RESUMEN

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.

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RESUMEN

The advancement of ischaemic stroke treatment relies on resource-intensive experiments and clinical trials. In order to improve ischaemic stroke treatments, such as thrombolysis and thrombectomy, we target the development of computational tools for in silico trials which can partially replace these animal and human experiments with fast simulations. This study proposes a model that will serve as part of a predictive unit within an in silico clinical trial estimating patient outcome as a function of treatment. In particular, the present work aims at the development and evaluation of an organ-scale microcirculation model of the human brain for perfusion prediction. The model relies on a three-compartment porous continuum approach. Firstly, a fast and robust method is established to compute the anisotropic permeability tensors representing arterioles and venules. Secondly, vessel encoded arterial spin labelling magnetic resonance imaging and clustering are employed to create an anatomically accurate mapping between the microcirculation and large arteries by identifying superficial perfusion territories. Thirdly, the parameter space of the problem is reduced by analysing the governing equations and experimental data. Fourthly, a parameter optimization is conducted. Finally, simulations are performed with the tuned model to obtain perfusion maps corresponding to an open and an occluded (ischaemic stroke) scenario. The perfusion map in the occluded vessel scenario shows promising qualitative agreement with computed tomography images of a patient with ischaemic stroke caused by large vessel occlusion. The results highlight that in the case of vessel occlusion (i) identifying perfusion territories is essential to capture the location and extent of underperfused regions and (ii) anisotropic permeability tensors are required to give quantitatively realistic estimation of perfusion change. In the future, the model will be thoroughly validated against experiments.

RESUMEN

The cerebral microvasculature plays a key role in the transport of blood and the delivery of nutrients to the cells that perform brain function. Although recent advances in experimental imaging techniques mean that its structure and function can be interrogated to very small length scales, allowing individual vessels to be mapped to a fraction of 1 µm, these techniques currently remain confined to animal models. In-vivo human data can only be obtained at a much coarser length scale, of order 1 mm, meaning that mathematical models of the microvasculature play a key role in interpreting flow and metabolism data. However, there are close to 10,000 vessels even within a single voxel of size 1 mm3. Given the number of vessels present within a typical voxel and the complexity of the governing equations for flow and volume changes, it is computationally challenging to solve these in full, particularly when considering dynamic changes, such as those found in response to neural activation. We thus consider here the governing equations and some of the simplifications that have been proposed in order more rigorously to justify in what generations of blood vessels these approximations are valid. We show that two approximations (neglecting the advection term and assuming a quasi-steady state solution for blood volume) can be applied throughout the cerebral vasculature and that two further approximations (a simple first order differential relationship between inlet and outlet flows and inlet and outlet pressures, and matching of static pressure at nodes) can be applied in vessels smaller than approximately 1 mm in diameter. We then show how these results can be applied in solving flow fields within cerebral vascular networks providing a simplified yet rigorous approach to solving dynamic flow fields and compare the results to those obtained with alternative approaches. We thus provide a framework to model cerebral blood flow and volume within the cerebral vasculature that can be used, particularly at sub human imaging length scales, to provide greater insight into the behaviour of blood flow and volume in the cerebral vasculature.

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