Molecular dynamics parameter maps by 1H Hahn echo and mixed-echo phase-encoding MRI

Residual dipolar couplings and averaged correlation time maps in soft matter were obtained by mixed echo phase-encoding solid imaging (MIPSI). Use of the mixed echo in soft matter NMR imaging experiments has two crucial advantages: the signal intensity is recovered with a weak incoherence losses, and second, the intervals during which the phase-encoding evolution due to the magnetic field gradients takes place can be chosen to be much larger than with all other spin echo experiments and hence, a higher special resolution can be achieved. The parameter maps are compared to those obtained by the Hahn-echo phase-frequency encoding method. For both MRI methods the density operator formalism is applied in the average Hamiltonian approximation to describe the encoding of the spin echoes by the molecular motions. The results of preliminary experiments are presented.

The heterogeneity of segmental dynamics of filled EPDM by (1)H transverse relaxation NMR

Residual second moment of dipolar interactions M(2) and correlation time segmental dynamics distributions were measured by Hahn-echo decays in combination with inverse Laplace transform for a series of unfilled and filled EPDM samples as functions of carbon-black N683 filler content. The fillers-polymer chain interactions which dramatically restrict the mobility of bound rubber modify the dynamics of mobile chains. These changes depend on the filler content and can be evaluated from distributions of M(2). A dipolar filter was applied to eliminate the contribution of bound rubber. In the first approach the Hahn-echo decays were fitted with a theoretical relationship to obtain the average values of the (1)H residual second moment <M(2)> and correlation time <τ(c)>. For the mobile EPDM segments the power-law distribution of correlation function was compared to the exponential correlation function and found inadequate in the long-time regime. In the second approach a log-Gauss distribution for the correlation time was assumed. Furthermore, using an averaged value of the correlation time, the distributions of the residual second moment were determined using an inverse Laplace transform for the entire series of measured samples. The unfilled EPDM sample shows a bimodal distribution of residual second moments, which can be associated to the mobile polymer sub-chains (M(2) ≅ 6.1 rad (2) s(-2)) and the second one associated to the dangling chains M(2) ≅ 5.4 rad(2) s(-2)). By restraining the mobility of bound rubber, the carbon-black fillers induce diversity in the segmental dynamics like the apparition of a distinct mobile component and changes in the distribution of mobile and free-end polymer segments.

Distributions of transverse relaxation times for soft-solids measured in strongly inhomogeneous magnetic fields

The single-sided NMR-MOUSE sensor that operates in highly inhomogeneous magnetic fields is used to record a CPMG (1)H transverse relaxation decay by CPMG echo trains for a series of cross-linked natural rubber samples. Effective transverse relaxation rates 1/T(2,short) and 1/T(2,long) were determined by a bi-exponential fit. A linear dependence of transverse relaxation rates on cross-link density is observed for medium to large values of cross-link density. As an alternative to multi-exponential fits the possibility to analyze the dynamics of soft polymer network in terms of multi-exponential decays via the inverse Laplace transformation was studied. The transient regime and the effect of the T(1)/T(2) ratio in inhomogeneous static and radiofrequency magnetic fields on the CPMG decays were studied numerically using a dedicated C++ program to simulate the temporal and spatial dependence of the CPMG response. A correction factor T(2)/T(2,eff) is derived as a function of the T(1)/T(2) ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T(1)-T(2) correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T(1)-T(2) experimental correlations maps were corrected for the T(1)/T(2) effect using the derived T(2)/T(2,eff) correction factor.

Self-diffusion anisotropy of water in sheep Achilles tendon

The principal values of the diffusion tensor of free water in the pores of sheep Achilles tendon were determined. For this purpose, the azimuthally angular dependence of the self-diffusion coefficient was measured using a radiofrequency tilt coil and pulsed-field-gradient stimulated-echo (PFGSE) NMR. Combining the PFGSE with multiple acquisitions of Hahn echoes using the Carr-Purcell-Meiboom-Gill pulse sequence reduced the measuring time. The diffusion measurements revealed two diffusion process characterized by a fast and a slow effective diffusion coefficient. A model which describes the stimulated-echo amplitude, encoded by the water diffusion and magnetization transfer, was used for evaluation of the fast diffusion coefficients. The fast diffusion process characterizes the water molecules in pores surrounding the collagen fibrils. The diffusion coefficients characterizing the fast process show a well-defined anisotropy. The principal values of the diffusion tensors were determined assuming the elongated pores to be oriented parallel to the tendon fibrils and thus the orientation distribution function of the pores followed that of the collagen fibrils. The average aspect ratio of pores was estimated from the principal values of the water diffusion tensor and is suitable to characterize quantitatively the changes in tendon morphology due to healing or aging. The methods in this investigation can also be applied to measurements of the diffusion anisotropy using ex situ NMR sensors.

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.

Order parameters of the orientation distribution of collagen fibers in Achilles tendon by 1H NMR of multipolar spin states

The angular distribution function of collagen fibrils in a sheep Achilles tendon was investigated by (1)H NMR of multipolar spin states represented by dipolar-encoded longitudinal magnetization and double-quantum filtered signals. For the first time the angular distribution function based on the Legendre moment expansion is used. Order parameters were obtained from the anisotropy of (1)H residual dipolar couplings of bond water, which were determined model-free from the excitation efficiency of the multipolar spin states and from double-quantum filtered line splitting. The orientation distribution function of collagen fibrils in Achilles tendon measured from the anisotropy of the residual dipolar couplings is characterized by the average values of beta0 = 1.8+/-0.2 degrees and order parameters [P2] = 0.93+/-0.04, [P4] = 0.78+/-0.04 and [P6] = 0.58+/-0.04. The order of many biological tissues in the presence of ageing, injuries or regeneration can be quantified by the order parameters of the angular distribution function.

Parameter maps of 1H residual dipolar couplings in tendon under mechanical load

Proton multipolar spin states associated with dipolar encoded longitudinal magnetization (DELM) and double-quantum (DQ) coherences of bound water are investigated for bovine and sheep Achilles tendon under mechanical load. DELM decay curves and DQ buildup and decay curves reveal changes of the 1H residual dipolar couplings for tendon at rest and under local compression forces. The multipolar spin states are used to design dipolar contrast filters for NMR 1H images of heterogeneous tendon. Heterogeneities in tendon samples were artificially generated by local compression parallel and perpendicular to the tendon plug axis. Quotient images obtained from DQ-filtered images by matched and mismatched excitation/reconversion periods are encoded only by the residual dipolar couplings. Semi-quantitative parameter maps of the residual dipolar couplings of bound water were obtained from these quotient images using a reference elastomer sample. This method can be used to quantify NMR imaging of injured ordered tissues.

Selective NMR excitation in strongly inhomogeneous magnetic fields

The NMR-MOUSE is a unilateral and mobile NMR sensor which operates with highly inhomogeneous magnetic fields. To produce a mobile NMR unit, RF excitation is sought, which can be produced with the most simple equipment, in particular nonlinear, low-power amplifiers, and to observe a free induction decay in strongly inhomogeneous fields, the excitation needs to be selective. The possibility to produce selective excitation by sequences of hard low-power radiofrequency pulses in the strongly inhomogeneous magnetic fields of the NMR-MOUSE is explored. The use of the DANTE sequence for selection of magnetization from parts of the sensitive volume was investigated for longitudinal and transverse magnetization by computer simulations and experiments. The spectra of the recorded FIDs and echo signals are in good agreement with those simulated for the excitation, which verifies the concept of the DANTE excitation. The results obtained are an important step towards a low-power operation of the NMR-MOUSE to improve its mobility.

Self-diffusion measurements by a constant-relaxation method in strongly inhomogeneous magnetic fields

The simple pulse sequence thetax-tau1-2thetay-tau1+tau2-2thetay-tau2-Hahn echo used to measure the self-diffusion coefficient D under constant-relaxation condition, i.e., for tau1+tau2=const. was investigated in the presence of strongly inhomogeneous static as well as radiofrequency magnetic fields. The encoding of the Hahn-echo amplitude by the pulse flip angle and diffusion was evaluated by taking into account the spatial distribution of the off-resonance field, the strength and orientation of the local field gradients, and the pulse flip angles by a computer simulation program. As input files, this program uses maps of static and radiofrequency fields, and the D coefficient can be evaluated from the time dependence of the Hahn-echo amplitude. The method was applied to a mobile one-sided NMR sensor, NMR-MOUSE with a bar magnet by measuring D for a series of liquids with different viscosities. The method was shown to be particularly useful for measuring D of solvents in elastomers without the need for measurements of the transverse relaxation rates. The self-diffusion coefficient of toluene in a series of crosslinked natural rubber samples was measured and correlated with the crosslink density. Finally, the method was applied to measure the diffusion anisotropy of free water in bovine Achilles tendon.

Anisotropy of collagen fiber orientation in sheep tendon by 1H double-quantum-filtered NMR signals

The anisotropy of the angular distribution of collagen fibrils in a sheep tendon was investigated by 1H double-quantum (DQ) filtered NMR signals. Double-quantum build-up curves generated by the five-pulse sequence were measured for different angles between the direction of the static magnetic field and the axis of the tendon plug. Proton residual dipolar couplings determined from the DQ build-up curves in the initial excitation/reconversion time regime which mainly represent the bound water are interpreted in terms of a model of spin-1/2 pairs with their internuclear axes oriented on average along the fibril direction in the presence of proton exchange. The angular distribution of collagen fibrils around the symmetry axis of the tendon measured by the anisotropy of the residual dipolar couplings was described by a Gaussian function with a standard deviation of 12 degrees +/-1 degrees and with the center of the distribution at 4 degrees +/-1 degrees. The existence of this distribution is directly reflected in the finite value of the residual dipolar couplings at the magic angle, the value of the angular contrast, and the oscillatory behavior of the DQ build-up curves. The 1H residual dipolar couplings were also measured from the doublets recorded by the DQ-filtered signals. From the angular dependence of the normalized splitting the angular distribution of the collagen fibrils was evaluated using a Gaussian function with a standard deviation of 19 degrees +/-1 degrees and with the center of distribution at 2 degrees +/-1 degrees. The advantages and disadvantages of these approaches are discussed.

Segmental anisotropy in strained elastomers detected with a portable NMR scanner

Single-side NMR is particularly suitable for measurements of segmental anisotropy induced in elastomers by uniaxial forces or local strain. Proton transverse nuclear magnetic relaxation was investigated with the NMR-MOUSE by recording the Hahn-echo decay in cross-linked natural rubber bands. This provided information on the dependence of the Hahn-echo decay on the angle between the direction of the uniaxial stretching force and the axis Z defined direction perpendicular to the magnet pole faces of the NMR-scanner. The anisotropy effect on the Hahn-echo decay is correlated with the extension ratio, and it is more evident in the liquid-like regime of the decay. A weaker segmental anisotropy is detected by 1H solid- and Hahn-echo decays recorded by multi-pulse sequences. A qualitative understanding of the angular dependence is obtained by an analytical theory of the Hahn-echo decay adapted to the case of stretched elastomers and to strongly inhomogeneous magnetic fields. Using angular-dependent 1H residual second van Vleck moments and correlation times reported previously [P.T. Callaghan and E.T. Samulski, Macromolecules 30, 113 (1997)] from stretched natural rubber bands the segmental anisotropy measured in inhomogeneous magnetic fields by the Hahn-echo decay was numerically simulated. As an example of a macroscopic distribution of local segmental anisotropy, 1H Hahn-echo decays were measured by the NMR-MOUSE sensor in a stretched cross-linked natural rubber plate with a circular cut in the center.