Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy.
Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy; FIAB S.p.A., Vicchio, Firenze, Italy; I.A.S.I. - C.N.R., Via dei Taurini, Roma, Italy.
J Theor Biol. 2023 Feb 7;558:111355. doi: 10.1016/j.jtbi.2022.111355. Epub 2022 Nov 17.
This paper presents a mathematical model capable to reproduce a celebrated phenomenon in blood microcirculation known as Fåhræus effect, since its discovery by Robin Fåhræus (1929). This consists in a decaying of the relative hematocrit in small vessels as the vessel diameter decreases. The key point of the model is a formula, direct consequence of the basic principles of fluid dynamics, that links the relative hematocrit to the reservoir hematocrit and the vessel diameter, which confirms the observed behavior. To test the model we selected, among the few experiments carried on since then, those performed by Barbee and Cokelet (1971). The agreement is remarkable. An extended comparison is also carried out with a celebrated empirical formula proposed by Pries et al. (1992) to describe the same phenomenon.
本文提出了一个数学模型，能够再现血液微循环中一个著名的现象，即 Fåhræus 效应，该现象由 Robin Fåhræus（1929 年）首次发现。该现象表现为随着血管直径的减小，相对血细胞比容在小血管中逐渐降低。该模型的关键在于一个公式，它是流体动力学基本原理的直接推论，将相对血细胞比容与储液器血细胞比容和血管直径联系起来，这证实了所观察到的行为。为了测试我们选择的模型，我们从那时起进行的少数实验中选择了 Barbee 和 Cokelet（1971 年）进行的实验。结果非常吻合。我们还与 Pries 等人（1992 年）提出的一个著名经验公式进行了扩展比较，该公式用于描述相同的现象。
