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Unlike PET, MRI is inherently non-invasive and relatively ubiquitous in modern medical centers. MRI is based on nuclear magnetic resonance (NMR), the process by which atomic nuclei absorb and re-emit electromagnetic radiation. In MRI, a strong magnetic field is used to polarize nuclear spin magnetic moments. Application of radiofrequency (RF) pulses matching a particular nuclei’s resonant (Larmor) frequency causes rotation of those moments into the plane perpendicular to the main field, and precession of the moments about the main field induces a measurable signal in RF coils via electromagnetic induction. This signal will decay with a time constant called the effective transverse relaxation rate (R2*). The portion of the signal decay due to static field

inhomogeneity can be removed by spin-echo refocusing, thus isolating the transverse relaxation rate (R2). These two quantities define a third relaxation rate, R2’, where R2’=R2*-R2. R2’

represents the rate of signal decay due to static magnetic field inhomogeneities, but is only an exponential decay constant when this inhomogeneous field distribution is Lorentzian. These relaxation rates are often defined in terms of relaxation times: T2*=1/R2*, T2=1/R2, and T2’=1/R2’.

Imaging is made possible by the application of magnetic field gradients, which result in spatial information being encoded into the resulting MR signal (54). While MRI is possible with any nuclei possessing non-zero spin magnetic moment, because the human body is mostly composed of hydrogen-containing water molecules, 1H is the nucleus of choice for most human MRI imaging. The varying chemical and structural properties of tissues have different effects on the time evolution of the MR signal, which can be exploited by different combinations of RF pulses and gradients (pulse sequences) to produce images with widely varying contrast. The tunability and variety of MR contrast has made it an enormously powerful tool for clinical diagnosis and scientific discovery.

A fundamental limitation of NMR and MRI is that the degree of polarization of nuclear magnetic moments is quite small, only a few parts per million, and the exponential time constant for

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repolarization (the T1) is quite long, on the order of seconds for many tissues of interest. For this

reason, tradeoffs between signal-to-noise-ratio (SNR), spatial resolution, and temporal resolution must be considered in almost all MRI applications, including CMRO2 quantification techniques.

While direct detection of oxygen with 17O MRI is possible, enriched 17O is enormously expensive, and the detection sensitivity is low. The Fick Principle offers an alternative approach as CBF can be measured non-invasively using either phase-contrast MRI (PC-MRI) (55) in large cerebral vessels or mapped on a voxel-wise basis with arterial spin labeling (ASL) (56,57). Ya can be

measured with pulse oximetry or assumed to be near 98 %HbO2 in normal conditions. This

leaves quantification of Yv, which is the crux of MR-based CMRO2 quantification methods. Yv is

itself of interest in certain applications, for instance, in stroke, where it may provide a marker for potentially salvageable tissue (29,30).

MR-based Yv quantification takes advantages of the unique magnetic properties of the

metalloprotein hemoglobin, first demonstrated by magnetic mass balance experiments conducted by Linus Pauling and Charles Coryell in 1936 (58). In the deoxygenated state, the Fe2+ heme iron’s six electrons in the five 3d orbitals are distributed across the egg and t2g orbitals, resulting in

four unpaired electrons and a spin S = 2. When the heme iron becomes oxygenated, the ligand field separating the t2g and egg orbitals is increased, making the configuration in which all

electrons occupy the three t2g orbitals more energetically favorable, and resulting in an electron

spin S = 0. Thus, only dHb is paramagnetic, whereas oHb is diamagnetic. dHb paramagnetism causes a linear increase in the magnetic susceptibility of blood, and also has varying effects on the relaxation rates of blood and surrounding tissue.

The paramagnetism of dHb is exploited in a variety of MR-based techniques to quantify Yv and

CMRO2, as summarized in Table 1.1 and detailed in the sections that follow. These methods can

be categorized based on the tissue compartment in which the effects of dHb are modeled (extravascular vs. intravascular) and the MR contrast method used to quantify these effects (T2*,

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measurements are made on a global, regional, or voxel-wise basis, and the resultant tradeoff between their spatial and temporal resolutions.

Signal Origin Contrast Spatial Res. Method (Ref) Yv Temp. Res. Simul. CBF?

Extravascular T2* Voxel-wise Calibrated BOLD (59) 0:03 YES

T2’ Voxel-wise qBOLD (60) 8:30 NO

Intravascular T2 Global TRUST (61) 0:24 NO

Regional TRU-PC (62) 2:50 NO

Projection-based T2 (63) 0:15 NO

Voxel-wise QUIXOTIC (64) 27:30 NO

VSEAN (65) 6:18 NO

Susceptibility Global OxFlow (66) 0:28 YES

Regional Quantitative Venography (67) 15:42 NO

Voxel-wise Zhang et al. (68) 60:00 NO

Table 1.1: Summary of MR-based Yv/CMRO2 quantification methods and their

respective features. ‘Signal origin’ is the tissue compartment in which signal used for Yv quantification is modeled. ‘Contrast’ is the MRI contrast mechanism used

in the Yv quantification model. ‘Spatial Res.’ is the spatial resolution for Yv

quantification in minutes:seconds. ‘Method (Ref)’ is the name/acronym or authors associated with the published method and the most relevant citation. ‘Yv Temp.

Res.’ is the reported approximate temporal resolution for a single Yv

measurement (ignoring any requisite planning or calibration scans). ‘Simul. CBF?’ denotes whether the method pulse sequence measures CBF simultaneously with Yv.