Modeling of blood flow through sutured micro-vascular anastomoses

Mathematical Modeling of Vessel Geometry and Circumference in Microvascular Surgery

Introduction

Microvascular anastomosis has traditionally been executed with a perpendicular transection through the vessel at the widest diameter to increase circumference and thus increase blood flow while decreasing resistance. In Chen's 2015 article, it was suggested that an "open Y" would improve vessel size match, and Wei and Mardini discuss angled transections of the vessels. This project aims to explore the geometric configurations feasible at the anastomotic transection and mathematically model the resulting hypothetical increases in circumference.

Materials and Methods

The mathematical models were theoretically developed by our team. The formulas model increases in circumference of the transection at different distances in relation to the bifurcation of a blood vessel, as well as changes in circumference at different transection angulations. An in vitro exploration as to the anastomotic feasibility of each geometric cut was completed on ten poultry tissue specimens.

Results

The mathematical models demonstrated the change in vessel circumference, with multiple geometric designs calculated, best shown through diagrams. For example, if the vessel width is 1 mm, the distance from the increasing vessel diameter to the final bifurcation is 1 mm, and the bifurcation angle is 45°, the circumference of the transected vessel increases by 82.8%. Models of transections at different angulations, for instance 30°, 45°, and 60°, yield an increase in elliptical circumference of 8.0%, 22.5%, and 58.1%, respectively. Additional derivations calculate the elliptical circumference at any angle in a single vessel, and at any angle in a bifurcating vessel.

Conclusion

The theoretical and clinical aim of this project is to increase awareness of the anastomotic creativity and mathematically demonstrate the optimal anastomotic geometry, which has not been objectively explored to our knowledge. An in vivo study would further support clinical improvements, with the aim to map postoperative fluid dynamics through the geometric anastomoses.

Micro-Rheological Changes of Red Blood Cells in the Presence of an Arterio-Venous Fistula or a Loop-Shaped Venous Graft in the Rat

Introduction: In case of kidney failure, hemodialysis is the primary kidney replacement technique. Several vascular access methods used for the therapy, one of which is the arterio-venous fistula (AVF). In the AVF, the blood flow is altered, which can elevate the mechanical stress on the red blood cells (RBCs). This can affect the RBC hemorheological properties, and it can further cause systemic changes. To lower the turbulence and shear stress, we performed a loop-shaped arterio-arterial venous interposition graft (loop-shaped graft) to compare its effect to the conventional AVF. Materials and Methods: Thirty male Wistar were used (permission registration Nr.: 25/2016/UDCAW). The animals were randomly divided into sham-operated, AVF, and loop groups (n = 10/each). The superficial inferior epigastric vein (SIEV) was used to create the AVF and the loop-shaped graft. Blood samples were taken before/after the surgery and at the 1st, 3rd, and 5th postoperative weeks. We measured hemorhelogical, hematological, and blood gas parameters. The microcirculation of the hind limbs was also monitored using Laser Doppler fluxmetry. Results: Hematocrit, RBC count, and hemoglobin decreased by the 1st postoperative week. The erythrocyte aggregation values significantly increased in the fistula group by the 5th week (6.43 ± 2.31 vs. 13.60; p < 0.0001; vs. before operation). At the postoperative 1st week in the loop group, the values showed a significant decrease in RBC deformability. During the maturation period, dominantly at the 5th week, all values were normalized. The operated hind limb's skin microcirculation significantly increased in the sham and loop group by the 1st week (39 ± 10.57 vs. 73.93 ± 1.97 BFU, p < 0.01). This increase wasn't observed in the fistula group probably due to a steal-effect. Conclusion: Unlike in the loop group, in the presence of the fistula, several rheological parameters have changed. The loop-shaped graft had only minimal impact on micro-rheological parameters.