In vivo tissue characterization of human brain by chisquares parameter maps: multiparameter proton T2-relaxation analysis

Multi-compartment T2 relaxometry using a spatially constrained multi-Gaussian model

The brain's myelin content can be mapped by T2-relaxometry, which resolves multiple differentially relaxing T2 pools from multi-echo MRI. Unfortunately, the conventional fitting procedure is a hard and numerically ill-posed problem. Consequently, the T2 distributions and myelin maps become very sensitive to noise and are frequently difficult to interpret diagnostically. Although regularization can improve stability, it is generally not adequate, particularly at relatively low signal to noise ratio (SNR) of around 100-200. The purpose of this study was to obtain a fitting algorithm which is able to overcome these difficulties and generate usable myelin maps from noisy acquisitions in a realistic scan time. To this end, we restrict the T2 distribution to only 3 distinct resolvable tissue compartments, modeled as Gaussians: myelin water, intra/extra-cellular water and a slow relaxing cerebrospinal fluid compartment. We also impose spatial smoothness expectation that volume fractions and T2 relaxation times of tissue compartments change smoothly within coherent brain regions. The method greatly improves robustness to noise, reduces spatial variations, improves definition of white matter fibers, and enhances detection of demyelinating lesions. Due to efficient design, the additional spatial aspect does not cause an increase in processing time. The proposed method was applied to fast spiral acquisitions on which conventional fitting gives uninterpretable results. While these fast acquisitions suffer from noise and inhomogeneity artifacts, our preliminary results indicate the potential of spatially constrained 3-pool T2 relaxometry.

Comparison of human brain metabolite levels using 1H MRS at 1.5T and 3.0T

Proton magnetic resonance spectroscopy (MRS) of the human brain has proven to be a useful technique in several neurological and psychiatric disorders and benefits from higher field scanners as signal intensity and spectral resolution are proportional to the magnetic field strength.

Magnetic resonance relaxation and quantitative measurement in the brain

Underlying the exquisite soft tissue contrast provided by magnetic resonance imaging are the inherent biophysical processes of relaxation. Through the intricate relationships between tissue microstructure and biochemistry and the longitudinal and transverse relaxation rates, quantitative measurement of these relaxation parameters is informative of tissue change associated with disease, neural plasticity, and other biological processes. Quantitative imaging studies can further facilitate more detailed characterizations of tissue, providing a more direct link between modern MR imaging and classic histochemical and histological studies. In this chapter, we briefly review the biophysical basis of relaxation, introducing and focusing specifically on the T(1), T(2), and T(2)(*) relaxation times and detail some of the more widely used and clinically feasible techniques for their in vivo measurement. Methods for analyzing relaxation data are covered, and a summary of significant results from reported neuroimaging studies is provided. Finally, the combination of relaxation time data with other quantitative imaging data, including diffusion tensor and magnetization transfer, is examined, with the aim of providing more thorough characterization of brain tissue.

Correction of main and transmit magnetic field (B0 and B1) inhomogeneity effects in multicomponent-driven equilibrium single-pulse observation of T1 and T2

Multicomponent-driven equilibrium single-component observation of T(1) and T(2) offers a new approach to multiple component relaxation time and myelin water analysis. The method derives two-component relaxation information from spoiled and fully balanced steady-state (SPGR and bSSFP) imaging data acquired over multiple flip angles. Although these steady-state imaging techniques afford rapid acquisition times and high signal-to-noise ratio efficiency, they are also sensitive to main (B(0) ) and transmit (B(1) ) magnetic field inhomogeneities. These effects alter the measured signal from their theoretical values and lead to substantive errors in the derived myelin volume fraction estimates. Here, we incorporate correction techniques to mitigate these effects. DESPOT1-HIFI is used to first calibrate the transmitted flip angles; and B(0) affects are removed through the inclusion of an additional parameter in the multicomponent-driven equilibrium single-component observation of T(1) and T(2) fitting, coupled with the acquisition of multiple phase-cycled bSSFP data. The performance of these correction techniques was evaluated using numerical simulations, demonstrating effective removal of B(0) and B(1)-induced errors in the derived myelin fraction relaxation parameters. The approach was also successfully demonstrated in vivo, with near artifact-free whole-brain, high spatial resolution (1.7 mm × 1.7 mm × 1.7 mm isotropic voxels) myelin water fraction maps acquired in a clinically feasible 16 min.

Intensity-adaptive segmentation of single-echo T1-weighted magnetic resonance images

A procedure for segmentation of intracranial tissues, including cerebrospinal fluid surrounding the brain, cortical and subcortical gray matter, and white matter, in a T1-weighted magnetic resonance image of the brain, has been developed. The proposed method utilizes information from the histogram of pixel intensities of the intracranial image. Based on this information, an unsupervised K-means clustering procedure separates various tissue regions. Information about the approximate location of anatomical regions within the intracranial space is used to detect ventricles and the caudate nuclei. First a description and justification for the procedure is presented. Then the performance of the procedure is evaluated by analysis of variance. In conclusion, the results of applying this procedure to 31 healthy subjects are presented and future improvements are discussed.

Gleaning multicomponent T1 and T2 information from steady-state imaging data

The driven-equilibrium single-pulse observation of T(1) (DESPOT1) and T(2) (DESPOT2) are rapid, accurate, and precise methods for voxelwise determination of the longitudinal and transverse relaxation times. A limitation of the methods, however, is the inherent assumption of single-component relaxation. In a variety of biological tissues, in particular human white matter (WM) and gray matter (GM), the relaxation has been shown to be more completely characterized by a summation of two or more relaxation components, or species, each believed to be associated with unique microanatomical domains or water pools. Unfortunately, characterization of these components on a voxelwise, whole-brain basis has traditionally been hindered by impractical acquisition times. In this work we extend the conventional DESPOT1 and DESPOT2 approaches to include multicomponent relaxation analysis. Following numerical analysis of the new technique, renamed multicomponent driven equilibrium single pulse observation of T(1)/T(2) (mcDESPOT), whole-brain multicomponent T(1) and T(2) quantification is demonstrated in vivo with clinically realistic times of between 16 and 30 min. Results obtained from four healthy individuals and two primary progressive multiple sclerosis (MS) patients demonstrate the future potential of the approach for identifying and assessing tissue changes associated with several neurodegenerative conditions, in particular those associated with WM.

Bias of cartilage T2 values related to method of calculation

PURPOSE

To determine how different methods for calculating T2 affect the resulting T2 values of patellar cartilage.

MATERIALS AND METHODS

T2-weighted images of patellar cartilage for 10 subjects were acquired using two MRI scanners. T2 values of patellar cartilage were calculated using linear, weighted and nonlinear fitting algorithms for a monoexponential decay equation. T2 values were also calculated for the superficial, middle and deep zones of the cartilage.

RESULTS

All three methods of calculation resulted in significantly different T2 values (P<.0001). The weighted calculation produced the highest T2 values, and the nonlinear calculation produced the lowest T2 values. The average difference of T2 value between the methods was under 5 ms. Similar results were found in a zonal analysis of the tissue. The nonlinear calculation of T2 consistently had the best fit to the acquired data.

CONCLUSION

The T2 value of patellar cartilage depends on the method of calculation. It is unclear if larger T2 value differences would be seen in subjects diagnosed with osteoarthritis. This study highlights the potential difficulty of comparing different studies with one another based on the method of T2 calculation.

Biexponential characterization of prostate tissue water diffusion decay curves over an extended b-factor range

Detailed measurements of water diffusion within the prostate over an extended b-factor range were performed to assess whether the standard assumption of monoexponential signal decay is appropriate in this organ. From nine men undergoing prostate MR staging examinations at 1.5 T, a single 10-mm-thick axial slice was scanned with a line scan diffusion imaging sequence in which 14 equally spaced b factors from 5 to 3,500 s/mm(2) were sampled along three orthogonal diffusion sensitization directions in 6 min. Due to the combination of long scan time and limited volume coverage associated with the multi-b-factor, multidirectional sampling, the slice was chosen online from the available T2-weighted axial images with the specific goal of enabling the sampling of presumed noncancerous regions of interest (ROIs) within the central gland (CG) and peripheral zone (PZ). Histology from prescan biopsy (n=9) and postsurgical resection (n=4) was subsequently employed to help confirm that the ROIs sampled were noncancerous. The CG ROIs were characterized from the T2-weighted images as primarily mixtures of glandular and stromal benign prostatic hyperplasia, which is prevalent in this population. The water signal decays with b factor from all ROIs were clearly non-monoexponential and better served with bi- vs. monoexponential fits, as tested using chi(2)-based F test analyses. Fits to biexponential decay functions yielded intersubject fast diffusion component fractions in the order of 0.73+/-0.08 for both CG and PZ ROIs, fast diffusion coefficients of 2.68+/-0.39 and 2.52+/-0.38 microm(2)/ms and slow diffusion coefficients of 0.44+/-0.16 and 0.23+/-0.16 um(2)/ms for CG and PZ ROIs, respectively. The difference between the slow diffusion coefficients within CG and PZ was statistically significant as assessed with a Mann-Whitney nonparametric test (P<.05). We conclude that a monoexponential model for water diffusion decay in prostate tissue is inadequate when a large range of b factors is sampled and that biexponential analyses are better suited for characterizing prostate diffusion decay curves.

Determination of optimal angles for variable nutation proton magnetic spin-lattice, T1, and spin-spin, T2, relaxation times measurement

T1 and T2 can be rapidly determined with a combination of multiangle spoiled gradient recalled echo (SPGR) and steady-state free precession (SSFP) imaging. Previously, we demonstrated a simple method for determining the set of SPGR and SSFP angles that provided greater T1 and T2 precision than a set of uniformly spaced angles. In this article a more rigorous approach for determining angles is described. Weighted least-squares is also introduced for T1 and T2 estimation and a novel weighting function described. This new approach, suited for imaging applications where large T1 and T2 ranges are anticipated, provides high and uniform precision over a wide range of T1 and T2 values.

Bi-exponential proton transverse relaxation rate (R2) image analysis using RF field intensity-weighted spin density projection: potential for R2 measurement of iron-loaded liver

A bi-exponential proton transverse relaxation rate (R(2)) image analysis technique has been developed that enables the discrimination of dual compartment transverse relaxation behavior in systems with rapid transverse relaxation enhancement. The technique is particularly well suited to single spin-echo imaging studies where a limited number of images are available for analysis. The bi-exponential R(2) image analysis is facilitated by estimation of the initial proton spin density signal within the region of interest weighted by the RF field intensities. The RF field intensity-weighted spin density map is computed by solving a boundary value problem presented by a high spin density, long T(2) material encompassing the region for analysis. The accuracy of the bi-exponential R(2) image analysis technique is demonstrated on a simulated dual compartment manganese chloride phantom system with relaxation rates and relative population densities between the two compartments similar to the bi-exponential transverse relaxation behavior expected of iron loaded liver. Results from analysis of the phantoms illustrate the potential of bi-exponential R(2) image analysis with RF field intensity-weighted spin density projection for quantifying transverse relaxation enhancement as it occurs in liver iron overload.

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

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.

Characterization of normal brain and brain tumor pathology by chisquares parameter maps of diffusion-weighted image data

OBJECTIVE

To characterize normal and pathologic brain tissue by quantifying the deviation of diffusion-related signal from a simple monoexponential decay, when measured over a wider than usual range of b-factors.

METHODS AND MATERIALS

Line scan diffusion imaging (LSDI), with diffusion weighting at multiple b-factors between 100 and 5000 s/mm(2), was performed on 1.5 T clinical scanners. Diffusion data of single slice sections were acquired in five healthy subjects and 19 brain tumor patients. In-patients, conventional T2-weighted and contrast-enhanced T1-weighted images were obtained for reference purposes. The chisquare (chi(2)) error parameter associated with the monoexponential fits of the measured tissue water signals was then used to quantify the departure from a simple monoexponential signal decay on a pixel-by-pixel basis.

RESULTS

Diffusion-weighted images over a wider b-factor range than typically used were successfully obtained in all healthy subjects and patients. Normal and pathologic tissues demonstrated signal decays, which clearly deviate from a simple monoexponential behavior. The chi(2) of cortical and deep grey matter was considerably lower than in white matter. In peritumoral edema, however, chi(2) was 68% higher than in normal white matter. In highly malignant brain tumors, such as glioblastoma multiforme (GBM) or anaplastic astrocytoma, chi(2) values were on average almost 400% higher than in normal white matter, while for one low grade astrocytoma and two cases of metastasis, chi(2) was not profoundly different from the chi(2) value of white matter. Maps of the chi(2) values provide good visualization of spatial details. However, the tumor tissue contrast generated appeared in many cases to be different from the enhancement produced by paramagnetic contrast agents. For example, in cases where the contrast agent only highlighted the rim of the tumor, chi(2) enhancement was present within the solid part of the tumor.

CONCLUSION

The deviation from a purely monoexponential diffusion signal decay becomes evident as diffusion encoding is extended well beyond the normal range. The chi(2) error parameter as a measure of this deviation seems to provide sufficient lesion contrast to permit differentiation of malignant brain tumors from normal brain tissue.

A self consistent normalized calibration protocol for three dimensional magnetic resonance gel dosimetry

In a clinical setting, mixed and inconsistent results have been reported using Magnetic Resonance Relaxation imaging of irradiated aqueous polymeric gels as a three-dimensional dosimeter, for dose verification of conformal radiation therapy. The problems are attributed to the difficulty of identifying an accurate dose calibration protocol for each delivered gel at the radiation site in a clinical setting. While careful calibration is done at the gel manufacturing site in a controlled laboratory setting, there is no guarantee that the dose sensitivity of the gels remains invariant upon delivery, irradiation, magnetic resonance imaging and storage at the clinical site. In this study, we have compared three different dose calibration protocols on aqueous polymeric gels for a variety of irradiation scenarios done in a clinical setting. After acquiring the three-dimensional proton relaxation maps of the irradiated gels, the dose distributions were generated using the off-site manufacturer provided calibration curve (Cal-1), the on-site external tube gel calibration (Cal-2) and the new on-site internal normalized gel calibration (Cal-3) protocols. These experimental dose distributions were compared with the theoretical dose distributions generated by treatment-planning systems. We observed that the experimental dose distributions generated from the Cal-1 and Cal-2 protocols were off by 10% to 40% and up to 200% above the predicted maximum dose, respectively. On the other hand, the experimental dose distributions generated from the Cal-3 protocol matched reasonably well with the theoretical dose distributions to within 10% difference. Our result suggests that an independent on-site normalized internal calibration must be performed for each batch of gel dosimeters at the time of MR relaxation imaging in order to account for the variations in dose sensitivity caused by various uncontrollable conditions in a clinical setting such as oxygen contamination, temperature changes and shelf life of the delivered gel between manufacturing and MR acquisitions.

B(0)-fluctuation-induced temporal variation in EPI image series due to the disturbance of steady-state free precession

Steady-state free precession (SSFP) can develop under a train of RF pulses, given the condition TR < T(2). SSFP in multi-shot imaging sequences has been well studied. It is shown here that serial single-shot echo-planar imaging (EPI) acquisition can also develop SSFP, and the SSFP can be disturbed by B(0) fluctuation, causing voxel-wise temporal variation. This SSFP disturbance is predominantly present in cerebrospinal fluid (CSF) regions due to the long T(2) value. By applying a sufficiently strong crusher gradient in the EPI pulse sequence, the temporal variation induced by SSFP disturbance can be suppressed due to diffusion. Evidence is provided to indicate that physiological motions such as cardiac pulsation and respiration could affect the voxel-wise time courses through the mechanism of SSFP disturbance. It is advised that if the disturbance is observed in serial EPI images, the crusher should be made stronger to eliminate the unwanted temporal variation.

Are mono-exponential fits to a few echoes sufficient to determine T2 relaxation for in vivo human brain?

T2 relaxation decay curves from in vivo human brain tissue are rarely mono-exponential. Partial volume averaging further reduces the chance of mono-exponential decay. Moreover, the parameters derived from few-echo mono-exponential fits change with the measurement echo times and have the largest possible variance. In this note, multi-exponential fits to 32-echo relaxation decay curves from in vivo human brain are used to design simulations (where the truth is known) to demonstrate the pitfalls of few-echo mono-exponential interpretations.

T2 relaxation of the parotid gland of patients affected by pleomorphic adenoma

The T2 behavior of parotid gland tissue was investigated in 11 patients affected by pleomorphic adenoma. A protocol that was previously set up to define acquisition and post-processing procedures, reaching an accuracy of 2.5% in phantoms and an in vivo long term reproducibility of 0.9-8.5%, was used for the evaluations. The measurements were carried out on a whole body, superconducting imager, using a neck coil as a receiver. Some reference gel samples were imaged together with the patient and used to correct T2 results. The sequence protocol was a multispin-echo, 16 echoes. Signals were fitted with mono and biexponential decay models and an automatic choice of the best model was performed using the two chisquared comparison. Two T2 maps (T2 monoexponential or short T2 component, and long T2 component) and chisquared maps were then produced. Pathologic and normal tissues showed a dominant monoexponential decay with a good level of biexponentiality (16%-27% of total fitted pixels) due to partial volume effects from the liquid content. Concerning the biexponentiality, no significant differences were found between the fitted pixel fraction of normal and pathologic tissue, because the T2 long component of the lesion was related both to the edema and saliva content, but probably the increase in the first compensated the decrease in the second. Chisquared maps showed that most of the lesions presented a monoexponential core surrounded by a biexponential border probably due to a solid component similar to normal tissue with partial volume effects from saliva content. Ninety-five percent confidence intervals for normal tissue were 69.40-87.80 ms (monoexponential relaxation), 38.19-44.67 ms and 285.84-691.28 ms (short and long components of biexponential relaxation). For pathologic tissue they resulted 172.17-275.83 ms, 53.86-89.98 ms and 442.10-814.58 ms. The monoexponential component, mostly present in the core of the lesion, was the parameter that better characterized pathologic tissue. A comparison was performed between normal tissue of patients and normal tissue of volunteers, whose statistics was collected in a previous study with the same evaluation protocol. Results showed no significant differences in the biexponential fitted fractions and the comparison of relaxation times. We conclude that, for tissue characterization, a multiexponential analysis should be carried out in order to improve accuracy and to obtain more reliable results. Moreover, other than relaxation calculations, a topographical analysis of relaxation distribution, using for instance the chisquared maps, might in the future give us more useful information on tissue structure.

Optimal time spacings for T2 measurements: monoexponential and biexponential systems

We have developed an optimal design strategy, i.e. a choice of times at which the magnetization should be measured, in spin-echo measurements, when the number of measurements is fixed in advance. Results are given for samples whose relaxation is described by either an exponential or biexponential decay curve. The analysis is based on having an initial estimate of the ranges in which the relaxation times are likely to lie. The optimal design consists of a set of easily parameterized non-uniformly spaced measurement times, as opposed to present implementation of spin-echo experiments. Analysis of the biexponential case shows that an order of magnitude greater signal-to-noise is required to achieve T2 estimates of comparable precision to monoexponential measurements with the same number of data points. The optimal designs lead to an improved ability to discriminate between two relatively similar relaxation times.

T2 relaxation time as a marker of brain myelination: experimental MR study in two neonatal animal models

The progress of myelination in the brain was evaluated by visualization of grey/white matter differentiation on magnetic resonance (MR) images and quantitative analysis of MR data. In vivo quantitative MR imaging was used to monitor the T2 transverse relaxation time changes associated with cerebral development and myelination. The progress of myelination was evaluated using two neonatal animal models, the monkey and the dog, known to mature at very different rates. Three beagles were studied from birth to 4 months of age and nine baboons from 1 to 30 months of age. The T2 values in the frontal, parietal and occipital white matter were calculated and the changes in these values with age were followed. Brain maturation in both species was found to correspond to decreasing T2 values in both grey and white matter. This decrease was observed both in the dog brain and, despite slower maturation, in the baboon brain, and appeared to fit with the myelination process in these models. Exploiting the physicochemical parameters of water in tissues via T2 determination is a convenient and reliable strategy for the documentation of brain development in both experimental approaches and clinical situations.

In vivo measurement of T2 distributions and water contents in normal human brain

Using a 32-echo imaging pulse sequence, T2 relaxation decay curves were acquired from five white- and six gray-matter brain structures outlined in 12 normal volunteers. The water contents of white and gray matter were 0.71 (0.01) and 0.83 (0.03) g/ml, respectively. All white-matter structures had significantly higher myelin water percentages (signal percentage with T2 between 10 and 50 ms) than all gray-matter structures. The range in geometric mean T2 of the main peak for both white and gray matter was from 70 to 86 ms. T2 distributions from the posterior internal capsules and splenium of the corpus callosum were significantly wider (width is related to water environment inhomogeneity) than those from any other white- or gray-matter structures. Thus, quantitative measurement and analysis of T2 relaxation reveals differences in brain tissue water environments not discernible on conventional MR images. These differences may make short T2 components reliable markers for normal myelin.

T2 maximum likelihood estimation from multiple spin-echo magnitude images

An optimal maximum likelihood (ML) method is described for an unbiased estimation of monoexponential T2 from magnitude spin-echo images. The algorithm is based on a Gaussian assumption of noise distribution. The validity of this assumption was checked by a statistical chi 2 test on spin-echo and fast low-angle shot surface coil images. Monte-Carlo simulations of magnitude data showed that the ML estimate standard deviation is lower than that produced by a weighted least-squares fitting on signal logarithm. Correction schemes are proposed to reduce bias deriving from magnitude reconstruction. The variance of the ML estimate converged rapidly toward the theoretical algebraic expression of the Cramér-Rao lower bound.

Statistical error mapping for reliable quantitative T1 imaging

We developed a statistically based error image for rapid appreciation of unreliable regions in quantitative water proton T1 images. The chi-squared error and co-efficient of variation of the fitted parameter were used to estimate uncertainties in the goodness-of-fit to mono-exponential T1 relaxation and the reliability of the calculated T1, respectively, for each pixel. Errors exceeding a statistical threshold based on a .1 acceptance criterion were displayed as a color-coded overlay on the T1 image. Error maps of quantitative T1 images from 31 healthy volunteers showed a characteristic error structure; few pixels within the parenchyma had excessive errors. Clinical cases with stroke and sickle cell disease showed deviations from the normal pattern in the spatial distribution and magnitude of chi-squared errors. Disease states may deviate from mono-exponential T1 relaxation more than normal brain does. The color-coded error map is a valuable tool for investigators using quantitative MR imaging to determine tissue relaxation parameters.

A three dimensional analysis of slotted tube resonator for MRI

A three dimensional model of a slotted tube resonator (STR) used as a probe in the magnetic resonance imaging (MRI), which is loaded by a dielectric body and surrounded by a conducting shield, is analyzed by using the variational method and the dyadic Green's function of a circular waveguide having a dielectric core. Three surface current modes are properly assumed to expand the currents on the STR. The characteristics such as the input impedance, the resonance frequency, the Q value, and the magnetic field distribution are obtained to show the effects of the dielectric body and the conducting shield. Some theoretical results are compared with the measured data to confirm the validity of the present analysis.