Assessment of hepatic arterial hemodynamics with 4D flow MRI: in vitro analysis of motion and spatial resolution related error and in vivo feasibility study in 20 volunteers.

OBJECTIVES: To assess the ability of four-dimensional (4D) flow MRI to measure hepatic arterial hemodynamics by determining the effects of spatial resolution and respiratory motion suppression in vitro and its applicability in vivo with comparison to two-dimensional (2D) phase-contrast MRI. METHODS: A dynamic hepatic artery phantom and 20 consecutive volunteers were scanned. The accuracies of Cartesian 4D flow sequences with k-space reordering and navigator gating at four spatial resolutions (0.5- to 1-mm isotropic) and navigator acceptance windows (± 8 to ± 2 mm) and one 2D phase-contrast sequence (0.5-mm in -plane) were assessed in vitro at 3 T. Two sequences centered on gastroduodenal and hepatic artery branches were assessed in vivo for intra - and interobserver agreement and compared to 2D phase-contrast. RESULTS: In vitro, higher spatial resolution led to a greater decrease in error than narrower navigator window (30.5 to -4.67% vs -6.64 to -4.67% for flow). In vivo, hepatic and gastroduodenal arteries were more often visualized with the higher resolution sequence (90 vs 71%). Despite similar interobserver agreement (κ = 0.660 and 0.704), the higher resolution sequence had lower variability for area (CV = 20.04 vs 30.67%), flow (CV = 34.92 vs 51.99%), and average velocity (CV = 26.47 vs 44.76%). 4D flow had lower differences between inflow and outflow at the hepatic artery bifurcation (11.03 ± 5.05% and 15.69 ± 6.14%) than 2D phase-contrast (28.77 ± 21.01%). CONCLUSION: High-resolution 4D flow can assess hepatic artery anatomy and hemodynamics with improved accuracy, greater vessel visibility, better interobserver reliability, and internal consistency. KEY POINTS: • Motion-suppressed Cartesian four-dimensional (4D) flow MRI with higher spatial resolution provides more accurate measurements even when accepted respiratory motion exceeds voxel size. • 4D flow MRI with higher spatial resolution provides substantial interobserver agreement for visualization of hepatic artery branches. • Lower peak and average velocities and a trend toward better internal consistency were observed with 4D flow MRI as compared to 2D phase-contrast.

Adaptive design of experiments to fit surrogate Gaussian process regression models allows fast sensitivity analysis of the input waveform for patient-specific 3D CFD models of liver radioembolization.

BACKGROUND AND OBJECTIVE: Patient-specific 3D computational fluid dynamics (CFD) models are increasingly being used to understand and predict transarterial radioembolization procedures used for hepatocellular carcinoma treatment. While sensitivity analyses of these CFD models can help to determine the most impactful input parameters, such analyses are computationally costly. Therefore, we aim to use surrogate modelling to allow relatively cheap sensitivity analysis. As an example, we compute Sobol's sensitivity indices for three input waveform shape parameters. METHODS: We extracted three characteristic shape parameters from our input mass flow rate waveform (peak systolic mass flow rate, heart rate, systolic duration) and defined our 3D input parameter space by varying these parameters within 75 %-125 % of their nominal values. To fit our surrogate model with a minimal number of costly CFD simulations, we developed an adaptive design of experiments (ADOE) algorithm. The ADOE uses 100 Latin hypercube sampled points in 3D input space to define the initial design of experiments (DOE). Subsequently, we re-sample input space with 10,000 Latin Hypercube sampled points and cheaply estimate the outputs using the surrogate model. In each of 27 equivolume bins which divide our input space, we determine the most uncertain prediction of the 10,000 points, compute the true outputs using CFD, and add these points to the DOE. For each ADOE iteration, we calculate Sobol's sensitivity indices, and we continue to add batches of 27 samples to the DOE until the Sobol indices have stabilized. RESULTS: We tested our ADOE algorithm on the Ishigami function and showed that we can reliably obtain Sobol's indices with an absolute error <0.1. Applying ADOE to our waveform sensitivity problem, we found that the first-order sensitivity indices were 0.0550, 0.0191 and 0.407 for the peak systolic mass flow rate, heart rate, and the systolic duration, respectively. CONCLUSIONS: Although the current study was an illustrative case, the ADOE allows reliable sensitivity analysis with a limited number of complex model evaluations, and performs well even when the optimal DOE size is a priori unknown. This enables us to identify the highest-impact input parameters of our model, and other novel, costly models in the future.

Simplification strategies for a patient-specific CFD model of particle transport during liver radioembolization.

BACKGROUND: Patient-specific 3D computational fluid dynamics (CFD) simulations have been used previously to identify the impact of injection parameters (e.g. injection location, velocity, etc.) on the particle distribution and the tumor dose during transarterial injection of radioactive microspheres for treatment of hepatocellular carcinoma. However, these simulations are computationally costly, so we aim to evaluate whether these can be reliably simplified. METHODS: We identified and applied five simplification strategies (i.e. truncation, steady flow modelling, moderate and severe grid coarsening, and reducing the number of cardiac cycles) to a patient-specific CFD setup. Subsequently, we evaluated whether these strategies can be used to (1) accurately predict the CFD output (i.e. particle distribution and tumor dose) and (2) quantify the sensitivity of the model output to a specific injection parameter (injection flow rate). RESULTS: For both accuracy and sensitivity purposes, moderate grid coarsening is the most reliable simplification strategy, allowing to predict the tumor dose with only a maximal deviation of 1.4 %, and a similar sensitivity (deviation of 0.7 %). The steady strategy performs the worst, with a maximal deviation in the tumor dose of 20 % and a difference in sensitivity of 10 %. CONCLUSION: The patient-specific 3D CFD simulations of this study can be reliably simplified by coarsening the grid, decreasing the computational time by roughly 45 %, which works especially well for sensitivity studies.

Spatiotemporal Analysis of Particle Spread to Assess the Hybrid Particle-Flow CFD Model of Radioembolization of HCC Tumors.

OBJECTIVE: Computational fluid dynamics (CFD) models can potentially aid in pre-operative planning of transarterial radioactive microparticle injections to treat hepatocellular carcinoma, but these models are computationally very costly. Previously, we introduced the hybrid particle-flow model as a surrogate, less costly modelling approach for the full particle distribution in truncated hepatic arterial trees. We hypothesized that higher cross-sectional particle spread could increase the match between flow and particle distribution. Here, we investigate whether truncation is still reliable for selective injection scenarios, and if spread is an important factor to consider for reliable truncation. METHODS: Moderate and severe up- and downstream truncation for selective injection served as input for the hybrid model to compare downstream particle distributions with non-truncated models. In each simulation, particle cross-sectional spread was quantified for 5-6 planes. RESULTS: Severe truncation gave maximum differences in particle distribution of ∼4-11% and ∼8-9% for down- and upstream truncation, respectively. For moderate truncation, these differences were only ∼1-1.5% and ∼0.5-2%. Considering all particles, spread increased downstream of the tip to 80-90%. However, spread was found to be much lower at specific timepoints, indicating high time-dependency. CONCLUSION: Combining domain truncation with hybrid particle-flow modelling is an effective method to reduce computational complexity, but moderate truncation is more reliable than severe truncation. Time-dependent spread measures show where differences might arise between flow and particle modelling. SIGNIFICANCE: The hybrid particle-flow model cuts down computational time significantly by reducing the physical domain, paving the way towards future clinical applications.

A Hybrid Particle-Flow CFD Modeling Approach in Truncated Hepatic Arterial Trees for Liver Radioembolization: A Patient-specific Case Study.

Hepatocellular carcinoma (HCC) is the most common form of primary liver cancer. At its intermediate, unresectable stage, HCC is typically treated by local injection of embolizing microspheres in the hepatic arteries to selectively damage tumor tissue. Interestingly, computational fluid dynamics (CFD) has been applied increasingly to elucidate the impact of clinically variable parameters, such as injection location, on the downstream particle distribution. This study aims to reduce the computational cost of such CFD approaches by introducing a novel truncation algorithm to simplify hepatic arterial trees, and a hybrid particle-flow modeling approach which only models particles in the first few bifurcations. A patient-specific hepatic arterial geometry was pruned at three different levels, resulting in three trees: Geometry 1 (48 outlets), Geometry 2 (38 outlets), and Geometry 3 (17 outlets). In each geometry, 1 planar injection and 3 catheter injections (each with different tip locations) were performed. For the truncated geometries, it was assumed that, downstream of the truncated outlets, particles distributed themselves proportional to the blood flow. This allowed to compare the particle distribution in all 48 "outlets" for each geometry. For the planar injections, the median difference in outlet-specific particle distribution between Geometry 1 and 3 was 0.21%; while the median difference between outlet-specific flow and particle distribution in Geometry 1 was 0.40%. Comparing catheter injections, the maximum median difference in particle distribution between Geometry 1 and 3 was 0.24%, while the maximum median difference between particle and flow distribution was 0.62%. The results suggest that the hepatic arterial tree might be reliably truncated to estimate the particle distribution in the full-complexity tree. In the resulting hybrid particle-flow model, explicit particle modeling was only deemed necessary in the first few bifurcations of the arterial tree. Interestingly, using flow distribution as a surrogate for particle distribution in the entire tree was considerably less accurate than using the hybrid model, although the difference was much higher for catheter injections than for planar injections. Future work should focus on replicating and experimentally validating these results in more patient-specific geometries.

Transarterial drug delivery for liver cancer: numerical simulations and experimental validation of particle distribution in patient-specific livers.

Background: Transarterial therapies are routinely used for the locoregional treatment of unresectable hepatocellular carcinoma (HCC). However, the impact of clinical parameters (i.e. injection location, particle size, particle density etc.) and patient-specific conditions (i.e. hepatic geometry, cancer burden) on the intrahepatic particle distribution (PD) after transarterial injection of embolizing microparticles is still unclear. Computational fluid dynamics (CFD) may help to better understand this impact.Methods: Using CFD, both the blood flow and microparticle mass transport were modeled throughout the 3D-reconstructed arterial vasculature of a patient-specific healthy and cirrhotic liver. An experimental feasibility study was performed to simulate the PD in a 3D-printed phantom of the cirrhotic arterial network.Results: Axial and in-plane injection locations were shown to be effective parameters to steer particles toward tumor tissue in both geometries. Increasing particle size or density made it more difficult for particles to exit the domain. As cancer burden increased, the catheter tip location mattered less. The in vitro study and numerical results confirmed that PD largely mimics flow distribution, but that significant differences are still possible.Conclusions: Our findings highlight that optimal parameter choice can lead to selective targeting of tumor tissue, but that targeting potential highly depends on patient-specific conditions.