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.     

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.     

Glassy dynamics: effective temperatures and intermittencies from a two-state model

We show the existence of intermittent dynamics in one of the simplest model of a glassy system: the two-state model, which has been used [Physica A 329 (2003) 357] to explain the origin of the violation of the fluctuation–dissipation theorem. The dynamics is analyzed through a Langevin equation for the evolution of the state of the system through its energy landscape. The results obtained concerning the violation factor and the non-Gaussian nature of the fluctuations are in good qualitative agreement with experiments measuring the effective temperature and the voltage fluctuations in gels and in polymer glasses. The method proposed can be useful to study the dynamics of other slow relaxation systems in which non-Gaussian fluctuations have been observed.     

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.     

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.     

A Comparative Multinuclear Relaxation Study of Protein-DMSO and Protein-Water Interactions

A comparative multinuclear relaxation study of DMSO-protein and water-protein interactions has been undertaken to discover whether cross relaxation between water and protein protons proceeds mainly by proton-exchange or direct dipolar interactions. The analysis suggests that the proton-exchange mechanism dominates the cross relaxation from water. In contrast, the high efficiency of dipolar cross relaxation in DMSO-protein gels, which lack exchangeable protons, arises from an unusually long lifetime of DMSO molecules at the protein interface. These results are important for understanding the origin of image contrast in clinical nuclear magnetic resonance imaging and the nature of protein-solvent interactions in nonaqueous systems.     

Effects of paramagnetic cations on the nonexponential spin-lattice relaxation of rare spin nuclei in solids

Nonexponential spin-lattice relaxation is often observed for rare spin nuclei in the solid state. Deviation from single-component decay may be amplified by the coupling of rare spin nuclei to paramagnetic centers. Nonexponential spin-lattice relaxation was observed in derivatized silica gels resins. This phenomenon was localized and enhanced when paramagnetic transition metal cations were bound to surface functional groups. A stretched exponential analysis method was determined to be robust in fitting nonexponential relaxation curves for silica gels both with and without bound paramagnetic ions. Spin-lattice relaxation rates (T₁⁻¹) for functional group nuclei increased as a function of percent surface coverage with metal ion. The magnitude of the relaxation rate increase was dependent upon internuclear distances from the paramagnetic center. At low surface coverages, a semi-random distribution of paramagnetic centers increased the degree of stretching of spin-lattice relaxation decays, as measured by decreases in the calculated stretching parameter β. At higher surface coverages, calculated β values reached a limiting value, indicating that while the spin-diffusion mechanism in metal-ex-changed silica gels is restricted, it is not completely diminished.     

Multi-center trial with an in vitro NMR protocol. EEC Concerted Research Project

The EEC Protocol for in vitro measurement of T1 and T2 presented in paper II of this series was tested in 15 centers on a variety of instruments. This article discusses the results of this protocol trial using biological samples (rat liver and thigh muscle) and two reference gel samples. Each reference gel was prepared as a single batch, dispensed into appropriate sample tubes and sent to all participants. Details of instrument types and operating conditions are given, along with measurement frequencies and temperatures and the results of precision testing. The relaxation time measurements from the gels for the trial are compared with temperature and frequency effects examined in independent centers under similar conditions. The relaxation time values for biological tissues are examined in the light of the scatter of such values in the general literature. To check the effects of data analysis methods on relaxation times, full relaxation data for one reference sample was provided by each group. This was re-analyzed in three centers using different methods; these results are compared with the values calculated by each group using its own method. In general, the results from different groups show good consistency with the reference values. The use of this Protocol has helped reduce scatter in results from biological samples and has provided information for improvement of individual operating conditions and improvement of the protocol to its final form.     

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.     

Dipolar Relaxation Times of Tryptophan and Tyrosine in Glycerol and in Proteins: A Direct Evaluation from Their Fluorescence Decays

The dipolar relaxation process induced around tryptophan, indole and tyrosine in viscous media, as well as in several single tryptophan-containing proteins (staphylococcal nuclease, ribonuclease T1, melittin and albumin), has been studied by dynamic fluorescence measurements. A new theoretical model has been developed, including the relaxation dynamics directly in the fluorescence decay function. The phase shift and demodulation data have been fitted with this new algorithm which allows to resolve the different relaxation times influencing the fluorophore excited state. These parameters are in a good agreement with those measured with the traditional time-resolved emission spectroscopy. The results indicate that indeed a correlation exists between the radiative rate change obtained with the new model and the temporal spectral shift reported in the literature. Finally, this new approach has also been extended to the case of superoxide dismutase and phosphofructokinase, allowing to measure the relaxation time even in proteins lacking a temporal spectral shift during the fluorphore's lifetime.     

Determination of the dispersion of the specific heat of glycerol by light scattering

We have performed light scattering experiments to study the Rayleigh-Mountain coupling in liquid and supercooled glycerol. The ratio of the Mountain widths on both sides of the coupling has been deduced and found to be about 1. This value is in good agreement with theoretical predictions for a structural relaxation, but not with experimental determinations by calorimetric methods.     

Solid-state 13C NMR study of poly(vinyl alcohol) gels

Poly(vinyl alcohol) (PVA) with 55% and 61% syndiotacticity, and their related dry and hydrated gels obtained by two different freeze–thawing cycles have been investigated using the solid-state ¹³C CP-MAS NMR technique. From a comparative analysis of the spectra, evidence was obtained that the gelation process largely disrupts the intramolecular hydrogen-bonded network of the PVA. The addition of water to the dry gels favours their swelling, destroying intra-chain hydrogen bonds between hydroxyl groups as a function of the degree of tacticity and the gelation procedure, and promotes the formation of new networks of interchain hydrogen bonds. Information on the dynamics of the polymeric domains in the kilohertz range has been obtained from the analysis of the spin relaxation times T_1ρ(¹H) and T_1ρ(¹³C), indicating that homogeneous arrangements of the amorphous or swollen polymeric chains exist, independent of the preparation method or the tacticity of the PVA chains.     

Relaxation and resonance ultrasound attenuation by Jahn-Teller centers in a GaAs:Cu crystal

The interaction of ultrasound with Cu_Ga4As in a GaAs:Cu crystal has been experimentally studied. The temperature dependences of the attenuation of all normal ultrasonic modes propagating in the ??110?? direction both in doped copper and in nominally pure gallium arsenide crystals have been measured. In the GaAs:Cu crystal, the attenuation peak has been revealed for a transverse wave polarized along the ??110?? axis whose elastic shifts correspond to the symmetry of the tetragonal mode of the Jahn-Teller effect. The temperature dependence of the attenuation of this wave indicates that two types of attenuation??relaxation and resonance??occur. The constructed temperature dependence of the relaxation time indicates that tunneling through the potential barrier between the minima of the adiabatic potential energy is the main relaxation mechanism at temperatures below 10 K. Tunneling splitting estimated from experimental data is in good agreement with the theoretical estimate.     

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.     

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.     

An NMR protocol for determining ice crystal size distributions during freezing and pore size distributions during freeze-drying

Nuclear magnetic resonance water proton relaxometry is widely used to investigate pore size distributions and pore connectivity in brine-saturated porous rocks and construction materials. In this paper we show that, by replacing water with acetone, a similar method can be used to probe the porous structure of freeze-dried starch gels and therefore the ice crystal size distribution in frozen starch gels. The method relies on the observation that the starch surface acts as a powerful relaxation sink for acetone proton transverse magnetization so that Brownstein-Tarr theory can be used to extract the pore size distribution from the relaxation data. In addition the relaxation time distribution is found to depend on the spectrometer frequency and the Carr-Purcell-Meiboom-Gill pulse spacing, consistent with the existence of large susceptibility-induced field gradients within the pores. The potential of this approach for noninvasively measuring ice crystal size distributions during freezing and pore size distributions during freeze-drying in other food systems is discussed.     

The polaronic nature of intraband relaxation in InAs/GaAs self-assembled quantum dots

Polaron relaxation processes in a series of n-type InAs quantum dots (QDS) have been investigated using energy-dependent far-infrared pump–probe spectroscopy. For energies up to 53 meV, polarons decay to 2 longitudinal acoustic phonons; above this energy additional decay channels open resulting in a reduction of the decay time. Inter-state transfer has been observed between closely spaced p-like excited states, with the measured transfer times in good agreement with calculations assuming acoustic phonon assisted transfer. Finally, for QDs containing 2 electrons we observe evidence of a spin-flip process resulting in long (700 ps) relaxation times.     

Agarose as a tissue equivalent phantom material for NMR imaging

Phantoms for evaluation of nuclear magnetic resonance (NMR) imaging systems were made from water-based agarose gels, according to a standard procedure herein described. Copper sulfate (CuSO4) was included in the gels to further affect their proton relaxation characteristics. The proton relaxation rates of each batch of gel are dependent on the concentrations of agarose and copper ions in it, with T1 depending more on copper than on agarose, and T2 depending more strongly on agarose than on copper. The wide range of T1 and T2 which can be covered, and the stability and physical characteristics of the agarose gel material make it well-suited for phantom use.     

Nuclear spin relaxation in paramagnetic systems (S>/=1) under fast rotation conditions

A new theoretical model for nuclear spin relaxation in paramagnetic systems in solution has been developed. Fast rotational motion is included in the model, both as a source of modulation of the static zero-field splitting, which provides a mechanism for electron spin relaxation, and as an origin of the stochastic variation of the electron spin-nuclear spin dipole-dipole interaction leading to nuclear spin relaxation. At the limit of low magnetic field, the model is essentially identical to the earlier formulations from our laboratory, but new closed-form expressions are given for the inner- and outer-sphere relaxation at the high-field limit. Numerical comparisons with a general theory are reported for the inner-sphere case. In addition, some nuclear magnetic relaxation dispersion (NMRD) profiles from the literature are considered for systems where experiments have been done with both low-molecular weight paramagnetic complexes and their adducts with proteins. Previously developed theories are used to interpret data for the slowly rotating protein adducts, and good fits of the fast-rotating counterparts are obtained by further adjustment of one or two additional parameters.     

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.