Transition from Lorentzian to Gaussian line shape of magnetization transfer spectrum in bovine serum albumin solutions

PhoenixMR: A GPU-based MRI simulation framework with runtime-dynamic code execution

BACKGROUND

Simulations of physical processes and behavior can provide unique insights and understanding of real-world problems. Magnetic Resonance Imaging (MRI) is an imaging technique with several components of complexity. Several of these components have been characterized and simulated in the past. However, several computational challenges prevent simulations from being simultaneously fast, flexible, and accurate.

PURPOSE

The simulation of MRI experiments is underutilized by medical physicists and researchers using currently available simulators due to reasons including speed, accuracy, and extensibility constraints. This paper introduces an innovative MRI simulation engine and framework that aims to overcome these issues making available realistic and fast MRI simulation.

METHODS

Using the CUDA C/C++ programing language, an MRI simulation engine (PhoenixMR), incorporating a Turing-complete virtual machine (VM) to simulate abstract spatiotemporal complexities, was developed. This engine solves a set of time-discrete Bloch equations using the symmetric operator splitting technique. An extensible front-end framework package (written in Python) aids the use of PhoenixMR to simplify simulation development.

RESULTS

The PhoenixMR library and front-end codes have been developed and tested. A set of example simulations were performed to demonstrate the ease of use and flexibility of simulation components such as geometrical setup, pulse sequence design, phantom design, and so forth. Initial validation of PhoenixMR is performed by comparing its accuracy and performance against a widely used MRI simulator using identical simulation parameters. Validation results show PhoenixMR simulations are three orders of magnitude faster. There is also strong agreement between models.

CONCLUSIONS

A novel MRI simulation platform called PhoenixMR has been introduced. This research tool is designed to be usable by physicists and engineers interested in performing MRI simulations. Examples are shown demonstrating the accuracy, flexibility, and usability of PhoenixMR in several key areas of MRI simulation.

Contribution of mitochondria to cardiac muscle water/macromolecule proton magnetization transfer

The contribution of mitochondria to water-macromolecule proton magnetization transfer (MT) was evaluated in porcine heart tissue. An examination of isolated mitochondria in suspension, at the same concentration as found in heart tissue, revealed MT effects very similar in magnitude and bandwidth to those in intact heart tissue. Disruption of the gross structure of the mitochondria by freeze-thawing or with detergent resulted in only approximately 25% decreases in MT, which suggests that the structure of the mitochondria is not critical for these effects. The current data indicate that mitochondria macromolecules contribute significantly to MT in the intact heart.

Precise estimate of fundamental in-vivo MT parameters in human brain in clinically feasible times

A methodology is presented for extracting precise quantitative MT parameters using a magnetisation-prepared spoiled gradient echo sequence. This method, based on a new mathematical model, provides relaxation parameters for human brain in-vitro and in-vivo. The in-vivo parameters have been obtained from three different regions of normal white matter: occipital white matter, frontal white matter and centrum semiovale; two regions of normal grey matter: cerebral cortex and cerebellum, and from five regions with MS lesions. All this has been achieved using MT images collected within a timeframe that is clinically feasible. We hope that this new technique will shed light on the properties and dynamics of water compartments within the brain.

Pulsed Z-spectroscopic imaging of cross-relaxation parameters in tissues for human MRI: theory and clinical applications

A new method of pulsed Z-spectroscopic imaging is proposed for in vivo visualization and quantification of the parameters describing cross-relaxation between protons with liquid-like and solid-like relaxation properties in tissues. The method is based on analysis of the magnetization transfer (MT) effect as a function of the offset frequency and amplitude of a pulsed off- resonance saturation incorporated in a spoiled gradient-echo MRI pulse sequence. The theoretical concept of the method relies on an approximated analytical model of pulsed MT that provides a simple three-parameter equation for a pulsed steady-state Z-spectrum taken far from resonance. Using this model, the parametric images of cross-relaxation rate constant, content, and T(2) of the semisolid proton fraction can be reconstructed from a series of MT-weighted images and a coregistered T(1) map. The method was implemented on a 0.5 T clinical MRI scanner, and it provided high-quality 3D parametric maps within an acceptable scanning time. The estimates of cross-relaxation parameters in brain tissues were shown to be quantitatively consistent with the literature data. Clinical examples of the parametric images of human brain pathologies (multiple sclerosis and glioma) demonstrated high tissue contrast and clear visualization of the lesions.

Proton exchange as a relaxation mechanism for T1 in the rotating frame in native and immobilized protein solutions

T1 relaxation in the rotating frame (T1rho) is a sensitive magnetic resonance imaging (MRI) contrast for acute brain insults. Biophysical mechanisms affecting T1rho relaxation rate (R1rho) and R1rho dispersion (dependency of R1rho on the spin-lock field) were studied in protein solutions by varying their chemical environment and pH in native, heat-denatured, and glutaraldehyde (GA) cross-linked samples. Low pH strongly reduced R1rho in heat-denatured phantoms displaying proton resonances from a number of side-chain chemical groups in high-resolution 1H NMR spectra. At pH of 5.5, R1rho dispersion was completely absent. In contrast, in the GA-treated phantoms with very few NMR visible side chain groups, acidic pH showed virtually no effect on R1rho. The present data point to a crucial role of proton exchange on R1rho and R1rho dispersion in immobilized protein solution mimicking tissue relaxation properties.

Quantitative interpretation of magnetization transfer in spoiled gradient echo MRI sequences

A method for analyzing general pulsed magnetization transfer (MT) experiments in which off-resonance saturation pulses are interleaved with on-resonance excitation pulses is presented. We apply this method to develop a steady-state signal equation for MT-weighted spoiled gradient echo sequences and consider approximations that facilitate its rapid computation. Using this equation, we assess various experimental designs for quantitatively imaging the fractional size of the restricted pool, cross-relaxation rate, and T(1) and T(2) relaxation times of the two pools in a binary spin bath system. From experiments on agar gel, this method is shown to reliably and accurately estimate the exchange and relaxation properties of a material in an imaging context, suggesting the feasibility of using this technique in vivo.

T1rho dispersion of rat tissues in vitro

The purpose of this study was to demonstrate T1rho dispersion in different rat tissues (liver, brain, spleen, kidney, heart, and skeletal muscle), and to compare the 1/T1rho data to previous 1/T1 data and magnetization transfer of rat tissues at low (0.1 T) B0 field. The 1/T1rho dispersion showed a fairly similar pattern in all tissues. The highest 1/T1rho relaxation rates were seen in liver and muscle followed by heart, whereas the values for spleen, kidney, and brain were quite similar. Compared to 1/T2 relaxation rate, the greatest difference was seen in liver and muscle. The rank order 1/T1rho value at each locking field B1 was the same as the transfer rate of magnetization from the water to the macromolecular pool (Rwm) for liver, muscle, heart, and brain. The potential value T1rho imaging is to combine high T1 contrast of low field imaging with the high signal to noise ratio of high static field imaging. When the T1rho value for a given tissue is known, the contrast between different tissues can be optimized by adjusting the locking time TL. Further studies are encouraged to fully exploit this. Targets for more detailed research include brain infarct, brain and liver tumors.

Combining CW and pulsed saturation allows in vivo quantitation of magnetization transfer observed for total creatine by (1)H-NMR-spectroscopy of rat brain

Selective saturation of bound nuclei attenuates the MR visible CH(2) and the CH(3) signal of total creatine (tCr) in rat brain in vivo. The low contrast to noise ratio achieved during the limited experiment time makes it difficult to quantify the effect. It is shown that by combining data from continuous-wave and pulsed saturation experiments, quantitation is possible using the standard magnetization transfer model. The model parameters obtained are the transverse relaxation time of the bound spin fraction B, T2R = 31 +/- 8 micros, the exchange rate r(x) = 0.36 +/- 0.04 s(-1), and the concentration ratio of bound nuclei taking part in the exchange to free tCr magnetization, f = M0B/M0A = 0.04 +/- 0.01. The phenomenon can be explained by either an intermolecular exchange of free and bound creatine molecules or by through-space interaction with bound nuclei showing not necessarily the same chemical shift. Magn Reson Med 42:222-227, 1999.

Magnetic relaxation contrast agents in magnetization transfer imaging

RATIONALE AND OBJECTIVES

The effects of magnetic relaxation agents are explored in the context of magnetization transfer pulse sequences using cross-linked protein gels as modeled tissue systems.

METHODS

Magnetization transfer pulse sequences were used to study contrast agents that are designed to bind to rotationally immobilized protein targets.

RESULTS

The dynamic range available from contrast agents, used in conjunction with magnetization transfer pulse sequences, is comparable with or better than that based on spin-echo imaging sequences with short repetition times. Furthermore, useful changes in the intensity of water resonances may be achieved by using this combined approach even though the paramagnetic metal center may not have a free coordination position in the chelate complex for water molecule exchange.

CONCLUSIONS

The inclusion of magnetization transfer acquisition protocols in the context of magnetic imaging with contrast agents presents new opportunities for control of the information content of the image and for new classes of contrast agent structure and delivery.

Integrated analysis of diffusion and relaxation of water in blood

Diffusion and T2 relaxation of water both inside and outside red blood cells (RBCs) in human blood were investigated using a hybrid NMR pulse sequence to obtain a more quantitative understanding of the diffusion and relaxation behavior of water in paramagnetic-doped blood samples. The data were analyzed by both examining the relaxation properties of the system after each diffusion weighting and looking at the diffusion properties at each echo time. The results illustrate how diffusion-sensitizing gradients affect the T2 spectra of blood and how relaxation weighting changes the curvature of the diffusion curves, thereby demonstrating the close coupling between diffusion and T2 relaxation. A three-pool model, consisting of RBCs, plasma, and macromolecular protons, was used to model the data from the diffusion-relaxation hybrid experiments. The model was found to describe all the characteristic features of the experimental data well and was used to evaluate the approximations involved in the conventional analysis methods and elucidate the nature of the relaxing and diffusing components. Compared with the separate diffusion and relaxation experiments, the diffusion-relaxation hybrid experiments are less time-consuming, result in better parameter determinations, and may be useful in analyzing diffusion-T2 coupling in tissues with more complicated multiexponential T2 behavior.

Understanding pulsed magnetization transfer

Using a two-pool exchange model of magnetization transfer (MT), numeric simulations were developed to predict the time dependence of longitudinal magnetization in both semisolid and liquid pools for arbitrary pulsed radiofrequency (RF) irradiation. Whereas RF excitation of the liquid pool was modeled using the time-dependent Bloch equations, RF saturation of the semisolid pool was described by a time-dependent rate proportional to both the absorption lineshape of the semisolid pool and the square of the RF pulse amplitude. Simulations show good agreement with experimental results for a 4% agar gel aqueous system in which the two-pool kinetics have been well studied previously. These simulations provide a method for interpreting pulsed MT effects, are easily extended to biologic tissues, and provide a basis for optimizing clinical imaging applications that exploit MT contrast.

A flexible magnetization transfer line shape derived from tissue experimental data

To summarize and compare magnetization transfer data from biological tissues, a method was developed to extract the average absorption lineshape of the semi-solid pool directly from magnetization transfer experimental data along with the four other parameters that characterize the two-pool model of exchange. Magnetization transfer data for several biological tissues were analyzed using this method and the resulting "flexible" lineshapes were compared with super-Lorentzian and "Kubo-Tomita" lineshapes. The use of flexible lineshapes noticeably improves the fit of the two-pool model to the data. The derived flexible lineshapes of all the tissues analyzed are physically realistic and show remarkably consistent behavior.

T1rho of protein solutions at very low fields: dependence on molecular weight, concentration, and structure

The effect of molecular weight, concentration, and structure on 1/T1rho, the rotating frame relaxation rate, was investigated for several proteins using the on-resonance spin-lock technique, for locking fields B1 < 200 microT. The measured values of 1/T1rho were fitted to a simple theoretical model to obtain the dispersion curves 1/T1rho(omega1) and the relaxation rate at zero B1 field, 1/T1rho(0). 1/T1rho was highly sensitive to the molecular weight, concentration, and structure of the protein. The amount of intra- and intermolecular hydrogen and disulfide bonds especially contributed to 1/T1rho. In all samples, 1/T1rho(0) was equal to 1/T2 measured at the main magnetic field Bo = 0.1 T, but at higher locking fields the dispersion curves monotonically decreased. The results of this work indicate that a model considering the effective correlation time of molecular motions as the main determinant for T1rho relaxation in protein solutions is not valid at very low B1 fields. The underlying mechanism for the relaxation rate 1/T1rho at B1 fields below 200 microT is discussed.

Magnetization transfer of pure DNA and purified sperm nuclei

Magnetization transfer (MT) imaging provides a novel opportunity to characterize interactions between tissue water and macromolecules. Although several in vitro investigations have shown that proteins and lipids are important determinants of MT, the contribution of DNA is still unknown. This study was designed to determine whether DNA and cell nuclear material exhibit MT. We measured the magnetization transfer effect of pure DNA strands and purified bovine sperm head nuclei. Although no transfer of magnetization could be detected in samples of pure DNA strands, the sperm head nuclei exhibited a strong MT effect that increased with increasing solid content of the samples. Since the purified bovine sperm head samples consist of large nuclei with only minor traces of perinuclear matrix, the measured MT effect arises from the chromatin of the nuclei. The DNA fills 90% of the nuclear volume and it is extremely tightly packed as chromatin fibers by nucleoproteins. We hypothesize that the numerous intra- and intermolecular disulfide bonds that stabilize the chromatin fibers restrict the movement of the surface water binding sites of both DNA and protamines and thus facilitate the transfer of magnetization. Therefore, the results indicate that the amount of nuclear material may positively contribute to MT in tissues.

1H magnetic cross-relaxation between multiple solvent components and rotationally immobilized protein

Magnetic cross-relaxation spectra or Z-spectra are presented for water, acetone, methanol, dimethylsulfoxide, and acetonitrile in cross-linked bovine serum albumin gels. Each solvent studied, reports the same Z-spectrum linewidth and shape for the solid component that follows from solutions of the coupled relaxation equations. The Z-spectra demonstrate competition among solvents for specific protein binding sites. The rate of magnetization transfer in the rotationally immobilized protein environment is approximated by 1/T2 for the solid component, which is shown to account for the observed magnetization transfer rates in the systems studied. The temperature dependence of the Z-spectra are different for water compared with the organic solvents. The cross-relaxation efficiency in the organic solvents decreases with increasing temperature because molecules bind less well at high temperature. For water, the hydrogen exchange path becomes increasingly important relative to the whole molecule path with increasing temperature, which improves the net cross-relaxation efficiency.

An interleaved sequence for accurate and reproducible clinical measurement of magnetization transfer ratio

We demonstrate an interleaved dual spin echo-based sequence for quantitative measurement of Magnetisation Transfer Ratio (MTR) in a clinical environment that overcomes the problems of patient motion between scans faced by noninterleaved methods. The sequence also provides proton density and T2-weighted images, allowing direct comparison among the three contrast regimes. Phantom studies and in vivo measurements on normal controls show the sequence to be robust in normal use. The values of MTR calculated from the sequence are shown to be precise and reproducible enough to allow regional variations to be identified within and between white matter and other brain tissues.

Magnetization transfer in protein solutions at 0.1 T: dependence on concentration, molecular weight, and structure

RATIONALE AND OBJECTIVES

We observed the magnetization transfer rates in a variety of protein solutions at 0.1-T magnetic field and compared our results with previous investigations at high magnetic fields (> 0.5 T). The effects of protein concentration, size, pH, denaturation, cross linking, and fiber formation were investigated.

METHODS

We used the saturation transfer technique to determine the transfer of magnetization in gamma globulin, fibronectin, collagen, fibrinogen, and albumin solutions.

RESULTS

The observed transfer rate increased with increasing concentration and size of the protein. Protein degradation decreased the transfer rate. Cross linking and fiber formation each increased the transfer rate, whereas buffer pH had no effect.

CONCLUSION

Protein denaturation, aggregation, and fiber formation are important determinants of magnetization transfer in vitro. The size, concentration, and cross linking of the proteins contribute strongly to the transfer of magnetization at low fields, and the effect seems to be at least as important as at the higher fields.

A model for magnetization transfer in tissues

Magnetization transfer in several tissues is measured and successfully modeled using a two-pool model of exchange. The line shape for the semi-solid pool is characterized by a superLorentzian and the liquid pool by a Lorentzian. The tissues investigated were white and gray matter, optic nerve, muscle, and liver. All tissues the authors studied are characterized by the same model but differ in the parameter values of the model. Blood and cerebral spinal fluid (CSF) were also investigated. The two-pool model with a Lorentzian line shape for both the semi-solid and liquid pools modeled the magnetization transfer in blood. In CSF, as expected, there is no measurable exchange of magnetization. The T2B associated with the semi-solid pool was short (approximately 10 microseconds) for all tissues indicating a fairly rigid semi-solid pool. In addition characterization of the line shape as superLorentzian indicates molecules such as integral membrane proteins or lipids in membranes are likely molecules participating in the exchange. Conversely, in blood large globular proteins are indicated due to the Lorentzian nature of the semi-solid pool and a T2B approximately 300 microseconds.