Structurally motivated damage models for arterial walls. Theory and application
The mechanical integrity of the arterial wall is vital for the health of the individual. This integrity is in turn dependent on the state of the central load bearing components of the wall: collagen fibres, elastic fibres and smooth muscle. Of these, the
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Structurally motivated damage models for arterial walls. Theory and application Anne M. Robertson, Michael R. Hill, and Dalong Li
6.1 Introduction The mechanical integrity of the arterial wall is vital for the health of the individual. This integrity is in turn dependent on the state of the central load bearing components of the wall: collagen fibres, elastic fibres and smooth muscle. Of these, the elastic fibres, composed largely of the protein elastin, are viewed as responsible for the highly elastic behaviour of the wall at low loads [92]. The collagen fibres are recruited under increasing extension, leading to a highly nonlinear behaviour of the arterial wall [117]. They are responsible for the structural integrity of the wall at elevated physiological loads. Changes in the quantity, distribution, orientation and mechanical properties of these components (the microstructure) are known to occur as part of a healthy response to changing stimuli (e.g. growth and remodelling) as well as during pathological and damage processes in disease and aging. For example, degradation of the elastic fibres is linked to pathological conditions including cerebral aneurysms [12, 15, 20, 65], dissection aneurysms [101], arteriosclerosis [11, 44, 86, 113, 114], and complications from balloon angioplasty [84]. Age related arterial stiffening is attributed to degradation of the elastic fibres, possibly from fatigue failure [11, 30]. The subject of arterial damage is addressed in Sect. 6.4. The mechanical behaviour of the arterial wall is modelled from several perspectives. Phenomenological models are based on bulk measurements of the mechanical response of the arterial wall, while structural theories directly integrate information Anne M. Robertson ( ) University of Pittsburgh, Pittsburgh, PA 15261 USA e-mail: [email protected] Michael R. Hill University of Pittsburgh, Pittsburgh, PA 15261 USA e-mail: [email protected] Dalong Li Ansys Inc., Canonsburg, PA USA e-mail: [email protected]
Ambrosi D., Quarteroni A., Rozza G. (Eds.): Modeling of Physiological Flows. DOI 10.1007/978-88-470-1935-5 6, © Springer-Verlag Italia 2012
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A.M. Robertson, M.R. Hill, and D. Li
on the tissue composition, structure, and load carrying mechanisms of individual components. In doing so, they provide more insight into the function and mechanics of tissue components, at the expense of requiring constitutive data for each of the elements. For example, recent experimental and modelling studies have addressed the mechanical behaviour of isolated arterial elastin [42, 43, 112]. In between these two extremes are so called structurally motivated models, which bring in an intermediate level of structural information such as the fibrous nature of the tissue without directly incorporating the response of individual components. For example, the mechanical behaviour of individual fibres is not prescribed. Mixture theories have been developed to describe the growth and mechanical response of individual wall constituents [59]. These models have shown great promise in stud
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