The complex vascular dynamics and wall deposition of systemically injected nanoparticles is regulated by their geometrical properties (size, shape) and biophysical parameters (ligand–receptor bond type and surface density, local shear rates). Although sophisticated computational models have been developed to capture the vascular behavior of nanoparticles, it is increasingly recognized that purely deterministic approaches, where the governing parameters are known a priori and conclusively describe behaviors based on physical characteristics, may be too restrictive to accurately reflect natural processes. Here, a novel computational framework is proposed by coupling the physics dictating the vascular adhesion of nanoparticles with a stochastic model. In particular, two governing parameters (i.e. the ligand–receptor bond length and the ligand surface density on the nanoparticle) are treated as two stochastic quantities, whose values are not fixed a priori but would rather range in defined intervals with a certain probability. This approach is used to predict the deposition of spherical nanoparticles with different radii, ranging from 750 to 6,000 nm, in a parallel plate flow chamber under different flow conditions, with a shear rate ranging from 50 to 90 $$\text {s}^{-1}$$s-1. It is demonstrated that the resulting stochastic model can predict the experimental data more accurately than the original deterministic model. This approach allows one to increase the predictive power of mathematical models of any natural process by accounting for the experimental and intrinsic biological uncertainties.

中文翻译：

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用于最大化纳米颗粒血管粘附的贝叶斯分层模型

全身注射纳米颗粒的复杂血管动力学和壁沉积受其几何特性（尺寸、形状）和生物物理参数（配体-受体键类型和表面密度、局部剪切速率）的调节。尽管已经开发了复杂的计算模型来捕捉纳米粒子的血管行为，但人们越来越认识到，纯粹的确定性方法，其中控制参数是先验已知的，并最终描述基于物理特性的行为，可能过于严格，无法准确反映自然过程. 在这里，通过将指示纳米颗粒血管粘附的物理学与随机模型相结合，提出了一种新的计算框架。特别是，两个控制参数（即 纳米颗粒上的配体-受体键长和配体表面密度）被视为两个随机量，其值不是先验固定的，而是以一定概率在定义的区间内变化。该方法用于预测具有不同半径的球形纳米粒子的沉积，范围为 750 至 6,000 nm，在不同流动条件下的平行板流动室中，剪切速率为 50 至 90 $$\text {s}^ {-1}$$s-1。结果表明，由此产生的随机模型可以比原始确定性模型更准确地预测实验数据。这种方法允许通过考虑实验和内在生物不确定性来增加任何自然过程的数学模型的预测能力。