Determining the critical buckling pressure of blood vessels through modeling and in vitro experiments

Introduction. Tortuous arteries are often associated with aging, hypertension, atherosclerosis, and degenerative vascular diseases, but the mechanisms are poorly understood. Our recent theoretical analysis and experimental observation suggested that mechanical instability (buckling) may lead to tortuous blood vessels. The theoretical analysis, however, needs careful validation with experimental results. In addition, the mechanism behind the propensity of tortuosity formation in elastin degraded arteries or arteries with geometric variations have not been addressed. The objectives of this study were to validate the critical buckling equation for blood vessels and to study the effect of elastin degradation and geometric variations on the mechanical stability of arteries. Methods. The mechanical properties and critical buckling pressures (CBP), at which arteries become unstable and deform into tortuous shapes, were previously determined for a group of eight veins and five arteries (normal groups) using pressurized inflation and buckling tests. Another group of six porcine arteries were treated with elastase (elastase group, 8 U/ml) and the mechanical stiffness and CBP's were obtained before and after treatment. The artery behavior was determined by finding the material constants of the Fung energy equation and the CPB was predicted using the MC's and the critical buckling equation. The material constants were also used in finding the CBP of arteries with geometric variations using finite element analysis. Results. The experimental CPB of the eight veins tested was 1.95 +/- 0.67 kPa; while the model predicted CPB was 1.91+/-0.69 kPa (at an axial stretch ratio of lambda=1.5). The CPB of the normal artery group was 17.10+/-5.11kPa, while model predicted critical pressures was 17.86+/-5.21kPa (lambda=1.5). The elastase group had a significant decrease in the CPB (p<0.01) post treatment. The CBP's of the 6 elastase treated arteries was 19.86 +/- 5.31 and 9.13 +/- 3.61 kPa before and after treatment, respectively (lambda=1.5); while the model predicted CBP's was 16.95 +/- 10.45 and 8.43 +/- 3.58 kPa before and after treatment, respectively (lambda=1.5). All arteries with geometric variations also had a decrease in their CPB. Conclusion. Artery buckling under lumen pressure can be predicted by a critical buckling equation. Elastin degradation and geometric variations reduce the critical buckling pressure which may lead to tortuous vessels. These results shed light on the buckling behavior of arteries and veins.