Measurement and analysis of ultimate mechanical properties, stress-strain curve fit, and elastic modulus formula of human abdominal aortic aneurysm and nonaneurysmal abdominal aorta

Abstract

The maximal strain, stress, elastic modulus, and stress-strain curve fitting of abdominal aortic aneurysms (AAA) and bidirectional nonaneurysmal abdominal aorta (NAA) were measured and analyzed to obtain the ultimate mechanical properties, the more approximate stress-strain curve-fitting, and the elastic modulus formula of AAA and NAA. Fourteen human AAA samples were harvested from patients undergoing elective aneurysm repair. Twelve NAA samples comprised of six longitudinal-circumferential pairs of NAA from six cadaveric organ donors were used as controls. Samples were mounted on a tensile-testing machine and force was applied until breakage occurred. The maximal strain, stress, and elastic modulus were calculated and a stress-strain curve was plotted for each sample. Exponential and second-order polynomial curves were used to fit the stress-strain curve, and the means were estimated by comparing the R2 (coefficient of determination that represents the strength of a curve fitting). Coefficients of elastic modulus were calculated and analyzed, and the incremental tendency of each modulus was evaluated by comparing the difference of coefficients. There was no significant difference in maximal stress among AAA, circumferential aortic aneurysms (CAA), and longitudinal aortic aneurysms (LAA). However, AAA maximal strain was significantly less (P < .01) than that of bidirectional NAA. AAA maximal elastic modulus was significantly greater than that of CAA and LAA (P < .01 and .05, respectively). R2 of AAA for second-order polynomial curve was significantly greater (P < .05) than that for the exponential curve. For the elastic modulus formula from the second-order polynomial curve, E = 2ax + b, the average value of a for the AAA was significantly greater (P < .01) than that for the bidirectional NAA, but there was no significant difference (P > .05) among the three groups for the average value of b. Tensile test measurements can successfully analyze ultimate mechanical properties of AAA and NAA. AAA is stiffer and less distensible than NAA under the same maximal stress. Second-order polynomial curve fitting provides a more approximate description for AAA stress-strain curve than exponential curve fitting does. Formula variables a of the elastic modulus formula from second-order polynomial curve fitting can determine the incremental tendency of the elastic modulus, while b has negligible effect on the incremental tendency of the elastic modulus.