Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter

A Weighted Stochastic Conjugate Direction Algorithm for Quantitative Magnetic Resonance Images—A Pattern in Ruptured Achilles Tendon T2-Mapping Assessment

This study presents an accurate biexponential weighted stochastic conjugate direction (WSCD) method for the quantitative T2-mapping reconstruction of magnetic resonance images (MRIs), and this approach was compared with the non-negative-least-squares Gauss–Newton (GN) numerical optimization method in terms of accuracy and goodness of fit of the reconstructed images from simulated data and ruptured Achilles tendon (AT) MRIs. Reconstructions with WSCD and GN were obtained from data simulating the signal intensity from biexponential decay and from 58 MR studies of postrupture, surgically repaired ATs. Both methods were assessed in terms of accuracy (closeness of the means of calculated and true simulated T2 values) and goodness of fit (magnitude of mean squared error (MSE)). The lack of significant deviation in correct T2 values for the WSCD method was demonstrated for SNR ≥ 20 and for GN–SNR ≥ 380. The MSEs for WSCD and GN were 287.52 ± 224.11 and 2553.91 ± 1932.31, respectively. The WSCD reconstruction method was better than the GN method in terms of accuracy and goodness of fit.

Evaluation of principal component analysis image denoising on multi-exponential MRI relaxometry

PURPOSE

Multi-exponential relaxometry is a powerful tool for characterizing tissue, but generally requires high image signal-to-noise ratio (SNR). This work evaluates the use of principal-component-analysis (PCA) denoising to mitigate these SNR demands and improve the precision of relaxometry measures.

METHODS

PCA denoising was evaluated using both simulated and experimental MRI data. Bi-exponential transverse relaxation signals were simulated for a wide range of acquisition and sample parameters, and experimental data were acquired from three excised and fixed mouse brains. In both cases, standard relaxometry analysis was performed on both original and denoised image data, and resulting estimated signal parameters were compared.

RESULTS

Denoising reduced the root-mean-square-error of parameters estimated from multi-exponential relaxometry by factors of ≈3×, for typical acquisition and sample parameters. Denoised images and subsequent parameter maps showed little or no signs of spatial artifact or loss of resolution.

CONCLUSION

Experimental studies and simulations demonstrate that PCA denoising of MRI relaxometry data is an effective method of improving parameter precision without sacrificing image resolution. This simple yet important processing step thus paves the way for broader applicability of multi-exponential MRI relaxometry.

Use of the NESMA Filter to Improve Myelin Water Fraction Mapping with Brain MRI

BACKGROUND AND PURPOSE

Myelin water fraction (MWF) mapping permits direct visualization of myelination patterns in the developing brain and in pathology. MWF is conventionally measured through multiexponential T₂ analysis which is very sensitive to noise, leading to inaccuracies in derived MWF estimates. Although noise reduction filters may be applied during postprocessing, conventional filtering can introduce bias and obscure small structures and edges. Advanced nonblurring filters, while effective, exhibit a high level of complexity and the requirement for supervised implementation for optimal performance. The purpose of this paper is to demonstrate the ability of the recently introduced nonlocal estimation of multispectral magnitudes (NESMA) filter to greatly improve the determination of MWF parameter estimates from gradient and spin echo (GRASE) imaging data.

METHODS

We evaluated the performance of the NESMA filter for MWF mapping from clinical GRASE imaging data of the human brain, and compared the results to those calculated from unfiltered images. Numerical and in vivo analyses of the brains of three subjects, representing different ages, were conducted.

RESULTS

Our results demonstrated the potential of the NESMA filter to permit high-quality in vivo MWF mapping. Indeed, NESMA permits substantial reduction of random variation in derived MWF estimates while preserving accuracy and detail.

CONCLUSIONS

In vivo estimation of MWF in the human brain from GRASE imaging data was markedly improved through use of the NESMA filter. The use of NESMA may contribute to the goal of high-quality MWF mapping in clinically feasible imaging times.

A multicomponent T2 relaxometry algorithm for myelin water imaging of the brain

PURPOSE

Models based on a sum of damped exponentials occur in many applications, particularly in multicomponent T2 relaxometry. The problem of estimating the relaxation parameters and the corresponding amplitudes is known to be difficult, especially as the number of components increases. In this article, the commonly used non-negative least squares spectrum approach is compared to a recently published estimation algorithm abbreviated as Exponential Analysis via System Identification using Steiglitz-McBride.

METHODS

The two algorithms are evaluated via simulation, and their performance is compared to a statistical benchmark on precision given by the Cramér-Rao bound. By applying the algorithms to an in vivo brain multi-echo spin-echo dataset, containing 32 images, estimates of the myelin water fraction are computed.

RESULTS

Exponential Analysis via System Identification using Steiglitz-McBride is shown to have superior performance when applied to simulated T2 relaxation data. For the in vivo brain, Exponential Analysis via System Identification using Steiglitz-McBride gives an myelin water fraction map with a more concentrated distribution of myelin water and less noise, compared to non-negative least squares.

CONCLUSION

The Exponential Analysis via System Identification using Steiglitz-McBride algorithm provides an efficient and user-parameter-free alternative to non-negative least squares for estimating the parameters of multiple relaxation components and gives a new way of estimating the spatial variations of myelin in the brain.

Bayesian estimation of changes in transverse relaxation rates

Although the biasing of R(2)* estimates by assuming magnitude MR data to be normally distributed has been described, the effect on changes in R(2)* (DeltaR(2)*), such as induced by a paramagnetic contrast agent, has not been reported. In this study, two versions of a novel Bayesian maximum a posteriori approach for estimating DeltaR(2)* are described and evaluated: one that assumes normally distributed data and the other, Rice-distributed data. The approach enables the robust, voxelwise determination of the uncertainty in DeltaR(2)* estimates and provides a useful statistical framework for quantifying the probability that a pixel has been significantly enhanced. This technique was evaluated in vivo, using ultrasmall superparamagnetic iron oxide particles in orthotopic murine prostate tumors. It is shown that assuming magnitude data to be normally distributed causes DeltaR(2)* to be underestimated when signal-to-noise ratio is modest. However, the biasing effect is less than is found in R(2)* estimates, implying that the simplifying assumption of normally distributed noise is more justifiable when evaluating DeltaR(2)* compared with when evaluating precontrast R(2)* values.

Adipose segmentation in small animals at 7T: a preliminary study

Background

Small animal MRI at 7 Tesla (T) provides a useful tool for adiposity research. For adiposity researchers, separation of fat from surrounding tissues and its subsequent quantitative or semi- quantitative analysis is a key task. This is a relatively new field and a priori it cannot be known which specific biological questions related to fat deposition will be relevant in a specific study. Thus it is impossible to predict what accuracy and what spatial resolution will be required in all cases and even difficult what accuracy and resolution will be useful in most cases. However the pragmatic time constraints and the practical resolution ranges are known for small animal imaging at 7T. Thus we have used known practical constraints to develop a method for fat volume analysis based on an optimized image acquisition and image post processing pair.

Methods

We designed a fat segmentation method based on optimizing a variety of factors relevant to small animal imaging at 7T. In contrast to most previously described MRI methods based on signal intensity of T1 weighted image alone, we chose to use parametric images based on Multi-spin multi-echo (MSME) Bruker pulse sequence which has proven to be particularly robust in our laboratory over the last several years. The sequence was optimized on a T1 basis to emphasize the signal. T2 relaxation times can be calculated from the multi echo data and we have done so on a pixel by pixel basis for the initial step in the post processing methodology. The post processing consists of parallel paths. On one hand, the weighted image is precisely divided into different regions with optimized smoothing and segmentation methods; and on the other hand, a confidence image is deduced from the parametric image according to the distribution of relaxation time relationship of typical adipose. With the assistance of the confidence image, a useful software feature was implemented to which enhances the data and in the end results in a more reliable and flexible method for adipose evaluation.

Results

In this paper, we describe how we arrived at our recommended procedures and key aspects of the post-processing steps. The feasibility of the proposed method is tested on both simulated and real data in this preliminary research. A research tool was created to help researchers segment out fat even when the anatomical information is of low quality making it difficult to distinguish between fat and non-fat. In addition, tool is designed to allow the operator to make adjustments to many of the key steps for comparison purposes and to quantitatively assess the difference these changes make. Ultimately our flexible software lets the researcher define key aspects of the fat segmentation and quantification.

Conclusions

Combining the full T2 parametric information with the optimized first echo image information, the research tool enhances the reliability of the results while providing more flexible operations than previous methods. The innovation in the method is to pair an optimized and very specific image acquisition technique to a flexible but tuned image post processing method. The separation of the fat is aided by the confidence distribution of regions produced on a scale relevant to and dictated by practical aspects of MRI at 7T.

Evidence of multiexponential T2 in rat glioblastoma

The aim of this study was to characterize multiexponential T(2) (MET(2)) relaxation in a rat C6 glioblastoma tumor model. To do this, rats (n = 11) were inoculated with the C6 cells via stereotaxic injection into the brain. Ten days later, MET(2) measurements were performed in vivo using a single-slice, multi-echo spin-echo sequence at 7.0 T. Tumor signal was biexponential in eight animals with a short-lived T(2) component (T(2) = 20.7 +/- 5.4 ms across samples) representing 6.8 +/- 6.2% of the total signal and a long-lived T(2) component (T(2) = 76.4 +/- 9.3 ms) representing the remaining signal fraction. In contrast, signal from contralateral grey matter was consistently monoexponential (T(2) = 48.8 +/- 2.3 ms). Additional ex vivo studies (n = 3) and Monte Carlo simulations showed that the in vivo results were not significantly corrupted by partial volume averaging or noise. The underlying physiological origin of the observed MET(2) components is unknown; however, MET(2) analysis may hold promise as a non-invasive tool for characterizing tumor microenvironment in vivo on a sub-voxel scale.

Time course of acute phase in mouse spinal cord injury monitored by ex vivo quantitative MRI

During the acute phase of spinal cord injury (SCI), major alterations of white and grey matter are a key issue, which determine the neurological outcome. The present study with ex vivo quantitative high-field magnetic resonance microimaging (MRI) was intended in order to identify sensitive parameters of tissue disruption in a well-controlled mouse model of ischemic SCI. MR imaging evidenced changes as early as the second hour after the lesion in the dorsal horns, which appear swollen. After 4 h, alterations of the white matter of dorsal and lateral funiculi were reflected by a progressive loss of white/grey matter contrast with further ventral extension by the 24th hour. Diffusion tensor imaging and multi-exponential T2 measurements permitted to quantify these physicochemical, time-related, alterations during the 24-h period. This characterization of spatial and temporal evolution of SCI will contribute to better define both the most appropriate targets for future therapies and more accurate therapeutic windows. Upcoming directions include the use of these parameters on in vivo animal models and their application to clinics. Indeed, magnetic resonance techniques appear now as a major non-invasive translation tool in CNS pathologies based on the development of more appropriate pre-clinical models.

Retrieval of transverse relaxation time distribution from spin-echo data by recurrent neural network

Inversion of transverse relaxation time decay curve from spin-echo experiments was carried out using Hopfield neural network, to obtain the transverse relaxation time distribution. The performance of this approach was tested against simulated and experimental data. The initial guess, necessary for the integration procedure, was established as the analytical Laplace inversion. Together with errors in the simulated data, inversion was also carried out with errors in this initial guess. The probability density function, calculated by the neural network, is used in multiple sclerosis diagnostics.

A post-processing method for multiexponential spin–spin relaxation analysis of MRI signals

Quantitative MR imaging is a potential tool for tissue characterization; in particular, proton density and proton relaxation times can be derived from MR signal analysis. However, MR image noise affects the accuracy of measurements and the number of tissue parameters that can be reliably estimated. Filtering can be used to limit image noise; however this reduces spatial resolution. In this work we studied, using both simulations and experiments, a filter called a 'selective blurring filter'. Compared to other classical filters, this filter achieves the best compromise between spatial resolution and noise reduction. The filter was specifically used to reliably determine the bi-component transverse relaxation of protons in adipose tissue. Long and short relaxation times and the relative proton fraction of each component were obtained with a degree of uncertainty of less than 10% and an accuracy of 95%.