Department of Mathematics, Aberystwyth University, UK.
Biocompatibles UK Ltd, a Boston Scientific Company, Lakeview, Camberley, Surrey, UK.
Biorheology. 2020;57(2-4):77-85. doi: 10.3233/BIR-201004.
Foam sclerotherapy is the process of using an aqueous foam to deliver surfactant to a varicose vein to damage vein wall endothelial cells, causing the vein to spasm, collapse and ultimately be re-absorbed into the body. Aqueous foams are complex fluids that can exhibit a significant yield stress and high effective viscosity which depend on their composition, particularly the bubble size and liquid fraction.
To characterise the properties of foams used for varicose vein sclerotherapy and determine their effectiveness in the displacement of blood during sclerotherapy.
Foams are modelled as yield stress fluids and their flow profiles in a model vein are predicted. Values of the yield stress are determined from experimental data for three different foams using the Sauter mean of the bubble size distribution. Along with the measured liquid fraction of the foams, this information is collected into a Bingham number which entirely characterises the process of sclerotherapy.
Polydispersity in bubble size has a strong effect on the yield stress of a foam and the Sauter mean of the size distribution better captures the effects of a few large bubbles. Reducing the polydispersity increases the yield stress, and a higher yield stress results in a larger plug region moving along the vein, which is more effective in displacing blood. The width of the plug region is proportional to the Bingham number, which also has a quadratic dependence on the liquid fraction of the foam. Assuming typical values for the rate of injection of a foam, we predict that for a vein of diameter 5 mm, the most effective foams have low liquid fraction, a narrow size distribution, and a Bingham number B ≈ 4.5.
The Sauter mean radius provides the most appropriate measure of the bubble size for sclerotherapy and the Bingham number then provides a simple measure of the efficacy of foam sclerotherapy in a vein of a given size, and explains the ability of different foams to remove varicose veins. Foams containing small bubbles, with a narrow size distribution, and a low liquid fraction are beneficial for sclerotherapy.
泡沫硬化疗法是利用水基泡沫将表面活性剂输送到静脉曲张处以破坏静脉壁内皮细胞，使静脉痉挛、塌陷并最终被身体重新吸收的过程。水基泡沫是复杂的流体，具有显著的屈服应力和高有效粘度，这取决于它们的组成，特别是气泡大小和液体分数。
描述用于静脉曲张硬化治疗的泡沫特性，并确定其在硬化治疗过程中血液置换的效果。
将泡沫模型化为屈服应力流体，并预测其在模型静脉中的流动曲线。使用气泡大小分布的萨奥特均值，从三种不同泡沫的实验数据中确定屈服应力值。除了泡沫的实测液体分数外，这些信息被收集到宾汉数中，它完全描述了硬化治疗过程。
气泡大小的多分散性对泡沫的屈服应力有很强的影响，而大小分布的萨奥特均值更好地捕捉了少数大气泡的影响。降低多分散性会增加屈服应力，而较高的屈服应力会导致更大的栓塞区域沿静脉移动，从而更有效地置换血液。栓塞区域的宽度与宾汉数成正比，宾汉数也与泡沫的液体分数呈二次依赖关系。假设泡沫注入速率的典型值，我们预测对于直径为 5mm 的静脉，最有效的泡沫具有低液体分数、窄尺寸分布和宾汉数 B≈4.5。
萨奥特均值为硬化治疗提供了最适合的气泡尺寸度量，宾汉数则为给定尺寸静脉中泡沫硬化治疗的效果提供了简单的度量，并解释了不同泡沫去除静脉曲张的能力。含有小气泡、尺寸分布窄和液体分数低的泡沫对硬化治疗有益。
