A Generalized Kinetic Model of Fractional Order Transport Dynamics with Transit Time Heterogeneity in Microvascular Space.

The aim of this study is to develop and validate a unifying kinetic model for microvascular transport by introducing an impulse response function that incorporates essential physiological parameters and integrates key features of existing models. This new methodology combines a one-compartment model of fractional order with a model that uses the gamma distribution to describe the distribution of capillary transit times. Central to this model are two primary parameters: [Formula: see text], representing the kurtosis of residue times, and [Formula: see text], signifying the width of the distribution of capillary transit times within a tissue voxel. To validate this proposed model, data from dynamic contrast-enhanced magnetic resonance imaging (DCI-MRI) were employed and the findings were compared with three existing models. Using the Akaike information criterion for model selection, the results demonstrate that the integrative model, especially at elevated blood flow rates, frequently offers superior fits in comparison to constrained models.

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

PURPOSE: 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. METHODS: 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. RESULTS: 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. CONCLUSIONS: 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.

Fractional calculus tracer kinetic compartment model for quantification of microvascular perfusion.

Objective. We evaluate a tracer kinetic model for quantification of physiological perfusion and microvascular residue time kurtosis (RTK) in skeletal muscle vasculature with first pass bolus experiments in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).Approach. A decreasing stretched Mittag-Leffler function (f1C model) was obtained as the impulse response solution of a rate equation of real-valued ('fractional') derivation order. The method was validated in skeletal muscle in the lower limb of seven female pigs examined by DCE-MRI. Dynamic imaging during blood pool contrast agent elimination was performed using a 3D gradient echo sequence with k-space sharing. Blood flow was augmented by continuous infusion of the vasodilator adenosine into the femoral artery increasing blood flow up to four times. Blood flow measured by a Doppler flow probe placed at the femoral artery served as ground truth.Main results. Goodness of fit and correlation with the Doppler measurements,r= 0.80 (P< 0.001), of the 4-parameter f1C model was comparable with the results obtained with a previously tested 6-parameter two-compartment (2C) model. The derivation orderαof the f1C model can be interpreted as a measure of microvascular RTK. With increasing blood flow,αdropped significantly, leading to an increase in RTK.Significance. The f1C model is a practical approach based on hemodynamic principles to quantify physiological microvascular perfusion but it is impaired due to its compartmental nature.

Liver function quantification of patients with portal vein embolization using dynamic contrast-enhanced MRI for assessment of hepatocyte uptake and elimination.

PURPOSE: We evaluated pharmacokinetic models which quantify liver function including biliary elimination based on a dynamic Gd-EOB-DTPA-enhanced magnetic resonance imaging (MRI) technique with sparse data collection feasible in clinical routine. METHODS: Twelve patients with embolized liver segments following interventional treatment of primary liver cancer or hepatic metastasis underwent MRI. During Gd-EOB-DTPA bolus administration, a 3D dynamic gradient-echo (GRE) MRI examination was performed over approx. 28 min. Interrupted data sampling was started approx. 5 min after contrast agent administration. Different implementations of dual-inlet models were tested, namely the Euler method (DE) and convolution with residue functions (C). A simple uptake model (U) and an uptake- elimination model (UE) extended by incorporating the biliary contrast agent elimination rate (Ke) were evaluated. RESULTS: The uptake-elimination model, calculated via the simple Euler method (UE- DE) and by convolution (UE-C), yielded similar overall estimates in terms of fitting quality and agreement with published values. The Euler method was approx. 50 times faster and yielded a mean elimination rate of Ke=1.8±1.2mL/(min·100 mL) in nonembolized liver tissue, which was significantly higher (p=8.8·10-4) than in embolized tissue Ke=0.4±0.4 mL/(min·100 mL). Fractional hepatocyte volume vh was not significantly higher in nonembolized tissue (52.4 ± 13.4 mL/100 mL) compared to embolized tissue (44.4 ± 26.1 mL/100 mL). CONCLUSIONS: Interrupted late enhancement MRI data sampling in conjunction with the uptake-elimination model, deconvolved by integration of the differential rate equation and combined with the simple uptake model implemented with the Euler method (U-DE), turned out to be a stable and practical method for reliable noninvasive assessment of liver function.

Assessment of micronecrotic tumor tissue using dynamic contrast-enhanced magnetic resonance imaging.

Compartmental models for evaluation of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) datasets assume a homogeneous interstitital volume distribution and homogeneous contrast agent (CA) distribution within each compartment, neglecting effects of CA diffusion within the compartments. When necrotic or micronecrotic tumor tissue is present, these assumptions may no longer be valid. Therefore, the present study investigates the validity of three compartmental models in assessing tumors with necrotic components. The general diffusion equation for inhomogeneous tissue was used to simulate the extravasation of a low-molecular-weight contrast agent from a feeding vessel into the interstitial space. The simulated concentration-time curves were evaluated using the extended Tofts model, a parallel 3-compartment model, and a sequential 3-compartment model. The extended Tofts model overestimated the interstitial volume fraction by a median of 6.9% resp. 10.0% and the parallel 3-compartment model by 8.6% resp. 15.5%, while the sequential 3-compartment model overestimated it by 0.2% resp. underestimated it by 18.8% when simulating a mean vessel distance of 100µm resp. 150µm. Overall, the sequential 3-compartment model provided more reliable results both for the total fractional interstitial volume and for the interstitial subcompartments.

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, [Formula: see text], 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.

Validation of Interstitial Fractional Volume Quantification by Using Dynamic Contrast-Enhanced Magnetic Resonance Imaging in Porcine Skeletal Muscles.

OBJECTIVES: The aim of our study was to assess the accuracy of fractional interstitial volume determination in low perfused and low vascularized tissue by using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). MATERIALS AND METHODS: The fractional interstitial volume (ve) was determined in the medial thigh muscle of 12 female pigs by using a 3-dimensional gradient echo sequence with k-space sharing and administering gadolinium-based contrast agent (gadoterate meglumine). Analysis was performed using 3 pharmacokinetic models: the simple Tofts model (TM), the extended TM (ETM), and the 2-compartment exchange model (2CXM). We investigated the effect of varying acquisition durations (ADs) on the model parameter estimates of the 3 models and compared the ve values with the results of histological examinations of muscle sections of the medial thigh muscle. RESULTS: Histological measurements yielded a median value (25%-75% quartile) of 4.8% (3.7%-6.2%) for ve. The interstitial fractional volume determined by DCE-MRI was comparable to the histological results but varied strongly with AD for the TM and ETM. For the TM and the ETM, the results were virtually the same. Choosing arterial hematocrit to Hcta = 0.4, the lowest median ve value determined by DCE-MRI was 5.2% (3.3%-6.1%) for the ETM at a 6-minute AD. The maximum ve value determined with the ETM at a 15-minute AD was 7.7% (4.5%-9.0%). The variation with AD of median ve values obtained with the 2CXM was much smaller: 6.2% (3.1%-9.2%) for the 6-minute AD and 6.3% (4.3%-9.8%) for the 15-minute AD. The best fit for the 2CXM was found at the 10-minute AD with ve values of 6.6% (3.7%-8.2%). No significant correlation between the histological and any DCE-MRI modeling results was found. Considering the expected accuracy of histological measurements, the medians of the MR modeling results were in good agreement with the histological prediction. A parameter determination uncertainty was identified with the use of the TMs. This is due to underfitting and has a major effect even on the analysis of tissues with low vascularization and low perfusion, where the estimated ve values depend on the AD. For the TM and ETM, the results best matched the histological measurements for an AD of 6 minutes. CONCLUSIONS: Owing to more fitting parameters, the 2CXM yielded better fits and the median interstitium-to-plasma rate constant kep was less depending on the AD; however, the uncertainty expressed by the 25% to 75% quartile range was found to be larger. An AD of 10 minutes was needed for the 2CXM to achieve accuracy comparable to those of the TMs with shorter ADs.

Validation of Perfusion Quantification with 3D Gradient Echo Dynamic Contrast-Enhanced Magnetic Resonance Imaging Using a Blood Pool Contrast Agent in Skeletal Swine Muscle.

The purpose of our study was to validate perfusion quantification in a low-perfused tissue by dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) with shared k-space sampling using a blood pool contrast agent. Perfusion measurements were performed in a total of seven female pigs. An ultrasonic Doppler probe was attached to the right femoral artery to determine total flow in the hind leg musculature. The femoral artery was catheterized for continuous local administration of adenosine to increase blood flow up to four times the baseline level. Three different stable perfusion levels were induced. The MR protocol included a 3D gradient-echo sequence with a temporal resolution of approximately 1.5 seconds. Before each dynamic sequence, static MR images were acquired with flip angles of 5°, 10°, 20°, and 30°. Both static and dynamic images were used to generate relaxation rate and baseline magnetization maps with a flip angle method. 0.1 mL/kg body weight of blood pool contrast medium was injected via a central venous catheter at a flow rate of 5 mL/s. The right hind leg was segmented in 3D into medial, cranial, lateral, and pelvic thigh muscles, lower leg, bones, skin, and fat. The arterial input function (AIF) was measured in the aorta. Perfusion of the different anatomic regions was calculated using a one- and a two-compartment model with delay- and dispersion-corrected AIFs. The F-test for model comparison was used to decide whether to use the results of the one- or two-compartment model fit. Total flow was calculated by integrating volume-weighted perfusion values over the whole measured region. The resulting values of delay, dispersion, blood volume, mean transit time, and flow were all in physiologically and physically reasonable ranges. In 107 of 160 ROIs, the blood signal was separated, using a two-compartment model, into a capillary and an arteriolar signal contribution, decided by the F-test. Overall flow in hind leg muscles, as measured by the ultrasound probe, highly correlated with total flow determined by MRI, R = 0.89 and P = 10-7. Linear regression yielded a slope of 1.2 and a y-axis intercept of 259 mL/min. The mean total volume of the investigated muscle tissue corresponds to an offset perfusion of 4.7mL/(min ⋅ 100cm3). The DCE-MRI technique presented here uses a blood pool contrast medium in combination with a two-compartment tracer kinetic model and allows absolute quantification of low-perfused non-cerebral organs such as muscles.

Establishment of a swine model for validation of perfusion measurement by dynamic contrast-enhanced magnetic resonance imaging.

The aim of the study was to develop a suitable animal model for validating dynamic contrast-enhanced magnetic resonance imaging perfusion measurements. A total of 8 pigs were investigated by DCE-MRI. Perfusion was determined on the hind leg musculature. An ultrasound flow probe placed around the femoral artery provided flow measurements independent of MRI and served as the standard of reference. Images were acquired on a 1.5 T MRI scanner using a 3D T1-weighted gradient-echo sequence. An arterial catheter for local injection was implanted in the femoral artery. Continuous injection of adenosine for vasodilation resulted in steady blood flow levels up to four times the baseline level. In this way, three different stable perfusion levels were induced and measured. A central venous catheter was used for injection of two different types of contrast media. A low-molecular weight contrast medium and a blood pool contrast medium were used. A total of 6 perfusion measurements were performed with a time interval of about 20-25 min without significant differences in the arterial input functions. In conclusion the accuracy of DCE-MRI-based perfusion measurement can be validated by comparison of the integrated perfusion signal of the hind leg musculature with the blood flow values measured with the ultrasound flow probe around the femoral artery.