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Cross-Relaxation Imaging with MR

 

In order to estimate the k and f parameters that we are interested in for characterization of the brain tissue, we used a method known as cross-relaxation imaging. A broad discussion of the theory and implications of the method can be found in a paper by Yarynkh and Yuan [1]. The method consists of two steps where we acquire data from the patient. Using theoretical models explaining the behavior of our measurements [1,4,7], we try to estimate some unknown parameters of interest.

 

 

Figure 1. Diagram of k and f map generation.

 

Figure 1 displays a summary of the outflow of the process. In the first part, we acquire data with four different flip angles and using these data we create PD and R1 maps (this step is labeled as A in Figure 1). In the second part, instead of changing the flip angle to get contrast in the measured data, we use a magnetization transfer pulse. By varying the offset frequency at which the pulse is applied, we get four different-contrast images. Using these data and the previous estimation results, we are able to generate k and f maps (this step is labeled as C in Figure 1). The creation of the synthetic image shown with letter B in Figure 1 is required for normalization purposes, to increase statistical stability of the estimation process. The details of the estimation steps are explained in later sections.

 

 

Pulse Sequence Selection

 

The pulse sequence selection is important for the estimation process, as it is directly going to effect our signal equations and the complexity of the estimations. We used a three-dimensional (3D) spoiled gradient recalled acquisition in steady-state (SPGR) sequence for data acquisitions. A basic pulse sequence diagram for 3D-SPGR is shown in Figure 2. In an SPGR sequence the transverse magnetization is destroyed by non-periodic phase changes in the RF pulse at each period (given by TR, repetition time). Therefore the magnetization for an SPGR sequence can be represented as a scalar rather than a three-dimensional vector in space. This property of SPGR makes it suitable for estimation problems.

 

 

Figure 2. Pulse sequence diagram for an SPGR sequence.

 

The reason for doing a 3D acquisition is fast volume coverage within short scan times and higher signal-to-noise ratio (SNR) that it provides. Short scan times make the data acquisition part of the process feasible as you cannot keep the patients for long periods of time in the scanner. SNR considerations are also important because we want to have a small amount of noise for minimizing our estimation error. Finally, a 3D acquisition with SPGR saturates signal coming from fresh-blood inflow, thereby blood itself does not appear bright in the images.

 

The sequence used for the experiments is a GE product sequence, Vascular TOF-SPGR. Data acquisition was performed on a 1.5T GE Signa 12X scanner with CV/i gradients. Two different protocols were used for imaging. For the acquisition with varying flip angles, TE = 2.4ms, TR = 20ms was used, while the flip angle had four different values 4o, 10o, 20o, 30o. For the second set of acquisitions, the flip angle was kept constant at 10o, to minimize the T1 weighting in the acquired images. However, an additional Fermi-shaped magnetization transfer pulse with 8ms duration and 670o flip angle was added. TE = 2.4ms and TR = 32ms were prescribed. For both acquisitions a matrix of 256x160x70 was used, where axial slice selection and anterior to posterior readout direction were applied. To minimize the acquisition time in the phase encode direction, half-Fourier encoding was carried out, reducing the total samples to 80 in that direction. The acquisition was completed in a single slab without any inter-slab overlap slices. The acquisition resolution of 1.4mm x 2.3mm x 2.8mm, was interpolated to 1.4mm x 1.4mm x 2.8mm during the scanner reconstruction. Later the DICOM images were interpolated to isotropic 1.4mm resolution. The auto pre-scan settings from the first data acquisition were kept the same through a manual pre-scan before each acquisition.

 

 

T1 Estimation

 

The T1 estimation problem consists of getting measurements with different flip angles ant using the theoretical signal equation shown below to find a fit for T1 on a pixel basis. The signal S is a function of the flip angle α, the repetition time TR, T1 and a multiplicative factor in front named as PD. In fact, PD is a multiplication of many factors itself which can all be grouped into one parameter for our purposes. The flip angle and the repetition time are already known. Therefore we have two unknowns.

 

 

 

 

 


The fitting is done with linear regression analysis as explained by Fram et al. [8]. The signal equation can be rearranged into a form that closely resembled a line equation where the exponential term exp(-TR/T1) is the slope. The term on the right with the factor PD in it, is a weak function of T1 and therefore can be assumed to be a constant.

 

 

 

 

 

 


MT Fitting

 

The MT fitting problem is much more complicated than the previous estimation problem as it involves the interaction of bound and free pool protons, leading to matrix equations. The magnetization vectors for both bound and free protons are given below, where each of the terms are matrices themselves. Even when the equations are scalarized the magnetization of free pool protons, which the directly measured quantity in MR experiments, is a non-linear function of many variables as seen. The flip angle and the offset frequency are preset by the user. Estimates for PD and T1 are obtained in the previous step. However, we are left with 5 unknowns.

 

 

 

 

 

 

 


In this form, the estimation problem is very complex and many measurements have to be made in order to get estimates for all of the parameters. This will increase the scan time beyond the practically acceptable limit. Therefore, an appropriate approach is putting in average values for some of the parameters that we are not directly interested in. T1B cannot be measured at all, and in generally assumed to be 1s. T2B has an average value that has little variation from person to person, which is about 11us. Finally the ratio of T2 to T1 of free pool protons in the brain has an average value of 0.055; we can use this ratio and our T1 estimates to figure out what T2 is. In the end, our problem is reduced to a two-unknown problem where the unknown are actually the parameters that we want to measure.

 

Once the MT measurements are completed, the brain extraction tool (BET) by [9],is used to crop out the extra-cranial tissue, followed by a T1 thresholding ( > 2s ) carried out to remove CSF from the images. A synthetic image that reflects the signal that should have been detected at a TR of 32ms without any magnetization transfer pulse is created using the PD, T1 maps obtained and the signal equation for SPGR in the absence of magnetization transfer. This step is important for increasing the statistical stability of the non-linear estimation process to be carried out. K and f maps are created using MATLAB implementation of the Levenberg-Marquardt [10] algorithm.