Charles S. Springer

Magnetic field and tissue dependencies of human brain longitudinal 1H2O relaxation in vivo

Brain water proton (1H2O) longitudinal relaxation time constants (T1) were obtained from three healthy individuals at magnetic field strengths (B0) of 0.2 Tesla (T), 1.0T, 1.5T, 4.0T, and 7.0T. A 5‐mm midventricular axial slice was sampled using a modified Look‐Locker technique with 1.5 mm in‐plane resolution, and 32 time points post‐adiabatic inversion. The results confirmed that for most brain tissues, T1 values increased by more than a factor of 3 between 0.2T and 7T, and over this range were well fitted by T1 (s) = 0.583(B0)0.382, T1(s) = 0.857(B0)0.376, and T1(s) = 1.35(B0)0.340 for white matter (WM), internal GM, and blood 1H2O, respectively. The ventricular cerebrospinal fluid (CSF) 1H2O T1 value did not change with B0, and its average value (standard deviation (SD)) across subjects and magnetic fields was 4.3 (±0.2) s. The tissue 1/T1 values at each field were well correlated with the macromolecular mass fraction, and to a lesser extent tissue iron content. The field‐dependent increases in 1H2O T1 values more than offset the well‐known decrease in typical MRI contrast reagent (CR) relaxivity, and simulations predict that this leads to lower CR concentration detection thresholds with increased magnetic field. Magn Reson Med 57:308–318, 2007.

Variation of the relaxographic “shutter‐speed” for transcytolemmal water exchange affects the CR bolus‐tracking curve shape

Contrast reagents (CRs) may enter the tissue interstitium for a period after a vascular bolus injection. As the amount of interstitial CR increases, the longitudinal relaxographic NMR “shutter‐speed” (T–1) for the equilibrium transcytolemmal water exchange process increases. The quantity T–1 is given by |r1o[CRo] + R1o0 – R1i| (where r1o and [CRo] represent the interstitial (extracellular) CR relaxivity and concentration, respectively, and R1o0 and R1i are the extra‐ and intracellular 1H2O relaxation rate constants, respectively, in the absence of exchange). The increase of T–1 with [CRo] causes the kinetics of the water exchange equilibrium to appear to decrease. Here, analytical theory for two‐site‐exchange processes is combined with that for pharmacokinetic CR delivery, extraction, and distribution in a method termed BOLus Enhanced Relaxation Overview (BOLERO©). The shutter‐speed effect alters the shape of the bolus‐tracking (B‐T) time‐course. It is shown that this is mostly accounted for by the inclusion of only one additional parameter, which measures the mean intracellular lifetime of a water molecule. Simulated and real data demonstrate that the effect of shutter‐speed variation on pharmacokinetic parameters can be very significant: neglecting this effect can lead to an underestimation of the parameter values by 50%. This phenomenon can be heterogeneous. Within a tiny gliosarcoma implanted in the rat brain, the interstitial CR in the tumor core never rises to a level sufficient to cause apparent slowing of the exchange process. However, within the few microns needed to reach the proliferating rim, this occurs to a significant degree. Thus, even relative pharmacokinetic quantities can be incorrectly represented in a parametric map that neglects this effect. The BOLERO analysis shows promise for in vivo vascular phenotyping in pathophysiology. It also includes a provision for approximating the separation of the perfusion and permeability contributions to CR extravasation. Magn Reson Med 50:1151–1169, 2003.

Equilibrium Water Exchange Between the Intra- and Extracellular Spaces of Mammalian Brain

This report describes the measurement of water preexchange lifetimes and intra/extracellular content in intact, functioning mammalian brain. Intra‐ and extracellular water magnetic resonance (MR) signals from rat brain in vivo were quantitatively resolved in the longitudinal relaxation domain following administration of an MR relaxation agent into the extracellular space. The estimated intracellular water content fraction was 81% ± 8%, and the intra‐ to extracellular exchange rate constant was 1.81 ± 0.89 s–1 (mean ± SD, N = 9), corresponding to an intracellular water preexchange lifetime of ∼550 ms. These results provide a temporal framework for anticipating the water exchange regime (fast, intermediate, or slow) underlying a variety of compartment‐sensitive measurements. The method also supplies a means by which to evaluate membrane water permeability and intra/extracellular water content serially in intact tissue. The data are obtained in an imaging mode that permits detection of regional variations in these parameters. Magn Reson Med 50:493–499, 2003.

Aqueous shift reagents for high-resolution cationic nuclear magnetic resonance. III. Dy(TTHA)3−, Tm(TTHA)3−, and Tm(PPP)27−

Abstract The isotropic hyperfine shifts induced in the 23Na+ resonance by the shift reagents Dy(DPA)33−, Dy(NTA)23−, Dy(PPP)27−, Tm(PPP)27−, Dy(TTHA)3−, and Tm(TTHA)3− are compared under similar conditions. The last three are introduced as shift reagents in this study. The Dy(PPP)37− and Tm(PPP)27− ions cause the largest shifts. However, these shifts are very pH dependent and are readily decreased by the presence of Ca2+ or Mg2+ ions. The Dy(TTHA)3− and Tm(TTHA)3− ions produce quite large shifts which are independent of pH (between 5.5 and 12) and less sensitive to Ca2+ and Mg2+. For a given chelate ligand, the analogous Dy(III) and Tm(III) complexes cause hyperfine shifts in opposite directions. However, while the Dy(PPP)27− ion induces an upfield shift, the Dy(TTHA)3− ion induces a downfield shift. Some data on shifts of the 25Mg2+, 39K+, and 87Rb+ resonances are also presented. In addition the 14N peak of NH4+ can be quite effectively shifted.

A unified magnetic resonance imaging pharmacokinetic theory: Intravascular and extracellular contrast reagents

A fundamental reworking of pharmacokinetic theory for the use of contrast reagents (CRs) in T1‐weighted MRI studies is presented. Unlike the standard model in common use, this derivation starts with the quantities measured, the intravascular, interstitial, and intracellular 1H2O signals. The time dependences of CR concentrations are introduced as perturbations of the T1 values of these. Since there is an explicit accounting for the equilibrium exchange of water molecules between tissue compartments, the approach here is a new (second) generation of the shutter‐speed model (S2M). When the first‐order rate constant measuring CR extravasation (Ktrans) is of sufficient magnitude, simulations presented here confirm that neglect of plasma CR, a feature of the first generation of S2M, is a valid approximation. The second S2M generation (S2M2) also automatically accommodates excursions of either or both of the two major equilibrium water exchange systems (transendothelial and transcytolemmal) into any or all possible exchange conditions, from their fast‐exchange limits to their slow‐exchange limits. This can happen not because the exchange kinetics themselves vary during the isothermal CR passage, but because the MR shutter speeds for these processes can vary. When Ktrans is sufficiently small, the S2M2 also naturally accounts for the hyperfine blood agent level dependent (BALD) effect that is easily detectable at high magnetic field. This can be seen for virtually all CRs in normal brain tissue and for virtually all tissues with sufficiently intravascular CRs. Thus, S2M2 represents a unified pharmacokinetic theory for intravascular and extracellular T1 contrast reagents. Magn Reson Med, 2005.

23Na and 39K nuclear magnetic resonance studies of perfused rat hearts. Discrimination of intra- and extracellular ions using a shift reagent

High-resolution 23Na and 39K nuclear magnetic resonance (NMR) spectra of perfused, beating rat hearts have been obtained in the absence and presence of the downfield shift reagent Dy(TTHA)3- in the perfusing medium. Evidence indicates that Dy(TTHA)3- enters essentially all extracellular spaces but does not enter intracellular spaces. It can thus be used to discriminate the resonances of the ions in these spaces. Experiments supporting this conclusion include interventions that inhibit the Na+/K+ pump such as the inclusion of ouabain in and the exclusion of K+ from the perfusing medium. In each of these experiments, a peak corresponding to intracellular sodium increased in intensity. In the latter experiment, the increase was reversed when the concentration of K+ in the perfusing medium was returned to normal. When the concentration of Ca2+ in the perfusing medium was also returned to normal, the previously quiescent heart resumed beating. In the beating heart where the Na+/K+ pump was not inhibited, the intensity of the intracellular Na+ resonance was less than 20% of that expected. Although the data are more sparse, the NMR visibility of the intracellular K+ signal appears to be no more than 20%.

Simultaneous measurement of arterial input function and tumor pharmacokinetics in mice by dynamic contrast enhanced imaging: Effects of transcytolemmal water exchange

A noninvasive technique for simultaneous measurement of the arterial input function (AIF) for gadodiamide (Omniscan) and its uptake in tumor was demonstrated in mice. Implantation of a tumor at a suitable location enabled its visualization in a cardiac short axis image. Sets of gated, low‐resolution saturation recovery images were acquired from each of five tumor‐bearing mice following intravenous administration of a bolus of contrast agent (CA). The AIF was extracted from the signal intensity changes in left ventricular blood using literature values of the CA relaxivity and a precontrast T1 map. The time‐dependent 1H2O relaxation rate constant (R1 = 1/T1) in the tumor was modeled using the BOLus Enhanced Relaxation Overview (BOLERO) method in two modes regarding the equilibrium transcytolemmal water exchange system: 1) constraining it exclusively to the fast exchange limit (FXL) (the conventional assumption), and 2) allowing its transient departure from FXL and access to the fast exchange regime (FXR), thus designated FXL/FXR. The FXL/FXR analysis yielded better fittings than the FXL‐constrained analysis for data from the tumor rims, whereas the results based on the two modes were indistinguishable for data from the tumor cores. For the tumor rims, the values of Ktrans (the rate constant for CA transfer from the vasculature to the interstitium) and ve (volume fraction of the tissue extracellular and extravascular space) returned from FXL/FXR analysis are consistently greater than those from the FXL‐constrained analysis by a factor of 1.5 or more corresponding to a CA dose of 0.05 mmole/kg. Magn Reson Med 52:248–257, 2004.

Effects of Equilibrium Exchange on Diffusion-Weighted NMR Signals: The Diffusigraphic "Shutter-Speed"

A general picture is presented of the implications for diffusion‐weighted NMR signals of the parsimonious two‐site‐exchange (2SX) paradigm. In particular, it is shown that the diffusigraphic “shutter‐speed,” τ−1 ≡ |q2(DA – DB)|, is a useful concept. The “wave‐number” q has its standard definition (given in the text), and DA and DB are the apparent diffusion coefficients (ADCs) of molecules in the two “sites,” A and B, if there is no exchange between them. At low gradient strengths (center of q‐space), τ−1 is less than rate constants for intercompartmental water molecule exchange in most tissue cases. Thus, the exchange reaction appears fast. However, q is increased during the course of most experiments and, as it is, the shutter‐speed becomes “faster” and the exchange reaction, the kinetics of which do not change, appears to slow down. This causes a multiexponential behavior in the diffusion‐weighting dimension, b, which also has its standard definition. This picture is found to be in substantial agreement with a number of different experimental observations. It is applied here to literature 1H2O data from a yeast cell suspension and from the human and the rat brain. Since the equilibrium transcytolemmal water exchange reaction appears to be in the fast‐exchange‐limit at small b, the initial slope represents the weighted‐average of the ADCs of intra‐ and extracellular water. Of course, in tissue the former is in the significant majority. Furthermore, a consideration of reasonable values for the other 2SX parameters suggests that, for resting brain tissue, the intracellular water ADC may be larger than the extracellular water ADC. There are some independent inferences of this, which would have ramifications for many applications of diffusion‐weighted MRI. Magn Reson Med 49:450–458, 2003. Published 2003 Wiley‐Liss, Inc.

The magnetic resonance shutter speed discriminates vascular properties of malignant and benign breast tumors in vivo

The pharmacokinetic analysis of dynamic-contrast-enhanced (DCE) MRI data yields Ktrans and kep, two parameters independently measuring the capillary wall contrast reagent transfer rate. The almost universally used standard model (SM) embeds the implicit assumption that equilibrium transcytolemmal water exchange is effectively infinitely fast. In analyses of routine DCE-MRI data from 22 patients with suspicious breast lesions initially ruled positive by institutional screening protocols, the SM Ktrans values for benign and malignant lesions exhibit considerable overlap. A form of the shutter-speed model (SSM), which allows for finite exchange kinetics, agrees with the SM Ktrans value for each of the 15 benign lesions. However, it reveals that the SM underestimates Ktrans for each of the seven malignant tumors in this population. The fact that this phenomenon is unique to malignant tumors allows their complete discrimination from the benign lesions, as validated by comparison with gold-standard pathology analyses of subsequent biopsy tissue samples. Likewise, the SM overestimates kep, particularly for the benign tumors. Thus, incorporation of the SSM into the screening protocols would have precluded all 68% of the biopsy/pathology procedures that yielded benign findings. The SM/SSM difference is well understood from molecular first principles.

Three-compartment T1 relaxation model for intracellular paramagnetic contrast agents

The goal of this work was to elaborate a model describing the effective longitudinal relaxation rate constant R1 for 1H2O in three cellular compartments experiencing possible equilibrium water exchange, and to apply this model to explain the effective R1 dependence on the overall concentration of a cell‐internalized Gd3+‐based contrast agent (CA). The model voxel comprises three compartments representing extracellular, cytoplasmic, and vesicular (e.g., endosomal, lysosomal) subcellular spaces. Relaxation parameters were simulated using a modified Bloch–McConnell equation including magnetization exchange between the three compartments. With the model, several possible scenarios for internalized CA distribution were evaluated. Relaxation parameters were calculated for contrast agent restricted to the cytoplasmic or vesicular compartments. The size or the number of CA‐loaded vesicles was varied. The simulated data were then separately fitted with empirical mono‐ and biexponential inversion recovery expressions. The voxel CA‐concentration dependencies of R1 can be used to qualitatively and quantitatively understand a number of different experimental observations reported in the literature. Most important, the simulations reproduced the relaxivity “quenching” for cell‐internalized contrast agent that has been observed. Magn Reson Med, 2009.