Mathematical Institute, University of Oxford, Oxford, UK.
Department for Numerical Analysis and Scientific Computing, Simula Research Laboratory, Lysaker, Norway.
Int J Numer Method Biomed Eng. 2021 Jan;37(1):e3412. doi: 10.1002/cnm.3412. Epub 2020 Dec 17.
Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty-from uncertain input parameters to uncertain output quantities-in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon standard Monte Carlo (MC) methods, but their applicability and performance in biomedical applications is underexplored. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of tracer transport within the brain. We show that QMC outperforms standard MC simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard MC methods and should therefore be preferred for brain transport models.
高效的不确定性量化算法是理解高分辨率脑生理数学模型中不确定性从不确定输入参数到不确定输出量传播的关键。先进的蒙特卡罗方法，如拟蒙特卡罗（QMC）和多层蒙特卡罗（MLMC）有潜力极大地改进标准蒙特卡罗（MC）方法，但它们在生物医学应用中的适用性和性能尚未得到充分探索。在本文中，我们设计并应用 QMC 和 MLMC 方法来量化脑内示踪剂传输对流扩散模型中的不确定性。我们表明，当随机输入数量较少时，QMC 优于标准 MC 模拟。MLMC 明显优于 QMC 和标准 MC 方法，因此应该优先用于脑传输模型。
