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

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.

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.

In silico modeling for the hepatic circulation and transport: From the liver organ to lobules

The function of the liver depends critically on its blood supply. Numerous in silico models have been developed to study various aspects of the hepatic circulation, including not only the macro-hemodynamics at the organ level, but also the microcirculation at the lobular level. In addition, computational models of blood flow and bile flow have been used to study the transport, metabolism, and clearance of drugs in pharmacokinetic studies. These in silico models aim to provide insights into the liver organ function under both healthy and diseased states, and to assist quantitative analysis for surgical planning and postsurgery treatment. The purpose of this review is to provide an update on state-of-the-art in silico models of the hepatic circulation and transport processes. We introduce the numerical methods and the physiological background of these models. We also discuss multiscale frameworks that have been proposed for the liver, and their linkage with the large context of systems biology, systems pharmacology, and the Physiome project. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering Cardiovascular Diseases > Computational Models.