Volume 602, Issue 4 p. 597-617
Research Article
Open Access

Role of tissue biomechanics in the formation and function of myocardial trabeculae in zebrafish embryos

Adriana Gaia Cairelli

Adriana Gaia Cairelli

Department of Bioengineering, Imperial College London, London, UK

Search for more papers by this author
Alex Gendernalik

Alex Gendernalik

Department of Pediatrics, Washington University in St. Louis, St. Louis, USA

Search for more papers by this author
Wei Xuan Chan

Wei Xuan Chan

Department of Bioengineering, Imperial College London, London, UK

Search for more papers by this author
Phuc Nguyen

Phuc Nguyen

Department of Bioengineering, University of Texas at Arlington, Arlington, USA

Search for more papers by this author
Julien Vermot

Julien Vermot

Department of Bioengineering, Imperial College London, London, UK

Search for more papers by this author
Juhyun Lee

Juhyun Lee

Department of Bioengineering, University of Texas at Arlington, Arlington, USA

Search for more papers by this author
David Bark Jr.

David Bark Jr.

Department of Pediatrics, Washington University in St. Louis, St. Louis, USA

Search for more papers by this author
Choon Hwai Yap

Corresponding Author

Choon Hwai Yap

Department of Bioengineering, Imperial College London, London, UK

Corresponding author C. H. Yap: Department of Bioengineering, Imperial College London, London, UK. Email: [email protected]

Search for more papers by this author
First published: 12 February 2024

Handling Editors: Bjorn Knollmann & Eleonora Grandi

The peer review history is available in the Supporting Information section of this article (https://doi.org/10.1113/JP285490#support-information-section).


Cardiac trabeculae are uneven ventricular muscular structures that develop during early embryonic heart development at the outer curvature of the ventricle. Their biomechanical function is not completely understood, and while their formation is known to be mechanosensitive, it is unclear whether ventricular tissue internal stresses play an important role in their formation. Here, we performed imaging and image-based cardiac biomechanics simulations on zebrafish embryonic ventricles to investigate these issues. Microscopy-based ventricular strain measurements show that the appearance of trabeculae coincided with enhanced deformability of the ventricular wall. Image-based biomechanical simulations reveal that the presence of trabeculae reduces ventricular tissue internal stresses, likely acting as structural support in response to the geometry of the ventricle. Passive ventricular pressure-loading experiments further reveal that the formation of trabeculae is associated with a spatial homogenization of ventricular tissue stiffnesses in healthy hearts, but gata1 morphants with a disrupted trabeculation process retain a spatial stiffness heterogeneity. Our findings thus suggest that modulating ventricular wall deformability, stresses, and stiffness are among the biomechanical functions of trabeculae. Further, experiments with gata1 morphants reveal that a reduction in fluid pressures and consequently ventricular tissue internal stresses can disrupt trabeculation, but a subsequent restoration of ventricular tissue internal stresses via vasopressin rescues trabeculation, demonstrating that tissue stresses are important to trabeculae formation. Overall, we find that tissue biomechanics is important to the formation and function of embryonic heart trabeculation.

Key points

  • Trabeculations are fascinating and important cardiac structures and their abnormalities are linked to embryonic demise.
  • However, their function in the heart and their mechanobiological formation processes are not completely understood.
  • Our imaging and modelling show that tissue biomechanics is the key here. We find that trabeculations enhance cardiac wall deformability, reduce fluid pressure stresses, homogenize wall stiffness, and have alignments that are optimal for providing load-bearing structural support for the heart.
  • We further discover that high ventricular tissue internal stresses consequent to high fluid pressures are needed for trabeculation formation through a rescue experiment, demonstrating that myocardial tissue stresses are as important as fluid flow wall shear stresses for trabeculation formation.


In the process of development of the ventricle, the myocardium differentiates into two layers, a compact and a trabeculated zone, both of which are likely essential for normal cardiac contractile function. The trabeculae are myocardial cells covered by an endocardial layer, that form a complex network of contractile bundles crisscrossing the inner surface of the ventricle. Interestingly, they only form on the outer curvature of the ventricle, opposite to the atrioventricular canal. The trabeculae appear to function as a rapid conduction system in cardiac electrophysiology (Srivastava & Olson, 2000) and are hypothesized to improve nutrition transport to the heart, before the development of the coronary arteries, by increasing the surface area available for biotransport (Samsa et al., 2013). Many mutants with defects in trabeculations or the suppression of genes involved in trabeculation formation, end with embryonic mortality (Gassmann et al., 1995; Lai et al., 2010; Liu et al., 2010), suggesting that they may be essential for life. However, whether and how the trabeculae contribute to the pumping function of the heart is not completely understood and is investigated here.

Previous research has demonstrated that ventricular chamber maturation and trabeculae formation are mechanosensitive processes (Duchemin et al., 2019; Hove et al., 2003; Miller, 2011), such that when the biomechanical environment is disrupted, defective heart morphogenesis and abnormalities occur (Foo et al., 2021; Lee et al., 2016; Rasouli & Stainier, 2017; Staudt et al., 2014). Many past authors have attributed trabeculae formation to stimuli provided by fluid shear stresses imposed on endothelial surface (or fluid wall shear stresses, WSS) (Boselli et al., 2015; Cavallero et al., 2021; Foo et al., 2021; Granados-Riveron & Brook, 2012; Hove et al., 2003; Lee et al., 2018; Vedula et al., 2017), as biomechanical disruption involving reduction of cardiac flow prevented trabeculation. However, on top of reducing fluid WSS, these disruptions likely caused a reduction in chamber fluid pressure and consequently ventricular tissue internal stresses as well (or tissue stresses, defined as stresses imposed by neighbouring pieces of ventricular wall tissues on one another). It is unclear whether tissue internal stresses played an important role as well. In our previous microscopy-based flow simulations (Cairelli et al., 2022), we found that there were widely varying fluid WSS characteristics at regions that trabeculated, and the general fluid WSS characteristics at regions that trabeculated did not differ from regions that did not. This suggested that fluid WSS may not be the only stimuli needed for trabeculation. We speculate that ventricular tissue internal stresses are a second stimuli important for this process, and we investigate this here.

In the current study, we firstly investigate whether, and how, embryonic cardiac trabeculation confers biomechanical advantages to the function of the heart and, secondly, test the hypothesis that ventricular tissue internal stresses play a role in trabeculation formation, using a combination of microscopy imaging of zebrafish embryonic hearts, image processing, cardiac finite-element (FE) modelling and experimental data.


Trabeculae enhance deformability of myocardial walls

To determine whether the presence of trabeculae alters the deformational behaviour of the embryonic heart walls, we first perform high-resolution 4D light sheet microscopy imaging of the zebrafish embryonic heart with myocardial tags, using the Tg(cmlc2:GFP) zebrafish transgenic line, between 2 and 3 days post-fertilization (dpf), before and after trabeculation. We performed segmentation and motion tracking of the embryonic heart from images, using a validated cardiac motion estimation algorithm (Wiputra et al., 2020), and calculated 3D strains of myocardial walls using previous methods (Ren et al., 2023; Zheng et al., 2022). Video S1 and Fig. 1A show that satisfactory segmentation and high-fidelity motion tracking are performed.

Details are in the caption following the image
Figure 1. High myocardial strains at the outer curvature zone and at trabeculae
A, microscopy images and 3D anatomical reconstruction of the developing zebrafish embryonic myocardium. Representative segmentation of the ventricle (left) and a single trabecular cluster (right), superimposed on the raw images, at 25%, 50% and 75% of the cardiac cycle. The 3D reconstructed volumes are in red, while the regions of the 3D reconstruction close to the plane of the shown image are plotted in cyan on a single 2D slice extracted from 4D image stacks of a zebrafish embryo from the Tg(cmlc2:GFP) line at 3 dpf. A, atrium; V, ventricle; ITS, intra-trabecular space; T, trabecula. Here, t denotes time, while T denotes cardiac cycle duration. B, 3D reconstruction of a representative zebrafish embryonic ventricle divided into the inner curvature zone (blue) and the outer curvature zone (grey). C, systole–diastole spatially averaged myocardial strain results for the two zones (n = 6 for each developmental stage). The red dashed line separated the pre-trabecular stage, 2 dpf, from the trabecular stage, from 3 dpf on. D, 3D reconstruction of a representative single trabecular cluster taken from the outer curvature zone of the ventricle, where trabeculae are formed. E, myocardial strain results for single trabecular clusters, comparing strains of trabeculae to those of inter-trabecular myocardium. Strains are quantified in the direction of myofibre alignment, and spatially averaged (n = 6 for bar plot). *P < 0.05 between inner curvature and outer curvature zones, and between trabeculae and inter-trabecular myocardium. [Colour figure can be viewed at wileyonlinelibrary.com]

Myocardial strain analysis (MSA) results for the zebrafish embryonic ventricle are shown in Fig. 1. The computed strains are between the end-diastolic and end-systolic time steps, with end-diastole as the zero reference, and are averaged spatially for specific zones. Strain components are quantified in the direction of the lowest eigenvector of the strain tensor, which represents the direction of maximum contraction and is likely close to the myocyte direction.

Results in Fig. 1C show that before and after trabeculation, the deformational characteristics change. In the pre-trabeculated ventricles, fibre direction strain at the inner curvature region is significantly higher than the one at the outer curvature region. In contrast, in the trabeculated ventricles, the opposite occurs, with the outer curvature region showing significantly higher fibre direction strain than inner curvature region. This suggests that the emergence of the trabeculation at the outer curvature region enhances wall strains at that region.

To understand this further, we focus on individual trabeculae and perform more detailed motion tracking and strain calculations (Fig. 1D, E). Results show that trabeculation bundles underwent significantly higher fibre direction contractile strains than their surrounding compact myocardial tissues, for all developmental stages investigated. The 3D reconstruction of the contractile motion of a typical trabecula and its surrounding compact myocardial tissue is demonstrated by Video S2, which clearly shows the trabecula exhibiting higher strain along its alignment direction than surrounding myocardial tissues. We speculate that this could be due to trabeculae having stronger contractile forces, or due to trabeculae experiencing reduced constraints from surrounding tissues, since they are structures protruding from the cardiac wall and have reduced surrounding tissue to constrain their motion. Myocardial tissues are composed mostly of water, so they are likely near to being incompressible, and as such, they need to expand laterally during contraction: having reduced surrounding tissues thus facilitates contractile deformations.

Taken together, our imaging and motion tracking show that the emergence of trabeculation enhanced contractile deformations of the cardiac wall, and that trabeculae exhibited stronger contractile deformations than surrounding tissues. Cardiac trabeculae could thus function to enhance contractile deformation.

Formation of trabeculae coincides with high myocardial tissue internal stresses

Our 4D light sheet microscopy images show visual geometrical changes across developmental stages at the outer curvature zones that suggest cardiac wall stresses are likely to change during the timing when trabeculation forms between 2 and 3 dpf. We assess these geometric changes and perform FE simulations to assess tissue stresses, as shown in Fig. 2.

Details are in the caption following the image
Figure 2. Ventricular geometry and myocardial stress changes during formation of cardiac trabeculae
A, 3D reconstructions of a 2 dpf and a 3 dpf zebrafish embryonic ventricle. Three circumferential planes (black dotted lines) near the middle of the ventricle were used for geodesic curvature evaluation, which are plotted in Fig. 2C. B, myocardial wall geodesic curvature is evaluated from the circumferential mid-wall line (dashed line) for the outer curvature zone (grey). C, spatially averaged circumferential myocardial geodesic curvature at the middle of the outer curvature zone of the ventricle from 2 dpf to 5 dpf (n = 6 for each developmental stage). D, 3D reconstruction of the hearts, boxed area demonstrates the part on the outer curvature region where myocardial thickness is assessed in E. E, estimation of the myocardial thickness at the outer curvature zone of the ventricle from 2 to 5 dpf (n = 6 for each developmental stage). F, colour contour plots of the Cauchy stress magnitude as extracted from the FE simulation at 2 dpf and 3 dpf (pre-trabecular versus trabeculated stages), demonstrating an accumulation of stresses on the myocardial walls at the outer curvature zone at 3 dpf. G, spatially averaged Cauchy stress for 2 dpf (dotted line) and 3 dpf (continuous line) embryos from FE simulations, for the inner curvature zone (blue) and outer curvature zone (grey). H, spatially averaged strains in the fibre direction for 2 dpf (dotted line) and 3 dpf (continuous line) embryos from FE simulations, for the inner curvature zone (blue) and outer curvature zone (grey). *P < 0.05. [Colour figure can be viewed at wileyonlinelibrary.com]

We assess the circumferential geodesic curvature of the ventricle by extracting three cross-sections at the middle 60% of the ventricle at end-systole, obtaining the mid-wall line (in between endo- and epicardial surfaces) of the myocardium on each cross-section, calculating the geodesic curvature of this mid-wall line, and spatially averaging geodesic curvatures for the outer curvature zone, as shown in Fig. 2A, B. Results in Fig. 2C show that there is a substantial increase in the circumferential geodesic curvature at the outer curvature zone from 2 dpf to 3 dpf, from before to after trabeculation, suggesting that the heart becomes more elliptical. In an elliptical pressure vessel, stresses tend to concentrate at the edge with sharper curvature (Utagikar & Naik, 2013), which corresponds to the outer curvature zone.

Further, myocardial wall thicknesses are evaluated from the 3D reconstruction at end-systole at the outer curvature region (indicated by the box in Fig. 2D) and spatially averaged. Results show that the outer curvature region becomes thinner from 2 to 3 dpf (Fig. 2D, E) and continues to become thinner at 4 dpf before thickening again at 5 dpf. The reduction in thickness from 2 to 3 dpf occurs during trabeculation formation, and although trabeculations increase the thickness locally where they are formed, the majority of the myocardial wall is composed of a compact layer only after trabeculation, and these locations experience thinning over the trabeculation development process.

Our geometric characterization thus suggests that stresses likely increase in the outer curvature zone mainly due to a decrease in wall thickness of the outer curvature zone, coupled with an increase in cavity pressure with age (Salehin et al., 2021). The ventricle also adopted a more elliptical shape, which is likely to contribute further to the increased tissue stress at this zone.

To assess ventricular tissue internal stresses, we perform subject-specific microscopy image-based FE simulations, using a model that is previously used to model adult and fetal cardiac biomechanics (Ong et al., 2021). Here, the 3D reconstruction of the ventricle is used for simulations of its contraction biomechanics as explained in the methods section. A transversely isotropic hyperelastic passive stiffness model (where stiffness is higher in the myofibre direction than other directions) and the Guccione active tension generation are specified in the simulations. The spatially varying direction of tension generation is specified as the minimum eigenvector of the 3D strain tensor from motion tracking of microscopy images, as this represents the direction of the greatest shortening and is the likely direction of force generation. A lumped-parameter model is coupled to the FE model to enable realistic pressure and flow rate calculations.

FE-simulated ventricular tissue stress results are shown in Fig. 2F, G. Results show that, from 2 to 3 dpf, as the outer curvature region becomes thinner and more curved, there is an accumulation of tissue stress magnitude (quantified as the L2 norm of the stress tensor) in this region (Fig. 2F). The spatial average of tissue stress magnitude is shown in Fig. 2G, demonstrating that at 2 dpf, the outer curvature region experiences lower stresses than the inner curvature zone, but at 3 dpf, this trend is reversed, and the outer curvature region starts experiencing higher stresses. Myocardial strains from our FE simulations corroborate observations from the image motion tracking discussed above, where the outer curvature region experiences increased fibre direction strains from 2 to 3 dpf, and while it is initially lower than strains at the inner curvature zone at 2 dpf, it becomes higher at 3 dpf (Fig. 2H).

Taken together, our data suggest that changes to cardiac wall geometry and tissue internal stresses occur around the time that trabeculation develops from 2 to 3 dpf, which, as our simulations show, leads to concentration of stresses at the outer curvature region. We hypothesize that the trabeculae are formed to reduce this tissue stress burden.

Trabeculae reduce the overall myocardial tissue stress burden

The 3dpf zebrafish embryonic heart is more curved circumferentially than longitudinally (Fig. 3A). To understand whether tissue stresses in the ventricular walls are aligned in the circumferential or the longitudinal direction, we performed image-based FE simulations of the 3 dpf ventricle during the diastolic passive pressure loading phase. We find that the consequent ventricular tissue stresses are higher in the circumferential direction than in the longitudinal direction (Fig. 3C and I). Interestingly, stresses in the two directions are approximately equal at 2 dpf, suggesting that as the ventricle becomes more elliptical with growth, directionality of stress develops.

Details are in the caption following the image
Figure 3. Cardiac trabeculae reduce overall stress burden on the myocardial walls
A, geodesic curvature of the outer curvature zone is higher in the circumferential direction than the longitudinal direction (n = 3). B, circumferential and longitudinal Cauchy stresses of the 3 dpf ventricle, averaged over the entire ventricle and over the cardiac cycle, from FE simulations, assuming all myofibres are aligned longitudinally (left) or circumferentially (right). Circumferential alignment of myofibres reduces myocardial tissue stresses, suggesting that the circumferential alignment of trabeculations can similarly reduce stresses (n = 3). C, spatially averaged, end-diastolic, whole-heart myocardial tissue stresses in the circumferential and longitudinal directions, from FE simulations, due to diastolic passive pressure loading of the 3 dpf ventricle. Circumferential tissue stresses are higher, suggesting a need for circumferential structural support (n = 3). D, 3D reconstruction of the outer curvature zone of a normal, trabeculated 3 dpf ventricle, and its artificially smoothed-out version with the same myocardial mass, for use in FE simulations. E, colour contour plots of Cauchy stress tensor magnitude of the same ventricles in (D) from FE simulations, from the lateral view. The presence of trabeculae appears to reduce stress concentration on the outer curvature walls (dotted box). F, pressure–volume loops comparing the smooth and trabeculated ventricles for the FE simulations in (E), performed with the same Windkessel circuit. G, spatially averaged Cauchy stresses over cardiac cycle for the FE simulations in (E). H, ratio of temporal peak, spatially averaged Cauchy stress of the smooth model over that of the trabeculated model, for the three 3 dpf ventricles (n = 3). The red dashed line indicates a ratio of 1. Stress burden is higher in smooth models than trabeculated models, confirming the role of trabeculae to reduce the overall tissue stress burden on the myocardial walls. I, top row: spatially averaged Cauchy stress magnitude in the circumferential and longitudinal directions for three embryonic samples at 2 dpf, before the formation of trabeculae. Bottom row: spatially averaged Cauchy stress magnitude in the circumferential and longitudinal directions for three embryonic samples at 3 dpf, after the formation of trabeculae. *P < 0.05. [Colour figure can be viewed at wileyonlinelibrary.com]

In the 3 dpf ventricle, given the typically circumferential direction of the trabeculae, they are ideal structures to provide bracing for the cardiac walls to counter elevated circumferential stresses. We perform further FE simulations to investigate whether a circumferential alignment of myofibres can reduce myocardial tissue stresses, to infer whether the circumferential alignment of trabeculation can reduce stresses as well. We perform simulations on the same ventricles, imposing a fully circumferential alignment of myofibres, and then a full longitudinal alignment of the myofibres. Ventricular tissue stress results in Fig. 3B show that a circumferential alignment of the myofibres allows a reduction of tissue stress in all directions (around 1.5 times for the circumferential stress and around two times for the longitudinal stress) compared with a longitudinal alignment. This shows that by aligning stress-bearing structures and contractile forces in the direction of highest passive stress, the overall myocardial tissue stress can be reduced. As such, by aligning the trabeculae circumferentially, they are in the best alignment to counter high circumferential stresses of the ventricular walls as load-bearing structures and contractile apparatus, to reduce overall myocardial tissue stresses.

To demonstrate that cardiac trabeculae act as structure bridges at high tissue stress locations to reduce stresses, we reperform FE simulations of 3 dpf embryonic hearts after smoothing out trabeculae features on the inner surface, to compare with original FE simulations with intact trabeculae, while maintaining the same myocardial mass for both simulations. FE simulations are run by coupling them to simplified lumped-parameter models (as shown in Fig. 7), using the same parameters for simulations with and without trabeculae. Parameter values are given in Table 2.

Fig. 3D shows a typical model before and after removing trabeculae. Fig. 3E shows the simulation results, demonstrating the presence of high myocardial tissue stresses (L2 norm of the stress tensor) at the outer curvature region, highlighted with the box outline, and demonstrating that in the trabeculated model, high stresses regions are broken up by regions of lower stress. Fig. 3F, G shows the pressure–volume (PV) loops from the simulations, as well as stress magnitudes, spatially averaged over the ventricle, over a cardiac cycle. In these simulations, the use of a lumped-parameter model allows modelling of ventricular–vascular coupling. From this, we observed a PV loop (Fig. 3F) that has substantial similarity with previous experimental measurements (Salehin et al., 2021), although there are minor features, such as a transient negative pressure during early diastole that is not captured by our simulation. Results in Fig. 3G show that the trabeculated model has lower ventricular tissue stresses than the smooth model at peak systole. In Fig. 3G, statistical testing shows that the ratio of peak systolic stress in smooth versus trabeculated models is significantly greater than one.

To ensure that our simulation conclusions are robust, we further perform simulations where the volume of the ventricle is prescribed by the volume measured from microscopy images across the cardiac cycle, instead of being calculated via the lumped-parameter model (Fig. 7). We similarly observed that stresses are higher in the myocardium of the smooth model compared with the trabeculated model, whether or not we adjusted to contractility to match the peak systolic pressure of the two models. This demonstrates that trabeculae reduce ventricular tissue stresses and can do so without sacrificing stroke volume and pressure generation cardiac functions.

Taken together, our results support our hypothesis that trabeculae morphology is optimized for structural support and to reduce the stresses of the ventricular tissues at the outer curvature region of the ventricle, to counter a concentration of high stress there.

High cardiac wall stress rescues disrupted trabeculation formation in Gata1 morpholino-treated zebrafish embryonic hearts

To investigate the hypothesis that cardiac tissue stresses are important stimuli for trabeculation formation, we study gata1 morphant zebrafish embryos, which feature disrupted trabecular development (Galloway et al., 2005). In this model, injected morpholino oligos are used to inhibit the formation of red blood cells, resulting in a blood composition of almost entirely plasma. This is likely to reduce blood viscosity by 4.9 times, as previous experimental measurements approximated zebrafish whole-blood viscosity to be 7.35 cP (Lee et al., 2017) with the corresponding blood plasma viscosity 1.5 cP, and thus the pressure required for cardiac fluid pumping will be similarly reduced. The reduction in ventricular pressure will subsequently reduce distention of the ventricle and reduce ventricular tissue tensile stresses. Previous investigators also anticipated that the lack of blood particles in blood will decrease fluid wall shear stresses imposed on the endocardial surface (Lee et al., 2018; Vedula et al., 2017). Likely consequent to these biomechanical disruptions, the gata1 morphants develop a ventricular surface that is much smoother than the wild-type zebrafish, with drastically reduced trabecular structures (Lee et al., 2018; Vedula et al., 2017).

To test whether increased ventricular tissue stresses can rescue trabeculation formation, gata1 morphants were treated with vasopressin, a potent vasoconstrictor (Ahuja et al., 2022) for 3 days starting at 1 dpf until 4 dpf. Previous measurements show that this treatment reduces zebrafish embryonic vascular dimensions, which should lead to elevated peripheral blood flow resistance and cardiac afterload, without reducing cardiac output (Ahuja et al., 2022). This will increase the pressures needed to drive circulation and elevate cardiac pressures, leading to increased distention of the ventricle, and thus increase ventricular tissue stresses.

At 4 dpf, the trabeculation morphology for the gata1 morphants, vasopressin-treated gata1 morphants, and non-morphant controls, which are all generated from the myocardial tagged line Tg(cmlc2:GFP), are investigated via 3D confocal microscopy. Results in Fig. 4A show that gata1 morphants have myocardium that is significantly smoother on the inner surfaces, but with the vasopressin treatment, the myocardium restores its complex undulating inner surface. The amount of trabecular layer tissue is estimated by manual segmentation of the entire myocardium as well as just the compact myocardium (Fig. 4B), followed by 3D reconstruction and volume estimation as previously described (Lee et al., 2016). The quantification of volume of trabeculation tissue is done by subtraction of the two abovementioned volumes. Results in Fig. 4C show a significantly reduced trabecular layer tissue volume in gata1 morphants, but with vasopressin, the amount of trabecular layer tissue volume restores close to that of controls and is significantly different from gata1 morphants.

Details are in the caption following the image
Figure 4. Vasopressin treatment can rescue disruption to trabeculae formation in gata1MO
A, representative microscopic images of 4 dpf control zebrafish embryo, gata1 morphant and vasopressin-treated gata1 morphant. Cardiac trabeculae are reduced in the gata1MO but are rescued after vasopressin treatment. B, demonstration of delineation of the compact layer (red) and trabecular layer (green) used for quantification in (C). C, manual quantification of 3D trabecular and compact myocardium volumes for control, gata1MO and vasopressin-treated gata1MO (n = 10). D, servo-null measurements of peak intraventricular pressures of controls, gata1 morphants and vasopressin-treated gata1 morphants at 4 dpf (n = 12, three measurements for each of four embryos per group). E, pressure–volume loops of the trabeculated 3 dpf ventricle from FE simulations assuming control group pressure compared with FE simulations assuming gata1MO pressure and gata1MO with vasopressin treatment pressure. Simulations are performed with a Windkessel circuit, resistance components of the circuit for the gata1MO simulation are scaled down by the ratio of peak pressure between controls and gata1MO from (D), while compliance components are scaled up by the same, so that peak pressure from simulations will match values in (D). Analogous for the gata1MO with vasopressin. F, spatially averaged Cauchy stress tensor magnitude over time for simulations in (E). *P < 0.05. [Colour figure can be viewed at wileyonlinelibrary.com]

To validate that intraventricular pressures were altered in gata1 morphants and with vasopressin treatment, we perform direct pressure measurements using a servo-null system as previously described (Salehin et al., 2021). Results in Fig. 4D confirm that gata1 morphants exhibit significantly lower peak ventricular pressures compared with healthy control embryonic hearts, the addition of vasopressin significantly increases peak ventricular pressures from gata1 morphants. To confirm that lower pressure in gata1 morphants is also leading lower myocardial tissue stresses, additional FE simulations are performed. In this case, the Windkessel resistances are scaled based on the ratio in peak pressure between controls and gata1 morphants (a 1.6× difference) with minor tuning to adjust the shape of the PV loop. The same pressure scaling is done between controls and gata1 morphants with vasopressin treatment, with a 1.2× ratio of pressures. The results in Fig. 4E, F confirmed that myocardial tissue stresses are reduced in gata1 morphants compared with controls, consequent to the lower ventricular blood pressures.

Taken together, our data show that tissue stresses in the ventricular wall are important stimuli for trabeculation formation, given that reduced stresses in gata1 morphants prevents the formation, and the subsequently increased tissue stresses via vasopressin treatment rescues the formation, and given that fluid wall shear stresses cannot account for these observations.

Trabeculation formation leads to spatial homogenization of ventricular wall stiffnesses

Given the stress-driven nature of the formation of the trabeculae and the trabeculae's ability to enhance the tissue deformability and reduce tissue stress, we investigate whether their presence influences the overall stiffness of the myocardial wall. To do this, we perform passive pressurizations of zebrafish embryonic hearts paired with subject-specific image-based FE modelling of the pressurization process, to determine the spatial variation of tissue stiffness.

Passive pressurization is achieved by stopping the heartbeat with 2,3-butanedione monoxime (BDM) and pushing fluid into the embryonic atria via a micropipette equipped with pressure control, as previously described (Gendernalik et al., 2021). 3D microscopy imaging and pressure measurements are concurrently performed during the pressurization and are later used in the FE modelling of the pressurization process. The same images from the pressurization experiments are used to estimate actual myocardial strains using the MSA technique described above. In the FE simulations, pressure-induced stretch with no active tension is modelled, using the assumption of a spatially uniform passive stiffness material property. Comparing longitudinal–circumferential areal stretch deformations from the FE results and image MSA, the regions where MSA stretch are lower than the FE stretch are where the stiffness are underestimated in the simulations, while regions with MSA stretch higher than the FE stretch are regions where stiffness is overestimated in the simulation. This thus enables an evaluation of the spatial variability of tissue stiffness.

Results of this analysis are presented in Fig. 5 and Table 1. The healthy control ventricles at 2 dpf, before trabeculation, consistently demonstrate clear bands of stiffness inhomogeneity, while in control ventricles at 3 dpf, these bands can no longer be clearly observed, suggesting a spatial stiffness homogeneity. Interestingly, in the gata1 morphants at 3 dpf, where trabeculation formation is disrupted, substantial spatial inhomogeneity and bands of stiffness differences can still be observed in two out of three samples examined. The results thus suggest that the formation of the trabeculations causes a spatial homogeneity of ventricular wall stiffness, while a disruption of the trabeculations formation process prevents this homogeneity. We thus speculate that a further function of the cardiac trabeculae is to achieve a spatial homogeneity of biomechanical behaviours.

Details are in the caption following the image
Figure 5. Cardiac trabeculae help ensure spatial homogenization of the ventricular wall stiffness
Areal stretch difference contour plots for 2 dpf normal embryonic ventricle, a 3 dpf normal embryonic ventricle and a 3 dpf gata1MO embryonic ventricle. In the normal ventricle, bands of different stiffnesses are visible at 2 dpf, but disappear after the formation of cardiac trabeculae at 3 dpf. In the GataMO ventricles, where trabeculation formation is disrupted, bands of different stiffness are still present. [Colour figure can be viewed at wileyonlinelibrary.com]
Table 1. The formation of trabeculae homogenizes the ventricular wall stiffness. Spatial standard deviation of the ventricular wall areal stretch difference (indicating ventricular wall stiffness) for controls, gata1MO and vasopressin-treated gata1MO groups (n = 4 each)
SD 2 dpf control SD 3 dpf control SD 2 dpf GataMO
0.093 0.060 0.173
0.083 0.075 0.084
0.101 0.054 0.063
0.103 0.061 0.096


In the current study, we find that ventricular tissue biomechanics is in fact an important aspect of embryonic heart trabeculation function and an important stimulus for trabeculation formation. Our results suggest three functions for trabeculations. First, they enhance tissue deformability to facilitate cardiac pumping actions; second, they counter high myocardial tissue stresses with active tension and reduce myocardial tissue stresses as structural support; and third, they reduce spatial inhomogeneity of tissue stiffness.

Our strain measurement results agrees well with the literature. Our observation that the embryonic heart deforms more in the circumferential direction than in the longitudinal direction corroborated with observations of the same in a recent earlier study by Salehin et al. (2022). Further, in both our strain measurements from image tracking (Fig. 1C) and strain results from FE simulations (Fig. 2H), the outer curvature region of the ventricle is more deformable after trabeculae formation. Our results corroborated a previous study by Teranikar et al. (2021) on myocardial areal stretch obtained from tracking of cardiomyocyte nuclei, which similarly found that the areal stretch of the outer curvature region is higher than that of the inner curvature region, and which found that the observation is consistently observed across developmental stages between 2 and 5 dpf, and despite increasing contractility with age (Teranikar, 2021). A further recent study by Priya et al. (2020) on the initial phases of trabeculation formation showed that cardiomyocytes with greater contractility delaminate from the compact layer and seed the trabecular layer, while less contractile ones stay in the compact layer. This suggests that trabecular myocytes will be more contractile and corroborates our observation that trabecular bundles undergo greater contractile strains than their surrounding compact myocardium (Fig. 1E).

In our strain measurements, we observe enhanced deformability of the trabeculate zone in both the longitudinal and circumferential directions. In the circumferential direction, this enhancement is likely due to the ability of trabeculae bundles to undergo larger contractions than the surrounding compact layer (Fig. 1E), as most trabeculae bundles are aligned circumferentially. As for the enhanced strain in the longitudinal direction, this is likely unrelated to contractile forces, but due to the thinning of the compact layer at the trabeculated regions and the consequently reduced passive stiffness of the corrugated surface structure after trabeculation formation, which thus enables larger longitudinal stretch in these trabeculated regions.

Our results further suggest that between 2 and 3 dpf, during trabeculation formation, there are thickness changes to the outer curvature of the ventricle and an overall change of ventricular shape to be elliptical, that leads to stress concentration in the outer curvature region, and that cardiac trabeculae formation can mitigate the high stresses, suggesting this mitigation as one of their functions. Our simulations also show that the circumferential orientation of the trabeculae has useful effects of countering high circumferential stresses and has an overall stress reduction effect in the myocardium. The morphology of the trabeculae is akin to that of a linear bracing beam bridging across a curved structural surface, the compact myocardium, to support the curved surface, which is a common structural engineering strategy. This can explain the wall stress differences between the trabeculated and smooth FE models (Fig. 2F, G), and makes it logical to assume that the trabeculae have structural load-bearing roles. Our results in Fig. 3B corroborated this notion, by showing that the typically circumferential alignment of structural fibres can lead to a reduction of overall myocardial stresses, consequent to the geometry of the heart, which is more curved circumferentially than longitudinally, suggesting that the typically circumferential alignment of trabeculae can reduce myocardial stresses. Previous studies by Priya et al. (2020) showed that the initiation of trabeculation formation relied on a spatial heterogeneity of tissue tension. It is thus likely that trabeculations modulate stresses where they are formed (Fig. 2F) and for their formation to bring about a smoothening of spatial inhomogeneity of wall tissue stiffness as observed in our study (Fig. 5B).

It should be clarified that although trabeculations form at 3 dpf, and our results show that trabeculations reduce outer curvature tissue stresses, this does not mean that tissue stresses will be lower at 3 dpf than 2 dpf. Rather, our results show that there is an increase in stresses from 2 dpf to the trabeculated 3 dpf ventricle, but without the trabeculation (smoothed ventricle) at 3 dpf, tissue stresses will be even higher.

Our results, however, do not suggest that the presence or absence of the trabeculation cause a catastrophic reduction in cardiac function, in terms of stroke volume or pressure generation (Fig. 3F), to be able to explain embryonic lethality in animal models with trabeculation defects. Rather, they suggest that both the trabeculated and non-trabeculated hearts are viable pumps capable of sustaining systemic perfusion needs. As such, inadequate biomechanical function is most likely not the reason for the abovementioned embryonic lethality associated with defective trabeculation formation.

One important issue that our study addresses is the relative role of fluid wall shear stresses induced by fluid drag forces on the endothelial walls and that of ventricular internal tissue tensile and compressive stresses. Many past mechanobiological studies on zebrafish embryos concluded that reduced flow wall shear stress stimuli is the cause of a disrupted trabeculation process (Boselli et al., 2015; Cavallero et al., 2021; Foo et al., 2021; Granados-Riveron & Brook, 2012; Hove et al., 2003; Lee et al., 2018; Vedula et al., 2017). However, in these scenarios in past studies, the intervention to reduce flow stimuli were likely to have also diminished ventricular pressure and myocardial tissue stresses, and it is not possible to determine the relative importance of the two types of biomechanical stimuli in causing disrupted trabeculation from these past data. For example, the use of BDM or blebbistatin to inhibit cardiac contractions or the use of the weak atrium mutant (wea) will lead to reduced ventricular blood flow, but it will also reduce ventricular pressure and tissue stresses (Foo et al., 2021; Lee et al., 2016), and it is difficult to decouple the effects of flow stimuli and wall stress stimuli. In our gata1-vasopressin model, the tissue stresses are altered between the gata1 morphant before and after vasopressin without significant changes to flow rates, thus enabling a better controlled experiment to determine whether ventricular tissue stresses are important for trabeculation. Our vasopressin rescue experiment shows that high tissue stresses can rescue disrupted trabeculation formations and that tissue stresses are indeed important biomechanical stimuli for trabeculation formation (Fig. 4A). Our results, however, do not indicate the unimportance of fluid wall shear stresses, and we speculate that both fluid wall shear stresses and ventricular tissue stresses are essential stimuli for proper trabeculation formation.

As FE models are not often applied to embryonic hearts, we briefly explain its assumptions and limitations. Our FE computational model uses previously established methodologies (Lashkarinia et al., 2023; Shavik et al., 2020), which utilizes previously established tissue mechanics theories and computational methods explained in these previous publications. It assumes that the myocardium has a stiffness model that is transversely isotropic and hyperelastic (Guccione et al., 1991), and that at any myocardial location there is a direction of higher stiffness that corresponds to the myofibre orientation and the direction of maximum shortening. We have further assumed that the myocardium follows the same active tension generation cycle as those observed in canine experiments (Guccione et al., 1993), but with a much smaller magnitude, tuned to fit pressures relevant to zebrafish embryos. The limitation of the modelling is that it is constructed based on theories and measurements from myocardial tissues of other animals, rather than directly from the zebrafish embryo, which might lead to deviations. Further, although the resulting PV loop has reasonable similarity to measured P–V loops (Salehin et al., 2021), it does not capture a transient early dip in diastole pressure to be negative, which is a limitation, but our conclusion of myocardial stress with regards to trabeculations are made based on simulation results during systole, rather than diastole, and will not be affected.

In conclusion, our results suggest that cardiac trabeculae are formed only on the outer curvature of the ventricle as a reaction to the reduced thickness and increased geodesic curvature of the outer curvature walls on the endocardial side. These geometrical changes induce higher tissue stress areas on the outer curvature, so once formed, the role of the trabeculae is to bridge across these areas and reduce the stress burden while retaining the same cardiac function. Our studies also showed that trabeculae formation enabled better deformability, likely enhancing cardiac function, and homogenizes spatial variability of ventricular wall stiffnesses. We also showed that high ventricular tissue stress is important to trabeculae formation via a rescue experiment.


Ethical approval

Ethical approval for experiments was provided by the Institutional Animal Care and Use Committee at Washington University in St. Louis and the UT Arlington Institutional Animal Care and Use Committee guidelines (IACUC protocols A17.014 and A17.016, respectively). Experiments were carried out according to guidelines laid down by the IACUC, and conform to Grundy (2015). All animals have ample access to food, water and housing.

Zebrafish line and imaging

The zebrafish embryos used in this study were from the Tg(cmlc2:GFP) line at 2, 3, 4, and 5 dpf, in which the targeted GFP is expressed in the myocardial cells allowing for a clear imaging of the zebrafish embryonic myocardium. All embryos used were bred in the animal care facility, and maintained at 28°C. A solution of 0.003% W/V of phenylthiourea in E3 medium was added around 24 h post-fertilization to inhibit pigment formation (Salehin et al., 2021).

The samples used for the research were imaged in the two different facilities abovementioned, using two different microscopes. In the first, at UT Arlington, the embryos were anaesthetized in 0.05% tricaine given to the media and immersed in 0.5% low melting point agarose. Before the agarose solidified, the embryos were transferred to a fluorinated ethylene propylene tube and vertically mounted on a stage such that the heart was aligned to the imaging light path. Images of the beating zebrafish hearts were acquired using a modified version of SPIM (Huisken & Stainier, 2009; Lee et al., 2016), as described previously (Salehin et al., 2021). GFP excitation was provided by a 473 nm laser and a 20× water dipping objective with a high numerical aperture (NA = 0.5) was used to eliminate spherical aberrations by minimizing refractive index mismatch. The sample was moved along the detection axis while image sequences were captured from the rostral to the caudal end. A Hamamatsu ORCA Flash 4.0 sCMOS camera was used to record 150−280 overlapping z-slices with a 10 ms exposure time, and each sequence consisted of 300 frames (512 × 512 pixels). 4D images were reconstructed by post-acquisition synchronization (Liebling et al., 2005). Tricaine overdose (2%) was used to kill the animals.

In the second facility, at Washington University in St. Louis, embryos were embedded in 1% low-melt agarose by aspiration into a glass capillary. The glass capillary with zebrafish embryo was loaded into the microscope (Zeiss Lightsheet 7) sample chamber, containing E3 media maintained at 28.5°C. The hardened agarose gel cylinder was extruded into the sample chamber and manoeuvred into the light-sheet plane until the fluorescent heart myocardium was visible. Image planes were selected and imaged sequentially for the entire volume of the heart using a water immersion 20× objective. At each plane, 500 frames were acquired at an exposure time of 7.5 ms and resolution of 0.23 μm2/pixel at 2 μm z-spacing by a pcoO.edge sCMOS camera (1920 × 1920 pixels, pixel size 6.5 μm × 6.5 μm). The actual framerate was 40 ms due to camera readout rate. 4D images were reconstructed by post-acquisition synchronization (Liebling et al., 2005). Embryos were not anaesthetized to avoid the anaesthetic agent affecting heart function, but environmental conditions were controlled to minimize discomfort. Tricaine overdose (0.5 mg/ml) or hypothermia (20 min in 0°C water) were used to kill them.

3D reconstruction and motion tracking

Segmentations of the whole 3D ventricular chambers were conducted with previously described methods (Wiputra et al., 2016), via a semi-automatic slice-by-slice approach using a custom-written lazy-snapping algorithm for pixel classification followed by Vascular Modelling ToolKit (www.vmtk.org) for surface reconstruction. The models were trimmed, smoothed and prepared using Geomagic Wrap (Geomagic Inc., USA) for the FE simulations. Care was taken not to smooth out the finer details of the trabecular layer of the myocardium. Next, cardiac motion tracking was performed using a well-validated cardiac motion estimation algorithm from our previous work (Wiputra et al., 2020). Segmentation was conducted only at one time point, and the reconstructed geometry could be animated to all other time points with the motion field. This motion extraction algorithm involved iterative curve-fitting of a global motion model, the spatial B-splines of temporal Fourier function, onto pair-wise image registration of all consecutive pairs of time points. As Supplementary video 1 can show, motion tracking enabled high-fidelity tracking of myocardial boundary motions.

Myocardial strain analysis

As our algorithm could track image features and not just cardiac structure boundaries, the tracking results could be used for computation of strains, by first computing the 3D deformational gradient tensor using spatial gradients of displacements, before computing the Green–Lagrange strain tensor according to the finite strain theory (Ren et al., 2023; Zheng et al., 2022). We have previously used the algorithm for strain calculations in microscopy and clinical cardiac images (Lashkarinia et al., 2023; Ren et al., 2023; Zheng et al., 2022). The reconstructed end-diastolic models were meshed using ANSYS and converted into a finely detailed volume mesh and strains were evaluated at the nodes of this mesh, as a means of evaluating strains at evenly distributed locations.

Direction conventions are demonstrated in Fig. 6. Spatially varying radial, circumferential and longitudinal directions were calculated according to previous methods (Zou et al., 2020). At any point in the myocardium, the radial directions were taken as the direction of temperature gradients in a heat transfer simulation from the endocardium to epicardium, the circumferential direction was taken as the cross product of a pre-defined longitudinal axis with the radial direction, while the longitudinal direction was the cross product of radial and circumferential directions. Components of the strain tensors in specific directions were then obtained via projection to those directions.

Details are in the caption following the image
Figure 6. Orthogonal axes for the 3D strain analysis
3D reconstruction of the ventricular myocardium with atrioventricular channel (AVC) and outflow tract (OFT) labelled. Computed circumferential (red), longitudinal (blue) and radial (green) directions are plotted on the ventricle. [Colour figure can be viewed at wileyonlinelibrary.com]

The minimum eigenvector of the strain tensor was computed to obtain the directions of maximum contraction, to inform the direction of contraction in our FE model. This approach was previously used as an approximation of the myocardial fibre direction (Pedrizzetti et al., 2014). To divide the embryonic ventricle into the outer and inner curvature regions, the ventricle was manually and equally divided into two with a slicing plane approximately perpendicular to the atrioventricular inflow direction. n = 6 for all groups (2, 3, 4 and 5 dpf).

Geodesic curvature calculation

The 3D reconstruction of the outer curvature of the ventricles was sliced in the circumferential and longitudinal directions. The mid-wall line in between endocardial and epicardial boundaries was extracted and discretized into 100 points. The geodesic curvature of the line at any point was calculated (n = 3) as:
κ i = d T d s = 1 2 T i + 1 T i α i + 1 α i + T i T i 1 α i α i 1 $$\begin{equation}{\mathrm{\;}}{\kappa _i} = \left\|\frac{{dT}}{{ds}}\right\| = \frac{1}{2}{\mathrm{\;}}\left( {\frac{{\|{T_{i + 1}} - {T_i}\|}}{{\|{\alpha _{i + 1}} - {\alpha _i}\|}} + \frac{{\|{T_i} - {T_{i - 1}}\|}}{{\|{\alpha _i} - {\alpha _{i - 1}}\|}}} \right)\end{equation}$$ (1)
where α i ${\alpha _i}$ was the coordinate of the i-th point on the line, s was the distance along the line and T i ${T_i}$ was the tangent vector at the i-th point.

Finite element analysis

The mechanical model and FE modelling of the zebrafish embryonic ventricle was adapted from previous work (Lashkarinia et al., 2023) and was performed using the open-source library FEniCS (https://fenicsproject.org/). The source code is available at https://github.com/WeiXuanChan/heartFEM. In this FE model, the ventricular stress was modelled as passive stiffness stress and active tension stress.

Ventricular tissue passive stiffness was modelled using a Fung-type transversely isotropic hyperelastic constitutive model (strain energy function) (Guccione et al., 1991):
W = 1 2 C e Q 1 $$\begin{equation}W{\mathrm{\;}} = {\mathrm{\;}}\frac{1}{2}C\left( {{e^Q} - 1} \right)\end{equation}$$ (2)
W = 1 2 C ( e b f f E f f 2 + b x x E s s 2 + E n n 2 + E s n 2 + E n s 2 + b f x E f n 2 + E n f 2 + E f s 2 + E s f 2 1 ) $$\begin{eqnarray}W &=& \frac{1}{2}C\big( {{e^{{b_{ff}}E_{ff}^2 + {b_{xx}}\left( {E_{ss}^2 + E_{nn}^2 + E_{sn}^2 + E_{ns}^2} \right) + {b_{fx}}\left( {E_{fn}^2 + E_{nf}^2 + E_{fs}^2 + E_{sf}^2} \right)}}}\nonumber\\ && - 1 \big)\end{eqnarray}$$ (3)
where E is the Green–Lagrange strain tensor with subscripts f, s and n represent myocardial fibre, sheet and sheet normal orientations. We used b f f ${b_{ff}}$ , b x x ${b_{xx}}$ and b f x ${b_{fx}}$ values as reported by (Ong et al., 2021) for eqn (3), but for C, we used 2 J/ml for 2 dpf and 5 J/ml for 3 dpf. For the zebrafish embryonic ventricle, the fibre direction was taken to be the direction of the minimum eigenvector of the strain tensor, which is the direction of maximum contraction, in accordance with previous studies (Pedrizzetti et al., 2014). The sheet normal direction was taken to be the radial direction.
The active stress (Pact) was prescribed to act in the local fibre direction using the Guccione active contraction model (Guccione et al., 1993). This is a calcium activation model that describes the sigmoidal relationship of chemical activation and tension of the cardiac muscle:
P a c t = T 0 L V C a 0 2 C a 0 2 + E C a 50 2 C t $$\begin{equation}{\mathrm{\;}}{P_{act}} = {\mathrm{\;}}{T_{0LV}}\frac{{Ca_0^2}}{{Ca_0^2 + {\mathrm{\;}}ECa_{50}^2}}{C_t}\end{equation}$$ (4)
where T0LV is the maximum tension, C a 0 2 $Ca_0^2$ (peak calcium concentration), E C a 50 2 $ECa_{50}^2$ (calcium sensitivity dependent in the sarcomere length) and C t ${C_t}$ (temporal variation) describe the calcium activation behaviour.
C t = 1 2 1 cos ω $$\begin{equation}{\mathrm{\;}}{C_t} = {\mathrm{\;}}\frac{1}{2}\left( {1 - {\mathrm{\;}}\cos \omega } \right)\end{equation}$$ (5)
ω is dependent on the cycle time:
ω = π t t 0 w h e n 0 t < t 0 π t t 0 + t r t r w h e n t 0 t < t 0 + t r 0 w h e n t 0 + t r t $$\begin{equation}\omega {\mathrm{\;}} = {\mathrm{\;}}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\pi \frac{t}{{{t_0}}}\;when\;0 \le t &lt; {t_0}}\\ {\pi \frac{{t - {t_0} + {t_r}}}{{{t_r}}}\;when\;{t_0} \le t &lt; {t_0} + {t_r}}\\ {0\;when\;{t_0} + {t_r} \le t} \end{array} } \right.\end{equation}$$ (6)
where t0 is the time to peak tension (amount of time that it takes for the myofibres to contract) and t r ${t_r}$ is the relaxation time, calculated as:
t r = m l + b $$\begin{equation}{\mathrm{\;}}{t_r} = {\mathrm{\;}}ml + b\end{equation}$$ (7)
where m $m\;$ is the gradient of linear relaxation duration with sarcomere length relation, b is the time intercept of linear relaxation duration with sarcomere length, and l $l\;$ is the sarcomere length, dependent on the degree of myocyte stretch.

The input geometry for the FE was taken slightly before the end-diastolic phase and from there, the zero-pressure unloaded state of the zebrafish embryonic ventricle was calculated using a backward displacement method (Finsberg et al., 2018), based on a specified end-diastolic pressure and myocardium stiffness. In essence, an initial guess of the pressure at the starting input geometry was made, and this pressure value was iteratively adjusted trying to match the end-diastolic pressure of the ventricle after pressure loading it to the end-diastolic volume. After that, an inverse displacement was applied to the starting input geometry, reducing the ventricle pressure to zero to obtain the estimated unloaded geometry. All the zebrafish embryonic ventricular models were meshed with a minimum of 5000 quadratic tetrahedral elements, surpassing the previous mesh convergence study (Ong et al., 2021), in order to retained as many details of the cardiac trabeculae as possible. The FE simulation was performed using FEniCS, minimizing the Lagrangian cost function detailed by Shavik et al. (2018). Boundary conditions were weak springs (spring constant = 90 Pa) over the entire epicardial surface emulating the effect of the tissues surrounding the heart, and a constraint at the atrio-ventricular channel in the circumferential direction but not in other directions.

During the simulations, parameters were adjusted until a reasonable match with experimental and literature measurements of the end-diastolic pressure, peak systolic pressure and general shape of the PV loops was achieved (Salehin et al., 2021). Specifically, the strain energy function coefficient C eqn (2)−(3), as there are no data available on the stiffness of the zebrafish embryonic ventricle), the time to peak tension t0 (eqn (6)), the relaxation time t r ${t_r}$ (eqn (7)) and the maximum tension T0LV (eqn (4)) were adjusted. C was increased where simulated ventricular pressure was too low, t0 was elevated where the P–V loop did not skew sufficiently to the left, while t r ${t_r}$ was reduced if the end-systolic pressure decreased too slowly. A simplified Windkessel model, as shown in Fig. 7, was also adopted to model the resistances of flow into and out of the zebrafish embryonic ventricle and pressure dynamics with outflow but was not intended to model other details of the embryonic circulation. This allowed to model systemic flow resistances and compliances to aid realistic pressure and flow rate calculations. The different sets of resistance and compliance in the simplified Windkessel lumped-parameter model were tuned to achieve the expected peak systolic pressures from the literature (Salehin et al., 2021) using the stroke volume as imaged, by scaling all resistance and compliance until a match was obtained. The resistance scaling was increased when systemic pressure was too low, while compliance was increased when aortic pulse pressure was too low. The FE and Windkessel parameters that enabled a good match are given in Table 2.

Details are in the caption following the image
Figure 7. Simplified Windkessel circuit used in the FE simulations
V is the volume, P is the pressure, R is the resistance, C is the compliance, q is the flow. PER stands for peripheral, AO stands for aortic, VEN stands for venous, MV stands for mitral valve, LA stands for left atrium, LV stands for left ventricle. [Colour figure can be viewed at wileyonlinelibrary.com]
Table 2. Modelling parameters for the finite element simulations. The parameters shown were either taken from the literature or tuned until a good match between simulated and experimental PV loops was reached
2 dpf 3 dpf
Cardiac cycle length (ms) 700 550
Time to peak tension (ms) 220 175
Active tension force (Pa) 4000 7500
End-diastolic pressure (mmHg) 1.36 1.36
Strain energy function coefficient (Pa) 2000 5000
Aortic valve resistance (mmHg s ml−1) 0.7118
Peripheral resistance (mmHg s ml−1) 4.5
Venous resistance (mmHg s ml−1) 0.005
Mitral valve resistance (mmHg s ml−1) 0.0101
Aortic compliance (ml/mmHg) 0.0117
Venous compliance (ml/mmHg) 3.5948
Left atrium compliance (ml/mmHg) 0.0018

The zebrafish embryonic ventricular pressure was solved via the coupled FE and lumped-parameter model at each time step over 20 cardiac cycles, and results in the last cycle were used (approach 1). In addition, we performed FE simulations without the lumped-parameter, prescribing the ventricular volume over time waveform as obtained from microscopy images, as a means of obtaining simulated volume over time waveforms that were closer to those from images (approach 2). In both approaches the same FE parameters as shown in Table 2 were used. Results for approach 1 are given in Figs 2 and 3, while results for approach 2 are given in Fig. 8A. With approach 2, in the comparison of smoothed, non-trabeculated models to the original trabeculated models, systolic pressures were higher for the smooth models, and it was difficult to judge whether the reduced stresses in trabeculated models were due to the presence of trabeculation structures or lower systolic pressure. As such, a third approach was adopted, where the active tension of the smooth models was reduced to ensure that smoothed and trabeculated models had the same peak systolic pressure. Results for approach 3 are given in Fig. 8B; n = 3 for all approaches.

Details are in the caption following the image
Figure 8. Cardiac trabeculae reduce the overall tissue stress burden on the myocardial walls
A, top row: pressure–volume loops comparing the smooth and trabeculated ventricular models from FE simulations performed using approach 1 (volume constraint FE) with the same simulation parameters for both models. Bottom row: spatially averaged Cauchy stress magnitude over time. Each column represents an embryonic sample. B, top row: pressure–volume loops comparing the smooth and trabeculated ventricular models from FE simulations performed using approach 2 (volume constraint FE) with the maximum tension reduced to match the peak pressure in both trabeculated and smooth models. Bottom row: spatially averaged Cauchy stress magnitude over time. Each column represents an embryonic sample.

Gene knockdown by morpholinos

The sequence 5’-CTGCAAGTGTAGTATTGAAGATGTC-3’ (Gene Tools) was used for the Gata1 morpholino, that was prepared for injection by dissolving in nuclease-free water at 1 mm. One nanolitre MO solution was injected into the yolk adjacent to the cells at the one to four-cell stage. Gata1 phenotype was confirmed by observing the dorsal aorta for flowing red blood cells after 24 h post-fertilization.

Vasopressin rescue experiment

Vasopressin (Arginine-Vasopressin Acetate Salt, Sigma, V9879) was dissolved to a concentration of 10 μM in E3 medium (5 mM NaCl, 0.17 mm KCl, 0.33 mm CaCl2, 0.33 mm MgSO4, and 0.1% Methylene Blue) and 0.003% PTU to inhibit pigmentation. Gata1 MO injected embryos were dechorionated and incubated in vasopressin solution beginning at 24 h post-fertilization with replenishment every 24 h until 4 dpf.

Intraventricular pressure measurements

Intraventricular pressure measurements were performed at UT Arlington. Four embryos for each group (control, gataMO and gataMO with vasopressin treatment) at 4 dpf were anaesthetized in 0.05% tricaine and placed in an agaraose-filled petri dish with customized depressions in the agarose to assist in stabilizing the embryo. Intraventricular pressure of zebrafish embryos was measured using a 900A servo-null micro-pressure system (World Precision Instruments). Three measurements were made for each embryo, making n = 12. The initial input vacuum and pressure values were given in the 900A Pressure Pod, a part of the 900A Micropressure System, and were delivered and controlled by PV820. The tip's diameter of about 2–5 μm permitted it to inject into the zebrafish's heart without causing any significant damage. The calibration step was crucial for generating an accurate pressure signal before measuring the target sample. A glass electrode (created with WIP's Pul-1000 Four-Step Micropipette Puller) with a tip diameter of 2–5 μm was made of borosilicate glass, filled with 1 m NaCl, and then its tip was put into the ventricle. Changes in ventricular pressure are related to a change in electrical resistance at the micropipette's tip, which is counterbalanced by the system's compensatory positive or negative pressure. Data were recorded at 200 samples/s and put through an IIR Butterworth filter with a cut-off frequency calculated from spectral analysis to remove high-frequency noise. A MATLAB (MathWorks) algorithm was used to filter the recorded analogue signals.

Cannulation and passive pressurization of embryonic hearts

Passive pressurization experiments were performed at Washington University in St. Louis (n = 4 for each of three groups, 2 dpf control, 3 dpf control and 3 dpf gataMO). The atrium was chosen as the point of cannulation as it was more easily accessible, and we needed to avoid damage to the ventricle. Pressure equilibrium could be achieved between the atrium and the ventricle due to the proximity, as explained below.

Embryos were prepared as follows. Dechorionated embryos were incubated in a 35 mm BDM solution in E3 to halt heart contractions, which were monitored until cessation. Embryos were then further incubated for approximately 20 min to allow for full sarcomere relaxation. Embryos were mounted on a microscope slide within a silicone well. A drop of 1% low-melt agarose in E3 and 35 mm BDM was deposited in the silicone well and embryos were embedded and positioned such that the cannula approached the embryo at a 90° angle. Additionally, embryos were positioned as close to the gel surface as possible to minimize cannula travel through the gel and limit light refraction. A slide with a mounted embryo was inserted into a temperature-controlled microscope stage insert (Bioscience Tools, Highland, CA) while the temperature was maintained at 28.5°C. A long working-distance 40× water immersion objective lens (Olympus, Waltham, MA, LUMPLFLN40XW) on an upright confocal microscope (Olympus, Waltham, MA, FV1000) was lowered until within 1 mm of the gel surface, where it was immersed into a droplet of 35 mm BDM in E3 solution to form a water immersion column.

Borosilicate glass capillary tubes were pulled and bevelled to a sharp point resulting in a cannula inner diameter of approximately 5 μm by 10 μm (short-axis by long-axis). Cannulae tips were filled with a solution of 1% casein in E3 containing 0.2% 0.5 μm red fluorescent beads (Thermo Scientific, Fremont, CA, Fluoro-Max R500) and 25 mm warfarin (Sigma Aldrich, St. Louis, MO, A4571). Casein prevented the sticking of tissue, while beads allowed tracking of flow. Warfarin prevented red blood cell clotting at the cannulation site. Cannulae were prepared in advance to allow the injection solution to back-fill via capillary action, thus filtering the solution to prevent clogging. Additionally, casein requires at least 1 h to bind to completely block glass surfaces from non-specific binding. After incubation, cannulae were back-filled with E3, warfarin and bead solution only, displacing the casein solution. A cannula was then attached to a needle holder (World Precision Instruments, inc., Sarasota, FL, MPH315) held by a motorized micromanipulator (Zaber, Vancouver, BC) allowing precise movement of the needle tip. A microfluidic pressure controller (Fluigent, Ile-de-France, France, 25 mbar Flow-EZ) was connected to the cannula to allow precise control of the applied pressure. The microfluidic reservoir was placed near the microscope stage. The reservoir water level must be level with the cannula tip to ensure accurate zero-pressure calibration. Before cannulation, the cannula tip was placed into the immersion water column and lowered to the gel surface. Precise zero pressure was achieved by adjusting the reservoir water level until halting bead flow was observed in the cannula. The cannula tip was then advanced into the embryo sinus venosus region, just posterior to the atrial inlet. Upon puncture of the vasculature, the pressure was again equalized until bead flow was halted.

Using the microfluidic pressure controller, the pressure was cycled five times from 0 to 0.5 mmHg and back to zero. This was performed to remove hysteresis in the heart tissue. After pressure cycling, a 3D image stack was acquired which denoted the initial zero-stress state of the cannulated heart. The pressure was then increased at 0.25 mmHg increments, with an equalization period of two minutes between each pressure step. 3D image stacks were acquired after each equalization period. Pressurization was halted when tissue failure or massive leakage was detected. The pressure step before failure was considered the final pressure value, with its corresponding 3D image stack.

Statistical analysis

All the results in the histograms for the strains were expressed as means ± SD. The Wilcoxon signed-rank test was used for hypothesis testing with P < 0.05 considered significant when the data were not normal, while the t test was used for hypothesis testing with P < 0.05 considered significant when the data were normally distributed.


  • image

    Adriana Gaia is a Bioengineering PhD Candidate at Imperial College London. Her PhD focuses on the mechanobiology origin of congenital heart diseases at embryonic stage; specifically, diseases arising from malformations of cardiac trabeculae. Alongside her studies, she has worked as a graduate teaching assistant, mentoring and supervising fellow students. She earned her master's degree in bioengineering with a minor in biomechanics and biomaterials from Politecnico di Milano. Adriana's academic journey includes a semester abroad in Stockholm at KTH University for her master's thesis. She additionally holds a bachelor's degree in Bioengineering from Politecnico di Milano.

Data availability statement

4D images, reconstructed embryonic heart anatomical models, and a list of parameters used for all simulations are available at https://doi.org/10.5281/zenodo.10323795. The source code for the finite-element analysis and modelling is already available at https://github.com/WeiXuanChan/heartFEM, while the motion-tracking code for myocardial strain analysis is available at https://github.com/WeiXuanChan/motionSegmentation.

Competing interests

The authors declare that the research was conducted in the absence of any commercial or financial relationship that could be construed as a potential conflict of interest.

Author contributions

A.G.C., C.H.Y, D.B. and J.V. designed the research. A.G.C., A.G., W.X.C, P.N. and J.L. performed the research and analysed the data. A.G.C and C.H.Y. wrote the paper. All authors contributed to the manuscript revision and read and approved the submitted version. All authors approved the final version of the manuscript and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.


This study is supported by the Imperial College PhD Scholarship for supporting A.G.C., Imperial College startup funding (C.H.Y.). All funders have no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Additional information