The effect of rotational angle and experimental parameters on the diffraction patterns and micro-structural information obtained from q-space diffusion NMR: implication for diffusion in white matter fibers

Diffusion NMR may provide, under certain experimental conditions, micro-structural information about confined compartments totally non-invasively. The influence of the rotational angle, the pulse gradient length and the diffusion time on the diffusion diffraction patterns and q-space displacement distribution profiles was evaluated for ensembles of long cylinders having a diameter of 9 and 20 microm. It was found that the diffraction patterns are sensitive to the rotational angle (alpha) and are observed only when diffusion is measured nearly perpendicular to the long axis of the cylinders i.e., when alpha= 90 degrees +/- 5 degrees under our experimental conditions. More importantly, we also found that the structural information extracted from the displacement distribution profiles and from the diffraction patterns are very similar and in good agreement with the experimental values for cylinders of 20 microm or even 9 microm, when data is acquired with parameters that satisfy the short gradient pulse (SGP) approximation (i.e., delta -->0) and the long diffusion time limit. Since these experimental conditions are hardly met in in vitro diffusion MRI of excised organs, and cannot be met in clinical MRI scanners, we evaluated the effect of the pulse gradient duration and the diffusion time on the structural information extracted from q-space diffusion MR experiments. Indeed it was found that, as expected, accurate structural information, and diffraction patterns are observed when Delta is large enough so that the spins reach the cylinders' boundaries. In addition, it was found that large delta results in extraction of a compartment size, which is smaller than the real one. The relevance of these results to q-space MRI of neuronal tissues and fiber tracking is discussed.     

Definition of displacement probability and diffusion time in q-space magnetic resonance measurements that use finite-duration diffusion-encoding gradients

In q-space diffusion NMR, the probability P(r,td) of a molecule having a displacement r in a diffusion time td is obtained under the assumption that the diffusion-encoding gradient g has an infinitesimal duration. However, this assumption may not always hold, particularly in human MRI where the diffusion-encoding gradient duration delta is typically of the same order of magnitude as the time offset Delta between encoding gradients. In this case, finite-delta effects complicate the interpretation of displacement probabilities measured in q-space MRI, and the form by which the signal intensity relates to them. By considering the displacement-specific dephasing, , of a set of spins accumulating a constant displacement vector r in the total time Delta+delta during which diffusion is encoded, the probability recovered by a finite-delta q-space experiment can be interpreted. It is shown theoretically that a data analysis using a modified q-space index q=gammadeltaetag, with gamma the gyromagnetic ratio and eta=square root (Delta-delta/3)/(Delta+delta), recovers the correct displacement probability distribution if diffusion is multi-Gaussian free diffusion. With this analysis, we show that the displacement distribution P(r,texp) is measured at the experimental diffusion-encoding time texp=Delta+delta, and not at the reduced diffusion time tr=Delta-delta/3 as is generally assumed in the NMR and MRI literature. It is also shown that, by defining a probability P(y,Delta) that a time tdeltac then eta is not equal to square root (Delta-delta/3)/(Delta+delta) which implies that we can no longer obtain the correct displacement probability from the displacement distribution. In the case that /g/=18 mT/m and Delta-delta=5 ms, the parameter deltac in ms is given by "deltac=0.49a2+0.24" where a is the sphere's radius expressed in microm. Simulation of q-space restricted diffusion MRI experiments indicate that if eta=square root (Delta-delta/3)/(Delta+delta), the recovered displacement probability is always better than the Gaussian approximation, and the measured diffusion coefficient matches the diffusion coefficient at time texp=Delta+delta better than it matches the diffusion coefficient at time tr=Delta-delta/3. These results indicate that q-space MRI measurements of displacement probability distributions are theoretically possible in biological tissues using finite-duration diffusion-encoding gradients provided certain compartment size and diffusion encoding gradient duration constraints are met.     

Probing restrictive diffusion dynamics at short time scales

Diffusion imaging gradients serve to spectrally filter the temporally evolving diffusion tensor. In this framework, the design of diffusion sensitizing gradients is reduced to the problem of adequately sampling q-space in the spectral domain. The practical limitations imposed by the requirement for delta-function type diffusion-sensitizing gradients to adequately sample q-space, can be relaxed if these impulse gradients are replaced with chirped oscillatory gradients. It is well known that in many systems of interest, dispersion of velocity will itself produce a peak in the velocity correlation function near w=0, while restricted diffusion will manifest itself in the dispersion spectrum at higher frequencies. In this paper, chirped diffusion-sensitizing gradients are proposed and analytically shown to yield an efficient sampling of q-space in a manner that asymptotically approaches that using delta-function diffusion-sensitizing gradient. The challenge is the consequent reduction in diffusion sensitivity as one probes higher frequency dynamics. This problem is addressed by restricting the gradient power to a spectral bandwidth corresponding to the diffusion spectral range of the underlying restrictive geometry. Simultaneous imaging of diffusion and flow at microscopic resolution and at temporally resolvable diffusion time scales thus becomes possible in vivo. Simulations and experiments validate the proposed approach.     

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.     

NMR 中非线性梯度场下扩散行为的理论描述和蒙特卡罗模拟

利用传播子方法研究了在一般非线性场梯度下NMR信号的扩散衰减. 在自由扩散和平板间的限制扩散情况下获得了扩散衰减因子的理论表达式. 该表达式适用范围宽，且具有较简单的数学形式和明确的物理意义. 文中还将理论预测与蒙特卡罗模拟结果进行了比较. 结果表明：文中所采用的理论方法适合于表述自由扩散和短脉冲近似下的受限扩散；蒙特卡罗模拟提供了一种定性研究MRI和NMR中非均匀场梯度扩散衰减的方法.     

q-Space high b value diffusion MRI of hemi-crush in rat spinal cord: evidence for spontaneous regeneration

The development of the damage following hemi-crush trauma in rat spinal cord was studied ex vivo using high b value (bmax = 1 x 10(7) s cm(-2)) q-space diffusion weighted MRI (DWI) at five days, ten days and six weeks post-trauma. Rat spinal cord trauma, produced by hemi-crush of 15s and 60s duration, was studied. The water signal decay in these diffusion experiments was found to be non mono-exponential and was analyzed using the q-space approach. The q-space MRI parameters were compared with T1 and T2 MR images, behavioral tests and histopathological osmium staining. A very good anatomical correlation was found between the q-space MRI parameters and the osmium staining. Interestingly, we found that in the 15s hemi-crush model significant recovery was observed in both the q-space MR images and the osmium staining six weeks post-trauma. However, in the 60s hemi-crush trauma model very little recovery was observed. These results paralleled those obtained from behavioral tests demonstrating that partial spontaneous recovery seems to occur in the 15s hemi-crush spinal cord model, which should be taken in consideration when using it to evaluate new therapies.     

NMR diffusometry and the short gradient pulse limit approximation

In NMR diffusometry, one often uses the short gradient pulse (SGP) limit approximation in the interpretation of data from systems with restricted diffusion. The SGP limit approximation means that the gradient pulse length, delta, is so short that the spins do not diffuse during the pulse duration, but this condition is rarely met. If the length scale of the pores corresponds to the molecular mean square displacement during the gradient pulse, the measured echo intensities become a function of the gradient pulse length. Here, we have studied highly concentrated emulsions to show how the length of the gradient pulse influences NMR diffusion experiments. We have focused on molecules confined to one pore and molecules that can migrate through the porous system. For the former the echo decays give smaller pores than the actual case and for the latter we show large changes in echo decay depending on the gradient pulse length, everything else being equal.     

High b-value q-space diffusion MRI in myelin-deficient rat spinal cords

In this study, we explore the effect of the lack of myelin on the diffusion characteristics and diffusion anisotropy obtained from high b-value q-space diffusion-weighted MRI (q-space DWI) in excised rat spinal cords. Twenty-one-day-old myelin-deficient (md) mutant (N=6) and control rats (N=6) were used in this study. The MRI protocol included multi-slice T(1), T(2), proton density (PD) MR images and high b-value q-space diffusion MRI measured perpendicular and parallel to the fibers of the spine. q-Space displacement and probability maps, in both directions, as well as displacement anisotropy maps, were computed from the diffusion data. At the end of the MRI protocol, representative spinal cords from both groups were subjected to electron microscopy (EM). The md spinal cords show different gray/white matter contrast in the T(1), T(2) and PD MR images as compared with controls. In addition, the mean displacement extracted from the high b-value q-space diffusion data was found to be dramatically higher in the white matter (WM) of the md spinal cords than the controls when diffusion was measured perpendicular and parallel to the fibers of the spine. However, interestingly, at the diffusion time used in the present study, the difference in the WM displacement anisotropies of the two groups was not found to be statistically significant. Myelin was found to have a pronounced effect on the diffusion characteristics of water in WM but less so on the diffusion anisotropy observed at the diffusion time used in the present study.     

Extension of the double-wave-vector diffusion-weighting experiment to multiple concatenations

Experiments involving two diffusion-weightings in a single acquisition, so-called double- or two-wave-vector experiments, have recently been applied to measure the microscopic anisotropy in macroscopically isotropic samples or to estimate pore or compartment sizes. These informations are derived from the signal modulation observed when varying the wave vectors’ orientations. However, the modulation amplitude can be small and, for short mixing times between the two diffusion-weightings, decays with increased gradient pulse lengths which hampers its detectability on whole-body MR systems. Here, an approach is investigated that involves multiple concatenations of the two diffusion-weightings in a single experiment. The theoretical framework for double-wave-vector experiments of fully restricted diffusion is adapted and the corresponding tensor approach recently presented for short mixing times extended and compared to numerical simulations. It is shown that for short mixing times (i) the extended tensor approach well describes the signal behavior observed for multiple concatenations and (ii) the relative amplitude of the signal modulation increases with the number of concatenations. Thus, the presented extension of the double-wave-vector experiment may help to improve the detectability of the signal modulations observed for short mixing times, in particular on whole-body MR systems with their limited gradient amplitudes.     

Observation of restricted diffusion in the presence of a free diffusion compartment: Single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion–diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.     

Cross-term-compensated pulsed-gradient stimulated echo MR with asymmetric gradient pulse lengths

The magic asymmetric gradient stimulated echo (MAGSTE) sequence developed to compensate background-gradient cross-terms in the preparation and readout interval independently, assumes identical lengths for the two gradient pulses applied in each interval. However, this approach is rather inefficient if some extra delay time is present in one half of an interval, e.g. as required for special RF excitations or spatial encoding prior to the stimulated echo in MR imaging. Therefore, a generalized version of the sequence is presented that considers different gradient pulse lengths within an interval. It is shown theoretically that (i) for any pulse lengths a "magic" amplitude ratio exists which ensures the desired cross-term compensation in each interval and that (ii) prolonging one of the gradients can deliver a considerably higher diffusion weighting efficiency. These results are confirmed in MR imaging experiments on phantoms and in vivo in the human brain at 3T using an echo-planar trajectory. In the examples shown, typically 10 times higher b values can be achieved or an echo time reduction with a 40% signal gain in brain white matter. Thus, in case of asymmetric timing requirements, the generalized MAGSTE sequence with different gradient pulse lengths may help to overcome signal-to-noise limitations in diffusion weighted MR.     

Quantitative measurement and imaging of transport processes in plants and porous media by 1H NMR.

NMR and MRI have been applied to transport processes, that is, net flow and diffusion/perfusion, of water in whole plants, cells, and porous materials. By choosing proper time windows and pulse sequences, magnetic resonance imaging can be made selective for each of the two transport processes. For porous media and plant cells the evolution of the spatial distribution of excited spins has been determined by q-space imaging, using a 20 MHz pulsed 1H NMR imager. The results of these experiments are explained by including spin-relaxation and exchange at boundaries. A 10 MHz portable 1H NMR spectrometer is described, particularly suitable to study the response of net flow in plants and canopies to changing external conditions.     

White matter changes in multiple sclerosis: correlation of q-space diffusion MRI and 1H MRS

OBJECTIVE: To explore the diagnostic usefulness of high b-value diffusion magnetic resonance brain imaging ("q-space" imaging) in multiple sclerosis (MS). More specifically, we aimed at evaluating the ability of this methodology to identify tissue damage in the so-called normal-appearing white matter (NAWM). DESIGN: In this study we examined the correlation between q-space diffusion imaging and magnetic resonance spectroscopy (MRS)-based two-dimensional 1H chemical shift imaging. Eight MS patients with different degree of disease severity and seven healthy subjects were scanned in a 1.5-T magnetic resonance imaging (MRI) scanner. The MRI protocol included diffusion tensor imaging (DTI) (with bmax of 1000 s/mm2), high b-value diffusion-weighted imaging (with bmax of 14,000 s/mm2) and 2D chemical shift imaging. The high b-value data set was analyzed using the q-space methodology to produce apparent displacement and probability maps. RESULTS: We found that the q-space diffusion displacement and probability image intensities correlated well with N-acetylaspartate levels (r=.61 and .54, respectively). Furthermore, NAWM that was abnormal on MRS was also found to be abnormal using q-space diffusion imaging. In these areas, the q-space displacement values increased from 3.8+/-0.2 to 4.6+/-0.6 microm (P<.02), the q-space probability values decreased from 7.4+/-0.3 to 6.8+/-0.3 (P<.002), while DTI revealed only a small, but still significant, reduction in fractional anisotropy values from 0.40+/-0.02 to 0.37+/-0.02 (P<.05). CONCLUSION: High b-value diffusion imaging can detect tissue damage in the NAWM of MS patients. Despite the theoretical limitation of this method, in practice it provides additional information which is clinically relevant for detection of tissue damage not seen in conventional imaging techniques.     

Dynamic NMR q-space studies of microstructure with the multigrade CPMG sequence

A new approach to q-space studies of microstructure is proposed, which exploits the combined information contained in the water proton transverse relaxation time distribution and the frequency dependence of the apparent water diffusivity in heterogeneous systems. Using an automated two-dimensional multigrade CPMG sequence, both the pulse spacing and the amplitude of the applied field gradient are varied systematically and used to measure the frequency and wave vector dependence of the multiple exponential echo decay constants and amplitudes. Undesirable crossterms in the applied and background field gradients are eliminated by a simple procedure involving a sign reversal in the applied gradient. Nonlinear, local susceptibility-induced field gradients are shown to lead to enhanced, frequency-dependent apparent water diffusivities that are sensitive to the local microstructure.     

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.     

Diffusion pore imaging with generalized temporal gradient profiles

In porous material research, one main interest of nuclear magnetic resonance diffusion (NMR) experiments is the determination of the shape of pores. While it has been a longstanding question if this is in principle achievable, it has been shown recently that it is indeed possible to perform NMR-based diffusion pore imaging. In this work we present a generalization of these previous results. We show that the specific temporal gradient profiles that were used so far are not unique as more general temporal diffusion gradient profiles may be used. These temporal gradient profiles may consist of any number of “short” gradient pulses, which fulfil the short-gradient approximation. Additionally, “long” gradient pulses of small amplitude may be present, which can be used to fulfil the rephasing condition for the complete profile. Some exceptions exist. For example, classical q-space gradients consisting of two short gradient pulses of opposite sign cannot be used as the phase information is lost due to the temporal antisymmetry of this profile.     

Displacement power spectrum measurement by CPMG in constant gradient

The modulation of spin phase produced by Carr-Purcell-Meiboom-Gill (CPMG) sequence in combination with constant magnetic field gradient is appropriate to probe the displacement power spectrum (DPS). The spin-echo attenuation is directly proportional to the DPS value at the applied modulation frequency. Relaxation and selective excitation effects can be factored out while probing the DPS. The modulation frequency is adjusted by varying the pulse separation time while the gradient strength and the time of acquisition are kept constant. In designing the experiment gradient strength limitations, imposed by off-resonance effects, as well as limitations arising from using Gaussian phase approximation must be considered. An effective experimental strategy is presented, supported by experimental results for free and restricted diffusion.     

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.