Noise-reduction techniques for 1H-FID-MRSI at 14.1T: Monte-Carlo validation & in vivo application

Proton magnetic resonance spectroscopic imaging (1H-MRSI) is a powerful tool that enables the multidimensional non-invasive mapping of the neurochemical profile at high-resolution over the entire brain. The constant demand for higher spatial resolution in 1H-MRSI led to increased interest in post-processing-based denoising methods aimed at reducing noise variance. The aim of the present study was to implement two noise-reduction techniques, the Marchenko-Pastur principal component analysis (MP-PCA) based denoising and the low-rank total generalized variation (LR-TGV) reconstruction, and to test their potential and impact on preclinical 14.1T fast in vivo 1H-FID-MRSI datasets. Since there is no known ground truth for in vivo metabolite maps, additional evaluations of the performance of both noise-reduction strategies were conducted using Monte-Carlo simulations. Results showed that both denoising techniques increased the apparent signal-to-noise ratio SNR while preserving noise properties in each spectrum for both in vivo and Monte-Carlo datasets. Relative metabolite concentrations were not significantly altered by either methods and brain regional differences were preserved in both synthetic and in vivo datasets. Increased precision of metabolite estimates was observed for the two methods, with inconsistencies noted on lower concentrated metabolites. Our study provided a framework on how to evaluate the performance of MP-PCA and LR-TGV methods for preclinical 1H-FID MRSI data at 14.1T. While gains in apparent SNR and precision were observed, concentration estimations ought to be treated with care especially for low-concentrated metabolites.Comment: Brayan Alves and Dunja Simicic are joint first authors. Currently in revision for NMR in Biomedicin

Superresolution Reconstruction for Magnetic Resonance Spectroscopic Imaging Exploiting Low-Rank Spatio-Spectral Structure

Magnetic resonance spectroscopic imaging (MRSI) is a rapidly developing medical imaging modality, capable of conferring both spatial and spectral information content, and has become a powerful clinical tool. The ability to non-invasively observe spatial maps of metabolite concentrations, for instance, in the human brain, can offer functional, as well as pathological insights, perhaps even before structural aberrations or behavioral symptoms are evinced. Despite its lofty clinical prospects, MRSI has traditionally remained encumbered by a number of practical limitations. Of primary concern are the vastly reduced concentrations of tissue metabolites when compared to that of water, which forms the basis for conventional MR imaging. Moreover, the protracted exam durations required by MRSI routinely approach the limits for patient compliance. Taken in conjunction, the above considerations effectively circumscribe the data collection process, ultimately translating to coarse image resolutions that are of diminished clinical utility. Such shortcomings are compounded by spectral contamination artifacts due to the system pointspread function, which arise as a natural consequence when reconstructing non-band-limited data by the inverse Fourier transform. These artifacts are especially pronounced near regions characterized by substantial discrepancies in signal intensity, for example, the interface between normal brain and adipose tissue, whereby the metabolite signals are inundated by the dominant lipid resonances. In recent years, concerted efforts have been made to develop alternative, non-Fourier MRSI reconstruction strategies that aim to surmount the aforementioned limitations. In this dissertation, we build upon the burgeoning medley of innovative and promising techniques, proffering a novel superresolution reconstruction framework predicated on the recent interest in low-rank signal modeling, along with state-of-the-art regularization methods. The proposed framework is founded upon a number of key tenets. Firstly, we proclaim that the underlying spatio-spectral distribution of the investigated object admits a bilinear representation, whereby spatial and spectral signal components can be effectively segregated. We further maintain that the dimensionality of the subspace spanned by the components is, in principle, bounded by a modest number of observable metabolites. Secondly, we assume that local susceptibility effects represent the primary sources of signal corruption that tend to disallow such representations. Finally, we assert that the spatial components belong to a class of real-valued, non-negative, and piecewise linear functions, compelled in part through the use of a total variation regularization penalty. After demonstrating superior spatial and spectral localization properties in both numerical and physical phantom data when compared against standard Fourier methods, we proceed to evaluate reconstruction performance in typical in vivo settings, whereby the method is extended in order to promote the recovery of signal variations throughout the MRSI slice thickness. Aside from the various technical obstacles, one of the cardinal prospective challenges for high-resolution MRSI reconstruction is the shortfall of reliable ground truth data prudent for validation, thereby prompting reservations surrounding the resulting experimental outcomes. [...

Autocalibration Region Extending Through Time: A Novel GRAPPA Reconstruction Algorithm to Accelerate 1H Magnetic Resonance Spectroscopic Imaging

Magnetic resonance spectroscopic imaging (MRSI) has the ability to noninvasively interrogate metabolism in vivo. However, excessively long scan times have thus far prevented its adoption into routine clinical practice. Generalized autocalibrating partially parallel acquisitions (GRAPPA) is a parallel imaging technique that allows one to reduce acquisition duration and use spatial sensitivity correlations to reconstruct the unsampled data points. The coil sensitivity weights are determined implicitly via a fully-sampled autocalibration region in k-space. In this dissertation, a novel GRAPPA-based algorithm is presented for the acceleration of 1H MRSI. Autocalibration Region extending Through Time (ARTT) GRAPPA instead extracts the coil weights from a region in k-t space, allowing for undersampling along each spatial dimension. This technique, by exploiting spatial-spectral correlations present in MRSI data, allows for a more accurate determination of the coil weights and subsequent parallel imaging reconstruction. This improved reconstruction accuracy can then be traded for more aggressive undersampling and a further reduction of acquisition duration. It is shown that the ARTT GRAPPA technique allows for approximately two-fold more aggressive undersampling than the conventional technique while achieving the same reconstruction accuracy. This accelerated protocol is then applied to acquire high-resolution brain metabolite maps in less than twenty minutes in three healthy volunteers at B0 = 7 T

MP-PCA denoising for diffusion MRS data: promises and pitfalls

Diffusion-weighted (DW) magnetic resonance spectroscopy (MRS) suffers from a lower signal to noise ratio (SNR) compared to conventional MRS owing to the addition of diffusion attenuation. This technique can therefore strongly benefit from noise reduction strategies. In the present work, the Marchenko-Pastur principal component analysis (MP-PCA) denoising is tested on Monte Carlo simulations and on in vivo DW-MRS data acquired at 9.4T in the rat brain. We provide a descriptive study of the effects observed following different MP-PCA denoising strategies (denoising the entire matrix versus using a sliding window), in terms of apparent SNR, rank selection, noise correlation within and across b-values and quantification of metabolite concentrations and fitted diffusion coefficients. MP-PCA denoising yielded an increased apparent SNR, a more accurate B0 drift correction between shots, and similar estimates of metabolite concentrations and diffusivities compared to the raw data. No spectral residuals on individual shots were observed but correlations in the noise level across shells were introduced, an effect which was mitigated using a sliding window, but which should be carefully considered.Comment: Cristina Cudalbu and Ileana O. Jelescu have contributed equally to this manuscrip

MP-PCA denoising for diffusion MRS data: promises and pitfalls.

Diffusion-weighted (DW) magnetic resonance spectroscopy (MRS) suffers from a lower signal to noise ratio (SNR) compared to conventional MRS owing to the addition of diffusion attenuation. This technique can therefore strongly benefit from noise reduction strategies. In the present work, Marchenko-Pastur principal component analysis (MP-PCA) denoising is tested on Monte Carlo simulations and on in vivo DW-MRS data acquired at 9.4T in rat brain and at 3T in human brain. We provide a descriptive study of the effects observed following different MP-PCA denoising strategies (denoising the entire matrix versus using a sliding window), in terms of apparent SNR, rank selection, noise correlation within and across b-values and quantification of metabolite concentrations and fitted diffusion coefficients. MP-PCA denoising yielded an increased apparent SNR, a more accurate B0 drift correction between shots, and similar estimates of metabolite concentrations and diffusivities compared to the raw data. No spectral residuals on individual shots were observed but correlations in the noise level across shells were introduced, an effect which was mitigated using a sliding window, but which should be carefully considered

Subspace estimation for subspace-based magnetic resonance spectroscopic imaging

Magnetic resonance spectroscopic imaging (MRSI) is a powerful technique that offers us the ability to non-invasively image chemical distributions within the human body. However, due to its inherently poor trade-off between imaging speed, resolution, and signal-to-noise ratio (SNR), MRSI has remained impractical for many research and clinical applications. A large body of work has been done to improve this trade-off. Recently new subspace-based imaging methods have also been proposed as a means of dramatically accelerating MRSI. By taking advantage of the properties of a partially separable (PS) signal model, subspace-based methods offer increased flexibility in acquisition as well as image reconstruction, and thereby allow high-resolution, high-SNR MRSI images to be obtained in a fraction of the time required by standard techniques. An important ingredient common to all subspace-based imaging methods is the estimation of the subspace structure of the high-dimensional image function. However, accurate subspace estimation in the presence of noise and inhomogeneity in the main magnetic field is challenging. To this end we propose a novel method for subspace estimation which utilizes a regularized-reconstruction approach to correct for the effects of field inhomogeneity and noise. Carefully designed numerical simulations and experimental studies have been performed to evaluate the performance of the proposed method in a variety of experimental conditions. Results from these data show that the proposed method is able to obtain an accurate subspace estimation, either in terms of a projection error metric or by inspecting the residual after projecting the fully sampled data onto the estimated subspaces. Additionally, in vivo MRSI data was acquired to illustrate that the subspace estimated by the proposed method leads to high-quality spatiospectral reconstructions

A subspace approach to high-resolution magnetic resonance spectroscopic imaging

With its unique capability to obtain spatially resolved biochemical profiles from the human body noninvasively, magnetic resonance spectroscopic imaging (MRSI) has been recognized as a powerful tool for in vivo metabolic studies. However, research and clinical applications of in vivo MRSI have been progressing more slowly than expected. The main reasons for this situation are the problems of long data acquisition time, poor spatial resolution and low signal-to-noise ratio (SNR) for this imaging modality. In the last four decades, significant efforts have been made to improve MRSI, resulting in a large number of fast pulse sequences and advanced image reconstruction methods. However, the existing techniques have yet to offer the levels of improvement in imaging time, spatial resolution and SNR necessary to significantly impact in vivo applications of MRSI. This thesis work develops a new subspace imaging approach to address these technical challenges to enable fast, high-resolution MRSI with high SNR. The proposed approach, coined SPICE (Spectroscopic Imaging by Exploiting Spatiospectral Correlation), is characterized by using a subspace model for integrative data acquisition, processing and image reconstruction. More specifically, SPICE represents the spectroscopic signals in MRSI using the partial separability (PS) model. The PS model implies that the high-dimensional spectroscopic signals reside in a low-dimensional subspace, which enables the design of special sparse sampling strategies for accelerated spatiospectral encoding and special image reconstruction strategies for determining the subspace and reconstructing the underlying spatiospectral function of interest from the sparse data. Using the SPICE framework, new data acquisition and image reconstruction methods are developed to enable high-resolution 1H-MRSI of the brain. We have evaluated SPICE using theoretical analysis, numerical simulations, phantom and in vivo experimental studies. Results obtained from these experiments demonstrate the unprecedented capability of SPICE in achieving accelerated MRSI with simultaneously very high resolution and SNR. We expect SPICE to provide a powerful tool for in vivo metabolic studies with many exciting applications. Furthermore, the SPICE framework also presents new opportunities for future developments in subspace-driven signal generation, signal encoding, data processing and image reconstruction methods to advance the research and clinical applications of high-resolution in vivo MRSI

Comparison of MRI Spectroscopy software packages performance and application on HCV-infected patients’ real data

Treballs Finals de Grau d'Enginyeria Biomèdica. Facultat de Medicina i Ciències de la Salut. Universitat de Barcelona. Curs: 2022-2023. Tutor/Director: Sala Llonch, Roser, Laredo Gregorio, Carlos1H MRS is conceived as a pioneer methodology for brain metabolism inspection and health status appraisal. Post-processing interventions are required to obtain explicit metabolite quantification values from which to derive diagnosis. On the grounds of addressing and covering such operation, multiple software packages have been recently developed and launched leading to an amorphous assortment of spectroscopic image processing tools, with lack of standardization and regulation. The current study thereby intends to judge the coherence and consistency of compound estimation outputs in terms of result variability by intercorrelation and intracorrelation analyses between appointed programs, being LCModel, Osprey, TARQUIN, and spant toolbox. The examination is performed on a 83-subject SVS short-TE 3T SIEMENS PRESS spectroscopic acquisitions’ collection, including healthy controls and HCV-infected patients assisted with DAA treatment. The analytical core of the project assesses software performance through the creation of a Python script in order to automatically compute and display the results sought. The statistical tests providing enough information to draw substantial conclusions stem from extraction of coefficient of determination (R2 ), Pearson’s coefficient (r), and intraclass correlation coefficient (ICC) together with representation of boxplots, rainclouds, and scatter plots easing data visualization. A clinical implementation is also entailed on the same basis, whose purpose is to reveal actual DAA treatment effect on HCV-infected patients by means of metabolite concentration alteration and hypothetical restoration. Conclusions declare evident and alarming variability among MRS platforms compromising the rigor, sharpness and systematization demanded in this discipline since quantification results hold incoherences, although they do not seem to affect or oppose medical determinations jeopardizing patient’s health. However, it would be interesting to extend the analysis to a greater cohort of subjects to reinforce and get to more solid resolutions

Improving the Clinical Use of Magnetic Resonance Spectroscopy for the Analysis of Brain Tumours using Machine Learning and Novel Post-Processing Methods

Magnetic Resonance Spectroscopy (MRS) provides unique and clinically relevant information for the assessment of several diseases. However, using the currently available tools, MRS processing and analysis is time-consuming and requires profound expert knowledge. For these two reasons, MRS did not gain general acceptance as a mainstream diagnostic technique yet, and the currently available clinical tools have seen little progress during the past years. MRS provides localized chemical information non-invasively, making it a valuable technique for the assessment of various diseases and conditions, namely brain, prostate and breast cancer, and metabolic diseases affecting the brain. In brain cancer, MRS is normally used for: (1.) differentiation between tumors and non-cancerous lesions, (2.) tumor typing and grading, (3.) differentiation between tumor-progression and radiation necrosis, and (4.) identification of tumor infiltration. Despite the value of MRS for these tasks, susceptibility differences associated with tissue-bone and tissue-air interfaces, as well as with the presence of post-operative paramagnetic particles, affect the quality of brain MR spectra and consequently reduce their clinical value. Therefore, the proper quality management of MRS acquisition and processing is essential to achieve unambiguous and reproducible results. In this thesis, special emphasis was placed on this topic. This thesis addresses some of the major problems that limit the use of MRS in brain tumors and focuses on the use of machine learning for the automation of the MRS processing pipeline and for assisting the interpretation of MRS data. Three main topics were investigated: (1.) automatic quality control of MRS data, (2.) identification of spectroscopic patterns characteristic of different tissue-types in brain tumors, and (3.) development of a new approach for the detection of tumor-related changes in GBM using MRSI data. The first topic tackles the problem of MR spectra being frequently affected by signal artifacts that obscure their clinical information content. Manual identification of these artifacts is subjective and is only practically feasible for single-voxel acquisitions and in case the user has an extensive experience with MRS. Therefore, the automatic distinction between data of good or bad quality is an essential step for the automation of MRS processing and routine reporting. The second topic addresses the difficulties that arise while interpreting MRS results: the interpretation requires expert knowledge, which is not available at every site. Consequently, the development of methods that enable the easy comparison of new spectra with known spectroscopic patterns is of utmost importance for clinical applications of MRS. The third and last topic focuses on the use of MRSI information for the detection of tumor-related effects in the periphery of brain tumors. Several research groups have shown that MRSI information enables the detection of tumor infiltration in regions where structural MRI appears normal. However, many of the approaches described in the literature make use of only a very limited amount of the total information contained in each MR spectrum. Thus, a better way to exploit MRSI information should enable an improvement in the detection of tumor borders, and consequently improve the treatment of brain tumor patients. The development of the methods described was made possible by a novel software tool for the combined processing of MRS and MRI: SpectrIm. This tool, which is currently distributed as part of the jMRUI software suite (www.jmrui.eu), is ubiquitous to all of the different methods presented and was one of the main outputs of the doctoral work. Overall, this thesis presents different methods that, when combined, enable the full automation of MRS processing and assist the analysis of MRS data in brain tumors. By allowing clinical users to obtain more information from MRS with less effort, this thesis contributes to the transformation of MRS into an important clinical tool that may be available whenever its information is of relevance for patient management

양성자 자기공명분광법을 사용한 딥러닝 기반 두뇌 대사체 정량화 기법

학위논문(박사) -- 서울대학교대학원 : 의과대학 의과학과, 2022.2. 김현진.Nonlinear-least-squares-fitting (NLSF) is widely used in proton magnetic resonance spectroscopy (MRS) for quantification of brain metabolites. However, it is known to subject to variability in the quantitative results depending on the prior knowledge. NLSF-based metabolite quantification is also sensitive to the quality of spectra. In combination with NLSF, Cramer-Rao lower Bounds (CRLB) are used as representing lower bounds of fit errors rather than actual errors. Consequently, a careful interpretation is required to avoid potential statistical bias. The purpose of this study was to develop more robust methods for metabolite quantification and uncertainty estimation in MRS by employing deep learning that has demonstrated its potential in a variety of different tasks including medical imaging. To achieve this goal, first, a convolutional neural network (CNN) was developed. It maps typical brain spectra that are degraded with noise, line-broadening and unknown baseline into noise-free, line-narrowed, baseline-removed spectra. Then, metabolites are quantified from the CNN-predicted spectra by a simple linear regression with more robustness against spectral degradation. Second, a CNN was developed that can isolate each individual metabolite signals from a typical brain spectrum. The CNN output is used not only for quantification but also for calculating signal-to-background-ratio (SBR) for each metabolite. Then, the SBR in combination with big training data are used for estimating measurement uncertainty heuristically. Finally, a Bayesian deep learning approach was employed for theory-oriented uncertainty estimation. In this approach, Monte Carlo dropout is performed for simultaneous estimation of metabolite content and associated uncertainty. These proposed methods were all tested on in vivo data and compared with the conventional approach based on NLSF and CRLB. The methods developed in this study should be tested more thoroughly on a larger amount of in vivo data. Nonetheless, the current results suggest that they may facilitate the applicability of MRS.두뇌 내 특정한 부위에 대한 대사체들의 종류와 농도 정보를 획득할 수 있는 자기공명분광 (MRS) 분야에서 일반적으로 활용하고 있는 비선형 최소제곱피팅 (Nonlinear least squares fitting; NSLF)은 주어진 사전 정보 (Prior knowledge)에 의존한 정량화 결과 변동 특성을 나타낸다. NLSF 기반한 두뇌 대사체 정량화는 MRS 신호품질에 민감하게 성능 변화를 나타낸다. 무엇 보다, NLSF를 통한 정량화 결과의 신뢰 지표인 크라메르-라오 하한 (Cramer-Rao lower Bound; CRLB)은 정량화 결과에 대한 오차정보를 반영하는 정확도가 아닌, 정밀도를 표현하므로, 이를 주의하여 활용하지 않으면 통계적 편향성을 나타낼 위험이 있다. 이러한 문제들로 인해 MRS는 현재까지도 제한적으로만 임상 활용되고 있는 상황이다. 따라서 본 연구는 자기공명분광법을 이용한 두뇌 대사체 정량화 과정에 있어서 딥 러닝 기술을 접목하여, 정량화 정확도를 개선하는 점에 주 목적을 두고 있다. 구체적으로 본 연구에서는 다음과 같이 두 부분에 대한 방법을 제안하였다. 첫번째로는 깊은 인공신경망을 통해 MRS 신호내의 두뇌 대사체 공명 신호만을 추출하여, 이를 간단한 선형 회귀 후처리를 통해 정량화를 할 수 있는 분석 기술을 개발하였다. 두번째로는 딥 러닝에서 예측하는 결과들에 대한 불확실성 지표를 표현하는 방법에 대해 개발하였다. 구체적으로는 빅데이터 기반의 경험적 불확실성 지표와, 베이지안 접근법에 기반한 정규분포를 따르는 불확실성 지표 표현 방법을 개발하였다. 결과적으로 제안된 방법들은 NLSF 대비 MRS 신호 품질에 덜 영향을 받으면서 낮은 정량화 결과 변동성을 나타내는 동시에, NLSF의 정량화 결과에 대한 신뢰지표인 CRLB에 비해 더 실제 오차와 상관성이 높은 불확실성 지표 성능을 보였다. 따라서 본 연구는, MRS를 활용한 두뇌 대사체 정량화에 대한 정확도 개선을 위해 딥 러닝 기술들을 활용한다면, MRS의 임상 적용 가능성을 높일 수 있음을 시사한다.Chapter 1. Introduction 1 1.1. Magnetic Resonance Spectroscopy 1 1.1.1. Nuclear Spin 1 1.1.2. Magnetization 4 1.1.3. MRS Signal 6 1.1.4. Chemical Shift 12 1.1.5. Indirect Spin-Spin Coupling 14 1.1.6. in vivo Metabolites 15 1.1.7. RF Pulses and Gradients 17 1.1.8. Water Suppression 19 1.1.9. Spatial Localized Methods in Single Voxel MRS 20 1.1.10. Metabolite Quantification 22 1.2. Deep Learning 24 1.2.1. Training for Regression Model 25 1.2.2. Training for Classification Model 27 1.2.3. Multilayer Perceptron 29 1.2.4. Model Evaluation and Selection 32 1.2.5. Training Stability and Initialization 35 1.2.6. Convolutional Neural Networks 36 1.3. Perpose of the Research 38 1.4. Preparation of MRS Spectra and Their Usage 40 Chapter 2. Intact metabolite spectrum mining by deep learning in proton magnetic resonance spectroscopy of the brain 45 2.1. Introduction 45 2.2. Methods and Materials 46 2.2.1. Acquisition of in vivo Spectra 46 2.2.2. Acquisition of Metabolite Phantom Spectra 47 2.2.3. Simulation of Brain Spectra 47 2.2.4. Design and Optimization of CNN 52 2.2.5. Evaluation of the Reproducibility of the Optimized CNN 52 2.2.6. Metabolite Quantification from the Predicted Spectra 53 2.2.7. Evaluation of CNN in Metabolite Quantification 53 2.2.8. Statistical Analysis 54 2.3. Results 54 2.3.1. SNR Distribution of the Simulated Spectra 54 2.3.2. Optimized CNN 56 2.3.3. Representative Simulated and CNN-predicted Spectra 56 2.3.4. Metabolite Quantification in Simulated Spectra 57 2.3.5. Representative in vivo and CNN-predicted Spectra 61 2.3.6. Metabolite Quantification in in vivo Spectra 64 2.4. Discussions 67 2.4.1. Motivation of Study 67 2.4.2. Metabolite Quantification on Simulated and in vivo Brain Spectra 68 2.4.3. Metabolite Quantification Robustness against Low SNR 69 2.4.4. Study Limitation 70 Chapter 3. Deep learning-based target metabolite isolation and big data-driven measurement uncertainty estimation in proton magnetic resonance spectroscopy of the brain 79 3.1. Introduction 79 3.2. Methods and Materials 80 3.2.1. Acquisition and Analysis of in vivo Rat Brain Spectra 80 3.2.2. Simulation of Metabolite Basis set 81 3.2.3. Acquisition of Metabolite Basis set in Phantom 81 3.2.4. Simulation of Rat Brain Spectra using Simulated Metabolite and Baseline Basis Sets 82 3.2.5. Simulation of Rat Brain Spectra using Metabolite Phantom Spectra and in vivo Baseline 87 3.2.6. Design and Optimization of CNN 87 3.2.7. Metabolite Quantification from the CNN-predicted Spectra 90 3.2.8. Prediction of Quantitative Error 90 3.2.9. Evaluation of Proposed Method 93 3.2.10. Statistical Analysis 93 3.3. Results 94 3.3.1. Performance of Proposed Method on Simulated Spectra Set I 94 3.3.2. Performance of Proposed Method, LCModel, and jMRUI on Simulated Spectra Set II 99 3.3.3. Proposed Method Applied to in vivo Spectra 105 3.3.4. Processing Time 105 3.4. Discussions 109 3.4.1. Summary of the Study 109 3.4.2. Performance of Proposed Method on Simulated Spectra 110 3.4.3. Proposed Method Applied to in vivo Spectra 111 3.4.4. Robustness of CNNs against Different SNR 111 3.4.5. CRLB and Predicted Error 112 3.4.6. Study Limitation 113 Chapter 4. Bayesian deep learning-based proton magnetic resonance spectroscopy of the brain: metabolite quantification with uncertainty estimation using Monte Carlo dropout 118 4.1. Introduction 118 4.2. Methods and Materials 119 4.2.1. Theory 119 4.2.2. Preparation of Spectra 124 4.2.3. BCNN 125 4.2.4. Evaluation of Proposed Method 126 4.2.5. Statistical Analysis 127 4.3. Results 127 4.3.1. Metabolite Content and Uncertainty Estimation on the Simulated Spectra 127 4.3.2. BCNN and LCModel on Modified in vivo Spectra 136 4.4. Discussions 144 4.4.1. Motivation of Study 144 4.4.2. Metabolite Quantification on Simulated Brain Spectra 144 4.4.3. Uncertainty Estimation on Simulated Brain Spectra 145 4.4.4. Aleatoric, Epistemic and Total Uncertainty as a Function of SNR, Linewidth or Concentration of NAA 147 4.4.5. Robustness of BCNN against SNR and Linewidth Tested on Modified in vivo Spectra 148 4.4.6. Study Limitation 148 Chapter 5. Conclusion 160 5.1. Research Summary 160 5.2. Future Works 160 Bibliography 163 Abstract in Korean 173박