The Role of Layer-Specific Residual Stresses in Arterial Mechanics: Analysis via a Novel Modelling Framework

Abstract

The existence of residual stresses in unloaded arteries has long been known. However, their effect is often neglected in experimental studies. Using a recently developed modelling framework, we aimed to investigate the role of residual stresses in the mechanical behaviour of the tri-layered wall of the pig thoracic aorta. The mechanical behaviour of the intact wall and isolated layers of n = 3 pig thoracic aortas was investigated via uniaxial tensile testing. After modelling the layer-specific mechanical data using a hyperelastic strain energy function, the layer-specific deformations in the unloaded vessel were estimated so that the mechanical response of the computationally assembled tri-layered flat wall would match that measured experimentally. Physiological tension–inflation of the cylindrical tri-layered vessel was then simulated, analysing changes in the distribution of stresses in the three layers when neglecting residual stresses. In the tri-layered model with residual stresses, layers exhibited comparable stresses throughout the physiological range of pressure. At 100 mmHg, intimal, medial, and adventitial circumferential load bearings were 16 $$\pm$$ ± 3%, 59 $$\pm$$ ± 4%, and 25 $$\pm$$ ± 2%, respectively. Adventitial stiffening at high pressures produced a shift in load bearing from the media to the adventitia. When neglecting residual stresses, in vivo stresses were highest at the intima and lowest at the adventitia. Consequently, the intimal and adventitial load bearings, 23 $$\pm$$ ± 2% and 18 $$\pm$$ ± 3% at 100 mmHg, were comparable at all pressures. Residual stresses play a crucial role in arterial mechanics guaranteeing a uniform distribution of stresses through the wall thickness. Neglecting these leads to incorrect interpretation of the layers’ role in arterial mechanics.

Constituent-Based Quasi-Linear Viscoelasticity: A Revised Quasi-Linear Modelling Framework to Capture Non-Linear Viscoelasticity in Arteries

“…Given that the relative contribution of the arterial layers to the wall mechanical response is pressuredependent(Giudici et al 2021a; Giudici and Spronck 2022), a more complex multi-layered cbQLV model with layer-speci c parameters could further improve the description of the non-linear viscoelasticity of arteries. Furthermore, because of the single-layer thin-wall assumption, tractation of residual stresses is greatly simpli ed in our modelling framework; because of the inclusion of deposition stretches in the model, each constituent may not be stress-free in κ u , but the transmural distribution of residual stresses cannot be captured(Giudici and Spronck 2022;Zhang et al 2022).…”

Tri-layered constitutive modelling unveils functional differences between the pig ascending and lower thoracic aorta

“…In this study, tri-layered constitutive modelling was used to investigate how observed regional differences in layer-specific mechanical behaviour affect the macroscopic response of the aortic wall. The existence of layer-specific residual stresses is known (Greenwald et al, 1997;Holzapfel et al, 2007;Peña et al, 2015), and their estimation represents the crucial link between the isolated layers' mechanical behaviour and that of the tri-layered wall (Giudici and Spronck, 2022). The most common approach to modelling of residual deformation consists of directly quantifying shape changes that strips of individual layers undergo when isolated from the wall (Díaz et al, 2021;Holzapfel et al, 2007).…”

“…The isolation and tensile testing of individual arterial layers is a useful technique that allows investigating how inter-regional differences in layers' microstructure affects their mechanical properties. This experimental technique has been used at different locations of the arterial tree and in different species, including the human thoracic and abdominal aorta (Teng et al, 2015;Weisbecker et al, 2012), carotid artery (Sommer et al, 2010), coronaries (Holzapfel et al, 2005) and ascending aortic aneurysm (Deveja et al, 2018;Sassani et al, 2015), and the pig descending thoracic aorta (Giudici et al, 2021a;Giudici and Spronck, 2022;Peña et al, 2015). Further, fitting the experimental data using constitutive models whose parameters aim to describe the mechanical behaviour of the wall constituents (typically elastin and collagen) provides additional quantitative information on region-and layer-specific arterial structure-mechanics (Peña et al, 2015;Weisbecker et al, 2012).…”

Inverse material parameter estimation of patient‐specific finite element models at the carotid bifurcation: The impact of excluding the zero‐pressure configuration and residual stress

“…Furthermore, it has been well documented in the literature that residual stresses are present in arterial vessels 33–38 . These residual stresses have a significant impact on the distribution of physiological stresses throughout the vessel wall and tend to homogenize the stress distribution within each arterial layer in the physiological state.…”

“…[29][30][31][32] Furthermore, it has been well documented in the literature that residual stresses are present in arterial vessels. [33][34][35][36][37][38] These residual stresses have a significant impact on the distribution of physiological stresses throughout the vessel wall and tend to homogenize the stress distribution within each arterial layer in the physiological state. Numerous studies have demonstrated that the inclusion of residual stresses under physiological loading conditions substantially reduces the variation in both the circumferential and axial residual stress within the vessel wall.…”