Phase jolt: 2nd spatial derivative of phase is a new contrast with benefits for SWI type processing

1921 

Abstract Submission 

Omer Faruk Gulban^1,2, Andreas Deistung³, Desmond Ho Yan Tse⁴, Saskia Bollmann⁵, Renzo Huber⁶, Rainer Goebel^1,2, Kendrick Kay⁷, Dimo Ivanov¹

¹Maastricht University, Maastricht, Netherlands, ²Brain Innovation, Maastricht, Netherlands, ³Polyclinic for Radiology, University Hospital Halle, Halle, Germany, ⁴Scannexus, Maastricht, Netherlands, ⁵School of Electrical Engineering and Computer Science, The University of Queensland, Brisbane, Queensland, ⁶National Institutes of Health, Washington, MD, ⁷Center for Magnetic Resonance Research, Department of Radiology, University of Minnesota, Minneapolis, MN

Omer Faruk Gulban  
Maastricht University|Brain Innovation
Maastricht, Netherlands|Maastricht, Netherlands

Andreas Deistung  
Polyclinic for Radiology, University Hospital Halle
Halle, Germany

Desmond Ho Yan Tse  
Scannexus
Maastricht, Netherlands

Saskia Bollmann  
School of Electrical Engineering and Computer Science, The University of Queensland
Brisbane, Queensland

Renzo Huber  
National Institutes of Health
Washington, MD

Rainer Goebel  
Maastricht University|Brain Innovation
Maastricht, Netherlands|Maastricht, Netherlands

Kendrick Kay  
Center for Magnetic Resonance Research, Department of Radiology, University of Minnesota
Minneapolis, MN

Dimo Ivanov  
Maastricht University
Maastricht, Netherlands

Unlike magnitude images, even simple averaging is difficult with phase images, because of the circular nature of phase, spanning 2pi radians range. There is a well-developed literature on how to process phase images [1-5]. However, there are also well-known challenges that arise, such as still remaining phase wraps in regions with low signal-to-noise ratio (SNR) after phase unwrapping or removal of background fields. While employing these methods help make phase images more accessible for end users, using phase data is less practical and less commonplace compared to magnitude images. In our own research that uses mesoscopic imaging (<0.5 mm iso.) at 7 T, we need to average multiple acquisitions to increase image signal-to-noise ratio (SNR). To address this problem, we propose to operate on the magnitude of the 2nd spatial derivative of phase images - coining the term "phase jolt".

We compute spatial partial derivatives of the phase images through the "circular differences". This operation accounts for the "phase wraps" at pairwise computations. For each voxel in a 3D MR phase image, we compute the circular differences along x, y, z axes to obtain the first spatial phase derivative image. The 1st spatial derivative is a "vector field", where each voxel has three values associated with it (as opposed to the initial scalar phase field, where each voxel has a single value associated with it). Note that the circular differences are always in -pi to pi radians range, where the sign indicates clockwise or counterclockwise direction. Once the 1st spatial derivative is computed, we quantify the magnitude of the vectors using the L1 norm divided by 3. We call this spatial operation "phase jump".

The phase jump images highlight tissue edges; however, they also reveal the large-scale phase variations originating from the background field (Fig 1). To account for this, we suggest the 2nd spatial derivative of the phase images. We compute this by taking the spatial derivative of the 1st spatial derivative vector field, resulting in a "tensor field" (where each voxel has 9 values associated). Then, we compute the magnitude of the 2nd spatial derivative using the L1 norm divided by 9. This magnitude calculation again results in a natural 0 to pi radians range. We call this spatial operation "phase jolt". The benefits of computing the phase jolt are the same as for the phase jump while further mitigating the bias field (Figure1). The downside is that it requires integrating even more information than the phase jump, therefore lowering the effective resolution.

We compute the phase jump and jolt on the data acquired as described by [6] using a multi echo gradient echo protocol [7] at 7 T with pTx [8]. Briefly, we have 6 echoes at 0.35 mm isot. resolution, using low acceleration.

Fig 1A shows the phase jump and jolt contrasts compared to the corresponding T2*-weighted magnitude and phase images. Fig 1B highlights that phase images are hard to average due to their circular nature. However, phase jolt images are easy to average due to their numerical range with natural zero and maximum (pi radians).

Fig 2 demonstrates the benefit of phase jolt over phase jump, especially for mitigating the background field.

Phase jolt contrast is easy to compute and implement (several voxel-wise circular subtractions, and L1 norm). It provides an informative image where vessels are enhanced while the background field is mitigated. Therefore, phase jolt images may provide an additional contrast in any setting where phase images are recorded. The exquisite contrast of venous vessels in the phase jolt image might be used in a similar setting as susceptibility weighted imaging (SWI) where it may serve to create a phase mask to enhance the sensitivity towards vessels in T2*-weighted images. Additionally, phase jolt images can also be computed on fMRI data. Our implementation is available within the LayNii software package [10] via LN2_PHASE_JOLT program.

Methods Development ¹

Anatomical MRI ²

ANGIOGRAPHY

Cortical Layers

HIGH FIELD MR

MR ANGIOGRAPHY

MRI

MRI PHYSICS

STRUCTURAL MRI

Structures

Sub-Cortical

Other - Mesoscopic