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.     

Two-dimensional nuclear magnetic resonance petrophysics

Two-dimensional nuclear magnetic resonance (2D NMR) opens a wide area for exploration in petrophysics and has significant impact to petroleum logging technology. When there are multiple fluids with different diffusion coefficients saturated in a porous medium, this information can be extracted and clearly delineated from CPMG measurements of such a system either using regular pulsing sequences or modified two window sequences. The 2D NMR plot with independent variables of T2 relaxation time and diffusion coefficient allows clear separation of oil and water signals in the rocks. This 2D concept can be extended to general studies of fluid-saturated porous media involving other combinations of two or more independent variables, such as chemical shift and T1/T2 relaxation time (reflecting pore size), proton population and diffusion contrast, etc.     

The Influence of the Magnetic Impurity Content on the Pore Size Distribution Determination via the DDIF Technique

The pore size distribution of porous media can be determined in a completely non-invasive manner using a new nuclear magnetic resonance (NMR) technique which monitors the magnetization decay due to diffusion in internal fields (DDIF). However, using of the DDIF technique is restricted to the low-phase encoding limit when only the relaxation mode and the first-order diffusion mode are excited. In the present work the fulfillment of such a limit is verified for a progressive increase of the magnetic impurity content of the porous media. If the higher order diffusion modes are excited they lead both to a stronger attenuation of the echo signal and to the appearance of ripples in the DDIF spectra which cannot be related to a pore size distribution. The samples used in this study are porous ceramics prepared using the replication technique and the magnetic impurity is iron (III) oxide which is introduced in an increasing concentration inside the porous matrix. All NMR experiments were done on water filling such porous ceramics using a low-field instrument operating at a proton resonance frequency of 20 MHz. The average pore dimension obtained with the DDIF technique in the weak encoding limit indicates a satisfactory agreement with that observed in optical microscopy images.     

Another approach to protons with constricted mobility in white matter: pilot studies using wideline and high-resolution NMR spectroscopy

We report a new approach for the identification of an independent method of studying the semi-solid pool of protons, i.e., protons with constrained motion as a result of being bound to lipid and protein matrices. These protons cannot be observed using conventional imaging techniques since their transverse relaxation times are much shorter than the minimum echo times that are currently available on clinical scanners. In this pilot study, in vitro multicomponent transverse relaxation experiments were made on human white matter slices, fixed in formalin (7 normal and 5 with multiple sclerosis). The transverse relaxation decay curves were multiexponential and were decomposed to yield three primary components. The shortest T(2) component that we obtained (a component too short to be seen by in vivo methods) was of the order of microseconds. We hypothesize that this might correspond to the macromolecular pool of lipid protons trapped within the myelin sheaths. To our knowledge, this is the first attempt at extracting this ultra short T(2) component from human white matter. Subsequently, an attempt was made to directly detect the lipid protons in a proton NMR spectrum and, if possible, measure their concentration in some of the tissues, using the technique of magic angle spinning.     

Cross-Relaxation Effects in Pulsed-Field-Gradient Stimulated-Echo Measurements on Water in a Macromolecular Matrix

Water diffusion in poly[2-hydroxyethyl-methacrylate] hydrogels has been measured by PFG NMR techniques, using both spin-echo and stimulated-echo methods. It is found that the results differ when evaluated using the standard equations for the echo attenuation. Furthermore, an apparent dependence of the diffusion coefficient on the diffusion time was found in stimulated-echo experiments. This effect is shown to be caused by cross relaxation between the protons of the water and those on the polymer matrix. An equation is derived describing the attenuation of a stimulated echo in the presence of cross relaxation. This equation shows that the additional damping due to cross relaxation depends on the gradient amplitude. If this equation is used with the measured cross-relaxation parameters, both methods are found to agree within experimental error, and no diffusion-time dependence is found for the stimulated-echo experiments. The equation predicts the effect of replacing part of the H₂O by D₂O; this has been experimentally verified. It is concluded that macromolecular systems should be checked for cross relaxation when stimulated-echo methods will be used for self-diffusion measurements.     

A global inversion method for multi-dimensional NMR logging

We describe a general global inversion methodology of multi-dimensional NMR logging for pore fluid typing and quantification in petroleum exploration. Although higher dimensions are theoretically possible, for practical reasons, we limit our discussion of proton density distributions as a function of two (2D) or three (3D) independent variables. The 2D can be diffusion coefficient and T(2) relaxation time (D-T(2)), and the 3D can be diffusion coefficient, T(2), and T(1) relaxation times (D-T(2)-T(1)) of the saturating fluids in rocks. Using the contrast between the diffusion coefficients of fluids (oil and water), the oil and water phases within the rocks can be clearly identified. This 2D or 3D proton density distribution function can be obtained from either two-window or regular type multiple CPMG echo trains encoded with diffusion, T(1), and T(2) relaxation by varying echo spacing and wait time. From this 2D/3D proton density distribution function, not only the saturations of water and oil can be determined, the viscosity of the oil and the gas-oil ratio can also be estimated based on a previously experimentally determined D-T(2) relationship.     

岩心孔隙介质中流体的核磁共振弛豫

弛豫时间是核磁共振研究中的一个重要参数,岩心孔隙介质流体的弛豫过程是自由流体弛豫机制、表面弛豫机制和流体的扩散弛豫机制共同作用的结果,它包含了丰富的孔隙和流体本身的信息. 弛豫时间和自扩散系数的测量及对弛豫时间的分析是核磁共振技术应用于岩心分析和石油勘测的重要内容.     

Probing the analogy of the proton relaxation in biological tissues and porous media

Summary Experimental data are reported that show the analogy of longitudinal and transverse proton relaxation in heterogeneous systems as different as biological tissues and water-saturated rocks. Published data on the τ-dependence of the transverse-relaxation rate for biological tissues with magnetite grains, used as a contrast agent in MRI, are discussed in the light of our recent results on water-saturated porous media, and give for the liver another case of a behaviour parallel to that in rocks. There are enough similarities between NMR relaxation in tissues and in other porous media that, for work in either area, attention to the other is likely to be fruitful. Work supported by Italian CNR and MURST grants     

Molecular Diffusion and DNP Enhancement in Aqueous Char Suspensions

The heterogeneous¹H dynamic nuclear polarization (DNP) effect is studied at low magnetic fields for a system consisting of several newly synthesized carbon chars suspended in water. By using Fourier Transform pulsed-field-gradient spin–echo NMR spectroscopy, several different self-diffusion coefficients have been observed in aqueous char suspensions, corresponding to regions of differing water mobility in the porous structure. Proton spin–lattice relaxation data generally confirm the results of molecular diffusion measurements. Through utilization of the Torrey model, the influence of “cage effects” on DNP enhancement in porous media is discussed. Results suggest that short-range nuclear–electronic interactions in pores have a dominant effect on DNP enhancement in char suspensions.     

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.     

Probing four orders of magnitude of the diffusion time in porous silica glass with unconventional NMR techniques

The combined use of two unconventional NMR diffusometry techniques permits measurements of the self-diffusion coefficient of fluids confined in porous media in the time range from 100 microseconds to seconds. The fringe field stimulated echo technique (FFStE) exploits the strong steady gradient in the fringe field of a superconducting magnet. Using a standard 9.4 T (400 MHz) wide-bore magnet, for example, the gradient is 22 T/m at 375 MHz proton resonance and reaches 60 T/m at 200 MHz. Extremely short diffusion times can be probed on this basis. The magnetization grid rotating frame imaging technique (MAGROFI) is based on gradients of the radio frequency (RF) field. The RF gradients not necessarily need be constant since the data are acquired with spatial resolution along the RF gradient direction. MAGROFI is also well suited for unilateral NMR applications where all fields are intrinsically inhomogeneous. The RF gradients reached depend largely on the RF coil diameter and geometry. Using a conic shape, a value of at least 0.3 T/m can be reached which is suitable for long-time diffusion measurements. Both techniques do not require any special hardware and can be implemented on standard high RF power NMR spectrometers. As an application, the influence of the tortuosity increasing with the diffusion time is examined in a saturated porous silica glass.     

Novel NMR techniques for porous media research

Diffusion in porous media has been used as a probe of pore geometry in various NMR techniques. We will examine the effect of time-dependent diffusion in CPMG by showing that the diffusion time in CPMG is approximately the echo time, even in grossly inhomogeneous magnetic fields. Extension of the diffusion time in modified CPMG sequences is discussed. Diffusion in the susceptibility-contrast induced internal field is discussed as a means to probe pore size and pore shape. Finally, we present the general concept of two-dimensional relaxation-type experiments for study of molecules, fluids, materials and their dynamics that are characterized by spin relaxation and diffusion.     

Diffusion-weighted spatial information from1H relaxation in restricted geometries

Summary NMR relaxation of water¹H confined in restricted geometries, whatever is the nature of the system (porous media saturated by water as well as biological tissues), exhibits common characteristics. Artificial microporous media saturated by water have been chosen as model systems to study the longitudinal and transverse relaxation of¹H magnetization of water molecules diffusing in restricted geometries. These systems are very stable, easy to prepare, with well-characterized pore size distribution and connections, and with highly homogeneous surface properties. The response was compared with that from more complex natural porous media. Scanning Electron Microscopy techniques demonstrated spatial characteristics and surface properties of the samples. The information content of longitudinal relaxation curves associated with spatial structure and due to restricted diffusion is shown in these samples. The effect on transverse relaxation of self-diffusion in the presence of spatially varying magnetic fields due to susceptibility differences is shown. A simple linear relationship has been found in all samples between the transverse relaxation rate and the interpulse delay in CPMG experiments, in spite of the variety of pore shapes and sizes. In general, one can say that relaxation curves beardiffusion-weighted information on the pore space framework. The role of the investigated relaxation mechanisms is important also in the response of biological tissues, including in the presence of MR Imaging contrast agents inducing microscopic magnetic-field gradients. Work partially supported by CNR and MURST Grants.     

The influence of chemical and diffusive exchange on water proton transverse relaxation in plant tissues

Transverse water proton relaxation in parenchyma tissue of courgette, onion and apple shows a dependence on CPMG pulse spacing characteristic of each tissue. An analysis of this dependence suggests that transverse relaxation in these tissues is caused by various combinations of fast proton exchange between water and cell biopolymers (or solutes) and diffusion through internally generated magnetic field gradients. Diffusion between intra- and extracellular water compartments also averages the water proton signal to an extent that depends on cell morphology and membrane permeability and this is calculated using a two-compartment model. No recourse need be made to popular concepts such as exchange between free and "bound" water. The implications of our results for NMR image contrast are discussed.     

Multi-dimensional inverse Laplace spectroscopy in the NMR of porous media

Multi-dimensional NMR methods based on Inverse Laplace Transformations (ILT) may be used to examine the behavior of liquid state molecules in a porous matrix. The ILT is particularly useful when the signal is characterized by multi-exponential decay, for example in spin relaxation or in the dephasing of the NMR spin echo signal associated with molecular diffusion under the influence of pulsed magnetic or internal field gradients. Both correlation and exchange experiments are possible, the latter providing insight regarding the migration of molecules between regions characterized by different local dynamics.     

Categories of coherence pathways for the CPMG sequence

The CPMG sequence has been extremely useful for efficient measurements of NMR signal, spin-spin relaxation, and diffusion, particularly in inhomogeneous magnetic fields, such as when samples are outside the magnet and RF coil. Due to the inaccuracy of the pulses and the off-resonance effects, the CPMG echoes have contributions from the Hahn echo as well as signals that are similar to stimulated echoes. The systematic understanding of the CPMG pulse sequence requires decomposing the magnetization dynamics into different coherence pathways. In this paper, we describe a method to classify the CPMG coherence pathways and illustrate the nature of these types of pathways. This classification shows that direct echo and stimulated echoes are the major contribution to the CPMG signal. It also provides a clear understanding of the effect of restricted diffusion in porous media.     

Determination of moisture fraction in wood by mobile NMR device

A mobile NMR probe has been used as a non-destructive and non-invasive tool for water content analysis on wood samples. The porosity index, express as the fraction of the sensitivity volume of the probe occupied by water, is here proposed as an alternative to the moisture content index, namely the amount of water mass with respect to the mass of dried sample. In principle the method can be applied to any kind of porous media that has not detectable proton signal from the rigid matrix as, for instance, in building materials. In wood, where proton signal can be detected also from cellulose and others macromolecular components, some considerations and artifices are here proposed for eliminating this contribution. The method has allowed performing moisture volume fraction analysis on wood samples characterized by different wood species, cutting and moisture contents. The NMR data of moisture detection as volume fraction have successfully been compared with those obtained by the gravimetric method.     

An NMR study of the interaction between Melanin Free Acid and Mn ions as a model to mimic the enhanced proton relaxation rates in melanotic melanoma

The interaction of a soluble Melanin Free Acid (MFA) from Sepia melanin with Mn²⁺ ions is investigated by measuring the proton water relaxation rates. The similarity between MFA and the parent melanin is assessed by means of their high resolution ¹³C cross polarization magic angle spinning NMR spectra. The observed marked increase in longitudinal proton relaxation rates and the characteristic 1/T₁ NMRD profile are associated to the formation of a macromolecular metal complex. The presence of similar paramagnetic species is expected to cause the high contrast shown by melanotic tissues in MRI.     

NMR relaxometry and imaging of water absorbed in biodegradable polymer scaffolds

Porous substrates made of poly(3-hydroxybutyrate-3-hydroxyvalerate) (PHBHV) were prepared by a particulate leaching method. After removing the salt by extraction in water, proton nuclear magnetic resonance (NMR) relaxometry and imaging were performed on sets of PHBHV substrates immersed in phosphate-buffered solution during 3 months at different time points. Polarized optical microscopy studies were performed on thin sections, 25 and 5 mum, of the PHBHV samples. The results of NMR relaxometry showed two (1)H nuclei populations, well distinguishable on the free induction decay (FID), due to the different decay time constants, a factor of 10(2) apart. Thus, it was possible to separate the two populations, giving separate distributions of T(1) relaxation times. One population could be associated with water protons in the pores and the other to macromolecular protons. The distributions of T(1) and T(2) of the water proton shifted to lower values with increasing immersion time to a constant value after 30 days. The results obtained by NMR imaging showed an initial increase in the apparent porosity, reaching a plateau after 25 days of immersion. This increase is attributed mainly to the absorption of water in the microporosity as supported by the results of the relaxometry measurements and shown by scanning electron microscopy. The average porosity measured by NMR imaging at the plateau, 78+/-3%, is slightly higher than that determined by optical microscopy, 73+/-9%, which may be due to the fact that the latter method did not resolve the microporosity. Overall, the results suggest that at early stages after immersing the scaffolds in the aqueous medium, first 30 days approximately, NMR imaging could underestimate the porosity of the substrate.     

Nuclear magnetic resonance for cultural heritage

Nuclear magnetic resonance (NMR) portable devices are now being used for nondestructive in situ analysis of water content, pore space structure and protective treatment performance in porous media in the field of cultural heritage. It is a standard procedure to invert T(1) and T(2) relaxation data of fully water-saturated samples to get "pore size" distributions, but the use of T(2) requires great caution. It is well known that dephasing effects due to water molecule diffusion in a magnetic field gradient can affect transverse relaxation data, even if the smallest experimentally available half echo time tau is used in Carr-Purcell-Meiboom-Gill experiments. When a portable single-sided NMR apparatus is used, large field gradients due to the instrument, at the scale of the sample, are thought to be the dominant dephasing cause. In this paper, T(1) and T(2) (at different tau values) distributions were measured in natural (Lecce stone) and artificial (brick samples coming from the Greek-Roman Theatre of Taormina) porous media of interest for cultural heritage by a standard laboratory instrument and a portable device. While T(1) distributions do not show any appreciable effect from inhomogeneous fields, T(2) distributions can show strong effects, and a procedure is presented based on the dependence of 1/T(2) on tau to separate pore-scale gradient effects from sample-scale gradient effects. Unexpectedly, the gradient at the pore scale can be, in some cases, strong enough to make negligible the effects of gradients at the sample scale of the single-sided device.