Diffusion in compartmental systems. II. Diffusion-weighted measurements of rat brain tissue in vivo and postmortem at very large b-values

Restriction-induced time-dependent transcytolemmal water exchange: Revisiting the Kӓrger exchange model

The Kӓrger model and its derivatives have been widely used to incorporate transcytolemmal water exchange rate, an essential characteristic of living cells, into analyses of diffusion MRI (dMRI) signals from tissues. The Kӓrger model consists of two homogeneous exchanging components coupled by an exchange rate constant and assumes measurements are made with sufficiently long diffusion time and slow water exchange. Despite successful applications, it remains unclear whether these assumptions are generally valid for practical dMRI sequences and biological tissues. In particular, barrier-induced restrictions to diffusion produce inhomogeneous magnetization distributions in relatively large-sized compartments such as cancer cells, violating the above assumptions. The effects of this inhomogeneity are usually overlooked. We performed computer simulations to quantify how restriction effects, which in images produce edge enhancements at compartment boundaries, influence different variants of the Kӓrger-model. The results show that the edge enhancement effect will produce larger, time-dependent estimates of exchange rates in e.g., tumors with relatively large cell sizes (>10 μm), resulting in overestimations of water exchange as previously reported. Moreover, stronger diffusion gradients, longer diffusion gradient durations, and larger cell sizes, all cause more pronounced edge enhancement effects. This helps us to better understand the feasibility of the Kärger model in estimating water exchange in different tissue types and provides useful guidance on signal acquisition methods that may mitigate the edge enhancement effect. This work also indicates the need to correct the overestimated transcytolemmal water exchange rates obtained assuming the Kärger-model.

Measuring water exchange on a preclinical MRI system using filter exchange and diffusion time dependent kurtosis imaging

PURPOSE

Filter exchange imaging (FEXI) and diffusion time (t)-dependent diffusion kurtosis imaging (DKI(t)) are both sensitive to water exchange between tissue compartments. The restrictive effects of tissue microstructure, however, introduce bias to the exchange rate obtained by these two methods, as their interpretation conventionally rely on the Kärger model of barrier limited exchange between Gaussian compartments. Here, we investigated whether FEXI and DKI(t) can provide comparable exchange rates in ex vivo mouse brains.

THEORY AND METHODS

FEXI and DKI(t) data were acquired from ex vivo mouse brains on a preclinical MRI system. Phase cycling and negative slice prewinder gradients were used to minimize the interferences from imaging gradients.

RESULTS

In the corpus callosum, apparent exchange rate (AXR) from FEXI correlated with the exchange rate (the inverse of exchange time, 1/τex ) from DKI(t) along the radial direction. In comparison, discrepancies between FEXI and DKI(t) were found in the cortex due to low filter efficiency and confounding effects from tissue microstructure.

CONCLUSION

The results suggest that FEXI and DKI(t) are sensitive to the same exchange processes in white matter when separated from restrictive effects of microstructure. The complex microstructure in gray matter, with potential exchange among multiple compartments and confounding effects of microstructure, still pose a challenge for FEXI and DKI(t).

Metabolic activity diffusion imaging (MADI): II. Noninvasive, high-resolution human brain mapping of sodium pump flux and cell metrics

We introduce a new ¹ H₂ O magnetic resonance approach: metabolic activity diffusion imaging (MADI). Numerical diffusion-weighted imaging decay simulations characterized by the mean cellular water efflux (unidirectional) rate constant (k_io ), mean cell volume (V), and cell number density (ρ) are produced from Monte Carlo random walks in virtual stochastically sized/shaped cell ensembles. Because of active steady-state trans-membrane water cycling (AWC), k_io reflects the cytolemmal Na⁺ , K⁺ ATPase (NKA) homeostatic cellular metabolic rate (^c MR_NKA ). A digital 3D "library" contains thousands of simulated single diffusion-encoded (SDE) decays. Library entries match well with disparate, animal, and human experimental SDE decays. The V and ρ values are consistent with estimates from pertinent in vitro cytometric and ex vivo histopathological literature: in vivo V and ρ values were previously unavailable. The library allows noniterative pixel-by-pixel experimental SDE decay library matchings that can be used to advantage. They yield proof-of-concept MADI parametric mappings of the awake, resting human brain. These reflect the tissue morphology seen in conventional MRI. While V is larger in gray matter (GM) than in white matter (WM), the reverse is true for ρ. Many brain structures have k_io values too large for current, invasive methods. For example, the median WM k_io is 22s^-1 ; likely reflecting mostly exchange within myelin. The k_io •V product map displays brain tissue ^c MR_NKA variation. The GM activity correlates, quantitatively and qualitatively, with the analogous resting-state brain ¹⁸ FDG-PET tissue glucose consumption rate (^t MR_glucose ) map; but noninvasively, with higher spatial resolution, and no pharmacokinetic requirement. The cortex, thalamus, putamen, and caudate exhibit elevated metabolic activity. MADI accuracy and precision are assessed. The results are contextualized with literature overall homeostatic brain glucose consumption and ATP production/consumption measures. The MADI/PET results suggest different GM and WM metabolic pathways. Preliminary human prostate results are also presented.

Metabolic activity diffusion imaging (MADI): I. Metabolic, cytometric modeling and simulations

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 H₂ 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, D₀ ) 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.

Improving MR cell size imaging by inclusion of transcytolemmal water exchange

The goal of the current study is to include transcytolemmal water exchange in MR cell size imaging using the IMPULSED model for more accurate characterization of tissue cellular properties (e.g., apparent volume fraction of intracellular space v in ) and quantification of indicators of transcytolemmal water exchange. We propose a heuristic model that incorporates transcytolemmal water exchange into a multicompartment diffusion-based method (IMPULSED) that was developed previously to extract microstructural parameters (e.g., mean cell size d and apparent volume fraction of intracellular space v in ) assuming no water exchange. For t diff ≤ 5 ms, the water exchange can be ignored, and the signal model is the same as the IMPULSED model. For t diff ≥ 30 ms, we incorporated the modified Kärger model that includes both restricted diffusion and exchange between compartments. Using simulations and previously published in vitro cell data, we evaluated the accuracy and precision of model-derived parameters and determined how they are dependent on SNR and imaging parameters. The joint model provides more accurate d values for cell sizes ranging from 10 to 12 microns when water exchange is fast (e.g., intracellular water pre-exchange lifetime τ in ≤ 100 ms) than IMPULSED, and reduces the bias of IMPULSED-derived estimates of v in , especially when water exchange is relatively slow (e.g., τ in > 200 ms). Indicators of transcytolemmal water exchange derived from the proposed joint model are linearly correlated with ground truth τ in values and can detect changes in cell membrane permeability induced by saponin treatment in murine erythroleukemia cancer cells. Our results suggest this joint model not only improves the accuracy of IMPULSED-derived microstructural parameters, but also provides indicators of water exchange that are usually ignored in diffusion models of tissues.

Measurement of cellular-interstitial water exchange time in tumors based on diffusion-time-dependent diffusional kurtosis imaging

PURPOSE

To assess the feasibility of using diffusion-time-dependent diffusional kurtosis imaging (tDKI) to measure cellular-interstitial water exchange time (τex ) in tumors, both in animals and in humans.

METHODS

Preclinical tDKI studies at 7 T were performed with the GL261 glioma model and the 4T1 mammary tumor model injected into the mouse brain. Clinical studies were performed at 3 T with women who had biopsy-proven invasive ductal carcinoma. tDKI measurement was conducted using a diffusion-weighted STEAM pulse sequence with multiple diffusion times (20-800 ms) at a fixed echo time, while keeping the b-values the same (0-3000 s/mm2 ) by adjusting the diffusion gradient strength. The tDKI data at each diffusion time t were used for a weighted linear least-squares fit method to estimate the diffusion-time-dependent diffusivity, D(t), and diffusional kurtosis, K(t).

RESULTS

Both preclinical and clinical studies showed that, when diffusion time t ≥ 200 ms, D(t) did not have a noticeable change while K(t) decreased monotonically with increasing diffusion time in tumors and t ≥ 100 ms for the cortical ribbon of the mouse brain. The estimated τex averaged median and interquartile range (IQR) of GL261 and 4T1 tumors were 93 (IQR = 89) ms and 68 (78) ms, respectively. For the cortical ribbon, the estimated τex averaged median and IQR were 41 (34) ms for C57BL/6 and 30 (17) ms for BALB/c. For invasive ductal carcinoma, the estimated τex median and IQR of the two breast cancers were 70 (94) and 106 (92) ms.

CONCLUSION

The results of this proof-of-concept study substantiate the feasibility of using tDKI to measure cellular-interstitial water exchange time without using an exogenous contrast agent.

Constant gradient FEXSY: A time-efficient method for measuring exchange

Filter-Exchange NMR Spectroscopy (FEXSY) is a method for measurement of apparent transmembranal water exchange rates. The experiment is comprised of two co-linear sequential pulsed-field gradient (PFG) blocks, separated by a mixing period in which exchange takes place. The first block remains constant and serves as a diffusion-based filter that removes signal coming from fast-diffusing water. The mixing time and the gradient area (q-value) of the second block are varied on repeated iterations to produce a 2D data set that is analyzed using a bi-compartmental model which assumes that intra- and extra-cellular water are slow and fast diffusing, respectively. Here we suggest a variant of the FEXSY method in which measurements for different mixing times are taken at a constant gradient. This Constant Gradient FEXSY (CG-FEXSY) allows for the determination of the exchange rate by using a smaller 1D data set, so that the same information can be gathered during a considerably shorter scan time. Furthermore, in the limit of high diffusion weighting, such that the extra-cellular water signal is removed while the intra-cellular signal is retained, CG-FEXSY also allows for determination of the intra-cellular mean residence time (MRT). The theoretical results are validated on a living yeast cells sample and on a fixed porcine optic nerve, where the values obtained from the two methods are shown to be in agreement.

Exploration of New Contrasts, Targets, and MR Imaging and Spectroscopy Techniques for Neuromuscular Disease - A Workshop Report of Working Group 3 of the Biomedicine and Molecular Biosciences COST Action BM1304 MYO-MRI

Neuromuscular diseases are characterized by progressive muscle degeneration and muscle weakness resulting in functional disabilities. While each of these diseases is individually rare, they are common as a group, and a large majority lacks effective treatment with fully market approved drugs. Magnetic resonance imaging and spectroscopy techniques (MRI and MRS) are showing increasing promise as an outcome measure in clinical trials for these diseases. In 2013, the European Union funded the COST (co-operation in science and technology) action BM1304 called MYO-MRI (www.myo-mri.eu), with the overall aim to advance novel MRI and MRS techniques for both diagnosis and quantitative monitoring of neuromuscular diseases through sharing of expertise and data, joint development of protocols, opportunities for young researchers and creation of an online atlas of muscle MRI and MRS. In this report, the topics that were discussed in the framework of working group 3, which had the objective to: Explore new contrasts, new targets and new imaging techniques for NMD are described. The report is written by the scientists who attended the meetings and presented their data. An overview is given on the different contrasts that MRI can generate and their application, clinical needs and desired readouts, and emerging methods.

Advances in Diffusion and Perfusion MRI for Quantitative Cancer Imaging

PURPOSE OF REVIEW

This article is to review recent technical developments and their clinical applications in cancer imaging quantitative measurement of cellular and vascular properties of the tumors.

RECENT FINDINGS

Rapid development of fast Magnetic Resonance Imaging (MRI) technologies over last decade brought new opportunities in quantitative MRI methods to measure both cellular and vascular properties of tumors simultaneously.

SUMMARY

Diffusion MRI (dMRI) and dynamic contrast enhanced (DCE)-MRI have become widely used to assess the tissue structural and vascular properties, respectively. However, the ultimate potential of these advanced imaging modalities has not been fully exploited. The dependency of dMRI on the diffusion weighting gradient strength and diffusion time can be utilized to measure tumor perfusion, cellular structure, and cellular membrane permeability. Similarly, DCE-MRI can be used to measure vascular and cellular membrane permeability along with cellular compartment volume fractions. To facilitate the understanding of these potentially important methods for quantitative cancer imaging, we discuss the basic concepts and recent developments, as well as future directions for further development.

Estimation of cellular-interstitial water exchange in dynamic contrast enhanced MRI using two flip angles

PURPOSE

To investigate the feasibility of using multiple flip angles in dynamic contrast enhanced (DCE) MRI to reduce the uncertainty in estimation of intracellular water lifetime (τ_i ).

METHODS

Numerical simulation studies were conducted to assess the uncertainty in estimation of τ_i using dynamic contrast enhanced MRI with one or two flip angles. In vivo experiments with a murine brain tumor model were conducted at 7T using two flip angles. The in vivo data were used to compare τ_i estimation using the single-flip-angle (SFA) protocol with that using the double-flip-angle (DFA) protocol. Data analysis was conducted using the two-compartment exchange model combined with the three-site-two-exchange model for water exchange.

RESULTS

In the numerical simulation studies with a range of contrast kinetic parameters and signal-to-noise ratio = 20, the median bias of τ_i estimation decreased from 72 ms with SFA to 65 ms with DFA, and the corresponding median inter-quartile range reduced from 523 ms to 156 ms. In the in vivo studies, τ_i estimation with SFA was not successful in most voxels in the tumors, as the estimated τ_i values reached the upper limit of the parameter range (2 s). In contrast, the estimated τ_i values with DFA were mostly between 0.2 and 1.5 s and homogeneously distributed spatially across the tumor. The τ_i estimation with DFA was less sensitive to arterial input function scaling but more sensitive to pre-contrast T₁ than the other contrast kinetic parameters.

CONCLUSION

This study results demonstrate the feasibility of using multiple flip angles to encode the post-contrast time-intensity curve with different weighting of water exchange effect to reduce the uncertainty in τ_i estimation.

INDIANA: An in-cell diffusion method to characterize the size, abundance and permeability of cells

NMR and MRI diffusion experiments contain information describing the shape, size, abundance, and membrane permeability of cells although extracting this information can be challenging. Here we present the INDIANA (IN-cell DIffusion ANAlysis) method to simultaneously and non-invasively measure cell abundance, effective radius, permeability and intrinsic relaxation rates and diffusion coefficients within the inter- and intra-cellular populations. The method couples an experimental dataset comprising stimulated-echo diffusion measurements, varying both the gradient strength and the diffusion delay, together with software to fit a model based on the Kärger equations to robustly extract the relevant parameters. A detailed error analysis is presented by comparing the results from fitting simulated data from Monte Carlo simulations, establishing its effectiveness. We note that for parameters typical of mammalian cells the approach is particularly effective, and the shape of the underlying cells does not unduly affect the results. Finally, we demonstrate the performance of the experiment on systems of suspended yeast and mammalian cells. The extracted parameters describing cell abundance, size, permeability and relaxation are independently validated.

Diffusion in Nanoporous Materials: Novel Insights by Combining MAS and PFG NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) allows recording of molecular diffusion paths (notably, the probability distribution of molecular displacements over typically micrometers, covered during an observation time of typically milliseconds) and has thus proven to serve as a most versatile means for the in-depth study of mass transfer in complex materials. This is particularly true with nanoporous host materials, where PFG NMR enabled the first direct measurement of intracrystalline diffusivities of guest molecules. Spatial resolution, i.e., the minimum diffusion path length experimentally observable, is limited by the time interval over which the pulsed field gradients may be applied. In “conventional” PFG NMR measurements, this time interval is determined by a characteristic quantity of the host-guest system under study, the so-called transverse nuclear magnetic relaxation time. This leads, notably when considering systems with low molecular mobilities, to severe restrictions in the applicability of PFG NMR. These restrictions may partially be released by performing PFG NMR measurements in combination with “magic-angle spinning” (MAS) of the NMR sample tube. The present review introduces the fundamentals of this technique and illustrates, via a number of recent cases, the gain in information thus attainable. Examples include diffusion measurements with nanoporous host-guest systems of low intrinsic mobility and selective diffusion measurement in multicomponent systems.

Cumulant expansions for measuring water exchange using diffusion MRI

The rate of water exchange across cell membranes is a parameter of biological interest and can be measured by diffusion magnetic resonance imaging (dMRI). In this work, we investigate a stochastic model for the diffusion-and-exchange of water molecules. This model provides a general solution for the temporal evolution of dMRI signal using any type of gradient waveform, thereby generalizing the signal expressions for the Kärger model. Moreover, we also derive a general nth order cumulant expansion of the dMRI signal accounting for water exchange, which has not been explored in earlier studies. Based on this analytical expression, we compute the cumulant expansion for dMRI signals for the special case of single diffusion encoding (SDE) and double diffusion encoding (DDE) sequences. Our results provide a theoretical guideline on optimizing experimental parameters for SDE and DDE sequences, respectively. Moreover, we show that DDE signals are more sensitive to water exchange at short-time scale but provide less attenuation at long-time scale than SDE signals. Our theoretical analysis is also validated using Monte Carlo simulations on synthetic structures.

Using 1H2O MR to measure and map sodium pump activity in vivo

The cell plasma membrane Na⁺,K⁺-ATPase [NKA] is one of biology's most [if not the most] significant enzymes. By actively transporting Na⁺ out [and K⁺ in], it maintains the vital trans-membrane ion concentration gradients and the membrane potential. The forward NKA reaction is shown in the Graphical Abstract [which is elaborated in the text]. Crucially, NKA does not operate in isolation. There are other transporters that conduct K⁺ back out of [II, Graphical Abstract] and Na⁺ back into [III, Graphical Abstract] the cell. Thus, NKA must function continually. Principal routes for ATP replenishment include mitochondrial oxidative phosphorylation, glycolysis, and creatine kinase [CrK] activity. However, it has never been possible to measure, let alone map, this integrated, cellular homeostatic NKA activity in vivo. Active trans-membrane water cycling [AWC] promises a way to do this with ¹H₂O MR. Inthe Graphical Abstract, the AWC system is characterized by active contributions totheunidirectional rate constants for steady-state water efflux and influx, respectively, k_io(a) and k_oi(a). The discovery, validation, and initial exploration of active water cycling are reviewed here. Promising applications in cancer, cardiological, and neurological MRI are covered. This initial work employed paramagnetic Gd(III)chelate contrast agents [CAs]. However, the significant problems associated with in vivo CA use are also reviewed. A new analysis of water diffusion-weighted MRI [DWI] is presented. Preliminary results suggest a non-invasive way to measure the cell number density [ρ (cells/μL)], the mean cell volume [V (pL)], and the cellular NKA metabolic rate [^cMR_NKA(fmol(ATP)/s/cell)] with high spatial resolution. These crucial cell biology properties have not before been accessible invivo. Furthermore, initial findings indicate their absolute values can be determined.

Tracing compartment exchange by NMR diffusometry: Water in lithium-exchanged low-silica X zeolites

The two-region model for analyzing signal attenuation in pulsed field gradient (PFG) NMR diffusion studies with molecules in compartmented media implies that, on their trajectory, molecules get from one region (one type of compartment) into the other one with a constant (i.e. a time-invariant) probability. This pattern has proved to serve as a good approach for considering guest diffusion in beds of nanoporous host materials, with the two regions ("compartments") identified as the intra- and intercrystalline pore spaces. It is obvious, however, that the requirements of the application of the two-region model are not strictly fulfilled given the correlation between the covered diffusion path lengths in the intracrystalline pore space and the probability of molecular "escape" from the individual crystallites. On considering water diffusion in lithium-exchanged low-silica X zeolite, we are now assuming a different position since this type of material is known to offer "traps" in the trajectories of the water molecules. Now, on attributing the water molecules in the traps and outside of the traps to these two types of regions, we perfectly comply with the requirements of the two-region model. We do, moreover, benefit from the option of high-resolution measurements owing to the combination of magic angle spinning (MAS) with PFG NMR. Data analysis via the two-region model under inclusion of the influence of nuclear magnetic relaxation yields satisfactory agreement between experimental evidence and theoretical estimates. Limitations in accuracy are shown to result from the fact that mass transfer outside of the traps is too complicated for being adequately reflected by simple Fick's laws with but one diffusivity.

Impact of transcytolemmal water exchange on estimates of tissue microstructural properties derived from diffusion MRI

PURPOSE

To investigate the influence of transcytolemmal water exchange on estimates of tissue microstructural parameters derived from diffusion MRI using conventional PGSE and IMPULSED methods.

METHODS

Computer simulations were performed to incorporate a broad range of intracellular water life times τin (50-∞ ms), cell diameters d (5-15 μm), and intrinsic diffusion coefficient Din (0.6-2 μm2 /ms) for different values of signal-to-noise ratio (SNR) (10 to 50). For experiments, murine erythroleukemia (MEL) cancer cells were cultured and treated with saponin to selectively change cell membrane permeability. All fitted microstructural parameters from simulations and experiments in vitro were compared with ground-truth values.

RESULTS

Simulations showed that, for both PGSE and IMPULSED methods, cell diameter d can be reliably fit with sufficient SNR (≥ 50), whereas intracellular volume fraction fin is intrinsically underestimated due to transcytolemmal water exchange. Din can be reliably fit only with sufficient SNR and using the IMPULSED method with short diffusion times. These results were confirmed with those obtained in the cell culture experiments in vitro.

CONCLUSION

For the sequences and models considered in this study, transcytolemmal water exchange has minor effects on the fittings of d and Din with physiologically relevant membrane permeabilities if the SNR is sufficient (> 50), but fin is intrinsically underestimated. Magn Reson Med 77:2239-2249, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Modeling white matter microstructure

Quantitative magnetic resonance imaging can be combined with advanced biophysical models to measure microstructural features of white matter. Non-invasive microstructural imaging has the potential to revolutionize neuroscience, and acquiring these measures in clinically feasible times would greatly improve patient monitoring and clinical studies of drug efficacy. However, a good understanding of microstructural imaging techniques is essential to set realistic expectations and to prevent over-interpretation of results. This review explains the methodology behind microstructural modeling and imaging, and gives an overview of the breakthroughs and challenges associated with it.

Evaluation and comparison of diffusion MR methods for measuring apparent transcytolemmal water exchange rate constant

Two diffusion-based approaches, CG (constant gradient) and FEXI (filtered exchange imaging) methods, have been previously proposed for measuring transcytolemmal water exchange rate constant k_in, but their accuracy and feasibility have not been comprehensively evaluated and compared. In this work, both computer simulations and cell experiments in vitro were performed to evaluate these two methods. Simulations were done with different cell diameters (5, 10, 20μm), a broad range of k_in values (0.02-30s^-1) and different SNR's, and simulated k_in's were directly compared with the ground truth values. Human leukemia K562 cells were cultured and treated with saponin to selectively change cell transmembrane permeability. The agreement between measured k_in's of both methods was also evaluated. The results suggest that, without noise, the CG method provides reasonably accurate estimation of k_in especially when it is smaller than 10s^-1, which is in the typical physiological range of many biological tissues. However, although the FEXI method overestimates k_in even with corrections for the effects of extracellular water fraction, it provides reasonable estimates with practical SNR's and more importantly, the fitted apparent exchange rate AXR showed approximately linear dependence on the ground truth k_in. In conclusion, either CG or FEXI method provides a sensitive means to characterize the variations in transcytolemmal water exchange rate constant k_in, although the accuracy and specificity is usually compromised. The non-imaging CG method provides more accurate estimation of k_in, but limited to large volume-of-interest. Although the accuracy of FEXI is compromised with extracellular volume fraction, it is capable of spatially mapping k_in in practice.

A comparative assessment of preclinical chemotherapeutic response of tumors using quantitative non-Gaussian diffusion MRI

BACKGROUND

Diffusion-weighted MRI (DWI) signal attenuation is often not mono-exponential (i.e. non-Gaussian diffusion) with stronger diffusion weighting. Several non-Gaussian diffusion models have been developed and may provide new information or higher sensitivity compared with the conventional apparent diffusion coefficient (ADC) method. However the relative merits of these models to detect tumor therapeutic response is not fully clear.

METHODS

Conventional ADC, and three widely-used non-Gaussian models, (bi-exponential, stretched exponential, and statistical model), were implemented and compared for assessing SW620 human colon cancer xenografts responding to barasertib, an agent known to induce apoptosis via polyploidy. Bayesian Information Criterion (BIC) was used for model selection among all three non-Gaussian models.

RESULTS

All of tumor volume, histology, conventional ADC, and three non-Gaussian DWI models could show significant differences between control and treatment groups after four days of treatment. However, only the non-Gaussian models detected significant changes after two days of treatment. For any treatment or control group, over 65.7% of tumor voxels indicate the bi-exponential model is strongly or very strongly preferred.

CONCLUSION

Non-Gaussian DWI model-derived biomarkers are capable of detecting tumor earlier chemotherapeutic response of tumors compared with conventional ADC and tumor volume. The bi-exponential model provides better fitting compared with statistical and stretched exponential models for the tumor and treatment models used in the current work.

Time-Dependent Influence of Cell Membrane Permeability on MR Diffusion Measurements

PURPOSE

To investigate the influence of cell membrane permeability on diffusion measurements over a broad range of diffusion times.

METHODS

Human myelogenous leukemia K562 cells were cultured and treated with saponin to selectively alter cell membrane permeability, resulting in a broad physiologically relevant range of 0.011-0.044 μm/ms. Apparent diffusion coefficient (ADC) values were acquired with the effective diffusion time (Δeff ) ranging from 0.42 to 3000 ms. Cosine-modulated oscillating gradient spin echo (OGSE) measurements were performed to achieve short Δeff from 0.42 to 5 ms, while stimulated echo acquisitions were used to achieve long Δeff from 11 to 2999 ms. Computer simulations were also performed to support the experimental results.

RESULTS

Both computer simulations and experiments in vitro showed that the influence of membrane permeability on diffusion MR measurements is highly dependent on the choice of diffusion time, and it is negligible only when the diffusion time is at least one order of magnitude smaller than the intracellular exchange lifetime.

CONCLUSION

The influence of cell membrane permeability on the measured ADCs is negligible in OGSE measurements at moderately high frequencies. By contrast, cell membrane permeability has a significant influence on ADC and quantitative diffusion measurements at low frequencies such as those sampled using conventional pulsed gradient methods.

Imaging of amide proton transfer and nuclear Overhauser enhancement in ischemic stroke with corrections for competing effects

Chemical exchange saturation transfer (CEST) potentially provides the ability to detect small solute pools through indirect measurements of attenuated water signals. However, CEST effects may be diluted by various competing effects, such as non-specific magnetization transfer (MT) and asymmetric MT effects, water longitudinal relaxation (T1 ) and direct water saturation (radiofrequency spillover). In the current study, CEST images were acquired in rats following ischemic stroke and analyzed by comparing the reciprocals of the CEST signals at three different saturation offsets. This combined approach corrects the above competing effects and provides a more robust signal metric sensitive specifically to the proton exchange rate constant. The corrected amide proton transfer (APT) data show greater differences between the ischemic and contralateral (non-ischemic) hemispheres. By contrast, corrected nuclear Overhauser enhancements (NOEs) around -3.5 ppm from water change over time in both hemispheres, indicating whole-brain changes that have not been reported previously. This study may help us to better understand the contrast mechanisms of APT and NOE imaging in ischemic stroke, and may also establish a framework for future stroke measurements using CEST imaging with spillover, MT and T1 corrections.

A combined analytical solution for chemical exchange saturation transfer and semi-solid magnetization transfer

Off-resonant RF irradiation in tissue indirectly lowers the water signal by saturation transfer processes: on the one hand, there are selective chemical exchange saturation transfer (CEST) effects originating from exchanging endogenous protons resonating a few parts per million from water; on the other hand, there is the broad semi-solid magnetization transfer (MT) originating from immobile protons associated with the tissue matrix with kilohertz linewidths. Recently it was shown that endogenous CEST contrasts can be strongly affected by the MT background, so corrections are needed to derive accurate estimates of CEST effects. Herein we show that a full analytical solution of the underlying Bloch-McConnell equations for both MT and CEST provides insights into their interaction and suggests a simple means to isolate their effects. The presented analytical solution, based on the eigenspace solution of the Bloch-McConnell equations, extends previous treatments by allowing arbitrary lineshapes for the semi-solid MT effects and simultaneously describing multiple CEST pools in the presence of a large MT pool for arbitrary irradiation. The structure of the model indicates that semi-solid MT and CEST effects basically add up inversely in determining the steady-state Z-spectrum, as previously shown for direct saturation and CEST effects. Implications for existing previous CEST analyses in the presence of a semi-solid MT are studied and discussed. It turns out that, to accurately quantify CEST contrast, a good reference Z-value, the observed longitudinal relaxation rate of water, and the semi-solid MT pool size fraction must all be known.

Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation

The adaptive variation of the gradient intensity with the diffusion time at a constant optimal b-value is proposed to enhance the contribution of the nuclei diffusing across permeable barriers, to the pulsed-gradient spin-echo (PGSE) signal. An exact simple formula the PGSE signal is derived under the narrow pulse approximation in the case of one-dimensional diffusion across a single permeable barrier. The barrier contribution to the signal is shown to be maximal at a particular b-value. The exact formula is then extended to multiple permeable barriers, while the PGSE signal is shown to be sensitive to the permeability and to the inter-barrier distance. Potential applications of the protocol to survey diffusion in three-dimensional domains with permeable membranes are illustrated through numerical simulations.

Parametric mapping of brain tissues from diffusion kurtosis tensor

Diffusion kurtosis imaging (DKI) is a new diffusion magnetic resonance imaging (MRI) technique to go beyond the shortages of conventional diffusion tensor imaging (DTI) from the assumption that water diffuse in biological tissue is Gaussian. Kurtosis is used to measure the deviation of water diffusion from Gaussian model, which is called non-Gaussian, in DKI. However, the high-order kurtosis tensor in the model brings great difficulties in feature extraction. In this study, parameters like fractional anisotropy of kurtosis eigenvalues (FAek) and mean values of kurtosis eigenvalues (Mek) were proposed, and regional analysis was performed for 4 different tissues: corpus callosum, crossing fibers, thalamus, and cerebral cortex, compared with other parameters. Scatterplot analysis and Gaussian mixture decomposition of different parametric maps are used for tissues identification. Diffusion kurtosis information extracted from kurtosis tensor presented a more detailed classification of tissues actually as well as clinical significance, and the FAek of D-eigenvalues showed good sensitivity of tissues complexity which is important for further study of DKI.

White matter characterization with diffusional kurtosis imaging

Diffusional kurtosis imaging (DKI) is a clinically feasible extension of diffusion tensor imaging that probes restricted water diffusion in biological tissues using magnetic resonance imaging. Here we provide a physically meaningful interpretation of DKI metrics in white matter regions consisting of more or less parallel aligned fiber bundles by modeling the tissue as two non-exchanging compartments, the intra-axonal space and extra-axonal space. For the b-values typically used in DKI, the diffusion in each compartment is assumed to be anisotropic Gaussian and characterized by a diffusion tensor. The principal parameters of interest for the model include the intra- and extra-axonal diffusion tensors, the axonal water fraction and the tortuosity of the extra-axonal space. A key feature is that these can be determined directly from the diffusion metrics conventionally obtained with DKI. For three healthy young adults, the model parameters are estimated from the DKI metrics and shown to be consistent with literature values. In addition, as a partial validation of this DKI-based approach, we demonstrate good agreement between the DKI-derived axonal water fraction and the slow diffusion water fraction obtained from standard biexponential fitting to high b-value diffusion data. Combining the proposed WM model with DKI provides a convenient method for the clinical assessment of white matter in health and disease and could potentially provide important information on neurodegenerative disorders.

Monte Carlo study of a two-compartment exchange model of diffusion

Multisite exchange models have been applied frequently to quantify measurements of transverse relaxation and diffusion in living tissues. Although the simplicity of such models is attractive, the precise relationship of the model parameters to tissue properties may be difficult to ascertain. Here, we investigate numerically a two-compartment exchange (Kärger) model as applied to diffusion in a system of randomly packed identical parallel cylinders with permeable walls, representing cells with permeable membranes, that may serve particularly as a model for axons in the white matter of the brain. By performing Monte Carlo simulations of restricted diffusion, we show that the Kärger model may provide a reasonable coarse-grained description of the diffusion-weighted signal in the long time limit, as long as the cell membranes are sufficiently impermeable, i.e. whenever the residence time in a cell is much longer than the time it takes to diffuse across it. For larger permeabilities, the exchange time obtained from fitting to the Kärger model overestimates the actual exchange time, leading to an underestimated value of cell membrane permeability.

Complex geometric models of diffusion and relaxation in healthy and damaged white matter

Which aspects of tissue microstructure affect diffusion weighted MRI signals? Prior models, many of which use Monte-Carlo simulations, have focused on relatively simple models of the cellular microenvironment and have not considered important anatomic details. With the advent of higher-order analysis models for diffusion imaging, such as high angular resolution diffusion imaging (HARDI), more realistic models are necessary. This paper presents and evaluates the reproducibility of simulations of diffusion in complex geometries. Our framework is quantitative, does not require specialized hardware, is easily implemented with little programming experience, and is freely available as open-source software. Models may include compartments with different diffusivities, permeabilities, and T2 time constants using both parametric (e.g. spheres and cylinders) and arbitrary (e.g. mesh-based) geometries. Three-dimensional diffusion displacement probability functions are mapped with high reproducibility, and thus can be readily used to assess reproducibility of diffusion-derived contrasts.

How does water diffusion in human white matter change following ischemic stroke?

PURPOSE

Temporal evolution of the water apparent diffusion coefficients (ADC) parallel (ADC parallel) and perpendicular (ADC perpendicular) to the human white matter tract following ischemia has not been investigated systematically. We attempted to quantify the evolution of ADC parallel and ADC perpendicular and examine whether it can be interpreted by a model of ischemic edema.

METHODS

We retrospectively selected 53 patients with ischemic lesions involving the posterior limb of the internal capsule (PLIC) and placed regions of interest in the right and left PLIC on ADC maps. We performed regression analysis of lesion-to-contralateral ratios of ADC parallel and ADC perpendicular against the time (t = 1-1600 h) from onset. We then fitted the estimated time courses of ADC parallel and ADC perpendicular obtained from the analysis to a model of nerve tissue composed of cylinders (axons) and spheres corresponding to isotropic structures, particularly focal cytoplasmic swellings of glial cells and axons seen in ischemic white matter.

RESULTS

The evolution of ADC perpendicular and ADC parallel differed. The estimated time course of ADC parallel in microm(2)*ms(-1) was 0.64 + 0.88 exp (-0.24t) for 1 < t < 54 h and 0.00059t + 0.61 for t >or= 54 h (contralateral normal value, 1.52). That of ADC perpendicular was 0.19-0.063 exp (-0.24t) for 1 < t < 54 h and 0.00040t + 0.17 for t >or=54 h (normal value 0.22). The model fitted to these values showed that the volume of the cylinders decreased, that of the spheres increased, and extracellular volume changed little from one hour to approximately one day after stroke onset.

CONCLUSION

In the human PLIC, ADC parallel continued to decrease from one hour to a few days after stroke onset, and ADC perpendicular tended to increase. The temporal evolution could be interpreted by progression of the focal cytoplasmic swelling of glial cells and axons previously observed in animal studies.

Diffusion-Exchange Weighted Imaging

A method has been developed whereby diffusion and exchange in micro cellular structures in the human brain are correlated to produce a new type of image contrast leading to determination of water exchange rates in vivo. The diffusion method relies on differential apparent diffusion coefficients as detectable nuclei exchange between adjacent compartments marked with different apparent diffusion coefficient values (e.g. intra- and extra-cellular compartments). A new pulse sequence was developed, and used to calculate water intra/extra mean residence times in brain, and the signal dependence on various experimental parameters was analysed. The method was tested in vivo at 3T field strength and produced 160 ms and 550 ms for extra-cellular and intra-cellular mean residence times, respectively.

NMR diffusometry with beds of nanoporous host particles: an assessment of mass transfer in compartmented two-phase systems

Molecular diffusion in a bed of zeolite crystallites is mimicked by dynamic Monte Carlo simulation of a particle hopping on a two-dimensional square lattice. The resulting probability distribution of molecular propagation (the "mean propagator") is used for a rigorous determination of the resulting dependencies of diffusion measurement by pulsed field gradient NMR. In the limiting cases of intracrystalline, restricted, and long-range diffusion, these dependencies are found to coincide with the well-known relations resulting from the application of a simplifying exchange model (the "two-region" approximation). The intensity of transport resistances on the boundary between the intra- and intercrystalline spaces, i.e., on the compartment boundaries, is only accessible in the intermediate case, i.e., for observation times comparable with the mean lifetimes within the different compartments. In this case, significant differences between the results of the rigorous treatment and the "two-region" approximation may occur.

Indirect measurement of regional axon diameter in excised mouse spinal cord with q-space imaging: simulation and experimental studies

Q-space imaging (QSI), a diffusion MRI technique, can provide quantitative tissue architecture information at cellular dimensions not amenable by conventional diffusion MRI. By exploiting regularities in molecular diffusion barriers, QSI can estimate the average barrier spacing such as the mean axon diameter in white matter (WM). In this work, we performed ex vivo QSI on cervical spinal cord sections from healthy C57BL/6 mice at 400 MHz using a custom-designed uniaxial 50T/m gradient probe delivering a 0.6 microm displacement resolution capable of measuring axon diameters on the scale of 1 microm. After generating QSI-derived axon diameter maps, diameters were calculated using histology from seven WM tracts (dorsal corticospinal, gracilis, cuneatus, rubrospinal, spinothalamic, reticulospinal, and vestibulospinal tracts) each with different axon diameters. We found QSI-derived diameters from regions drawn in the seven WM tracts (1.1 to 2.1 microm) to be highly correlated (r(2)=0.95) with those calculated from histology (0.8 to 1.8 microm). The QSI-derived values overestimated those obtained by histology by approximately 20%, which is likely due to the presence of extra-cellular signal. Finally, simulations on images of synthetic circular axons and axons from histology suggest that QSI-derived diameters are informative despite diameter and axon shape variation and the presence of intra-cellular and extra-cellular signal. QSI may be able to quantify nondestructively changes in WM axon architecture due to pathology or injury at the cellular level.

Quantification of water compartmentation in cell suspensions by diffusion-weighted and T(2)-weighted MRI

When studying water diffusion in biological systems, any specific signal attenuation curve may be reproduced by a broad range of mathematical functions. Our goals were to quantify the diffusion and T(2) relaxation properties of water in a simple biological system and to study the changes that occur in osmotically stressed cells. Human breast cancer cells were incubated in isotonic or hypotonic osmotic buffers. Diffusion-weighted and T(2)-weighted magnetic resonance images were acquired during sedimentation over 12 h. Diffusion-weighted imaging (DWI) data were analyzed with a biexponential fit, the Kärger model for exchange between two freely diffusing populations and the Price-modified Kärger model accounting for restricted diffusion in spherical geometry. We found that only the Price model provided an accurate quantitative description for water diffusion in both cell systems, independent of acquisition parameters, over the entire density range. Model-derived cell radii, intracellular volume fractions and transmembrane water exchange times were in good agreement with results calculated from light microscopy and with model-free exchange times. T(2) data indicated two populations in fast exchange, with volume fractions clearly different from DWI populations. Hypotonic stress led to higher slow apparent diffusion coefficient, longer T(2) and lower membrane permeability. The tortuosity in a hypotonic cell suspension complied with the Wang model for spherical geometry. Quantitative characterization of biological systems is obtainable by DWI, using appropriate modeling, accounting for water restriction and exchange between compartments.

Exploring the surface permeability of nanoporous particles by pulsed field gradient NMR

A new method to determine the surface permeability of nanoporous particles is proposed. It is based on the comparison of experimental data on tracer exchange and intracrystalline molecular mean square displacements as obtained by the PFG NMR tracer desorption technique with the corresponding solutions of the diffusion equation via dynamical Monte Carlo simulations. The method is found to be particularly sensitive in the "intermediate" regime, when the influence of intracrystalline diffusion and surface resistances of the nanoporous crystal on molecular transport are comparable and the conventional method fails. As an example, the surface permeabilities of two samples of zeolite NaCaA with different crystal sizes are determined with methane, as a probe molecule, at room temperature.

Microstructural changes in ischemic cortical gray matter predicted by a model of diffusion-weighted MRI

PURPOSE

To understand the diffusion attenuated MR signal from normal and ischemic brain tissue in order to extract structural and physiological information using mathematical modeling, taking into account the transverse relaxation rates in gray matter.

MATERIALS AND METHODS

We fit our diffusion model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and exchange between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each compartment. A global optimum was found from a wide range of parameter permutations using cluster computing. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia.

RESULTS

Our model estimates an extracellular volume fraction of 0.19 in accordance with the accepted value from histology. The absolute apparent diffusion coefficient obtained from the model was similar to that of experiments. The model and the experimental results indicate significant differences in diffusion and transverse relaxation between the tissue compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms.

CONCLUSION

Our modeling suggests that transverse relaxation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling as the primary cause of the diffusion changes seen in the acute phase of brain ischemia.

Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart

The time dependence of the apparent diffusion tensor of ex vivo calf heart and tongue was measured for diffusion times (tau(d)) between 32 and 810 ms. The results showed evidence of restricted diffusion in the muscle tissues of both organs. In regions where the myofibers are parallel, the largest eigenvalue (lambda(1)) of the diffusion tensor remained the same for all diffusion times measured, while the other eigenvalues (lambda(2), lambda(3)) decreased by 29-36% between tau(d) = 32 ms and tau(d) = 400 ms. In regions where the fibers cross, the lambda(1) also changed, decreasing by 17% between tau(d) = 32 ms and tau(d) = 400 ms. The restricting compartment size and volume fraction were effectively estimated by fitting the time courses of the eigenvalues to a model consisting of a nonrestricted compartment and a cylindrically restricted compartment. To our knowledge, this study is the first demonstrating diffusion time dependence of measured water diffusion tensor in muscular tissue. With improvement in scanning technology, future studies may permit noninvasive, in vivo detection of changes in muscle myoarchitecture due to disease, treatment, and exercise.

Neurochemical and oedematous changes in 1,3-dinitrobenzene-induced astroglial injury in rat brain from a 1H-nuclear magnetic resonance perspective

1,3-Dinitrobenzene (1,3-DNB), an intermediate used in the chemical industry, has toxic effects in the brain and testes. It produces focal lesions with marked astroglial necrosis in the rat brain upon repeated administration. Astrocytic death occurs in parallel with elevated local blood flow and is followed by damage to the cerebral vasculature and neurones. (1)H-nuclear magnetic resonance spectroscopic analysis before the onset of astrocytic damage, showed a global elevation of lactate, whereas choline containing compounds increased in the non-vulnerable cerebral cortex, yet decreased in the vulnerable brainstem. Similarly, glutamate increased in the cerebral cortex, cerebellum and midbrain, but decreased in the susceptible brainstem. In vivo T2-weighted NMR imaging showed high signal intensities in brain nuclei shown to develop astroglial loss by conventional neuropathology at 24 hours after completion of dosing, but not at 6-10 hours. Hence the early neurochemical changes in susceptible areas contribute to the aetiology of degeneration, and those seen elsewhere may represent adaptive responses dependent on the particular phenotype of different cell groups and underlying metabolic relationships.

Biexponential parameterization of diffusion and T2 relaxation decay curves in a rat muscle edema model: decay curve components and water compartments

Quantitative T2 relaxation and diffusion imaging studies of a rat muscle edema model were performed in order to determine the effects of intra- and extracellular water compartmentation on the respective decay curves. The right hind paw of rats was injected with a carrageenan solution to generate edematous muscle. A Carr-Purcell-Meiboom-Gill (CPMG) imaging sequence was used to acquire T2 relaxation decay curves from both paws. A line scan diffusion imaging (LSDI) sequence was then used to acquire diffusion decay curves from the same paws over a wide b-factor range. Measurements were made from both edematous muscle (EM) and control muscle (CM). The EM and CM T2 relaxation decay curves were best fit with biexponential functions. The fraction of the fast T2 component dropped dramatically from approximately 0.95 in CM to 0.45 in EM, consistent with a water compartmentation model in which the fast and slow T2 components reflect intra- and extracellular water, respectively. Both CM and EM diffusion decay curves required biexponential fitting functions, and the diffusion coefficients of the fast and slow components were substantially larger in EM than CM. The fraction of the fast diffusion component, however, was not radically altered between CM and EM conditions (0.84 versus 0.89 for CM versus EM). Assuming a model in which intra- and extracellular water compartments are responsible for the fast and slow T2-decay components and for the slow and fast diffusion decay components, respectively, leads to fractional sizes of the diffusion components that are not supported by experiment. We conclude that intra- and extracellular water compartmentation is a reasonable interpretation for the two T2-decay components in both CM and EM but that other factors, such as restricted diffusion and/or alternate forms of water compartmentation like surface versus volume water, most probably have profound influences on the precise shapes of the diffusion decay curves, a complete understanding of which will require significant theoretical work.

Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain

High b value diffusion-weighted images sampled at high angular resolution were analyzed using a composite hindered and restricted model of diffusion (CHARMED). Measurements and simulations of diffusion in white matter using CHARMED provide an unbiased estimate of fiber orientation with consistently smaller angular uncertainty than when calculated using a DTI model or with a dual tensor model for any given signal-to-noise level. Images based on the population fraction of the restricted compartment provide a new contrast mechanism that enhances white matter like DTI. Nevertheless, it is assumed that these images might be more sensitive than DTI to white matter disorders. We also provide here an experimental design and analysis framework to implement CHARMED MRI that is feasible on human clinical scanners.

Uncovering of intracellular water in cultured cells

The complexity of biologic tissues, with multiple compartments each with its own diffusion and relaxation properties, requires complex formalisms to model water signal in most magnetic resonance imaging or magnetic resonance spectroscopy experiments. In this article, we describe a magnetic susceptibility-induced shift in the resonance frequency of extracellular water by the introduction of a gadolinium contrast agent to medium perfusing a hollow fiber bioreactor. The frequency shift of the extracellular water (+185 Hz at 9.4 T) uncovers the intracellular water and allows direct measurement of motional and relaxation properties of the intracellular space. The proposed method provides a unique tool for understanding the mechanisms underlining diffusion and relaxation in the intracellular space.

Shutter-speed analysis of contrast reagent bolus-tracking data: Preliminary observations in benign and malignant breast disease

The standard pharmacokinetic model applied to contrast reagent (CR) bolus-tracking (B-T) MRI (dynamic-contrast-enhanced) data makes the intrinsic assumption that equilibrium transcytolemmal water molecule exchange is effectively infinitely fast. Theory and simulation have suggested that this assumption can lead to significant errors. Recent analyses of animal model experimental data have confirmed two predicted signature inadequacies: a specific temporal mismatch with the B-T time-course and a CR dose-dependent underestimation of model parameters. The most parsimonious adjustment to account for this aspect leads to the "shutter-speed" pharmacokinetic model. Application of the latter to the animal model data mostly eliminates the two signature inadequacies. Here, the standard and shutter-speed models are applied to B-T data obtained from routine human breast examinations. The signature standard model temporal mismatch is found for each of the three invasive ductal carcinoma (IDC) cases and for each of the three fibroadenoma (FA) cases studied. It is effectively eliminated by use of the shutter-speed model. The size of the mismatch is considerably greater for the IDC lesions than for the FA lesions, causing the shutter-speed model to exhibit improved discrimination of malignant IDC tumors from the benign FA lesions compared with the standard model. Furthermore, the shutter-speed model clearly reveals focal "hot spots" of elevated CR perfusion/permeation present in only the malignant tumors.

Evidence for shutter-speed variation in CR bolus-tracking studies of human pathology

The standard pharmacokinetic model for the analysis of MRI contrast reagent (CR) bolus-tracking (B-T) data assumes that the mean intracellular water molecule lifetime (tau(i)) is effectively zero. This assertion is inconsistent with a considerable body of physiological measurements. Furthermore, theory and simulation show the B-T time-course shape to be very sensitive to the tau(i) magnitude in the physiological range (hundreds of milliseconds to several seconds). Consequently, this standard model aspect can cause significant underestimations (factors of 2 or 3) of the two parameters usually determined: K(trans), the vascular wall CR transfer rate constant, and v(e), the CR distribution volume (the extracellular, extravascular space fraction). Analyses of animal model data confirmed two predicted behaviors indicative of this standard model inadequacy: (1) a specific temporal pattern for the mismatch between the best-fitted curve and data; and (2) an inverse dependence of the curve's K(trans) and v(e) magnitudes on the CR dose. These parameters should be CR dose-independent. The most parsimonious analysis allowing for realistic tau(i) values is the 'shutter-speed' model. Its application to the experimental animal data essentially eliminated the two standard model signature inadequacies. This paper reports the first survey for the extent of this 'shutter-speed effect' in human data. Retrospective analyses are made of clinical data chosen from a range of pathology (the active multiple sclerosis lesion, the invasive ductal carcinoma breast tumor, and osteosarcoma in the leg) that provides a wide variation, particularly of K(trans). The signature temporal mismatch of the standard model is observed in all cases, and is essentially eliminated by use of the shutter-speed model. Pixel-by-pixel maps show that parameter values from the shutter-speed analysis are increased by more than a factor of 3 for some lesion regions. This endows the lesions with very high contrast, and reveals heterogeneities that are often not seen in the standard model maps. Normal muscle regions in the leg allow validation of the shutter-speed model K(trans), v(e), and tau(i) magnitudes, by comparison with results of previous careful rat leg studies not possible for human subjects.

Magnetization transfer studies of the fast and slow tissue water diffusion components in the human brain

Magnetization transfer (MT) properties of the fast and slow diffusion components recently observed in the human brain were assessed experimentally. One set of experiments, performed at 1.5 T in healthy volunteers, was designed to determine whether the amplitudes of fast and slow diffusion components, differentiated on the basis of biexponential fits to signal decays over a wide range of b-factors, demonstrated a different or similar magnetization transfer ratio (MTR). Another set of experiments, performed at 3 T in healthy volunteers, was designed to determine whether MTRs differed when measured from high signal-to-noise images acquired with b-factor weightings of 350 vs 3500 s/mm2. The 3 T studies included measurements of MTR as a function of off-resonance frequency for the MT pulse at both low and high b-factors. The primary conclusion drawn from all the studies is that there appears to be no significant difference between the magnetization transfer properties of the fast and slow tissue water diffusion components. The conclusions do not lend support to a direct interpretation of the 'components' of the biexponential diffusion decay in terms of the 'compartments' associated with intra- and extracellular water.

MultiexponentialT2-relaxation analysis in cerebrally damaged rats in the absence and presence of a gadolinium contrast agent

An analysis of the multiexponential relaxation of transverse nuclear magnetization with and without a gadolinium-based paramagnetic contrast agent in spontaneously hypertensive stroke-prone rats (SHR-SP) and in the rat model of ischemia induced by middle cerebral artery occlusion is described. From the multiexponential relaxation, the presence of two T(2) relaxation times in the range of 0.03-0.5 s, T(2A) (shortest) and T(2B) (longest), with very different relative weights (respectively, A and B), is evidenced. In our models of cerebral damage, the changes in A and B were more evident than those in T(2A) and T(2B). The two T(2) values were interpreted as belonging to water molecules in two different compartments; therefore, the difference between the damaged and normal regions revealed by means of standard T(2)-weighted images is suggested to be due to a different water distribution in the two compartments, rather than different T(2)'s. The T(2) relaxation in the SHR-SP stroke model is analyzed for the first time using a multiexponential method. The power of a detailed analysis of MRI relaxation times is confirmed by the correspondence between the revealed changes in T(2A), T(2B), A and B, and the known T(2)W and DWI results about blood-brain barrier functionality.

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.