Department of Health Technology, Technical University of Denmark, Kgs. Lyngby 2800, Denmark.
Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, 2650, Denmark; Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby 2800, Denmark.
J Magn Reson. 2021 Dec;333:107103. doi: 10.1016/j.jmr.2021.107103. Epub 2021 Nov 5.
MRI can be utilized for quantitative characterization of tissue. To assess e.g. water fractions or diffusion coefficients for compartments in the brain, a decomposition of the signal is necessary. Imposing standard models carries the risk of estimating biased parameters if model assumptions are violated. This work introduces a data-driven multicomponent analysis, the monotonous slope non-negative matrix factorization (msNMF), tailored to extract data features expected in MR signals.
The msNMF was implemented by extending the standard NMF with monotonicity constraints on the signal profiles and their first derivatives. The method was validated using simulated data, and subsequently applied to both ex vivo DWI data and in vivo relaxometry data. Reproducibility of the method was tested using the latter.
The msNMF recovered the multi-exponential signals in the simulated data and showed superiority to standard NMF (based on the explained variance, area under the ROC curve, and coefficient of variation). Diffusion components extracted from the DWI data reflected the cell density of the underlying tissue. The relaxometry analysis resulted in estimates of edema water fractions (EWF) highly correlated with published results, and demonstrated acceptable reproducibility.
The msNMF can robustly separate MR signals into components with relation to the underlying tissue composition, and may potentially be useful for e.g. tumor tissue characterization.
MRI 可用于组织的定量特征描述。例如，为了评估大脑中各腔室的水分数或扩散系数，需要对信号进行分解。如果违反了模型假设，那么使用标准模型来估计可能会导致有偏差的参数。本研究引入了一种数据驱动的多分量分析方法，单调斜率非负矩阵分解（msNMF），旨在提取 MR 信号中预期的数据特征。
通过对信号轮廓及其一阶导数施加单调性约束，对标准 NMF 进行扩展，实现了 msNMF。该方法使用模拟数据进行了验证，随后应用于离体 DWI 数据和体内弛豫测量数据。使用后者测试了该方法的可重复性。
msNMF 恢复了模拟数据中的多指数信号，并优于标准 NMF（基于解释方差、ROC 曲线下面积和变异系数）。从 DWI 数据中提取的扩散分量反映了基础组织的细胞密度。弛豫测量分析得到的水肿水分数（EWF）与已发表的结果高度相关，并且具有可接受的可重复性。
msNMF 可以稳健地将 MR 信号分解为与基础组织成分相关的分量，可能对肿瘤组织特征分析等具有潜在的应用价值。
