Relaxation times in paramagnetically doped agarose gels as a function of temperature and ion concentration

Tissue equivalent gels of NMR phantoms have been investigated at 3.4 MHz. The proton T1 and T2 relaxation times have been measured in Ni++ and Cu++ doped agarose gels as a function of temperature and ion concentration. Ni-agarose gels have the lower T1 temperature dependence, but gels containing both Cu++ and Ni++ can be produced for which T1 has virtually no temperature dependence.     

Ion transport studies in calcium alginate gels by magnetic resonance microscopy

Polyelectrolyte biopolymers such as calcium alginate are becoming increasingly important for the recovery of heavy metals from aqueous solutions. To understand the mechanism of ion transport in these biopolymer systems, the transport of copper ions into calcium alginate gels was investigated using proton nuclear magnetic resonance (NMR) microscopy. Copper ion transport was imaged using an inversion recovery technique which utilizes the paramagnetic effect of copper on water proton relaxation times. Diffusion experiments were performed in a diffusion cell designed to approximate a semi-infinite slab geometry at temperatures between 278 and 313 K using copper reservoir concentrations between 10 and 60 mM. The diffusion coefficient of copper in these gels was calculated from the NMR data to fit a combined diffusion-reaction model involving a diffusion term (D) and a kinetic binding term (k). At 23 °C, the diffusion coefficients in 1, 2, and 3% (w/v) gels were 3.1 · 10⁻¹⁰, 2.0 · 10⁻¹⁰, and 1.4 · 10⁻¹⁰ m²/s, respectively. The activation energy for diffusion in the 2% (w/v) gel was 28 kJ/mol.     

The effects of morphology and exchange on proton N.M.R. relaxation in agarose gels

The effects of morphology and exchange on N.M.R. relaxation times in agarose gels are interpreted within a unified theoretical framework based on the generalized Bloch equations. By acknowledging the spacial dependence of the N.M.R. parameters it is shown how the relaxation behaviour depends on the distance scale characterizing the heterogeneity of the gel. If this distance scale is sufficiently small to allow complete diffusive averaging we recover the traditional results based on the Bloch-McConnell equations describing relaxation in a homogeneous system. This is the case for fresh agarose gels which show monoexponential relaxation and has been widely interpreted in terms of the rapid exchange of protons between populations of ‘free’ and ‘bound’ water. Conversely, if the distance scale characterizing the heterogeneity is sufficiently large to prevent complete diffusive averaging our model predicts multiexponential relaxation. This is the case with the transverse magnetization in agarose gels that have been slowly frozen then thawed. These results show how it is possible to probe the degree of microheterogeneity in gel samples using N.M.R. For the purpose of deriving simple analytical expressions for the N.M.R. relaxation times we only consider one-dimensional solutions to our model. More realistic morphologies can be treated using numerical methods.     

Development of high-radiation-sensitive polymer gel for magnetic resonance imaging in three-dimensional dosimetry

We developed a high radiation sensitive polymer gel by modifying the amounts of the gel components and the temperature for the gel preparation. We evaluated its relaxation time linearity against dose and compared the measured dose distribution with the calculated one. For the relaxation time-dose linearity, irradiations were carried out with a linear accelerator using 6 MV photons and doses ranging from 0-5.0 Gy. The relationship between dose and R(2) value (reciprocal of T(2) relaxation time) was measured and it had good linearity over a wide range (0.3-5 Gy). The measured dose distributions were in good agreement with calculated ones. Since the present gel has higher sensitivity and it is synthesized more easily at lower cost than conventional polymer gels, we expect to see improved three-dimensional (3D) dosimetry using it.     

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.     

Temperature-dependent chemical shift and relaxation times of (23)Na in Na(4)HTm[DOTP

We describe the characterization of a (23)Na temperature-dependent chemical shift and relaxation rates in the complex, Na(4)HTm[DOTP]. This is the first characterization of a (23)Na temperature-dependent chemical shift in a nonmetallic sample. The (23)Na temperature-dependent chemical shift coefficient is approximately -0. 5 PPM/ degrees C for both an aqueous solution and a 6% agarose gel of this compound. This is 50 times the magnitude of the temperature-dependent chemical shift coefficient of water protons. The relaxation times, T(1), T(2f), and T(2s) increased by 0.1, 0.01, and 0.05 ms/ degrees C, respectively. Applications of these unique properties for designing an MRI technique for monitoring heat deposition in tissue and tissue phantoms are discussed.     

Mri measurements of T1, T2 and D for gels undergoing volume phase transition

Gels consist of crosslinked polymer network swollen in solvent. The network of flexible long-chain molecules traps the liquid medium they are immersed in. Some gels undergo abrupt volume change, a phase transition process, by swelling-shrinking in response to external stimuli changes in solvent composition, temperature, pH, electric field, etc. We report that during volume phase transition changes of NMR longitudinal relaxation time T(1), NMR transverse relaxation time T(2), and diffusion coefficient D of the PMMA gel, and D of the NIPA gel. We describe how the gels were synthesized and the reason of using the snapshot FLASH imaging sequence to measure T(1), T(2), and D. Since T(1), T(2) and D maps have identical field of view and data are extracted from identical areas from their respective maps, these values can be correlated quantitatively on a pixel-by-pixel basis. Thus a complete set of NMR parameters is measured in-situ: the gels are in their natural state, immersed in the liquid, during the phase transition. The results of spectroscopic method agree with that of snapshot FLASH imaging method. For the PMMA gel T(1), T(2) and D decrease when gels undergo volume phase transition between deuterated acetone concentration of 30% and 40%. At its contracted state, T(1) is reduced to a little less than one order of magnitude, T(2) over two orders of magnitude, and D over one order of magnitude, smaller from values of PMMA gel at the swollen state. At an elevated temperature of 54 degrees C the thermosensitive NIPA gel is at a contracted state, with its D reduced to almost one order of magnitude smaller from that of the swollen NIPA at room temperature.     

Estimation of free copper ion concentrations in blood serum using T(1) relaxation rates

The water proton relaxation rate constant R(1)=1/T(1) (at 60 MHz) of blood serum is substantially increased by the presence of free Cu2+ ions at concentrations above normal physiological levels. Addition of chelating agents to serum containing paramagnetic Cu2+ nulls this effect. This was demonstrated by looking at the effect of adding a chelating agent-D-penicillamine (D-PEN) to CuSO4 and CuCl2 aqueous solutions as well as to rabbit blood serum. We propose that the measurement of water proton spin-lattice relaxation rate constants before and after chelation may be used as an alternative approach for monitoring the presence of free copper ions in blood serum. This method may be used in the diagnosis of some diseases (leukaemia, liver diseases and particularly Wilson's disease) because, in contrast to conventional methods like spectrophotometry which records the total number of both bound and free ions, the proton relaxation technique is sensitive solely to free paramagnetic ions dissolved in blood serum. The change in R(1) upon chelation was found to be less than 0.06 s(-1) for serum from healthy subjects but greater than 0.06 s(-1) for serum from untreated Wilson's patients.     

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.     

The influence of macromolecular polymerization of spin-lattice relaxation of aqueous solutions

The docking or polymerization of globular proteins is demonstrated to cause changes in proton NMR spin-lattice (T1) relaxation times. Studies on solutions of lysozyme, bovine serum albumin, actin, and tubulin are used to demonstrate that two mechanisms account for the observed changes in T1. Polymerization displaces the hydration water sheath surrounding globular proteins in solution that causes an increase in T1. Polymerization also slows the average tumbling rate of the proteins, which typically causes a contrary decrease in T1. The crystallization reaction of lysozyme in sodium chloride solution further demonstrates that the "effective" molecular weight can either decrease or increase T1 depending on how much the protein is slowed. The displacement of hydration water increases T1 because it speeds up the mean motional state of water in the solution. Macromolecular docking typically decreases T1 because it slows the mean motional state of the solute molecules. Cross-relaxation between the proteins and bound water provides the mechanism that allows macromolecular motion to influence the relaxation rate of the solvent. Fast chemical exchange between bound, structured, and bulk water accounts for monoexponential spin-lattice relaxation. Thus the spin-lattice relaxation rate of water in protein solutions is a complex reflection of the motional properties of all the molecules present containing proton magnetic dipoles. It is expected, as a result, that the characteristic relaxation times of tissues will reflect the influence of polymerization changes related to cellular activities.     

Relaxation-selective magnetization preparation based on T1 and T2

A magnetization-preparation scheme is described that combines the spin-echo and inversion-recovery (SEIR) to select spins based on both T1 and T2 characteristics. The inclusion of T2 weighting allows for greater relative suppression of some tissues with respect to others, depending on their respective relaxation times, than does inversion-recovery alone. Formulae describing the observed magnetization following SEIR and double-SEIR (DSEIR) are presented with the corresponding formulae for inversion-recovery (IR) and double-IR (DIR). The formulae are validated with experimental studies on MnCl2 solutions and compared numerically for a variety of possible applications. Results indicate that DSEIR may yield 2x or more signal than DIR in some potential applications.     

A two-compartment phosphate-doped gel phantom for localized spectroscopy.

Acrylamide gel loaded with phosphate has been used in two compartment phantoms designed to assess localized spectroscopy techniques. A chemical shift difference of 2.3 ppm was produced by changing the pH from 6 to 8.9. The 31P relaxation times were modified by doping the gels with paramagnetic ions. For a T1 of approximately 1 sec nickel doping gave a T2 of approximately 110 msec and manganese doping gave a T2 of approximately 8 msec. Gel phantoms are more robust than their liquid equivalent and are not prone to leakage. The construction of small compartments with very thin walls is possible, making this type of phantom suitable for small bore imaging/spectroscopy systems.     

Anomalous NMR relaxation in cartilage matrix components and native cartilage: fractional-order models

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T(1) and T(2)). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T(1) and T(2) relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T(2) relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T(1) was observed in BNC. In the single-component gels, for T(2) measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T(2) NMR relaxation processes in biological tissues.     

Temperature dependence of proton relaxation times in vitro

Accurate measurement of tissue relaxation characteristics is dependent on many factors, including field strength and temperature. The purpose of this study was to evaluate the relationship between sample temperature, viscosity and proton spin-lattice relaxation time (T1) and spin-spin relaxation time (T2). A review of two basic models of relaxation the simple molecular motion model and the fast exchange two state model is given with reference to their thermal dependencies. The temperature dependence for both T1 and T2 was studied on a 0.15 Tesla whole body magnetic resonance imager. Thirteen samples comprising both simple and complex materials were investigated by using a standard spin-echo (SE) technique and a modified Carr-Purcell-Meiboom-Gill (CPMG) multi-echo sequence. A simple linear relationship between T1 and temperature was observed for all samples over the range of 20 degrees C to 50 degrees C. There is an inverse relationship between viscosity and T1 and T2. A quantity called the temperature dependence coefficient (TDC) is introduced and defined as the percent rate of change of the proton relaxation time referenced to a specific temperature. The large TDC found for T1 values, e.g. 2.37%/degrees C for CuSO4 solutions and 3.59%/degrees C for light vegetable oils at 22 degrees C, indicates that a temperature correction should be made when comparing in-vivo and in-vitro T1 times. The T2 temperature dependence is relatively small.     

Paramagnetic relaxation in sandstones: distinguishing T1 and T2 dependence on surface relaxation, internal gradients and dependence on echo spacing

This work provides a generalized theory of proton relaxation in inhomogeneous magnetic fields. Three asymptotic regimes of relaxation are identified depending on the shortest characteristic time scale. Numerical simulations illustrate that the relaxation characteristics in the regimes such as the T(1)/T(2) ratio and echo spacing dependence are determined by the time scales. The theoretical interpretation is validated for fluid relaxation in porous media in which field inhomogeneity is induced due to susceptibility contrast of fluids and paramagnetic sites on pore surfaces. From a set of measurements on model porous media, we conclude that when the sites are small enough, no dependence on echo spacing is observed with conventional low-field NMR spectrometers. Echo spacing dependence is observed when the paramagnetic materials become large enough or form a 'shell' around each grain such that the length scale of the region of induced magnetic gradients is large compared to the diffusion length during the time of the echo spacing. The theory can aid in interpretation of diffusion measurements in porous media as well as imaging experiments in presence of contrast agents used in MRI.     

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

The structure of polyacrylamide gels was studied using proton spin–lattice relaxation and PFG diffusion methods. Polyacrylamide gels, with total polymer concentrations ranging from 0.25 to 0.35 g/ml and crosslinker concentrations from 0 to 10% by weight, were studied. The data showed no effect of the crosslinker concentration on the diffusion of water molecules. The Ogston–Morris and Mackie–Meares models fit the general trends observed for water diffusion in gels. The diffusion coefficients from the volume averaging method also fit the data, and this theory was able to account for the effects of water-gel interactions that are not accounted for in the other two theories. The averaging theory also did not require the physically unrealistic assumption, required in the other two theories, that the acrylamide fibers are of similar size to water molecules. Contrary to the diffusion data,T₁relaxation measurements showed a significant effect of crosslinker concentration on the relaxation of water in gels. The model developed using the Bloch equations and the volume averaging method described the effects of water adsorption on the gel medium on both the diffusion coefficients and the relaxation measurements. In the proposed model the gel medium was assumed to consist of three phases (i.e., bulk water, uncrosslinked acrylamide fibers, and a bisacrylamide crosslinker phase). The effects of the crosslinker concentration were accounted for by introducing the proton partition coefficient,K^eq, between the bulk water and crosslinker phase. The derived relaxation equations were successful in fitting the experimental data. The partition coefficient,K^eq, decreased significantly as the crosslinker concentration increased from 5 to 10% by weight. This trend is consistent with the idea that bisacrylamide tends to form hydrophobic regions with increasing crosslinker concentration.     

Spin dynamics and magnetic correlation length in two-dimensional quantum heisenberg antiferromagnets

The correlated spin dynamics and temperature dependence of the correlation length xi(T) in two-dimensional quantum (S = 1/2) Heisenberg antiferromagnets (2DQHAF) on a square lattice are discussed in light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate. In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as La2CuO4 and Sr2CuO2Cl2. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out to be in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of xi(T) is in agreement with high-temperature expansions, quantum Monte Carlo simulations, and the pure quantum self-consistent harmonic approximation. Contrary to the predictions of the theories based on the nonlinear sigma model, no evidence of crossover between different quantum regimes is observed.     

Morphology and chain dynamics during collapse transition of PNIPAM gels studied by combined imaging, relaxometry and 129Xe spectroscopy techniques

The temperature-induced shape transition of poly(N-isopropylacrylamide) gels of different cross-link densities was investigated by a combination of NMR techniques allowing the characterization of both the macroscopic collapse as well as the changes on a molecular scale related to the expulsion of water from the gel network. The proton-containing gel phase was visualized by swelling in heavy water, and the volume change was monitored by proton imaging for cross-link densities between 0.5% and 2.5%. Above the transition temperature of 35 degrees C, gel collapse led to a volume change of up to a factor of 17 for the gel of smallest cross-link density. Two spectral lines of 129Xe are found in the gel state and are assigned to the hydrophobic and hydrophilic parts of the network. In the collapsed state, the hydrophobic peak shows a strong shift while the hydrophilic peak disappears. A considerable shortening of both T1 and T2 of the gel protons upon collapse was found at a field of 4.7 T. At lower fields, the effect becomes more pronounced and qualitatively different dispersion behaviors between the swollen and the collapsed states are observed.     

Mathematical Characterization of Thermo-reversible Phase Transitions of Agarose Gels

The thermal phase transition temperatures of high (HMP) and low melting point (LMP) agarose gels were investigated by using UV–vis spectroscopy techniques. Transmitted light intensities from the gel samples with different agarose concentrations were monitored during the heating (gel-sol) and cooling (sol–gel) processes. It was observed that the transition temperatures, T_m, defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from the UV–vis technique, slightly increased by increasing the agarose concentration in both the HMP and LMP samples. Here, we express the phase transitions of the agar-water system, as a representative of reversible physical gels, in terms of a modified Susceptible-Infected-Susceptible epidemic model whose solutions are the well-known 5-point sigmoidal curves. The gel point is hard to determine experimentally and various computational techniques are used for its characterization. Based on previous work, we locate the gel point, T₀, of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating), T₀ is greater than T_m, i.e. later in time, and the difference between T₀ and T_m is reduced as the agarose content increases. For the sol-gel transition (cooling), T₀ is again greater than T_m, but it is earlier in time for all agarose contents and moves forward in time and gets closer to T_m as the agarose content increases.     

Magic sandwich echo relaxation mapping of anisotropic systems

The main objective of this article was (i) to refocus the residual dipolar and quadrupolar interactions in anisotropic tissues employing magic sandwich echo (MSE) imaging and to compare the results with that of conventional spin-echo (SE) imaging, and (ii) to quantify MSE relaxation and dispersion characteristics in bovine Achilles tendon and compare with spin-lattice relaxation time constant in the rotating frame (T(1rho)). Magic sandwich echo weighted images are approximately 75-100% higher in signal-to-noise ratio than the corresponding T(2)-weighted images. Magic sandwich echo relaxation times varied from 13+/-2 to 19+/-3 ms (mean+/-S.D.), depending upon the structural location of tendon. T(2) relaxation times only varied from 4+/-1 to 10+/-3 ms (mean+/-S.D.) on the same corresponding locations. Magic sandwich echo provides approximately 100% enhancement in relaxation times compared to T(2). Preliminary results based on bovine Achilles tendon and cartilage specimens suggest that the MSE technique has potential for refocusing residual dipolar as well as quadrupolar interactions in anisotropic systems and yields higher intensities than conventional SE imaging as well as T(1rho)-encoded imaging, especially at low-burst pulse amplitudes (250 and 500 Hz).