Quantitative phenomenological model of the BOLD contrast mechanism

Unraveling the major role of vascular (R2') contributions to R2* signal relaxation at ultra-high-field MRI: A comprehensive analysis with quantitative gradient recalled echo in mouse brain

PURPOSE

Ultra-high-field (UHF) R2* relaxometry is often used for in vivo analysis of biological tissue microstructure without accounting for vascular contributions to R2* signal, that is, the BOLD signal component, and magnetic field inhomogeneities. These effects are especially important at UHF as their contribution to R2* scales linearly with magnetic field. Our study aims to report on the results of separate contributions of R2t* (tissue-specific sub-component) and R2' (vascular BOLD sub-component), corrected for the adverse effects of magnetic field inhomogeneities, to the total R2* signal at in vivo UHF MRI of mouse brain.

METHODS

Four healthy, 8-week-old C57BL/6J mice were imaged in vivo with multi-gradient echo MRI at 9.4 T and analyzed using the quantitative gradient recalled echo (qGRE) approach. A segmentation protocol was established using the Dorr Mouse Brain Atlas and ANTs Syn registration to warp template brain region labels to subject qGRE maps.

RESULTS

By separating R2' contribution from R2* signal, we have established normative R2t* data in mouse brain. Our findings revealed significant contributions of R2' to R2*, with approximately 42% of the R2* signal arising from vascular contributions, thus suggesting the R2t* as a more accurate metric for quantifying tissue microstructural information and its changes in neurodegenerative diseases.

CONCLUSION

qGRE approach allows efficient separation of tissue microstructure-specific (R2t*), vascular BOLD (R2'), and background gradients contributions to the total R2* relaxation at UHF MRI. Due to low concentration of non-heme iron in mouse brain, major contribution to R2t* results from tissue cellular components.

Microstructure-Informed Myelin Mapping (MIMM) from routine multi-echo gradient echo data using multiscale physics modeling of iron and myelin effects and QSM

PURPOSE

Myelin quantification is used in the study of demyelination in neurodegenerative diseases. A novel noninvasive MRI method, Microstructure-Informed Myelin Mapping (MIMM), is proposed to quantify the myelin volume fraction (MVF) from a routine multi-gradient echo sequence (mGRE) using a multiscale biophysical signal model of the effects of microstructural myelin and iron.

THEORY AND METHODS

In MIMM, the effects of myelin are modeled based on the Hollow Cylinder Fiber Model accounting for anisotropy, while iron is considered as an isotropic paramagnetic point source. This model is used to create a dictionary of mGRE magnitude signal evolution and total voxel susceptibility using finite elements of size 0.2 μm. Next, voxel-by-voxel stochastic matching pursuit between acquired mGRE data (magnitude+QSM) and the pre-computed dictionary generates quantitative MVF and iron susceptibility maps. Dictionary matching was evaluated under three conditions: (1) without fiber orientation (basic), (2) with fiber orientation obtained using DTI, and (3) with fiber orientation obtained using an atlas (atlas). MIMM was compared with the three-pool complex fitting (3PCF) using T2-relaxometry myelin water fraction (MWF) map as reference.

RESULTS

The DTI MIMM and atlas MIMM approaches were equally effective in reducing the overestimation of MVF in certain white matter tracts observed in the basic MIMM approach, and they both showed good agreement with T2-relaxometry MWF. MIMM MVF reduced myelin overestimation of globus pallidus observed in 3PCF MWF.

CONCLUSION

MIMM processing of mGRE data can provide MVF maps from routine clinical scans without requiring special sequences.

Navigator-based slice tracking for prospective motion correction in kidney vessel architecture imaging

OBJECTIVES

To apply a navigator-based slice tracking method to prospectively compensate the respiratory motion for kidney vessel architecture imaging (VAI).

MATERIALS AND METHODS

A dual gradient echo spin echo 2D EPI sequence was developed for kidney VAI. A single gradient-echo slice selection and projection readout at the location of the diaphragm along the inferior-superior direction was applied as a navigator. Navigator acquisition and fat suppression were inserted before each transverse imaging slice. Motion information was calculated after exclusion of the signal saturation in the navigator signal caused by imaging slices. The motion information was then directly sent back to the sequence and slice positioning was adjusted in real-time. The whole sequence was applied during a contrast agent pass-through.

RESULTS

VAI parametric maps show the structural heterogeneity of the renal vasculature. The respiratory motion from the navigator signal was precisely calculated and slice positioning was changed in real-time based on the motion information. The vibration amplitude of the signal intensity of the liver tissue at the liver-lung interface in the case of prospective motion correction (PMC) on is about 28% of the PMC off case. Compared to the case of PMC off, the coefficient of variation was reduced 30% of the case of PMC on.

CONCLUSIONS

This study demonstrates the feasibility of the motion-compensating technique in kidney VAI. The sequence may improve the evaluation of microvasculature in kidney diseases.

Mapping oxidative metabolism in the human brain with calibrated fMRI in health and disease

Conventional functional MRI (fMRI) with blood-oxygenation level dependent (BOLD) contrast is an important tool for mapping human brain activity non-invasively. Recent interest in quantitative fMRI has renewed the importance of oxidative neuroenergetics as reflected by cerebral metabolic rate of oxygen consumption (CMR_O2) to support brain function. Dynamic CMR_O2 mapping by calibrated fMRI require multi-modal measurements of BOLD signal along with cerebral blood flow (CBF) and/or volume (CBV). In human subjects this "calibration" is typically performed using a gas mixture containing small amounts of carbon dioxide and/or oxygen-enriched medical air, which are thought to produce changes in CBF (and CBV) and BOLD signal with minimal or no CMR_O2 changes. However non-human studies have demonstrated that the "calibration" can also be achieved without gases, revealing good agreement between CMR_O2 changes and underlying neuronal activity (e.g., multi-unit activity and local field potential). Given the simpler set-up of gas-free calibrated fMRI, there is evidence of recent clinical applications for this less intrusive direction. This up-to-date review emphasizes technological advances for such translational gas-free calibrated fMRI experiments, also covering historical progression of the calibrated fMRI field that is impacting neurological and neurodegenerative investigations of the human brain.

Whole-brain 3D mapping of oxygen metabolism using constrained quantitative BOLD

Quantitative BOLD (qBOLD) MRI permits noninvasive evaluation of hemodynamic and metabolic states of the brain by quantifying parametric maps of deoxygenated blood volume (DBV) and hemoglobin oxygen saturation level of venous blood (Y_v), and along with a measurement of cerebral blood flow (CBF), the cerebral metabolic rate of oxygen (CMRO₂). The method, thus should have potential to provide important information on many neurological disorders as well as normal cerebral physiology. One major challenge in qBOLD is to separate de-oxyhemoglobin’s contribution to R₂′ from other sources modulating the voxel signal, for instance, R₂, R₂′ from non-heme iron (R′_2,nh), and macroscopic magnetic field variations. Further, even with successful separation of the several confounders, it is still challenging to extract DBV and Y_v from the heme-originated R₂′ because of limited sensitivity of the qBOLD model. These issues, which have not been fully addressed in currently practiced qBOLD methods, have so far precluded 3D whole-brain implementation of qBOLD. Thus, the purpose of this work was to develop a new 3D MRI oximetry technique that enables robust qBOLD parameter mapping across the entire brain. To achieve this goal, we employed a rapid, R₂′-sensitive, steady-state 3D pulse sequence (termed ‘AUSFIDE’) for data acquisition, and implemented a prior-constrained qBOLD processing pipeline that exploits a plurality of preliminary parameters obtained via AUSFIDE, along with additionally measured cerebral venous blood volume. Numerical simulations and in vivo studies at 3 T were performed to evaluate the performance of the proposed, constrained qBOLD mapping in comparison to the parent qBOLD method. Measured parameters (Y_v, DBV, R′_2,nh, nonblood magnetic susceptibility) in ten healthy subjects demonstrate the expected contrast across brain territories, while yielding group-averages of 64.0 ± 2.3 % and 62.2 ± 3.1 % for Y_v and 2.8 ± 0.5 % and 1.8 ± 0.4 % for DBV in cortical gray and white matter, respectively. Given the Y_v measurements, additionally quantified CBF in seven of the ten study subjects enabled whole-brain 3D CMRO₂ mapping, yielding group averages of 134.2 ± 21.1 and 79.4 ± 12.6 µmol/100 g/min for cortical gray and white matter, in good agreement with literature values. The results suggest feasibility of the proposed method as a practical and reliable means for measuring neurometabolic parameters over an extended brain coverage.

In vivo evaluation of heme and non-heme iron content and neuronal density in human basal ganglia

Non-heme iron is an important element supporting the structure and functioning of biological tissues. Imbalance in non-heme iron can lead to different neurological disorders. Several MRI approaches have been developed for iron quantification relying either on the relaxation properties of MRI signal or measuring tissue magnetic susceptibility. Specific quantification of the non-heme iron can, however, be constrained by the presence of the heme iron in the deoxygenated blood and contribution of cellular composition. The goal of this paper is to introduce theoretical background and experimental MRI method allowing disentangling contributions of heme and non-heme irons simultaneously with evaluation of tissue neuronal density in the iron-rich basal ganglia. Our approach is based on the quantitative Gradient Recalled Echo (qGRE) MRI technique that allows separation of the total R2* metric characterizing decay of GRE signal into tissue-specific (R2t*) and the baseline blood oxygen level-dependent (BOLD) contributions. A combination with the QSM data (also available from the qGRE signal phase) allowed further separation of the tissue-specific R2t* metric in a cell-specific and non-heme-iron-specific contributions. It is shown that the non-heme iron contribution to R2t* relaxation can be described with the previously developed Gaussian Phase Approximation (GPA) approach. qGRE data were obtained from 22 healthy control participants (ages 26-63 years). Results suggest that the ferritin complexes are aggregated in clusters with an average radius about 100nm comprising approximately 2600 individual ferritin units. It is also demonstrated that the concentrations of heme and non-heme iron tend to increase with age. The strongest age effect was seen in the pallidum region, where the highest age-related non-heme iron accumulation was observed.

Advances in translational imaging of the microcirculation

The past few decades have seen an explosion in the development and use of methods for imaging the human microcirculation during health and disease. The confluence of innovative imaging technologies, affordable computing power, and economies of scale have ushered in a new era of "translational" imaging that permit us to peer into blood vessels of various organs in the human body. These imaging techniques include near-infrared spectroscopy (NIRS), positron emission tomography (PET), and magnetic resonance imaging (MRI) that are sensitive to microvascular-derived signals, as well as computed tomography (CT), optical imaging, and ultrasound (US) imaging that are capable of directly acquiring images at, or close to microvascular spatial resolution. Collectively, these imaging modalities enable us to characterize the morphological and functional changes in a tissue's microcirculation that are known to accompany the initiation and progression of numerous pathologies. Although there have been significant advances for imaging the microcirculation in preclinical models, this review focuses on developments in the assessment of the microcirculation in patients with optical imaging, NIRS, PET, US, MRI, and CT, to name a few. The goal of this review is to serve as a springboard for exploring the burgeoning role of translational imaging technologies for interrogating the structural and functional status of the microcirculation in humans, and highlight the breadth of current clinical applications. Making the human microcirculation "visible" in vivo to clinicians and researchers alike will facilitate bench-to-bedside discoveries and enhance the diagnosis and management of disease.

Dependence of the frequency distribution around a sphere on the voxel orientation

Microscopically small magnetic field inhomogeneities within an external static magnetic field cause a free induction decay in magnetic resonance imaging that generally exhibits two transverse components that are usually summarized to a complex entity. The Fourier transform of the complex-valued free induction decay is the purely real and positive-valued frequency distribution which allows an easy interpretation of the underlying dephasing mechanism. Typically, the frequency distribution inside a cubic voxel as caused by a spherical magnetic field inhomogeneity is determined by a histogram technique in terms of subdivision of the whole voxel into smaller subvoxels. A faster and more accurate computation is achieved by analytical expressions for the frequency distribution that are derived in this work. In contrast to the usually assumed simplified case of a spherical voxel, we also consider the tilt angles of the cubic voxel to the external magnetic field. The typical asymmetric form of the frequency distribution is reproduced and analyzed for the more realistic case of a cubic voxel. We observe a splitting of frequency distribution peaks for increasing tilt of the cubic voxel against the direction of the external magnetic field in analogy to the case for dephasing around cylindrical, vessel-like objects inside cubic voxels. These results are of value, e.g., for the analysis of susceptibility-weighted images or in quantitative susceptibility imaging since the reconstruction of these images is performed in cubic-shaped voxels.

High spatiotemporal vessel-specific hemodynamic mapping with multi-echo single-vessel fMRI

High-resolution fMRI enables noninvasive mapping of the hemodynamic responses from individual penetrating vessels in animal brains. Here, a 2D multi-echo single-vessel fMRI (MESV-fMRI) method has been developed to map the fMRI signal from arterioles and venules with a 100 ms sampling rate at multiple echo times (TE, 3-30 ms) and short acquisition windows (<1 ms). The T₂*-weighted signal shows the increased extravascular effect on venule voxels as a function of TE. In contrast, the arteriole voxels show an increased fMRI signal with earlier onset than venules voxels at the short TE (3 ms) with increased blood inflow and volume effects. MESV-fMRI enables vessel-specific T2* mapping and presents T2*-based fMRI time courses with higher contrast-to-noise ratios (CNRs) than the T2*-weighted fMRI signal at a given TE. The vessel-specific T2* mapping also allows semi-quantitative estimation of the oxygen saturation levels (Y) and their changes (ΔY) at a given blood volume fraction upon neuronal activation. The MESV-fMRI method enables vessel-specific T2* measurements with high spatiotemporal resolution for better modeling of the fMRI signal based on the hemodynamic parameters.

Numerical simulation of the blood oxygenation level-dependent functional magnetic resonance signal using finite element method

Since the introduction of functional magnetic resonance imaging (fMRI), several computational approaches have been developed to examine the effect of the morphology and arrangement of blood vessels on the blood oxygenation-level dependent (BOLD) signal in the brain. In the present work, we implemented the original Ogawa's model using a numerical simulation based on the finite element method (FEM) instead of the analytical models. In literature, there are different works using analytical methods to analyse the transverse relaxation rate ( R2∗ ), which BOLD signal is related to, modelling the vascular system with simple and canonical geometries such as an infinite cylinder model (ICM) or a set of cylinders. We applied the numerical simulation to the extravascular BOLD signal as a function of angular vessel distribution (perpendicular vs parallel to the static magnetic field) relevant for anatomical districts characterized by geometrical symmetries, such as spinal cord. Numerical simulations confirmed analytical results for the canonical ICM. Moreover, the perturbation to the magnetic field induced by blood deoxyhaemoglobin, as quantified assuming Brownian diffusion of water molecules around the vessel, revealed that vessels contribute the most to the variation of the R2∗ when they are preferentially perpendicular to the external magnetic field, regardless of their size. Our results indicate that the numerical simulation method is sensitive to the effects of different vascular geometry. This work highlights the opportunity to extend R2∗ simulations to realistic models of vasculature based on high-resolution anatomical images.

Simulations of the effect of diffusion on asymmetric spin echo based quantitative BOLD: An investigation of the origin of deoxygenated blood volume overestimation

Quantitative BOLD (qBOLD) is a technique for mapping oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) in the human brain. Recent measurements using an asymmetric spin echo (ASE) based qBOLD approach produced estimates of DBV which were systematically higher than measurements from other techniques. In this study, we investigate two hypotheses for the origin of this DBV overestimation using simulations and consider the implications for experimental measurements. Investigations were performed by combining Monte Carlo simulations of extravascular signal with an analytical model of the intravascular signal. HYPOTHESIS 1: DBV overestimation is due to the presence of intravascular signal which is not accounted for in the analysis model. Intravascular signal was found to have a weak effect on qBOLD parameter estimates. HYPOTHESIS 2: DBV overestimation is due to the effects of diffusion which are not accounted for in the analysis model. The effect of diffusion on the extravascular signal was found to result in a vessel radius dependent variation in qBOLD parameter estimates. In particular, DBV overestimation peaks for vessels with radii from 20 to 30 μm and is OEF dependent. This results in the systematic underestimation of OEF. IMPLICATIONS: The impact on experimental qBOLD measurements was investigated by simulating a more physiologically realistic distribution of vessel sizes with a small number of discrete radii. Overestimation of DBV consistent with previous experiments was observed, which was also found to be OEF dependent. This results in the progressive underestimation of the measured OEF. Furthermore, the relationship between the measured OEF and the true OEF was found to be dependent on echo time and spin echo displacement time. The results of this study demonstrate the limitations of current ASE based qBOLD measurements and provide a foundation for the optimisation of future acquisition approaches.

A Novel Gradient Echo Plural Contrast Imaging Method Detects Brain Tissue Abnormalities in Patients With TBI Without Evident Anatomical Changes on Clinical MRI: A Pilot Study

RESEARCH OBJECTIVES

It is widely accepted that mild traumatic brain injury (mTBI) causes injury to the white matter, but the extent of gray matter (GM) damage in mTBI is less clear.

METHODS

We tested 26 civilian healthy controls and 14 civilian adult subacute-chronic mTBI patients using quantitative features of MRI-based Gradient Echo Plural Contrast Imaging (GEPCI) technique. GEPCI data were reconstructed using previously developed algorithms allowing the separation of R2t*, a cellular-specific part of gradient echo MRI relaxation rate constant, from global R2* affected by BOLD effect and background gradients.

RESULTS

Single-subject voxel-wise analysis (comparing each mTBI patient to the sample of 26 control subjects) revealed GM abnormalities that were not visible on standard MRI images (T1w and T2w). Analysis of spatial overlap for voxels with low R2t* revealed tissue abnormalities in multiple GM regions, especially in the frontal and temporal regions, that are frequently damaged after mTBI. The left posterior insula was the region with abnormalities found in the highest proportion (50%) of mTBI patients.

CONCLUSIONS

Our data suggest that GEPCI quantitative R2t* metric has potential to detect abnormalities in GM cellular integrity in individual TBI patients, including abnormalities that are not detectable by a standard clinical MRI.

Spin echoes: full numerical solution and breakdown of approximative solutions

The spin echo signal from vessels in Krogh's capillary model as well in the random distribution vessel model are studied by numerically solving the Bloch-Torrey equation. A comparison is made with the Gaussian local phase approximation, the Gaussian phase approximation and the strong-collision approximation. Differences between the Gaussian local phase approximation and the Gaussian phase approximation are explained. In the intermediate diffusion regime, the full numerical solution shows oscillations which are absent in any of the approximate solutions. In the limit of large diffusion coefficients, where the approximations become exact, the signal shows a linear-exponential decay governed by a single parameter. The features of the exact numerical solution can be explained by an analytically solvable discrete two-level model. There is a one-to-one correspondence between the different diffusion regimes and the three cases of the damped harmonic oscillator.

MRI techniques to measure arterial and venous cerebral blood volume

The measurement of cerebral blood volume (CBV) has been the topic of numerous neuroimaging studies. To date, however, most in vivo imaging approaches can only measure CBV summed over all types of blood vessels, including arterial, capillary and venous vessels in the microvasculature (i.e. total CBV or CBVtot). As different types of blood vessels have intrinsically different anatomy, function and physiology, the ability to quantify CBV in different segments of the microvascular tree may furnish information that is not obtainable from CBVtot, and may provide a more sensitive and specific measure for the underlying physiology. This review attempts to summarize major efforts in the development of MRI techniques to measure arterial (CBVa) and venous CBV (CBVv) separately. Advantages and disadvantages of each type of method are discussed. Applications of some of the methods in the investigation of flow-volume coupling in healthy brains, and in the detection of pathophysiological abnormalities in brain diseases such as arterial steno-occlusive disease, brain tumors, schizophrenia, Huntington's disease, Alzheimer's disease, and hypertension are demonstrated. We believe that the continual development of MRI approaches for the measurement of compartment-specific CBV will likely provide essential imaging tools for the advancement and refinement of our knowledge on the exquisite details of the microvasculature in healthy and diseased brains.

Spin dephasing around randomly distributed vessels

We analyze the gradient echo signal in the presence of blood vessel networks. Both, diffusion and susceptibility effects are analytically emphasized within the Bloch-Torrey equation. Solving this equation, we present the first exact description of the local magnetization around a single vessel. This allows us to deduce the gradient echo signal of parallel vessels randomly distributed in a plane, which is valid for arbitrary mean vessel diameters in the range of physiological relevant blood volume fractions. Thus, the results are potentially relevant for gradient echo measurements of blood vessel networks with arbitrary vessel size.

Mapping hepatic blood oxygenation by quantitative BOLD (qBOLD) MRI

PURPOSE

Abnormalities in hepatic oxygen delivery and oxygen consumption may serve as a significant indicator of hepatic cellular dysfunction and may predict treatment response. However, conventional and oxygen-enhanced hepatic BOLD MRI can only provide semiquantitative assessment of hepatic oxygenation.

METHODS

A hepatic quantitative BOLD (qBOLD) model was proposed for noninvasive mapping of hepatic venous blood oxygen saturation (Y_v ) and deoxygenated blood volume (DBV) in human subjects. The validity and the estimation bias of the proposed model were evaluated by Monte Carlo simulations. Eight healthy subjects were scanned after written consent with institutional review board approval.

RESULTS

Monte Carlo simulations demonstrated that the proposed single-compartment hepatic qBOLD model leads to significant deviation of the predicted T₂ ^* decay profile from the simulated signal due to high hepatic blood volume fraction. Small relative estimation bias for hepatic Y_v and significant overestimation for hepatic DBV were observed, which can be corrected by applying the calibration curves established from simulations. After correction, the mean hepatic Y_v in human subjects was 56.8 ± 6.8%, and the mean hepatic DBV was 0.190 ± 0.035, consistent with measurements from other invasive approaches. Except in regions with significant vascular contamination, the maps for hepatic Y_v and DBV were relatively homogenous.

CONCLUSIONS

With estimation bias correction, the hepatic qBOLD approach enables noninvasive mapping of hepatic blood volume and oxygenation in human subjects. The established protocol may be used to quantitatively assess hepatic tissue hypoxia in multiple liver diseases.

Transverse NMR relaxation in biological tissues

Transverse NMR relaxation is a fundamental physical phenomenon underpinning a wide range of MRI-based techniques, essential for non-invasive studies in biology, physiology and neuroscience, as well as in diagnostic imaging. Biophysically, transverse relaxation originates from a number of distinct scales - molecular (nanometers), cellular (micrometers), and macroscopic (millimeter-level MRI resolution). Here we review the contributions to the observed relaxation from each of these scales, with the main focus on the cellular level of tissue organization, commensurate with the diffusion length of spin-carrying molecules. We discuss how the interplay between diffusion and spin dephasing in a spatially heterogeneous tissue environment leads to a non-monoexponential time-dependent transverse relaxation signal that contains important biophysical information about tissue microstructure.

Genetically defined cellular correlates of the baseline brain MRI signal

fMRI revolutionized neuroscience by allowing in vivo real-time detection of human brain activity. While the nature of the fMRI signal is understood as resulting from variations in the MRI signal due to brain-activity-induced changes in the blood oxygenation level (BOLD effect), these variations constitute a very minor part of a baseline MRI signal. Hence, the fundamental (and not addressed) questions are how underlying brain cellular composition defines this baseline MRI signal and how a baseline MRI signal relates to fMRI. Herein we investigate these questions by using a multimodality approach that includes quantitative gradient recalled echo (qGRE), volumetric and functional connectivity MRI, and gene expression data from the Allen Human Brain Atlas. We demonstrate that in vivo measurement of the major baseline component of a GRE signal decay rate parameter (R2t*) provides a unique genetic perspective into the cellular constituents of the human cortex and serves as a previously unidentified link between cortical tissue composition and fMRI signal. Data show that areas of the brain cortex characterized by higher R2t* have high neuronal density and have stronger functional connections to other brain areas. Interestingly, these areas have a relatively smaller concentration of synapses and glial cells, suggesting that myelinated cortical axons are likely key cortical structures that contribute to functional connectivity. Given these associations, R2t* is expected to be a useful signal in assessing microstructural changes in the human brain during development and aging in health and disease.

Oxygen metabolism in acute ischemic stroke

Gaining insights into brain oxygen metabolism has been one of the key areas of research in neurosciences. Extensive efforts have been devoted to developing approaches capable of providing measures of brain oxygen metabolism not only under normal physiological conditions but, more importantly, in various pathophysiological conditions such as cerebral ischemia. In particular, quantitative measures of cerebral metabolic rate of oxygen using positron emission tomography (PET) have been shown to be capable of discerning brain tissue viability during ischemic insults. However, the complex logistics associated with oxygen-15 PET have substantially hampered its wide clinical applicability. In contrast, magnetic resonance imaging (MRI)-based approaches have provided quantitative measures of cerebral oxygen metabolism similar to that obtained using PET. Given the wide availability, MRI-based approaches may have broader clinical impacts, particularly in cerebral ischemia, when time is a critical factor in deciding treatment selection. In this article, we review the pathophysiological basis of altered cerebral hemodynamics and oxygen metabolism in cerebral ischemia, how quantitative measures of cerebral metabolism were obtained using the Kety-Schmidt approach, the physical concepts of non-invasive oxygen metabolism imaging approaches, and, finally, clinical applications of the discussed imaging approaches.

Spin dephasing in a magnetic dipole field around large capillaries: Approximative and exact results

We present an analytical solution of the Bloch-Torrey equation for local spin dephasing in the magnetic dipole field around a capillary and for ensembles of capillaries, and adapt this solution for the study of spin dephasing around large capillaries. In addition, we provide a rigorous mathematical derivation of the slow diffusion approximation for the spin-bearing particles that is used in this regime. We further show that, in analogy to the local magnetization, the transverse magnetization of one MR imaging voxel in the regime of static dephasing (where diffusion effects are not considered) is merely the first term of a series expansion that constitutes the signal in the slow diffusion approximation. Theoretical results are in agreement with experimental data for capillaries in rat muscle at 7T.

MRI-based methods for quantification of the cerebral metabolic rate of oxygen

The brain depends almost entirely on oxidative metabolism to meet its significant energy requirements. As such, the cerebral metabolic rate of oxygen (CMRO2) represents a key measure of brain function. Quantification of CMRO2 has helped elucidate brain functional physiology and holds potential as a clinical tool for evaluating neurological disorders including stroke, brain tumors, Alzheimer's disease, and obstructive sleep apnea. In recent years, a variety of magnetic resonance imaging (MRI)-based CMRO2 quantification methods have emerged. Unlike positron emission tomography - the current "gold standard" for measurement and mapping of CMRO2 - MRI is non-invasive, relatively inexpensive, and ubiquitously available in modern medical centers. All MRI-based CMRO2 methods are based on modeling the effect of paramagnetic deoxyhemoglobin on the magnetic resonance signal. The various methods can be classified in terms of the MRI contrast mechanism used to quantify CMRO2: T2*, T2', T2, or magnetic susceptibility. This review article provides an overview of MRI-based CMRO2 quantification techniques. After a brief historical discussion motivating the need for improved CMRO2 methodology, current state-of-the-art MRI-based methods are critically appraised in terms of their respective tradeoffs between spatial resolution, temporal resolution, and robustness, all of critical importance given the spatially heterogeneous and temporally dynamic nature of brain energy requirements.

On the relationship between cellular and hemodynamic properties of the human brain cortex throughout adult lifespan

Establishing baseline MRI biomarkers for normal brain aging is significant and valuable for separating normal changes in the brain structure and function from different neurological diseases. In this paper for the first time we have simultaneously measured a variety of tissue specific contributions defining R2* relaxation of the gradient recalled echo (GRE) MRI signal in human brains of healthy adults (ages 22 to 74years) and related these measurements to tissue structural and functional properties. This was accomplished by separating tissue (R2t(⁎)) and extravascular BOLD contributions to the total tissue specific GRE MRI signal decay (R2(⁎)) using an advanced version of previously developed Gradient Echo Plural Contrast Imaging (GEPCI) approach and the acquisition and post-processing methods that allowed the minimization of artifacts related to macroscopic magnetic field inhomogeneities, and physiological fluctuations. Our data (20 healthy subjects) show that in most cortical regions R2t(⁎) increases with age while tissue hemodynamic parameters, i.e. relative oxygen extraction fraction (OEFrel), deoxygenated cerebral blood volume (dCBV) and tissue concentration of deoxyhemoglobin (Cdeoxy) remain practically constant. We also found the important correlations characterizing the relationships between brain structural and hemodynamic properties in different brain regions. Specifically, thicker cortical regions have lower R2t(⁎) and these regions have lower OEF. The comparison between GEPCI-derived tissue specific structural and functional metrics and literature information suggests that (a) regions in a brain characterized by higher R2t(⁎) contain higher concentration of neurons with less developed cellular processes (dendrites, spines, etc.), (b) regions in a brain characterized by lower R2t(⁎) represent regions with lower concentration of neurons but more developed cellular processes, and (c) the age-related increases in the cortical R2t(⁎) mostly reflect the age-related increases in the cellular packing density. The baseline GEPCI-based biomarkers obtain herein could serve to help distinguish age-related changes in brain cellular and hemodynamic properties from changes which occur due to the neurodegenerative diseases.

Separation of cellular and BOLD contributions to T2* signal relaxation

PURPOSE

The development of a reliable clinical technique for quantitative measurements of the parameters defining the BOLD effect, i.e., oxygen extraction fraction (OEF), and deoxygenated cerebral blood volume, dCBV, is needed to study brain function in health and disease. Herein we propose such a technique that is based on a widely available gradient recalled echo (GRE) MRI.

THEORY AND METHODS

Our method is based on GRE with multiple echoes and a model of signal decay (Yablonskiy, MRM 1998) that takes into account microscopic cellular (R2), mesoscopic (BOLD), and macroscopic (background field gradients) contributions to the GRE signal decay with additional accounting for physiologic fluctuations.

RESULTS

Using 3 Tesla MRI, we generate high resolution quantitative maps of R2*, R2, R2', and tissue concentration of deoxyhemoglobin, the latter providing a quantitative version of SWI. Our results for OEF and dCBV in gray matter are in a reasonable agreement with the literature data.

CONCLUSION

The proposed approach allows generating high resolution maps of hemodynamic parameters using clinical MRI. The technique can be applied to study such tissues as gray matter, tumors, etc.; however, it requires further development for use in tissues where extra- and intracellular compartments possess substantially different frequencies and relaxation properties (e.g., white matter).

A novel Bayesian approach to accounting for uncertainty in fMRI-derived estimates of cerebral oxygen metabolism fluctuations

Calibrated blood oxygenation level dependent (BOLD) imaging is a multimodal functional MRI technique designed to estimate changes in cerebral oxygen metabolism from measured changes in cerebral blood flow and the BOLD signal. This technique addresses fundamental ambiguities associated with quantitative BOLD signal analysis; however, its dependence on biophysical modeling creates uncertainty in the resulting oxygen metabolism estimates. In this work, we developed a Bayesian approach to estimating the oxygen metabolism response to a neural stimulus and used it to examine the uncertainty that arises in calibrated BOLD estimation due to the presence of unmeasured model parameters. We applied our approach to estimate the CMRO2 response to a visual task using the traditional hypercapnia calibration experiment as well as to estimate the metabolic response to both a visual task and hypercapnia using the measurement of baseline apparent R2' as a calibration technique. Further, in order to examine the effects of cerebral spinal fluid (CSF) signal contamination on the measurement of apparent R2', we examined the effects of measuring this parameter with and without CSF-nulling. We found that the two calibration techniques provided consistent estimates of the metabolic response on average, with a median R2'-based estimate of the metabolic response to CO2 of 1.4%, and R2'- and hypercapnia-calibrated estimates of the visual response of 27% and 24%, respectively. However, these estimates were sensitive to different sources of estimation uncertainty. The R2'-calibrated estimate was highly sensitive to CSF contamination and to uncertainty in unmeasured model parameters describing flow-volume coupling, capillary bed characteristics, and the iso-susceptibility saturation of blood. The hypercapnia-calibrated estimate was relatively insensitive to these parameters but highly sensitive to the assumed metabolic response to CO2.

Free induction decay caused by a dipole field

We analyze the free induction decay of nuclear spins under the influence of restricted diffusion in a magnetic dipole field around cylindrical objects. In contrast to previous publications no restrictions or simplifications concerning the diffusion process are made. By directly solving the Bloch-Torrey equation, analytical expressions for the magnetization are given in terms of an eigenfunction expansion. The field strength-dependent complex nature of the eigenvalue spectrum significantly influences the shape of the free induction decay. As the dipole field is the lowest order of the multipole expansion, the obtained results are important for understanding fundamental mechanisms of spin dephasing in many other applied fields of nuclear magnetic resonance such as biophysics or material science. The analytical methods are applied to interpret the spin dephasing in the free induction decay in cardiac muscle and skeletal muscle. A simple expression for the relevant transverse relaxation time is found in terms of the underlying microscopic parameters of the muscle tissue. The analytical results are in agreement with experimental data. These findings are important for the correct interpretation of magnetic resonance images for clinical diagnosis at all magnetic field strengths and therapy of cardiovascular diseases.

Technical considerations on the validity of blood oxygenation level-dependent-based MR assessment of vascular deoxygenation

A blood oxygenation level-dependent (BOLD)-based apparent relative oxygen extraction fraction (rOEF) as a semi-quantitative marker of vascular deoxygenation has recently been introduced in clinical studies of patients with glioma and stroke, yielding promising results. These rOEF measurements are based on independent quantification of the transverse relaxation times T2 and T2* and relative cerebral blood volume (rCBV). Simulations demonstrate that small errors in any of the underlying measures may result in a large deviation of the calculated rOEF. Therefore, we investigated the validity of such measurements. For this, we evaluated the quantitative measurements of T2 and T2* at 3 T in a gel phantom, in healthy subjects and in healthy tissue of patients with brain tumors. We calculated rOEF maps covering large portions of the brain from T2, T2* and rCBV [routinely measured in patients using dynamic susceptibility contrast (DSC)], and obtained rOEF values of 0.63 ± 0.16 and 0.90 ± 0.21 in healthy-appearing gray matter (GM) and white matter (WM), respectively; values of about 0.4 are usually reported. Quantitative T2 mapping using the fast, clinically feasible, multi-echo gradient spin echo (GRASE) approach yields significantly higher values than much slower multiple single spin echo (SE) experiments. Although T2* mapping is reliable in magnetically homogeneous tissues, uncorrectable macroscopic background gradients and other effects (e.g. iron deposition) shorten T2*. Cerebral blood volume (CBV) measurement using DSC and normalization to WM yields robust estimates of rCBV in healthy-appearing brain tissue; absolute quantification of the venous fraction of CBV, however, is difficult to achieve. Our study demonstrates that quantitative measurements of rOEF are currently biased by inherent difficulties in T2 and CBV quantification, but also by inadequacies of the underlying model. We argue, however, that standardized, reproducible measurements of apparent T2, T2* and rCBV may still allow the estimation of a meaningful apparent rOEF, which requires further validation in clinical studies.

Comparison of R2' measurement methods in the normal brain at 3 Tesla

PURPOSE

R2', the reversible component of transverse relaxation, is an important susceptibility measurement for studies of brain physiology and pathologies. In existing literature, different R2' measurement methods are used with assumption of equivalency. This study explores the choice of measurement method in healthy, young subjects at 3T.

METHODS

In this study, a modified gradient-echo sampling of free induction decay and echo (GESFIDE) sequence was used to compare four standard R2' measurement methods: asymmetric spin echo (ASE), standard GESFIDE, gradient echo sampling of the spin echo (GESSE), and separate R2 and R2* mapping.

RESULTS

GESSE returned lower R2' measurements than other methods (P < 0.05). Intersubject mean R2' in gray matter was found to be 2.7 s(-1) using standard GESFIDE and GESSE, versus 3.4-3.8 s(-1) using other methods. In white matter, mean R2' from GESSE was 2.3 s(-1) while other methods produced 3.7-4.3 s(-1) . R2 correction was applied to partially reduce the discrepancies between the methods, but significant differences remained, likely due to violation of the fundamental assumption of a single-compartmental tissue model, and hence monoexponential decay.

CONCLUSION

R2' measurements are influenced significantly by the choice of method. Awareness of this issue is important when designing and interpreting studies that involve R2' measurements.

On the role of neuronal magnetic susceptibility and structure symmetry on gradient echo MR signal formation

PURPOSE

Phase images obtained by gradient-recalled echo (GRE) MRI provide new contrast in the brain that is distinct from that obtained with conventional T1-weighted and T2-weighted images. The results are especially intriguing in white matter where both signal amplitude and phase display anisotropic properties. However, the biophysical origins of these phenomena are not well understood. The goal of this article is to provide a comprehensive theory of GRE signal formation based on a realistic model of neuronal structure.

METHODS

We use Maxwell equations to find the distribution of magnetic field induced by myelin sheath and axon. We account for both anisotropy of neuronal tissue "magnetic micro-architecture" and anisotropy of myelin sheath magnetic susceptibility.

RESULTS

Model describes GRE signal comprising of three compartments-axonal, myelin, and extracellular. Both axonal and myelin water signals have frequency shifts that are affected by the magnetic susceptibility anisotropy of long molecules forming lipid bilayer membranes. These parts of frequency shifts reach extrema for axon oriented perpendicular to the magnetic field and are zeros in a parallel case. Myelin water signal is substantially non-monoexponential.

CONCLUSIONS

Both, anisotropy of neuronal tissue "magnetic micro-architecture" and anisotropy of myelin sheath magnetic susceptibility, are important for describing GRE signal phase and magnitude.

MR vascular fingerprinting: A new approach to compute cerebral blood volume, mean vessel radius, and oxygenation maps in the human brain

In the present study, we describe a fingerprinting approach to analyze the time evolution of the MR signal and retrieve quantitative information about the microvascular network. We used a Gradient Echo Sampling of the Free Induction Decay and Spin Echo (GESFIDE) sequence and defined a fingerprint as the ratio of signals acquired pre- and post-injection of an iron-based contrast agent. We then simulated the same experiment with an advanced numerical tool that takes a virtual voxel containing blood vessels as input, then computes microscopic magnetic fields and water diffusion effects, and eventually derives the expected MR signal evolution. The parameter inputs of the simulations (cerebral blood volume [CBV], mean vessel radius [R], and blood oxygen saturation [SO2]) were varied to obtain a dictionary of all possible signal evolutions. The best fit between the observed fingerprint and the dictionary was then determined by using least square minimization. This approach was evaluated in 5 normal subjects and the results were compared to those obtained by using more conventional MR methods, steady-state contrast imaging for CBV and R and a global measure of oxygenation obtained from the superior sagittal sinus for SO2. The fingerprinting method enabled the creation of high-resolution parametric maps of the microvascular network showing expected contrast and fine details. Numerical values in gray matter (CBV=3.1±0.7%, R=12.6±2.4μm, SO2=59.5±4.7%) are consistent with literature reports and correlated with conventional MR approaches. SO2 values in white matter (53.0±4.0%) were slightly lower than expected. Numerous improvements can easily be made and the method should be useful to study brain pathologies.

Numerical modeling of susceptibility-related MR signal dephasing with vessel size measurement: phantom validation at 3T

PURPOSE

MRI is used to obtain quantitative oxygenation and blood volume information from the susceptibility-related MR signal dephasing induced by blood vessels. However, analytical models that fit the MR signal are usually not accurate over the range of small blood vessels. Moreover, recent studies have demonstrated limitations in the simultaneous assessment of oxygenation and blood volume. In this study, a multiparametric MRI framework that aims to measure vessel radii in addition to magnetic susceptibility and volume fraction was introduced.

METHODS

The protocol consisted of gradient-echo sampling of the spin-echo, diffusion, T2, and B0 acquisitions. After correction steps, the data were postprocessed with a versatile numerical model of the MR signal. An important analytical model was implemented for comparison. The approach was validated in phantoms with coiling strings as proxy for blood vessels.

RESULTS

The feasibility of the vessel radius measurement is demonstrated. The numerical model shows an improved accuracy compared with the analytical approach. However, both methods overestimate the radius. The simultaneous measurement of the magnetic susceptibility and the volume fraction remains challenging.

CONCLUSION

The results suggest that this approach could be interesting in vivo to better characterize the microvasculature without contrast agent.

The physics of functional magnetic resonance imaging (fMRI)

Functional magnetic resonance imaging (fMRI) is a methodology for detecting dynamic patterns of activity in the working human brain. Although the initial discoveries that led to fMRI are only about 20 years old, this new field has revolutionized the study of brain function. The ability to detect changes in brain activity has a biophysical basis in the magnetic properties of deoxyhemoglobin, and a physiological basis in the way blood flow increases more than oxygen metabolism when local neural activity increases. These effects translate to a subtle increase in the local magnetic resonance signal, the blood oxygenation level dependent (BOLD) effect, when neural activity increases. With current techniques, this pattern of activation can be measured with resolution approaching 1 mm(3) spatially and 1 s temporally. This review focuses on the physical basis of the BOLD effect, the imaging methods used to measure it, the possible origins of the physiological effects that produce a mismatch of blood flow and oxygen metabolism during neural activation, and the mathematical models that have been developed to understand the measured signals. An overarching theme is the growing field of quantitative fMRI, in which other MRI methods are combined with BOLD methods and analyzed within a theoretical modeling framework to derive quantitative estimates of oxygen metabolism and other physiological variables. That goal is the current challenge for fMRI: to move fMRI from a mapping tool to a quantitative probe of brain physiology.

Blood oxygenation level-dependent (BOLD)-based techniques for the quantification of brain hemodynamic and metabolic properties - theoretical models and experimental approaches

The quantitative evaluation of brain hemodynamics and metabolism, particularly the relationship between brain function and oxygen utilization, is important for the understanding of normal human brain operation, as well as the pathophysiology of neurological disorders. It can also be of great importance for the evaluation of hypoxia within tumors of the brain and other organs. A fundamental discovery by Ogawa and coworkers of the blood oxygenation level-dependent (BOLD) contrast opened up the possibility to use this effect to study brain hemodynamic and metabolic properties by means of MRI measurements. Such measurements require the development of theoretical models connecting the MRI signal to brain structure and function, and the design of experimental techniques allowing MR measurements to be made of the salient features of theoretical models. In this review, we discuss several such theoretical models and experimental methods for the quantification of brain hemodynamic and metabolic properties. The review's main focus is on methods for the evaluation of the oxygen extraction fraction (OEF) based on the measurement of the blood oxygenation level. A combination of the measurement of OEF and the cerebral blood flow (CBF) allows an evaluation to be made of the cerebral metabolic rate of oxygen consumption (CMRO2 ). We first consider in detail the magnetic properties of blood - magnetic susceptibility, MR relaxation and theoretical models of the intravascular contribution to the MR signal under different experimental conditions. We then describe a 'through-space' effect - the influence of inhomogeneous magnetic fields, created in the extravascular space by intravascular deoxygenated blood, on the formation of the MR signal. Further, we describe several experimental techniques taking advantage of these theoretical models. Some of these techniques - MR susceptometry and T2 -based quantification of OEF - utilize the intravascular MR signal. Another technique - quantitative BOLD - evaluates OEF by making use of through-space effects. In this review, we target both scientists just entering the MR field and more experienced MR researchers interested in the application of advanced BOLD-based techniques to the study of the brain in health and disease.

Biophysical and physiological origins of blood oxygenation level-dependent fMRI signals

After its discovery in 1990, blood oxygenation level-dependent (BOLD) contrast in functional magnetic resonance imaging (fMRI) has been widely used to map brain activation in humans and animals. Since fMRI relies on signal changes induced by neural activity, its signal source can be complex and is also dependent on imaging parameters and techniques. In this review, we identify and describe the origins of BOLD fMRI signals, including the topics of (1) effects of spin density, volume fraction, inflow, perfusion, and susceptibility as potential contributors to BOLD fMRI, (2) intravascular and extravascular contributions to conventional gradient-echo and spin-echo BOLD fMRI, (3) spatial specificity of hemodynamic-based fMRI related to vascular architecture and intrinsic hemodynamic responses, (4) BOLD signal contributions from functional changes in cerebral blood flow (CBF), cerebral blood volume (CBV), and cerebral metabolic rate of O(2) utilization (CMRO(2)), (5) dynamic responses of BOLD, CBF, CMRO(2), and arterial and venous CBV, (6) potential sources of initial BOLD dips, poststimulus BOLD undershoots, and prolonged negative BOLD fMRI signals, (7) dependence of stimulus-evoked BOLD signals on baseline physiology, and (8) basis of resting-state BOLD fluctuations. These discussions are highly relevant to interpreting BOLD fMRI signals as physiological means.