Mechanically Induced Deformation of Nuclei in the Tricuspid Valve Interstitial Cells: Experimental Measurements and Multi-scale Computational Simulation

The tricuspid valve (TV), located on the pulmonary side of the heart, ensures unidirectional blood flow from the right atrium to the right ventricle (Fig. 1). The TV function may be compromised, leading to a backward flow of blood from the ventricle to the atrium, known as tricuspid regurgitation. Whether occurring in isolation or alongside other valvular issues, tricuspid regurgitation is linked to a more than two-fold increase in cardiac mortality when left untreated [1,2]. However, surgical intervention on the TV, especially an isolated TV surgery, is often discouraged due to elevated in-hospital mortality rates ranging from 10% to 25% [3–6]. These sobering statistics, combined with our incomplete understanding of the pathogenesis of tricuspid regurgitation, underscore the importance of unraveling the mechanisms behind its development. Without elucidating such mechanisms, our capacity to establish precise patient selection criteria for surgery and to improve long-term outcomes remains limited.

Proper TV function relies on the biomechanical behavior of its three leaflets: the anterior, posterior, and septal leaflets. TV leaflets have complex microstructure that significantly affects the macro-scale biomechanical responses of the valve [7,8]. Specifically, proper coaptation of the leaflets, i.e., how the edges of the leaflets join together to close and seal the valve, is required for normal TV function. In atrioventricular valves, leaflet coaptation can be affected by changes in the mechanical integrity of the extracellular matrix (ECM) constituents, such as collagen and/or elastin [9]. Biomechanical remodeling of the ECM in TV leaflet may lead to valvular insufficiency and regurgitation [10]. For instance, Marfan syndrome is a genetic disorder characterized by an abnormal coding of the FBN1 gene for fibrillin-1. Fibrillin-1, part of the microfibril family that, in conjunction with an amorphous core made of elastin, constitutes the elastic fibers typically known as elastin [11–15]. While collagen provides structural stiffness to maintain leaflet coaptation during systole [16], elastin contributes long-range elastic properties such that the leaflet can recoil and extend during systole and diastole, respectively [11,16]. Marfan syndrome impacts 1 in every 3000–5000 individuals in the United States [17]. The mechanisms by which these genetically induced ECM changes affect the function of TV, especially in the context of tricuspid regurgitation induced by Marfan syndrome, remain poorly understood and warrant thorough investigation. Such a lack of knowledge is not unexpected, given that the TV has been referred to as the “forgotten valve” over the years [18].

The TV leaflets have a layer-like structure composed of the ECM and the residing valve interstitial cells (VICs) [19]. The VICs play a critical role in maintaining the mechanical integrity of the valve [20]. Among different functions, the VICs contribute to ECM protein synthesis and maintain a structurally competent leaflet. As such, it is important to identify changes in the biomechanical micro-environment of the TV interstitial cells in response to the ECM structural changes (Fig. 1). The VICs have the ability to sense its environment via mechanotransduction [21] and translate physical stimuli into biochemical activity that triggers intracellular signaling. This sensing mechanism is primarily initiated via fibrillar and focal adhesion points on the surface of the VICs [22]. Where fibrillar adhesions are small and/or elongated adhesion complexes, focal adhesions are much larger and contain cytoplasmic proteins (e.g., paxillin and vinculin) [23–25]. It is through the focal adhesion points on VICs that a robust anchorage to the ECM is made [23,25–29].

To the point that VICs respond via mechanotransduction, recent findings from Refs. [30,31] have documented that certain types of cells are able to sense confinement by means of nuclei deformation [30,31]. In addition, aortic valve interstitial cells have been found to respond to mechanical deformations. Ku et al. have documented that under sustained mechanical stretching, aortic VICs up-regulate the production of collagen type-III [32]. The physical stimuli that VICs receive may translate to different outcomes that may be tissue specific. In canine mitral valve, for instance, increased stretch (be it static or cyclic) has been found to induce cellular signaling that is favorable toward myxomatous pathology [33].

The objective of this study was to identify the relationship between the deformation of VICs—particularly that of VICs nuclei—and tissue-level mechanical loading. While existing computational models can capture the overall responses of the TV, they fall short in accurately predicting cellular deformation in response to changes of the ECM [7,34–38]. Prior experimental research has highlighted the variability of VIC nuclear shape in response to macro-scale mechanical loading in TV leaflets [36]. Our experimental/computational approach has helped us to extend such findings by identifying the correlation between the orientation of the ECM fibers and the nuclear shape in VICs of the TV. We examined cells in various alignments relative to the ECM fiber orientation, using a computational approach since such studies were not possible via experimental methods. Our computational scheme allowed for a more nuanced examination of how cellular orientation and ECM structure interplay in determining cell deformation and valve mechanics.

Fresh porcine hearts were acquired and delivered in phosphate buffered saline (PBS) to our facilities by a known provider of biological specimens (Animal Technologies Inc., Tyler, TX). Once the hearts were received, the TV apparatus was located and the anterior leaflet was carefully isolated while maintaining some of the annulus for orientation purposes. This step allowed for differentiating the radial from the circumferential directions on the anterior leaflet specimen. Following the excision of the anterior leaflet, the specimens were kept at 4 $∘$C until the time of mounting on a custom-made biaxial tensile machine. Details for the mounting procedure have been thoroughly explained in previous publications [39–44]. Briefly, the specimen was carefully sized and trimmed with the use of a tissue template that was placed such that the edges coincided with the radial and circumferential directions.

Prior to mounting the specimen on the biaxial tensile machine, the thickness of the tissue was recorded using a leaflet gauge with a resolution of 0.001 in. (25.4 $μ$m). The thickness of each specimen was used in determining, via the onboard software, the required equibiaxial load needed to achieve the following target equi-biaxial stress levels: 0, 5, 10, 40, 90, and 130 kPa. The tissue was mounted such that one axis of the specimen coincided with the radial direction, and the other axis with the circumferential direction of the leaflet. Once mounted, a total of ten preconditioning cycles were applied prior to specimen fixation in a bath of 4% para-formaldehyde in PBS. The biaxial tensile machine then executed a script that maintained the target stress level during the 2-h fixation process. Each fixation stress load included a sample size of 3, leading to a total count of 18 samples across all load levels. The samples were fixed under mechanical loading because the cross-linking of the ECM fibers due to fixation guaranteed that any morphological changes in the nuclei would be present after removal of the loads and during imaging as shown previously [45]. Following fixation, the samples were carefully removed and a surface sub-millimeter glass marker was attached to the top-right corner so as to establish orientation (radial from circumferential) for the forthcoming steps. In addition, a small notch was placed adjacent to the glass marker as a precautionary measure should the marker become dislodged. Specimens were subsequently stored in 70% ethanol.

Much the same with previous approaches [46,47], fixed specimens were processed and 20 $μ$m-sections were obtained along the transmural-circumferential direction, coinciding with the bulk of collagen in the fibrosa layer of the leaflet. Following de-parafinazation, the sectioned tissue was permeabilized with Triton X-100 (Sigma Aldrich, SKU: X100-500ML), at a concentration of 1:1000, for 20 min, after which the VIC nuclei were stained with SYTOX Green (Thermo Fisher Scientific, Cat. No.: S7020) at 1:2000 for 15 min. The excess staining solution was then removed and the slide was mounted with Fluormount-G (Thermo Fisher Scientific, Cat. No. 50-187-88).

Specimens were imaged on a Zeiss LSM 880 having multi-photon capability with a Zeiss Plan-Apochromat 10$×$/0.45 objective. The stained VICs were imaged at an excitation wavelength of 504 nm, laser power set at approximately 1.5%, and the photomultiplier level at 550. The Z-stack acquired, throughout the thickness of the specimen, was captured at a resolution of $1024×1024$ (16-bit).

Processing for the microscope images was carried out in imaris (Oxford Instruments, v. 9.9.0). Once the microscopy images were converted into native imaris format, the segmentation of VICs took place. In this step, VICs were identified as “Surfaces” and segmented with the background segmentation set at 7 $μ$m and a seed point of 4.5 as a starting point. Seed placement was based on an “Intensity Mean” filter such that segmentation took place outward from the volume of higher average intensity of the stained VICs. After completing the segmentation wizard, further manual adjustments took place to ensure that the surface segmentation accurately represented that VICs in the Z-stack. Any surfaces segmented within 2 $μ$m from the XYZ border was discarded so as to not include erroneous artifacts in subsequent analysis. A sample image set displaying native image acquisition with imaris-segmented surfaces can be seen in Fig. 2(a).

An approximation of the complex cell–ECM fiber matrix mechanism was considered as our VIC deformation model. Mechanical stresses are transmitted to the cell nuclei from the ECM fibers through a sophisticated network involving focal adhesions and intracellular structures. Focal adhesions serve as the connection points between cells and the external ECM at the cell membrane, facilitated by transmembrane proteins known as integrins [29]. Omitting the intricate intracellular structural components, we developed a representative model to predict the nuclear deformation in coordination with the deformation of the fiber network in response to applied macro-scale loading.

To evaluate changes in the response of the nuclei of TV interstitial cells to macro-scale equibiaxial mechanical loading, as predicted by our nuclear deformation model, numbers of fiber networks were randomly selected from three layers of the TV anterior leaflet. We determined the changes in the NAR under equibiaxial mechanical load in four different scenarios in initial configurations (Table 1):

• A single representative fiber network, wherein nuclei with the same initial NAR value (2.57, identified as the average of microscopy data) was oriented in 80 different directions relative to the network.

• A single representative fiber network, encompassing nuclei with 80 different initial NAR values but all aligned with the main fiber direction of the fiber network.

• A total of 80 fiber networks with nuclei of the same initial NAR value (2.57) aligned with the mean fiber directions of their respective encompassing fiber network.

• A total of 80 fiber networks with various initial NAR and random cell alignments relative to the mean fiber orientation.

Based on microscopy and subsequent image analysis, the average NAR of the overall population of segmented VIC nuclei exhibited an upward trend as mechanical loading increased. The NAR values, starting from the traction-free state to the highest loading conditions, were 2.57 $±$ 0.72 (mean $±$ standard deviation), 2.45 $±$ 0.70, 3.13 $±$ 1.21, 2.81 $±$ 0.91, 3.19 $±$ 1.14, and 3.4 $±$ 1.29 for 0, 5, 10, 40, 90, and 130 kPa loading conditions, respectively. Microscopy also showed that VIC nuclei are predominantly circumferentially oriented, aligning with the primary fiber direction in the valve leaflet, albeit with some deviations in out-of-plane directions (data not included).

As shown in Fig. 4, and similar to our previous published works [7,51], we were able to fit the experimentally obtained mechanical testing outcomes to the micro-structurally accurate multi-scale model reasonably well (⁠$R2=0.94$⁠). Figure 5 displays the undeformed and deformed configurations of the finite element model under two levels of equibiaxial loading conditions. Additionally, it demonstrates the changes in NAR within a representative fiber network when subjected to various mechanical loads. It should be noted that the nucleus in this specific case was aligned with the main fiber direction in the undeformed configuration.

Figure 6 shows how NAR alterations were apparent under increasing stress levels in all four tested scenarios as compared to the measurements obtained experimentally. Figure 6(a) illustrates changes in NAR that occur at various loading levels when the nucleus are oriented at different angles relative to the mean fiber direction (scenario I). Our model response revealed an increase in NAR, increasing from 2.57 to 4.00. Notably, the computational findings align consistently within the experimentally measured values, and the model response mainly falls within the standard deviation of the experimental finding.

Figure 6(b) shows the model response under different loading levels in one representative fiber network (scenario II), where initial NAR varied between 1.33 and 4.69. The mean NAR values increased from 2.57 to 4.27 under the increase in loading level from $0$ to $130$ kPa. Additionally, the results obtained from the computational model has the same increasing trend as those values measured through microscopy. As shown in Fig. 6(⁠$c$⁠), similar trend was observed in scenario III (i.e., nuclei in 80 fiber networks all with the same initial NAR value of 2.57) where NAR increased with rising stress levels with an increase in NAR from 2.57 to 3.66.

The mean NAR values of randomly oriented nuclei in relation to the mean fiber direction of 80 different networks (scenario IV) are shown in Fig. 6(d). A rapid initial rise in the NAR followed by a continued increase but at a reduced rate (increasing from 2.57 to 3.91) is shown in Fig. 6(d). The predictions of the computational model under scenario IV further increased our confidence in its capability for investigating the biomechanical behavior of nuclei in fiber networks subjected to various loading conditions. As shown in Fig. 6(d), the model responses matched the trend observed in experimental findings.

Research on the TV has traditionally been overshadowed by more extensive studies on the aortic and mitral valves, largely due to the greater prevalence of left heart diseases that involve these latter valves. [18,73]. However, with the increasing focus on right heart disease, the significance of tricuspid valve disease as a major contributor to morbidity and mortality is now being acknowledged [74–76]. In the realm of biomechanics, many researchers in recent years have extensively examined the structure, function, and malfunction of TV [36,77–81]. A pivotal aspect in advancing our comprehension of tricuspid valve disease involves distinguishing the connection between the microstructure of the tissue and the mechanics of the leaflets, initially in a healthy state and subsequently in disease.

The findings of this study provide valuable insights into the intricate relationship between VIC nuclear deformation and tissue-level mechanical loading within the TV complex. By leveraging a combined experimental and computational approach, we were able to elucidate the correlation between ECM fiber orientation and nuclear shape in VICs. Although research on the mechanobiology of VIC nuclei in relation to macro-scale loading in both healthy and diseased hearts is scarce, the importance of NAR in the mechanobiology of other cell types is well established [82–84]. The morphology of the cell nucleus is continuously modulated by various mechanical forces applied to the cell [83]. Changes in nuclear shape, influenced by cellular geometry and mechanical stress, significantly impact gene expression. For instance, cells cultured on different geometries, such as elongated rectangles and small circles, exhibit distinct nuclear shapes. These variations lead to changes in gene expression due to alterations in nuclear architecture [85]. Altering the shape of the nucleus can disrupt the homeostasis between cell and nuclear mechanics [82], leading to irregular nuclear morphology and affecting the ability of the cell to generate force and follow chemical gradients. This disruption can influence gene expression, particularly of proteins associated with cell migration. Such changes are crucial in physiological processes like wound healing and immune response and pathophysiological conditions such as cancer metastasis [86]. Considering such an important role of nuclear mechanobiology in cell function, it was not surprising to observe micro-structurally dependent changes in nuclear shape in VIC, a cell type that is subjected to high levels of macro-scale scale strains during opening and closure of the valve leaflets [77,87].

A more detailed analysis of our experimental data revealed a consistent alignment of cell nuclei with the surrounding collagen [88]. Such an observation was consistent with previously published work [36]. Given the complexity of the deformation of an entire cell (including the membrane and cytoplasm in addition to that of the nucleus) within intact tissues, NAR as a measurement of overall cellular deformation was deemed a more appropriate metric. However, it should be noted that exclusion of intracellular structure and organelles from the computational model was a limiting factor in our study.

A key aspect of our modeling approach was our ability to examine cells in different orientations relative to the ECM fiber architecture. Such a strategy has the potential for a more nuanced understanding of how cellular orientation and ECM structure interplay in determining cell deformation and valve mechanics. We examined the NAR alteration under equibiaxial mechanical loading in four different scenarios pertaining to the initial population of the cell nuclei (Table 1). As shown in Fig. 6, an initial rapid increase in NAR, followed by a more gradual rise, was most probably due to the decreased undulation of ECM fibers and the eventual full recruitment of collagen, for all four scenarios. Such an observation was consistent with trends in prior experimental studies in soft tissues (e.g., refer to the study of Foong et al. in the corneoscleral shell [89]). It also underscores the predictive capability of our computational model in simulating the biomechanical behavior of fiber networks under different loading levels. In our computational approach (Fig. 6), we primarily focused on the responses of a cell population, as this method seemed most relevant for comparison with experimental data. Interestingly, the mean responses of the nuclei under increasing stress were similar across all four simulated scenarios and aligned with the experimental outcomes. These responses, characterized by an initial rapid rise followed by a slower increase, were consistent with the observations of Lee et al. in mitral valve leaflets [90].

It should be noted, however, that the computational model has the capability of providing detailed information for individual cells, which is valuable for understanding the multi-scale mechanobiology of the VIC. For example, Fig. 7 shows the comparative deformation of two nuclei with the same initial shape, exposed to identical macro-scale mechanical loading. However, the network in Fig. 7(a) consisted of fibers primarily aligned with the circumferential direction of the leaflet, whereas the network in Fig. 7(b) had fibers predominantly aligned in the radial direction (i.e., perpendicular to those in Fig. 7(a)). In other words, the nucleus in Fig. 7(a) was aligned with the main fiber direction, whereas the nucleus in Fig. 7(b) had its main axis perpendicular to the main fiber direction. The comparison of loading-induced changes in the NAR is intriguing. In the case of Fig. 7(a), the NAR initially increased rapidly before the rate of increase slowed down. Conversely, in the case shown in Fig. 7(b), the changes in NAR were much smaller, and it appeared that the NAR did not change with loading after a certain point. This differential behavior between the two fiber networks underscores the significance of ECM fiber alignment in dictating the mechanical response of the cell nuclei. The link between macro-scale mechanical loading and ECM collagen remodeling has been well established [91,92]. The aforementioned example illustrates how such changes in the ECM network could be directly linked to nuclear mechanobiology.

Finally, the interdependency between VIC NAR and macro-scale mechanical loading is of great importance, as heart valves experience significant cyclic mechanical strain throughout an individual’s life. In our previous in vivo studies, we demonstrated how surgical procedures such as ring annuloplasty could drastically alter the macro-scale deformation of the mitral valve anterior leaflet in an ovine model [93]. Our current modeling suggests that the deformation of VIC nuclei in the tricuspid valve would be altered during each cardiac cycle when macro-scale loading is changed from that of a healthy valve, following surgical procedures such as ring annuloplasty.

Our study was not without limitations. The discrepancy between the model and the experimental data could stem from several factors. The anisotropic contribution of the intricate intracellular structure was not included in the computational model. In this study, we assumed that nuclei undergo affine deformation in correspondence with the positional changes of the ECM at the focal adhesion point within each representative volume element. Our model can be improved upon by the addition of the non-affine deformation of the intracellular structure such as actin microfilaments, microtubules, and/or intermediate filaments. Moreover, it has been shown that nuclear properties vary by leaflet and depth in similar ways that collagen orientation varies by leaflet and depth [36,88]. Our simulation, however, assumed similar structure along the thickness of the valve. Another limitation of our experimental approach was the inability to image the same leaflet under different mechanical loads. Utilizing imaging techniques that allow for the mechanical deformation of the valve while being imaged (e.g., see Ref. [94]) could better represent the load-dependent deformation of the nuclei. Despite such limitations, we found reasonable agreement between the outcomes of the computational model and the experiments.

In this study, we conducted a comprehensive analysis of the impact of mechanical loading on nuclei deformation in the TV anterior leaflet. Our observations revealed a notable influence of mechanical forces on nuclear shape, with significant changes in average NAR potentially triggering deviations in gene expression and protein synthesis. We also identified a relation between the orientation of collagen fibers and the NAR of VICs. Our findings highlight the importance of considering ECM fiber alignment in future studies of valve biomechanics to develop more accurate models for predicting cellular responses to mechanical stimuli. Overall, our study highlights the complex interplay between the mechanical environment of the valve and the cellular responses, providing insights into how mechanical forces impact the health and function of the tricuspid valve.

The authors acknowledge the funding provided for this work by the National Science Foundation (NSF CAREER Award 2049088). They also recognize the computational facilities from Research Computing at Northeastern University. The use of the research computing reserved cluster from Sinan Müftü is gratefully acknowledged. The authors also thank the Institute for Chemical Imaging of Living Systems at Northeastern University for consultation and imaging support.

This article does not include research in which human participants were involved. Informed consent not applicable. This article does not include any research in which animal participants were involved.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$f$ =

fiber axial force

$v$ =

ellipsoid center

$x^$ =

ellipsoid surface

$y¯$ =

experimental measurement mean

$y^$ =

simulated measurement

$a$ =

cell nuclei tertiary axis

$b$ =

cell nuclei secondary axis

$c$ =

cell nuclei primary axis

$G$ =

shear modulus

$J$ =

deformation gradient tensor determinant

$L$ =

total fiber length

$V$ =

volume

$fj$ =

boundary cross-link force in j-direction

$nk$ =

RVE surface normal vector

$ri$ =

fiber direction unit vector

$sij$ =

microscopic volume-averaged Cauchy stress tensor

$uk,i$ =

displacement gradient

$yi$ =

experimental measurement

$Af$ =

mean fiber cross-sectional area

$Bij$ =

left Cauchy–Green deformation tensor

$Dij$ =

ellipsoid shape tensor

$Ef$ =

dimensionless fiber stiffness parameter

$Fij$ =

deformation gradient tensor

$Hij$ =

orientation tensor

$Qij$ =

eigenvector matrix

$e(i)$ =

SALS reference frame vectors

$R2$ =

coefficient of determination

$V′$ =

non-dimensionalized volume

$V(i)$ =

ellipsoid eigenvector

$wi(k)$ =

orientation tensor eigenvalue

$xi′$ =

boundary cross-link position

$Sij′$ =

macroscopic volume-averaged Cauchy stress tensor

$Sijm$ =

matrix stress tensor

$α$ =

anisotropy index

$β$ =

dimensionless nonlinearity parameter

$γ$ =

RVE edge length

$δij$ =

Kronecker delta function

$εG$ =

fiber Green strain

$εGc$ =

critical fiber Green strain

$θ$ =

fiber direction

$Λij$ =

diagonal eigenvalue matrix

$λ(i)$ =

orientation tensor eigenvector

$λfc$ =

critical stretch

$λf$ =

fiber stretch

$μ$ =

primary fiber direction

$ν$ =

Poisson’s ratio

$ψ$ =

fiber volume fraction

ECM =

extracellular matrix

FE =

finite element

NAR =

nuclear aspect ratio

PBS =

phosphate buffered saline

RVE =

representative volume element

SALS =

small angle light scattering

TV =

tricuspid valve

VIC =

valve interstitial cell

To further extend the impact of our research and in line with our prior efforts [7,44,95–98], we have created an educational component related to the findings presented in this paper. In this appendix, we include a learning exercise suitable for a graduate-level introductory course in biomechanics or continuum mechanics.

Problem—Approximate changes in the NAR by assuming that the nuclear shape deforms affinely with the macro-scale tissue deformation. As a first approximation, consider a two-dimensional shape (i.e., an ellipse) for the nuclei with an initial NAR of 2.57. Use the experimental data for tissue-level tension and displacement provided in Fig. 4 for a 7 mm $×$ 7 mm $×$ 0.432 mm sample. Compare your results with the mean of the experimental and computational outcomes presented in Fig. 6.