Constitutive description of human femoropopliteal artery aging

Abstract

Femoropopliteal artery (FPA) mechanics play a paramount role in pathophysiology and the artery's response to therapeutic interventions, but data on FPA mechanical properties are scarce. Our goal was to characterize human FPAs over a wide population to derive a constitutive description of FPA aging to be used for computational modeling. Fresh human FPA specimens ([Formula: see text]) were obtained from [Formula: see text] predominantly male (80 %) donors 54±15 years old (range 13-82 years). Morphometric characteristics including radius, wall thickness, opening angle, and longitudinal pre-stretch were recorded. Arteries were subjected to multi-ratio planar biaxial extension to determine constitutive parameters for an invariant-based model accounting for the passive contributions of ground substance, elastin, collagen, and smooth muscle. Nonparametric bootstrapping was used to determine unique sets of material parameters that were used to derive age-group-specific characteristics. Physiologic stress-stretch state was calculated to capture changes with aging. Morphometric and constitutive parameters were derived for seven age groups. Vessel radius, wall thickness, and circumferential opening angle increased with aging, while longitudinal pre-stretch decreased ([Formula: see text]). Age-group-specific constitutive parameters portrayed orthotropic FPA stiffening, especially in the longitudinal direction. Structural changes in artery wall elastin were associated with reduction of physiologic longitudinal and circumferential stretches and stresses with age. These data and the constitutive description of FPA aging shed new light on our understanding of peripheral arterial disease pathophysiology and arterial aging. Application of this knowledge might improve patient selection for specific treatment modalities in personalized, precision medicine algorithms and could assist in device development for treatment of peripheral artery disease.

Keywords: Biaxial testing; Constitutive modeling; Femoropopliteal artery; Mechanical properties; Peripheral artery disease; Remodeling.

Figure 1

Intramural structure of the FPA from a 17-year-old male in the transverse and longitudinal directions. VVG stain: elastin black, collagen red, smooth muscle brown.

Figure 2

A) Bootstrap procedure schematics demonstrating how constitutive parameters for each age group were obtained, and B) bootstrap results demonstrating unimodal distributions of parameters, and C) curve fit obtained with these parameters. Multiple curves of the same color represent multi-ratio loading protocols in the longitudinal (blue) and circumferential (red) directions.

Figure 3

Changes in A) load-free outer radius (ρ_o), stress-free B) outer (R_o) and C) inner ((R_i) radii, D) opening angle (α), E) inner radius in the stress-free longitudinal strip (R_zo), and F) in situ longitudinal pre-stretch (${\lambda }_z^{\mathit{\text{in situ}}}$). Note that stress-free longitudinal strip is curved intima (I) outward. Box plots represent data between 25^th and 75^th percentiles with median and mean marked with a red line and a blue asterisk respectively.

Figure 4

Reduction of total strain energy per unit reference volume (W, kPα) with age. Strain energy density was calculated by using P_sc constitutive parameters at stretches that corresponded to 100 kPa equibiaxial Cauchy stress. Reduction of strain energy density at the equibiaxial stress state indicates overall stiffening of the FPA with age.

Figure 5

Cauchy stress - stretch curves for each of the age groups in longitudinal (A, z) and circumferential (B, θ) directions. Legend summarizes average ages (years) for each of the groups. Figure demonstrates longitudinal and circumferential stiffening with age. Curves of the same color demonstrate multiple loading protocols for the same age group. Stress-stretch curves for all age groups are statistically different from each other (p<0.01) except 21–30 (average age 25 years) and 31–40 (average age 36 years) groups in the longitudinal direction (orange and yellow colors in the left panel).

Figure 6

Physiologic stresses A) $\overline{t_{zz}}$, B) $\overline{t_{\theta \theta }}$, C) $\overline{t_{rr}}$, stretches D) θ_z, E) λ_θ and tethering force F) F_z at 120 mmHg pressure. Correlation with age is measured with Spearman's rank correlation coefficient ρ, while the quality of linear fit is assessed with coefficient of determination R².

Figure 7

Histopathological changes in the FPAs with age demonstrating increase in tunica media thickness (A) and elastic fiber discontinuity (F), and decrease in thickness of the External Elastic Lamina (EEL) (B), thickness of individual elastic fibers (C), total elastin composition (D), and elastin density in the EEL (E) with age. Box plots represent data between 25^th and 75^th percentiles with median and mean marked with a red line and a blue asterisk respectively.