Trans-membrane water transport and co-transport is ubiquitous in cell biology. Integrated over all the cell’s H2O transporters and co-transporters, the rate of homeostatic, bidirectional trans-cytolemmal water “exchange” is synchronized with the metabolic rate of the crucial Na+,K+-ATPase (NKA) enzyme: the active trans-membrane water cycling (AWC) phenomenon. Is AWC futile, or is it consequential? Conservatively representative literature metabolomic and proteinomic results enable comprehensive free energy (ΔG) calculations for the many transport reactions with known water stoichiometries. Including established intracellular pressure (Pi) magnitudes, these reveal an outward trans-membrane H2O barochemical ΔG gradient comparable to that of the well-known inward Na+ electrochemical ΔG gradient. For most co-influxers, these two gradients are finely balanced to maintain intracellular metabolite concentration values near their consuming enzyme Michaelis constants. Our analyses include glucose, glutamate−, gamma-aminobutyric acid (GABA), and lactate− transporters. 2

The phenomenon of active trans-membrane water cycling (AWC) has emerged in little over a decade. Here, we consider H2O transport across cell membranes from the origins of its study. Historically, trans-membrane water transport processes were classified into: A) compensating bidirectional fluxes ("exchange"), and B) unidirectional flux ("net flow") categories. Recent literature molecular structure determinations and molecular dynamic (MD) simulations indicate probably all the many different hydrophilic substrate membrane co-transporters have membrane-spanning hydrophilic pathways and co-transport water along with their substrates, and that they individually catalyze category A and/or B water flux processes, although usually not simultaneously. The AWC name signifies that, integrated over the all the cell's co-transporters, the rate of homeostatic, bidirectional trans-cytolemmal water exchange (category A) is synchronized with the metabolic rate of the crucial Na+,K+-ATPase (NKA) enzyme. A literature survey indicates the stoichiometric (category B) water/substrate ratios of individual co-transporters are often very large. The MD simulations also suggest how different co-transporter reactions can be kinetically coupled molecularly. Is this (Na+,K+-ATPase rate-synchronized) cycling futile, or is it consequential? Conservatively representative literature metabolomic and proteinomic results enable comprehensive free energy analyses of the many transport reactions with known water stoichiometries. Free energy calculations, using literature intracellular pressure (Pi) values reveals there is an outward trans-membrane H2O barochemical gradient of magnitude comparable to that of the well-known inward Na+ electrochemical gradient. For most co-influxers, these gradients are finely balanced to maintain intracellular metabolite concentration values near their consuming enzyme Michaelis constants. The thermodynamic analyses include glucose, glutamate-, gamma-aminobutyric acid (GABA), and lactate- transporters. 2%-4% Pi alterations can lead to disastrous concentration levels. For the neurotransmitters glutamate- and GABA, very small astrocytic Pi changes can allow/disallow synaptic transmission. Unlike the Na+ and K+ electrochemical steady-states, the H2O barochemical steady-state is in (or near) chemical equilibrium. The analyses show why the presence of aquaporins (AQPs) does not dissipate the trans-membrane pressure gradient. A feedback loop inherent in the opposing Na+ electrochemical and H2O barochemical gradients regulates AQP-catalyzed water flux as an integral AWC aspect. These results also require a re-consideration of the underlying nature of Pi. Active trans-membrane water cycling is not futile, but is inherent to the cell's "NKA system" - a new, fundamental aspect of biology.

Evidence mounts that the steady‐state cellular water efflux (unidirectional) first‐order rate constant (k io [s −1 ]) magnitude reflects the ongoing, cellular metabolic rate of the cytolemmal Na + , K + ‐ATPase (NKA), c MR NKA (pmol [ATP consumed by NKA]/s/cell), perhaps biology's most vital enzyme. Optimal 1 H 2 O MR k io determinations require paramagnetic contrast agents (CAs) in model systems. However, results suggest that the homeostatic metabolic k io biomarker magnitude in vivo is often too large to be reached with allowable or possible CA living tissue distributions. Thus, we seek a noninvasive (CA‐free) method to determine k io in vivo. Because membrane water permeability has long been considered important in tissue water diffusion, we turn to the well‐known diffusion‐weighted MRI (DWI) modality. To analyze the diffusion tensor magnitude, we use a parsimoniously primitive model featuring Monte Carlo simulations of water diffusion in virtual ensembles comprising water‐filled and ‐immersed randomly sized/shaped contracted Voronoi cells. We find this requires two additional, cytometric properties: the mean cell volume (V [pL]) and the cell number density ( ρ [cells/μL]), important biomarkers in their own right. We call this approach metabolic activity diffusion imaging (MADI). We simulate water molecule displacements and transverse MR signal decays covering the entirety of b‐space from pure water ( ρ = V = 0; k io undefined; diffusion coefficient, D 0 ) to zero diffusion. The MADI model confirms that, in compartmented spaces with semipermeable boundaries, diffusion cannot be described as Gaussian: the nanoscopic D (D n ) is diffusion time‐dependent, a manifestation of the “diffusion dispersion”. When the “well‐mixed” (steady‐state) condition is reached, diffusion becomes limited, mainly by the probabilities of (1) encountering ( ρ , V), and (2) permeating (k io ) cytoplasmic membranes, and less so by D n magnitudes. Importantly, for spaces with large area/volume (A/V; claustrophobia) ratios, this can happen in less than a millisecond. The model matches literature experimental data well, with implications for DWI interpretations.

The relationship between the classic magnetic resonance density matrix relaxation theories of Bloch and Hubbard and the modern Lindbladian master equation methods are explored. These classic theories are in full agreement with the latest results obtained by the modern methods. A careful scrutiny shows that this also holds true for Redfield's later treatment, offered in 1965. The early contributions of Bloch and Hubbard to rotating-frame relaxation theory are also highlighted. Taken together, these seminal efforts of Bloch and Hubbard can enjoy a new birth of contemporary relevance in magnetic resonance.

The relationship between the classic magnetic resonance density matrix relaxation theories of Bloch and Hubbard, and the modern Lindbladian master equation methods are explored. These classic theories are in full agreement with the latest results obtained by the modern methods. A careful scrutiny shows that this also holds true for Redfields later treatment, offered in 1965. The early contributions of Bloch and Hubbard to rotating frame relaxation theory are also highlighted. Taken together, these seminal efforts of Bloch and Hubbard can enjoy a new birth of contemporary relevance in magnetic resonance.

T 1ρ relaxation imaging is a quantitative imaging technique that has been used to assess cartilage integrity, liver fibrosis, tumors, cardiac infarction, and Alzheimer's disease. T 1 , T 2 , and T 1ρ relaxation time constants have each demonstrated different degrees of sensitivity to several markers of fibrosis and inflammation, allowing for a potential multi‐parametric approach to tissue quantification. Traditional magnetic resonance fingerprinting (MRF) has been shown to provide quick, quantitative mapping of T 1 and T 2 relaxation time constants. In this study, T 1ρ relaxation is added to the MRF framework using spin lock preparations. An MRF sequence involving an RF‐spoiled sequence with T R , flip angle, T 1ρ , and T 2 preparation variation is described. The sequence is then calibrated against conventional T 1 , T 2 , and T 1ρ relaxation mapping techniques in agar phantoms and the abdomens of four healthy volunteers. Strong intraclass correlation coefficients (ICC > 0.9) were found between conventional and MRF sequences in phantoms and also in healthy volunteers (ICC > 0.8). The highest ICC correlation values were seen in T 1 , followed by T 1ρ and then T 2 . In this study, T 1ρ relaxation has been incorporated into the MRF framework by using spin lock preparations, while still fitting for T 1 and T 2 relaxation time constants. The acquisition of these parameters within a single breath hold in the abdomen alleviates the issues of movement between breath holds in conventional techniques.

A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging.

A thorough exposition and analysis of the role of the Lorentz sphere in magnetic resonance is presented from the fundamental standpoint of macroscopic magnetostatics. The analysis will be useful to those interested in understanding susceptibility and chemical shift contributions to frequency shifts in magnetic resonance. Though the topic is mature, recent research on white matter shifts in the brain promotes the notion of replacing the Lorentz sphere with a generalized Lorentzian cylinder, and has put into question the long standing spherical approach when elongated structures are present. The cavity shape issue can be resolved by applying Helmholtz's theorem, which can be expressed in a differential and an integral formulation. The general validity of the Lorentz sphere for any situation is confirmed. Furthermore, a clear exposition of the "generalized approach" is offered, using the language of Lorentz's theory. With the rehabilitation of the Lorentz sphere settled, one must consider alternative contributions to white matter shifts and a likely candidate is the effect of molecular environment on chemical shifts.

The 1H2O NMR Larmor frequency and R2* relaxation rate constant in white matter tissue show dependencies on the sample orientation in the static magnetic field (B0) (1, 2) that have been attributed in part to sub-voxel magnetic structure associated with so called ‘susceptibility inclusions’ (atoms, molecules or compounds with differing magnetic susceptibility) (3). A number of publications (3–5), the most recent of which is published in this journal (5), have introduced the so-called “Generalized Lorentzian Approach” (GLA) to offer a theoretical basis for this orientation dependence, in particular the frequency shift Δf in major white matter fiber bundles that may have contributions from inclusions with both elongated and isotropic (rotationally symmetric) geometry. Here it is argued that, although sub-voxel magnetic structure can significantly affect frequency and R2*, the GLA per-se is not needed to explain the observations, that its underlying concept is problematic, and its applicability to white matter rather limited. These concerns are elaborated upon in the following. Prior to the observations in white matter, the effect of an anisotropic magnetic structure (i.e., a bulk magnetization that has rotational asymmetry) on the NMR resonance frequency has been studied at various scales, e.g., the shape of the solvent volume constrained in sample tubes (e.g., (6, 7)), and subvoxel structure in trabecular bone (8), lung alveoli (9), red blood cells (10, 11) and muscle fibers (12). Because for biological tissues, the spatial magnetic susceptibility distribution is generally complex and not precisely known, modeling its effects requires some simplification. An established approach for this is to consider a (water hydrogen) proton’s average magnetic environment, which may be spatially non-uniform. However, when averaging over the many other protons and structural details in a voxel, the average environment can be approximated by incorporating an immediate region (or set of regions) with uniform continous magnetization (13). The aggregate near-field effects of the discrete magnetic dipoles in the proton’s immediate environment can be shown to be negligibly small by invoking the ‘sphere of Lorentz (SL)’ concept (see (6, 13) and references therein), whereas the calculation of the effects of the continuum magnetization on the proton frequency is facilitated by the use of demagnetization factors specific for the shapes of the boundaries between regions (e.g., (14, 15), for review see (13, 16)). For example, the average magnetic environment of a water hydrogen proton in white matter, and specifically the excised optic nerve studied in (5), may be approximated by a spherical, mostly water pocket with magnetic susceptibility χw centered on the proton, which is embedded in an elongated (prolate) ellipsoid with uniform magnetic susceptibility χ1, surrounded by nerve tissue with magnetic susceptibility χ2 and suspended in a liquid with magnetic susceptibility χe, with the angle α (degrees) between the ellipsoid’s major axis and the B0 direction [see Figure; Cf. Figure 7 and accompanying text in (13)]. The difference Δω in average 1H2O frequency within and outside the nerve then follows from Δff=13(χ1-χe)-12sin2α(χ1-χe), in analogy with previous results for red blood cells and muscle fibers (7, 11, 12), and consistent with numerical simulations (17). The first term derives from the asserted spherical boundary separating nearby water (and other molecule) electron cloud dipoles from magnetic continuum both inside and outside the nerves, and the spherical boundaries between magnetization areas of water without and with ‘isotropic’ inclusions (volumes with χw and χ1 inside the nerve and χw and χe outside the nerve); the sin2 α term results from the elongated ellipsoidal boundaries between areas without and with oriented, elongated inclusions (volumes with susceptibilities χ1, χ2, and χe). This resembles the results found with the GLA, e.g., Eq. [5] of (5), if one considers that χ1 contains the contributions from isotropic inclusions (with magnetic susceptibility χiso in Eq. [5]). What then, conceptually and computationally, distinguishes these approaches? The GLA applied in (5) appears to assume that the average proton is surrounded by two separately considered distributions of spherical and elongated susceptibility inclusions, whose near-field effects on the proton frequency are further assumed to be approximately zero when inclusions are randomly distributed and a proper averaging volume is used. The authors of (5) then make the point that for this to be the case, the ‘isotropic’ inclusions require a spherical averaging volume (in analogy with the SL), and the elongated inclusions require an elongated ellipsoidal averaging volume. Apart from the fact that the necessity of the latter is not explicitly demonstrated, this approach implicitly assumes infinitely small volume fractions of the two inclusion types and considers their distributions to be independent. Finite inclusion volumes, as may be the case in white matter, may affect not only the randomness of their distribution, but also restrict each type of inclusion to the space that is not occupied by inclusions of the other type. For example, for elongated inclusions with volume fraction VL, the local concentration of ‘isotropic’ inclusions increases by 1/(1−VL). Thus, χ1 above is equivalent to χiso/(1− VL), and this value should replace χiso in Eq. [5] of (5), but not in Eq. [4] of (5). Stated differently, χiso in Eq. [5] of (5) is the contribution of ‘isotropic’ inclusions to the average susceptibility of the whole nerve compartment, whereas the model described above yields a dependence on χ1, [and thus χiso/(1− VL)], the susceptibility of ‘isotropic’ inclusions within the volume that they occupy. Having found that GLA is unnecessary and, in the case of finite inclusion volume fractions, leads to systematic errors, what about the primary rationale for using the GLA, i.e, the presumed presence of elongated susceptibility inclusions in nerve tissue? Luo et al. argue that the different magnitudes of the sin2α dependence outside and within the nerve (Eqs. [4] and [5] of (5), respectively) is evidence for such presence. However, accumulating evidence suggests the magnetic susceptibility of nerve tissue itself is anisotropic (18–21). This obviates the need to assert prolate inclusions. For example, for the simple case of a uniform (but anisotropic) susceptibility (with χ⊥ and χ|| the magnetic susceptibilities along and perpendicular to the fiber, respectively), the standard SL approach leads to coefficients for the sin2α dependences outside and within the nerve being {χ⊥2-χe2} and {χe2-χ⊥+2χ||6} respectively [replacing {χiso+χL2-χe2} and {χe2-χiso2} in Eqs. [4] and [5] of (5)]. Note that our derivation results in different slope magnitudes, without requiring elongated inclusions, the GLA, or even the non-spherical demagnetization factor inside the nerve as used in Fig. 1. Thus, in the presence of anisotropy, the primary contention in (5) that “the frequency observed in the optic nerve ……is inconsistent with Lorentzian sphere approximation” appears unwarranted and non-parsimonious. FIGURE Model of average water environment in optic nerve with both oriented and elongated and isotropic magnetic susceptibility inclusions. Because of correlations between the space occupied by water space and the distribution of elongated inclusions, water ...

The progression toward small sample volumes for use in high-resolution liquids NMR, solid-state NMR, and MR microimaging is outlined, with an emphasis on the design issues pertinent to scaling sample volumes down to microliters or nanoliters. Distinct advantages of the use of very small sample volumes are mass sensitivity, RF field strength, and MAS spinning speeds. Keywords: microprobes; microcoils; probe technology

A statistical mechanical perturbation theory for the equilibrium properties of nematic liquid crystals is presented in which the reference potential function is non-spherical and consists of the short-range rapidly varying repulsive part of the pair potential. Calculations are made for a trial system in which molecules are assumed to interact via a pair potential which has repulsive part represented by a repulsion between hard spherocylinders and an attractive part which is function of only r 12 and Ω12 (r 12 is the center of mass distance and Ω12 the relative orientation between the two molecules), and represent approximately the interaction arising from dispersion interaction between two asymmetric molecules. Assuming that the pair correlation function g(r l2, Ω12) for a fluid of hard spherocylinders scales as g[r 12/D(Ω12] where D(Ω12) is angle-dependent range parameter the properties of the reference system and the first order perturbation term are evaluated. The agreement found between the calculated values of the compressibility factor for isotropic phase of fluids of hard spherocylinders and the values obtained from machine simulations is excellent. The functional form and the density dependence of the effective one-body orientational potential ψ(Ω) is discussed in detail. It is shown that the nematic-isotropic transition properties are very sensitive to the form of ψ(Ω). The biaxial symmetry of the low temperature smectic phase of N-(4-n-hexyloxybenzylidene)-4-n-hexylaniline is demonstrated through observation of the deuterium NMR resonance of CDCl3 probe molecules dissolved in this phase. The biaxial ordering is revealed in the observed powder spectrum as well as in a complete rotation study of a uniformly aligned sample.

The target field method of designing gradient coils is extended to the case where the gradient producing currents lie on cylinders of a general orientation with respect to the polarizing magnetic field. This provides a general approach for designing coils that require unusual sample geometries such as those required for magic angle spinning (MAS) applications. A detailed example of a magic angle gradient coil set for MAS is given.

A general-purpose method for the simulation of a spin-12 response to a multipulse train is presented. This is used to calculate the results of tune-up sequences often used in spectrometer calibration and characterization. The method is capable of including effects arising from RF and magnetic field inhomogeneities, finite amplitude and duration of pulses, and spin relaxation for T1 = T2. The pulses may also be of arbitrary shape in amplitude and phase, allowing for the inclusion of phase glitch and finite rise-time effects. Results are presented for the usual tune-up sequences and in particular for the Haubenreisser-Schnabel sequence for tuning the transmitter phase. The effects of symmetric and asymmetric phase glitch, field inhomogeneities, etc., are illustrated by Fourier transforming the data array. This procedure produces an antiphase doublet with a splitting proportional to the transmitter phase. The accuracy of this technique in measuring small-angle phase shifts is discussed.

Quadrature-corrected data for the solid-state homonuclear decoupling sequences MREV8, BR24, and CORY24 are obtained, using a new method that combines experiments from a set of properly chosen preparation pulses. This method is compared to the usual approach that requires sampling in more than one data window per cycle. An overview of the data available in all large windows for these sequences is presented.