An efficient method for calculating kinetic parameters in a dual-input single-compartment model

Dynamic contrast enhanced (DCE) MRI estimation of vascular parameters using knowledge-based adaptive models

We introduce and validate four adaptive models (AMs) to perform a physiologically based Nested-Model-Selection (NMS) estimation of such microvascular parameters as forward volumetric transfer constant, Ktrans, plasma volume fraction, vp, and extravascular, extracellular space, ve, directly from Dynamic Contrast-Enhanced (DCE) MRI raw information without the need for an Arterial-Input Function (AIF). In sixty-six immune-compromised-RNU rats implanted with human U-251 cancer cells, DCE-MRI studies estimated pharmacokinetic (PK) parameters using a group-averaged radiological AIF and an extended Patlak-based NMS paradigm. One-hundred-ninety features extracted from raw DCE-MRI information were used to construct and validate (nested-cross-validation, NCV) four AMs for estimation of model-based regions and their three PK parameters. An NMS-based a priori knowledge was used to fine-tune the AMs to improve their performance. Compared to the conventional analysis, AMs produced stable maps of vascular parameters and nested-model regions less impacted by AIF-dispersion. The performance (Correlation coefficient and Adjusted R-squared for NCV test cohorts) of the AMs were: 0.914/0.834, 0.825/0.720, 0.938/0.880, and 0.890/0.792 for predictions of nested model regions, vp, Ktrans, and ve, respectively. This study demonstrates an application of AMs that quickens and improves DCE-MRI based quantification of microvasculature properties of tumors and normal tissues relative to conventional approaches.

Estimation of contrast agent bolus arrival delays for improved reproducibility of liver DCE MRI

Delays between contrast agent (CA) arrival at the site of vascular input function (VIF) sampling and the tissue of interest affect dynamic contrast enhanced (DCE) MRI pharmacokinetic modelling. We investigate effects of altering VIF CA bolus arrival delays on liver DCE MRI perfusion parameters, propose an alternative approach to estimating delays and evaluate reproducibility.

Thirteen healthy volunteers (28.7  ±  1.9 years, seven males) underwent liver DCE MRI using dual-input single compartment modelling, with reproducibility (n  =  9) measured at 7 days. Effects of VIF CA bolus arrival delays were assessed for arterial and portal venous input functions. Delays were pre-estimated using linear regression, with restricted free modelling around the pre-estimated delay. Perfusion parameters and 7 days reproducibility were compared using this method, freely modelled delays and no delays using one-way ANOVA. Reproducibility was assessed using Bland–Altman analysis of agreement.

Maximum percent change relative to parameters obtained using zero delays, were  −31% for portal venous (PV) perfusion, +43% for total liver blood flow (TLBF), +3247% for hepatic arterial (HA) fraction, +150% for mean transit time and  −10% for distribution volume. Differences were demonstrated between the 3 methods for PV perfusion (p  =  0.0085) and HA fraction (p  <  0.0001), but not other parameters. Improved mean differences and Bland–Altman 95% Limits-of-Agreement for reproducibility of PV perfusion (9.3 ml/min/100 g, ±506.1 ml/min/100 g) and TLBF (43.8 ml/min/100 g, ±586.7 ml/min/100 g) were demonstrated using pre-estimated delays with constrained free modelling.

CA bolus arrival delays cause profound differences in liver DCE MRI quantification. Pre-estimation of delays with constrained free modelling improved 7 days reproducibility of perfusion parameters in volunteers.

Robustness to noise of arterial blood flow estimation methods in CT perfusion

BACKGROUND

Perfusion CT is a technology which allows functional evaluation of tissue vascularity. Due to this potential, it is finding increasing utility in oncology. Although since its introduction continuous advances have interested CT technique, some issues have to be still defined, concerning both clinical and technical aspects. In this study, we dealt with the comparison of two widely employed mathematical models (dual input one compartment model - DOCM - and maximum slope - SM -) analyzing their robustness to the noise.

METHODS

We carried out a computer simulation process to quantify effect of noise on the evaluation of an important perfusion parameter (Arterial Blood Flow - BFa) in liver tumours. A total of 4500 liver TAC, corresponding to 3 fixed BFa values, were simulated using different arterial and portal TAC (computed from 5 real CT images) at 10 values of signal to noise ratio (SNR). BFa values were calculated by applying four different algorithms, specifically developed, to these noisy simulated curves. Three algorithms were developed to implement SM (one semiautomatic, one automatic and one automatic with filtering) and the last for the DOCM method.

RESULTS

In all the simulations, DOCM provided the best results, i.e., those with the lowest percentage error compared to the reference value of BFa. Concerning SM, the results are variable. Results obtained with the automatic algorithm with filtering are close to the reference value, but only if SNR is higher than 50. Vice versa, results obtained by means of the semiautomatic algorithm gave, in all simulations, the lowest results with the lowest standard deviation of the percentage error.

CONCLUSIONS

Since the use of DOCM is limited by the necessity that portal vein is visible in CT scans, significant restriction for patients' follow-up, we concluded that SM can be reliably employed. However, a proper software has to be used and an estimation of SNR would be carried out.

A simple and inexpensive system for controlling body temperature in small animal experiments using MRI and the effect of body temperature on the hepatic kinetics of Gd-EOB-DTPA

The purpose of this study was to develop a simple and inexpensive system for controlling body temperature in small animal experiments using magnetic resonance imaging (MRI) and to investigate the effect of body temperature on the kinetic behavior of gadolinium ethoxybenzyl diethylenetriamine pentaacetic acid (Gd-EOB-DTPA) in the liver. In our temperature-control system, body temperature was controlled using a feedback-regulated heated or cooled air flow generated by two Futon dryers. The switches of the two Futon dryers were controlled using a digital temperature controller, in which the rectal temperature of a mouse measured by an optical fiber thermometer was used as the input. In experimental studies, male ICR mice aged 8weeks old were used and allocated into 5 groups (39-, 36-, 33-, 30-, and 27-degree groups, n=10), in which the body temperature was maintained at 39 °C, 36 °C, 33 °C, 30 °C, and 27 °C, respectively, using our system. The dynamic contrast-enhanced MRI (DCE-MRI) data were acquired with an MRI system for animal experiments equipped with a 1.5-Tesla permanent magnet, for approximately 43min, after the injection of Gd-EOB-DTPA into the tail vein. After correction of the image shift due to the temperature-dependent drift of the Larmor frequency using the gradient-based image registration method with robust estimation of displacement parameters, the kinetic behavior of Gd-EOB-DTPA was analyzed using an empirical mathematical model. With the use of this approach, the upper limit of the relative enhancement (A), the rates of contrast uptake (α) and washout (β), the parameter related to the slope of early uptake (q), the area under the curve (AUC), the maximum relative enhancement (REmax), the time to REmax (Tmax), and the elimination half-life of the contrast agent (T1/2) were calculated. The body temperature of mice could be controlled well by use of our system. Although there were no significant differences in α, AUC, and q among groups, there were significant differences in A, REmax, β, Tmax, and T1/2, indicating that body temperature significantly affects the kinetic behavior of Gd-EOB-DTPA in the liver. In conclusion, our system will be useful for controlling body temperature in small animal experiments using MRI. Because body temperature significantly affects the kinetic behavior of Gd-EOB-DTPA in the liver, the control of body temperature is essential and should be carefully considered when performing DCE-MRI studies in small animal experiments.

GPU-accelerated voxelwise hepatic perfusion quantification

Voxelwise quantification of hepatic perfusion parameters from dynamic contrast enhanced (DCE) imaging greatly contributes to assessment of liver function in response to radiation therapy. However, the efficiency of the estimation of hepatic perfusion parameters voxel-by-voxel in the whole liver using a dual-input single-compartment model requires substantial improvement for routine clinical applications. In this paper, we utilize the parallel computation power of a graphics processing unit (GPU) to accelerate the computation, while maintaining the same accuracy as the conventional method. Using compute unified device architecture-GPU, the hepatic perfusion computations over multiple voxels are run across the GPU blocks concurrently but independently. At each voxel, nonlinear least-squares fitting the time series of the liver DCE data to the compartmental model is distributed to multiple threads in a block, and the computations of different time points are performed simultaneously and synchronically. An efficient fast Fourier transform in a block is also developed for the convolution computation in the model. The GPU computations of the voxel-by-voxel hepatic perfusion images are compared with ones by the CPU using the simulated DCE data and the experimental DCE MR images from patients. The computation speed is improved by 30 times using a NVIDIA Tesla C2050 GPU compared to a 2.67 GHz Intel Xeon CPU processor. To obtain liver perfusion maps with 626 400 voxels in a patient's liver, it takes 0.9 min with the GPU-accelerated voxelwise computation, compared to 110 min with the CPU, while both methods result in perfusion parameters differences less than 10(-6). The method will be useful for generating liver perfusion images in clinical settings.

Assessment of liver function in thioacetamide-induced rat acute liver injury using an empirical mathematical model and dynamic contrast-enhanced MRI with Gd-EOB-DTPA

PURPOSE

To evaluate thioacetamide (TAA)-induced acute liver injury in rats using an empirical mathematical model (EMM) and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) with gadolinium ethoxybenzyl diethylenetriamine pentaacetic acid (Gd-EOB-DTPA).

MATERIALS AND METHODS

Eighteen rats were divided into three groups (normal control [n = 6], TAA [140] [n = 6], and TAA [280] groups [n = 6]). The rats of the TAA (140) and TAA (280) groups were intravenously injected with 140 and 280 mg/kg body weight (BW) of TAA, respectively, while those of the normal control group were intravenously injected with the same volume of saline. DCE-MRI studies were performed using Gd-EOB-DTPA (0.025 mmol Gd/kg; 0.1 mL/kg BW) as the contrast agent 48 hours after TAA or saline injection. After the DCE-MRI study, blood was sampled and serum aspartate aminotransferase (AST) and alanine aminotransferase (ALT) were measured. We calculated the rate of contrast uptake (α), the rate of contrast washout (β), the elimination half-life of relative enhancement (RE) (T(1/2)), the maximum RE (RE(max)), and the time to (RE(max)) (T(max)) from time-signal intensity curves using EMM.

RESULTS

The RE(max) values in the TAA (140) groups and TAA (280) groups were significantly smaller than that in the normal control group. The T(max) value in the TAA (280) group was significantly greater than that in the normal control group. The β value in the TAA (280) group was significantly smaller than those in the normal control and TAA (140) groups, whereas there were no significant differences in β among groups. The T(1/2) value in the TAA (280) group was significantly greater than those in the normal control and TAA (140) groups. The RE(max), T(max), β, and T(1/2) values significantly correlated with AST and ALT.

CONCLUSION

The EMM is useful for evaluating TAA-induced acute liver injury using DCE-MRI with Gd-EOB-DTPA.

Error analysis of the quantification of hepatic perfusion using a dual-input single-compartment model

We performed an error analysis of the quantification of liver perfusion from dynamic contrast-enhanced computed tomography (DCE-CT) data using a dual-input single-compartment model for various disease severities, based on computer simulations. In the simulations, the time-density curves (TDCs) in the liver were generated from an actually measured arterial input function using a theoretical equation describing the kinetic behavior of the contrast agent (CA) in the liver. The rate constants for the transfer of CA from the hepatic artery to the liver (K(1a)), from the portal vein to the liver (K(1p)), and from the liver to the plasma (k(2)) were estimated from simulated TDCs with various plasma volumes (V(0)s). To investigate the effect of the shapes of input functions, the original arterial and portal-venous input functions were stretched in the time direction by factors of 2, 3 and 4 (stretching factors). The above parameters were estimated with the linear least-squares (LLSQ) and nonlinear least-squares (NLSQ) methods, and the root mean square errors (RMSEs) between the true and estimated values were calculated. Sensitivity and identifiability analyses were also performed. The RMSE of V(0) was the smallest, followed by those of K(1a), k(2) and K(1p) in an increasing order. The RMSEs of K(1a), K(1p) and k(2) increased with increasing V(0), while that of V(0) tended to decrease. The stretching factor also affected parameter estimation in both methods. The LLSQ method estimated the above parameters faster and with smaller variations than the NLSQ method. Sensitivity analysis showed that the magnitude of the sensitivity function of V(0) was the greatest, followed by those of K(1a), K(1p) and k(2) in a decreasing order, while the variance of V(0) obtained from the covariance matrices was the smallest, followed by those of K(1a), K(1p) and k(2) in an increasing order. The magnitude of the sensitivity function and the variance increased and decreased, respectively, with increasing disease severity and decreased and increased, respectively, with increasing stretching factor except for V(0). Identifiability analysis showed that the identifiability between K(1)(p) and k(2) was lower than that between K(1)(a) and k(2) or between K(1a) and K(1p). In conclusion, this study will be useful for understanding the accuracy and reliability of the quantitative measurement of liver perfusion using a dual-input single-compartment model and DCE-CT data.

A quantitative method for estimating hepatic blood flow using a dual-input single-compartment model

The purpose of this study was to investigate the accuracy of a quantitative method for estimating arterial hepatic blood flow and portal hepatic blood flow separately using a dual-input single-compartment model compared with the maximum slope method using computer simulations and clinical data. In computer simulations, the rate constants for the transfer of contrast agent (CA) from the hepatic artery to the liver (K(1a)), from the portal vein to the liver (K(1p)) and from the liver to the blood (k(2)) were estimated from simulated time-density curves with various transit times of CA from the aorta to the liver (tau(a)) and from the portal vein to the liver (tau(p)) using the linear least-squares (LLSQ) method. In clinical studies, dynamic CT data were acquired from 27 patients, and parametric maps of K(1a), K(1p) and k(2) were generated by applying the LLSQ method pixel by pixel. In simulation studies, tau(a) and tau(p) were found to have a large and a small effect on the estimates of K(1a) and K(1p), respectively. In clinical studies, the K(1a) and K(1p) values estimated with the maximum slope method were underestimated by 60+/-29% and 37+/-12%, respectively, compared with those estimated by the LLSQ method. In conclusion, our results suggest that correction of tau(a) is necessary for accurately estimating K(1a) and K(1p). Our method is therefore promising for the evaluation of hepatic blood flow in various liver diseases because it allows us to evaluate arterial hepatic blood flow and portal hepatic blood flow separately and visually.