Two-compartment Exchange Model Research Articles

Textural Features of Mouse Glioma Models Measured by Dynamic Contrast-Enhanced MR Images with 3D Isotropic Resolution.

This paper investigates the effect of anisotropic resolution on the image textural features of pharmacokinetic (PK) parameters of a murine glioma model using dynamic contrast-enhanced (DCE) MR images acquired with an isotropic resolution at 7T with pre-contrast T1 mapping. The PK parameter maps of whole tumors at isotropic resolution were generated using the two-compartment exchange model combined with the three-site-two-exchange model. The textural features of these isotropic images were compared with those of simulated, thick-slice, anisotropic images to assess the influence of anisotropic voxel resolution on the textural features of tumors. The isotropic images and parameter maps captured distributions of high pixel intensity that were absent in the corresponding anisotropic images with thick slices. A significant difference was observed in 33% of the histogram and textural features extracted from anisotropic images and parameter maps, compared to those extracted from corresponding isotropic images. Anisotropic images in different orthogonal orientations demonstrated 42.1% of the histogram and textural features to be significantly different from those of isotropic images. This study demonstrates that the anisotropy of voxel resolution needs to be carefully considered when comparing the textual features of tumor PK parameters and contrast-enhanced images.

Simultaneous estimation of the cellular water exchange rate, intracellular volume fraction, and longitudinal relaxation rate in cancer cells.

The purpose of the current study was to investigate the feasibility of simultaneously estimating the cellular water efflux rate ( ), intracellular longitudinal relaxation rate ( ), and intracellular volume fraction ( ) of a cell suspension using multiple samples with different gadolinium concentrations. Numerical simulation studies were conducted to assess the uncertainty in the estimation of , , and from saturation recovery data using single (SC) or multiple concentrations (MC) of gadolinium-based contrast agent (GBCA). In vitro experiments with 4 T1 murine breast cancer and SCCVII squamous cell cancer models were conducted at 11 T to compare parameter estimation using the SC protocol with that using the MC protocol. The cell lines were challenged with a Na+ /K+ -ATPase inhibitor, digoxin, to assess the treatment response in terms of , , and . Data analysis was conducted using the two-compartment exchange model for parameter estimation. The simulation study data demonstrate that the MC method, compared with the SC method, reduces the uncertainty of the estimated by decreasing the interquartile ranges from 27.3% ± 3.7% to 18.8% ± 5.1% and the median differences from ground truth from 15.0% ± 6.3% to 7.2% ± 4.2%, while estimating and simultaneously. In the cell studies, the MC method demonstrated reduced uncertainty in overall parameter estimation compared with the SC approach. MC method-measured parameter changes in cells treated with digoxin increased by 11.7% (p = 0.218) and by 5.9% (p = 0.234) for 4 T1 cells, respectively, and decreased by 28.8% (p = 0.226) and by 1.6% (p = 0.751) for SCCVII cells, respectively. did not change noticeably by the treatment. The results of this study substantiate the feasibility of using saturation recovery data of multiple samples with different GBCA concentrations for simultaneous measurement of the cellular water efflux rate, intracellular volume fraction, and intracellular longitudinal relaxation rate in cancer cells.

Histogram analysis of intravoxel incoherent motion and dynamic contrast-enhanced MRI with the two-compartment exchange model in glioma

Histogram analysis of intravoxel incoherent motion and dynamic contrast-enhanced MRI with the two-compartment exchange model in glioma

Histogram analysis of intravoxel incoherent motion and dynamic contrast-enhanced MRI with the two-compartment exchange model in glioma

Histogram analysis of intravoxel incoherent motion and dynamic contrast-enhanced MRI with the two-compartment exchange model in glioma

Five-dimensional quantitative low-dose Multitasking dynamic contrast- enhanced MRI: Preliminary study on breast cancer.

To develop a low-dose Multitasking DCE technique (LD-MT-DCE) for breast imaging, enabling dynamic T1 mapping-based quantitative characterization of tumor blood flow and vascular properties with whole-breast coverage, a spatial resolution of 0.9 × 0.9 × 1.1 mm3 , and a temporal resolution of 1.4 seconds using a 20% gadolinium dose (0.02 mmol/kg). Magnetic resonance Multitasking was used to reconstruct 5D images with three spatial dimensions, one T1 recovery dimension for dynamic T1 quantification, and one DCE dimension for contrast kinetics. Kinetic parameters , , , and were estimated from dynamic T1 maps using the two-compartment exchange model. The LD-MT-DCE repeatability and agreement against standard-dose MT-DCE were evaluated in 20 healthy subjects. In 7 patients with triple-negative breast cancer, LD-MT-DCE image quality and diagnostic results were compared with that of standard-dose clinical DCE in the same imaging session. One-way unbalanced analysis of variance with Tukey test was performed to evaluate the statistical significance of the kinetic parameters between control and patient groups. The LD-MT-DCE technique was repeatable, agreed with standard-dose MT-DCE, and showed excellent image quality. The diagnosis using LD-MT-DCE matched well with clinical results. The values of , , and were significantly different between malignant tumors and normal breast tissue (P < .001, < .001, and < .001, respectively), and between malignant and benign tumors (P = .020, .003, and < .001, respectively). The LD-MT-DCE technique was repeatable and showed excellent image quality and equivalent diagnosis compared with standard-dose clinical DCE. The estimated kinetic parameters were capable of differentiating between normal breast tissue and benign and malignant tumors.

Robust predictive control for respiratory CO2 gas removal in closed-loop mechanical ventilation: An in-silico study

Abstract In this study a physiological closed-loop system for arterial CO2 partial pressure control was designed and comprehensively tested using a set of models of the respiratory CO2 gas exchange. The underlying preclinical data were collected from 12 pigs in presence of severe changes in hemodynamic and pulmonary condition. A minimally complex nonlinear state space model of CO2 gas exchange was identified post hoc in different lung conditions. The control variable was measured noninvasively using the endtidal CO2 partial pressure. For the simulation study the output signal of the controller was defined as the alveolar minute volume set value of an underlying adaptive lung protective ventilation mode. A linearisation of the two-compartment CO2 gas exchange model was used for the design of a model predictive controller (MPC). It was augmented by a tube based controller suppressing prediction errors due to model uncertainties. The controller was subject to comparative testing in interaction with each of the CO2 gas exchange models previously identified on the preclinical study data. The performance was evaluated for the system response towards the following five tests in comparison to a PID controller: recruitment maneuver, PEEP titration maneuver, stepwise change in the CO2 production, breath-hold maneuver and a step in the reference signal. A root mean square error of 2.69 mmHg between arterial CO2 partial pressure and the reference signal was achieved throughout the trial. The reference-variable response of the model predictive controller was superior regarding overshoot and settling time.

Observation of Reduced Homeostatic Metabolic Activity and/or Coupling in White Matter Aging.

Transvascular water exchange plays a key role in the functional integrity of the blood-brain barrier (BBB). In white matter (WM), a variety of imaging modalities have demonstrated age-related changes in structure and metabolism, but the extent to which water exchange is altered remains unclear. Here, we investigated the cumulative effects of healthy aging on WM capillary water exchange. A total of 38 healthy adults (aged 36-80 years) were studied using 7T dynamic contrast enhanced MRI. Blood volume fraction (vb ) and capillary water efflux rate constant (kpo ) were determined by fitting changes in the 1 H2 O longitudinal relaxation rate constant (R1 ) during contrast agent bolus passage to a two-compartment exchange model. WM volume was determined by morphometric analysis of structural images. R1 values and WM volume showed similar trajectories of age-related decline. Among all subjects, vb and kpo averaged 1.7 (±0.5) mL/100 g of tissue and 2.1 (±1.1) s-1 , respectively. While vb showed minimal changes over the 40-year-age span of participants, kpo declined 0.06 s-1 (ca. 3%) per year (r = -.66; P< .0005), from near 4 s-1 at age 30 to ca. 2 s-1 at age 70. The association remained significant after controlling for WM volume. Previous studies have shown that kpo tracks Na+ , K+ -ATPase activity-dependent water exchange at the BBB and likely reflects neurogliovascular unit (NGVU) coupled metabolic activity. The age-related decline in kpo observed here is consistent with compromised NGVU metabolism in older individuals and the dysregulated cellular bioenergetics that accompany normal brain aging.

Toward precise arterial input functions derived from DCE-MRI through a novel extracorporeal circulation approach in mice.

Dynamic contrast-enhanced MRI can be used in pharmacokinetic models to quantify functional parameters such as perfusion and permeability. However, precise quantification in preclinical models is challenged by the difficulties to dynamically measure the true arterial blood contrast agent concentration. We propose a novel approach toward a precise and experimentally feasible method to derive the arterial input function from DCE-MRI in mice. Arterial blood was surgically shunted from the femoral artery to the tail vein and led through an extracorporeal circulation that resided on the head of brain tumor-bearing mice inside the FOV of a 9.4T MRI scanner. Dynamic 3D-FLASH scanning was performed after injection of gadobutrol with an effective resolution of 0.175 × 0.175 × 1 mm and a temporal resolution of 4seconds. Pharmacokinetic modeling was performed using the extended Tofts and two-compartment exchange model. Arterial input functions measured inside the extracorporeal circulation showed little noise, small interindividual variance, and typical curve shapes. Ex vivo and mass spectrometry validation measurements documented the influence of shunt flow velocity and hematocrit on estimation of contrast agent concentrations. Modeling of tumors and muscles allowed fitting of the recorded dynamic concentrations, resulting in quantitative plausible parameters. The extracorporeal circulation allows deriving the contrast agent dynamics in arterial blood with high robustness and at acceptable experimental effort from DCE-MRI, previously not achievable in mice. It sets the basis for quantitative precise pharmacokinetic modeling in small animals to enhance the translatability of preclinical DCE-MRI measurements to patients.

Hierarchical Bayesian myocardial perfusion quantification.

Myocardial blood flow can be quantified from dynamic contrast-enhanced magnetic resonance (MR) images through the fitting of tracer-kinetic models to the observed imaging data. The use of multi-compartment exchange models is desirable as they are physiologically motivated and resolve directly for both blood flow and microvascular function. However, the parameter estimates obtained with such models can be unreliable. This is due to the complexity of the models relative to the observed data which is limited by the low signal-to-noise ratio, the temporal resolution, the length of the acquisitions and other complex imaging artefacts. In this work, a Bayesian inference scheme is proposed which allows the reliable estimation of the parameters of the two-compartment exchange model from myocardial perfusion MR data. The Bayesian scheme allows the incorporation of prior knowledge on the physiological ranges of the model parameters and facilitates the use of the additional information that neighbouring voxels are likely to have similar kinetic parameter values. Hierarchical priors are used to avoid making a priori assumptions on the health of the patients. We provide both a theoretical introduction to Bayesian inference for tracer-kinetic modelling and specific implementation details for this application. This approach is validated in both in silico and in vivo settings. In silico, there was a significant reduction in mean-squared error with the ground-truth parameters using Bayesian inference as compared to using the standard non-linear least squares fitting. When applied to patient data the Bayesian inference scheme returns parameter values that are in-line with those previously reported in the literature, as well as giving parameter maps that match the independant clinical diagnosis of those patients.

Dynamic contrast-enhanced MRI model selection for predicting tumor aggressiveness in papillary thyroid cancers.

The purpose of this study was to identify the optimal tracer kinetic model from T1 -weighted dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data and evaluate whether parameters estimated from the optimal model predict tumor aggressiveness determined from histopathology in patients with papillary thyroid carcinoma (PTC) prior to surgery. In this prospective study, 18 PTC patients underwent pretreatment DCE-MRI on a 3T MR scanner prior to thyroidectomy. This study was approved by the institutional review board and informed consent was obtained from all patients. The two-compartment exchange model, compartmental tissue uptake model, extended Tofts model (ETM) and standard Tofts model were compared on a voxel-wise basis to determine the optimal model using the corrected Akaike information criterion (AICc) for PTC. The optimal model is the one with the lowest AICc. Statistical analysis included paired and unpaired t-tests and a one-way analysis of variance. Bonferroni correction was applied for multiple comparisons. Receiver operating characteristic (ROC) curves were generated from the optimal model parameters to differentiate PTC with and without aggressive features, and AUCs were compared. ETM performed best with the lowest AICc and the highest Akaike weight (0.44) among the four models. ETM was preferred in 44% of all 3419 voxels. The ETM estimates of Ktrans in PTCs with the aggressive feature extrathyroidal extension (ETE) were significantly higher than those without ETE (0.78±0.29 vs. 0.34±0.18min-1 , P = 0.005). From ROC analysis, cut-off values of Ktrans , ve and vp , which discriminated between PTCs with and without ETE, were determined at 0.45 min-1 , 0.28 and 0.014 respectively. The sensitivities and specificities were 86 and 82% (Ktrans ), 71 and 82% (ve ), and 86 and 55% (vp ), respectively. Their respective AUCs were 0.90, 0.71 and 0.71. We conclude that ETM Ktrans has shown potential to classify tumors with and without aggressive ETE in patients with PTC.

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

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

Extended quantitative dynamic contrast-enhanced cardiac perfusion imaging in mice using accelerated data acquisition and spatially distributed, two-compartment exchange modeling.

The objective of the present work was to improve data acquisition and quantification of dynamic contrast-enhanced perfusion imaging in the in vivo murine heart. Four-fold undersampled data were acquired in 14 mice and reconstructed using k-t SPARSE. A two-compartment exchange model was employed to provide additional characterization of myocardial tissue based on compartment volumes and the permeability surface area product. The feasibility of the proposed method was tested using compartment-based analysis of contrast-enhanced perfusion data acquired with intravascular and extracellular contrast agents. A significantly different permeability surface area product was measured for the intravascular versus extracellular contrast agent (0.13-0.15ml/g/min vs 0.86-0.88ml/g/min). The reduced extravasation also resulted in significantly smaller interstitial volumes of the intravascular versus extracellular agent (9.8-11% vs 45-47%). No difference was found for myocardial blood flow (6.5-7.2ml/g/min vs 6.0-7.0ml/g/min). The results presented here show that two-compartment exchange modeling in the in vivo murine heart is feasible and gives access to tissue parameters beyond myocardial blood flow.

Quality-based pharmacokinetic model selection on DCE-MRI for characterizing orbital lesions.

Although several studies have evaluated dynamic contrast-enhanced (DCE) MRI in the orbit, showing its utility when detecting and diagnosing orbital lesions, none have evaluated the pharmacokinetic models. To provide a quality-based pharmacokinetic model selection for characterizing orbital lesions using DCE-MRI at 3.0T. Prospective. From December 2015 to April 2017, 151 patients with an orbital lesion underwent MRI prior to surgery, including a high temporal resolution DCE sequence, divided into one training and one test dataset with 100 and 51 patients, respectively. 3T/DCE. Six different pharmacokinetic models were tested. Univariate and multivariate analyses were performed using Wilcoxon-2-sample tests and a logistic regression to compare parameters between malignant and benign tumors for each pharmacokinetic model for the whole cohort. Receiver operating characteristic (ROC) curve analyses were performed on the training dataset to determine area under curve (AUC) and optimal cutoff values for each pharmacokinetic model, then validated on the test dataset to calculate sensitivity, specificity, and accuracy. Regardless of the model, tissue blood flow and tissue blood volume values were significantly higher in malignant vs. benign lesions: 103.8-195.1 vs. 65-113.8, P [<10-4 -2.10-4 ] and 21.3-36.9 vs. 15.6-33.6, P [<10-4 -0.03] respectively. Extracellular volume fraction and permeability-surface area product or transfer constant appeared to be less relevant: 17.3-27.5 vs. 22.8-28.2, P [0.01-0.7], 1.7-4.9, P [0.2-0.9] and 9.5-38.8 vs. 8.1-22.8, P [<10-4 -0.6], respectively. ROC curves showed no significant differences in AUC between the different models. The two-compartment exchange (2CX) model ranked first for quality. DCE MRI pharmacokinetic model-derived parameters appeared to be useful for discriminating benign from malignant orbital lesions. The 2CX model provided the best quality of modeling and should be recommended. Perfusion-related DCE parameters appeared to be significantly more relevant to the diagnostic process. Level of Evidence 1 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2019;50:1514-1525.

Robust estimation of hemo-dynamic parameters in traditional DCE-MRI models.

PurposeIn dynamic contrast enhanced (DCE) MRI, separation of signal contributions from perfusion and leakage requires robust estimation of parameters in a pharmacokinetic model. We present and quantify the performance of a method to compute tissue hemodynamic parameters from DCE data using established pharmacokinetic models.MethodsWe propose a Bayesian scheme to obtain perfusion metrics from DCE MRI data. Initial performance is assessed through digital phantoms of the extended Tofts model (ETM) and the two-compartment exchange model (2CXM), comparing the Bayesian scheme to the standard Levenberg-Marquardt (LM) algorithm. Digital phantoms are also invoked to identify limitations in the pharmacokinetic models related to measurement conditions. Using computed maps of the extra vascular volume (ve) from 19 glioma patients, we analyze differences in the number of un-physiological high-intensity ve values for both ETM and 2CXM, using a one-tailed paired t-test assuming un-equal variance.ResultsThe Bayesian parameter estimation scheme demonstrated superior performance over the LM technique in the digital phantom simulations. In addition, we identified limitations in parameter reliability in relation to scan duration for the 2CXM. DCE data for glioma and cervical cancer patients was analyzed with both algorithms and demonstrated improvement in image readability for the Bayesian method. The Bayesian method demonstrated significantly fewer non-physiological high-intensity ve values for the ETM (p<0.0001) and the 2CXM (p<0.0001).ConclusionWe have demonstrated substantial improvement of the perceptive quality of pharmacokinetic parameters from advanced compartment models using the Bayesian parameter estimation scheme as compared to the LM technique.

Impact of fitting algorithms on errors of parameter estimates in dynamic contrast-enhanced MRI

Parameter estimation in dynamic contrast-enhanced MRI (DCE MRI) is usually performed by non-linear least square (NLLS) fitting of a pharmacokinetic model to a measured concentration-time curve. The two-compartment exchange model (2CXM) describes the compartments ‘plasma’ and ‘interstitial volume’ and their exchange in terms of plasma flow and capillary permeability. The model function can be defined by either a system of two coupled differential equations or a closed-form analytical solution. The aim of this study was to compare these two representations in terms of accuracy, robustness and computation speed, depending on parameter combination and temporal sampling. The impact on parameter estimation errors was investigated by fitting the 2CXM to simulated concentration-time curves. Parameter combinations representing five tissue types were used, together with two arterial input functions, a measured and a theoretical population based one, to generate 4D concentration images at three different temporal resolutions. Images were fitted by NLLS techniques, where the sum of squared residuals was calculated by either numeric integration with the Runge–Kutta method or convolution. Furthermore two example cases, a prostate carcinoma and a glioblastoma multiforme patient, were analyzed in order to investigate the validity of our findings in real patient data. The convolution approach yields improved results in precision and robustness of determined parameters. Precision and stability are limited in curves with low blood flow. The model parameter ve shows great instability and little reliability in all cases. Decreased temporal resolution results in significant errors for the differential equation approach in several curve types. The convolution excelled in computational speed by three orders of magnitude. Uncertainties in parameter estimation at low temporal resolution cannot be compensated by usage of the differential equations. Fitting with the convolution approach is superior in computational time, with better stability and accuracy at the same time.

Evaluation of pharmacokinetic models for perfusion imaging with dynamic contrast-enhanced magnetic resonance imaging in porcine skeletal muscle using low-molecular-weight contrast agents.

Pharmacokinetic models for perfusion quantification with a low-molecular-weight contrast agent (LMCA) in skeletal muscle using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) were evaluated. Tissue perfusion was measured in seven regions of interest (ROIs) placed in the total hind leg supplied by the femoral artery in seven female pigs. DCE-MRI was performed using a 3D gradient echo sequence with k-space sharing. The sequence was acquired twice, first after LMCA and then after blood pool contrast agent injection. Blood flow was augmented by continuous infusion of the vasodilator adenosine into the femoral artery, resulting in up to four times increased blood flow. The results obtained with several LMCA models were compared with those of a two-compartment blood pool model (2CBPM) consisting of a capillary and an arteriolar compartment. Measurements performed with a Doppler flow probe placed at the femoral artery served as ground truth. The two-compartment exchange model extended by an arteriolar compartment (E2CXM) showed the highest fit quality of all LMCA models and the most significant correlation with the Doppler measurements, r = 0.78 (P < 0.001). The best correspondence between the capillary perfusion measurements of the LMCA models and those of the 2CBPM was found with the E2CXM (slope of the regression line equal to 1, r = 0.85, P < 0.001). The results for the clinical patient data corresponded very well with the results obtained in the animal experiments. Double-contrast agent DCE-MRI in combination with the E2CXM yields the most reliable results and can be used in clinical routine. Magn Reson Med 79:3154-3162, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

The prognostic value of dynamic contrast-enhanced MRI contrast agent transfer constant Ktrans in cervical cancer is explained by plasma flow rather than vessel permeability

Background:The microvascular contrast agent transfer constant Ktrans has shown prognostic value in cervical cancer patients treated with chemoradiotherapy. This study aims to determine whether this is explained by the contribution to Ktrans of plasma flow (Fp), vessel permeability surface-area product (PS), or a combination of both.Methods:Pre-treatment dynamic contrast-enhanced MRI (DCE-MRI) data from 36 patients were analysed using the two-compartment exchange model. Estimates of Fp, PS, Ktrans, and fractional plasma and interstitial volumes (vp and ve) were made and used in univariate and multivariate survival analyses adjusting for clinicopathologic variables tumour stage, nodal status, histological subtype, patient age, tumour volume, and treatment type (chemoradiotherapy vs radiotherapy alone).Results:In univariate analyses, Fp (HR=0.25, P=0.0095) and Ktrans (HR=0.20, P=0.032) were significantly associated with disease-free survival while PS, vp and ve were not. In multivariate analyses adjusting for clinicopathologic variables, Fp and Ktrans significantly increased the accuracy of survival predictions (P=0.0089).Conclusions:The prognostic value of Ktrans in cervical cancer patients treated with chemoradiotherapy is explained by microvascular plasma flow (Fp) rather than vessel permeability surface-area product (PS).

Two-compartment modeling of tissue microcirculation revisited.

Conventional two-compartment modeling of tissue microcirculation is used for tracer kinetic analysis of dynamic contrast-enhanced (DCE) computed tomography or magnetic resonance imaging studies although it is well-known that the underlying assumption of an instantaneous mixing of the administered contrast agent (CA) in capillaries is far from being realistic. It was thus the aim of the present study to provide theoretical and computational evidence in favor of a conceptually alternative modeling approach that makes it possible to characterize the bias inherent to compartment modeling and, moreover, to approximately correct for it. Starting from a two-region distributed-parameter model that accounts for spatial gradients in CA concentrations within blood-tissue exchange units, a modified lumped two-compartment exchange model was derived. It has the same analytical structure as the conventional two-compartment model, but indicates that the apparent blood flow identifiable from measured DCE data is substantially overestimated, whereas the three other model parameters (i.e., the permeability-surface area product as well as the volume fractions of the plasma and interstitial distribution space) are unbiased. Furthermore, a simple formula was derived to approximately compute a bias-corrected flow from the estimates of the apparent flow and permeability-surface area product obtained by model fitting. To evaluate the accuracy of the proposed modeling and bias correction method, representative noise-free DCE curves were analyzed. They were simulated for 36 microcirculation and four input scenarios by an axially distributed reference model. As analytically proven, the considered two-compartment exchange model is structurally identifiable from tissue residue data. The apparent flow values estimated for the 144 simulated tissue/input scenarios were considerably biased. After bias-correction, the deviations between estimated and actual parameter values were (11.2±6.4) % (vs. (105±21) % without correction) for the flow, (3.6±6.1) % for the permeability-surface area product, (5.8±4.9) % for the vascular volume and (2.5±4.1) % for the interstitial volume; with individual deviations of more than 20% being the exception and just marginal. Increasing the duration of CA administration only had a statistically significant but opposite effect on the accuracy of the estimated flow (declined) and intravascular volume (improved). Physiologically well-defined tissue parameters are structurally identifiable and accurately estimable from DCE data by the conceptually modified two-compartment model in combination with the bias correction. The accuracy of the bias-corrected flow is nearly comparable to that of the three other (theoretically unbiased) model parameters. As compared to conventional two-compartmentmodeling, this feature constitutes a major advantage for tracer kinetic analysis of both preclinical and clinical DCE imaging studies.

Parameter estimation using weighted total least squares in the two-compartment exchange model.

The linear least squares (LLS) estimator provides a fast approach to parameter estimation in the linearized two-compartment exchange model. However, the LLS method may introduce a bias through correlated noise in the system matrix of the model. The purpose of this work is to present a new estimator for the linearized two-compartment exchange model that takes this noise into account. To account for the noise in the system matrix, we developed an estimator based on the weighted total least squares (WTLS) method. Using simulations, the proposed WTLS estimator was compared, in terms of accuracy and precision, to an LLS estimator and a nonlinear least squares (NLLS) estimator. The WTLS method improved the accuracy compared to the LLS method to levels comparable to the NLLS method. This improvement was at the expense of increased computational time; however, the WTLS was still faster than the NLLS method. At high signal-to-noise ratio all methods provided similar precisions while inconclusive results were observed at low signal-to-noise ratio. The proposed method provides improvements in accuracy compared to the LLS method, however, at an increased computational cost. Magn Reson Med 79:561-567, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Validation of Blood Volume Fraction Quantification with 3D Gradient Echo Dynamic Contrast-Enhanced Magnetic Resonance Imaging in Porcine Skeletal Muscle.

The purpose of this study was to assess the accuracy of fractional blood volume (vb) estimates in low-perfused and low-vascularized tissue using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). The results of different MRI methods were compared with histology to evaluate the accuracy of these methods under clinical conditions. vb was estimated by DCE-MRI using a 3D gradient echo sequence with k-space undersampling in five muscle groups in the hind leg of 9 female pigs. Two gadolinium-based contrast agents (CA) were used: a rapidly extravasating, extracellular, gadolinium-based, low-molecular-weight contrast agent (LMCA, gadoterate meglumine) and an extracellular, gadolinium-based, albumin-binding, slowly extravasating blood pool contrast agent (BPCA, gadofosveset trisodium). LMCA data were evaluated using the extended Tofts model (ETM) and the two-compartment exchange model (2CXM). The images acquired with administration of the BPCA were used to evaluate the accuracy of vb estimation with a bolus deconvolution technique (BD) and a method we call equilibrium MRI (EqMRI). The latter calculates the ratio of the magnitude of the relaxation rate change in the tissue curve at an approximate equilibrium state to the height of the same area of the arterial input function (AIF). Immunohistochemical staining with isolectin was used to label endothelium. A light microscope was used to estimate the fractional vascular area by relating the vascular region to the total tissue region (immunohistochemical vessel staining, IHVS). In addition, the percentage fraction of vascular volume was determined by multiplying the microvascular density (MVD) with the average estimated capillary lumen, , where d = 8μm is the assumed capillary diameter (microvascular density estimation, MVDE). Except for ETM values, highly significant correlations were found between most of the MRI methods investigated. In the cranial thigh, for example, the vb medians (interquartile range, IQRs) of IHVS, MVDE, BD, EqMRI, 2CXM and ETM were vb = 0.7(0.3)%, 1.1(0.4)%, 1.1(0.4)%, 1.4(0.3)%, 1.2(1.8)% and 0.1(0.2)%, respectively. Variances, expressed by the difference between third and first quartiles (IQR) were highest for the 2CXM for all muscle groups. High correlations between the values in four muscle groups—medial, cranial, lateral thigh and lower leg - estimated with MRI and histology were found between BD and EqMRI, MVDE and 2CXM and IHVS and ETM. Except for the ETM, no significant differences between the vb medians of all MRI methods were revealed with the Wilcoxon rank sum test. The same holds for all muscle regions using the 2CXM and MVDE. Except for cranial thigh muscle, no significant difference was found between EqMRI and MVDE. And except for the cranial thigh and the lower leg muscle, there was also no significant difference between the vb medians of BD and MVDE. Overall, there was good vb agreement between histology and the BPCA MRI methods and the 2CXM LMCA approach with the exception of the ETM method. Although LMCA models have the advantage of providing excellent curve fits and can in principle determine more physiological parameters than BPCA methods, they yield more inaccurate results.