Stress-Relaxation and Cyclic Behavior of Human Carotid Plaque Tissue

Abstract

Atherosclerotic plaque rupture is a catastrophic event that contributes to mortality and long-term disability. A better understanding of the plaque mechanical behavior is essential for the identification of vulnerable plaques pre-rupture. Plaque is subjected to a natural dynamic mechanical environment under hemodynamic loading. Therefore, it is important to understand the mechanical response of plaque tissue under cyclic loading conditions. Moreover, experimental data of such mechanical properties are fundamental for more clinically relevant biomechanical modeling and numerical simulations for risk stratification. This study aims to experimentally and numerically characterize the stress-relaxation and cyclic mechanical behavior of carotid plaque tissue. Instron microtester equipped with a custom-developed setup was used for the experiments. Carotid plaque samples excised at endarterectomy were subjected to uniaxial tensile, stress-relaxation, and cyclic loading protocols. Thirty percent of the underlying load level obtained from the uniaxial tensile test results was used to determine the change in mechanical properties of the tissue over time under a controlled testing environment (Control tests). The stress-relaxation test data was used to calibrate the hyperelastic (neo-Hookean, Ogden, Yeoh) and linear viscoelastic (Prony series) material parameters. The normalized relaxation force increased initially and slowly stabilized toward the end of relaxation phase, highlighting the viscoelastic behavior. During the cyclic tests, there was a decrease in the peak force as a function of the cycle number indicating mechanical distension due to repeated loading that varied with different frequencies. The material also accumulated residual deformation, which increased with the cycle number. This trend showed softening behavior of the samples. The results of this preliminary study provide an enhanced understanding of in vivo stress-relaxation and cyclic behavior of the human atherosclerotic plaque tissue.

Keywords: carotid plaque; cyclic test; mechanical behavior; stress-relaxation test; tensile test.

FIGURE 1

(a) Low energy X-ray used to identify the calcium content; (b) Sample collected from hospital with cutting direction (circumferential).

FIGURE 2

(a) Sample fixed to the custom designed frame with sandpaper and LOCTITE glue; (b) Experimental setup showing tubes connected to the hot water bath to maintain physiological temperature; (c) Sample hydration was maintained using DMEM supplemented with 20% fetal bovine serum (FBS), 50 μg/ml L-ascorbic acid and 50 IU/mL Penicillin-Streptomycin.

FIGURE 3

Preparation of test specimens: (a) Carotid plaque sample collected from the hospital; (b) Representative segments cut from the plaque tissue sample; (c) Sandpaper glued to the frame; (d) Sample glued to the sandpaper.

FIGURE 4

Displacement controlled profiles (A) Stress-relaxation loading protocol; (B) Cyclic test loading protocol.

FIGURE 5

Cauchy Stress and stretch response of the carotid plaque strip (A) without calcification; (B) with calcification.

FIGURE 6

(A) A typical curve representing the ultimate load (F_ult), 0.3F_ult and the corresponding displacement; (B) Relative stiffness of the carotid plaque samples over time in supplemented DMEM at 37°C.

FIGURE 7

Carotid plaque tissue was subjected to 30% stretch at 0.1 and 1 mm/s strain rate. The stretch was maintained for 1 h. Normalized variation in force as a function of time was represented for three samples (S1, S3, and S4) at two different strain rates. S1-low calcification, S3-high calcification, S4- medium calcification.

FIGURE 8

(A) Comparison of experimental and numerical results for the non-linear behavior (extension portion of stress-relaxation test data); (B) Comparison of experimental and numerical results for the linear viscoelastic behavior (stress-relaxation portion of the stress-relaxation test data).

FIGURE 9

Carotid plaque tissue was subjected to 30% stretch at 0.1 mm/s, followed by a sinusoidal waveform (amplitude corresponding to 20% stretch) of 1 Hz and 1.5 Hz frequencies for 2 h. (A) Normalized variation in peak force as a function of time; (B) Residual strain accumulation as a function of cycle number (The function used for logarithmic curve fitting is y = a × ln(x) + b).

FIGURE 10

Variation in the tangent modulus of the unloading curve of the tissue. (The function used for logarithmic curve fitting is y = a × ln(x) + b).

FIGURE 11

Hysteresis loops of selected cycles for a 1.5 Hz frequency profile (C- Cycle number).