Computational modelling suggests good, bad and ugly roles of glycosaminoglycans in arterial wall mechanics and mechanobiology

Abstract

The medial layer of large arteries contains aggregates of the glycosaminoglycan hyaluronan and the proteoglycan versican. It is increasingly thought that these aggregates play important mechanical and mechanobiological roles despite constituting only a small fraction of the normal arterial wall. In this paper, we offer a new hypothesis that normal aggregates of hyaluronan and versican pressurize the intralamellar spaces, and thereby put into tension the radial elastic fibres that connect the smooth muscle cells to the elastic laminae, which would facilitate mechanosensing. This hypothesis is supported by novel computational simulations using two complementary models, a mechanistically based finite-element mixture model and a phenomenologically motivated continuum hyperelastic model. That is, the simulations suggest that normal aggregates of glycosaminoglycans/proteoglycans within the arterial media may play equally important roles in supporting (i.e. a structural role) and sensing (i.e. an instructional role) mechanical loads. Additional simulations suggest further, however, that abnormal increases in these aggregates, either distributed or localized, may over-pressurize the intralamellar units. We submit that these situations could lead to compromised mechanosensing, anoikis and/or reduced structural integrity, each of which represent fundamental aspects of arterial pathologies seen, for example, in hypertension, ageing and thoracic aortic aneurysms and dissections.

Keywords: anoikis; hyaluronan; mechanosensing; stress analysis; versican.

Figure 1.

Finite-element model of a segment of a murine common carotid artery, where g2 represents a possible ‘good’ situation with FCD_Med2 =−70, FCD_Med1 = −40 and FCD_Adv = −20 mEq l⁻¹. Mechanical properties (i.e. strain energy parameters) were prescribed separately for the media and adventitia and similarly for the swelling related fixed charge density (FCD), with the exception of radial differences in FCD also within the media.

Figure 2.

Schematic diagram of key configurations that were used either in the nonlinear regression or to test the predictive ability of the constitutive formulations for the mouse carotid artery. , homeostatic (swollen homeostatic) configuration at a mean arterial pressure of 93 mmHg and in vivo axial stretch (). κ_p (), loaded (swollen loaded) configurations at  () and any pressure P, with representative values shown for P = 220 mmHg. κ_tf (), intact (swollen intact), traction-free configuration. κ_c (), radially cut (swollen radially cut), traction-free configuration. κ_n, natural (i.e. stress-free) configurations for individual constituents.

Figure 3.

Representative luminal pressure–outer diameter responses for a simulated (lines) and experimental (closed circles) biaxial pressurization and axial extension protocol, consistent with that in Ferruzzi et al. [19]. Shown, specifically, are the biaxial responses for the CM (solid line) and for both a unilayered (FEM 1 layer; dotted-dashed line) and bilayered (FEM 2 layers; dashed line) finite-element model.

Figure 4.

Volume change (a,c), relative to κ_tf (cf. figure 2), for the finite-element (open squares) and continuum (solid line) models for two cases of swelling (g1 and g2, that represent ‘good’ situations associated with FCD_Med2 = −50 and −70 mEq l⁻¹, respectively), which generated two different residual stress-related opening angles . Note the good agreement between the two different modelling approaches. (b,d) Associated transmural distributions of circumferential (solid line) and axial (dashed line) Cauchy wall stress calculated using the continuum model for an axial stretch of (top) and (bottom) and an internal pressure of 93.3 mmHg. Also shown is the mean circumferential stress obtained via the classical Laplace relation (dotted-dashed line).

Figure 5.

Volume change (a,c), relative to κ_tf (cf. figure 1), for the finite-element (open squares) and continuum (solid line) models for two cases of swelling (b1 and b2, that represent ‘bad’ situations associated with FCD_Med2 = −120 and −160 mEq l⁻¹, respectively), which generated two different residual stress-related opening angles . (b,d) Associated transmural distributions of circumferential (solid line) and axial (dashed line) Cauchy wall stress calculated using the continuum model for an axial stretch of (top) and (bottom) and an internal pressure of 93.3 mmHg. Also shown is the mean circumferential stress obtained via the classical Laplace relation (dotted-dashed line).

Figure 6.

Representative transmural distributions of circumferential Cauchy stress for (a) systolic and (b) acutely elevated blood pressure, each evaluated for five different degrees of swelling: good g1 (dashed line) and g2 (dotted line) distributions (see figure 4), bad b1 (dotted-dashed line) and b2 (solid black line) distributions (figure 5), and a non-swollen homogeneous (grey solid line) distribution, i.e. J = 1 at every point of the wall. The effect of the intramural swelling was similar in some ways to an increase in luminal pressure: it increased the tensile stress in the adventitia while decreasing it in the medial layer. The same trend can be seen for the mean arterial pressure (MAP) by comparing circumferential values of the Cauchy stress in figures 4 and 5.

Figure 7.

Transmural distribution of radial stretch for the different cases of swelling considered in figures 4 and 5: g1, dashed line; g2, dotted line; b1, dotted-dashed line; b2, solid black line and the case of no swelling (solid grey line). Because the homeostatic configuration is taken as a reference, the radial stretches represented here are ‘real’ not ‘relative’ and the numerical values can be interpreted as fold-changes owing to swelling.

Figure 8.

(a) Final quarter-symmetric finite-element model (approx. 150 000 hexahedral elements) of the overall 250 × 250 × 84 μm rectangular portion of the murine carotid wall, including a single centrally located GAG/PG inclusion (volume of 574.7 μm³). The value of the fixed charge density equals −160 mEq l⁻¹ for the GAG inclusion and −50 mEq l⁻¹ for the non-affected aortic wall. The far-field stresses correspond to those developed in the wall owing to the homeostatic blood pressure evaluated in a unilayer cylindrical simulation (radial = −6 kPa, circumferential and axial = 100 kPa) and induced here via appropriate displacement boundary conditions. (b­–d) Shown is a greyscale representation of multi-axial stresses in and near the GAG/PG inclusion. Note, in particular, the transition of radial stress from compressive to highly tensile near the leading edge of the inclusion.