Nuclear magnetic resonance signal decay in the presence of a background gradient: Normal and anomalous diffusion

A novel way for calculating the diffusion-weighted nuclear magnetic resonance (NMR) attenuation signal expression in the presence of a background gradient is developed. This method is easily applicable to NMR-attenuated signals arising from any pulse field gradient sequence experiments. Here, we provide detailed calculations for the classical pulsed gradient stimulated echo and the pulsed gradient spin echo, as the particular cases. Within this general theoretical framework, devised for Gaussian processes with stationary increments, we recover and extend the previous Stejskal-Tanner results in the case of normal diffusion and we furnish a new expression in the case of anomalous diffusion.

Microstructural features assessment of different waterlogged wood species by NMR diffusion validated with complementary techniques

Wood is a hygroscopic, multi-scale and anisotropic natural material composed of pores with different size and differently oriented. In particular, archaeologically excavated wood generally is waterlogged wood with very high moisture content (400%-800%) that need to have a rapid investigation at the microstructural level to obtain the best treatment with preservative agents. Time-dependent diffusion coefficient D(t) quantified by Pulse Field Gradient (PFG) Nuclear Magnetic Resonance (NMR) techniques provides useful information about complex porous media, such as the tortuosity (τ) describing pore connectivity and fluid transport through media, the average-pore size, the anisotropic degree (a_n). However, diffusion NMR is intrinsically limited since it is an indirect measure of medium microstructure and relies on inferences from models and estimation of relevant diffusion parameters. Therefore, it is necessary to validate the information obtained from NMR diffusion parameters through complementary investigations. In this work, the structures of five waterlogged wood species were studied by PFG of absorbed water. D(t) and τ of water diffusing along and perpendicular to vessels/tracheids main axes together with relaxation times and a_n were quantified. From these parameters, the pore sizes distribution and the wood microstructure characterization were obtained. Results among wood species were compared, validated and integrated by micro-imaging NMR (μ-MRI), environmental-scanning electron-microscope (ESEM) images, wood dry density and imbibition times measurement of all woods. The work suggests that a_n vs τ rather than the estimated pore size diversifies and characterize the different wood species. As a consequence diffusion-anisotropy vs tortuosity could be an alternative method to characterize and differentiate wood species of waterlogged wood when high resolution images (μ-MRI and ESEM) are not available. Moreover, the combined use of D(t) and micro-MRI expands the scale of dimensions observable by NMR covering all the interesting length scales of wood.

Multimodal-3D imaging based on μMRI and μCT techniques bridges the gap with histology in visualization of the bone regeneration process

Bone repair/regeneration is usually investigated through X-ray computed microtomography (μCT) supported by histology of extracted samples, to analyse biomaterial structure and new bone formation processes. Magnetic resonance imaging (μMRI) shows a richer tissue contrast than μCT, despite at lower resolution, and could be combined with μCT in the perspective of conducting non-destructive 3D investigations of bone. A pipeline designed to combine μMRI and μCT images of bone samples is here described and applied on samples of extracted human jawbone core following bone graft. We optimized the coregistration procedure between μCT and μMRI images to avoid bias due to the different resolutions and contrasts. Furthermore, we used an Adaptive Multivariate Clustering, grouping homologous voxels in the coregistered images, to visualize different tissue types within a fused 3D metastructure. The tissue grouping matched the 2D histology applied only on 1 slice, thus extending the histology labelling in 3D. Specifically, in all samples, we could separate and map 2 types of regenerated bone, calcified tissue, soft tissues, and/or fat and marrow space. Remarkably, μMRI and μCT alone were not able to separate the 2 types of regenerated bone. Finally, we computed volumes of each tissue in the 3D metastructures, which might be exploited by quantitative simulation. The 3D metastructure obtained through our pipeline represents a first step to bridge the gap between the quality of information obtained from 2D optical microscopy and the 3D mapping of the bone tissue heterogeneity and could allow researchers and clinicians to non-destructively characterize and follow-up bone regeneration.

The γ-parameter of anomalous diffusion quantified in human brain by MRI depends on local magnetic susceptibility differences

Motivated by previous results obtained in vitro, we investigated the dependence of the anomalous diffusion (AD) MRI technique on local magnetic susceptibility differences (Δχ) driven by magnetic field inhomogeneity in human brains. The AD-imaging contrast investigated here is quantified by the stretched-exponential parameter γ, extracted from diffusion weighted (DW) data collected by varying diffusion gradient strengths. We performed T₂* and DW experiments in eight healthy subjects at 3.0T. T₂*-weighted images at different TEs=(10,20,35,55)ms and DW-EPI images with fourteen b-values from 0 to 5000s/mm² were acquired. AD-metrics and Diffusion Tensor Imaging (DTI) parameters were compared and correlated to R₂* and to Δχ values taken from literature for the gray (GM) and the white (WM) matter. Pearson's correlation test and Analysis of Variance with Bonferroni post-hoc test were used. Significant strong linear correlations were found between AD γ-metrics and R₂* in both GM and WM of the human brain, but not between DTI-metrics and R₂*. Depending on Δχ driven magnetic field inhomogeneity, the new contrast provided by AD-γ imaging reflects Δχ due to differences in myelin orientation and iron content within selected regions in the WM and GM, respectively. This feature of the AD-γ imaging due to the fact that γ is quantified by using MRI, may be an alternative strategy to investigate, at high magnetic fields, microstructural changes in myelin, and alterations due to iron accumulation. Possible clinical applications might be in the field of neurodegenerative diseases.

Early detection of human glioma sphere xenografts in mouse brain using diffusion MRI at 14.1 T

Glioma models have provided important insights into human brain cancers. Among the investigative tools, MRI has allowed their characterization and diagnosis. In this study, we investigated whether diffusion MRI might be a useful technique for early detection and characterization of slow-growing and diffuse infiltrative gliomas, such as the proposed new models, LN-2669GS and LN-2540GS glioma sphere xenografts. Tumours grown in these models are not visible in conventional T₂ -weighted or contrast-enhanced T₁ -weighted MRI at 14.1 T. Diffusion-weighted imaging and diffusion tensor imaging protocols were optimized for contrast by exploring long diffusion times sensitive for probing the microstructural alterations induced in the normal brain by the slow infiltration of glioma sphere cells. Compared with T₂ -weighted images, tumours were properly identified in their early stage of growth using diffusion MRI, and confirmed by localized proton MR spectroscopy as well as immunohistochemistry. The first evidence of tumour presence was revealed for both glioma sphere xenograft models three months after tumour implantation, while no necrosis, oedema or haemorrhage were detected either by MRI or by histology. Moreover, different values of diffusion indices, such as mean diffusivity and fractional anisotropy, were obtained in tumours grown from LN-2669GS and LN-2540GS glioma sphere lines. These observations highlighted diverse tumour microstructures for both xenograft models, which were reflected in histology. This study demonstrates the ability of diffusion MRI techniques to identify and investigate early stages of slow-growing, invasive tumours in the mouse brain, thus providing a potential imaging biomarker for early detection of tumours in humans.

Structural disorder and anomalous diffusion in random packing of spheres

Nowadays Nuclear Magnetic Resonance diffusion (dNMR) measurements of water molecules in heterogeneous systems have broad applications in material science, biophysics and medicine. Up to now, microstructural rearrangement in media has been experimentally investigated by studying the diffusion coefficient (D(t)) behavior in the tortuosity limit. However, this method is not able to describe structural disorder and transitions in complex systems. Here we show that, according to the continuous time random walk framework, the dNMR measurable parameter α, quantifying the anomalous regime of D(t), provides a quantitative characterization of structural disorder and structural transition in heterogeneous systems. To demonstrate this, we compare α measurements obtained in random packed monodisperse micro-spheres with Molecular Dynamics simulations of disordered porous media and 3D Monte Carlo simulation of particles diffusion in these kind of systems. Experimental results agree well with simulations that correlate the most used parameters and functions characterizing the disorder in porous media.

In vivo 19F MR imaging and spectroscopy for the BNCT optimization

The aim of this study was to evaluate in vivo the boron biodistribution and pharmacokinetics of 4-borono-2-fluorophenylalanine ((19)F-BPA) using (19)F MR Imaging ((19)F MRI) and Spectroscopy ((19)F MRS). The correlation between the results obtained by both techniques, (19)F MRI on rat brain and (19)F MRS on blood samples, showed the maximum (19)F-BPA uptake in C6 glioma model at 2.5h after infusion determining the optimal irradiation time. Moreover, the effect of L-DOPA as potential enhancer of (19)F-BPA tumour intake was assessed using (19)F MRI.

Boronophenylalanine uptake in C6 glioma model is dramatically increased by L-DOPA preloading

One of the main limitations for BNCT effectiveness is the insufficient intake of (10)B nuclei within tumour cells. This work was aimed at investigating the use of L-DOPA as enhancer for boronophenylalanine (BPA) uptake in the C6 glioma model. The investigation was first performed in vitro, and then extended in vivo to the animal model. BPA accumulation in C6 glioma cells was assessed, using radiowave dielectric spectroscopy (RDS), with and without L-DOPA preloading. C6 glioma cells were also implanted in the brain of 25 rats, randomly assigned to two experimental branches: (1) intra-carotid BPA infusion; (2) intra-carotid BPA infusion after pre-treatment with L-DOPA, administrated 24 h before BPA infusion. All animals were sacrificed, and assessment of BPA concentrations in tumour tissue, normal brain, and blood samples was performed using high performance liquid chromatography (HPLC). L-DOPA preloading induced a massive increase of BPA concentration either in vitro on C6 glioma cells or in vivo in the animal model tumour. Moreover, no significant difference was found in the normal brain and blood samples between the two animal groups. This study suggests the potential use of L-DOPA as enhancer for BPA accumulation in malignant gliomas eligible for BNCT.

Nonergodic Arrested State in Diluted Clay Suspensions Monitored by Triple-Quantum 23Na Nuclear Magnetic Resonance

The aging of water suspension of the synthetic clay Laponite has been studied by liquid-state triple-quantum filter nuclear magnetic resonance techniques, in a range of clay weight concentration (Cw = 0.012-0.028) known as the isotropic phase. Counterions dynamic parameters (rotational correlation time tauc and quadrupolar coupling constant e2qQ/h) have been extracted from sodium triple-quantum filtered experimental data within the multi-exponential quadrupolar relaxation theory in the fast exchange approximation. By monitoring quadrupolar sodium ions dynamical (tauc and e2qQ/h) and static (counterion concentration pb) properties during the aging, we find two different mechanisms of transition toward an arrested state. Our experimental findings match with the description which states, at low concentration, the formation of clusters of Laponite disks trigger the reaching of the arrested state, while at high concentration, single disks are the basic units of the arrested phase. The procedure proposed in this paper, based on multiple quantum filtered NMR data analysis, results to be a useful means to study the routes to arrested states in aqueous colloidal dispersions.

Diffusion tensor imaging to study anisotropy in a particular porous system: the trabecular bone network

During the last decade, considerable effort has been invested into the development of diffusion tensor imaging (DTI) mainly used to investigate cerebral morphology. The aim of this paper is to review and to discuss our recent results about high magnetic field DTI application to study spongy bone tissue. Due to its peculiar properties, spongy bone represents a particular porous system sample. Strategies to perform DTI on porous systems and issues linked to DTI outcome interpretation are presented on the basis of our results concerning trabecular bone network characterization.

NMR applications to low porosity carbonate stones

The purpose of this paper is to investigate NMR applications to porous materials widely employed in artistic and historical monuments and largely studied in the Cultural Heritage conservation field. Carrara marble, Candoglia marble and travertine samples were studied and data from relaxation times measurements were compared. Very interesting results from treated samples are reported and explained under the structure related spin lattice relaxation time point of view. Images of Carrara marble aged sample (XIX century), coming from the Florence Cathedral obtained for short absorption time of water by capillary rise and for relatively small thickness slices together show the fluid's spatial distribution within the stone. Comparative images showing untreated sample with the treated ones were obtained suggesting very useful applications for the determination of treatment effectiveness.

New openings for porous systems research from intermolecular double-quantum NMR

It has been recently recognized that residual intermolecular double-quantum coherences (iDQcs) provide a novel contrast mechanism to study heterogeneity in liquid systems. This is of much interest in the field of the physics of matter and biomedicine. Nowadays, literature concerning the behaviour of the iDQc signal originated by highly heterogeneous systems such as fluids in porous media is scarce. In this paper, we report and discuss our principal results about iDQc signal behaviour in confined liquid systems (trabecular bone, travertine, porous standard systems) and also some new results obtained on doped water in glass capillary pipes.

Intermolecular double quantum coherences (iDQc) and diffusion-weighted imaging (DWI) imaging of the human brain at 1.5 T

To study the sensitivity of intermolecular double quantum coherences (iDQc) imaging contrast to brain microstructure and brain anisotropy, we investigated the iDQC contrast between differently structured areas of the brain according to the strength and the direction of the applied correlation gradient. Thus diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) maps have been obtained. This procedure, which consists of analyzing both iDQc and DWI images at different gradient strength and gradient direction, could be a promising tool for clinical brain investigations performed with higher than 1.5 T magnetic fields.

Intermolecular double-quantum NMR techniques to probe microstructures on porous media

In heterogeneous systems the amplitude of the intermolecular double-quantum (DQ) signal depends on sample heterogeneity over a correlation distance dc=pi/(gammaGct). In this paper two different CRAZED-type sequences were applied in a porous medium phantom. One of these sequences gives rise to a DQ-T2 weighted signal, while the other one gives rise to a DQ-T2* weighted signal. Experimental results indicate that tuning of the correlation distance dc in a porous medium can alter the DQ signal in a manner which depends on the microstructure. This is evident only using the CRAZED-type sequence which gives rise to a DQ-T2* weighted signal.

NMR study on the early stages of hydration of a porous carbonate stone

Nuclear Magnetic Resonance was employed to obtain information on the pore filling during the absorption process. A porous carbonate stone, largely employed for buildings and mainly outdoor decorations was studied during water absorption by capillary rise, and filled pores radii were evaluated by comparison between experimental and theoretical parametric magnetization decay curves. Non mono-exponential T2 allowed spin populations to be split among the associated different relaxation times.

In vivo multiple spin echoes imaging of trabecular bone on a clinical 1.5 T MR scanner

In vivo multiple spin echoes (MSE) images of bone marrow in trabecular bone were obtained for the first time on a clinical 1.5 T scanner. Despite of a reduced sensitivity of the MSE trabecular bone images with respect to the cerebral matter ones, it is possible to observe some features in the MSE trabecular bone images that may be useful in the diagnosis of osteopenic states. Two different CRAZED-type MSE imaging sequences based on spin-echo and EPI imaging modalities were applied in phantom and in vivo. Preliminary experimental results indicate that EPI imaging readout seems to conceal the MSE contrast correlated with pore dimension in porous media. However it is still possible to detect anisotropy effects related to the bone structure in MSE-EPI images. Some strategies are suggested to optimize the quality of MSE trabecular bone images.

Multiple spin echoes in heterogeneous systems: physical origins of the observed dips

Dipolar interactions in liquids have recently offered a new challenge to investigate porous media by exploiting intermolecular quantum coherences, which are obtained through a simple two-pulse sequence (90 degrees -tau-120 degrees ). This sequence, in the presence of an external gradient (G), refocuses a train of echoes at multiple integer values of time tau. The first and second echo amplitudes are acquired for heterogeneous systems such as porous media at different time values (tau). In our first experiments on bovine bone samples we have observed unpredicted dips on the second echo time behavior. We argue that a strict relation occurs between the average pore dimensions and the dips time position through the correlation distance d=pi/(gamma G tau) (defined as half a cycle of the magnetization helix, which originates in the presence of an external gradient). Although the experimental results have revealed an exceptional connection between the porous structure and the correlation distance, no physical explanation was so far provided. In this paper we propose a possible physical cause of the observed phenomenon. In addition we report an accurate analysis of new experiments performed on glass beads phantoms, which confirms our conclusions.

Multiple spin echoes for the evaluation of trabecular bone quality

We report a simple and efficient MR method for the evaluation of trabecular bone quality. This technique is based on detection and imaging of Multiple Spin-Echoes (MSE), a manifestation of the dipolar field generated by residual intermolecular dipolar couplings in liquids. In the particular implementation we have used, originally proposed by Bowtell [J. Magn. Reson. 100 (1992) 1; J. Magn. Reson. 88 (1990) 643; Phys. Rev. Lett. 76 (1996) 4971], multiple spin echoes (MSE) are refocused in a two-pulse experiment in the presence of a correlation linear magnetic field gradient G(c). This gradient generates a magnetisation helix and results in the spatial modulation of the sample magnetisation. In heterogeneous systems, the amplitude of the MSE signal depends on sample heterogeneity over a distance d=pi/(gammaG(c)tau) which is half a cycle of the magnetisation helix, thus providing a novel contrast mechanism that can be tuned to a specific length scale. We have exploited this mechanism to study young bovine trabecular bone samples ex-vivo. We show that MSE images present a different contrast from conventional MR images, and that, by varying the experimental parameters, the image contrast can be related to specific trabecular pore sizes. The potential of this technique for the early diagnosis of osteoporotic diseases is discussed.

Characterization of trabecular bone by dipolar demagnetizing field MRI

A multiple spin-echo (MSE) sequence has been applied for the first time to study trabecular bone ex vivo. The second echo generated by the demagnetizing field presents discrete drops in signal intensity for certain values of the pitch of the magnetization helix created by the correlation gradient. These dips may reflect characteristic pore sizes in the trabecular bone specimens. This hypothesis is supported by similar experiments performed on a phantom with uniform pore size distribution. Trabecular bone images weighted in the MSE contrast mechanism are reported.

Effects of higher rank multipoles on relaxation of an I = 3 spin system

Magnetic multipoles of rank higher than one become active in spin systems with I > 1/2 and their contribution to relaxation depends on dynamics. The appearance of multipole terms complicates the relaxation description and supports the multiexponential behavior of relaxation. In this paper the effects of high-rank multipoles on lineshape and longitudinal relaxation of I = 3 spin systems are presented. Results obtained from both numerical simulation and experimental data show that longitudinal and transverse relaxation are strongly influenced by these multipole terms, especially at lower temperature where, due to lower molecular mobility, the extreme narrowing condition is not fulfilled.

Characterization of porous media structure by non linear NMR methods

In this paper we discuss the possibility of modifying the multiple spin echoes existing theory, developed for a homogeneous system, to describe also an inhomogeneous system such as a porous medium. We report here the first experimental application of MSE methods to materials like travertine. The ratio A(2)/A(1) from water in travertine presents minima for characteristic values of the delay time tau, like what was previously observed in the trabecular bone. By a judicious choice of the delay time tau and of the G gradient strength, the MSE sequence can be made sensitive to a specific length-scale of the sample heterogeneity. Furthermore the MSE image shows a particular new contrast that makes the non linear NMR method very attractive for the assessment of variations of the porous structure in porous systems.

13C imaging by double resonance scalar-coupling editing

The two-dimensional FT Imaging of 13C-glucose obtained with twin spin-echo double resonance sequence is presented. The images have been obtained by a doubly tuned surface coil on samples containing water and 13C-enriched glucose in water. It is shown, both theoretically and experimentally, that the whole editing capability of the twin spin-echo double resonance imaging sequence is also preserved in the presence of the radiofrequency field inhomogeneity produced by the surface coil. As in an efficient selective irradiation method, the enhancement in the signal-to-noise ratio with respect to the direct 13C detection, depends on the number of protons J-coupled to 13C.