Matthias C. Schabel

Uncertainty and bias in contrast concentration measurements using spoiled gradient echo pulse sequences

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a widely used technique for assessing tissue physiology. Spoiled gradient echo (SPGR) pulse sequences are one of the most common methods for acquisition of DCE-MRI data, providing high temporal and spatial resolution with strong T(1)-weighting. Conversion of SPGR signal to concentration is briefly reviewed, and a new closed-form expression for concentration measurement uncertainty for finite signal-to-noise ratio (SNR) and baseline scan time is derived. This result is applicable to arbitrary concentration-dependent relaxation rate and is valid over the same domain as the theoretical SPGR signal equation. Expressions for the lower and upper bounds on measurable concentration are also derived. The existence of a concentration- and tissue-dependent optimal flip angle that minimizes concentration uncertainty is demonstrated and it is shown that, for clinically relevant pulse sequence parameters, this optimal flip angle is significantly larger than the corresponding Ernst angle. Analysis of three pulse sequences from the DCE-MRI literature shows that optimization of flip angle using the methods discussed here leads to potential improvements of 10-1166% in effective SNR over the 0.5-5.0 mM concentration range with minimal or no loss of measurement accuracy down to 0.1 mM. In vivo data from three study patients provide further support for our theoretical expression for concentration measurement uncertainty, with predicted and experimental estimates agreeing to within +/- 30%. Equations for concentration bias resulting from biases in flip angle and from pre-contrast relaxation time and contrast relaxivity (both longitudinal and transverse) are also derived in closed-form. The resulting equations show the potential for significant contributions to bias in concentration measurement arising from even relatively small mis-specification of flip angle and/or pre-contrast longitudinal relaxation time, particularly at high contrast concentrations.

Uncertainty in T1 mapping using the variable flip angle method with two flip angles

Propagation of errors, in conjunction with the theoretical signal equation for spoiled gradient echo pulse sequences, is used to derive a theoretical expression for uncertainty in quantitative variable flip angle T(1) mapping using two flip angles. This expression is then minimized to derive a rigorous expression for optimal flip angles that elucidates a commonly used empirical result. The theoretical expressions for uncertainty and optimal flip angles are combined to derive a lower bound on the achievable uncertainty for a given set of pulse sequence parameters and signal-to-noise ratio (SNR). These results provide a means of quantitatively determining the effect of changing acquisition parameters on T(1) uncertainty.

Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints

A number of methods using temporal and spatial constraints have been proposed for reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. The complex data can be constrained or regularized in a number of different ways, for example, the time derivative of the magnitude and phase image voxels can be constrained separately or jointly. Intuitively, the performance of different regularizations will depend on both the data and the chosen temporal constraints. Here, a complex temporal total variation (TV) constraint was compared to the use of separate real and imaginary constraints, and to a magnitude constraint alone. Projection onto Convex Sets (POCS) with a gradient descent method was used to implement the diverse temporal constraints in reconstructions of DCE MRI data. For breast DCE data, serial POCS with separate real and imaginary TV constraints was found to give relatively poor results while serial/parallel POCS with a complex temporal TV constraint and serial POCS with a magnitude-only temporal TV constraint performed well with an acceleration factor as large as R=6. In the tumor area, the best method was found to be parallel POCS with complex temporal TV constraint. This method resulted in estimates for the pharmacokinetic parameters that were linearly correlated to those estimated from the fully-sampled data, with K(trans,R=6)=0.97 K(trans,R=1)+0.00 with correlation coefficient r=0.98, k(ep,R=6)=0.95 k(ep,R=1)+0.00 (r=0.85). These results suggest that it is possible to acquire highly undersampled breast DCE-MRI data with improved spatial and/or temporal resolution with minimal loss of image quality.

Model‐based blind estimation of kinetic parameters in dynamic contrast enhanced (DCE)‐MRI

A method to simultaneously estimate the arterial input function (AIF) and pharmacokinetic model parameters from dynamic contrast‐enhanced (DCE)‐MRI data was developed. This algorithm uses a parameterized functional form to model the AIF and k‐means clustering to classify tissue time‐concentration measurements into a set of characteristic curves. An iterative blind estimation algorithm alternately estimated parameters for the input function and the pharmacokinetic model. Computer simulations were used to investigate the algorithms sensitivity to noise and initial estimates. In 12 patients with sarcomas, pharmacokinetic parameter estimates were compared with “truth” obtained from model regression using a measured AIF. When arterial voxels were included in the blind estimation algorithm, the resulting AIF was similar to the measured input function. The “true” Ktrans values in tumor regions were not significantly different than the estimated values, 0.99 ± 0.41 and 0.86 ± 0.40 min−1, respectively, P = 0.27. “True” kep values also matched closely, 0.70 ± 0.24 and 0.65 ± 0.25 min−1, P = 0.08. When only tissue curves free of significant vascular contribution are used (vp < 0.05), the resulting AIF showed substantial delay and dispersion consistent with a more local AIF such as has been observed in dynamic susceptibility contrast imaging in the brain. Magn Reson Med, 2009.

Model-based registration for dynamic cardiac perfusion MRI

To assess the accuracy of a model‐based approach for registration of myocardial dynamic contrast‐enhanced (DCE)‐MRI corrupted by respiratory motion.

A Model-Constrained Monte Carlo Method for Blind Arterial Input Function Estimation in Dynamic Contrast-Enhanced MRI: I) Simulations

Accurate quantification of pharmacokinetic model parameters in tracer kinetic imaging experiments requires correspondingly accurate determination of the arterial input function (AIF). Despite significant effort expended on methods of directly measuring patient-specific AIFs in modalities as diverse as dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), dynamic positron emission tomography (PET), and perfusion computed tomography (CT), fundamental and technical difficulties have made consistent and reliable achievement of that goal elusive. Here, we validate a new algorithm for AIF determination, the Monte Carlo blind estimation (MCBE) method (which is described in detail and characterized by extensive simulations in a companion paper), by comparing AIFs measured in DCE-MRI studies of eight brain tumor patients with results of blind estimation. Blind AIFs calculated with the MCBE method using a pool of concentration-time curves from a region of normal brain tissue were found to be quite similar to the measured AIFs, with statistically significant decreases in fit residuals observed in six of eight patients. Biases between the blind and measured pharmacokinetic parameters were the dominant source of error. Averaged over all eight patients, the mean biases were +7% in K(trans), 0% in k(ep), -11% in v(p) and +10% in v(e). Corresponding uncertainties (median absolute deviation from the best fit line) were 0.0043 min(-1) in K(trans), 0.0491 min(-1) in k(ep), 0.29% in v(p) and 0.45% in v(e). The use of a published population-averaged AIF resulted in larger mean biases in three of the four parameters (-23% in K(trans), -22% in k(ep), -63% in v(p)), with the bias in v(e) unchanged, and led to larger uncertainties in all four parameters (0.0083 min(-1) in K(trans), 0.1038 min(-1) in k(ep), 0.31% in v(p) and 0.95% in v(e)). When blind AIFs were calculated from a region of tumor tissue, statistically significant decreases in fit residuals were observed in all eight patients despite larger deviations of these blind AIFs from the measured AIFs. The observed decrease in root-mean-square fit residuals between the normal brain and tumor tissue blind AIFs suggests that the local blood supply in tumors is measurably different from that in normal brain tissue and that the proposed method is able to discriminate between the two. We have shown the feasibility of applying the MCBE algorithm to DCE-MRI data acquired in brain, finding generally good agreement with measured AIFs and decreased biases and uncertainties relative to the use of a population-averaged AIF. These results demonstrate that the MCBE algorithm is a useful alternative to direct AIF measurement in cases where acquisition of high-quality arterial input function data is difficult or impossible.

Preoperative dynamic contrast-enhanced MRI correlates with molecular markers of hypoxia and vascularity in specific areas of intratumoral microenvironment and is predictive of patient outcome

BACKGROUND Measures of tumor vascularity and hypoxia have been correlated with glioma grade and outcome. Dynamic contrast-enhanced (DCE) MRI can noninvasively map tumor blood flow, vascularity, and permeability. In this prospective observational cohort pilot study, preoperative imaging was correlated with molecular markers of hypoxia, vascularity, proliferation, and progression-free and overall patient survival. METHODS Pharmacokinetic modeling methods were used to generate maps of tumor blood flow, extraction fraction, permeability-surface area product, transfer constant, washout rate, interstitial volume, blood volume, capillary transit time, and capillary heterogeneity from preoperative DCE-MRI data in human glioma patients. Tissue was obtained from areas of peritumoral edema, active tumor, hypoxic penumbra, and necrotic core and evaluated for vascularity, proliferation, and expression of hypoxia-regulated molecules. DCE-MRI parameter values were correlated with hypoxia-regulated protein expression at tissue sample sites. RESULTS Patient survival correlated with DCE parameters in 2 cases: capillary heterogeneity in active tumor and interstitial volume in areas of peritumoral edema. Statistically significant correlations were observed between several DCE parameters and tissue markers. In addition, MIB-1 index was predictive of overall survival (P = .044) and correlated with vascular endothelial growth factor expression in hypoxic penumbra (r = 0.7933, P = .0071) and peritumoral edema (r = 0.4546). Increased microvessel density correlated with worse patient outcome (P = .026). CONCLUSIONS Our findings suggest that DCE-MRI may facilitate noninvasive preoperative predictions of areas of tumor with increased hypoxia and proliferation. Both imaging and hypoxia biomarkers are predictive of patient outcome. This has the potential to allow unprecedented prognostic decisions and to guide therapies to specific tumor areas.

Pharmacokinetics and Tissue Retention of (Gd-DTPA)-Cystamine Copolymers, a Biodegradable Macromolecular Magnetic Resonance Imaging Contrast Agent

No HeadingPurpose.To investigate the pharmacokinetics, long-term tissue retention of Gd(III) ions, and magnetic resonance imaging (MRI) contrast enhancement of extracellular biodegradable macromolecular Gd(III) complexes, (Gd-DTPA)-cystamine copolymers (GDCC), of different molecular weights.Methods.The pharmacokinetics of blood clearance and long-term Gd(III) retention of GDCC were investigated in Sprague-Dawley rats. Pharmacokinetic parameters were calculated by using a two-compartment model. The blood pool contrast enhancement of GDCC was evaluated in Sprague-Dawley rats on a Siemens Trio 3T MR scanner. Gd-(DTPA-BMA) was used as a control.Results.The α phase half-life of Gd-(DTPA-BMA) and GDCC with molecular weights of 18,000 (GDCC-18) and 60,000 Da (GDCC-60) was 0.48 ± 0.16 min, 1.08 ± 0.24 min, and 1.74 ± 0.57 min, and the β phase half-life was 21.2 ± 5.5 min, 26.5 ± 5.9 min, and 53.7 ± 15.9 min, respectively. GDCC had minimal long-term Gd tissue retention comparable to that of Gd-(DTPA-BMA). GDCC resulted in more significant contrast enhancement in the blood pool than Gd-(DTPA-BMA).Conclusions.GDCC provides a prolonged blood pool retention time for effective MRI contrast enhancement and then clears rapidly with minimal accumulation of Gd (III) ions. It is promising for further development as a blood pool MRI contrast agent.

Reconstruction of 3D dynamic contrast-enhanced magnetic resonance imaging using nonlocal means

To develop and test a nonlocal means‐based reconstruction algorithm for undersampled 3D dynamic contrast‐enhanced (DCE) magnetic resonance imaging (MRI) of tumors.

A unified impulse response model for DCE-MRI.

We describe the gamma capillary transit time model, a generalized impulse response model for DCE‐MRI that mathematically unifies the Tofts‐Kety, extended Tofts‐Kety, adiabatic tissue homogeneity, and two‐compartment exchange models. By including a parameter (α−1) representing the width of the distribution of capillary transit times within a tissue voxel, the GCTT model discriminates tissues having relatively monodisperse transit time distributions from those having a large degree of heterogeneity. All five models were compared using in vivo data acquired in three brain tumors (one glioblastoma multiforme, one pleomorphic xanthoastrocytoma, and one anaplastic meningioma) and Monte Carlo simulations. Our principal findings are : (1) The four most commonly used models for dynamic contrast‐enhanced magnetic resonance imaging can be unified within a single formalism. (2) Application of the GCTT model to in vivo data incurs only modest penalties in parameter uncertainty and computational cost. (3) Measured nonparametric impulse response functions in human brain tumors are well described by the GCTT model. (4) Estimation of α−1 is feasible but achieving statistical significance requires higher SNR than is typically obtained in single voxel dynamic contrast‐enhanced magnetic resonance imaging data. These results suggest that the GCTT model may be useful for extraction of information about tumor physiology beyond what is obtained using current modeling methodologies. Magn Reson Med, 2012.