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WIREs Syst Biol Med
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Virtual endovascular treatment of intracranial aneurysms: models and uncertainty

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Virtual endovascular treatment models (VETMs) have been developed with the view to aid interventional neuroradiologists and neurosurgeons to pre‐operatively analyze the comparative efficacy and safety of endovascular treatments for intracranial aneurysms. Based on the current state of VETMs in aneurysm rupture risk stratification and in patient‐specific prediction of treatment outcomes, we argue there is a need to go beyond personalized biomechanical flow modeling assuming deterministic parameters and error‐free measurements. The mechanobiological effects associated with blood clot formation are important factors in therapeutic decision making and models of post‐treatment intra‐aneurysmal biology and biochemistry should be linked to the purely hemodynamic models to improve the predictive power of current VETMs. The influence of model and parameter uncertainties associated to each component of a VETM is, where feasible, quantified via a random‐effects meta‐analysis of the literature. This allows estimating the pooled effect size of these uncertainties on aneurysmal wall shear stress. From such meta‐analyses, two main sources of uncertainty emerge where research efforts have so far been limited: (1) vascular wall distensibility, and (2) intra/intersubject systemic flow variations. In the future, we suggest that current deterministic computational simulations need to be extended with strategies for uncertainty mitigation, uncertainty exploration, and sensitivity reduction techniques. WIREs Syst Biol Med 2017, 9:e1385. doi: 10.1002/wsbm.1385 This article is categorized under: Analytical and Computational Methods > Computational Methods
An ideal virtual endovascular treatment model is comprised of sub‐models in which the vascular surface, virtual treatment, and biomechanics and biochemistry are modeled, respectively. Patient's angiogram (a) is segmented and a vascular surface model (b) is reconstructed and used for virtual treatment with coils or flow diverting stents (c). Computational fluid dynamics (CFD) simulations then are performed to calculate blood velocity field (d) in the presence of device‐induced intra‐aneurysmal clot, from which the shear stresses on the vessel wall (e) can be computed.
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Possible mechanisms of intra‐aneurysmal thrombosis.
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Forest plot showing the overestimation of maximum peak systolic aneurysmal wall shear stress (WSS) produced by the rigid arterial wall assumption. The plot illustrates effect sizes, Hedges’ g (represented by a square), and the confidence intervals (the horizontal lines) for each study and the pooled effect (the centre of the diamond) and its confidence interval (the width of the diamond) across all studies. Vertical dotted lines for each study show the study mean and the green squares are sized according to the study weight.
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Forest plot showing the overestimation of space‐and‐time‐averaged aneurysmal wall shear stress (WSS) produced by the generalized inflow boundary conditions. The plot illustrates effect sizes, Hedges’ g (represented by a square), and the confidence intervals (the horizontal lines) for each study and the pooled effect (the center of the diamond) and its confidence interval (the width of the diamond) across all studies. Vertical dotted lines for each study show the study mean and the green squares are sized according to the study weight.
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Forest plot showing the overestimation of space‐and‐time‐averaged aneurysmal wall shear stress (WSS) produced by the non‐Newtonian blood rheology. The plot illustrates effect sizes, Hedges’ g (represented by a square), and the confidence intervals (the horizontal lines) for each study and the pooled effect (the center of the diamond) and its confidence interval (the width of the diamond) across all studies. Vertical dotted lines for each study show the study mean and the green squares are sized according to the study weight.
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(a) shows overall structure of a typical mathematical model with xd and xu as vectors of deterministic and uncertain model inputs, respectively; f describing the model structure; and y as vector of model outputs. (b) shows error analysis and uncertainty quantification as processes to identify and quantify errors and uncertainties, respectively; and sensitivity analysis as a process to propagate the quantified errors and uncertainties to the model outputs.
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