Analytical solution and verification of diffusion effect in SSFP

Insights into human cerebral white matter maturation and degeneration across the adult lifespan

White matter (WM) microstructural properties change across the adult lifespan and with neuronal diseases. Understanding microstructural changes due to aging is paramount to distinguish them from neuropathological changes. Conducted on a large cohort of 147 cognitively unimpaired subjects, spanning a wide age range of 21 to 94 years, our study evaluated sex- and age-related differences in WM microstructure. Specifically, we used diffusion tensor imaging (DTI) magnetic resonance imaging (MRI) indices, sensitive measures of myelin and axonal density in WM, and myelin water fraction (MWF), a measure of the fraction of the signal of water trapped within the myelin sheets, to probe these differences. Furthermore, we examined regional correlations between MWF and DTI indices to evaluate whether the DTI metrics provide information complementary to MWF. While sexual dimorphism was, overall, nonsignificant, we observed region-dependent differences in MWF, that is, myelin content, and axonal density with age and found that both exhibit nonlinear, but distinct, associations with age. Furthermore, DTI indices were moderately correlated with MWF, indicating their good sensitivity to myelin content as well as to other constituents of WM tissue such as axonal density. The microstructural differences captured by our MRI metrics, along with their weak to moderate associations with MWF, strongly indicate the potential value of combining these outcome measures in a multiparametric approach. Furthermore, our results support the last-in-first-out and the gain-predicts-loss hypotheses of WM maturation and degeneration. Indeed, our results indicate that the posterior WM regions are spared from neurodegeneration as compared to anterior regions, while WM myelination follows a temporally symmetric time course across the adult life span.

Explicit phenomenological solutions for magnetization exposed to an arbitrary NMR diffusion steady state pulse sequence

Explicit phenomenological solutions to recurrence relations for the bulk transverse and longitudinal magnetization found using the Torrey-Bloch equations with relaxation effects are used to investigate nuclear magnetic resonance (NMR) diffusion measurements. Of particular interest are steady state NMR (self-)diffusion measurements that reduce experimental time that can extend the techniques to quickly reacting systems. The solutions for bulk transverse and longitudinal magnetization presented here are used to investigate the average behavior of the transverse and longitudinal magnetization in forming a steady state and are used to derive new expressions for the steady state longitudinal magnetization. These solutions can be applied to a noninteracting spin 1/2 ensemble undergoing free diffusion exposed to an arbitrary NMR pulse sequence containing arbitrary magnetic field gradient waveforms. The closed algebraic form method presented here has an advantage over iterative procedures for calculating transverse and longitudinal magnetization for the analysis and development of steady state pulse sequences. Previous theoretical results for steady state diffusion measurements are also reproduced. The Mathematica code for these solutions is provided in the supplementary material.

Investigation of the association between cerebral iron content and myelin content in normative aging using quantitative magnetic resonance neuroimaging

Myelin loss and iron accumulation are cardinal features of aging and various neurodegenerative diseases. Oligodendrocytes incorporate iron as a metabolic substrate for myelin synthesis and maintenance. An emerging hypothesis in Alzheimer’s disease research suggests that myelin breakdown releases substantial stores of iron that may accumulate, leading to further myelin breakdown and neurodegeneration. We assessed associations between iron content and myelin content in critical brain regions using quantitative magnetic resonance imaging (MRI) on a cohort of cognitively unimpaired adults ranging in age from 21 to 94 years. We measured whole-brain myelin water fraction (MWF), a surrogate of myelin content, using multicomponent relaxometry, and whole-brain iron content using susceptibility weighted imaging in all individuals. MWF was negatively associated with iron content in most brain regions evaluated indicating that lower myelin content corresponds to higher iron content. Moreover, iron content was significantly higher with advanced age in most structures, with men exhibiting a trend towards higher iron content as compared to women. Finally, relationship between MWF and age, in all brain regions investigated, suggests that brain myelination continues until middle age, followed by degeneration at older ages. This work establishes a foundation for further investigations of the etiology and sequelae of myelin breakdown and iron accumulation in neurodegeneration and may lead to new imaging markers for disease progression and treatment.

Modeling an equivalent b-value in diffusion-weighted steady-state free precession

PURPOSE

Diffusion-weighted steady-state free precession (DW-SSFP) is shown to provide a means to probe non-Gaussian diffusion through manipulation of the flip angle. A framework is presented to define an effective b-value in DW-SSFP.

THEORY

The DW-SSFP signal is a summation of coherence pathways with different b-values. The relative contribution of each pathway is dictated by the flip angle. This leads to an apparent diffusion coefficient (ADC) estimate that depends on the flip angle in non-Gaussian diffusion regimes. By acquiring DW-SSFP data at multiple flip angles and modeling the variation in ADC for a given form of non-Gaussianity, the ADC can be estimated at a well-defined effective b-value.

METHODS

A gamma distribution is used to model non-Gaussian diffusion, embedded in the Buxton signal model for DW-SSFP. Monte-Carlo simulations of non-Gaussian diffusion in DW-SSFP and diffusion-weighted spin-echo sequences are used to verify the proposed framework. Dependence of ADC on flip angle in DW-SSFP is verified with experimental measurements in a whole, human postmortem brain.

RESULTS

Monte-Carlo simulations reveal excellent agreement between ADCs estimated with diffusion-weighted spin-echo and the proposed framework. Experimental ADC estimates vary as a function of flip angle over the corpus callosum of the postmortem brain, estimating the mean and standard deviation of the gamma distribution as 1.50 · 10 - 4  mm2 /s and 2.10 · 10 - 4  mm2 /s.

CONCLUSION

DW-SSFP can be used to investigate non-Gaussian diffusion by varying the flip angle. By fitting a model of non-Gaussian diffusion, the ADC in DW-SSFP can be estimated at an effective b-value, comparable to more conventional diffusion sequences.

Dictionary-Free MRI PERK: Parameter Estimation via Regression with Kernels

This paper introduces a fast, general method for dictionary-free parameter estimation in quantitative magnetic resonance imaging (QMRI) parameter estimation via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PERK then takes these parameter-measurement pairs as labeled training points and learns from them a nonlinear regression function using kernel functions and convex optimization. PERK admits a simple implementation as per-voxel nonlinear lifting of MRI measurements followed by linear minimum mean-squared error regression. We demonstrate PERK for $ {\textit {T}_{1}}, {\textit {T}_{2}}$ estimation, a well-studied application where it is simple to compare PERK estimates against dictionary-based grid search estimates and iterative optimization estimates. Numerical simulations as well as single-slice phantom and in vivo experiments demonstrate that PERK and other tested methods produce comparable $ {\textit {T}_{1}}, {\textit {T}_{2}}$ estimates in white and gray matter, but PERK is consistently at least $140\times $ faster. This acceleration factor may increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel.

Clinical high-resolution mapping of the proteoglycan-bound water fraction in articular cartilage of the human knee joint

PURPOSE

We applied our recently introduced Bayesian analytic method to achieve clinically-feasible in-vivo mapping of the proteoglycan water fraction (PgWF) of human knee cartilage with improved spatial resolution and stability as compared to existing methods.

MATERIALS AND METHODS

Multicomponent driven equilibrium single-pulse observation of T₁ and T₂ (mcDESPOT) datasets were acquired from the knees of two healthy young subjects and one older subject with previous knee injury. Each dataset was processed using Bayesian Monte Carlo (BMC) analysis incorporating a two-component tissue model. We assessed the performance and reproducibility of BMC and of the conventional analysis of stochastic region contraction (SRC) in the estimation of PgWF. Stability of the BMC analysis of PgWF was tested by comparing independent high-resolution (HR) datasets from each of the two young subjects.

RESULTS

Unlike SRC, the BMC-derived maps from the two HR datasets were essentially identical. Furthermore, SRC maps showed substantial random variation in estimated PgWF, and mean values that differed from those obtained using BMC. In addition, PgWF maps derived from conventional low-resolution (LR) datasets exhibited partial volume and magnetic susceptibility effects. These artifacts were absent in HR PgWF images. Finally, our analysis showed regional variation in PgWF estimates, and substantially higher values in the younger subjects as compared to the older subject.

CONCLUSIONS

BMC-mcDESPOT permits HR in-vivo mapping of PgWF in human knee cartilage in a clinically-feasible acquisition time. HR mapping reduces the impact of partial volume and magnetic susceptibility artifacts compared to LR mapping. Finally, BMC-mcDESPOT demonstrated excellent reproducibility in the determination of PgWF.

Optimizing MR Scan Design for Model-Based ${T}_{1}$ , ${T}_{2}$ Estimation From Steady-State Sequences

Rapid, reliable quantification of MR relaxation parameters T1 and T2 is desirable for many clinical applications. Steady-state sequences such as Spoiled Gradient-Recalled Echo (SPGR) and Dual-Echo Steady-State (DESS) are fast and well-suited for relaxometry because the signals they produce are quite sensitive to T1 and T2 variation. However, T1, T2 estimation with these sequences typically requires multiple scans with varied sets of acquisition parameters. This paper describes a systematic framework for selecting scan types (e.g., combinations of SPGR and DESS scans) and optimizing their respective parameters (e.g., flip angles and repetition times). The method is based on a Cramér-Rao Bound (CRB)-inspired min-max optimization that finds scan parameter combinations that robustly enable precise object parameter estimation. We apply this technique to optimize combinations of SPGR and DESS scans for T1, T2 relaxometry in white matter (WM) and grey matter (GM) regions of the human brain at 3T field strength. Phantom accuracy experiments show that SPGR/DESS scan combinations are in excellent agreement with reference measurements. Phantom precision experiments show that trends in T1,T2 pooled sample standard deviations reflect CRB-based predictions. In vivo experiments show that in WM and GM, T1 and T2 estimates from a pair of optimized DESS scans exhibit precision (but not necessarily accuracy) comparable to that of optimized combinations of SPGR and DESS scans. To our knowledge, T1 maps from DESS acquisitions alone are new. This example application illustrates that scan optimization may help reveal new parameter mapping techniques from combinations of established pulse sequences.

Rapid simultaneous high-resolution mapping of myelin water fraction and relaxation times in human brain using BMC-mcDESPOT

A number of central nervous system (CNS) diseases exhibit changes in myelin content and magnetic resonance longitudinal, T₁, and transverse, T₂, relaxation times, which therefore represent important biomarkers of CNS pathology. Among the methods applied for measurement of myelin water fraction (MWF) and relaxation times, the multicomponent driven equilibrium single pulse observation of T₁ and T₂ (mcDESPOT) approach is of particular interest. mcDESPOT permits whole brain mapping of multicomponent T₁ and T₂, with data acquisition accomplished within a clinically realistic acquisition time. Unfortunately, previous studies have indicated the limited performance of mcDESPOT in the setting of the modest signal-to-noise range of high-resolution mapping, required for the depiction of small structures and to reduce partial volume effects. Recently, we showed that a new Bayesian Monte Carlo (BMC) analysis substantially improved determination of MWF from mcDESPOT imaging data. However, our previous study was limited in that it did not discuss determination of relaxation times. Here, we extend the BMC analysis to the simultaneous determination of whole-brain MWF and relaxation times using the two-component mcDESPOT signal model. Simulation analyses and in-vivo human brain studies indicate the overall greater performance of this approach compared to the stochastic region contraction (SRC) algorithm, conventionally used to derive parameter estimates from mcDESPOT data. SRC estimates of the transverse relaxation time of the long T₂ fraction, T_2,l, and the longitudinal relaxation time of the short T₁ fraction, T_1,s, clustered towards the lower and upper parameter search space limits, respectively, indicating failure of the fitting procedure. We demonstrate that this effect is absent in the BMC analysis. Our results also showed improved parameter estimation for BMC as compared to SRC for high-resolution mapping. Overall we find that the combination of BMC analysis and mcDESPOT, BMC-mcDESPOT, shows excellent performance for accurate high-resolution whole-brain mapping of MWF and bi-component transverse and longitudinal relaxation times within a clinically realistic acquisition time.

Analysis of mcDESPOT- and CPMG-derived parameter estimates for two-component nonexchanging systems

PURPOSE

To compare the reliability and stability of the multicomponent-driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) and Carl-Purcell-Meiboom-Gill (CPMG) approaches to parameter estimation.

METHODS

The stability and reliability of mcDESPOT and CPMG-derived parameter estimates were compared through examination of energy surfaces, evaluation of model sloppiness, and Monte Carlo simulations. Comparisons were performed on an equal time basis and assuming a two-component system. Parameter estimation bias, reflecting accuracy, and dispersion, reflecting precision, were derived for a range of signal-to-noise ratios (SNRs) and relaxation parameters.

RESULTS

The energy surfaces for parameters incorporated into the mcDESPOT signal model exhibit flatness, a complex structure of local minima, and instability to noise to a much greater extent than the corresponding surfaces for CPMG. Although both mcDESPOT and CPMG performed well at high SNR, the CPMG approach yielded parameter estimates of considerably greater accuracy and precision at lower SNR.

CONCLUSION

mcDESPOT and CPMG both permit high-quality parameter estimates under SNR that are clinically achievable under many circumstances, depending upon available hardware and resolution and acquisition time constraints. At moderate to high SNR, the mcDESPOT approach incorporating two-step phase increments can yield accurate parameter estimates while providing values for longitudinal relaxation times that are not available through CPMG. However, at low SNR, the CPMG approach is more stable and provides superior parameter estimates. Magn Reson Med 75:2406-2420, 2016. © 2015 Wiley Periodicals, Inc.

High resolution diffusion-weighted imaging in fixed human brain using diffusion-weighted steady state free precession

High resolution diffusion tensor imaging and tractography of ex vivo brain specimens has the potential to reveal detailed fibre architecture not visible on in vivo images. Previous ex vivo diffusion imaging experiments have focused on animal brains or small sections of human tissue since the unfavourable properties of fixed tissue (including short T(2) and low diffusion rates) demand the use of very powerful gradient coils that are too small to accommodate a whole, human brain. This study proposes the use of diffusion-weighted steady-state free precession (DW-SSFP) as a method of extending the benefits of ex vivo DTI and tractography to whole, human, fixed brains on a clinical 3 T scanner. DW-SSFP is a highly efficient pulse sequence; however, its complicated signal dependence precludes the use of standard diffusion tensor analysis and tractography. In this study, a method is presented for modelling anisotropy in the context of DW-SSFP. Markov Chain Monte Carlo sampling is used to estimate the posterior distributions of model parameters and it is shown that it is possible to estimate a tight distribution on the principal axis of diffusion at each voxel using DW-SSFP. Voxel-wise estimates are used to perform tractography in a whole, fixed human brain. A direct comparison between 3D diffusion-weighted spin echo EPI and 3D DW-SSFP-EPI reveals that the orientation of the principal diffusion axis can be inferred on with a higher degree of certainty using a 3D DW-SSFP-EPI even with a 68% shorter acquisition time.

Sensitivity of diffusion weighted steady state free precession to anisotropic diffusion

Diffusion-weighted steady-state free precession (DW-SSFP) accumulates signal from multiple echoes over several TRs yielding a strong sensitivity to diffusion with short gradient durations and imaging times. Although the DW-SSFP signal is well characterized for isotropic, Gaussian diffusion, it is unclear how the DW-SSFP signal propagates in inhomogeneous media such as brain tissue. This article presents a more general analytical expression for the DW-SSFP signal which accommodates Gaussian and non-Gaussian spin displacement probability density functions. This new framework for calculating the DW-SSFP signal is used to investigate signal behavior for a single fiber, crossing fibers, and reflective barriers. DW-SSFP measurements in the corpus callosum of a fixed brain are shown to be in good agreement with theoretical predictions. Further measurements in fixed brain tissue also demonstrate that 3D DW-SSFP out-performs 3D diffusion weighted spin echo in both SNR and CNR efficiency providing a compelling example of its potential to be used for high resolution diffusion tensor imaging.

Systematic investigation of balanced steady-state free precession for functional MRI in the human visual cortex at 3 Tesla

Previous studies have applied balanced steady-state free precession (bSSFP) to functional brain imaging. Methods that exploit the strong frequency dependence of the MR signal in the bSSFP transition band are strongly affected by field inhomogeneity and frequency drifts. Recent bSSFP studies using "on-resonance" (in the bSSFP passband) acquisition claimed that higher sensitivity was achieved compared to traditional fMRI methods. However, the contrast mechanism that generates activation-related signal changes in bSSFP imaging is not yet fully understood. We performed a systematic study of on-resonance bSSFP signal behavior using a multiecho balanced SSFP sequence with different TRs at 3 Tesla. We conclude that intravoxel dephasing, or the off-resonance averaged steady state, dominates the bSSFP signal decay and determines the bSSFP fMRI contrast. Experimental findings were confirmed by simulations based on existing theories for signal formation around blood vessels in inhomogeneous tissues. The activation-induced signal change in on-resonance bSSFP increases with TE, and the TE dependence of the contrast-to-noise ratio (CNR) in bSSFP is similar to that in gradient echo-planar imaging (GE-EPI). However, GE-EPI has a significantly higher CNR efficiency.

Steady-state free precession with hyperpolarized 3He: experiments and theory

The magnetization response of hyperpolarized 3He gas to a steady-state free precession (SSFP) sequence was simulated using matrix product operators. The simulations included the effects of flip angle (alpha), sequence timings, resonant frequency, gas diffusion coefficient, imaging gradients, T1 and T2. Experiments performed at 1.5 T, on gas phantoms and with healthy human subjects, confirm the predicted theory, and indicate increased SNR with SSFP through use of higher flip angles when compared to optimized spoiled gradient echo (SPGR). Simulations and experiments show some compromise to the SNR and some point spread function broadening at high alpha due to the incomplete refocusing of transverse magnetization, caused by diffusion dephasing from the readout gradient. Mixing of gas polarization levels by diffusion between slices is also identified as a source of signal loss in SSFP at higher alpha through incomplete refocusing. Nevertheless, in the sample experiments, a SSFP sequence with an optimized flip angle of alpha=20 degrees, and 128 sequential phase encoding views, showed a higher SNR when compared to SPGR (alpha=7.2 degrees) with the same bandwidth. Some of the gas sample experiments demonstrated a transient signal response that deviates from theory in the initial phase. This was identified as being caused by radiation damping interactions between the large initial transverse magnetization and the high quality factor (Q=250) birdcage resonator. In 3He NMR experiments, performed without imaging gradients, diffusion dephasing can be mitigated, and the effective T2 is relatively long (1 s). Under these circumstances the SSFP sequence behaves like a CPMG sequence with sinalpha/2 weighting of SNR. Experiments and simulations were also performed to characterize the off-resonance behaviour of the SSFP HP 3He signal. Characteristic banding artifacts due to off-resonance harmonic beating were observed in some of the in vivo SSFP images, for instance in axial slices close to the diaphragm where B0 inhomogeneity is highest. Despite these artifacts, a higher SNR was observed with SSFP in vivo when compared to the SPGR sequence. The trends predicted by theory of increasing SSFP SNR with increasing flip angle were observed in the range alpha=10-20 degrees without compromise to image quality through blurring caused by excessive k-space filtering.

Thermal diffusivity and nuclear spin relaxation: a continuous wave free precession NMR study

Continuous wave free precession (CWFP) nuclear magnetic resonance is capable of yielding quantitative and easily obtainable information concerning the kinetics of processes that change the relaxation rates of the nuclear spins through the action of some external agent. In the present application, heat flow from a natural rubber sample to a liquid nitrogen thermal bath caused a large temperature gradient leading to a non-equilibrium temperature distribution. The ensuing local changes in the relaxation rates could be monitored by the decay of the CWFP signals and, from the decays, it was possible to ascertain the prevalence of a diffusive process and to obtain an average value for the thermal diffusivity.

Fast and simultaneous measurement of longitudinal and transverse NMR relaxation times in a single continuous wave free precession experiment

The purpose of this communication is to describe a method for rapid and simultaneous determination of longitudinal (T1) and transversel (T2) relaxation times, based on a single continuous wave free precession (CWFP) experiment which employs RF pulses with a pi/2 flip angle. We analyze several examples, involving nuclei such as 1H, 31P, and 19F, where good agreement with T1 and T2 measurements obtained by traditional methods is apparent. We also compare with the more time-consuming steady-state free precession (SSFP) method of Kronenbitter and Schwenk where several experiments are needed to determine the optimum flip angle. The role of an inhomogeneous magnetic field on the observed decays and its effect upon the accuracy of relaxation times obtained by these methods is examined by comparing numerical simulations with experimental data. Possible sources of error and conditions to minimize its effects are described.

Quantitative diffusion imaging with steady-state free precession

The addition of a single, unbalanced diffusion gradient to the steady-state free precession (SSFP) imaging sequence sensitizes the resulting signal to free diffusion. Unfortunately, the confounding influence of both longitudinal (T1) and transverse (T2) relaxation on the diffusion-weighted SSFP (dwSSFP) signal has made it difficult to quantitatively determine the apparent diffusion coefficient (ADC). Here, a multistep method in which the T1, T2, and spin density (Mo) constants are first determined using a rapid mapping technique described previously is presented. Quantitative ADC can then be determined through a novel inversion of the appropriate signal model. The accuracy and precision of our proposed method (which we term DESPOD) was determined by comparing resulting ADC values from phantoms to those calculated from traditional diffusion-weighted echo planar imaging (dwEPI) images. Error within the DESPOD-derived ADC maps was found to be less than 3%, with good precision over a biologically relevant range of ADC values.

An image-based finite difference model for simulating restricted diffusion

Water diffusion in tissues is generally restricted and often anisotropic. Neural tissue is of particular interest, since it is well known that injury alters diffusion in a characteristic manner. Both Monte Carlo simulations and approximate analytical models have previously been reported in attempts to predict water diffusion behavior in the central nervous system. These methods have relied on axonal models, which assume simple geometries (e.g., ellipsoids, cylinders, and square prisms) and ignore the thickness of the myelin sheath. The current work describes a method for generating models using synthetic images. The computations are based on a 3D finite difference (FD) approximation of the diffusion equation. The method was validated with known analytic solutions for diffusion in a cylindrical pore and in a hexagonal array of cylinders. Therefore, it is envisioned that, by exploiting histologic images of neuronal tissues as input model, current method allows investigating the water diffusion behavior inside biological tissues and potentially assessing the status of neural injury and regeneration.

Diffusion MRI: precision, accuracy and flow effects

After a decade of evolution and application of diffusion imaging, a large body of literature has been accumulated. It is in this context that the accuracy and precision of diffusion-weighted and quantitative diffusion MRI are reviewed. The emphasis of the review is on practical methods for clinical human imaging, particularly in the brain. The requirements for accuracy and precision are reviewed for various clinical and basic science applications. The methods of measuring and calculating diffusion effects with MRI are reviewed. The pulse gradient spin echo (PGSE) methods are emphasized as these methods are used most commonly in the clinical setting. Processing of PGSE data is reviewed. Various PGSE encoding schemes are also reviewed in terms of the accuracy and precision of isotropic and anisotropic diffusion measurements. The broad range of factors impacting the accuracy of the PGSE methods and other encoding schemes is then considered. Firstly, system inaccuracies such as background imaging gradients, gradient linearity, refocusing RF pulses, eddy currents, image misregistration, noise and dynamic range are considered. A second class of inaccuracies is contributed by the bulk effects of the imaged object, and include sample background gradients, subject motion of cerebrospinal fluid and organs, and aperiodic organ motion. A final category of potential inaccuracies is classified as being contributed by microscopic, biophysical tissue properties and include partial volume effects, anisotropy, restriction, diffusion distance, compartmentation, exchange, multiexponential diffusion decay, T2 weighting and microvascular perfusion. Finally, the application of diffusion methods to studies of blood flow in the microvasculature (i.e. the arterioles, capillaries and venules) are reviewed in detail, particularly in terms of feasibility and the stringent accuracy and precision requirements. Recent provocative studies examining the use of PGSE approaches to suppress microvascular signals in brain functional MRI (fMRI) are also reviewed.

Simultaneous calculation of flow and diffusion sensitivity in steady-state free precession imaging

In this paper the authors quantitatively evaluate the combined effect of both flow and diffusion in steady-state free precession (SSFP) imaging. A partition analysis (PA) is used to derive a fourth order approximation (in E2) of the signal in an echo SSFP sequence. The authors also introduce a novel very fast simulation technique, based on a circular convolution, which accurately accounts for both flow and diffusion. A 2D SSFP-echo sequence was implemented to obtain experimental data from a phantom containing three different solutions. Excellent agreement between the theory and the experimental data was found. Then by using the simulation algorithm and experimental measurements of in vivo brain motion, the authors estimated the artifacts to be expected in SSFP diffusion imaging of the brain and found them to be comparable with those of pulsed gradient spin echo. Finally, the authors point out the equivalence between the flow sensitivity of SSFP and RF spoiling commonly used in fast imaging.

The diffusion sensitivity of fast steady-state free precession imaging

Steady-state free precession (SSFP) imaging with an added field gradient pulse is strongly sensitive to self-diffusion and other motions of water. In an earlier theoretical analysis of diffusion attenuation due to a single gradient pulse Wu and Buxton (J. Magn. Reson. 90, 243, 1990) concluded that the diffusion sensitivity would be increased with smaller flip angles. In this paper a partial partition analysis of the different echo pathways contributing to the signal is used to illustrate the contribution of stimulated echo pathways with long diffusion times as the source of the enhanced diffusion sensitivity with low flip angles. Experimental imaging studies in phantoms and the brain of a human subject demonstrate substantially greater signal attenuation with small flip angles (< 30 degrees). The theoretical equation of Wu and Buxton provides a reasonable fit to the experimental data, accounting for the flip angle and TR dependence, but the estimated diffusion coefficients are larger than expected from previous studies. The large attenuation observed in the human studies, particularly in cerebrospinal fluid, is most likely due to other tissue motions. Both the theoretical calculations and the experimental data show that for the same gradient strength the diffusion sensitivity of SSFP is much greater than the diffusion sensitivity of conventional spin-echo methods.