David A. Vorp, PhD, M.L. Raghavan, BS, Marshall W. Webster, MD

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Presentation transcript:

Mechanical wall stress in abdominal aortic aneurysm: Influence of diameter and asymmetry David A. Vorp, PhD, M.L. Raghavan, BS, Marshall W. Webster, MD Journal of Vascular Surgery Volume 27, Issue 4, Pages 632-639 (April 1998) DOI: 10.1016/S0741-5214(98)70227-7 Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 1 Representative, three-dimensional, virtual AAA model (top) and midsectional cross section (bottom). rp and ra, maximum posterior and anterior wall dimensions, respectively, measured from the dashed longitudinal line defined by the centers of the two undilated ends. rp + ra = maximum diameter. Inflection points (IP) are defined as points on the AAA surface at which the local AAA wall shape changes from concave outward to concave inward and are indicated here only for the anterior and posterior surfaces. The angular circumferential coordinate Θ is defined as shown. Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 2 Three-dimensional models of AAA represents the two extreme cases studied for each protocol. Protocol 1, variation of asymmetry parameter β from 1.0 (axisymmetric) to 0.3 while maximum diameter (Dmax) was held constant at 6 cm. Protocol 2, variation of maximum diameter from 4 cm to 8 cm while β was held constant at 0.4. Three intermediate cases were studied between the two extremes for each protocol. Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 3 Distribution of mechanical wall stress in all ten virtual AAAs. A, Models for protocol 1 (varying asymmetry). B, Models for protocol 2 (varying maximum diameter). Each model is shown in two views. The left columns of both A and B provide a view of the anterior, left lateral surface of the virtual AAA. The right column provides a view of the posterior, right lateral surface. The sketch at the top of each column shows the vertebral column and provides anatomic reference. The magnitude of the mechanical wall stress for both protocols is given on the individual color scales in Newtons/cm2 (note: 1 Newton/cm2 = 105 dynes/cm2). Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 3 Distribution of mechanical wall stress in all ten virtual AAAs. A, Models for protocol 1 (varying asymmetry). B, Models for protocol 2 (varying maximum diameter). Each model is shown in two views. The left columns of both A and B provide a view of the anterior, left lateral surface of the virtual AAA. The right column provides a view of the posterior, right lateral surface. The sketch at the top of each column shows the vertebral column and provides anatomic reference. The magnitude of the mechanical wall stress for both protocols is given on the individual color scales in Newtons/cm2 (note: 1 Newton/cm2 = 105 dynes/cm2). Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 4 Effect of asymmetry parameter β (A) and maximum diameter (B) on circumferential distribution of wall stresses at the midsection of the AAA (along dashed curve in Fig. 1). The Θ coordinate is as defined in Fig. 1. A position of Θ = 0 degrees corresponds to the posterior surface, and ±180 degrees corresponds to the anterior surface. For this and subsequent Figures, a decrease in β corresponds to an increase in asymmetry. Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 5 Effect of asymmetry parameter β (A) and maximum diameter (B) on longitudinal distribution of wall stresses along the anterior surface of an AAA. Axial positions of z = 0 cm and z = 12 cm correspond to the superior and inferior undilated ends of the AAA; z = 6 cm corresponds to the midsection. Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 6 Effect of asymmetry parameter β (A) and maximum diameter (B) on longitudinal distribution of wall stresses along the posterior surface of an AAA. The longitudinal axis is the same as in Fig. 5. Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions

Fig. 7 Effect of asymmetry parameter β (bottom axis) and maximum diameter (top axis) on magnitude of peak stress within a virtual AAA. Both increasing diameter and increasing asymmetry (decreasing β) cause a nonlinear increase in peak stress. Journal of Vascular Surgery 1998 27, 632-639DOI: (10.1016/S0741-5214(98)70227-7) Copyright © 1998 Society for Vascular Surgery and International Society for Cardiovascular Surgery, North American Chapter Terms and Conditions