. 2. Within each tissue type, the distribution of possible T1, T2 and proton density values are obtained from literature. We are mainly interested in evaluating T2 estimation techniques for small lesions in the liver, so special care was taken to achieve the proper variability of parameter values within the liver. High resolution, high SNR, spin-echo scans of ex vivo cow liver were taken on a Bruker 4.7T scanner. From these images, measures of spatial variability and the range of possible parameter values were calculated.

To estimate coil sensitivity functions, experiments with a body coil and an 8-channel phased array coil were performed on a GE NV-CV/I Signa scanner at 1.5T. By taking the ratio of the phased array coil data and the uniform sensitivity body coil, realistic coil sensitivity functions were estimated. These estimates were fitted to 2D polynomials to obtain coil sensitivity functions which are scalable to the resolution of our phantom and cover the entire field of view (Fig. 3). Many clinical sequences incorporate fat suppression. This technique was modeled by performing analogous water suppression experiments at 1.5T. Once the phantom is completely specified, k-space data can be generated from a 2D Fourier transform, a Radon transform, or more sophisticated MR simulators like OD1N [5] or SIMRI [6].

Even though our phantom is defined discretely, it has approximately 10 times the resolution of typical clinical scans, so it approximates well the continuous nature of the human body. In-plane partial volume effects are created by this difference in resolution. Through-slice partial volume is modeled for the tumors by considering the slice to be of finite thickness and placing the 3-D tumor randomly along the slice direction.

Results: An example of a reconstruction obtained for T2-weighted radial data generated from our phantom is shown in Fig. 4. The phantom data produces reconstructed images which closely match those obtained in vivo.

Conclusions: The phantom has been developed to evaluate T2 estimation techniques for small lesions in the liver, but the same procedure can be used to evaluate accuracy on any similar type of estimation task. The ability to generate realistic simulated data, where the true underlying tissue parameters are known, is a valuable tool which will become increasingly important as more sophisticated imaging techniques are developed.

Acknowledgement: This work is supported by NIH grants CA099074 and HL085385.
References: [1] Collins IEEE TMI 17 (1998) 463-468. [2] Morgan MRM 46 (2001) 510-514. [3] Lustig Proc. ISMRM 07 [4] Ackerman Proc. IEEE 86 (1998) 504-511. [5] Jochimsen JMR 170 (2004) 67-78. [6] Benoit-Cattin JMR 173 (2005) 97-115.

“Lipid T2* Determination by Modeling the Intra-Molecular Chemical Shift Effect”

ABSTRACT

The measurement of T2* and/or T2† (which is derived from T2* and T2) are important for the quantification of physiological events or pathologies related to susceptibility changes in tissue. In bone, for example, changes in T2† and T2* are caused by susceptibility changes between the trabecular bone and bone marrow and it has been shown that T2* and T2† correlate with the changes in bone microstructure [1-3].

Since bone marrow has both a water and a fat component, the signal decay versus time in T2* measurements depend on the properties and ratios of these two species. One phenomenon that is usually ignored in modeling the T2* signal decay of fat is the intra-molecular chemical shift. Different from water, which has two magnetically equivalent hydrogen atoms (and thus resonating at the same frequency), the hydrogen atoms that make up the fat molecule are not magnetically equivalent. Thus different groups within the fat molecule resonate at different frequencies [4]. The main lipid peak (formed mainly by the CH2 groups in the molecule) resonates at ~1.2 ppm whereas the terminal CH3 groups resonate at ~0.8 ppm. This chemical shift difference causes a modulation in the T2* decay curve and the single exponential approximation, typically used to fit T2*, leads to erroneous results.

In this work we present a signal equation model for extracting T2* for fat, minimizing the effects of the intra-molecular chemical shift.
Theory: If we approximate the CH2 and CH3 peaks with delta functions, the signal decay magnitude I for a pure lipid sample can be modeled by Eq. 1, where Cs is the relative chemical shift between the CH2 and CH3 resonances, and ICH2, ICH3 are the magnitudes of each peak. This equation is a non-linear function of the unknown parameters, and thus must be fitted using a non-linear least squares technique. The Levenberg-Marquardt algorithm was used for this study.

I ║ICH2   ICH3 exp(iCSTE)║ exp(–TE/T2*)   (1)

Methods: In order to test the model we measure T2* in compounds mimicking human fat (hexane and baby oil). Images were acquired at 1.5T on a GE Signa NV-CV/i scanner, with a spoiled gradient echo pulse sequence (flip angle=90, TR=500, NEX=1, BW=±32kHz) at 14 TE values ranging from 4.2 to 58.8 ms. For baby oil, we performed spectroscopic experiments at 11.7 T in order to determine the ratio of the CH2/CH3 peaks and their chemical shift differences. At this high field, the resonances corresponding to the CH2 and CH3 groups were resolved thus the ratio and chemical shifts for these two groups were easily estimated. For hexane, the CH2/CH3 ratio was determined from the molecular structure and their chemical shift differences from the literature.

Results: Figure 1 shows the signal decay versus TE curves for (A) hexane (B) baby oil, and (C) a phantom containing a sponge embedded in baby oil (the sponge is used to reduce T2*). The data in black are the measured points. The red and blue curves (shown in the left panel of Fig. 1) are the experimental fits to the data using the single exponential decay typically used for T2* measurements (ie, I=Ioexp(-TE/T2*)). In the fitting represented by the blue curves we only used data points in the 4.2 to 21 ms TE range. In the fitting represented by the blue curves we used the full range of TE values. The green curves (shown in the right panel of Fig. 1) represent the fitting of the data to Eq. 1. In general, the single exponential does not fit the data properly and the calculated T2* values (Table 1) depend on the range of points used. On the other hand, Eq. 1 fits the data well thus we can expect a more accurate calculation of the T2* value. Also note that the calculated CH2/CH3 ratio and the CH2/CH3 chemical shift differences match well the expected values.

Acknowledgement: This work is supported by NIH grants CA099074 and HL085385.
References: [1] Wehrli FH et al Radiology 2000; 217, 527. [2] Link TM et al Radiology 1998; 209. [3] Majumdar S, et al JMRI 1992; 2:209. [4] Wehrli FH et al Magn Reson Imaging, 5; 157, 1987.