Effective removal of nuisance signals (3 or 4 orders of magnitude larger than metabolite signals) is often challenging for practical $$$^1$$$H-MRSI experiments. Conventional methods resort to water and lipid suppression pulses followed by post processing to remove any residual nuisance signals.^1-4 While these methods perform reasonably well for $$$^1$$$H-MRSI data collected with long T$$$_\text{E}$$$, Nyquist sampling of (k,t)-space, and suppression pulses, they cannot handle sparsely sampled $$$^1$$$H-MRSI data collected with short T$$$_\text{E}$$$ and no suppression pulses. This paper presents a new method to address this problem. A key feature lies in the use of spectral bases generated for water and subcutaneous lipids using quantum simulation (Fig. 1). With these spectral bases, the proposed method can effectively remove water and lipid signals from sparsely sampled $$$^1$$$H-MRSI data acquired without suppression pulses. The method will be particularly useful for accelerated MRSI applications.

In order to incorporate prior spectral information for water and subcutaneous lipids into our method, we express the MR signal of water or lipids as $$\rho(t)=s(t)e(t)=\sum_{n=1}^N{c_n e^{-t/T_{2n}-j2\pi f_nt}}\sum_{p=1}^P{g_p e^{j2\pi p\Delta f t}},$$ where $$$s(t)$$$ represents the ideal Lorentzian-shaped spectrum, and $$$e(t)$$$ is the generalized series (GS)⁵ compensating any line-shape distortions caused by local field inhomogeneity. It is well-known that under ideal conditions, water protons have one spectral component at 4.7ppm, and triglycerides (the principal MR measurable subcutaneous lipids)^6,7 possess protons experiencing different electron shielding effects and generate multiple resonance components (Fig. 1a). The ideal spectral structures for both water and lipids can be generated through quantum simulation.⁸ An example of triglyceride spectrum is shown in Fig. 1b. Note that: 1) the concentration ratios between the different spectral components are not spatially uniform since the saturation of triglycerides varies; 2) different spectral components have different T$$$_2$$$ relaxation constants.⁷

Given the spectral bases, the proposed method uses a small set of model parameters denoted as $$$\boldsymbol{\theta}=\{\{c_n\},\{T_{2n},\{g_p\}\}\}$$$ to ensure that the model matches with given experimental data. We propose to estimate $$$\boldsymbol{\theta}$$$ by solving the optimization problem below and then subtract the estimated nuisance signals from the original signal: $$\hat{\boldsymbol{\theta}}=\text{arg}\min_{\boldsymbol{\theta}}{\|\mathbf{d}-\mathbf{\Omega}_{\mathbf{k}t} \mathbf{F}\sum_{m} \mathbf{\Omega}_{\mathbf{x}}^{(m)}\boldsymbol{\rho}^{(m)}(\boldsymbol{\theta})\|_2^2+R(\boldsymbol{\theta})},$$where $$$\mathbf{d}$$$, $$$\boldsymbol{\rho}$$$, and $$$\mathbf{n}$$$ are each discretized and vectorized, $$$\mathbf{\Omega}_{\mathbf{k}t}$$$ is the (k,t)-space sampling operator, $$$\mathbf{F}$$$ represents the transform from x-space to k-space, $$$\mathbf{\Omega}_{\mathbf{x}}^{(m)}$$$ is the spatial support for the $$$m$$$-th type of tissue (e.g., fat layer, white matter, gray matter, and CSF, as in the brain), and $$$R(\boldsymbol{\theta})$$$ is a regularization term imposing both spatial and spectral constraints on $$$\boldsymbol{\theta}$$$.

In practice, the spatial constraints can be obtained from auxiliary anatomical scans. The optimization problem can be efficiently solved by alternatively determining $$$\boldsymbol{\theta}_1=\{\{c_n\},\{T_{2n}\}\}$$$ and $$$\boldsymbol{\theta}_2=\{g_p\}$$$. Specifically, when $$$\boldsymbol{\theta}_1$$$ is fixed, it is a linear least-squares (LS) problem and can be solved by standard convex optimization tools; when $$$\boldsymbol{\theta}_2$$$ is fixed, it is a large-scale nonlinear LS problem, and we can resort to quasi-Newton methods such as the limited-memory BFGS algorithm.⁹

We have evaluated the performance of the proposed method using experimental data acquired from the brain of healthy volunteers on a 3T Siemens Trio MRI scanner. The acquisition sequence was a 2D bipolar echo-planar spectroscopic imaging (EPSI) sequence, with echo time T$$$_\text{E}$$$=20ms, echo-spacing 1.74ms, and in-plane nominal resolution 3.75mm (64x64 matrix size). A corresponding anatomical image was also acquired and segmented into different tissue types (Fig. 2). Note lipid signals were assumed to be generated from the fat layer.

The nuisance removal effect is shown in Fig. 3. As can be seen, the nuisance was removed to a negligible level, even when no suppression pulses were applied in the data acquisition. In nuisance signal removal, it is important that metabolite signals are protected. To demonstrate the ability of the proposed method to preserve metabolite signals during nuisance removal, two sets of MRSI reconstruction results are shown in Fig. 4, 5. The reconstructions were obtained using: 1) the conventional Fourier method, with a hamming window; and 2) the SPICE reconstruction method.¹⁰ As can be seen, the metabolite signals are well-preserved in the reconstructions by the proposed nuisance removal method.

A novel method is presented for removing nuisance signals from $$$^1$$$H-MRSI data. The proposed method uses spectral bases for water and lipids generated using quantum simulation. To our knowledge, this is the first time that prior spectral information for water and lipids are used for nuisance signals removal for $$$^1$$$H-MRSI. Experimental results demonstrate that the method can handle sparsely sampled $$$^1$$$H-MRSI data acquired without nuisance suppression pulses. The proposed method will enhance the flexibility and practical usefulness of accelerated $$$^1$$$H-MRSI.