A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall

Abstract

Gradual collagen recruitment has been hypothesized as the underlying mechanism for the mechanical stiffening with increasing stress in arteries. In this work, we investigated this hypothesis in eight rabbit carotid arteries by directly measuring the distribution of collagen recruitment stretch under increasing circumferential loading using a custom uniaxial (UA) extension device combined with a multi-photon microscope (MPM). This approach allowed simultaneous mechanical testing and imaging of collagen fibers without traditional destructive fixation methods. Fiber recruitment was quantified from 3D rendered MPM images, and fiber orientation was measured in projected stacks of images. Collagen recruitment was observed to initiate at a finite strain, corresponding to a sharp increase in the measured mechanical stiffness, confirming the previous hypothesis and motivating the development of a new constitutive model to capture this response. Previous constitutive equations for the arterial wall have modeled the collagen contribution with either abrupt recruitment at zero strain, abrupt recruitment at finite strain or as gradual recruitment beginning at infinitesimal strain. Based on our experimental data, a new combined constitutive model was presented in which fiber recruitment begins at a finite strain with activation stretch represented by a probability distribution function. By directly including this recruitment data, the collagen contribution was modeled using a simple Neo-Hookean equation. As a result, only two phenomenological material constants were required from the fit to the stress stretch data. Three other models for the arterial wall were then compared with these results. The approach taken here was successful in combining stress-strain analysis with simultaneous microstructural imaging of collagen recruitment and orientation, providing a new approach by which underlying fiber architecture may be quantified and included in constitutive equations.

Figure 1

Schematic of reference configurations and notation used for fiber recruitment kinematics.

Figure 2

Schematic displaying the geometric variables used in modelling the distribution of collagen fiber orientation for (a) general 3D distribution and (b) planar or “fan splay” distribution.

Figure 3

Illustration of the methodology used to determine model parameters. Top row, left to right: specimen of carotid artery between the clamps of the UA-MPM device, illustration of collagen recruitment analysis, depiction of collagen orientation analysis. Middle row, left to right: raw stress-stretch results from testing, tortuosity data and the Gamma cumulative distribution function plotted against stretch, orientation distribution histogram. Bottom: final results from UA-MPM testing of a rabbit carotid artery. Raw stress-stretch data (blue dots) and structural model fit (blue line) from uniaxial tension tests in the circumferential direction with overlaid recruitment probability distribution function (green line).

Figure 4

Planar slice from 3D reconstructed unloaded artery. Circumferential direction is left to right and radial direction is up and down with lumen side at top. Moving down from lumen side, the media with layered crimped collagen fibers (red) and elastin fibers can be seen. Below this is the loose, wavy adventitial collagen. Bar = 50μm

Figure 5

Raw (blue dots) and fitted (blue line) data from uniaxial extension of a rabbit carotid artery, plotted alongside the recruitment function (green line) (associated MPM images given in Fig. 6).

Figure 6

Multi-photon images (MetaMorph) of collagen at stretches of (a) 1.40, (b) 1.60, (c) 1.70, (d) 1.80, (e) 1.90, and (f) 2.00, corresponding to Fig. 6. Bars = 50μm

Figure 7

Raw mechanical data from the uniaxial device (blue dots), with fitted response (blue line) and fiber recruitment distribution function d₁ of model D. Specimens 01–08 are labeled with Roman numerals.

Figure 8

3D reconstruction of multipho-ton image stacks with superposed fiber tracings shown in white. Three orientations are shown with largest image for the e₁ ⊗ e₂, the right image for the e₂ ⊗ e₃ plane, and the bottom image of the e₁ ⊗ e₃ plane, Bar = 50μm.

Figure 9

Distribution of magnitude of angle between fiber and e₁ axis for (a) projection on e₁ ⊗ e₂ plane (red) and (b) projection on e₁ ⊗ e₃ plane (blue).

Figure 10

MPM image of adventitial collagen at λ = 2.0 for Sample 07.