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

Unified Bayesian network for uncertainty quantification of physiological parameters in dynamic contrast enhanced (DCE) MRI of the liver

Objective. Physiological parameter estimation is affected by intrinsic ambiguity in the data such as noise and model inaccuracies. The aim of this work is to provide a deep learning framework for accurate parameter and uncertainty estimates for DCE-MRI in the liver.Approach. Concentration time curves are simulated to train a Bayesian neural network (BNN). Training of the BNN involves minimization of a loss function that jointly minimizes the aleatoric and epistemic uncertainties. Uncertainty estimation is evaluated for different noise levels and for different out of distribution (OD) cases, i.e. where the data during inference differs strongly to the data during training. The accuracy of parameter estimates are compared to a nonlinear least squares (NLLS) fitting in numerical simulations andin vivodata of a patient suffering from hepatic tumor lesions.Main results. BNN achieved lower root-mean-squared-errors (RMSE) than the NLLS for the simulated data. RMSE of BNN was on overage of all noise levels lower by 33% ± 1.9% forktrans, 22% ± 6% forveand 89% ± 5% forvpthan the NLLS. The aleatoric uncertainties of the parameters increased with increasing noise level, whereas the epistemic uncertainty increased when a BNN was evaluated with OD data. For thein vivodata, more robust parameter estimations were obtained by the BNN than the NLLS fit. In addition, the differences between estimated parameters for healthy and tumor regions-of-interest were significant (p< 0.0001).Significance. The proposed framework allowed for accurate parameter estimates for quantitative DCE-MRI. In addition, the BNN provided uncertainty estimates which highlighted cases of high noise and in which the training data did not match the data during inference. This is important for clinical application because it would indicate cases in which the trained model is inadequate and additional training with an adapted training data set is required.

Vastly accelerated linear least-squares fitting with numerical optimization for dual-input delay-compensated quantitative liver perfusion mapping

PURPOSE

To propose an efficient algorithm to perform dual input compartment modeling for generating perfusion maps in the liver.

METHODS

We implemented whole field-of-view linear least squares (LLS) to fit a delay-compensated dual-input single-compartment model to very high temporal resolution (four frames per second) contrast-enhanced 3D liver data, to calculate kinetic parameter maps. Using simulated data and experimental data in healthy subjects and patients, whole-field LLS was compared with the conventional voxel-wise nonlinear least-squares (NLLS) approach in terms of accuracy, performance, and computation time.

RESULTS

Simulations showed good agreement between LLS and NLLS for a range of kinetic parameters. The whole-field LLS method allowed generating liver perfusion maps approximately 160-fold faster than voxel-wise NLLS, while obtaining similar perfusion parameters.

CONCLUSIONS

Delay-compensated dual-input liver perfusion analysis using whole-field LLS allows generating perfusion maps with a considerable speedup compared with conventional voxel-wise NLLS fitting. Magn Reson Med 79:2415-2421, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Improved hepatic arterial fraction estimation using cardiac output correction of arterial input functions for liver DCE MRI

Liver dynamic contrast enhanced (DCE) MRI pharmacokinetic modelling could be useful in the assessment of diffuse liver disease and focal liver lesions, but is compromised by errors in arterial input function (AIF) sampling. In this study, we apply cardiac output correction to arterial input functions (AIFs) for liver DCE MRI and investigate the effect on dual-input single compartment hepatic perfusion parameter estimation and reproducibility.

Thirteen healthy volunteers (28.7  ±  1.94 years, seven males) underwent liver DCE MRI and cardiac output measurement using aortic root phase contrast MRI (PCMRI), with reproducibility (n  =  9) measured at 7 d. Cardiac output AIF correction was undertaken by constraining the first pass AIF enhancement curve using the indicator-dilution principle. Hepatic perfusion parameters with and without cardiac output AIF correction were compared and 7 d reproducibility assessed.

Differences between cardiac output corrected and uncorrected liver DCE MRI portal venous (PV) perfusion (p  =  0.066), total liver blood flow (TLBF) (p  =  0.101), hepatic arterial (HA) fraction (p  =  0.895), mean transit time (MTT) (p  =  0.646), distribution volume (DV) (p  =  0.890) were not significantly different. Seven day corrected HA fraction reproducibility was improved (mean difference 0.3%, Bland–Altman 95% limits-of-agreement (BA95%LoA)  ±27.9%, coefficient of variation (CoV) 61.4% versus 9.3%, ±35.5%, 81.7% respectively without correction). Seven day uncorrected PV perfusion was also improved (mean difference 9.3 ml min⁻¹/100 g, BA95%LoA  ±506.1 ml min⁻¹/100 g, CoV 64.1% versus 0.9 ml min⁻¹/100 g, ±562.8 ml min⁻¹/100 g, 65.1% respectively with correction) as was uncorrected TLBF (mean difference 43.8 ml min⁻¹/100 g, BA95%LoA  ±586.7 ml min⁻¹/ 100 g, CoV 58.3% versus 13.3 ml min⁻¹/100 g, ±661.5 ml min⁻¹/100 g, 60.9% respectively with correction). Reproducibility of uncorrected MTT was similar (uncorrected mean difference 2.4 s, BA95%LoA  ±26.7 s, CoV 60.8% uncorrected versus 3.7 s, ±27.8 s, 62.0% respectively with correction), as was and DV (uncorrected mean difference 14.1%, BA95%LoA  ±48.2%, CoV 24.7% versus 10.3%, ±46.0%, 23.9% respectively with correction).

Cardiac output AIF correction does not significantly affect the estimation of hepatic perfusion parameters but demonstrates improvements in normal volunteer 7 d HA fraction reproducibility, but deterioration in PV perfusion and TLBF reproducibility. Improved HA fraction reproducibility maybe important as arterialisation of liver perfusion is increased in chronic liver disease and within malignant liver lesions.

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.

Assessment of blood flow in hepatocellular carcinoma: correlations of computed tomography perfusion imaging and circulating angiogenic factors

Hepatocellular carcinoma (HCC) is a highly vascular tumor through the process of angiogenesis. To evaluate more non-invasive techniques for assessment of blood flow (BF) in HCC, this study examined the relationships between BF of HCC measured by computer tomography (CT) perfusion imaging and four circulating angiogenic factors in HCC patients. Interleukin 6 (IL-6), interleukin 8 (IL-8), vascular endothelial growth factor (VEGF), and platelet derived growth factor (PDGF) in plasma were measured using Bio-Plex multiplex immunoassay in 21 HCC patients and eight healthy controls. Circulating IL-6, IL-8 and VEGF showed higher concentrations in HCC patients than in controls (p < 0.05), and predicted HCC occurrence better than chance (p < 0.01). Twenty-one patients with HCC received 21-phase liver imaging using a 64-slice CT. Total BF, arterial BF, portal BF, arterial fraction (arterial BF/total BF) of the HCC and surrounding liver parenchyma, and HCC-parenchyma ratio were measured using a dual-vessel model. After analyzing the correlations between BF in HCC and four circulating angiogenic factors, we found that the HCC-parenchyma ratio of arterial BF showed a significantly positive correlation with the level of circulating IL-8 (p < 0.05). This circulating biomarker, IL-8, provides a non-invasive tool for assessment of BF in HCC.

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.

Correction of arterial input function in dynamic contrast-enhanced MRI of the liver

PURPOSE

To develop a postprocessing method to correct saturation of arterial input function (AIF) in T1-weighted dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) for quantification of hepatic perfusion.

MATERIALS AND METHODS

The saturated AIF is corrected by parameterizing the first pass of the AIF as a smooth function with a single peak and minimizing a least-squares error in fitting the liver DCE-MRI data to a dual-input single-compartment model. Sensitivities of the method to the degree of saturation in the AIF first-pass peak and the image contrast-to-noise ratio were assessed. The method was also evaluated by correlating portal venous perfusion with an independent overall liver function measurement.

RESULTS

The proposed method corrects the distorted AIF with a saturation ratio up to 0.45. The corrected AIF improved hepatic arterial perfusion by -23.4% and portal venous perfusion by 26.9% in a study of 12 patients with liver cancers. The correlation between the mean voxelwise portal venous perfusion and overall liver function measurement was improved by using the corrected AIFs (R(2) = 0.67) compared with the saturated AIFs (R(2) = 0.39).

CONCLUSION

The method is robust for correcting AIF distortion and has the potential to improve quantification of hepatic perfusion for assessment of liver tissue response to treatment in patients with hepatic cancers.

CT hepatic perfusion measurement: comparison of three analytic methods

OBJECTIVES

To compare the efficacy of three analytic methods, maximum slope (MS), dual-input single-compartment model (CM) and deconvolution (DC), for CT measurements of hepatic perfusion and assess the effects of extra-hepatic systemic factors.

MATERIALS AND METHODS

Eighty-eight patients who were suspected of having metastatic liver tumors underwent hepatic CT perfusion. The scans were performed at the hepatic hilum 7-77 s after administration of contrast material. Hepatic arterial and portal perfusions (HAP and HPP, ml/min/100 ml) and arterial perfusion fraction (APF, %) were calculated with the three methods, followed by correlation assessment. Partial correlation analysis was used to assess the effects on hepatic perfusion values by various factors such as age, sex, risk of cardiovascular diseases, arrival time of contrast material at abdominal aorta, transit time from abdominal aorta to hepatic parenchyma, and liver dysfunction.

RESULTS

Mean HAP of MS was significantly higher than DC. HPP of CM was significantly higher than MS and CM, and HPP of MS was significantly higher than DC. There was no significant difference in APF. HAP and APF showed significant and moderate correlations among the methods. HPP showed significant and moderate correlations between CM and DC, and poor correlation between MS and CM or DC. All methods showed weak correlations between HAP or APF and age or sex. Finally, MS showed weak correlations between HAP or HPP and arrival time or cardiovascular risks.

CONCLUSIONS

Hepatic perfusion values arrived at with the three methods are not interchangeable. CM and DC are less susceptible to extra-hepatic systemic factors.

Perfusion magnetic resonance imaging of the liver

Perfusion magnetic resonance imaging (MRI) studies quantify the microcirculatory status of liver parenchyma and liver lesions, and can be used for the detection of liver metastases, assessing the effectiveness of anti-angiogenic therapy, evaluating tumor viability after anti-cancer therapy or ablation, and diagnosis of liver cirrhosis and its severity. In this review, we discuss the basic concepts of perfusion MRI using tracer kinetic modeling, the common kinetic models applied for analyses, the MR scanning techniques, methods of data processing, and evidence that supports its use from published clinical and research studies. Technical standardization and further studies will help to establish and validate perfusion MRI as a clinical imaging modality.

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.