论文标题
用多级和准蒙特卡洛的大脑间隙流体中示踪剂分布的快速不确定性定量
Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo
论文作者
论文摘要
在高分辨率的数学模型中，有效的不确定性定量算法是了解不确定性传播的关键 - 从不确定的输入参数到不确定的输出量。先进的蒙特卡洛方法，例如准蒙特卡洛（QMC）和多级蒙特卡洛（MLMC）具有对标准蒙特卡洛（MC）方法显着改进的潜力，但是它们在生物医学应用中的适用性和性能均未被倍增。在本文中，我们设计并应用QMC和MLMC方法来量化大脑内示踪剂传输模型的不确定性。我们表明，当随机输入的数量很少时，QMC优于标准MC模拟。 MLMC的表现均优于QMC和标准MC方法，因此对于脑运输模型来说应该优选。
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.
