James. R. Ewing

A review of the selection of models in dynamic contrast‐enhanced MRI (DCE‐MRI) is conducted, with emphasis on the balance between the bias and variance required to produce stable and accurate estimates of vascular parameters. The vascular parameters considered as a first‐order model are the forward volume transfer constant K^trans, the plasma volume fraction v_p and the interstitial volume fraction v_e. To illustrate the critical issues in model selection, a data‐driven selection of models in an animal model of cerebral glioma is followed. Systematic errors and extended models are considered. Studies with nested and non‐nested pharmacokinetic models are reviewed; models considering water exchange are considered. Copyright © 2013 John Wiley & Sons, Ltd.

Purpose: To test the hypothesis that a noninvasive dynamic contrast enhanced MRI (DCE‐MRI) derived interstitial volume fraction (v_e) and/or distribution volume (V_D) were correlated with tumor cellularity in cerebral tumor.Methods: T₁‐weighted DCE‐MRI studies were performed in 18 athymic rats implanted with U251 xenografts. After DCE‐MRI, sectioned brain tissues were stained with Hematoxylin and Eosin for cell counting. Using a Standard Model analysis and Logan graphical plot, DCE‐MRI image sets during and after the injection of a gadolinium contrast agent were used to estimate the parameters plasma volume (v_p), forward transfer constant (K^trans), v_e, and V_D.Results: Parameter values in regions where the standard model was selected as the best model were: (mean ± S.D.): v_p = (0.81 ± 0.40)%, K^trans = (2.09 ± 0.65) × 10⁻² min⁻¹, v_e = (6.65 ± 1.86)%, and V_D = (7.21 ± 1.98)%. The Logan‐estimated V_D was strongly correlated with the standard model's v_p + v_e (r = 0.91, P < 0.001). The parameters, v_e and/or V_D, were significantly correlated with tumor cellularity (r ≥ −0.75, P < 0.001 for both).Conclusion: These data suggest that tumor cellularity can be estimated noninvasively by DCE‐MRI, thus supporting its utility in assessing tumor pathophysiology. Magn Reson Med 71:2206–2214, 2014. © 2013 Wiley Periodicals, Inc.

Dynamic contrast enhanced T₁‐weighted MRI using the contrast agent gadopentetate dimeglumine (Gd‐DTPA) was performed on 10 patients with glioblastoma. Nested models with as many as three parameters were used to estimate plasma volume or plasma volume and forward vascular transfer constant (K^trans) and the reverse vascular transfer constant (k_ep). These constituted models 1, 2, and 3, respectively. Model 1 predominated in normal nonleaky brain tissue, showing little or no leakage of contrast agent. Model 3 predominated in regions associated with aggressive portions of the tumor, and model 2 bordered model 3 regions, showing leakage at reduced rates. In the patient sample, v_p was about four times that of white matter in the enhancing part of the tumor. K^trans varied by a factor of 10 between the model 2 (1.9 ↔ 10⁻³ min⁻¹) and model 3 regions (1.9 ↔ 10⁻² min⁻¹). The mean calculated interstitial space (model 3) was 5.5%. In model 3 regions, excellent curve fits were obtained to summarize concentration‐time data (mean R² = 0.99). We conclude that the three parameters of the standard model are sufficient to fit dynamic contrast enhanced T₁ data in glioblastoma under the conditions of the experiment. Magn Reson Med, 2012.

Tumor interstitial fluid pressure (TIFP) has the potential to predict tumor response to nonsurgical cancer treatments, including radiation therapy. At present the only quantitative measures available are of limited use, since they are invasive and yield only point measurements. We present the mathematical framework for a quantitative, noninvasive measure of TIFP. The model describes the distribution of interstitial fluid pressure in three distinct tumor regions: vascularized tumor rim, central tumor region, and normal tissue. A relationship between the TIFP and the fluid flow velocity at the periphery of a tumor is presented. This model suggests that a measure of fluid flow rate from a tumor into normal tissue reflects TIFP. We demonstrate that the acquisition of serial images of a tumor after the injection of a contrast agent can provide a noninvasive and potentially quantitative measure of TIFP.

The apparent forward transfer constant, K, for albumin was measured in 9L cerebral tumors in 15 rats. An MRI study using gadolinium‐labeled bovine serum albumin was followed by terminal quantitative autoradiography (QAR) using radioiodinated serum albumin. Look‐Locker MRI estimates of T₁ followed gadolinium‐labeled bovine serum albumin blood and tissue concentration. QAR and MRI maps of K were coregistered, a region of interest (ROI) that included the tumor and its surround was selected, and the two estimates of K from the ROI on QAR and MRI maps were compared by either mean per animal ROI or on pixel‐by‐pixel data using a generalized estimating equation. An ROI analysis showed a moderate correlation between the two measures (r = 0.57, P = 0.026); pixel‐by‐pixel generalized estimating equation analysis concurred (r = 0.54, P < 0.0001). The estimates of QAR with MRI of last time points (e.g., 25 min) showed a moderate correlation (ROI r = 0.55, P < 0.035; generalized estimating equation r = 0.58, P < 0.0001). Differences between the QAR and MRI estimates of K did not differ from zero, but the MRI 25‐min estimate was significantly lower than the QAR estimate. Thus, noninvasive MRI estimates of vascular permeability can serve as a surrogate for QAR measures. Magn Reson Med, 2011.

This paper models the behavior of the longitudinal relaxation rate of the protons of tissue water R₁ (R₁ = 1/T₁), measured in a Look‐Locker experiment at 7 Tesla after administration of a paramagnetic contrast agent (CA). It solves the Bloch‐McConnell equations for the longitudinal magnetization of the protons of water in a three‐site two‐exchange (3S2X) model with boundary conditions appropriate to repeated sampling of magnetization. The extent to which equilibrium intercompartmental water exchange kinetics affect monoexponential estimates of R₁ after administration of a CA in dynamic contrast enhanced experiment is described. The relation between R₁ and tissue CA concentration was calculated for CA restricted to the intravascular, or to the intravascular and extracellular compartments, by varying model parameters to mimic experimental data acquired in a rat model of cerebral tumor. The model described a nearly linear relationship between R₁ and tissue concentration of CA, but demonstrated that the apparent longitudinal relaxivity of CA depends upon tissue type. The practical consequence of this finding is that the extended Patlak plot linearizes the ΔR₁ data in tissue with leaky microvessels, accurately determines the influx rate of the CA across these microvessels, but underestimates the volume of intravascular blood water. Magn Reson Med, 2011.

Purpose To demonstrate in the rat 9L cerebral tumor model that repeated MRI measurements can quantitate acute changes in the blood‐brain distribution of Gadomer after dexamethasone administration. Materials and Methods A total of 16 Fischer 344 rats were studied at 7T, 15 days after cerebral implantation of a 9L tumor. MRI procedures employed a T‐One by Multiple Read Out Pulses (TOMROP) sequence to estimate R₁ (R₁ = 1/T₁) at 145‐second intervals before and after administration of Gadomer (Bayer), a macromolecular contrast agent (CA). Two baseline studies preceded Gadomer administration and 10 subsequent R₁ maps tracked CA concentration in blood and brain for 25 minutes. Thereafter, either dexamethasone (N = 10) or normal saline (N = 6) was administered intravenously. A total of 90 minutes later a second series of 12 TOMROP measurements of Gadomer distribution was performed. The influx constant, K₁, plasma distribution volume, v_D, backflux constant, k_b, and interstitial space, v_e, were determined, and the test‐retest differences of each of four vascular parameters were calculated. Results Dexamethasone decreased K₁ approximately 60% (P = 0.02), lowered k_b and v_D (P = 0.03 and P < 0.01, respectively), and marginally but insignificantly decreased v_e. Conclusion This noninvasive MRI technique can detect drug effects on blood‐brain transfer constants of CAs within two hours of administration. J. Magn. Reson. Imaging 2008;27:1430–1438.

Purpose: To present a single‐step deterministic procedure for unwrapping MRI phase maps.Materials and Methods: Using an algorithm previously developed for optical applications, Laplacian operators were applied in the Fourier space of the MRI phase map. The original Fourier‐based phase unwrapping algorithm was modified so that demodulation accomplished the required signal symmetrization in Fourier space. To evaluate the method's performance in the presence of thermal noise, a set of wrapped phase maps were simulated at different levels of noise in k‐space, and the response of the algorithm at different levels of signal‐to‐noise ratio (SNR) was evaluated for stability. To demonstrate its utility in MRI, the algorithm was applied to the wrapped phase maps of susceptibility‐weighted imaging (SWI) studies, which were then used to generate venograms.Results: In simulated phase wrapping, the algorithm correctly reproduced the original phase for a wide range of phase gradients and noise. The procedure was fast and produced useful maps of venous structures in SWI images.Conclusion: A fast and stable single‐step deterministic method for unwrapping MRI phase maps is available for such applications as SWI and mapping of static magnetic field inhomogeneity. J. Magn. Reson. Imaging 2008.

Using an MRI T₁ by multiple readout pulses (TOMROP) image set, an adaptive neural network (ANN) was trained to directly estimate the concentration of a contrast agent (CA), gadolinium-bovine serum albumin (Gd-BSA), in tissue. In nine rats implanted with a 9L cerebral tumor, MRI acquisition of TOMROP inversion-recovery data was followed by quantitative autoradiography (QAR) using radioiodinated serum albumin (RISA). QAR autoradiograms were used as a training set for the ANN. Precontrast and 25 min postcontrast TOMROP image sets were shown to the ANN in the form of a physical feature set related to 24 inversion-recovery images; QAR autoradiograms at 30 min after injection of RISA were taken as the training standard for the network. After training and optimization, the ANN produced a map of Gd-BSA concentration [g-moles/liter]. The prediction by the ANN of CA concentration at 25 min after injection was well correlated (r = 0.82, P < 0.0001) with the corresponding autoradiogram's measure of CA concentration. Magn Reson Med 58:290–297, 2007.