J Thorac Cardiovasc Surg 2006;131:1420-1421
© 2006 The American Association for Thoracic Surgery
Residual strain in the aorta
Thoralf M. Sundt, III, MD
Division of Cardiovascular Surgery, Mayo Clinic and Foundation, 200 First St, SW, Rochester, MN 55905
(Email: sundt.thoralf{at}mayo.edu).
To the Editor:
We were excited to see yet another seminal contribution to the literature on aortic aneurysmal disease arising from the laboratories of Dr Elefteriades and his colleagues.
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Their work continues to broaden our fundamental understanding of this lethal but treatable disease. The recently reported work demonstrates a remarkable correlation between the predicted behavior of the aorta based on mechanical properties and the natural history of this disorder as observed previously by this same group of investigators. In the course of their discussion of the significance of their work, the authors graciously referenced our previous work touching on the mechanical properties of the ascending aorta, with particular emphasis on bicuspid aortic valve disease and changes with aging.
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An additional finding from our study relevant to the author's work, however, perhaps should be made. As one might have anticipated, we observed changes in the intrinsic mechanical properties of the aorta, as defined by the elastic properties determined by means of biaxial testing. Of greater interest, perhaps, were our observed changes with age in the opening angle as a reflection of residual strain.
Residual stress and strain are critical concepts in understanding the mechanical properties of the arterial wall. Absent residual strain, intraluminal pressure within a thick-walled tube will result in an uneven distribution of stress across the wall, with the greatest stress born by the inner portion and the least stress by the outer. The pioneering work by Chuong and Fung
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demonstrated over 2 decades ago that the distribution of stresses and strains within a vessel wall are nonuniform, both circumferentially and longitudinally. Calculations based on the assumption that the unloaded vessel is at zero stress result in remarkably high stress concentrations at the inner wall. The unloaded vessel, however, is not physiologic. The vessel wall exhibits residual strain to effect a more even distribution of stress across the thickness of media and adventitia in the loaded state. Just as a concrete beam can be prestressed in anticipation of the loaded state, the effect of residual strain in a vessel wall is to make more uniform the distribution of circumferential wall stress under physiologic conditions with intraluminal pressure. Experimental observations confirm this phenomenon in vivo. Variations in residual strain have been observed in differing segments of the aorta in the rat, just as one would anticipate given differences in pressure wave forms.
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Liu and Fung
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further demonstrated that residual strain is subject to remarkably rapid changes with cellular remodeling caused by altered hemodynamics.
The existence of residual strain is easily demonstrated in the operating room by using a test that is, in fact, familiar to all cardiovascular surgeons. If one resects a tubular segment of a vessel and then cuts the resulting ring open, the vessel will spring open (the opening angle) to a zero-stress state.
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This reflects residual tensile stress in the outer wall, while the inner wall has residual compressive stress. Accordingly, the ring will tend to turn itself inside out.
Of what possible clinical relevance is this phenomenon? Aneurysm rupture and dissection represent structural failures of the aortic wall. We also know that, despite arguments over the relative contributions of cellular apoptosis and fiber degradation, all would agree that rather dramatic changes in the structure of the wall itself can be observed with aging or against the backdrop of connective tissue disease. One can well imagine that concomitant changes in residual strain and other material properties might occur, as well as changes in vessel diameter and thickness in response to aging and hemodynamic forces. Could these alterations affect stress distribution across the wall of the aorta? It is tempting to hypothesize that alterations in vessel wall structure leading to disproportionate loading of the outer portion of the aortic wall could lead to primary failure of the subadventitia. Could this be an alternative explanation for the phenomenon of intramural hematoma? Could primary mechanical failure of the adventitia lead to creation of a potential space that fills with blood as a secondary phenomenon?
Although this theory is unsubstantiated by experimental work, it demonstrates the potential importance of accounting for residual strain among the mechanical properties of the aortic wall. In this regard we must respectfully disagree with the authors' statement that "a full profile of the mechanical properties of the aorta can be gleaned by measuring six specific physical characteristics: blood pressure (systolic and diastolic), aortic diameter (systolic and diastolic), and thickness of the aortic wall (systolic and diastolic)." We believe there is more to it than that. The intrinsic properties of this highly complex amalgam of connective tissue and cellular elements must enter into the equation.
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References
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- Koullias G, Modak R, Tranquilli M, Korkolis DP, Barash P, Elefteriades JA. Mechanical deterioration underlies malignant behavior of aneurysmal human ascending aorta. J Thorac Cardiovasc Surg 2005;130:677-683.[Abstract/Free Full Text]
- Okamoto ref Okamoto RJ, Xu HD, Kouchoukos NT, Moon MR, Sundt TM. The influence of mechanical properties on wall stress and distensibility of the dilated ascending aorta. J Thorac Cardiovasc Surg 2003;126:842-850.[Abstract/Free Full Text]
- Chuong CJ, Fung YC. Three-dimensional stress distribution in arteries. J Biomech Eng 1983;105:268-274.[Medline]
- Liu SQ, Fung YC. Zero-strees states of arteries. J Biomed Eng 1988;110:82-84.
- Liu SQ, Fung YC. Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction. J Biomed Eng 1989;111:325-335.
- Chuong CJ, Fung YC. On residual stress in arteries. J Biomed Eng. 1986;108:189-192.
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