QSM (Quantitative Susceptibility Mapping) estimates tissue magnetic susceptibility which quantifies subtle changes in magnetic phase due to dipole convolution. Image phase is inevitably contaminated by background phase induced by non-tissue sources such as magnetic field inhomogeneity and air-tissue interfaces, and is several orders of magnitude larger than phase from tissue sources. Therefore, in order to attain valid tissue phase from which QSM can be computed, non-biological background phase must be thoroughly removed.

Recent background phase removal (BPR) methods approximate the background phase of an image using spherical mean values (SMV)¹. In these methods, the SMV kernel size plays a key role. Conventionally, kernel sizes range from being as large as 5 to 9 mm at the center of the brain, gradually decreasing to smaller values near the air-tissue interface (distance adaptive BPR)^2,3. However, using such large kernel sizes near the center of the brain have proven insufficient for removing phase induced by localized air-tissue interfaces in more central areas such as the sinuses, causing artifacts.

In this paper, we propose a novel adaptive kernel BPR method which reduces QSM artifacts by automatically adapting conventional SMV kernels size to more optimal values for different brain region (region adaptive BPR). Brain regions are automatically detected using machine learning techniques.

QSM Processing

The proposed QSM method is shown in Fig 1. To detect the positions of four anatomical regions in the brain, a knowledge-based region detection technique using extremely randomized trees⁴ is applied to the input image magnitude (Fig. 1A). These four anatomical regions are known to contain high background signal even after distance adaptive BPR (Fig. 1B), and include the anterior cranial fossa, the left and right middle cranial fossa and the superior sagittal sinus.

Next, two tissue phase images $$$\varphi_{s1} $$$ and $$$\varphi_{s2} $$$ (Fig. 1D and E) are generated from the unwrapped phase image (Fig. 1C) using two different SMV kernel sizes, $$$s1$$$ and $$$s2$$$. The first kernel size $$$s1$$$ is set to a value typical for the center of the brain. The second kernel size $$$s2$$$ is set to a value less than $$$s1$$$, which is typically recommended for areas near the air-tissue interface. In this paper, $$$s1$$$ and $$$s2$$$ are set to 9 mm and 3 mm, respectively.

Then, $$$\varphi_{s1} $$$ near each of the four identified brain regions are fitted with 3D generalized Gaussians centered at the spatial positions detected in Fig. 1B. The modeled Gaussian distributions are used to compute a normalized map $$$\alpha$$$ (Fig. 1F), corresponding to weights per voxel. These weights are used to compute a weighted sum of tissue phase images $$$\varphi_{s1} $$$ and $$$\varphi_{s2} $$$, yielding a final tissue phase image $$$\varphi$$$ (Fig. 1G).

Finally, a susceptibility map $$$\chi^\ast$$$ is generated by solving the field to source inverse problem using L1-regularized optimization: $$$\chi^\ast={\rm argmin}_{\chi}\| F^{-1}DF\chi-\varphi\|_2+\lambda\|G\chi\|_1$$$, where $$$D$$$ denotes the dipole kernel, $$$F$$$ denotes the 3D Fourier transform operator, $$$G$$$ denotes the 3D gradient operator and $$$\lambda$$$ is the regularization coefficient.

Data acquisition

Seventy-five datasets were acquired from 75 healthy volunteers on a 3T MRI scanner using a 3D gradient echo sequence with the following parameters: TE/TR = 40/60 ms, FA = 20, 1 mm isotropic resolution, FOV = 256 x 256 x 150 mm.

Evaluation

To evaluate the automatic region detection algorithm, distance between detected coordinates and two human-annotated coordinates were measured for each region. Errors was computed separately for each dataset using the leave-one-out cross-validation method and compared to interobserver errors.

The region adaptive BPR method was evaluated based on its ability to eliminate artifacts in both the tissue phase image and susceptibility image compared to the conventional distance adaptive BPR which only uses kernel size (Fig. 1D).

For the proposed region detection algorithm, we confirmed that the algorithm successfully detected all four anatomical regions in all 75 datasets. An example of detected coordinates is shown in Fig. 2. The average error was 3.8 mm which is lower than interobserver errors (Fig. 3) and the processing time was approximately 0.2 seconds on a 3.5-GHz CPU.

For the proposed adaptive kernel BPR method, we confirmed that the algorithm successfully eliminates phase artifacts due to localized air-tissue interfaces more central to the brain. Artifacts were reduced in both the tissue phase image (yellow arrows in Fig. 4) as well as the computed susceptibility images (red arrows in Fig. 5), especially streak artifacts.