Potential damage in pulmonary arterial hypertension: An experimental study of pressure-induced damage of pulmonary artery

Abstract

Pulmonary arterial hypertension (PAH) is associated with elevated pulmonary arterial pressure. PAH prognosis remains poor with a 15% mortality rate within 1 year, even with modern clinical management. Previous clinical studies proposed wall shear stress (WSS) to be an important hemodynamic factor affecting cell mechanotransduction, growth and remodeling, and disease progress in PAH. However, WSS in vivo is typically at most 2.5 Pa and a doubt has been cast whether WSS alone can drive disease progress. Furthermore, our current understanding of PAH pathology largely comes from small animals’ studies in which caliber enlargement, a hallmark of PAH in humans, is rarely reported. Therefore, a large-animal experiment on pulmonary arteries (PAs) is needed to validate whether increased pressure can induce enlargement of PAs caliber. In this study, we use an inflation testing device to characterize the mechanical behavior, both nonlinear elastic behavior and irreversible damage of porcine arteries. The parameters of elastic behavior are estimated from the inflation test at a low-pressure range before and after over-pressurization. Then, histological images are qualitatively examined for medial and adventitial layers. This study sheds light on the relevance of pressure-induced damage mechanism in human PAH.

1 |. INTRODUCTION

Arteries have, primarily, a mechanical function, which is influenced heavily by the vessels’ mechanical characteristics. It has been hypothesized that perturbations of the mechanical homeostatic state could be a driving force for physiopathological adaptation in arteries. For example, data suggest that pressure-induced stress concentrations may play an important role in the formation and progression of atherosclerotic plaques (Thubrikar & Robicsek, 1995). In addition, it is widely accepted that arterial stiffening plays an important role in hypertension progression (Mitchell, 2014). Furthermore, a large longitudinal study recently established that, on one hand, arterial stiffening precedes an increase in systolic blood pressure and, on the other hand, initial blood pressure was not independently predictive of a subsequent aortic increase in stiffness (Kaess et al., 2012). These studies highlight the importance of understanding the mechanisms underlying the initiation and progression of arterial maladaptation in relation to hypertension, and of determining the temporal relationship between arterial stiffening, blood pressure increase, and cardiovascular disease progression (Sun & Chan, 2018; Weisbrod et al., 2013).

Pulmonary arterial hypertension (PAH) is associated with elevated pulmonary arterial pressure. Despite remarkable advances in the clinical management of this cardiovascular disease, PAH prognosis remains poor, with a 15% mortality rate within 1 year as highlighted by McLaughlin, Shah, Souza, and Humbert (2015). Several hypotheses have been made to explain the mechanisms that lead to arterial mechanical dysfunction that aggravate, or possibly trigger, PAH. These are complicated by the multifactorial nature of the disease, involving: (a) maladaptive arterial wall remodeling that leads to medial hypertrophy, adventitial thickening, and neointimal lesions (Botney, 1999); (b) degradation of molecular tissue components linked with age-related changes (Akhtar, Sherratt, Cruickshank, & Derby, 2011); and (c) mechanical damage mechanism triggered by abnormally large stresses exerted by hemodynamic forces (Humphrey & Tellides, 2019; Zambrano et al., 2016). Although the role of mechanics within PAH’s disease progression is still unclear, hemodynamic conditions, especially wall shear stress (WSS), are generally thought to influence it by affecting cell mechanotransduction and microstructural remodeling. Recent studies proposed that WSS is the primary mechanical force affecting cell mechanotransduction in PAH (Bürk et al., 2012), causing an inflammatory response and change in cell expression from contractile to proliferative (Li, Scott, Shandas, Stenmark, & Tan, 2009; Li, Stenmark, Shandas, & Tan, 2009). In the systemic vasculature, there is increasing evidence, that low WSS is a promoter of increased wall stiffness and atherogenic vascular states, and could be an independent predictor of cardiovascular mortality (Cunningham & Gotlieb, 2005), and numerical studies suggested that a 30% increase in flow rate can produce a 9% increase in systemic arterial diameter (Valentin, Cardamone, Baek, & Humphrey, 2009). People affected by PAH, however, present a significantly higher increase in arterial diameter, specifically more than 50% in young patients (Truong et al., 2013) and 30% in adult patients (Edwards, Bull, & Coulden, 1998). Clearly, diameter enlargement is one of the most prominent features of PAH in humans, and the distribution of WSS was found to have a substantial influence on both the diameter and the shape of the vessels in the lungs (Vorp, Wang, Webster, & Federspiel, 1998), yet it seems improbable that low WSS alone could be responsible for the significant increase in arterial caliber observed in PAH. Furthermore, previous studies also suggested that changes in the mechanical characteristics of the arterial wall could be involved in aggravating PAH pathology. For example, Sanz et al. (2009) observed that, in exercise-induced PAH, the pulmonary arteries (PAs) stiffness increase preceded the observation of an increase in both pressure and luminal diameter. The authors of that study suggested that PAH progression could be driven by the interplay between various factors (i.e., variations of wall stiffness, wall stress, and WSS), as opposed to one isolated cause.

Little is known about the response to damage of PAs, however, some studies focused on investigating damage mechanisms in other elastic arteries, both theoretically and experimentally. In 1987, one of the first attempts to model damage at large strains was pursed by Simo (1987). The author proposed a nonlinear viscoelastic constitutive model, capable of accommodating general anisotropic response and relaxation functions. This viscoelastic model successfully predicted the progressive loss of stiffness and increasing dissipation with increasing maximum amplitude of strain energy, which agrees with the so-called Mullin’s effect. Several studies have then focused on modeling damage in soft biological tissues (Balzani, Schröder, & Gross, 2006; Calvo, Peña, Martinez, & Doblaré, 2007; Hokanson & Yazdani, 1997). Experimentally, Sommer, Regitnig, Költringer, and Holzapfel (2010) performed quasi-static extension–inflation tests of human common carotid arteries to probe the mechanical effect of loads beyond the physiological domain. The results of this study showed that the burst pressure of ~60 kPa (~450 mmHg) may lead to damage, or rupture, of the medial-intimal layer in the human carotid artery. A similar study, performed on human left anterior descending coronary arteries (Holzapfel, Sommer, Gasser, & Regitnig, 2005) identified the “jacket like” behavior of the adventitial layer at higher pressure that prevent arteries from overstretch and rupture. Finally, several previous experimental and numerical studies have demonstrated that central arteries could sustain blood pressure values >200 mmHg and as high as 1,000 mmHg, without sustaining damage, which is well over the physiologic range (Ferrara & Pandolfi, 2008a; Ferrara & Pandolfi, 2008b; MacLean, Dudek, & Roach, 1999; Martin, Sun, Pham, & Elefteriades, 2013; Richens, Field, Neale, & Oakley, 2002). While pulmonary arterial pressure is approximately one-sixth that of the systemic pressure (Lammers et al., 2011), we do not know if the mechanical strength of the pulmonary arterial wall is comparable to other elastic arteries.

There are important aspects of the mechanics of PAs, which could be contributing to PAH initiation and progression, which have yet to be addressed. The goal of this study is to investigate the irreversible mechanical damage that occurs in PAs when subjected to supraphysiological loading conditions. This large animal experimental study aims to achieve this goal by completing the following objectives.

1. To characterize experimentally the elastic and inelastic (irreversibly damaged) mechanical behavior of PAs;

2. To identify changes in the arterial wall microstructure associated with damage, using the modeling and histological analysis.

2 |. MATERIALS AND METHODS

2.1 |. Specimen preparation

Chest cavities (i.e., heart, lungs, trachea, and esophagus) are obtained from six adult pigs from the MEAT laboratory at Michigan State University and then stored at −20°C for up to 2 weeks. NIH guidelines for the care and use of laboratory animals (NIH Publication #85–23 Rev. 1985) have been observed. Prior to testing, samples are thawed at room temperature for 24 hr, then the PA is separated from the right ventricle and from the aorta by removing the connective tissue. We then isolated the PA from the lungs, up to the second bifurcation, which allowed us to identify a right and left branch. One of the branches was selected for mechanical testing, randomized between left and right, while a ring was cut from the other branch for histology (referred to as “before damage” in Section 2.2.1). Before the mechanical test, small branches were sutured to allow pressurization of the sample, up to obtain a length of ~10 cm for the overall sample. The samples were then stored in Hank’s balanced salt solution in the fridge (2°C) until testing, up to 24 hr.

2.2 |. Mechanical testing

Before mounting the samples for pressurization, geometrical characteristics have been recorded. Specifically, we recorded each sample’s thickness at four different locations, along the circumferential direction, and total axial length, employing a Vernier caliper. Mechanical tests were carried out in a custom-built inflation–extension testing device (Figure 1a), as previously published (Kim & Baek, 2011). The system has the capability to apply, simultaneously, axial pre-stretch via a linear motor, and luminal pressure via a remote-controlled syringe pump. The samples’ diameter was then recorded throughout the test using a CCD camera (Hitachi KP-M2A), while the pressure was measured using a pressure transducer (Honeywell FP2000). The fluid used for pressurization was an NaCl solution at 9% concentration.

FIGURE 1.

(a) Inflation–extension testing device (no sample mounted in this picture). (b) Representative pulmonary artery (PA) sample mounted on the device

The main branch of the PA specimen was secured to a cannula on one end, to allow pressurization, and to a vertically placed support on the other end (Figure 1b). The axial pre-stretch was adjusted to ~10% of the original length. Previous studies showed that the mean in vivo axial stretch measured in the murine proximal aorta was 1.15 (Guo, Kono, Mattrey, & Kassab, 2002), while in the canine and swine descending aortas the value was 1.2 (Han & Fung, 1995). Since it is believed that the in vivo longitudinal stretch of the PA is generally smaller than that of the aorta, we chose to use an axial pre-stretch of 10% for our mechanical tests. This value was also employed in Tian et al. (2012) to test calf PAs.

Using a custom LabVIEW program, we subjected each sample to a biaxial testing protocol consisting of three parts. After preconditioning (i.e., 5 cycles of pressurization from 0 to 30 mmHg) each vessel was pressurized for three sets of 10 loading–unloading cycles, as follows: first, from 0 to 50 mmHg (Part 1); second, from 0 to 100 mmHg, to induce damage (Part 2); and third, from 0 to 50 mmHg (Part 3). Figure 2 shows the pressure—diameter raw data recorded over the course of the mechanical test for one representative specimen. The diameter recorded in these datasets was measured as follows: (a) a region of interest was selected at the beginning of the test—to include most of the artery’s axial length, from just below the top suture to just above the bottom suture, after axial pre-stretch was applied; (b) for each value of pressure, the diameter was measured along with the entire top-to-bottom height of the area of interest—at every pixel along the height was associated the corresponding diameter value; (c) an average diameter was calculated as the mathematical average of all the recorded diameters for each specific value of pressure. The protocol also included a 1-min recovery period between every two successive parts of the test. We used the pressure-diameter curves collected during Part 1 of the test to identify the mechanical behavior of the vessels before damage, and the curves collected during Part 3 of the test to identify the mechanical behavior of the vessels after damage. After testing, we repeated the measurement of thickness and axial length.

FIGURE 2.

Luminal pressure and outer diameter raw data for a representative sample, as collected throughout the mechanical test. Specifically, Part 1 (dark gray line) describes the mechanical behavior of the pulmonary artery (PA) before the damage, Part 2 (light gray line) describes the response to over-pressurization which generates damage within the wall, and Part 3 (dark gray line) describes the mechanical behavior of the PA after damage. Also shown, the preconditioning protocol (dotted light gray line)

2.2.1 |. Histological analysis

Sections from samples collected before damage (from the untested PA branch) and after damage (from the PA tested branch, after completion of the test) were processed for histological analysis. Briefly, the samples were fixed in a 10% formalin solution for an hour and then stored at room temperature in 30% ethanol before being embedded in paraffin and sectioned. Sectioning and staining were carried out by the MSU Histopathology Lab. Histological analyses were focused on determining qualitative changes in the collagen and elastin fibers’ structures, by comparing samples collected before and after damage. To analyze collagen fibers’ integrity, we stained the samples using picrosirius red (PSR) and we imaged them with polarized light. Finally, to investigate the elastin fibers’ structure we employed the Verhoeff-van Gieson (VVG) stain.

2.2.2 |. Mechanical model

The structural properties of the PA specimens before and after damage were characterized using two nonlinear, hyperelastic, constitutive models, to aid in the interpretation of the experimental results. Assuming an incompressible material, the Cauchy stress can be computed as

$$T=-PI+2\mathbf{F}\frac{\partial W}{\partial C}{\mathbf{F}}^T,$$ (1)

where P is the Lagrange multiplier enforcing incompressibility, and F and C are the deformation gradient and right Cauchy–Green tensor, respectively; a thin-walled model was used to calculate the stresses (Humphrey, 2013; Humphrey & Delange, 2016). In addition, W is the strain energy function that describes the tissue’s constitutive behavior. For this study, we have employed two constitutive models to describe the PA behavior before and after damage; specifically, we used the two-fiber-family model (Holzapfel, Gasser, & Ogden, 2000) and the Gasser–Ogden–Holzapfel (GOH) model (Gasser, Ogden, & Holzapfel, 2006). Histological analyses on the arteries showed that the arterial wall is comprised of layers of elastin and collagen fibers. Mechanical response of the elastin content of the arterial wall is predominantly isotropic (Gundiah, Ratcliffe, & Pruitt, 2009), and thus is described as a neo-Hookean material in both models.

Two-fiber-family model

In this model, the contribution of two families of collagen fibers, oriented symmetrically with respect to the longitudinal axis, was described by an exponential function, proposed by Holzapfel et al. (2000). Specifically, the total strain energy function was written as the summation of an isotropic part and an anisotropic part

$$W=\frac{c_1}{2}\left(I_1-2\right)+\sum _{K=1,2}\frac{c_1^k}{4c_2^k}\left\{\text{exp}\left[c_2^k{\left({\lambda }^k\right)}^2-1{)}^2\right]-1\right\},$$ (2)

are material parameters, I₁ is the first invariant of the right Cauchy–Green tensor (i.e., I₁=tr C), and the stretch ratio of the k-th fiber family is defined as ${\lambda }^k=\sqrt{{\lambda }_{\theta }^2{\text{sin}}^2{\alpha }^k+{\lambda }_z^2{\text{cos}}^2{\alpha }^k}$, where α^k is the angle between each fiber family direction and the axial direction.

GOH model

In this model, the overall mechanical behavior of the arterial wall, under the assumption of a transversely isotropic material, was expressed by a strain energy function as

$$W=\frac{c_1}{2}\left(I_1-2\right)+\sum _{k=1,2}\frac{c_1^k}{2c_2^k}\left\{\text{exp}\left[c_2^k{E}_k^2\right]-1\right\},$$ (3)

where E_k = κ I₁ + (1 − 3κ)(λ^k)² − 1, and κ is a dispersion parameter representing the fiber distribution. The limits for the parameter κ are 0 ≤ κ ≤ 1/3, where κ = 0 represents collagen fibers that are perfectly aligned along with two symmetric directions (which recover the two-fiber-family model), and κ = 1/3 represents fibers that are perfectly randomly oriented, resulting in an isotropic response.

We have decided to include two models because, while the GOH model has a more direct connection with the microstructure, represented by the dispersion parameter, it has been shown before that a model with a discrete set of families of collagen fibers can have better predictive capabilities than that of GOH model (Schroeder, Polzer, Slažanský, Man, & Skácel, 2018).

In this study, we aim to quantify the mechanical changes associated with damage due to supraphysiological pressure. Therefore, we decided to use the same constitutive forms to describe samples before and after damage. Best-fit values for the parameters of each model have been determined separately, to best describe the before and after damage conditions of each specimen. Specifically, using a fminsearch function (MATLAB), we minimized the objective function (Baek, Gleason, Rajagopal, & Humphrey, 2007).

$$e=\sqrt{\frac{\sum {\left(P_{\text{est}}-P_{\text{data}}\right)}^2}{\sum {\left(P_{\text{data}}\right)}^2}}+\gamma {\left({\lambda }_z-{\overline{\lambda }}_z\right)}^2$$ (4)

where P_data and P_est are the measured and computed intramural pressure, respectively. Moreover, the axial stretch in the experiments is fixed to be ~10% with respect to the unloaded control specimen ${\overline{\lambda }}_z=1.1$). Therefore, this constraint is added to the objective function with a penalty parameter γ that has been taken to be equal to 10 for all samples and all models. In this study, we have considered the collagen fibers to behave symmetrically with respect to the longitudinal axis for both models (i.e.,$c_1^1=c_1^2=c_1^{1,2};c_2^1=c_2^2=c_2^{1,2};{\alpha }^1={\alpha }^2=\alpha$). In addition, we have constrained the material parameters to be positive (i.e., $c_1,c_1^{1,2},c_2^{1,2}>$0), as well as the dispersion parameter to be included in the range κ ∈ [0, 1/3]. For each specimen, the last (10th) loading curve from Parts 1 (before damage) and 3 (after damage) are used for parameter estimation. While, ideally, we aimed to start from a pressure of 0 mmHg for each loading cycle, due to the tendency of the PA to collapse at low pressures, the lower value of pressure we have been consistently able to apply was 2 mmHg. In a similar way, due to the fluctuation of the testing system, the highest pressure we could reach for all samples was 45 mmHg (as opposed to 50 mmHg). It follows that the pressure range employed to estimate material parameters was 2–45 mmHg.

2.2.3 |. Statistical analysis

All data are reported as mean ± SD; groups were compared employing two-tailed Student’s t test. When comparing controls and damaged samples (n = 5 for each group) we identified differences between groups using a paired t tests. For all comparisons, a p-value <.05 was considered significant.

2.3 |. Results

Of the six samples tested, only five were considered for our analysis; one sample was discarded due to excessive noise in the data. Pretest measurements of samples showed an initial length of 117.90 ± 13.8 mm, the wall thickness of 0.89 ± 0.063 mm, and an initial outer diameter of 13.71 ± 2.42 mm. Post-test measurements concluded that there was no significant change in the overall length of the specimens, whereas, the average wall thickness decreased to 0.79 ± 0.044 mm.

In Figure 2 we show a representative set of raw pressure-diameter data as collected throughout the mechanical test. During the initial mechanical test (Part 1), the vessel exhibited pseudo-elastic characteristics, showing repeatable behavior for consecutive loading cycles. In the following, we will refer to the last loading curve of this portion of the test as the before-damage behavior of the PAs. During over-pressurization (Part 2), conversely, we observed a pronounced rightward shift of each consecutive loading cycle, which suggests the development of mechanical damage within the arterial wall. Finally, in Part 3 of the test, the vessel displayed some level of recovery of the pseudo-elastic behavior, shown by the fact that consecutive loading cycles generate repeatable curves. All specimens, however, showed qualitatively a significant increase in diameter for each value of pressure, when comparing curves from Part 1 to curves from Part 3 of the test. This seems to confirm the hypothesis that the application of supraphysiological pressures can damage the arterial wall in a potentially permanent way. In the following, we will refer to the last loading curve of Part 3 of the test as the after-damage behavior of the PAs.

We then quantified the diameter increase associated with over-pressurization by comparing diameters before and after damage, for each value of pressure. First, we normalized the diameter values recorded throughout the test by the diameter value at ~0 mmHg after preconditioning (i.e., the lowest pressure recorded), for each sample. Then, we performed an across-sample average of the normalized diameter before damage (i.e., D_A=$D_{A_0}$) and after damage (i.e., D_B=$D_{A_0}$) for values of pressures included between 0 and 50 mmHg, shown in Figure 3. Statistical analysis confirms that the normalized diameter increase observed when comparing before and after damage behaviors is significant (p < .05 for each value of pressure). The damaged specimens showed an enlargement amounting to ~20% of the diameter.

FIGURE 3.

Average pressure versus normalized diameter curve for all specimens. D_A and D_B correspond to before and after damage diameters, respectively. The before damage behaviors have been collected during Part 1 of the test, while the after damage behavior have been collected during Part 3 of the test. The asterisk indicates that the normalized diameters were significantly different, at p < .05, when comparing before and after damage behaviors

In an effort to identify the pressure for which the damage starts occurring, we compared the first three consecutive loading curves for Part 2 of the test. Specifically, the difference between the diameters of the first and second loading curves, and the difference between the diameters of the second and third loading curves are compared in Figure 4. A significant oftening or yielding behavior can be observed during the first over-pressurization to 100 mmHg. Arteries are enlarged after the first loading cycle, while the change in size is significantly smaller over the next cycles. This result confirms that the irreversible damage of mechanical behavior was caused by a high pressure. Particularly, a pressure of 50–60 mmHg, where the diameter difference is the largest, seems to be a reasonable candidate to quantify the onset of damage. However, it is not clear if mechanical damage was present during Part 1 of the test.

FIGURE 4.

Change in diameter during different loading curves. Black circles represent the diameter difference between the first and second loading curves of Part 2 of the test, gray squares represent the difference in diameter between the second and third loading curves. The * indicates that the diameters were significantly different at p < .05

Figure 5 shows histological images of representative specimens, before and after damage. Polarized PSR images show a color shift from bright red (larger diameters fibers) to yellow-green fibers (smaller diameter fibers), which could indicate damage in collagen fibers. On the other hand, although the elastin sheets appear to be more dispersed in the VVG stained image of the damaged specimen, there are no clear qualitative indications of increased damage in the elastin fiber network.

FIGURE 5.

Histology images of tissue samples from the pulmonary artery (PA). Top row: Picrosirius red under polarized light (collagen fibers in red, yellow, and green); bottom row: VVG (elastin in black, nuclei in purple, and cytoplasm and collagen in pink). Left: before damage samples; right: after damage samples. Bar in each image represents 500 μm; the letter “L” indicates the luminal side, and the letter “A” indicates the abluminal side

The two-fiber-family model describes the results accurately, according to the computed R², for both the before and after damage specimens, as shown in Table 1. All the constitutive parameters of the model are significantly affected by the damage. Collagen fiber stiffness parameters, $c_1^{1,2},c_2^{1,2}$, and the fiber directions α seem to incur significant changes during the over-pressurization of arteries, which is consistent with the observation in histology images. The results indicate a softening in collagen fibers with an approximately 66% decrease in the dimensionless material parameter $c_2^{1,2}$. The fiber orientation α suggests a significant change of the fiber distribution toward the longitudinal direction. Furthermore, the stiffness of elastin c₁ decreased significantly, by 50% on average. This result seems to interestingly contradict what was observed in the histology images, which qualitatively suggest that elastin is not strongly affected by over-pressurization.

TABLE 1.

Best-fit material parameters for the two-fiber-family model

Specimen\parameter	c1 (kPa)	$c_1^{1,2}$ (kPa)	$c_2^{1,2}$	α (deg)	R 2
Control
1	18.04	5.36	8.97	53.66	0.975
2	17.38	7.65	5.55	52.07	0.986
3	13.42	26.75	4.73	53.69	0.976
4	10.99	19.01	3.25	52.80	0.994
5	16.63	14.48	2.99	50.94	0.980
Avg ± SD	15.29 ± 2.99	14.65 ± 8.67	5.10 ± 2.41	52.63 ± 1.16
Damaged
1	4.84	13.46	1.57	45.85	0.975
2	7.17	12.37	1.86	46.49	0.986
3	10.73	28.45	2.49	51.28	0.976
4	0.53	24.86	0.92	47.74	0.994
5	14.60	14.63	1.81	47.88	0.980
Avg ± SD	7.57 ± 5.40	18.76 ± 7.37	1.73 ± 0.57	47.85 ± 2.10
p	.03	05	.04	.01
% Change	−50.47	28.01	−66.09	−9.09

Table 2 reports the best-fit values for the constitutive parameters for the GOH model, which seem to confirm what was observed in Table 1 for the two-fiber-family model. Briefly, the GOH model also highlights a significant change in most collagen-associated material parameters, namely $c_1^{1,2}$ is increased sharply after over-pressurization, by over 100% on average, and $c_2^{1,2}$ is decreased by about 70% on average, although this change does not rise to the level of significance. We also observe a similar change in the distribution angle α as was observed for the two-fiber-family model, which suggests a rearrangement of the fibers in the longitudinal direction. We also observe a similar change of the parameter c₁, which seems to suggest an effect of over-pressurization on elastin. Finally, while the dispersion parameter seems to not be significantly different between the two groups, we detected a decrease of 60% in the samples after damage, as compared to before.

TABLE 2.

Best-fit material parameters for the Gasser–Ogden–Holzapfel (GOH) model

Specimen\parameter	c1 (kPa)	$c_1^{1,2}$ (kPa)	$c_2^{1,2}$	α (deg)	κ	R 2
Control
1	20.29	7.85	16.03	55.22	0.11	0.979
2	18.83	11.61	8.99	53.01	0.10	0.988
3	14.97	30.65	5.72	54.31	0.04	0.976
4	10.32	25.53	3.73	53.19	0.05	0.993
5	20.73	16.83	5.38	51.69	0.10	0.984
Avg ± SD	17.03 ± 4.38	18.50 ± 9.50	7.97 ± 4.89	53.48 ± 1.34	0.13 ± 0.04
Damaged
1	4.89	30.19	2.54	45.09	0.16	0.988
2	6.93	26.60	2.86	46.14	0.14	0.982
3	8.26	46.42	2.81	51.64	0.07	0.979
4	0.63	60.69	1.20	47.89	0.17	0.991
5	16.06	22.24	2.80	47.82	0.11	0.989
Avg ± SD	7.35 ± 5.66	37.23 ± 15.99	2.44 ± 0.7	47.72 ± 2.49	0.08 ± 0.03
p	.007	.019	.058	.011	.057
% Change	−56.82	101.30	−69.341	−10.78	−60.54

Finally, we have evaluated the stored elastic energy (area under the curve) throughout the pressurization test (W), as well as the circumferential and longitudinal localized stiffnesses for a luminal pressure of 45 mmHg (E_θθ and E_zz), following the small on large approximation introduced by Baek et al. (2007), reported in Table 3. The circumferential localized stiffness decreased after over-pressurization, which supports the observed qualitative softening of the specimens (Figure 3), and is in accordance with the reorientation of the collagen fibers toward the axial direction after damage. In addition, the longitudinal stiffness was statistically increased after over-pressurization. The increase in stored energy after the damage is also in accordance with the higher deformability observed in the pressure-diameter data, especially since the test is performed controlling the value of pressure. Finally, the increase in the value of stored energy seems to support the idea that elastin, which dominates the elastic behavior of the vessel wall, is still contributing significantly to the vessels’ mechanics after damage.

TABLE 3.

Circumferential and longitudinal localized stiffnesses (E_θθ and E_zz), evaluated for a luminal pressure of 45 mmHg, and stored elastic energy (W) evaluated throughout the pressurization test

Specimen\parameter	Eθθ (kPa)	Ezz (kPa)	W (kPa)
Control
1	277.36	54.20	4.31
2	270.56	57.86	5.62
3	275.10	59.89	4.81
4	207.56	45.56	5.91
5	264.58	61.94	7.04
Avg ± SD	259.03 ± 29.19	55.89 ± 6.44	5.54 ± 1.05
Damaged
1	260.93	66.525	8.4478
2	253.70	64.792	8.3286
3	263.99	62.102	6.3853
4	210.60	50.958	8.8758
5	252.81	65.266	9.3008
Avg ± SD	248.41 ± 21.66	61.93 ± 6.34	8.27 ± 1.12
p	.04	.03	.003
% change	−4.10	10.80	49.29

Note: Parameters were evaluated with respect to the two-fiber-family constitutive model.

2.4 |. Discussion

Characterizing dissipative behavior of vasculature, such as softening and yielding, is an emerging area of research, in predicting the potential risk of diseases and elucidating mechanisms of disease progression. Previous studies have investigated the mechanical behavior of arteries in pressures higher than the physiological range (e.g., over 150 mmHg) mostly in the systemic circulation systems; however, significant enlargement of lumen diameter in this kind of vessel is not a common feature in hypertension (Sommer et al., 2010). On the other hand, a larger caliber of the vessels in the lungs is a characteristic feature of PAH patients when compared to healthy individuals, for example, 20% larger arterial diameter in adult PAH patients and 30% larger arterial diameter in pediatric PAH patients (Edwards et al., 1998; Truong et al., 2013). The central hypothesis that we sought to test in this study is that over-pressurization could lead to a permanent increase in the luminal diameter of proximal PAs. To this end, we designed a mechanical testing protocol to characterize the change in mechanical behaviors of porcine PAs in response to damage. Then, we employed two constitutive laws to interpret the results and hypothesize which tissue components could be more affected by the damage process. Finally, we employed histological images to qualitatively support the proposed damage mechanisms.

While previous studies have investigated the irreversible mechanical response of the arteries both in physiological and pathological conditions (Scott, Ferguson, & Roach, 1972), to the authors’ knowledge, this study is first to investigate the mechanical damage in the PAs. Large PAs are the main conduits in a low-pressure system, in comparison to the systemic circulation, and this physiological function could result in a significantly different structure when compared to other elastic vessels. For example, in cerebral arterial tissues, the mechanical response to cyclic loading to a maximum pressure of 100 mmHg was shown to have no effect on the pressure-diameter curves (Li & Robertson, 2009). In this study, we showed that in PAs, however, a pressure of 100 mmHg appeared to induce an irreversible effect on the mechanical behavior of the wall (Figure 2). Furthermore, the mechanical test we performed showed that preconditioning to a pressure of 30 mmHg did not change the mechanical behavior of the artery significantly, indicating that no damage incurred for this pressure level. In addition, a relatively small softening behavior is observed in Part 1 of the tests, where the highest pressure is 50 mmHg (data not shown, not significant). However, our results indicated that a more pronounced damage across all five specimens was associated with Part 2 of the test (Figure 3), where all of the vessels have a significantly larger dimensionless diameter after the inflation test (p < .05). The results of Part 3 demonstrated that after the over-pressurization, the arterial wall is more compliant, yet the cyclic pressure-diameter curves exhibit an elastic behavior. Schriefl, Schmidt, Balzani, Sommer, and Holzapfel (2015) observed similar more deformable but elastic behavior when the arterial collagen was enzymatically removed in human abdominal aorta samples.

The compliant behavior is also reflected in terms of the material parameters for both constitutive models considered, shown in Tables 1 and 2, where the parameter c₁ and $c_2^{1,2}$ significantly decreased (difference not significant for $c_2^{1,2}$ for the GOH material model), when comparing behavior before and after damage. The parameters $c_1^{1,2}$ and $c_2^{1,2}$ represent, in the model employed here, the constitutive properties of the collagen in the arterial wall as well as its effectiveness at different pressure domains (Roach & Burton, 1957), while c₁ represents the behavior of elastin. This suggests that both elastin and collagen are affected by over-pressurization, and underscores the need of further investigation in future works to deepen the understanding of the mechanisms of the damage. Our results, however, suggest that elastin is still strongly contributing to the overall mechanical behavior after damage, as proved by the pseudo-elastic behavior that is conserved by the vessel after over-pressurization, as well as by the amount of elastic energy stored throughout the test that increases after damage (see Table 3). Furthermore, we have detected changes not just in material parameters associated with the collagen fibers in both models but also changes in the angle that defines the direction of the fibers. Indeed, Tables 1 and 2 suggest that the collagen fiber directions could significantly change before and after damage. Particularly, the angle α between the effective fiber orientation with respect to the axial direction of the artery show an average ~5° decrease in the fiber orientation for both models, which could suggest that the circumferentially oriented collagen fibers are damaged. Similarly, Converse et al. (2018) observed that the direction of the damage conforms to the direction of the overstretch using a collagen hybridizing peptide in the ovine middle cerebral artery specimens. Finally, the observed histological characteristics seem to also suggest that elastin’s integrity is not significantly affected by over-pressurization, while the collagen structure appears to have qualitatively changed. This hypothesis is also supported by previous studies, for example, in Dobrin, Baker, and Gley (1984) the authors suggest that in arteries “tensile strength and wall integrity depended on intact collagen, [but] not elastin.” Similarly, in PAs, Lammers et al. (2008) performed an in vitro test and revealed that the elastin is load-bearing only in the low blood pressure range, but at high pressures, the collagen fibers network is carrying most of the load, which would lead to the damage of collagen in the case of over-pressurization.

Furthermore, Bellini, Ferruzzi, Roccabianca, Di Martino, and Humphrey (2014) suggest that, in elastic arteries, the adventitia behaves like a protective sheet against over-pressurization. In their article, the authors developed a thick-wall, two-layered model which showed that, when the pressure increases significantly above the homeostatic values, there is a load transfer toward the adventitial layer; while in homeostatic conditions the medial layer is carrying most of the load. These results support the proposed mechanism for which the collagen within the adventitial layer is damaged before the elastin sheets within the medial layer, despite having higher strength. In addition, the elastic lamina, within the medial layer, is thought to be mostly responsible for the elastic behavior of large vessels. In support of this idea, one can observe how vessels behave once the medial layer is chemically removed, as shown in Ferruzzi, Collins, Yeh, and Humphrey (2011). In their study, the authors chemically removed the elastin in the media, by applying the enzyme elastase, and recorded how the mechanical behavior of the vessel was affected by this change. What they observed is that the vessel after this treatment seems to lose the ability to elastically recoil after pressurization, and it behaves in a manner similar to a vein. This supports the hypothesis made here by contrast, since we still observe a pseudo-elastic behavior in the PA after over-pressurization, suggesting that the elastin layer is still functional because if it would have been significantly damaged the vessels would have reasonably lost its ability to elastically recoil.

Finally, the significantly large difference between the first-second and second-third consecutive loading curves during Part 2 of the test demonstrates that a pressure higher than 50 mmHg induces sudden irreversible changes in the structure of the PAs, whereas the pressure below 50 mmHg induces relatively smaller mechanical damage (Figure 4). Specifically, the abrupt change in the slope of the curve suggests that the damaging pressure is ~60 mmHg. The continuous softening behavior throughout Part 2 may imply that the damage threshold in each following sets of loading curves may be decreasing. However, this behavior may be due to a constant softening in the arterial structure.

This study has some limitations. First, the tests were performed in open air and room temperature, while other studies perform the tensile tests in a saline solution (Schrauwen et al., 2012). Second, we did not account for the mechanical response (active or passive) of smooth muscle cells in our study. Third, while we kept the specimens axially stretched at 10%, we did not measure the axial force induced in the specimens during the pressurization. Fourth, we did not use a dissipative modeling of the damage process but only compared the hyperelastic behavior before and after damage. Despite these limitations, this is the first study to investigate the mechanical damage as a result of over-pressurization in the PAs.

PAH is a complex and multifaceted disease in which the structure of the proximal PAs changes as a result of a variety of biomechanical and biochemical factors. In this study, we aimed to analyze only the mechanical response of the proximal PAs under elevated pressure. The results presented here suggest that mechanical damage of the arterial wall, associated with significantly increased blood pressure, could be contributing to the pathology of PAH. Furthermore, the combination of model and histological images seem to suggest that the damage is localized in the collagen fibers network in the adventitial layer.