The beneficial influence of prior knowledge on the quantitation of in vivo magnetic resonance spectroscopy signals.

RATIONALE AND OBJECTIVES: This work concerns quantitation of in vivo magnetic resonance spectroscopy signals and the influence of prior knowledge on the precision of parameter estimates. The authors point out how prior knowledge can be used for experiments. METHODS: The Cramer-Rao lower bounds formulae of the noise-related standard deviations on spectral parameters for doublets and triplets were derived. Chemical prior knowledge of the multiplet structures was used. RESULTS: The benefit of chemical prior knowledge was estimated for doublet and triplet structures of arbitrary shape. Then, it was used to quantify in vivo 31P time-series signals of rat brain. CONCLUSIONS: Analytic expressions of errors on parameter estimates were derived, enabling prediction of the benefit of prior knowledge on quantitation results. These formulae allow us to state, for a given noise level, if the quantitation of strongly overlapping peaks such as adenosine triphosphate multiplets can be performed successfully.

Frequency-selective MRS data quantification with frequency prior knowledge.

Various signal processing techniques have been proposed to improve spectral estimation of closely spaced sinusoids in the presence of noise. This paper exploits frequency prior knowledge information to extract single peaks in magnetic resonance spectra, corresponding to metabolites of interest, by means of a highly selective finite impulse response filter. Thereafter the estimation of the parameters of the peaks is carried out using a singular-value-decomposition-based method known as HTLS. The new technique improves the performance of fully automated magnetic resonance spectroscopy data quantification when frequency prior knowledge is available.

Time-domain quantification of series of biomedical magnetic resonance spectroscopy signals.

Quantification of individual magnetic resonance spectroscopy (MRS) signals is possible in the time domain using interactive nonlinear least-squares fitting methods which provide maximum likelihood parameter estimates under certain assumptions or using fully automatic, but statistically suboptimal, black-box methods. In kinetic experiments time series of consecutive MRS spectra are measured in which information concerning the time evolution of some of the signal parameters is often present. The purpose of this paper is to show how AMARES, a representative example of the interactive methods, can be extended to the simultaneous processing of all spectra in the time series using the common information present in the spectra. We show that this approach yields statistically better results than processing the individual signals separately.

Reduced lipid contamination in in vivo 1H MRSI using time-domain fitting and neural network classification.

It is a well-known problem that metabolite maps, reconstructed from in vivo 1H MRSI data sets, may suffer from contamination caused by the presence of strong lipid signals. In the present investigation, the lipid problem was addressed by applying specific signal processing and data-analysis techniques, combined with pattern recognition based on the concept of the artificial neural network. In order to arrive at images, cleaned from lipid artifacts, we have applied our previously introduced iterative and noniterative time-domain fitting procedures. Furthermore, reduction in computational time of the image reconstructions could be realized by using information provided by a neural network classification of the spectra, calculated from the MRSI data sets.

A distributed computing system for magnetic resonance imaging: Java-based processing and binding of XML.

Recently we have developed a Java-based heterogeneous distributed computing system for the field of magnetic resonance imaging (MRI). It is a software system for embedding the various image reconstruction algorithms that we have created for handling MRI data sets with sparse sampling distributions. Since these data sets may result from multi-dimensional MRI measurements our system has to control the storage and manipulation of large amounts of data. In this paper we describe how we have employed the extensible markup language (XML) to realize this data handling in a highly structured way. To that end we have used Java packages, recently released by Sun Microsystems, to process XML documents and to compile pieces of XML code into Java classes. We have effectuated a flexible storage and manipulation approach for all kinds of data within the MRI system, such as data describing and containing multi-dimensional MRI measurements, data configuring image reconstruction methods and data representing and visualizing the various services of the system. We have found that the object-oriented approach, possible with the Java programming environment, combined with the XML technology is a convenient way of describing and handling various data streams in heterogeneous distributed computing systems.

Quantitation with QUEST of brain HRMAS-NMR signals: application to metabolic disorders in experimental epileptic seizures.

Quantitation of High Resolution Magic Angle Spinning (HRMAS) Nuclear Magnetic Resonance (NMR) signals enables establishing reference metabolite profiles of ex vivo tissues. Signals are often contaminated by a background signal originating mainly from macromolecules and lipids and by residual water which hampers proper quantitation. We show that automatic quantitation of HRMAS signals, even in the presence of a background, can be achieved by the semi-parametric algorithm QUEST based on prior knowledge of a metabolite basis-set. The latter was quantum-mechanically simulated with NMR-SCOPE and requires accurate spin parameters. The region of interest of spectra is a small part of the full spectral bandwidth. Reducing the computation time inherent to the large number of data-points is possible by using ER-Filter in a preprocessing step. Through Monte-Carlo studies, we analyze the performances of quantitation without and with ER-Filtering. Applications of QUEST to quantitation of 1H ex vivo HRMAS-NMR data of mouse brains after intoxication with soman, are demonstrated. Metabolic profiles obtained during status epilepticus and later when neuronal lesions are installed, are established. Acetate, Alanine, Choline and gamma-amino-butyric acid concentrations increase in the piriform cortex during the initial status epilepticus, when seizures are maximum; Lactate and Glutamine concentrations increase while myo-Inositol and N-acetylaspartate concentrations decrease when neuronal lesions are clearly installed.

Semi-parametric estimation in magnetic resonance spectroscopy: automation of the disentanglement procedure.

Semi-parametric disentanglement of parametric parts from non-parametric parts of a signal is a universal problem. This study concerns estimation of metabolite concentrations from in vivo Magnetic Resonance Spectroscopy (MRS) signals. Due to in vivo conditions, so-called macro-molecules contribute non-parametric components to the signals. Disentanglement is achieved by exploiting prior knowledge about the parametric and non-parametric parts directly in the measurement domain. Moreover, Cramér-Rao bounds on the non-parametric part are derived. These expressions are used to automate the disentanglement procedure.

Time-domain semi-parametric estimation based on a metabolite basis set.

A novel and fast time-domain quantitation algorithm--quantitation based on semi-parametric quantum estimation (QUEST)--invoking optimal prior knowledge is proposed and tested. This nonlinear least-squares algorithm fits a time-domain model function, made up from a basis set of quantum-mechanically simulated whole-metabolite signals, to low-SNR in vivo data. A basis set of in vitro measured signals can be used too. The simulated basis set was created with the software package NMR-SCOPE which can invoke various experimental protocols. Quantitation of 1H short echo-time signals is often hampered by a background signal originating mainly from macromolecules and lipids. Here, we propose and compare three novel semi-parametric approaches to handle such signals in terms of bias-variance trade-off. The performances of our methods are evaluated through extensive Monte-Carlo studies. Uncertainty caused by the background is accounted for in the Cramér-Rao lower bounds calculation. Valuable insight about quantitation precision is obtained from the correlation matrices. Quantitation with QUEST of 1H in vitro data, 1H in vivo short echo-time and 31P human brain signals at 1.5 T, as well as 1H spectroscopic imaging data of human brain at 1.5 T, is demonstrated.

Influence of digital audio filters on image reconstruction in MRI.

This paper deals with the influence of the transient response and group delay of digital filters on the MRI signal and its aspects in image reconstruction. The consequence of digital filtration on the acquired signal will be shown in the time domain (k-space) for three basic imaging methods-echo scan, radial scan and spiral scan. The influence of the group delay and transient response of filters will be explained and a method will be proposed which compensates both these phenomena while retaining all the advantages of digital filtration. The proposed method is based on applying the principle of signal superposition and on using the consequences of the sampling principle. The method works in the time domain. It is very simple and rapid and does not depend on the properties of the acquired signal or reconstruction algorithm. It will be shown and explained in which cases the transient response can be neglected and in which it has to be compensated. In the end, the results of the proposed methods will be shown for mentioned cases on a simulated signal in the image domain.

Cramer-Rao bound expressions for parametric estimation of overlapping peaks: influence of prior knowledge

We have derived analytical expressions of the Cramer-Rao lower bounds on spectral parameters for singlet, doublet, and triplet peaks in noise. We considered exponential damping (Lorentzian lineshape) and white Gaussian noise. The expressions, valid if a sufficiently large number of samples is used, were derived in the time domain for algebraic convenience. They enable one to judge the precision of any unbiased estimator as a function of the spectral and experimental parameters, which is useful for quantitation objectives and experimental design. The influence of constraints (chemical prior knowledge) on parameters of the peaks of doublets and triplets is demonstrated both analytically and numerically and the inherent benefits for quantitation are shown. Our expressions also enable analysis of spectra comprising many peaks. Copyright 2000 Academic Press.

Time-domain quantitation of 1H short echo-time signals: background accommodation.

Quantitation of 1H short echo-time signals is often hampered by a background signal originating mainly from macromolecules and lipids. While the model function of the metabolite signal is known, that of the macromolecules is only partially known. We present time-domain semi-parametric estimation approaches based on the QUEST quantitation algorithm (QUantitation based on QUantum ESTimation) and encompassing Cramér-Rao bounds that handle the influence of 'nuisance' parameters related to the background. Three novel methods for background accommodation are presented. They are based on the fast decay of the background signal in the time domain. After automatic estimation, the background signal can be automatically (1) subtracted from the raw data, (2) included in the basis set as multiple components, or (3) included in the basis set as a single entity. The performances of these methods combined with QUEST are evaluated through extensive Monte Carlo studies. They are compared in terms of bias-variance trade-off. Because error bars on the amplitudes are of paramount importance for diagnostic reliability, Cramér-Rao bounds accounting for the uncertainty caused by the background are proposed. Quantitation with QUEST of in vivo short echo-time (1)H human brain with estimation of the background is demonstrated.

Determination of concentrations by time domain fitting of proton NMR echo signals using prior knowledge.

A fast and flexible time domain iterative fitting procedure that can be used to fit free induction decays as well as echo-like signals is described. Damping constants of the first and second part of the echo do not have to be identical. Prior knowledge can be used to diminish the number of parameters to be fitted, which results in an improved accuracy. It is shown how prior knowledge is mathematically incorporated in the Gauss-Newton method. From proton NMR measurements of model solutions actual prior knowledge is extracted. With this knowledge relative concentrations are determined from a mixture of metabolites. The fitted results agree with the true values within the margins of the noise. After some minor changes the same prior knowledge was successfully used to analyze a series of in vivo rat brain measurements.

Cramér-Rao bounds: an evaluation tool for quantitation.

The Cramér-Rao lower bounds (CRBs) are the lowest possible standard deviations of all unbiased model parameter estimates obtained from the data. Consequently they give insight into the potential performance of quantitation estimators. Using analytical CRB expressions for spectral parameters of singlets and doublets in noise, one is able to judge the precision as a function of spectral and experimental parameters. We point out the usefulness of these expressions for experimental design. The influence of constraints (chemical prior knowledge) on spectral parameters of the peaks of doublets is demonstrated and the inherent benefits for quantitation are shown. Abbreviations used: CRB Cramér-Rao lower bounds

Current awareness.

In order to keep subscribers up-to-date with the latest developments in their field, John Wiley & Sons are providing a current awareness service in each issue of the journal. The bibliography contains newly published material in the field of NMR in biomedicine. Each bibliography is divided into 9 sections: 1 Books, Reviews ' Symposia; 2 General; 3 Technology; 4 Brain and Nerves; 5 Neuropathology; 6 Cancer; 7 Cardiac, Vascular and Respiratory Systems; 8 Liver, Kidney and Other Organs; 9 Muscle and Orthopaedic. Within each section, articles are listed in alphabetical order with respect to author. If, in the preceding period, no publications are located relevant to any one of these headings, that section will be omitted.

Accurate quantification of in vivo 31P NMR signals using the variable projection method and prior knowledge.

Free induction decay signals are analyzed by fitting a model function directly in the time domain. No starting values are needed for linear model parameters, and omission of corrupted data points poses no problems. A significant gain of accuracy is achieved by imposing prior knowledge about the model parameters.

Application of linear prediction and singular value decomposition (LPSVD) to determine NMR frequencies and intensities from the FID.

A parametric spectral analysis based on linear prediction and singular value decomposition has been applied to the 31P FID of a tumor implanted in a mouse. It is found that a number of complications that may arise in in vivo FFT NMR can be circumvented. The new method yields all parameters of the spectral components, i.e., the frequency, amplitude, damping constant, and phase.

Dynamic magnetic resonance imaging paragraph sign with radial scanning: a post-acquisition paragraph sign keyhole approach.

A method - PA-keyhole - for 2D/3D dynamic magnetic resonance imaging with radial scanning is proposed. PA-keyhole exploits the inherent strong oversampling in the center of k-space, which contains crucial temporal information regarding contrast evolution. The method is based on: (1). a rearrangement of the temporal order of 2D/3D isotropic distributions of trajectories during the scan into subdistributions according to the desired time resolution, (2). a new post-acquisition keyhole approach based on the replacement of the central disk/sphere in k-space using data solely from a subdistribution, and (3). reconstruction of 2D/3D dynamic (time-resolved) images using 2D/3D-gridding with Pipe's approach to the sampling density compensation and 2D/3D-IFFT. The scan time is not increased with respect to a conventional 2D/3D radial scan of the same spatial resolution; in addition, one benefits from the dynamic information. The abilities of PA-keyhole and the sliding window techniques to restore simulated dynamic contrast changes are compared. Results are shown both for 2D and 3D dynamic imaging using experimental data. An application to in-vivo ventilation of rat lungs using hyperpolarized helium is demonstrated.

Evaluation of signal processing methods for the quantification of a multi-exponential signal: the glycogen 13C-1 NMR signal.

The 13C-1 NMR peak in proton-decoupled spectra of liver glycogen solution was quantitatively analyzed by three types of model-function fitting algorithms: iterative line-fitting in the frequency domain (MDCON); iterative least-squares fitting (VARPRO) in the time domain; and noniterative singular value decomposition-based analysis (HTLS), also in the time domain. Quantification results were compared with manual integration values. Performance of the algorithms was tested at different signal-to-noise ratios (S/N) of the glycogen C-1 peak. This was achieved by varying the number of scans summed prior to analysis. Since T2 relaxation in glycogen has been shown to be multiexponential [Overloop, K. et al. Magn. Reson. Med. 36, 45-51 (1996], the exact quantification of the C-1 glycogen signal requires a model function comprising a sum of Lorentzian components, each with a different broadening at the glycogen frequency. This paper focuses on the performances of the above methods to fit such a multicomponent resonance line. In the frequency domain, line fitting with two Lorentz lines gives good results at sufficiently high S/N. In the time domain, VARPRO performs better than HTLS because fixed values can be imposed to the linewidth of the components at the common C-1 frequency, thereby reducing convergence problems at low S/N.

Application of time-domain fitting in the quantification of in vivo 1H spectroscopic imaging data sets.

Time-domain model function fitting techniques were applied to improve the reconstruction of metabolite maps from the data sets obtained from in vivo 1H spectroscopic imaging (SI) experiments. First, residual water-related signals were removed from the SI data sets by using SVD-based linear time-domain fitting based upon the HSVD (State Space) approach. Second, peak integrals of the metabolites of interest were obtained by quantifying the proton spin-echoes of the voxels by means of non-linear time-domain fitting based upon the maximum likelihood principle. Third, in order to save computational time, interpolation of the metabolite images (from size 32 x 32 to 128 x 128) was performed in the image-domain by applying one-dimensional cubic splines. It was found that the residual water signals can be almost completely removed from the SI data sets by applying the linear HSVD fitting method. Furthermore, it was found that voxel dependency of certain NMR parameters (e.g., variations of the spin-echo offset frequencies and/or phase factors) can be accounted for automatically by applying the nonlinear time-domain fitting technique. For that purpose it appeared to be essential to employ prior knowledge of the NMR spectral parameters.

MR image reconstruction algorithms for sparse k-space data: a Java-based integration.

We have worked on multi-dimensional magnetic resonance imaging (MRI) data acquisition and related image reconstruction methods that aim at reducing the MRI scan time. To achieve this scan-time reduction we have combined the approach of 'increasing the speed' of k-space acquisition with that of 'deliberately omitting' acquisition of k-space trajectories (sparse sampling). Today we have a whole range of (sparse) sampling distributions and related reconstruction methods. In the context of a European Union Training and Mobility of Researchers project we have decided to integrate all methods into one coordinating software system. This system meets the requirements that it is highly structured in an object-oriented manner using the Unified Modeling Language and the Java programming environment, that it uses the client-server approach, that it allows multi-client communication sessions with facilities for sharing data and that it is a true distributed computing system with guaranteed reliability using core activities of the Java Jini package.