Constitutive modelling of vascular tissue has been a challenging area for several decades [1,2]. Structural constitutive models, in particular, attempt to integrate information on composition and structural arrangements of tissue to avoid ambiguities in material characterization. In this way, they offer an insight into the function, structure and mechanics of the principal wall components i.e. elastin, collagen and vascular smooth muscle cells. Structural constitutive models have been developed for a variety of tissues and tissue components including blood vessels [3-8], skin [9], pericardium [10], heart valves [11], tendons and ligaments [12], articular cartilage [13].
In blood vessels, collagen fibres appear in coiled and wavy bundles in their unloaded state [14,15] and the individual collagen fibres have a deviation from their mean orientations [16,17]. In the media, collagen fibres are strongly co-aligned [17]. Canham et al. [18] reported the angular standard deviation of fibres in the media as 5.2° in brain arteries and 5.6° in coronary arteries [18]. However, within the adventitia layer, collagen fibres have large angular dispersion [17]. A complete structural constitutive model for vascular collagen should incorporate both waviness and orientational distribution of fibres.
Perhaps the most complete framework for structural modelling of fibrous tissue has been presented by Lanir et al. [19-21]. In this framework, the total strain energy function (SEF) is assumed to be a result of the collective contribution of the individual fibres linked with tensor transformations from the fibre coordinates to the global tissue coordinates. A number of previous studies have followed this approach and have incorporated waviness [22,23] or orientational distribution of collagen fibres [10,11,24], to study the effects of collagen micro-organization on the macroscopic behaviour of vascular tissue. Other studies have followed a different approach and involved the use of invariants [22,23,25]. Yet, to the best of our knowledge, currently, there is no structure-based SEF for the vascular wall, which includes both waviness and angular distribution of collagen fibres and which has been verified using standard inflation-extension tests. We have therefore set as goals of this study to, first, extend our previously developed model [22,23] to include both waviness and angular distribution of collagen fibres, second, to perform a parametric study to analyze the effects of orientational distribution parameters on the macro-mechanical behaviour of the vascular tissue and, third, to assess the suitability and importance of including fibres' orientational distribution by applying the model to experimental data from inflation-extension tests.
In blood vessels, collagen fibres appear in coiled and wavy bundles in their unloaded state [14,15] and the individual collagen fibres have a deviation from their mean orientations [16,17]. In the media, collagen fibres are strongly co-aligned [17]. Canham et al. [18] reported the angular standard deviation of fibres in the media as 5.2° in brain arteries and 5.6° in coronary arteries [18]. However, within the adventitia layer, collagen fibres have large angular dispersion [17]. A complete structural constitutive model for vascular collagen should incorporate both waviness and orientational distribution of fibres.
Perhaps the most complete framework for structural modelling of fibrous tissue has been presented by Lanir et al. [19-21]. In this framework, the total strain energy function (SEF) is assumed to be a result of the collective contribution of the individual fibres linked with tensor transformations from the fibre coordinates to the global tissue coordinates. A number of previous studies have followed this approach and have incorporated waviness [22,23] or orientational distribution of collagen fibres [10,11,24], to study the effects of collagen micro-organization on the macroscopic behaviour of vascular tissue. Other studies have followed a different approach and involved the use of invariants [22,23,25]. Yet, to the best of our knowledge, currently, there is no structure-based SEF for the vascular wall, which includes both waviness and angular distribution of collagen fibres and which has been verified using standard inflation-extension tests. We have therefore set as goals of this study to, first, extend our previously developed model [22,23] to include both waviness and angular distribution of collagen fibres, second, to perform a parametric study to analyze the effects of orientational distribution parameters on the macro-mechanical behaviour of the vascular tissue and, third, to assess the suitability and importance of including fibres' orientational distribution by applying the model to experimental data from inflation-extension tests.
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