Nonlinear Dynamics of Human Aortas for Material Characterization

Evaluating the nonlinear dynamics of human descending thoracic aortas is essential for building the next generation of vascular prostheses. This study characterizes the nonlinear dynamics, viscoelastic material properties, and fluid-structure interaction of 11 ex-vivo human descending thoracic aortas the full range of physiological heart rates. The aortic segments are harvested from heart-beating donors screened for transplants. A mock circulatory loop is developed to reproduce physiological pulsatile pressure and flow. The results show cyclic axisymmetric diameter changes, which are satisfactorily compared to in-vivo measurements at a resting pulse rate of 60 bpm, with an additional bending vibration. An increase of the dynamic stiffness (i.e., storage modulus) with age is also observed. This increase is accompanied by a strong reduction with age of the cyclic diameter change during the heart pulsation at 60 bpm and by a significant reduction of the loss factor (i.e., damping). Large dissipation is observed at higher pulse rates due to the combined effects of fluid-structure interaction and viscoelasticity of the aortic wall. This study presents data necessary for developing innovative grafts that better mimic the dynamics of the aorta.

Popular Summary

Cardiovascular disease is the leading cause of death in North America, motivating researchers to better understand the mechanical properties of arteries for designing compatible vascular grafts. Identifying the dynamical material properties of the human descending thoracic aorta—a section of the main artery leaving the heart—is essential to this aim. Here, we report on the response of the aorta to a physiological pulsating flow, which has not been adequately investigated in the literature and is essential for building a database of material design parameters.

We test 11 human thoracic aortas on a mock circulatory loop that was developed to simulate physiological pulsations. Our results show cyclic diameter changes, which we satisfactorily compare to in vivo measurements at a resting heart rate. We also observe an increase of the dynamic stiffness with age, accompanied by a strong reduction with age of the cyclic diameter change during the heart pulsation at rest and by a significant reduction of the energy dissipation. At higher pulse rates, we see a large damping of the aortic wall oscillation due to the combined effects of fluid-structure interaction and viscous elasticity of the aortic wall.

From these results, researchers could create innovative biomaterials that better reproduce the aortic dynamic behavior. Our findings complement expanding avenues in advanced materials, with the aim of creating improved and mechanically compatible cardiovascular devices such as grafts and stents.

Figure 1

Experimental setup with dynamic measurement schematic: (a) scheme of the MCL: Harvard Apparatus volumetric pump, expansion chamber, test section, second expansion chamber, pinch valve, atmospheric tank with thermal heater and temperature control; (b) test section of the MCL with the assembled aorta from donor VII, two flowmeters and two catheter pressure gauges (the thin wires coming out from them are clearly visible); the reflecting tapes with laser spots are visible; (c) top: cyclic change of the aortic diameter, shown in a cross-section, measured by two aligned laser Doppler vibrometers (LDV), bottom: bending oscillation of the aorta, shown in a cross-section, measured by two aligned LDV; (d) axisymmetric diameter change of the aortic segment; (e) bending oscillation of the aortic segment.

Figure 2

Specimen preparation and microscopy imaging: (a) thoracic aorta from donor IX: aortic arch separated from the descending thoracic aorta; the aortic branches and part of the periaortic connective tissue were previously removed; (b) image of the cross-section of the aorta from donor VI, $20\mu \mathrm{m}$ thickness, obtained by nonlinear laser scanning microscopy with second-harmonic generation to show collagen fibers. I: intima, M: media; A: adventitia.

Figure 3

Time responses of the aorta segment from donor XI at 60 bpm: (a) fluid variables; (b) cyclic change of the aortic diameter and pressures; (c) cyclic bending oscillation of the aortic segment; at 125 bpm: (d) fluid variables; (e) cyclic change of the aortic diameter and pressures; (f) cyclic bending oscillation of the aortic segment; at 170 bpm: (g) fluid variables; (h) cyclic change of the aortic diameter and pressures; (i) cyclic bending oscillation of the aortic segment. Blue line, inlet pressure; blue dashed line outlet pressure; pink line outlet flowrate; red line change of the aortic diameter measured in vertical direction at mid-length of the aortic segment; red dashed line, change of the aortic diameter measured in horizontal direction; violet line bending amplitude at mid-length of the aortic segment measured in vertical direction; violet dashed line bending amplitude measured in horizontal direction.

Figure 4

Donor XI at 170 bpm: (a) FFT of the bending oscillation in vertical direction where the numbers 1, 2 and 3 correspond to the first, second and third harmonics, respectively; (b) FRF between the bending oscillation and the inlet pressure.

Figure 5

Hysteresis loop of the pressure-diameter change: (a) donor IX at 63 bpm in the vertical direction at mid-length of the aortic segment. Area inside the loop is proportional to the energy loss. The average of areas $S_1$ and $S_2$, found using the middle line of the loop (red line) and the horizontal line passing through it at $x=0$, is proportional to the storage energy. The triangle (violet line) describes the storage modulus computed as the slope at the origin ($dp/d\mathrm{\Delta }d$); (b) donor XI hysteresis loop obtained from the cyclic change of aortic diameter and inlet pressure measured in horizontal direction:, red line 60 bpm; green line 100 bpm; blue line, 170 bpm.

Figure 6

Correlation for cyclic diameter change and viscoelastic parameters with age at 60 bpm, for the eleven donors: (a) maximum diameter change at 60 bpm pulse rate normalized with respect to the diameter ($\mathrm{\Delta }d/\mathrm{diameter}$, experimental points diamond) with linear regression ($0.12889-0.00156\mathrm{A}$, $\mathrm{A}=\text{age}$ (years); p-value $=0.000013$; Pearson’s $\mathrm{R}=-0.912$). Data obtained as the average of diameter changes at the proximal and distal extremities of thoracic descending aortas from in vivo CT images from literature is reported for comparison [7]; average values and standard deviations for two age groups ($41\pm 7\mathrm{years}$; $68\pm 6\mathrm{years}$) of seven individuals each are given (two red error bars); (b) loss factor with linear regression ($0.20602-0.00151\mathrm{A}$, $\mathrm{A}=\text{age}$ (years); p-value $=0.0915$; Pearson’s $\mathrm{R}=-0.535$); (c) storage modulus with linear regression ($-636.26+35.024A$, $\mathrm{A}=\text{age}$ (years); p-value $=0.0129$; Pearson’s $\mathrm{R}=0.706$); (d) parallel coordinate plot demonstrating the relationship between the relative diameter change $\mathrm{\Delta }d/\mathrm{diameter}$, storage modulus and loss factor with age, for 3 age groups: green line, 25–44 years old; blue line, 45–59 years old; red line, 60–85 years old.

Figure 7

Statistical analysis of the viscoelastic parameters at different pulse rates; maximum, minimum, 1st quartile, 3rd quartile, average (black horizontal line inside the box) and median (white horizonal line in the box) are reported for 3 age groups, green rectangular box, 25–44 years old; blue rectangular box, 45–59 years old; red rectangular box, 60–85 years old: (a) maximum relative diameter change; (b) loss factor; (c) storage modulus.

Figure 8

Comparison of the maximum relative diameter change for human aortas within the 60–85 years age group and woven Dacron aortic grafts at different pulse rates. red box, statistical analysis of the data for human aortas for the 60–85 years group; green diamond, Dacron graft tested in [5] with an axial pre-stretch of 1.3; blue diamond, Dacron graft tested by the present authors with an axial pre-stretch of 1.33.

Figure 9

Bending displacement of one period showing vibrations; red line, pressure; blue line, lateral displacement at mid-length of the aortic segment. (a) Donor XVIII at 126 bpm in the horizontal direction, showing vibrations at 10.1 Hz; (b) donor XVI at 155 bpm in the horizontal direction showing vibrations at 46.4 Hz.

Figure 10

Comparison of viscoelastic parameters obtained for uniaxial harmonic tests on circumferential and axial strips and in the MCL at around 60 bpm pulse rate. Axial strips: uniaxial harmonic tests at 1 and 3 Hz at physiological cyclic strain according to donor age (donor $\mathrm{XVI}=5\%$; $\mathrm{XVII}=5\%$; $\mathrm{XVIII}=2.5\%$ in engineering strain) under physiological initial pre-stretch (donor $\mathrm{XVI}=1.33$; $\mathrm{XVII}=1.40$; $\mathrm{XVIII}=1.23$ corresponding to about 70 kPa of nominal stress). Circumferential (circ.) strips: uniaxial harmonic tests at 1 and 3 Hz at physiological cyclic strain according to donor’s age (donor $\mathrm{XVI}=5\%$; $\mathrm{XVII}=5\%$; $\mathrm{XVIII}=1.5\%$ in engineering strain) under physiological initial pre-stretch (donor $\mathrm{XVI}=1.59$; $\mathrm{XVII}=2.07$; $\mathrm{XVIII}=1.39$ corresponding to about 70 kPa of nominal stress): (a) loss factor; (b) storage modulus. maroon box, axial 1 Hz; dark brown box, axial 3 Hz; light brown box, circ. 1 Hz; light blue box, circ. 3 Hz; dark blue box, circulatory loop at 60 bpm.