Arch Hand Microsurg.  2021 Dec;26(4):285-292. 10.12790/ahm.21.0118.

Hemodynamic Principles in Free Tissue Transfer: Vascular Changes at the Anastomosis Site

• Doh G
• Kim B
• Lee D
• Yoon J
• Lim S
• Han YS
• Eo S

• KMID: 2522627
• DOI: http://doi.org/10.12790/ahm.21.0118

Abstract

Purpose
Various factors such as blood velocity, turbulent flow,and intimal injury are the most basic elements in free tissue transfers. However, how blood flow is reestablished, maintained, and changed after vascular anastomosis has rarely been studied.
Methods
A 54-year-old male sustained an unreplantable severe crushing injury to his right hand. The middle finger was transferred to the thumb as an ectopic replantation using an anastomosis between the radial and digital arteries. However, secondary reconstruction for the first web space defect was inevitable and an anteromedial thigh free flap procedure was performed 2 months later using the previously anastomosed vessels. During the procedures, we noted morphologic changes in the microvessels and tried to explain those phenomena by applying the principles of hemodynamics.
Results
Due to the discrepancy in vascular size between the radial and digital arteries, the velocity of the blood flow in the post-anastomotic site, which was the digital artery, must have been increased by Poiseuille’s law. Supposing that the velocity through the post-anastomotic site of the digital artery was increased, the pressure exerted by that flow decreased, resulting in more shrinkage of the vessel lumen of the digital artery by Bernoulli’s principle. Pascal’s law could also be applied in confined spaces with a static flow; where there is a constant pressure, as the radius of the post-anastomotic digital artery diminishes, the tension within the digital artery’s wall also simultaneously decreases. By Laplace’s law, the post-anastomotic digital artery’s wall thickens as less tension is exerted on the wall.
Conclusion
Understanding these simple flow mechanics will enable microsurgeons to better avoid the risk factors causing thrombosis, which is related to flap failure.

Keyword

Hemodynamic principles; Free tissue transfer; Poiseuille’s law; Bernoulli’s principle; Laplace’s law

Figure

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  Fig. 1. (A, B) A 54-year-old male patient sustained a severe crushing injury to his right hand and received a middle finger ectopic replantation to make a thumb. The radial artery was anastomosed to the digital artery. (C) Two months later, he had an additional anteromedial thigh (AMT) free flap procedure to resurface the web space. After the excision of the stenotic microvessels in the previous anastomosed site, a Y-shaped vein graft was performed. (D) Postoperative 4 months view.

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  Fig. 2. The radial artery was anastomosed with the digital artery for the ectopic replantation. The edge of the digital artery was bevel-cut to overcome the size discrepancy.

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  Fig. 3. Changes in the microvessels after 2 months of microvascular anastomosis. (A) The post-anastomotic digital artery was constricted and its wall was thickened compared to the preoperative vessel. (B) The size of the vascular lumen and wall thickness were compared.

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  Fig. 4. Poiseuille’s law. The blood volume flowing through a vessel is directly proportional to the pressure drop along with the distance of the vessel (P1–P2) and the fourth power of the radius of the vessel and inversely proportional to the length of the vessel (L) and the viscosity of the blood (η).Volume flow rate (F)=pressure difference (P1–P2)/viscous resistance (R)=π×(P1-P2)×r48×η×L

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  Fig. 5. Assuming that a constant amount of flow is maintained, the velocity of blood flow increases as it passes through the narrower vascular lumen.

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  Fig. 6. Bernoulli’s principle. When the blood flow speeds up in a constricted vessel area, its exerted pressure is decreased in that region, assuming that the density is constant (V1P2).

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  Fig. 7. Laplace’s law. (A) Simple illustration of Laplace’s law. At constant pressure, the wall tension (T) of the vessel can be decreased simply by increasing the thickness of the vessel wall. The thicker the wall, the lower the exerted wall tension. (B) Assuming that the thickness of the vessel wall is very small compared to the diameter of the vessel lumen, its exerted pressure (P) is related to the wall tension (T) of the vessel. The wall tension is proportional to the radius (R) of the vessel for a given exerted pressure.

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