Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries.

Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.

Detectable Bias between Vascular Ultrasound Echo-Tracking Systems: Relevance Depends on Application.

The Esaote MyLab70 ultrasound system has been extensively used to evaluate arterial properties. Since it is reaching end-of-service-life, ongoing studies are forced to seek an alternative, with some opting for the Esaote MyLabOne. Biases might exist between the two systems, which, if uncorrected, could potentially lead to the misinterpretation of results. This study aims to evaluate a potential bias between the two devices. Moreover, by comparing two identical MyLabOne systems, this study also aims to investigate whether biases estimated between the MyLabOne and MyLab70 employed in this study could be generalized to any other pair of similar scanners. Using a phantom set-up, we performed n = 60 measurements to compare MyLab70 to MyLabOne and n = 40 measurements to compare the two MyLabOne systems. Comparisons were performed to measure diameter, wall thickness, and distension. Both comparisons led to significant biases for the diameter (relative bias: −0.27% and −0.30% for the inter- and intra-scanner model, respectively, p < 0.05) and wall thickness (relative bias: 0.38% and −1.23% for inter- and intra-scanner model, respectively p < 0.05), but not for distension (relative bias: 0.48% and −0.12% for inter- and intra-scanner model, respectively, p > 0.05). The biases estimated here cannot be generalized to any other pair of similar scanners. Therefore, longitudinal studies with large sample sizes switching between scanners should perform a preliminary comparison to evaluate potential biases between their devices. Furthermore, caution is warranted when using biases reported in similar comparative studies. Further work should evaluate the presence and relevance of similar biases in human data.

Improved Quantification of Cell Density in the Arterial Wall-A Novel Nucleus Splitting Approach Applied to 3D Two-Photon Laser-Scanning Microscopy.

Accurate information on vascular smooth muscle cell (VSMC) content, orientation, and distribution in blood vessels is indispensable to increase understanding of arterial remodeling and to improve modeling of vascular biomechanics. We have previously proposed an analysis method to automatically characterize VSMC orientation and transmural distribution in murine carotid arteries under well-controlled biomechanical conditions. However, coincident nuclei, erroneously detected as one large nucleus, were excluded from the analysis, hampering accurate VSMC content characterization and distorting transmural distributions. In the present study, therefore, we aim to (1) improve the previous method by adding a "nucleus splitting" procedure to split coinciding nuclei, (2) evaluate the accuracy of this novel method, and (3) test this method in a mouse model of VSMC apoptosis. After euthanasia, carotid arteries from SM22α-hDTR Apoe -/- and control Apoe -/- mice were bluntly dissected, excised, mounted in a biaxial biomechanical tester and brought to in vivo axial stretch and a pressure of 100 mmHg. Nuclei and elastin fibers were then stained using Syto-41 and Eosin-Y, respectively, and imaged using 3D two-photon laser scanning microscopy. Nuclei were segmented from images and coincident nuclei were split. The nucleus splitting procedure determines the likelihood that voxel pairs within coincident nuclei belong to the same nucleus and utilizes these likelihoods to identify individual nuclei using spectral clustering. Manual nucleus counts were used as a reference to assess the performance of our splitting procedure. Before and after splitting, automatic nucleus counts differed -26.6 ± 9.90% (p < 0.001) and -1.44 ± 7.05% (p = 0.467) from the manual reference, respectively. Whereas the slope of the relative difference between the manual and automated counts as a function of the manual count was significantly negative before splitting (p = 0.008), this slope became insignificant after splitting (p = 0.653). Smooth muscle apoptosis led to a 33.7% decrease in VSMC density (p = 0.008). Nucleus splitting improves the accuracy of automated cell content quantification in murine carotid arteries and overcomes the progressively worsening problem of coincident nuclei with increasing cell content in vessels. The presented image analysis framework provides a robust tool to quantify cell content, orientation, shape, and distribution in vessels to inform experimental and advanced computational studies on vascular structure and function.