Paired Pressure–Volume Loop Analysis and Biaxial Mechanical Testing Characterize Differences in Left Ventricular Tissue Stiffness of Volume Overload and Angiotensin-Induced Pressure Overload Hearts

Abstract

Pressure overload (PO) and volume overload (VO) of the heart result in distinctive changes to geometry, due to compensatory structural remodeling. This remodeling potentially leads to changes in tissue mechanical properties. Understanding such changes is important, as tissue modulus has an impact on cardiac performance, disease progression, and influences on cell phenotype. Pressure–volume (PV) loop analysis, a clinically relevant method for measuring left ventricular (LV) chamber stiffness, was performed in vivo on control rat hearts and rats subjected to either chronic PO through Angiotensin-II infusion (4-weeks) or VO (8-weeks). Immediately following PV loops, biaxial testing was performed on LV free wall tissue to directly measure tissue mechanical properties. The β coefficient, an index of chamber stiffness calculated from the PV loop analysis, increased 98% in PO (n = 4) and decreased 38% in VO (n = 5) compared to control (n = 6). Material constants of LV walls obtained from ex vivo biaxial testing (n = 9–10) were not changed in Angiotensin-II induced PO and decreased by about half in VO compared to control (47% in the circumferential and 57% the longitudinal direction). PV loop analysis showed the expected increase in chamber stiffness of PO and expected decrease in chamber stiffness of VO. Biaxial testing showed a decreased modulus of the myocardium of the VO model, but no changes in the PO model, this suggests the increased chamber stiffness in PO, as shown in the PV loop analysis, may be secondary to changes in tissue mass and/or geometry but not an increase in passive tissue mechanical properties.

Introduction

Heart failure can develop as a result of hemodynamic stresses due to volume overload (e.g., aortic or mitral valve regurgitation) and/or pressure overload (e.g., hypertension or aortic stenosis). These stresses lead to fundamentally different patterns of left ventricular (LV) remodeling. Chronic pressure overload (PO) is associated with increased LV extracellular matrix (ECM) deposition and concentric myocyte hypertrophy, resulting in a dramatic increase in the LV wall thickness-to-chamber diameter ratio [1]. In contrast, volume overload (VO) results in a progressive dilatation, characterized by a disproportionate decrease in the LV wall thickness-to-diameter ratio, increased myocardial wall stress, eccentric myocyte hypertrophy, and net ECM loss [2–4].

While PO and VO have well-characterized effects on the structural and geometric properties of the heart, their impact on the mechanical properties of the heart are relatively less understood. Cardiac mechanics is important in design considerations for tissue-engineered strategies for treatments of heart disease, understanding cardiac performance in different disease states, and understanding how mechanical properties may affect disease progression. There is growing evidence that cardiac cell phenotype, including gene expression [5], myocyte sarcomeric structure [6], contractility and force generation [7], fibroblast activation into myofibroblasts [8], and ECM regulation [9] is controlled by substrate modulus, or the intrinsic stiffness of the material to which the cells attach.

Despite the importance of biomechanics to heart failure pathophysiology, there is currently no consensus on the relationship between hemodynamic load and myocardial stiffness. For example, there are variable reports on whether or not passive LV tissue stiffness increases, decreases or stays the same in VO [2,10,11], and increases or stays the same in PO [12,13]. This lack of consensus may be due to the use of different methods to assess stiffness, use of different models to create hemodynamic overload, or variations in time points investigated during heart failure progression. Overall, estimates of mechanical properties in the myocardium tend to use one of two approaches: assessment of chamber stiffness using in vivo pressure–volume (PV) data or ex vivo uniaxial tensile testing.

Catheter-based PV loop analysis has been widely used since the 1970s. Several factors are known to affect stiffness values obtained by PV loops, including tissue geometry (e.g., thickening of the heart wall or changes in chamber dimensions), catheter calibration, and blood viscosity. Despite these limitations, it is considered by many a gold standard for myocardial stiffness assessment in animal models of heart failure and in the clinical setting and continues to be used even in recent literature [10,14].

The stiffness of a tissue depends on both its mechanical properties (e.g., modulus) and geometric properties (e.g., thickness). There are a variety of methods to directly measure the geometry-independent myocardial mechanical properties. One common method is mechanical testing, such as uniaxial tensile testing. In the heart, this is commonly performed on isolated cardiomyocytes [15,16] or isolated papillary muscles [1,17]. Additionally, although more complicated to perform and less frequently used, biaxial testing has been used to assess mechanical properties of the LV [18–20] and right ventricle (RV) tissue [21,22]. Biaxial testing can capture the anisotropic properties of the myocardium as well as recreate the multidirectional loads it experiences during the cardiac cycle to characterize anisotropy, or variation due to tissue orientation.

In this study, we performed paired in vivo PV loop analysis with ex vivo biaxial tensile testing in rat models of PO and VO to: (1) better characterize the in-plane mechanical properties of the PO and VO myocardium and (2) examine the ability of PV loops to estimate tissue mechanical properties by comparing results with direct measures of mechanical properties via biaxial mechanical testing. This is the first time, to our knowledge, that there has been a direct comparison of PO and VO using biaxial tensile testing or a direct comparison of PV loops to biaxial tensile testing of any heart tissue in a single study.

Materials and Methods

Animals.

Sprague–Dawley male rats (∼200 g, Envigo, Indianapolis, IN) were housed in a temperature and humidity-controlled environment with a 12 h light/dark cycle. Animals were provided free access to water and standard chow. All studies conformed to NIH Guide for the Care and Use of Laboratory Animals. The protocol was approved by the IACUC of the Research Institute at Nationwide Children's Hospital. There were three groups of animals: PO, VO, and control. Control rats (n = 14) with no other treatments were age- and weight-matched to their PO and VO counterparts. VO of the LV was induced by aortocaval fistula (ACF, n = 15) [23] for 8 weeks, and PO was induced by osmotic mini-pump infusion of Angiotensin II (Ang II, n = 14) [24] for 4 weeks as described in more detail in the Supplemental Materials on the ASME Digital Collection. These time points were selected to achieve a similar stage of compensation and heart failure in both models. Ang-II infusion was chosen over transverse aortic constriction since it is technically easier and since both PO models result in similar remodeling of the heart from a structural and functional perspective. It should be noted that Angiotensin-II is not isolated PO but also results in increases in circulating and intracardiac levels of Ang-II in addition to increased blood pressure (BP) [25,26]. All animals were sacrificed under 2–4% isoflurane (Baxter, Deerfield, IL) by exsanguination followed by cardiac dissection.

Pressure–Volume Loops

Pressure–Volume Loop Data Acquisition.

Invasive LV PV loop measurements were performed on a subset of animals (n = 4 or 5 per group), as previously published [23] and described in more detail in the Supplemental Materials.

Pressure–Volume Loop Data Analysis.

The β coefficient was determined by fitting the left ventricle pressure (P) and volume values (V) at the end of diastole with the equation

$$P=A+c{e}^{\beta V}$$ (1)

where β is an index of chamber stiffness; A and c are constants. In an effort to normalize to chamber size, a dimensionless index of chamber stiffness, β_w, was calculated by multiplying β by the wall volume, estimated by LV weight divided by tissue density, as described by Burkhoff et al. [27]. Both β and β_w are common methods to assess chamber stiffness. Other models, such as Refs. [28] and [29], also utilize PV data to assess chamber stiffness. While these models are useful in assessing the chamber stiffness of the LV of the heart, as a structural property, they do not assess the heart's intrinsic mechanical properties. Mirsky et al. showed that incremental modulus (E_inc) can be estimated from the measured pressure, cavity volume, wall volume (V_w), and calculated outer and midwall (R_o and R_m, respectively, Eq. (2)) or endocardial (Eq. (3)) [30] radii

$$E_{\mathrm{inc}M}=\frac{3}{4}P\frac{V}{V_w}{\left(\frac{R_o}{R_m}\right)}^3$$ (2)

$$E_{\mathrm{inc}E}=\frac{9}{4}V(1+\frac{V}{V_w})\frac{dP}{dV}$$ (3)

These estimated incremental moduli are based on a model assuming a homogeneous isotropic material with a simplified spherical geometry with a constant wall thickness.

Tissue Preparation for Mechanical Testing.

Immediately after PV loop assessment and subsequent sacrifice, hearts were rinsed, cannulated, and subjected to retrograde perfusion in a Langendorff apparatus using 100 mL cold perfusion buffer solution for ∼10 min at constant flow (∼10 mL/min). The perfusion buffer, described in more detail in the Supplemental Materials on the ASME Digital Collection, is similar to Tyrode's solution. This type of buffer has been utilized in other studies to relax muscle tissue while leaving titin and ECM-cell attachments intact [2,31]. H&E staining of perfused and nonperfused hearts is presented in supplemental Fig. 1, available in the Supplemental Materials.

Biaxial Mechanical Testing.

The biaxial testing protocol was adapted from a previously published protocol using the same testing system (ElectroForce Planar Biaxial TestBench, Bose Corp., Eden Prairie, MN) [32]. Following perfusion, the LV free wall was cut into approximately a 10 mm × 10 mm square with the direction of the papillary muscles (i.e., the direction of base to apex) corresponding to the longitudinal-axis direction. Here, a cardiac coordinate system (longitudinal/circumferential) was used, opposed to microstructural coordinates (fiber/cross-fiber) since full-thickness samples do not have a single fiber orientation. The tissue was mounted on the device with sets of hooks attached to a pulley system, similar to the previous publication [32] and as described in more detail in the Supplemental Materials.

After the tissue was loaded, a high-frequency ultrasound imaging system (Vevo660, VisualSonics, Toronto, ON, Canada) was used to take longitudinal- and circumferential-direction tissue cross-sectional images for thickness measurements, as previously published [32]. The tissue was preloaded at approximately 0.5 gf and preconditioned with nine loading cycles using an equibiaxial force-controlled tensile ramp in the range of 0.5 gf to 50 gf at 0.5 gf/s controlled by wintest 7 software (Bose Corp.). Strains were tracked with a digital video extensometer built into the Bose biaxial testing system. The tenth loading cycle measurement was used for analysis.

Constitutive Modeling.

To ensure our results were not based on the constitutive model chosen, the stress–strain data from each sample was fit to two different models. The first, presented in the main text below, is a reduced Fung type strain energy function. A second alternative constitutive model is presented in the supplement and is a model that reduces parameter covariance compared to other models [22].

The reduced Fung-type strain energy function (Eq. (4)) [33] similar to a previously published [32] model is presented here

$$W=\frac{C}{2}(e^{C_1{E}_{11}^2+C_2{E}_{22}^2+{2C}_3{E}_{11}{E}_{22}}-1)$$ (4)

$$S_{ij}=\frac{\partial W}{\partial E_{ij}}$$ (5)

W is the strain energy, or the amount of energy stored in the tissue undergoing the deformation. E₁₁ and E₂₂ are Green strains in two-orthogonal loading directions approximating the longitudinal axis direction and circumferential axis direction, respectively. S₁₁ and S₂₂ are the second Piola–Kirchoff stresses in either direction, and C and A₁, A₂, A₃ are material constants.

The experimental data were fit with these equations simultaneously (Eqs. (4) and (5)) to generate estimates of the material constants with a constrained nonlinear minimization algorithm based on the subspace thrust region method in matlab (MathWorks, Natick, MA). Positive constant constraints were added to avoid nonconvex strain energy function as suggested by others [33,34]. Convexity was checked, as described in the Supplemental Materials on the ASME Digital Collection. We have attempted to address the identifiability of the parameters by comparing the results with the more commonly used Levenberg–Marquardt algorithm. We found that both search/minimization algorithms yielded similar results (within 0.02% of each other, or less), suggesting good identifiability of the parameters. The goodness of fit was also confirmed (R² = 0.97 ± 0.05). Initial guesses for each parameter were varied simultaneously over several orders of magnitude to verify the independence from the initial values.

Lagrangian stresses (T_ij) were calculated from the cross-sectional dimensions of the sample, measured in the reference state with digital calipers for width and ultrasound measurements for tissue thickness and the force output from the load cells. S_ij were computed from the measured T_ij using the deformation gradient calculated from the Green strains, as previously published [32,35].

Histology.

From each experimental group, five animals were anesthetized and perfusion fixed with 4% paraformaldehyde with 60 mM KCl. As detailed in the Supplemental Materials, histological sections were prepared, stained with Masson's Trichrome or hematoxylin and eosin stain, imaged, and used to quantify cardiomyocyte area and percent collagen coverage.

Statistical Analysis.

Results are reported as mean  ±  standard deviation (SD) unless otherwise noted. Error bars in figures are standard error of the mean (SEM). Statistical comparisons across groups were analyzed by one-way analysis of variance (ANOVA). Differences between groups and control were determined with Dunnett's test for multiple comparisons. Two-way ANOVA with repeated measures was used to compare differences between longitudinal and circumferential stress–strain data, and Tukey's post hoc test was used to assess differences in the stress–strain data between groups. The statistical significance level was set at 0.05 in all tests.

Results

Verification and Characterization of Hemodynamic Overload Models.

To assess both PO and VO, we measured cardiac structure, function, and BP as shown in Table 1. As expected, we observed eccentric remodeling in the VO hearts, with a 42% increase in LV-end-diastolic diameter (LVEDD) (p < 0.001). Posterior wall thickness (PWT) was unchanged, yielding a 29% increased LVEDD/PWT ratio (p < 0.001), indicative of eccentric remodeling in VO and similar to previous reports [36,37]. In PO, we expected to observe concentric hypertrophy. PO animals had a relatively unchanged LVEDD (4% decrease, p = 0.25), but a significantly thicker PWT (18% increase, p = 0.0048), resulting in a decreased LVEDD/PWT ratio (20% decrease, p = 0.017), which is a characteristic of concentric hypertrophy.

Table 1.

Left ventricular remodeling and animal model parameters taken from echocardiographic measurements unless otherwise noted

	Control	Volume overload	Pressure overload
LV end-diastolic diameter (mm)	7.5 ± 0.3	10.6 ± 0.5a	7.1 ± 0.2
Posterior wall thickness (mm)	1.7 ± 0.09	1.9 ± 0.2	2.0 ± 0.2a
LVEDD/PWT	4.4 ± 0.3	5.6 ± 0.5a	3.5 ± 0.4a
LV weight (g)	1.4 ± 0.1	2.4 ± 0.3a	1.4 ± 0.2
Body weight (g)	391 ± 15	423 ± 40a	359 ± 27
LV: body ratio (g/kg)	3.6 ± 0.2	5.8 ± 0.8a	4.1 ± 0.4a
End-diastolic volume (μL)	259 ± 71	308 ± 97	252 ± 70
Systolic BP (mm Hg)b	121 ± 6	114 ± 15	189 ± 16a
Diastolic BP (mm Hg)b	87 ± 6	71 ± 5a	132 ± 9a
End-systolic pressure (mm Hg)b	128 ± 17	110 ± 14a	134 ± 3
End-diastolic pressure (mm Hg)b	9 ± 3	12 ± 4	14 ± 3
Total sample size (n)	14	15	14
Sample size for PV catheter measurements (n)b	4	5	4

^ap < 0.05 when compared to control.

^bMeasurements from the subset of rats with PV loop catheterization.

Values are mean  ±  SD.

The LV weight and LV weight to body ratio are also indicators of cardiac hypertrophy. As expected, VO increased the LV weight to body ratio increased 62% (p < 0.001 compared to control). VO animals showed an 8% increase in body weight compared to control animals (p = 0.027), which was likely due to increased water retention that was visible in some animals after dissection. PO animals exhibited a 14% increase in LV to body weight ratio (p = 0.0027, compared to control), consistent with hypertrophic cardiac remodeling.

Hemodynamic overload was also confirmed in both models. VO was supported by the significant 42% increase in LVEDD (p < 0.001) and the 19% increase in end diastolic volume, although it did not reach statistical significance (p = 0.12, compared to control). Increased blood pressure due to the pressor dosage of Ang II was confirmed by a 45% and 41% increase in systolic (p < 0.001) and diastolic (p < 0.001) BP, respectively. Additionally, there was a ∼55% increase in end-diastolic pressure (EDP), which did not reach statistical significance (p = 0.053). These responses in heart structure and hemodynamics in response to Ang II infusion are similar to previous reports [24,38].

Increased Myocyte Thickness in Volume Overload and Pressure Overload and Increased Collagen Content in Pressure Overload.

Macroscopic remodeling of the LV in PO and VO was visually evident in H&E-stained tissue sections (Fig. 1, top row). Myocyte cross-sectional area increased 20% in VO (p = 0.024) and 15% in PO (p = 0.037, Fig. 1, second row) with a similar trend seen in myocyte diameter with a 19% increase in VO and PO compared to control (p = 0.01, Fig. 1, third row). Quantification of interstitial fibrosis via Masson's Trichrome (Fig. 1, fourth row) staining revealed a 53% increase in interstitial collagen in PO hearts compared to control (p = 0.041), while there was no difference between VO and control (p = 0.43).

Fig. 1.

Top row: low magnification images showing concentric remodeling with thicker ventricle walls in PO and increased chamber size with decreased wall thickness-to-chamber diameter ratio in VO compared to control. Second row: Hematoxylin and eosin staining for measurement of myocyte cross-sectional area. Both VO and PO hearts show increased cross-sectional area compared to control. Third row: Hematoxylin and eosin staining for measurement of myocyte widths. Bottom row: Masson's trichrome staining for quantification of interstitial collagen content. PO has increased percent collagen coverage compared to control. N = 5 for each group. ANOVA followed by post hoc Dunnett's test was performed. Error bars are SEM, * indicates p < 0.05.

Experimental Observations of Tissue Mechanics

Pressure–Volume Loops Suggest Increased Chamber Stiffness in Pressure Overload and Decreased Chamber Stiffness in Volume Overload.

The average end-diastolic pressure–volume relationship (EDPVR) of VO was shifted to the right (suggesting decreased chamber stiffness, p < 0.001) relative to control (Fig. 2). Conversely, the EDPVR of PO was shifted to the left (suggesting increased chamber stiffness, p = 0.001) relative to control (Fig. 2).

Fig. 2.

Average fits of LV-EDPVR curves for each group (n = 4 for control and PO, n = 5 for VO). The shift up and to the left demonstrates an increase in PO chamber stiffness. The shift down and to the right shows a decrease in chamber stiffness in VO chambers. Error bars are SEM.

Biaxial Testing Indicates Decreased Left Ventricular Myocardium Modulus in Volume Overload but No Change in Pressure Overload Compared to Control.

The average stress–strain relationship in the control (n = 9), PO (n = 9), and VO (n = 10) groups is shown in Fig. 3. A characteristic J-shaped nonlinear stress–strain relationship was observed in all groups (Fig. 3). In general, a more horizontal curve corresponds to a material that requires less stress to deform it (i.e., a lower modulus or decreased stiffness). For all groups, the hearts had a greater stiffness in the circumferential direction than the longitudinal direction. For example, the circumferential and longitudinal strains at the same stress level were significantly different from each other in control, PO, and VO groups (p < 0.001). Compared with the control group, circumferential axis strains were 83–96% larger in the VO group at the same stress levels (at 3 kPa and above), as (p = 0.020) (Fig. 3). The stress–strain responses were not significantly different between the control and PO groups in either longitudinal or circumferential direction. Shear strain was small in all groups (∼1% or less maximum shear strain throughout the tests), so models without shear are utilized (Eqs. (4) and (5)).

Fig. 3.

(Left) Average stress–strain curves from equibiaxial testing in the longitudinal and circumferential direction. N = 9 for PO and control, n = 10 for VO. ANOVA followed by Dunnett's test was performed, error bars are SEM, and * indicates p < 0.05 compared to control. (Right) Circumferential versus longitudinal stress–strain curves for each group.

Calculated Parameters Related to Mechanical Properties

Pressure–Volume Loops Suggest Increased Chamber Stiffness in Pressure Overload and Decreased Chamber Stiffness in Volume Overload.

Relative to control hearts, the β-coefficient, from Eq. (1) (R² = 0.90 ± 0.06), was increased 98% in PO (p = 0.0058) and decreased 38% for VO (p = 0.014) (Fig. 4(a)). Moreover, β_w, the index of chamber stiffness normalized for chamber geometry, for PO animals was approximately twofold larger than control (p = 0.011), but was unchanged in VO (p = 0.69) (Fig. 4(b)). The calculated incremental modulus from the midwall stresses (E_{inc M}) did not show any significant differences (Fig. 4(c)), and the incremental modulus using calculated endocardial stresses and strains (E_{inc E}) showed a 75% decrease in VO (p = 0.089) and no significant change in PO (p = 0.27) compared to control (Fig. 4(d)).

Fig. 4.

(a) β index of chamber stiffness from EDPVR curves. (b) β normalized with wall volume. (c) Calculated incremental modulus using modeled strains from the midwall and (d) modeled strains from the endocardium. N = 4 for PO and VO, n = 5 for control. ANOVA followed by Dunnett's test was performed. Error bars are SEM, *p < 0.05 compared to control.

Biaxial Testing Showed Anisotropy in All Conditions and Decreased Myocardium Modulus in Volume Overload.

The material constants (Table 2) derived from biaxial mechanical testing data with model fitting quantitatively confirmed the trends seen in the average stress–strain curves in Fig. 3 including the mechanical anisotropy in all groups and the differences of mechanical properties between groups. For example, the material constant in the circumferential direction (C*C₁, 246 ± 151 kPa) was greater than that for the longitudinal direction (C*C₂, 140 ± 80 kPa) for all groups (p = 0.002 for all groups). This corresponds to the observation that the stress–strain curves for the circumferential direction was to the left of the corresponding curves in the longitudinal direction (Fig. 3), and that the strain was greater in the longitudinal direction compared to the circumferential (Table 2); both observations indicate that the LV myocardium was stiffer in the circumferential direction (Table 2). Specifically, C*C₁ was 112 ± 45%, 85 ± 30%, and 90 ± 29% greater than C*C₂ in the control, VO, and PO groups, respectively. This result was consistent with another report of an ∼87% greater stiffness in the circumferential axis compared to the longitudinal axis in full thickness rat LV tissue as measured by uniaxial tensile testing [39]. Differences in strain between the circumferential and longitudinal axes, at a constant stress (10 kPa), were assessed to evaluate whether the degree of anisotropy was different in PO and VO groups as compared to the control group. The results showed that the degree of anisotropy was not different in either PO or VO group as compared to control (p = 0.11, VO versus control; p = 0.15, PO versus control). The material constants were smaller in VO as compared to control, ∼47% smaller in the circumferential (C*C₁, p = 0.03) and 57% smaller in the longitudinal direction (C*C₂, p = 0.0054) (Fig. 5). The material constants in PO were not significantly different from control in either direction (p = 0.3 in longitudinal axis, C*C₁, and p = 0.11 in circumferential axis, C*C₂) (Fig. 5). Shear was not included in this model due to its small magnitude, as estimated from model available in the Supplemental Materials on the ASME Digital Collection, relative to the normal stresses (<2%), similar to other reports [18,20].

Table 2.

Constitutive model parameters from biaxial testing stress–strain data

	ELL at 10 kPa	ECC at 10 kPa	C (kPa)	C 1	C 2	C 3	C*C1 > C*C2
Control	0.034 ± 0.015	0.021 ± 0.01	0.77 ± 0.39	273 ± 170	532 ± 315	22 ± 15	p = 0.03
Volume Overload	0.048 ± 0.015	0.037 ± 0.02a	0.62 ± 0.31	184 ± 101	329 ± 241	44 ± 16	p = 0.04
Pressure Overload	0.040 ± 0.009	0.026 ± 0.009	0.81 ± 0.42	195 ± 91	348 ± 172	22 ± 15	p = 0.02
ANOVA	p = 0.1	p = 0.02	p = 0.5	p = 0.3	p = 0.1	p = 0.5

^aindicates p < 0.05 compared to control.

Values are mean ± SD. p-values for paired comparisons of longitudinal (C*C₁) and circumferential (C*C₂) within groups are presented in the last column. p-values between groups are presented in the last row.

Fig. 5.

Parameters related to the mechanical properties of the tissue in the longitudinal and circumferential direction. N = 9 for PO and control, n = 10 for VO. ANOVA followed by Dunnett's test was performed, error bars are SEM, and * indicates p < 0.05 compared to control.

Stiffness at Small and Large Strains.

Since stiffness in nonlinear stress–strain curves depends on the level of strain applied, we present the secant modulus at small (0.5%) and large strains (3%). The secant modulus was calculated by stress divided by strain. Comparing secant modulus we see a trend consistent with the results from the constitutive equation (Fig. 6). Control tissue was significantly stiffer than VO in both directions and at both strain values. PO was not significantly different from control.

Fig. 6.

Secant moduli calculated at small (0.5%) and large (3%) strains in the circumferential and longitudinal axes directions. *indicates p < 0.05 compared to control.

Discussion

The limitations of using in vivo PV loops and ex vivo mechanical testing of excised cardiac tissues to assess the mechanical properties of the heart are widely recognized and summarized below. Knowledge of these limitations motivated us to use both of these commonly used approaches in our study together instead of relying solely on one or the other. We suggest that having these complimentary data from the same animals gives a better picture of the changes in the mechanical properties induced by pressure overload and volume overload than would be afforded by either single technique. Of course, using both approaches entails additional work, and perhaps more significantly, the technical expertise and the specialized equipment to make the measurements. This may be why we were unable to find other examples from the literature that paired measurements of mechanical properties of hearts using both in vivo PV loop testing and ex vivo biaxial testing in the same animals.

Limitations of Experimental Methods.

Using PV loops to accurately evaluate passive tissue mechanical properties can be difficult due to complex geometries, heterogeneous anisotropic material, and varying pressures and stresses between disease states. Several sophisticated methods exist for estimating tissue mechanical properties from PV data, including the use of finite element models using patient-specific CT data [40] and magnetic resonance elastography [41]. Here, we use a simple analytic model to estimate material properties using catheter-based PV data, typically used by clinicians and physiologists. The importance of considering the geometry of the heart and range of pressures during testing has been previously highlighted [27]. For these reasons, Mirsky derived equations to estimate myocardial modulus (reported here as E_{inc M} incremental modulus calculated from midwall stresses and E_{inc E} incremental modulus calculated from endocardial stresses) are derived based on PV loop data [27,30]. Care must be used, however, when interpreting these calculated moduli since the derivation of the equations make simplifying assumptions not fully consistent with what is known about the heart. Several of the simplifying assumptions include: (1) a simplified geometry such as a spherical LV, (2) the LV has a constant wall thickness, and (3) uniform mechanical properties in all directions. Data in Fig. 1(a) and Table 2 illustrate the inconsistency of these assumptions about chamber geometry, wall thicknesses, and mechanical properties.

Biaxial mechanical testing gives a direct measurement of the passive mechanical properties of the LV wall, but it, too, is not without its limitations. Tensile testing's widespread use is greatly hindered by the fact that it requires large portions of the heart to be excised. Many factors make it difficult to use ex vivo biaxial measurements to infer properties of the intact beating heart in vivo, several which are listed here. (1) Ex vivo heart tissue used in biaxial tissue lacks normal relaxation and contraction of the chamber. While in vivo PV loop analysis also attempts to focus on the passive mechanics by targeting analysis during the passive filling phase of diastole; PV loops are likely influenced by the active relaxation of the heart [30]. (2) Excising and mechanically testing a section of the LV free wall alter the tissue's geometry from convex to flat resulting in different loading conditions. (3) in vivo, the heart is in a state of pretension that is released ex vivo. The change in shape and removal of tension make it challenging to correctly identify the state of zero stress of the tissue when it is loaded into the biaxial testing setup. This could lead to a potential underestimation of actual strain on the tissue. (4) While the biaxial mechanical testing is a step forward from uniaxial testing by applying stresses in multiple directions, which assesses anisotropy, this does not perfectly simulate in vivo stresses. in vivo, LV filling pressures cause transmural stresses that are not replicated in biaxial testing. In addition, many mechanical characterization experiments utilize more than one loading protocol to explore a larger space of the strain energy function to accomplish a more complete biomechanical characterization. The scope of our study did not include more than one loading protocol so our characterization is limited.

In addition to the limitations of mechanical testing techniques, one must consider that the results of this study are from a single time point in two progressive diseases. The time point chosen for this study was chosen to match a preheart failure stage of VO we used in our previous in vivo work with this model [3]. In addition, different animal models exist for creating both volume overload (e.g., chordal rupture [42]) and pressure overload (e.g., atrial banding [43]). For instance, although both Ang-II- and transverse aortic constriction-induced PO have characteristic increases in intracardiac Ang-II [25,26,44,45], the two treatments may have different effects on ventricular mechanics since Ang-II-induced remodeling is not due to PO alone. Highlighting this point, Ang-II infusion can induce cardiac remodeling both directly via AT1 receptor activation within myocardial tissue, even in the absence of high blood pressure [46], and indirectly as a result of increased afterload caused by increased blood pressure. It should be noted that in many patients, hypertension is not the result of aortic constriction or other forms of stenosis but instead is reflective of a mosaic of contributing factors that not only includes the renin-angiotensin-aldosterone system but also the autonomic nervous system and the kidney. While it is not expected that Ang-II infusion fully mimics the neurohormonal changes observed in these patients with hypertension, Ang-II infusion might be a better model of this type of PO than one that induces PO by partially constricting the aorta. Alternatively, transverse aortic constriction may be a better model of patients with aortic valve stenosis. A more complete discussion of different models of heart failure can be found in a recent review by Bacmeister et al. [47], which includes a detailed discussion of transverse aortic constriction and Ang-II-infusion models. Thus, it is important not to overgeneralize our findings and recognize that different disease models or even different stages of disease progression within a given model could yield different results and that each model has merits and limitations.

Motivation for Our Work.

Despite the limitations noted above, the results from this study helped us answer the question that initially motivated our study—how does the modulus of the heart change during volume overload? This question was asked within the context of understanding how changes of the mechanical properties of the heart might impact cellular behavior. We and others previously have reported that VO hearts have decreased ECM synthesis [3,4] and content [4,36], despite increased profibrotic factors such as TGF-β [3,4] and angiotensin II [43]. We recently reported that cultured fibroblasts isolated from VO hearts exhibit a hypo-fibrotic phenotype characterized by markers of decreased ECM synthesis, increased ECM degradation, and decreased responsiveness to the profibrotic factor TGF-β1 [4]. Since other fibroblast types on soft matrices fail to initiate a profibrotic response to TGF-β1 [48,49], we hypothesized that the modulus of VO hearts was decreased, leading to the hypo-fibrotic phenotype observed in the isolated cardiac fibroblasts. Our results in this study show that in VO, relative to control hearts, chamber stiffness (from PV loop testing) and tissue material constants related to mechanical properties (from biaxial testing) both decreased, which are consistent with the hypothesis.

Additional preliminary studies beyond the scope of this study suggest that cardiac fibroblasts from normal hearts cultured on soft substrates exhibit many of the features of fibroblasts isolated from VO hearts including a failure to upregulate ECM synthesis in response to TGF-β. Taken together, these observations suggest that the decrease in modulus in VO hearts we report here may play an important role in VO induced heart failure by diminishing the responsiveness of cardiac fibroblasts to profibrotic stimuli.

Study Results With Respect to Related Literature.

Our data show that the parameters corresponding to tissue mechanical properties of VO hearts are approximately half that of those from normal myocardium is a new finding. Chaturvedi et al. showed that VO tissue was less stiff than PO using human biopsy samples, as measured by uniaxial testing, but did not compare to normal tissue due to lack of sufficient sample numbers [2]. It is well established that VO results in decreased chamber stiffness, as assessed by PV loop analysis [3,11]; however, this may not reflect a change in tissue mechanical properties since chamber stiffness is also affected by geometry (e.g., wall thickness and chamber dimensions). Hutchinson et al. reported that mice with heart failure due to VO had decreased EDPVR, which returned to control levels after normalization with chamber geometry using a spherical model analysis [10], similar to Eq. (2) here, which is consistent with our results (Figs. 2 and 4(c)). However, Hutchinson et al. also reported increased stiffness in VO measured by uniaxial testing of skinned (permeabilized) muscle fibers in mice [10]. These discrepancies may be due to the mechanical testing method (uniaxial testing of muscle fibers versus biaxial testing of whole myocardium), animal (mice versus rats), or stage/time point of heart failure. Previously, we noted that there was a net decrease in ECM production by VO cardiac fibroblasts [4] and a net decrease in ECM in cardiac tissue during acute and compensated VO-induced heart failure which corresponded with decreased chamber stiffness [3]. Together these results support the notion that the decreased VO myocardium modulus was likely due to a reduction in ECM.

In PO, relative to control hearts, we found that chamber stiffness doubled, but the material constants were unchanged. This contrasts with the decrease in chamber stiffness of VO, which is due, in part, to changes in tissue mechanical properties. The increase in chamber stiffness in PO is likely due to changes in geometry and compensatory remodeling (tissue thickening), and not due to an increase in passive tissue mechanical properties. Chamber stiffness in PO, as measured by PV loop data, has been consistently reported as higher than that in normal hearts [13,50]. However, findings related to myocardial tissue mechanical property changes due to PO were variable. A few studies reported increased myocardial tissue stiffness in PO, as calculated from PV data fit to a spherical model of the LV [51,52], or uniaxial tests of isolated papillary muscles [1]. There are also reports of increased right ventricular stiffness (as measured with equibiaxial testing) due to right ventricular PO [22]. Conversely, others have reported no significant changes in myocardial mechanical properties in PO [53,54]. Mirsky et al. suggested that PO tissue has approximately the same modulus as normal tissue when controlling for chamber pressure [30]. Since increased chamber pressure causes increased material modulus in vivo, reducing pressure, to that of controls, by administering the Ca²⁺ channel blocker nifedipine, Mirsky estimated that normal and PO hearts have approximately the same incremental modulus at equal pressures [30]. Therefore, the increase in apparent chamber stiffness in PO hearts, here and in the cases of Mirsky and others, is likely due to an increase in tissue mass and thickness, changes in geometry, and/or higher chamber pressures, rather than an increase in the material modulus of the relaxed myocardium tissue. In this study, while no increase in material modulus was observed in PO hearts relative to controls hearts, there was ∼50% increase in interstitial collagen. This result indicates that it is not always the case that increased interstitial collagen will correlate with increased modulus. Potential reasons for this are discussed in the supplement.

We recognize that maximal strain values we used in biaxial testing are lower than some other reports in the literature. Tissue was strained until there was evidence of tearing, typically near the fishing hooks. This lower strain at failure could be due to the difficulty in knowing what the unloaded point of the tissue is. We attempted to control for this by using a small tare load (0.5 gf providing a prestress of ∼400 Pa) which provides a similar or smaller prestress as the (0.25 gf or ∼50 Pa) tare load [55] used on thinner RV tissue samples. Another potential explanation of the differences in strain values is the difference of tissue used in other studies. Many studies utilize RV tissue, which is less stiff compared to the LV tissue [18]. Therefore, the RV would have higher strains compared to our LV tissue. In addition, we utilize full thickness tissue, which does not have one preferred fiber orientation like tissue slices. In either case, since in our study, the tissue in each of our experimental groups was treated the same, we do not expect this to change the fundamental conclusions of our study.

The results from this study highlight the differences in tissue remodeling and mechanical properties between PO and VO via two methods of mechanical testing. Based on the combination of the PV loop analysis and measures of mechanical properties via biaxial testing, the increase in chamber stiffness in PO is likely due to changes in geometry and not changes in material modulus, while the decrease in chamber stiffness in VO is likely a result of a decrease in myocardial intrinsic stiffness as confirmed by biaxial testing. This information may be useful to the design and interpretation of in vitro experiments investigating the effect of modulus on cardiac cell behavior and inform further research using computational models of the remodeling in heart failure. We have shown that chamber stiffness measured by PV loops does not necessarily correspond to the tissue mechanical property estimates, or even trends, measured by biaxial testing.

Supplementary Material

Supplementary Material

Supplementary Figures

Funding Data

• Howard Hughes Medical Institute Med Into Grad Fellowship (to RCC; Funder ID: 10.13039/100000011).

• American Heart Association (AHA, No. 15PRE19830015 to RCC; No. 15GRNT2579003 to KJG, PAL, and AJT; No. 17GRNT33700288 to KJG and PAL; Funder ID: 10.13039/100000968).

• National Institutes of Health (Nos. NIH R00HL116769 and R21EB026518 to AJT and RO1EY020929 to JL: Funder ID: 10.13039/100000002).

• Nationwide Children's Hospital (to PAL and AJT; Funder ID: 10.13039/100007520).

Nomenclature

BP =

blood pressure

C =

material constant from Eqs. (4) and (5)

C₁ =

material constant from Eq. (4) in circumferential direction

C₂ =

material constant from Eq. (4) in longitudinal direction

C₃ =

material constant from Eq. (4) in respect to axes interactions

E_CC =

green strains in the circumferential direction

E_inc =

incremental modulus

E_{inc E} =

incremental modulus calculated from endocardial stresses

E_{inc M} =

incremental modulus calculated from midwall stresses

E_LL =

green strains in the longitudinal direction

ECM =

extracellular matrix

LV =

left ventricle

LVEDD =

left ventricular end-diastolic diameter

LV-EDPVR =

left ventricular end-diastolic pressure–volume relationship

PO =

pressure overload

PV =

pressure–volume

PWT =

posterior wall thickness

R_m =

radius of LV measured to the midwall, between the endocardial and outer radii

R_o =

outer radius of left ventricle

S_CC =

second Piola–Kirchoff stress for circumferential direction

S_LL =

second Piola–Kirchoff stress for longitudinal direction

VO =

volume overload

V_w =

left ventricular wall volume

β =

index of chamber stiffness

β_w =

dimensionless index of chamber stiffness normalized to wall volume