1. Measurement and analysis of ultimate mechanical properties, stress-strain curve fit, and elastic modulus formula of human abdominal aortic aneurysm and nonaneurysmal abdominal aorta 
Jiang Xiong, MD, Shen Ming Wang, MD, Wei Zhou, PhD, Jan Guo Wu, PhD 
Journal of Vascular Surgery 
Volume 48, Issue 1, Pages (July 2008)
DOI: /j.jvs
Copyright © 2008 The Society for Vascular Surgery Terms and Conditions

2. Fig 1
Tissue tensile test and the curves of pull force-displacement transferred to stress-strain curves. A, Schematic diagram of the tensile stress test. Tissue was mounted between two clamps and stretched at a constant rate of elongation. The original length (L) was not recorded at zero load, although it had been stretched. Rather, recording was done when the tissue was slightly elongated (L0). Thus, loading and elongation are represented as (ΔF and ΔL−L0, respectively. Strain, ε, is modified as ε = (ΔL−L0)/(L+L0). B, The curve of pull force vs displacement. Dot P1 identified the original length and dot P2 identified the elongation (ΔL−L0). From 0 to P1,the tissue was at zero load. C, The dots of stress vs strain and the fitting curves of AAA samples. The formula of exponential curve fitting was Y = e27.52x, and R2 was 0.882; the formula of second-order polynomial curve fitting was Y = x x, and R2 was
Journal of Vascular Surgery  , DOI: ( /j.jvs )
Copyright © 2008 The Society for Vascular Surgery Terms and Conditions

3. Fig 2
R2 of curve fitting of mechanical properties and the difference of coefficient of elastic modulus formula of abdominal aortic aneurysms (AAA) and bidirectional nonaneurysmal abdominal aorta (NAA) walls. A, Exponential curve and second-order polynomial curve fittings were both done for each sample data, and the formula and R2 were determined. R2 of exponential fitting in AAA, circumferential aortic aneurysms (CAA), and longitudinal aortic aneurysms (LAA) were 0.94 ± 0.04, 0.94 ± 0.06, and 0.98 ± 0.01, respectively. R2 of second polynomial fitting were 0.98 ± 0.01, 0.98 ± 0.01, and 0.99 ± 0.01 (same respective order). *P < .05, compared with polynomial fitting in AAA. B, The elastic modulus formula E = 2ax + b (a and b are the second and first order parameters of second-order polynomial formula, respectively) was obtained by calculating the derivative of the second-order polynomial curve equation. The a of AAA, CAA, and LAA were ± 3.01, 3.93 ± 2.48, and 4.74 ± 1.74, respectively. **P < .01, compared with AAA. The b of AAA, CAA, and LAA were −1.10 ± 0.52, −0.714 ± 0.95, and −1.27 ± 0.83, respectively. C, Stress-strain diagram and the elastic modulus formula of AAA (black line), CAA (pink line), and LAA (blue line) walls. Curves for AAA wall are shifted to left and their slopes are greater than bidirectional NAA wall. The first order parameters of AAA are greater than those of bidirectional NAA.
Journal of Vascular Surgery  , DOI: ( /j.jvs )
Copyright © 2008 The Society for Vascular Surgery Terms and Conditions

4. Fig 3
Mechanical properties of abdominal aortic aneurysms (AAA) and bidirectional nonaneurysmal abdominal aorta (NAA) walls. A, Maximum stress of AAA, circumferential aortic aneurysms (CAA), and longitudinal aortic aneurysms (LAA) were 0.93 ± 0.25 N/mm2, 95% CI [0.683, 1.179] N/mm2, 1.03 ± 0.33 N/mm2, 95% CI [0.678, 1.358] N/mm2,and 1.15 ± 0.28 N/mm2, 95% CI [0.872, 1.426] N/mm2, respectively. B, Maximum strain of AAA, CAA, and LAA were 0.32 ± 0.09, 95% CI [0.257, 0.383], 0.62 ± 0.14, 95% CI [0.493, 0.746], and 0.60 ± 0.11, 95% CI [0.495, 0.695], respectively. **P < .01, compared with AAA. C, the maximum elastic modulus of AAA, CAA, and LAA was 9.14 ± 3.31 MPa, 95% CI [5.831, ] MPa, 3.96 ± 1.67 MPa, 95% CI [2.287, 5.634] MPa and 6.04 ± 2.02 MPa, 95% CI [4.024, 8.057] MPa, respectively. *P < 0.05, compared with AAA. **P < .01, compared with AAA.
Journal of Vascular Surgery  , DOI: ( /j.jvs )
Copyright © 2008 The Society for Vascular Surgery Terms and Conditions