Sensitivity Analysis of a Phenomenological Thrombosis Model and Growth Rate Characterisation

Abstract

Aortic dissection is a severe cardiovascular disease caused by the occurrence of a tear in the aortic wall. As a result, the blood penetrates the wall and makes a new blood channel called the false lumen. The haemodynamic conditions in the false lumen may contribute to the formation of thrombi, which influence the patient's diagnosis and outcomes. In this study, the focus is on a haemodynamic-based model of thrombus formation. Since the model construction entails uncertainties in the model parameters, a variance-based sensitivity analysis is performed. Thrombus formation at a backward-facing step is considered as a benchmark for the numerical simulations and sensitivity analysis. This geometry is capable of representing the main contributions of the model in thrombus formation. The study aims at improving the understanding of the model's structure and at preparing model simplifications to enable efficient patient-specific simulations in the future. A polynomial chaos expansion is employed as a surrogate model, from which the quantitative sensitivity indices are derived. In this study, nine model parameters are selected, whose proper values are not well known. The model responses taken into account are the maximum volume fraction of thrombus, its time development, and the thrombus growth rate. The results show that the model lends itself to model reduction since some of the model parameters show little to no influence on the model's outputs. A threshold value related to the concentration of bounded platelets and the bounded platelets reaction rate are identified as the key input parameters dominating the thrombus model predictions in the current geometry. Furthermore, the introduced thrombus characteristic growth time is driven by both the aforementioned variables.

Uncertainty quantification of a thrombosis model considering the clotting assay PFA‐100®

“…Six parameters showed significant influence in both quantities of interests considering their first Sobol' indices. This is in line with a recent study conducted by Melito et al 29 in which the authors found that only four of the nine parameters in the model of Menichini 7 were influential for predicting volume fraction of thrombus in a backwards step. However, investigation of parameter interaction via the total Sobol' indices revealed influence of a subset of the nine “non‐influential” parameters according to the first Sobol' indices.…”

“…Previous investigators have introduced several uncertainty quantification (UQ) strategies to evaluate the effect of such uncertainties on model performance in the context of blood flows 22–25 . UQ analyses in thrombosis models have been performed to identify the sensitivity of input parameters 26–29 . In most sensitivity studies, the global Morris method 30 or the Sobol' indices method 31 have been used.…”

“…The Sobol' method produces indices based on variance that quantifies the output uncertainty related to each input parameter. For example, Melito et al 29 performed a variance based sensitivity analysis on the thrombosis model of Menichini et al 7 considering thrombosis in a backward facing step. Their results suggest that only four of the nine parameters included in their thrombosis model had significant impact in thrombus formation implying that the model could be made sparser to optimize computational resources.…”

“…[22][23][24][25] UQ analyses in thrombosis models have been performed to identify the sensitivity of input parameters. [26][27][28][29] In most sensitivity studies, the global Morris method 30 or the Sobol' indices method 31 have been used. The Morris method is used as a screening tool to identify important parameters in models with a large number of input variables.…”

Shear-driven modelling of thrombus formation in type B aortic dissection

“…To reduce the complexity of the model and make it more efficient, it is beneficial to reduce the number of equations and variables. Melito et al (2020) performed a sensitivity analysis on Menichini and Xu’s 2016 model and showed that not all the model parameters influence thrombus formation, meaning that the model can be reduced. Model reduction is of interest for several reasons.…”