Pulmonary arterial hypertension (PAH) commonly leads to right ventricular (RV) hypertrophy and fibrosis that affect the mechanical properties of the RV myocardium (MYO). To investigate the effects of PAH on the mechanics of the RV MYO and extracellular matrix (ECM), we compared RV wall samples, isolated from rats in which PAH was induced using the SuHx protocol, with samples from control animals before and after the tissues were decellularized. Planar biaxial mechanical testing, a technique first adapted to living soft biological tissues by Fung, was performed on intact and decellularized samples. Fung's anisotropic exponential strain energy function fitted the full range of biaxial test results with high fidelity in control and PAH samples both before and after they were decellularized. Mean RV myocardial apex-to-outflow tract and circumferential stresses during equibiaxial strain were significantly greater in PAH than control samples. Mean RV ECM circumferential but not apex-to-outflow tract stresses during equibiaxial strain were significantly greater in the PAH than control group. The ratio of ECM to myocardial stresses at matched strains did not change significantly between groups. Circumferential stresses were significantly higher than apex-to-outflow tract stresses for all groups. These findings confirm the predictions of a mathematical model based on changes in RV hemodynamics and morphology in rat PAH, and may provide a foundation for a new constitutive analysis of the contributions of ECM remodeling to changes in RV filling properties during PAH.

## Introduction

Right ventricular (RV) function is a good prognostic indicator in pulmonary arterial hypertension (PAH), a progressive vasculopathy that commonly results in intractable RV failure and premature death [1]. It has been shown in humans with and animal models of PAH [24] that the RV hypertrophies, in response to increased RV systolic pressure, can be associated with tissue fibrosis and altered end-diastolic stiffness.

Our recent analysis of right ventricular hemodynamics in the monocrotaline-treated rat model of PAH [5] showed that, while systolic function remained compensated against increased pulmonary artery pressure by increased RV volume and contractility, there was also a significant increase in end-diastolic myocardial stiffness though chamber compliance was unaltered due to the RV dilation. Previous multi-axial testing studies of RV myocardium (MYO) in small animal models of RV hypertrophy have reported increased myocardial stiffness [68]. Therefore, we sought to determine whether RV myocardial biaxial mechanical properties were also altered in an animal model of PAH. We used the Sugen-hypoxia (SuHx) rat model, considered the most realistic and well-characterized small animal model of PAH due to it closely mimicking the development of plexiform lesions in patients with PAH, a hallmark of the disease [9].

Since RV myocardial fibrosis has also been reported in humans [2,4] and animals [3] with pulmonary hypertension, we further investigated whether the mechanical properties of the RV myocardial extracellular matrix (ECM) were altered during pulmonary arterial hypertension by retesting RV samples after they had been decellularized. Stress–strain measurements from biaxial testing protocols obtained from mechanical testing of intact and decellularized RV tissues were well approximated by the anisotropic exponential strain-energy function first proposed by Fung [10]. The analysis showed that significant changes in myocardial and matrix stiffness occur in SuHx-treated rats.

## Methods

### Animal Model, Tissue Preparation, and Mechanical Test.

All experiments were performed with the approval of the Animal Care and Use Committee at the University of Illinois, Chicago. The SuHx animal model was chosen as it develops vascular lesions that resemble those seen at autopsy in PAH patients [9] and undergo ventricular remodeling as a consequence of the RV pressure overload. Twelve adult male Sprague-Dawley rats (Charles River, Chicago, IL) weighing 200 g were injected subcutaneously with a single dose of 20 mg/kg of Sugen (SU5416, Sigma-Aldrich, St. Louis, MO), a vascular endothelial growth factor receptor 2 inhibitor, and kept in hypoxic chambers supplied with 10% oxygen for three weeks [11]. Two–three weeks post returning to normoxia, in vivo hemodynamic measurements were taken as previously described [12] to obtain pulmonary arterial pressures and confirm PAH in the treated group, which is defined by a mean pulmonary arterial pressure greater than 25 mmHg at rest [2]. Briefly, the animals underwent a tracheotomy where the animals were intubated (E-Z Anesthesia Ventilation System, Palmer, PA) and supplied with 2.5% of isoflurane mixed with oxygen as an anesthetic. This was followed by a thoracotomy to expose the heart and great vessels. A 1.6-F dual pressure sensor catheter (Transonic Scisense, London, ON, Canada) was inserted into the right ventricle and advanced to the main pulmonary artery via the pulmonic valve to obtain blood pressure time series. The control group (CTL) of thirteen male animals was untreated and maintained in normoxic conditions.

Immediately after the hemodynamic measurements, the heart was harvested and the RV isolated and dissected. A square sample of the free wall was excised and oriented with the one axis aligned along the apex to the RV outflow-tract (AOT), often also referred to as the longitudinal direction. We defined this axis as x1 and the circumferential axis as x2. Right ventricular myocardial sample thickness, weight, and edge lengths were measured. For a more robust measure of thickness, three measurements were taken within the center region of the sample using a thickness gauge (1010Z, Starrett, Athol, MA). Four custom-made hooks were placed on each side of the sample and mounted in the pulley system of a Bose Electro Force planar biaxial testing device (TA Instruments, New Castle, DE). While kept in a temperature-controlled bath of phosphate-buffered saline (PBS; 137 mM NaCl, 2.7 mM KCl, 1.8 mM KH2PO4, 10 mM Na2HPO4), five material markers placed on the surface of the specimen were brought into the visual field of the optical tracking system for computing the deformation gradient tensor off-line (Fig. 1). The samples were preloaded equally to 0.2 g to align them with the suture and pulley-system and thus secure a two-dimensional mechanical test. The mechanical testing consisted of 10% stretch-controlled biaxial tests at 0.5 Hz with biaxial ratios of x1:x2 = 1:0.5, 1:0.25, 1:1, 0.5:1, and 0.25:1, all recorded after 15 cycles of preconditioning each. After obtaining the mechanical properties of the RV myocardium, the sample underwent a decellularization protocol to isolate the myocardial RV ECM. The decellularization protocol was adapted from Xu et al. [13] and consisted of stirring the sample in 10 mM Tris-HCl buffer with 0.5% sodium-dodecyl sulfate solution for 72 h (normotensive samples) or 144 h (hypertensive samples) at room temperature on a rotating mixer (Labnet International, Edison, NJ) while refreshing the solution every 24 h. The difference in time was based on the thickness of the samples in the hypertensive group, which were about twice as thick as the controls. At the conclusion of the decellularization protocol, the ECM-only specimens were kept in a −4 °C refrigerator for 24 h in PBS before mechanical testing. In room-temperature PBS, the RV ECM specimens underwent the same biaxial testing protocol as the RV myocardium after the matrix sample dimensions were measured, except that the decellularized samples were only stretched to a maximum of 8% to prevent microstructural damage.

RV myocardial samples adjacent to the region used for mechanical testing were placed in 10% formalin for 48 h. The samples were then transferred to 70% ethanol, paraffin embedded, and sectioned tangent to the plane of the epicardium. The tissues were stained with Masson's trichrome, which stains collagen blue, nuclei black, and cytoplasm, muscle, and erythrocytes red. Images were then taken with an inverted, bright-field light microscope (Nikon Eclipse TI-S, Nikon Corporation, Tokyo, Japan). Decellularized ECM samples underwent the same tissue preparation and imaging after mechanical testing.

### Data Processing and Modeling Efforts.

Biaxial loads (Model WMCP-1000 g, Interface, AZ, 1000 ± 1.5 g) and pixel coordinates of the outer four material markers on the surface of the sample were used to compute stress and strain components with respect to the x1 and x2 axes to characterize the mechanical properties of the RV myocardium and ECM. Forces were normalized by the cross-sectional area of the samples to compute the first Piola-Kirchhoff (PK) stress tensor P. The reference configuration was the preloaded state of the samples at 0.2 g, post-preconditioning, prior to the equibiaxial cycles. The recorded pixels of the outer four material markers on the surface of the sample were used to compute the deformation gradient tensor F via isoparametric mapping of a quadrilateral element [14,15]. The signals were interpolated to synchronize sampling frequencies of 200 Hz between the camera system and the software of the Bose ElectroForce device motors. A Savitzky–Golay filter was applied to the camera system data using the sgolay function in matlab (version 2018b, The Math Works, Natick, MA). The delay between the start of the two signals was resolved by correlating the peaks between two data sets and truncating points from the beginning of the lagging data vector using the alignsignals function in matlab. A local minimum in the two signals was used to ensure the same start time.

From the marker positions, the outer four markers were used to compute the deformation gradient tensor F throughout the biaxial test by interpolating displacement gradients relative to the tare-loaded reference state at the center of a bilinear Lagrange finite element [16]. The last three cycles of each biaxial loading protocol were averaged to compute the representative loading and unloading curves; only the loading curves were used for the constitutive analysis. From F, the components of the in-plane Green strain tensor E were calculated using $E=1/2(FTF−I)$. The shear components of E were negligible in all test specimens, so only the normal apex-outflow tract and circumferential component E11 and E22 were analyzed. The second PK stress tensor S was then determined using the following relation S = PF–T [10]. Assuming a pseudoelastic, hyperelastic material response, the tissue second PK membrane stress S as a result of the planar biaxial test [14] was derived from the membrane strain-energy (per unit area) function (Ψ) as
$S=∂Ψ(E)∂E$
(1)
where C = FTF is the Right Cauchy–Green strain tensor. Since the shear components were negligible, differentiating a strain-energy function with respect to the Lagrangian-Green strain yields the second PK stress in the principal axes. The strain-energy function chosen was a Fung-type constitutive equation with four model parameters θ = {c, a1, a2, a3}
$Ψ(E11,E22)=c(ea1E112+a2E222+a3E11E22−1)$
(2)
The model parameters θ for each specimen were obtained via the least-squares method through the loading cycles with an objective function defined as
$θ̂=arg minθ Σj=1N‖S(tj;θ)−Sj‖2$
(3)
where S(tj; θ) are strain-energy derived stress components in Eq. (2) and Sj are the measured stresses. Optimal parameter sets describing the RV myocardium and ECM in samples from control and PAH animals were determined using the Nelder–Mead simplex (direct search) method fminsearch function implemented in matlab. The goodness of fit for each specimen was determined from the coefficient of determination
$R2=1−SSresSStot$
(4)

where $SSres=Σj=1N(S(tj;θ)−Sj)2$ and $SStot=Σj=1N(Sj−Σ(1/N)(S(tj;θ)−Sj)2)2$ for j =1…N data points.

### Statistical Analysis.

Summary statistics were computed for mean pulmonary arterial pressures (mPAP), sample thicknesses, the different measures of ratios, and the model parameters of the myocardium and ECM of the normo- and hypertensive groups. To determine if statistical differences existed in the means among groups, multiple comparisons were performed using a two-tailed t-test assuming unequal variance. T-test analyses were carried out in the Data Analysis ToolPak of Excel (version Office 365, Microsoft Corporation, Redmond, WA). To compare stress–strain relations between control and PAH groups, two-factor analysis of variance (ANOVA) was performed with a least-squares model using JMP Statistical Software (Version 14.0.0, SAS Institute, Inc., Cary, NC). The linear statistical model had the following form:
$Sijk=S¯+αi+Ej+(αE)ij+ϵijk$

where $S¯$ is the overall mean stress, αi is the treatment effect (i = CTL, PAH), Ej is the strain level, (αE)ij is the interaction between the treatment and strain level, and ϵijk is an independent and identically distributed random variable error term, the null hypothesis being $∀(αE)ij=0$. If the interaction effects was not rejected, then the main effect of each factor was tested. For all statistical tests, significance level was set at 0.05. All values are presented as mean ± standard errors unless specified otherwise.

## Results

### Morphological Changes Due to Disease and Decellularization.

Mean pulmonary arterial pressure measurements confirmed PAH in the treated groups (Fig. 2(a)). RV myocardial thickness (Fig. 2(b)) was significantly greater in the PAH group as a result of increased pulmonary arterial pressures p 0.001. Mean ECM sample thickness also increased in the PAH group but this increase was not proportional to the myocardial thickening (p =0.051), consistent with a faster rate of myocyte hypertrophy than matrix accumulation during the remodeling period. In-plane shrinkage during decellularization quantified through the stretch tensor was ≈20% in both directions in all tissue samples (Fig. 2(c)). The mean ratio of decellularized:intact myocardial volumes, calculated from the in-plane area multiplied by the thickness, decreased from 0.08 in normotensive samples to 0.05 in the PAH group. Masson's trichrome-stained sections of RV myocardium showed evidence of collagen fiber accumulation in SuHx rats and confirmed the successful removal of myocytes from the decellularized matrix samples as seen in the representative micrographs shown in Fig. 3).

### Mechanical Data.

Mechanical test results were confirmed to be reproducible between successive biaxial tests both for the myocardial and ECM samples. The five biaxial ratios spanned a wide range of the Green-strain space for the intact and decellularized samples. And while the maximum stretch ratio used for the ECM samples was only 8%, the Green strain space of intact and decellularized samples closely over-lapped. Equibiaxial stress–strain relationships of the control and PAH samples showed that both the myocardium and ECM are anisotropic, with the circumferential direction being the stiffer in both preparations (Fig. 4).

### Constitutive Modeling—Parameter Estimation and Model Fitting.

Parameter estimation was robust. This was verified by modifying the initial set of parameters and obtaining the same local minimum. For all the parameter estimation routines, the goodness of fit was never below 0.9. The summary statistics of these optimal set of parameters are depicted in the bar graph (Fig. 5). The distribution of the parameters was tight across the groups. The stiffness-scaling coefficient c was significantly higher in the ECM samples than in the counterpart myocardium for the PAH group (p <0.05), but not in the control group (p =0.054). The exponents a1, a2, and a3 related to stiffness in the AOT direction, circumferential direction, and interaction term, respectively, were significantly higher for PAH myocardium versus control myocardium (p <0.05). The exponents fitted to ECM tests of PAH animals were also higher than those of control animals but without reaching statistical significance: a1(p =0.33), a2(p =0.26), and a3(p =0.10)). Using the parameters obtained with Eq. (3), the membrane strain-energy function was retrieved. The goodness of fit can be seen by the close approximation between the data (blue) and model prediction (black) in the membrane strain-energy over the surface and the stress–strain relations in Fig. 4.

### Right Ventricular Myocardial and Extracellular Matrix Biaxial Properties.

Using the fitted set of model parameters $θ̂$, principal stresses were derived for a common Green-strain space for equibiaxial strains. The mean stresses obtained from the derived stress–strain relations in the PAH myocardial samples were significantly greater both in the apex-outflow tract direction (p <0.0005 by two-factor ANOVA) and in the circumferential direction (p <0.0002 by two-factor ANOVA) (see Fig. 6). Mean ECM stresses derived for biaxial strains in decellularized samples from the PAH group (black) were significantly greater in the circumferential direction when compared with the hearts from the control (blue) group (p <0.005 by two-factor ANOVA), but not in the apex-outflow tract direction (p =0.09 by two-factor ANOVA). Under equibiaxial strain loading, circumferential stresses were also significantly greater than apex-outflow tract stresses (p <0.0001 by ANOVA) for the intact and decellularized, control and PAH groups.

Of the 13 control and 12 SuHx animals, we obtained mechanical measurements of RV intact tissue from 11 control animals and 10 SuHx animals, and 7 decellularized samples from control and 8 decellularized samples from SuHx animals. In the nine samples for which we had paired mechanical measurements in intact and decellularized tissues, the mean ratio of ECM to myocardial stress at an equibiaxial Green's strain of 0.08 was 0.85 ± 0.25 and was not significantly different between the circumferential and AOT directions nor between the PAH and control groups. Since the distribution of these ratios was not Gaussian, we also computed the median ratio, which was 0.37.

## Discussion

Recently, we used a model of RV mechanics based on measurements of global hemodynamics and morphology to predict that end-diastolic RV myocardial stiffness increases in a rat model of PAH [5]. Therefore, in this study, we used planar biaxial mechanical testing, first adapted for soft living tissues by Fung, to measure the anisotropic mechanical properties of RV myocardium and the changes in the well-characterized SuHx rat model of PAH. Five–six weeks after SuHx exposure, we observed significantly increased AOT and circumferential stresses in RV myocardial tissues subjected to equibiaxial strain compared with normotensive control samples. Since RV myocardial fibrosis has been observed in pulmonary hypertension [24], we also investigated whether the mechanical properties of the RV myocardial extracellular matrix were altered in this PAH model by retesting RV samples after they had been decellularized. Extracellular matrix samples from PAH rats were significantly stiffer in the circumferential but not AOT direction than decellularized control samples. However, the ratio of matrix to myocardial stress at matched strain was not changed significantly with PAH for either material axis. These findings are the first report of RV myocardial and matrix biaxial mechanical properties in an animal model of PAH and are consistent with the predictions of our recent analysis of global RV hemodynamics and shape in the monocrotaline-treated rat model of PAH [5].

Several previous studies have reported the results of biaxial mechanical testing of resting RV myocardium in normal normotensive rats [7,8,17,18]. In agreement with Witzenburg et al. [18], we also found RV control myocardium to be significantly stiffer in the circumferential direction than the AOT direction, both in the intact and decellularized states, though the ratio of circumferential to AOT stresses that we measured was much less than the 5:1 value reported by those investigators. In contrast, Hill et al. [8], Jang et al. [7], and Valdez-Jasso et al. [17] reported that normal RV myocardium was significantly stiffer in the AOT than circumferential direction, by ratios of less than 2:1. Hence, estimates of normal rat passive RV myocardial anisotropy vary, though our current findings in normotensive controls fall in between these previous reports. Previous studies of left ventricular wall slices have concluded that resting myocardium is stiffer in the myofiber than cross-fiber direction [19]. Given the importance of myofiber orientation to myocardial anisotropy, the position and orientation of the RV specimens relative to the anatomy are likely to be important determinants of these mechanical measurements. These findings suggest that more detailed investigations of RV fiber-to-crossfiber myocardial and matrix anisotropy are still required.

Although there have been no previous studies of changes in RV biaxial mechanics in PAH, myocardial mechanics have been measured in a rat model of RV hypertrophy. In the pulmonary artery-banded rat, Hill et al. [8] and Jang et al. [7] also observed a significant increase in biaxial myocardial stiffness. While we found a greater increase in circumferential than AOT stress during hypertrophic remodeling in the SuHx rat, AOT stiffness increased more than circumferential stiffness in the PA-banded rat [7,8]. Based on histology and a microstructural constitutive analysis [6], those authors also concluded that the anisotropic changes seen in the PA-banded rat were due to reorientation of myofibers and matrix during hypertrophy.

There are several possible reasons for the specific differences in RV myocardial mechanical alterations between the banded and PAH models. Whereas banding results in a sudden increase in RV afterload, RV systolic pressures take approximately three weeks to increase in the monocrotaline and SuHx rat models of PAH. In the rat, a sudden increase in aortic pressure in the transverse aortic constriction model of left-ventricular hypertrophy is associated with more pronounced chamber remodeling than the more gradual spontaneously hypertensive rat [20]. Although most RV hemodynamic measurements were not different between rats 5 and 6 weeks after SuHx as used here, 4 weeks after monocrotaline [5], and 3 weeks after PA banding [8], one exception was mean RV end-diastolic volume. It averaged 260–300 μL in the PAH models compared with 223 μL in the PA-banded rat. This could be a reflection of less RV dilation or more fibrosis in the banded animals. In fact, PA banding is often used as a rat model of profound RV, left-ventricular and septal fibrosis [21]. There are also important physiological and biological differences between arterial banding and hypertension. PA banding increases RV afterload, but it decreases pulmonary arterial pressure and flows. Indeed, PA banding is used clinically in congenital heart disease with pulmonary hypertension associated with elevated pulmonary blood flow [22]. The key role of the lungs in regulating angiotensin II levels is well recognized, since angiotensin converting enzyme that generates angiotensin II from angiotensin I is produced by the pulmonary endothelium. PAH leads to the activation of the renin-angiotensin-aldosterone system [23], which has long been known to promote myocardial hypertrophy [24] in humans and rodent models. Therefore, given the differences in the hemodynamic time-courses, physiology, and biology of PA banding versus PAH, it is not surprising that there are differences in myocardial remodeling between these models despite the similarities in right ventricular systolic hemodynamics.

Our histology showed fibrosis and collagen accumulation in RV myocardium and matrix samples from PAH animals. This should be confirmed with hydroxyproline assay on our decellularized samples in future studies. To obtain a better estimate of the matrix stress in vivo, future studies could attempt to more closely recapitulate the strains experienced in the intact myocardium. Our comparisons and constitutive models of the anisotropic mechanical responses of intact and decellularized tissues did not take into account the significant ≈20% shrinkage that occurs during decellularization. The resulting prestrain the matrix would therefore increase its contributions to tensile load bearing in the intact myocardium. In addition to the effects of prestretch, it would be informative to attempt to osmotically restore the original volume of the intact myocardium in the decellularized samples. In spite of these limitations and the unknown mechanical contributions of nonlinear matrix–myocyte interactions in the myocardium, the present results are consistent with the conclusion that the ECM is an important contributor to the resting stiffness of RV myocardium and that increased RV myocardial stiffness in PAH is at least partly explained by increased ECM stiffness. Possible mechanisms of such an increase in intrinsic ECM stiffness could include an increase in coiled perimysial collagen fiber diameter [25] or a decrease in their tortuosity [26]. Alternatively, alterations in the molecular composition or structure of the ECM such as an increase in the ratio of types I to III collagen [27], or increased enzymatic [28] or glycated [29] crosslinks have all been reported to increase myocardial matrix stiffness too. Since diastolic RV chamber stiffening limits RV end-diastolic volume [5], RV myocardial stiffening may be a protective response, at least initially, since elevated RV volume is associated with worse clinical outcomes in PAH [30,31].

We designed this study to investigate the contribution of the collagenous ECM to the biaxial mechanical properties of intact ventricular myocardium. Previous approaches have included the formulation of microstructural constitutive laws from histological measurements [25,32] and the use of experimental preparations in which the matrix has been enzymatically degraded [33] or genetically ablated [34]. Collagenase treatment in rat hearts decreased collagen content by 36% and increased mean circumferential (but not longitudinal) strain at matched left ventricular pressure by 35% at low pressure and 15% at high pressure [33]. There was also a change in ventricular shape and dimensions as a result of collagenase treatment in that study consistent with the endomysial matrix being pretensioned. In the osteogenesis imperfecta murine model that lacks normal type I collagen, RV papillary muscles were approximately half as stiff as those from wild-type controls. The findings from our current approach are consistent with these previous studies, though our results suggest a lower contribution of the collagen matrix to myocardial stiffness. The ratio of ECM to matrix stress in our experiments varied with load and between samples but was not inconsistent with these previous studies. For samples in which we had paired measurements of intact and decellularized tissue, we observed a median ratio of ECM to myocardial stresses of 37% at a strain of 0.08.

In this study, Fung's famous exponential planar strain energy function was able to fit the full range of biaxial test results with high fidelity both in control and PAH samples and in myocardial and matrix specimens. The variability of the fitted material parameters between animals was low enough that there were statistically significant differences between almost all parameters between myocardium and matrix and between PAH and control groups, with the exception of the comparison between the models fitted to decellularized PAH and control samples. However, how the properties of the intact myocardium can be decomposed into measured contributions of the ECM and the unknown contributions of the cells and their interactions with the ECM remains unclear. There is also a need for models of tissue growth and remodeling that can account both for the hypertrophy of the myocytes and the remodeling of the ECM that occurs during PAH. As it has been previously suggested by Fomovsky et al. [35], Bovendeerd [36], and most recently by Lee et al. [37], there is a need for a mathematical framework that can account for the changes in cell and matrix compartments found in cardiac remodeling, specifically, growth and remodeling models that can include the different rates of remodeling of the myocytes and collagen, and the rate of fibroblast production. While volumetric growth and remodeling has been most developed in cardiac tissue, constrained mixture theory [38] would allow us to also account for the differential rates of matrix remodeling.

## Limitations

One limitation of this study is the accuracy of the dimensional measurements of the decellularized tissue, which consists of matrix and fluid, making it difficult to relate to the collagen content of the intact myocardium. We attempted to minimize the variability due to this limitation by carefully measuring sample dimensions under standard conditions, but it would be informative to vary the tonicity and osmolarity of the solutions and to measure the protein dry weight of the samples in future studies. In addition, the full thickness of the RV samples was assumed to be homogeneous in the constitutive analysis, which did not account for transmural variations in myofiber and collagen fiber orientations across the RV free wall. More detailed experiments could allow for the inclusion of these dimensions. All the animals included in this study were male rats. Given that PAH is a disease that afflicts females almost twice more than men [39], future studies should include female animals. Finally, our strain-energy analysis did not account for the prestretch of the matrix and consequent precompression of the myocytes in the intact myocardium.

## Conclusions

This study was the first to measure the biaxial mechanical properties of RV myocardium and ECM in an animal model of PAH. The RV hypertrophy and fibrosis in PAH were associated with significantly increased myocardial stiffnesses in the circumferential and apex-outflow tract directions that were explained at least in part by comparably increased ECM stiffness. These mechanical alterations are large enough to have significant functional effects on RV filling, but the contributions of specific structural alterations in the myocardium to these changes remain to be determined.

## Acknowledgment

The authors would like to acknowledge Victoria Perizes, Michael Godoy, Jacqueline Olness, Amador Lagunas, and Dallin George who contributed to the data acquisition, data processing, and histological tissue scanning. This work builds on the foundation of biomechanics established by Professor Y-C Fung. The authors congratulate him on the occasion of his 100th birthday (Fig. 7).

## Funding Data

• American Heart Association Scientist Development Grant, Award No. 16SDG29670010.

## References

References
1.
Lai
,
Y. C.
,
Potoka
,
K. C.
,
Champion
,
H. C.
,
Mora
,
A. L.
, and
,
M. T.
,
2014
, “
Pulmonary Arterial Hypertension the Clinical Syndrome
,”
Circ. Res.
,
115
(
1
), pp.
115
130
.
2.
Rain
,
S.
,
Handoko
,
M. L.
,
Trip
,
P.
,
Gan
,
C. T.-J.
,
Westerhof
,
N.
,
Stienen
,
G. J.
,
Paulus
,
W. J.
,
Ottenheijm
,
C. A. C.
,
Marcus
,
J. T.
,
Dorfmüller
,
P.
,
Guignabert
,
C.
,
Humbert
,
M.
,
Macdonald
,
P.
,
Dos Remedios
,
C.
,
Postmus
,
P. E.
,
Saripalli
,
C.
,
Hidalgo
,
C. G.
,
Granzier
,
H. L.
,
Vonk-Noordegraaf
,
A.
,
van der Velden
,
J.
, and
de Man
,
F. S.
,.
2013
, “
Right Ventricular Diastolic Impairment in Patients With Pulmonary Arterial Hypertension
,”
Circulation
,
128
(
18
), pp.
2016
2025
.
3.
Rain
,
S.
,
Andersen
,
S.
,
Najafi
,
A.
,
Gammelgaard Schultz
,
J.
,
da Silva Gonçalves Bós
,
D.
,
Handoko
,
M. L.
,
Bogaard
,
H. J.
,
Vonk-Noordegraaf
,
A.
,
Andersen
,
A.
,
van der Velden
,
J.
,
Ottenheijm
,
C. A.
, and
de Man
,
F. S.
,
2016
, “
Right Ventricular Myocardial Stiffness in Experimental Pulmonary Arterial Hypertension: Relative Contribution of Fibrosis and Myofibril Stiffness
,”
Circ.: Heart Failure
,
9
(
7
), p.
e002636
.
4.
Trip
,
P.
,
Rain
,
S.
,
Handoko
,
M. L.
,
van der Bruggen
,
C.
,
Bogaard
,
H. J.
,
Marcus
,
J. T.
,
Boonstra
,
A.
,
Westerhof
,
N.
,
Vonk-Noordegraaf
,
A.
, and
de Man
,
F. S.
,
2015
, “
Clinical Relevance of Right Ventricular Diastolic Stiffness in Pulmonary Hypertension
,”
Eur. Respir. J.
,
45
(
6
), pp.
1603
1612
.
5.
Vélez-Rendón
,
D.
,
Zhang
,
X.
,
Gerringer
,
J. W.
, and
Valdez-Jasso
,
D.
,
2018
, “
Compensated Right Ventricular Function of the Onset of Pulmonary Hypertension in a Rat Model Depends on Chamber Remodeling and Contractile Augmentation
,”
Pulm. Circ.
,
8
(
4
), p.
2045894018800439
.
6.
,
R.
,
Hill
,
M.
,
Simon
,
M.
, and
Sacks
,
M.
,
2017
, “
Transmural Remodeling of Right Ventricular Myocardium in Response to Pulmonary Arterial Hypertension
,”
APL Bioeng.
,
1
(
1
), p.
016105
.
7.
Jang
,
S.
,
Vanderpool
,
R. R.
,
,
R.
,
Lapshin
,
E.
,
Bachman
,
T. N.
,
Sacks
,
M.
, and
Simon
,
M. A.
,
2017
, “
Biomechanical and Hemodynamic Measures of Right Ventricular Diastolic Function: Translating Tissue Biomechanics to Clinical Relevance
,”
J. Am. Heart Assoc.
,
6
(
9
), p.
e006084
.
8.
Hill
,
M. R.
,
Simon
,
M. A.
,
Valdez-Jasso
,
D.
,
Zhang
,
W.
,
Champion
,
H. C.
, and
Sacks
,
M. S.
,
2014
, “
Structural and Mechanical Adaptations of Right Ventricle Free Wall Myocardium to Pressure Overload
,”
Ann. Biomed. Eng.
,
42
(
12
), pp.
2451
2465
.
9.
Abe
,
K.
,
Toba
,
M.
,
Alzoubi
,
A.
,
Ito
,
M.
,
Fagan
,
K. A.
,
Cool
,
C. D.
,
Voelkel
,
N. F.
,
McMurtry
,
I. F.
, and
Oka
,
M.
,
2010
, “
Formation of Plexiform Lesions in Experimental Severe Pulmonary Arterial Hypertension
,”
Circulation
,
121
(
25
), pp.
2747
54
.
10.
Fung
,
Y. C.
,
1993
,
Biomechanics: Mechanical Properties of Living Tissues
,
2nd ed.
,
Springer
, Springer-Verlag, NY.
11.
Taraseviciene-Stewart
,
L.
,
Kasahara
,
K.
,
Alger
,
L.
,
Hirth
,
P.
,
Mc Mahon
,
G.
,
Waltenberger
,
J.
,
Voelkel
,
N. F.
, and
Tuder
,
R. M.
,
2001
, “
Inhibition of the VEGF Receptor 2 Combined With Chronic Hypoxia Causes Cell Death-Dependent Pulmonary Endothelial Cell Proliferation and Severe Pulmonary Hypertension
,”
FASEB J.
,
15
(
2
), pp.
427
437
.
12.
Gerringer
,
J. W.
,
Wagner
,
J. C.
,
Vélez-Rendón
,
D.
, and
Valdez-Jasso
,
D.
,
2018
, “
Lumped-Parameter Models of the Pulmonary Vasculature During the Progression of Pulmonary Arterial Hypertension
,”
Physiol. Rep.
,
6
(
3
), p.
e13586
.
13.
Xu
,
H.
,
Xu
,
B.
,
Yang
,
Q.
,
Li
,
X.
,
Ma
,
X.
,
Xia
,
Q.
,
Zhang
,
Y.
,
Zhang
,
C.
,
Wu
,
Y.
, and
Zhang
,
Y.
,
2014
, “
Comparison of Decellularization Protocols for Preparing a Decellularized Porcine Annulus Fibrosis Scaffold
,”
PLoS One
,
9
(
1
), p.
e86723
.
14.
Sacks
,
M. S.
,
2000
, “
Biaxial Mechanical Evaluation of Planar Biological Materials
,”
J. Elasticity
,
61
(
1/3
), pp.
199
246
.
15.
Hollenstein
,
M.
,
Ehret
,
A. E.
,
Itskov
,
M.
, and
Mazza
,
E.
,
2010
, “
A Novel Experimental Protocol Based on Pure Shear Testing of Dermatome-Cut Samples Applied to Porcine Skin
,”
Biomech. Model Mechanobiol.
,
10
(
5
), pp.
651
661
.
16.
Waldman
,
L. K.
, and
McCulloch
,
A. D.
,
1993
, “
Nonhomogeneous Ventricular Wall Strain: Analysis of Errors and Accuracy
,”
ASME J. Biomech. Eng.
,
115
(
4B
), pp.
497
502
.
17.
Valdez-Jasso
,
D.
,
Simon
,
M. A.
,
Champion
,
H. C.
, and
Sacks
,
M. S.
,
2012
, “
A Murine Experimental Model for the Mechanical Behavior of Viable Right-Ventricular Myocardium
,”
J. Physiol.
,
590
(
18
), pp.
4571
4584
.
18.
Witzenburg
,
C.
,
Raghupathy
,
R.
,
Kren
,
S. M.
,
Taylor
,
D. A.
, and
Barocas
,
V. H.
,
2012
, “
Mechanical Changes in the Rat Right Ventricle With Decellularization
,”
J. Biomech.
,
45
(
5
), pp.
842
849
.
19.
McCulloch
,
A. D.
,
2000
, “
Cardiac Biomechanics
,”
The Biomedical Engineering Handbook
,
J. D.
Bronzino
, ed.,
2nd ed.
, Vol.
I
,
CRC Press
,
Boca Raton, FL
, pp.
28
46
.
20.
Zhou
,
N.
,
Ma
,
B.
,
Stoll
,
S.
,
Hays
,
T. T.
, and
Qiu
,
H.
,
2017
, “
The Valosin-Containing Protein Is a Novel Repressor of Cardiomyocyte Hypertrophy Induced by Pressure Overload
,”
Aging Cell
,
16
(
5
), pp.
1168
1179
.
21.
Andersen
,
S.
,
Birkmose Axelsen
,
J.
,
Ringgaard
,
S.
,
Randel Nyengaard
,
J.
,
Holm Nielsen
,
S.
,
Genovese
,
F.
,
Asser Karsdal
,
M.
,
,
J.
,
Brandt Sørensen
,
C.
,
de Man
,
F. S.
,
Jan Bogaard
,
H.
,
Erik Nielsen-Kudsk
,
J.
, and
Andersen
,
A.
,
2019
, “
Pressure Overload Induced Right Ventricular Remodeling Is Not Attenuated by the Anti-Fibrotic Agent Pirfenidone
,”
Pulm. Circ.
,
9
(
2
), p.
204589401984865
.
22.
Sharma
,
R.
,
2012
, “
Pulmonary Artery Banding: Rationale and Possible Indications in the Current Era
,”
Ann. Pediatr. Cardiol.
,
5
(
1
), pp.
40
43
.https://www.ncbi.nlm.nih.gov/pubmed/22529600
23.
Maron
,
B. A.
, and
Leopold
,
J. A.
,
2015
, “
Emerging Concepts in the Molecular Basis of Pulmonary Arterial Hypertension—Part II: Neurohormonal Signaling Contributes to the Pulmonary Vascular and Right Ventricular Pathophenotype of Pulmonary Arterial Hypertension
,”
Circulation
,
131
(
23
), pp.
2079
2091
.
24.
Yamazaki
,
T.
,
Komuro
,
I.
, and
Yazaki
,
Y.
,
1999
, “
Role of the Renin-Angiotensin System in Cardiac Hypertrophy
,”
Am. J. Cardiol.
,
83
(
12A
), pp.
53H
57H
.
25.
MacKenna
,
D. A.
,
Vaplon
,
S. M.
, and
McCulloch
,
A. D.
,
1997
, “
Microstructural Model of Perimysial Collagen Fibers for Resting Myocardial Mechanics During Ventricular Filling
,”
Am. J. Physiol.
,
273
(
3 Pt 2
), pp.
H1576
H1586
.
26.
MacKenna
,
D. A.
,
Omens
,
J. H.
, and
Covell
,
J. W.
,
1996
, “
Left Ventricular Perimysial Collagen Fibers Uncoil Rather Than Stretch During Diastolic Filling
,”
Basic Res. Cardiol.
,
91
(
2
), pp.
111
122
.
27.
Contard
,
F.
,
Koteliansky
,
V.
,
Marotte
,
F.
,
Dubus
,
I.
,
Rappaport
,
L.
, and
Samuel
,
J. L.
,
1991
, “
Specific Alterations in the Distribution of Extracellular Matrix Components Within Rat Myocardium During the Development of Pressure Overload
,”
Lab. Invest.
,
64
(
1
), pp.
65
75
.https://www.ncbi.nlm.nih.gov/pubmed/1824954
28.
Norton
,
G.
,
Tsotetsi
,
J.
,
Trifunovic
,
B.
,
Hartford
,
C.
,
Candy
,
G.
, and
Woodiwiss
,
A.
,
1997
, “
Myocardial Stiffness Is Attributed to Alterations in Cross-Linked Collagen Rather Than Total Collagen or Phenotypes in Spontaneously Hypertensive Rats
,”
Circulation.
,
96
(
6
), pp.
1991
1998
.
29.
Herrmann
,
K. L.
,
McCulloch
,
A. D.
, and
Omens
,
J. H.
,
2003
, “
,”
Am. J. Physiol. Heart Circ. Physiol.
,
284
(
4
), pp.
H1277
HI284
.
30.
Pinksy
,
M. R.
,
2016
, “
The Right Ventricle: Interaction With the Pulmonary Circulation
,”
Crit. Care
,
20
, p.
266
.
31.
Altmayer
,
S. P. L.
,
Han
,
Q. J.
,
,
K.
,
Patel
,
A. R.
,
Forfia
,
P. R.
, and
Han
,
Y.
,
2018
, “
Using All-Cause Mortality to Define Severe RV Dilation With RV/LV Volume Ratio
,”
Sci. Rep.
,
8
(
1
), p.
7200
.
32.
,
R.
,
Hill
,
M. R.
,
Simon
,
M. A.
,
Zhang
,
W.
, and
Sacks
,
M. S.
,
2017
, “
A Novel Constitutive Model for Passive Right Ventricular Myocardium: Evidence for Myofiber-Collagen Fiber Mechanical Coupling
,”
Biomech. Model Mechanobiol.
,
16
(
2
), pp.
561
581
.
33.
MacKenna
,
D. A.
,
Omens
,
J. H.
,
McCulloch
,
A. D.
, and
Covell
,
J. W.
,
1994
, “
Contribution of the Endomysial Collagen Matrix to Passive Left Ventricular Mechanics in the Isolated Rat Heart
,”
Am. J. Physiol.
,
266
, pp.
H1007
H1018
.
34.
Weis
,
S. M.
,
Emery
,
J. L.
,
Becker
,
D.
,
McBride
,
D. J.
,
Omens
,
J. H.
, and
McCulloch
,
A. D.
,
2000
, “
Myocardial Mechanics and Collagen Structure in the Osteogenesis Imperfecta Murine
,”
Circ. Res.
,
87
(
8
), pp.
663
669
.
35.
Fomovsky
,
G. M.
,
Thomopoulos
,
S. T.
, and
Holmes
,
J. W.
,
2010
, “
Contribution of Extracellular Matrix to the Mechanical Properties of the Heart
,”
J. Mol. Cell Cardiol.
,
48
(
3
), pp.
490
496
.
36.
Bovendeerd
,
P. H. M.
,
2012
, “
Modeling of Cardiac Growth and Remodeling of Myofiber Orientation
,”
J. Biomech.
,
45
(
5
), pp.
872
881
.
37.
Lee
,
L. C.
,
Kassab
,
G. S.
, and
Guccione
,
J. M.
,
2016
, “
Mathematical Modeling of Cardiac Growth and Remodeling
,”
WIREs Syst. Biol. Med.
,
8
(
3
), pp.
211
226
.
38.
Humphrey
,
J. D.
, and
Rajagopal
,
K. R.
,
2002
, “
A Constrained Mixture Model for Growth and Remodeling of Soft Tissues
,”
Math. Models Methods Appl. Sci.
,
12
(
3
), pp.
407
430
.
39.
Foderaro
,
A.
, and
Ventetuolo
,
C. E.
,
2016
, “
Pulmonary Arterial Hypertension and the Sex Hormone Paradox
,”
Curr. Hypertens. Rep.
,
18
(
11
), p.
84
.