On the Sensitivity Analysis of Porous Finite Element Models for Cerebral Perfusion Estimation

Abstract

Computational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter. The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification. The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees

“…As part of the INSIST project [ 64 ], we are developing computational models of AIS at multiple scales to aid in optimising AIS treatments and developing medical devices. The micro-scale models presented here and in previous works [ 37 , 40 ] can in future be coupled with organ-scale models of AIS [ 65 – 67 ] and play a key role in predicting the secondary tissue damage caused by microthrombi after an unsuccessful thrombectomy [ 68 – 70 ].…”

Advancing treatment of retinal disease through in silico trials

“…Crucially, this trial was able to make predictions on what different outcomes may occur if the population was primarily hypertensive or normotensive using individuals as their own control, leveraging a major strength of ISCTs. The ischaemic stroke clinical trials expanded to consider more than just the localised area of intervention, considering whole brain oxygen and perfusion models [147,211]. Intervention models, such as thrombectomy, were developed and validated against in vitro models [178].…”

In silico thrombectomy trials for acute ischemic stroke

“…There are several approaches to surrogate modelling. One approach is a reduction in model complexity, for example, a simplification of the physics [16] or a reduction of element order and/or grid resolution in finite element modelling [17] . Alternatively, one can train a statistical model using results from the full model.…”