Fast Exchange Limit Research Articles

NMR Spin Relaxation Theory of Biomolecules Undergoing Highly Asymmetric Exchange with Large Interaction Partners

The transient interactions of proteins and other molecules with much larger structures, such as synthetic or biological nanoparticles, lead to certain types of enhanced nuclear magnetic resonance (NMR) spin relaxation effects, which can be accurately measured by multidimensional solution NMR techniques. These relaxation effects provide new information about the nanostructures and the protein, their interactions, internal dynamics, and associated kinetic and thermodynamic parameters, such as exchange rates and populations. Although theoretical treatments exist that cover either the fast or slow exchange limits, a theoretical treatment that applies to all practically relevant exchange processes is still missing. A unified theoretical framework is presented for this purpose based on a stochastic Liouville equation (SLE). It covers nuclear spin dynamics, overall rotational diffusion of both the protein and the nanostructure, the exchange process between a free state and a bound state, and internal protein dynamics. Although the numerical implementation of the SLE typically involves large matrices, it is shown here that it is computationally still tractable for situations relevant in practice. Application of the theory demonstrates how transverse relaxation is substantially impacted by the kinetics of binding on a wide range of exchange timescales. It is further shown that when exchange occurs on the appropriate timescale, transverse relaxation is able to report on internal dynamics far slower than observable by traditional transverse relaxation experiments. The SLE will allow the realistic and quantitative interpretation of experimental NMR data reporting about transient protein-nanoparticle interactions, thereby providing a powerful tool for the characterization of protein dynamics modes on a vast range of timescales including motions that may be functionally relevant.

Solid-State NMR Spectroscopy Study of Molecular Dynamics of Pyridine 1-Oxide Encapsulated in p-tert-Butylcalix[4]arene.

The mixture of guests 25% pyridine 1-oxide (PNO) and 75% nitrobenzene (NB) encapsulated in a host cavity of p-tert-butylcalix[4]arene (p-tBC) is a suitable system for the study of intermolecular weak interactions, and the preferred orientation of the guest molecules within the host was derived. Variable temperature deuterium nuclear magnetic resonance line shape and spin-lattice relaxation studies were performed on three samples of 25% PNO as a guest (selectively and entirely deuterated) with 75% NB encapsulated in p-tBC as a host system. It is found that the PNO molecular motion supports the two-site jump model and is highly mobile throughout the temperature range from -130 to 20 °C. PNO reorients about its C2 molecular symmetry axis followed by reorientation around the compound's C4 axis of symmetry of a host. Calculation showed that besides precise molecular jumping, the guest also experiences the vibrational motion with a variation angle dispute about 15°. The correlation times for the molecular guest motion and two-dimensional exchange spectroscopy confirmed a fast exchange limit inside the cavity. These molecular dynamics follow an Arrhenius behavior motion from which the small activation energy is delivered that strongly suggests a relatively weak intermolecular interaction between the host and guest species. PNO has definite dipole orientational motion in the cavity where its aromatic covalent bond structure minimizes contact with the host p-tert-butyl groups. Experimentally found, PNO-d5 deuterons in the single crystal collapse at 55 and 125° at ambient temperature. The first splitting of 124 kHz belongs to D3(D5), the second splitting of 100 kHz belongs to D2(D6), and the last splitting of 52 kHz belongs to D4 of the ring of PNO inside the p-tBC.

Shutter-speed dynamic contrast-enhanced MRI: Is it fit for purpose?

To test the ability of shutter-speed dynamic contrast-enhanced (DCE) MRI to estimate water exchange (WX) using simulations and assess its performance in clinical case studies of malignant and benign breast tumors. Data were simulated using a 1-compartment tracer kinetic (TK) model combined with a 2-pool WX model (2PX) and with a 2-compartment TK model. Typical DCE-MRI acquisition parameters were used with both WX-sensitive (8°) and -insensitive (25°) flip angles. Clinical data were obtained from patients with malignant and benign breast tumors. Data were fitted using a 2-compartment TK model and a 1-compartment TK model combined with 4 WX models: fast exchange limit (FXL), no exchange, 2PX, and shutter-speed. Fits to the 1-compartment simulated data were excellent, but estimates of WX obtained using the 2PX and shutter-speed models were poor. One-compartment TK model fits to the clinical malignant tumor data were bad, except for the shutter-speed model. However, that overestimated TK parameters compared to the best-fit 2-compartment TK model, which predicted a significant blood volume and leaky capillaries (1 tracer compartment is insufficient, 2 are necessary). All models produced excellent fits to the clinical benign tumor data with little variation between parameter estimates (1 tracer compartment is sufficient). The 2PX and shutter-speed models were unable to estimate WX from the DCE-MRI data. A good fit to malignant tumor data using the shutter-speed model was not explained by WX, but the choice of an inappropriate TK model leading to distorted parameter estimates.

Towards interpretation of intermolecular paramagnetic relaxation enhancement outside the fast exchange limit.

In an exchanging system between major and minor species, the transverse paramagnetic relaxation enhancement rate observed on the resonances of the major species (Γ 2 (app) ) is dependent upon the exchange regime between the species. Quantitative analysis of PRE data in such systems typically assumes that the overall exchange rate k ex between the species is fast on the PRE time scale (k ex≫Γ2). Recently, we have characterized the kinetics of binding of the model protein ubiquitin to large (LUV) and small (SUV) unilamellar lipid-based nanoparticles or liposomes (Ceccon A, Tugarinov V, Bax A, Clore GM (2016). J Am Chem Soc 138:5789-5792). Building upon these results and taking advantage of a strong paramagnetic agent with an isotropic g-tensor, Gd(3+), we were able to measure intermolecular methyl carbon and proton PREs between paramagnetically-tagged liposomes and ubiquitin. In the limit of fast exchange (k ex≫Γ2) the ratio of the apparent proton to carbon methyl PREs, ((1)Hm-Γ 2 (app) )/((13)Cm-Γ 2 (app) ), is equal to the square of the ratio of the gyromagnetic ratios of the two nuclei, (γΗ/γC)(2). However, outside the fast exchange regime, under intermediate exchange conditions (e.g. when Γ2 is comparable in magnitude to k ex) the ((1)Hm-Γ 2 (app) )/((13)Cm-Γ 2 (app) ) ratio provides a reliable measure of the 'true' methyl PREs.

Relative sensitivities of DCE-MRI pharmacokinetic parameters to arterial input function (AIF) scaling

Dynamic-Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) has been used widely for clinical applications. Pharmacokinetic modeling of DCE-MRI data that extracts quantitative contrast reagent/tissue-specific model parameters is the most investigated method. One of the primary challenges in pharmacokinetic analysis of DCE-MRI data is accurate and reliable measurement of the arterial input function (AIF), which is the driving force behind all pharmacokinetics. Because of effects such as inflow and partial volume averaging, AIF measured from individual arteries sometimes require amplitude scaling for better representation of the blood contrast reagent (CR) concentration time-courses. Empirical approaches like blinded AIF estimation or reference tissue AIF derivation can be useful and practical, especially when there is no clearly visible blood vessel within the imaging field-of-view (FOV). Similarly, these approaches generally also require magnitude scaling of the derived AIF time-courses. Since the AIF varies among individuals even with the same CR injection protocol and the perfect scaling factor for reconstructing the ground truth AIF often remains unknown, variations in estimated pharmacokinetic parameters due to varying AIF scaling factors are of special interest. In this work, using simulated and real prostate cancer DCE-MRI data, we examined parameter variations associated with AIF scaling. Our results show that, for both the fast-exchange-limit (FXL) Tofts model and the water exchange sensitized fast-exchange-regime (FXR) model, the commonly fitted CR transfer constant (Ktrans) and the extravascular, extracellular volume fraction (ve) scale nearly proportionally with the AIF, whereas the FXR-specific unidirectional cellular water efflux rate constant, kio, and the CR intravasation rate constant, kep, are both AIF scaling insensitive. This indicates that, for DCE-MRI of prostate cancer and possibly other cancers, kio and kep may be more suitable imaging biomarkers for cross-platform, multicenter applications. Data from our limited study cohort show that kio correlates with Gleason scores, suggesting that it may be a useful biomarker for prostate cancer disease progression monitoring.

Rate of Molecular Transfer of Allyl Alcohol across an AOT Surfactant Layer Using Muon Spin Spectroscopy.

The transfer rate of a probe molecule across the interfacial layer of a water-in-oil (w/o) microemulsion was investigated using a combination of transverse field muon spin rotation (TF-μSR), avoided level crossing muon spin resonance (ALC-μSR), and Monte Carlo simulations. Reverse microemulsions consist of nanometer-sized water droplets dispersed in an apolar solvent separated by a surfactant monolayer. Although the thermodynamic, static model of these systems has been well described, our understanding of their dynamics is currently incomplete. For example, what is the rate of solute transfer between the aqueous and apolar solvents, and how this is influenced by the structure of the interface? With an appropriate choice of system and probe molecule, μSR offers a unique opportunity to directly probe these interfacial transfer dynamics. Here, we have employed a well characterized w/o microemulsion stabilized by bis(2-ethylhexyl) sodium sulfosuccinate (Aerosol OT), with allyl alcohol (CH2═CH-CH2-OH, AA) as the probe. Resonances due to both muoniated radicals, CMuH2-C*H-CH2-OH and C*H2-CHMu-CH2-OH, were observed with the former being the dominant species. All resonances displayed solvent dependence, with those in the microemulsion observed as a single resonance located at intermediate magnetic fields to those present in either of the pure solvents. Observation of a single resonance is strong evidence for interfacial transfer being in the fast exchange limit. Monte Carlo calculations of the ΔM = 0 ALC resonances are consistent with the experimental data, indicating exchange rates greater than 10(9) s(-1), placing the rate of interfacial transfer at the diffusion limit.

Large-scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis.

We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high-performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta-cyclodextrin-heptanoate host-guest system in the context of one- and two-dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle.

Correction to “Local Isotropic Diffusion Approximation for Coupled Internal and Overall Molecular Motions in NMR Spin Relaxation”

The original version of Figure ​Figure6666 is incorrect; the corrected figure is shown below. In addition, the sentence “The experimental data are fit in the fast-exchange limit with a population of the B state of 0.68, yielding an average τm = 5.29 ns and S2 = 0.13” (p 11126) should read “The experimental data are fit in the fast-exchange limit with S2 = 1 (by construction, eq 21) and a population of the B state of 0.67 and k2 = 1.6 × 109 s–1, yielding an average τm = 5.19 ns.” The population of 0.68 reported in the caption to Figure 7 also should be 0.67. No conclusions of the paper are affected by these corrections. Figure 6 Calculated relaxation rate constants for enzyme I. The R2/R1 ratio is shown as a function of k2, the rate constant for transitions from closed to open conformations. (a, b) The R2/R1 ratio is shown versus (a) the residue sequence position or (b) Y20(θ) ...

1H Solid-State NMR Study of Nanothin Nafion Films

The unique behaviors of Nafion nanothin films with thicknesses of 10 nm (ultrathin) and 160 nm (thin) were evaluated using variable-temperature and variable-humidity solid-state 1H NMR spectroscopy. These unprecedented measurements of nanothin films stacked within an NMR rotor represent a remarkable experimental achievement and demonstrate that 1H NMR spectroscopy of such minute amounts of ionomer might be possible within active catalyst layers in polymer electrolyte fuel-cell electrodes. This study was motivated by the observation, in a separate work, of thickness-dependent and highly suppressed conductivity in nanothin films of Nafion (4–300 nm) compared to counterpart free-standing Nafion membranes. Trends in the line width and, more precisely, the T2 relaxation, as probed using a Hahn echo, showed that the local mobility within the hydrogen-bonded domain is equivalent for 10 and 160 nm films and is governed by the fast exchange limit in terms of NMR time scales. Subtle differences in the chemical shif...

Evaluating the uncertainty in exchange parameters determined from off-resonance R1ρ relaxation dispersion for systems in fast exchange

Spin relaxation in the rotating frame (R1ρ) is a powerful NMR technique for characterizing fast microsecond timescale exchange processes directed toward short-lived excited states in biomolecules. At the limit of fast exchange, only kex=k1+k−1 and Φex=pGpE(Δω)2 can be determined from R1ρ data limiting the ability to characterize the structure and energetics of the excited state conformation. Here, we use simulations to examine the uncertainty with which exchange parameters can be determined for two state systems in intermediate-to-fast exchange using off-resonance R1ρ relaxation dispersion. R1ρ data computed by solving the Bloch–McConnell equations reveals small but significant asymmetry with respect to offset (R1ρ (ΔΩ)≠R1ρ (−ΔΩ)), which is a hallmark of slow-to-intermediate exchange, even under conditions of fast exchange for free precession chemical exchange line broadening (kex/Δω>10). A grid search analysis combined with bootstrap and Monte-Carlo based statistical approaches for estimating uncertainty in exchange parameters reveals that both the sign and magnitude of Δω can be determined at a useful level of uncertainty for systems in fast exchange (kex/Δω<10) but that this depends on the uncertainty in the R1ρ data and requires a thorough examination of the multidimensional variation of χ2 as a function of exchange parameters. Results from simulations are complemented by analysis of experimental R1ρ data measured in three nucleic acid systems with exchange processes occurring on the slow (kex/Δω=0.2; pE=∼0.7%), fast (kex/Δω=∼10–16; pE=∼13%) and very fast (kex=39,000s−1) chemical shift timescales.

Structural and dynamical relationships of Ca2+ and H2O in smectite/2H2O systems

We present an X-ray diffraction and multi-nuclear (2H and 43Ca) NMR study of Ca-exchanged hectorite (a smectite clay) that provides important new insight into molecular behavior at the smectite-H2O interface. Variable-temperature 43Ca MAS NMR and controlled humidity XRD indicate that Ca2+ occurs as proximity-restricted outer-sphere hydration complexes between –120 and +25 °C in a two-layer hydrate and at T ≤ –50 °C in a 2:1 water/solid paste. Changes in the 43Ca NMR peak width and position with temperature are more onsistent with diffusion-related processes than with dynamics involving metal-surface interactions such as site exchange. The 2H NMR signal between –50 and +25 °C for a two-layer hydrate of Ca-hectorite is similar to that of Na- and other alkali metal hectorites and represents 2H2O molecules experiencing anisotropic motion describable using the 2H C2/C3 jump model we proposed previously. 2H T1 relaxation results for Ca- and Na-hectorite are well fit with a fast-exchange limit, rotational diffusion model for 2H2O dynamics, yielding GHz-scale rotational reorientation rates compatible with the C3 component of the C2/C3 hopping model. The apparent activation energy for 2H2O rotational diffusion in the two-layer hydrate is greater for Ca-hectorite than Na-hectorite (25.1 vs. 21.1 kJ/mol), consistent with the greater affinitymore » of Ca2+ for H2O. The results support the general principle that the dynamic mechanisms of proximity-restricted H2O are only weakly influenced by the cation in alkali metal and alkaline earth metal smectites and provide critical evidence that the NMR resonances of charge-balancing cations in smectites become increasingly influenced by diffusion-like dynamic processes at low temperatures as the charge density of the unhydrated cation increases.« less

Cardiac T 1 Imaging

T(1) mapping of the heart has evolved into a valuable tool to evaluate myocardial tissue properties, with or without contrast injection, including assessment of myocardial edema and free water content, extracellular volume (expansion), and most recently cardiomyocyte hypertrophy. The magnetic resonance imaging pulse sequence techniques developed for these applications have had to address at least 2 important considerations for cardiac applications: measure magnetization-inversion recoveries during cardiac motion with sufficient temporal resolution for the shortest expected T(1) values, and, second, obtain these measurements within a time during which a patient can comfortably suspend breathing. So-called Look-Locker techniques, and variants thereof, which all sample multiple points of a magnetization recovery after each magnetization preparation, have therefore become a mainstay in this field. The rapid pace of advances and new findings based on cardiac T(1) mapping for assessment of diffuse fibrosis or myocardial edema show that these techniques enrich the capabilities of magnetic resonance imaging for myocardial tissue profiling, which is arguably unmatched by other cardiac imaging modalities.

Generating Accurate Contact Maps of Transient Long-Range Interactions in Intrinsically Disordered Proteins by Paramagnetic Relaxation Enhancement

Generating Accurate Contact Maps of Transient Long-Range Interactions in Intrinsically Disordered Proteins by Paramagnetic Relaxation Enhancement

MR chemical exchange imaging with spin-lock technique (CESL): a theoretical analysis of the Z-spectrum using a two-pool R1ρ relaxation model beyond the fast-exchange limit

The chemical exchange (CE) process has been exploited as a novel and powerful contrast mechanism for MRI, which is primarily performed in the form of chemical exchange saturation transfer (CEST) imaging. A spin-lock (SL) technique can also be used for CE studies, although traditionally performed and interpreted quite differently from CEST. Chemical exchange imaging with spin-lock technique (CESL), theoretically based on the Bloch–McConnell equations common to CEST, has the potential to be used as an alternative to CEST and to better characterize CE processes from slow and intermediate to fast proton exchange rates through the tuning of spin-lock pulse parameters. In this study, the Z-spectrum and asymmetric magnetization transfer ratio (MTRasym) obtained by CESL are theoretically analyzed and numerically simulated using a general two-pool R1ρ relaxation model beyond the fast-exchange limit. The influences of spin-lock parameters, static magnetic field strength B0 and physiological properties on the Z-spectrum and MTRasym are quantitatively revealed. Optimization of spin-lock frequency and spin-lock duration for the maximum CESL contrast enhancement is also investigated. Numerical simulation results in this study are compatible with the findings in the existing literature on CE imaging studies.

Novel magnetic resonance imaging marker of diffuse myocardial fibrosis in hypertensive heart disease: the role of transcytolemmal water-exchange

Summary Transcytolemal water exchange and its effect on myocardial T1 relaxation can, if neglected, lead to a significant underestimate of the myocardial extracellular volume fraction, a novel marker of diffuse fibrosis. Background LGE may fail to detect diffuse fibrosis in several cardiac conditions. A novel approach uses the myocardial extracellular volume-fraction (MECVF), measured as distribution volume of a gadolinium constrast, as a marker of extracellular expansion. Previous studies have assumed the fast-exchange (FX) limit for the transcytolemal waterexchange, yet the administration of an extracellular-agent can create significant transcytolemal T1-differences, and cause an underestimation of extracellular volume fraction under the FX assumption. We hypothesized that the quantitative measure of MECVF with using a 2-site H-exchange model (2SX-model) correlates positively with the extracellular volume fraction, while the FX approach underestimates extra-cellular matrix expansion in a rodent model of hypertensive heart disease and diffuse myocardial fibrosis created by administration of L-NAME. Methods L-NAME(3mg/ml) or placebo was administered respectively to 22(bw=36.9±2.3g) and 15(bw=37.6±2.5g) wildtype mice. Animals were imaged at baseline and 7weeks after treatment on a 4.7T small-animal MRI-system. T1(#of T1’s>5/mouse) was quantified with a modified Look-Locker gradient-echo-cine technique, before and after fractionated Gd-DPTA administration (mean max. R1 in blood post-contrast=5.0±2.26 1/s). MECVF obtained from the T1 measurements with the 2SX and FX-models, and by using blood hematocrit to adjust the partition coefficient. Connective tissue volume fraction (CTVF) was measured using Masson’s trichrome.

Statistical comparison of dynamic contrast‐enhanced MRI pharmacokinetic models in human breast cancer

By fitting dynamic contrast-enhanced MRI data to an appropriate pharmacokinetic model, quantitative physiological parameters can be estimated. In this study, we compare four different models by applying four statistical measures to assess their ability to describe dynamic contrast-enhanced MRI data obtained in 28 human breast cancer patient sets: the chi-square test (χ(2)), Durbin-Watson statistic, Akaike information criterion, and Bayesian information criterion. The pharmacokinetic models include the fast exchange limit model with (FXL_v(p)) and without (FXL) a plasma component, and the fast and slow exchange regime models (FXR and SXR, respectively). The results show that the FXL_v(p) and FXR models yielded the smallest χ(2) in 45.64 and 47.53% of the voxels, respectively; they also had the smallest number of voxels showing serial correlation with 0.71 and 2.33%, respectively. The Akaike information criterion indicated that the FXL_v(p) and FXR models were preferred in 42.84 and 46.59% of the voxels, respectively. The Bayesian information criterion also indicated the FXL_v(p) and FXR models were preferred in 39.39 and 45.25% of the voxels, respectively. Thus, these four metrics indicate that the FXL_v(p) and the FXR models provide the most complete statistical description of dynamic contrast-enhanced MRI time courses for the patients selected in this study.

Conformation and Dynamics of 18-Membered Hexathiametacyclophanes: A Two Step Racemization as Studied by Deuterium NMR in Chiral Lyotropic Liquid Crystals

The conformation and interconversion dynamics of two derivatives of the 18-membered hexathia metacyclophane 1 and 2 were studied by (1)H NMR spectroscopy in isotropic solvents and by (2)H NMR in chiral liquid crystalline (CLC) solutions, as well as by molecular structure computations. For the analysis of the dynamic effects, we made use of the concepts of "average symmetry" and "isodynamic groups", introduced by Altmann (Altmann, Proc. R. Soc.1967, 184, A298). Compound 1, which is unsubstituted in the inner aromatic site, has, according to the NMR and molecular force field calculations, a boat shaped ground conformation with C(2) symmetry. It is highly flexible and in the NMR spectrum exhibits two successive dynamic processes. There is a low temperature (170-210 K, E(a) = 10.5 kcal/mol) alternate "wing flipping", which corresponds to interchange between pairs of enantiomers and results, in the fast exchange limit, in an average prochiral molecule with C(2v) symmetry. This process is followed, at higher temperatures (290-320 K, E(a) = 28.5 kcal/mol), by an umbrella flipping type inversion with an average structure of D(2h) symmetry. This second process involves averaging of effective enantiotopic into homotopic sites and can only be studied in chiral solvents. The origin of the chiral discrimination and of their stepwise averaging is discussed. Compound 2, which is substituted with methoxy groups at the inner sites of the benzene rings, is much less flexible and exhibits dynamic effects in the NMR spectrum only at temperatures above 370 K. We were able to study the kinetic parameters of this process in isotropic solvents (E(a) = 21.4 kcal/mol). As for 1, the detailed mechanism of this process can in principle be established using dynamic NMR in CLC; however, experimental limitation precluded us from doing so. Possible alternatives and their effect on the 1D and 2D exchange spectra in CLC are discussed in a concluding section.

Control of Cross Relaxation of Multiple‐Quantum Coherences Induced by Fast Chemical Exchange under Heteronuclear Double‐Resonance Irradiation

A fully analytical description of the control of the cross-correlated cross relaxation of multiple-quantum coherences in the presence of local dynamics under heteronuclear double-resonance radio-frequency (RF) irradiation is presented. The contribution of chemical exchange to relaxation can be partly or fully quenched by RF fields. We assume a correlated two-site chemical exchange model with arbitrary populations, and show that in the limit of fast exchange the dependence of the effective multiple-quantum cross-relaxation rate on the applied RF amplitude can be described by a compact analytical expression. Numerical simulations and preliminary experiments support our theoretical results. The relaxation dispersion as a function of RF amplitude can provide accurate information on the kinetics of correlated processes.

Analysis of Prostate DCE-MRI

The ability to detect and identify malignant lesions within the prostate with conventional T2-weighted imaging is still limited. Although lesion conspicuity is improved with dynamic contrast-enhanced imaging there still remains some ambiguity as all tissues within the prostate may enhance. The aim of the current study was to take advantage of the improved signal-to-noise ratio at 3 T and assess the ability of 2 alternative pharmacokinetic models to clearly identify malignant areas within the prostate. We also aspire to assess the impact of tissue heterogeneity on variation in estimated pharmacokinetic parameters. Quantitative dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the prostate was implemented using multiple flip angles for T1 determination, and a rapid dynamic 3D T1-weighted acquisition with parallel imaging and a temporal resolution of 6.7 s. Pharmacokinetic analysis was performed for regions of tumor, normal-appearing peripheral zone (PZ), and central gland (CG) using fast exchange limit (FXL) or fast exchange regimen (FXR) models. Cell density was obtained from hematoxylin and eosin stained whole mount radical prostatectomy specimens. Native tissue T1 was significantly lower in tumor and PZ tissue than in CG. The FXL model revealed increased mean K(trans), k(ep), and v(e) in tumor and CG compared with PZ. With the FXR model, fitting was improved and all parameters were significantly increased, however, there were no longer significant differences between regions for v(e). The additional parameter of the FXR model, tau(i), nominally representing mean lifetime of intracellular water, was significantly decreased in tumor compared with both PZ and CG. Rate constants for CG were significantly lower than those of tumor for both models. In addition, for all tissues, K(trans) and v(e) were positively correlated with cell density. Accounting for a finite water exchange rate between cells and their environment improves the discrimination of malignant from benign tissues within the prostate and may aid staging accuracy and ability to monitor response to treatment.

NMR mechanisms in gel dosimetry

Nuclear magnetic resonance was critical to the development of gel dosimetry, as it established the potential for three dimensional dosimetry with chemical dosimeter systems through magnetic resonance imaging [1]. In the last two decades MRI has served as the gold standard for imaging, while NMR relaxometry has played an important role in the development and understanding of the behaviour of new gel dosimetry systems. Therefore, an appreciation of the relaxation mechanisms determining the NMR behaviour of irradiated gel dosimeters is important for a full comprehension of a considerable component of the literature on gel dosimetry. A number of excellent papers have presented this important theory, this brief review will highlight some of the salient points made previously [1–5].The spin relaxation of gel dosimeters (which determines the dose dependence in most conventional MR imaging) is determined principally by the protons on water molecules in the system. These water protons exist in different environments, or groups (see Figure 1): on bulk water, on water hydrating the chemical species that are being modified under irradiation, and on water hydrating the gel matrix used to spatially stabilize the dosimeter (e.g., gelatin, agarose, etc). The spin relaxation depends on the inherent relaxation rate of each spin group, that is, on the relaxation rate which would be observed for the specific group if it were isolated. Also, the different water environments are not isolated from each other, and the observed relaxation rate also depends on the rate of exchange of magnetization between the groups, and on the fraction of protons in each group. In fact, the water exchanges quickly between the environments, so that relaxation is in what is usually termed the fast exchange regime. In the limit of fast exchange, the relaxation of the water protons is well characterized by a single exponential and hence by a single apparent relaxation rate. In irradiated gel dosimeters this observed rate is a function of the absorbed dose.In this review I will first develop the fast exchange model for the spin lattice relaxation Fricke gel dosimeter system, as this is conceptually the simpler system. Fundamental concepts such as relaxivity (which specifies the ability of some species to enhance the relaxation of water protons) and chemical yield will be presented. The linear dose relationship for Fricke gel dosimeters, and the reduced dose sensitivity of Fricke dosimeters containing chelators, will be explained. The model will then be extended to the spin-spin relaxation of polymer gel systems and the main differences discussed. The reasons for the enhanced dose sensitivy and dynamic range for spin-spin (R2) rather than spin-lattice (R1) relaxation will be presented.