Morphology-adaptive total variation for the reconstruction of quantitative susceptibility map from the magnetic resonance imaging phase

RESEARCH ARTICLE Morphology-adaptive total variation for the reconstruction of quantitative susceptibility map from the magnetic resonance imaging phase Li Guo1, Yingjie Mei1,2, Jijing Guan1, Xiangliang Tan3, Yikai Xu3, Wufan Chen1*, Qianjin Feng1, Yanqiu Feng1* a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 1 Guangdong Provincial Key Laboratory of Medical Image Processing, School of Biomedical Engineering, Southern Medical University, Guangzhou, China, 2 Philips Healthcare, Guangzhou, China, 3 Department of Medical Imaging Center, Southern Medical University Nanfang Hospital, Guangzhou, China * (WC); (YF) Abstract OPEN ACCESS Citation: Guo L, Mei Y, Guan J, Tan X, Xu Y, Chen W, et al. (2018) Morphology-adaptive total variation for the reconstruction of quantitative susceptibility map from the magnetic resonance imaging phase. PLoS ONE 13(5): e0196922. https://doi.org/10.1371/journal.pone.0196922 Editor: Dzung Pham, UNITED STATES Received: July 20, 2017 Accepted: April 23, 2018 Published: May 8, 2018 Copyright: © 2018 Guo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: In this study, two in vivo brain datasets were used. The in vivo dataset 1 was downloaded from the Cornell University website (http://weill.cornell.edu/mri/QSM/Online. zip) and the in vivo dataset 2 was downloaded from the QSM reconstruction challenge website (http:// qsm.neuroimaging.at). Funding: This research was funded by the National Natural Science Funds of China [61671228 and 61728107, http://www.nsfc.gov.cn/] and the Guangdong Provincial Science & Technology Program [2017B090912006, http://pro.gdstc.gov. Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that quantifies the magnetic susceptibility distribution within biological tissues. QSM calculates the underlying magnetic susceptibility by deconvolving the tissue magnetic field map with a unit dipole kernel. However, this deconvolution problem is ill-posed. The morphology enabled dipole inversion (MEDI) introduces total variation (TV) to regularize the susceptibility reconstruction. However, MEDI results still contain artifacts near tissue boundaries because MEDI only imposes TV constraint on voxels inside smooth regions. We introduce a Morphology-Adaptive TV (MATV) for improving TV-regularized QSM. The MATV method first classifies imaging target into smooth and nonsmooth regions by thresholding magnitude gradients. In the dipole inversion for QSM, the TV regularization weights are a monotonically decreasing function of magnitude gradients. Thus, voxels inside smooth regions are assigned with larger weights than those in nonsmooth regions. Using phantom and in vivo datasets, we compared the performance of MATV with that of MEDI. MATV results had better visual quality than MEDI results, especially near tissue boundaries. Preliminary brain imaging results illustrated that MATV has potential to improve the reconstruction of regions near tissue boundaries. Introduction Magnetic susceptibility is a fundamental physical property that describes the response of biological tissues to an applied magnetic field. The magnetic susceptibility inhomogeneity field map may be measured from the magnetic resonance imaging (MRI) phase data [1]. In quantitative susceptibility mapping (QSM), tissue magnetic susceptibility distribution is determined by deconvolving the local tissue field map with a dipole kernel [1–5]. Given the zero values of the dipole kernel along the magic angle in the k-space, the inversion of the local tissue field PLOS ONE | https://doi.org/10.1371/journal.pone.0196922 May 8, 2018 1 / 14 Quantitative susceptibility map with morphology-adaptive total variation cn/egrantweb/] to YF. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The commercial affiliation Philips Healthcare does not alter our adherence to PLOS ONE policies on sharing data and materials. map to the tissue magnetic susceptibility distribution is an ill-conditioned problem that causes streaking artifacts and amplifies noise in reconstructed susceptibility maps [6, 7]. To achieve accurate susceptibility reconstruction, one approach is to collect phase data at multiple head orientations with respect to the main magnetic field and calculate susceptibility maps by using methods such as the calculation of susceptibility through multiple orientation sampling (COSMOS) [8] and the susceptibility tensor imaging (STI) [9]. Multiple orientation sampling is not clinically feasible for QSM because it substantially prolongs scan time. Moreover, the repositioning of imaging subjects in a fixed magnet is restricted to a narrow range in multiple orientation methods. Therefore, the reconstruction of susceptibility maps from single orientation phase data is the primary approach in practice. The results obtained by COSMOS or STI from multiple orientation phase data are the references for evaluating the performance of single orientation methods. Compared with multiple orientation techniques, single orientation QSM has the advantage of reduced scan time but suffers from streaking artifacts and noise amplification due to the illposedness of the inversion problem. To mitigate artifacts and noise, various QSM methods have been developed to address dipole inversion from single orientation sampling [10–25]. Among Bayesian regularization approaches, morphology enabled dipole inversion (MEDI) [11, 12, 26] combine total variation (TV) and morphological information in magnitude to regularize the susceptibility reconstruction. However, the susceptibility maps generated by MEDI may still contain artifacts near tissue edges because it imposes no constraints in these regions. Here, we introduce a Morphology-Adaptive TV (MATV) regularization method for single orientation QSM to improve the susceptibility reconstruction in regions with tissue edges. The MATV method enforces the TV penalty on the whole susceptibility map and the TV penalty weights are a monotonically decreasing function of magnitude gradient maps. Small regularization weights are added to nonsmooth regions and large regularization weights are added to smooth regions. Gadolinium phantom and in vivo experiments were performed to evaluate the performance of MATV. Methods Relation between magnetic susceptibility and field The tissue magnetic susceptibility χ is a measure for the amount of magnetization induced in tissue that is exposed to the main magnetic field of an MRI scanner. Convolving χ with the zcomponent of the dipole kernel yields the local tissue magnetic field, φ, the change in magnetic susceptibility relative to the main magnetic field. In r-space, the susceptibil (...truncated)