Moving domain computational fluid dynamics to interface with an embryonic model of cardiac morphogenesis

Abstract

Peristaltic contraction of the embryonic heart tube produces time- and spatial-varying wall shear stress (WSS) and pressure gradients (∇P) across the atrioventricular (AV) canal. Zebrafish (Danio rerio) are a genetically tractable system to investigate cardiac morphogenesis. The use of Tg(fli1a:EGFP) (y1) transgenic embryos allowed for delineation and two-dimensional reconstruction of the endocardium. This time-varying wall motion was then prescribed in a two-dimensional moving domain computational fluid dynamics (CFD) model, providing new insights into spatial and temporal variations in WSS and ∇P during cardiac development. The CFD simulations were validated with particle image velocimetry (PIV) across the atrioventricular (AV) canal, revealing an increase in both velocities and heart rates, but a decrease in the duration of atrial systole from early to later stages. At 20-30 hours post fertilization (hpf), simulation results revealed bidirectional WSS across the AV canal in the heart tube in response to peristaltic motion of the wall. At 40-50 hpf, the tube structure undergoes cardiac looping, accompanied by a nearly 3-fold increase in WSS magnitude. At 110-120 hpf, distinct AV valve, atrium, ventricle, and bulbus arteriosus form, accompanied by incremental increases in both WSS magnitude and ∇P, but a decrease in bi-directional flow. Laminar flow develops across the AV canal at 20-30 hpf, and persists at 110-120 hpf. Reynolds numbers at the AV canal increase from 0.07±0.03 at 20-30 hpf to 0.23±0.07 at 110-120 hpf (p< 0.05, n=6), whereas Womersley numbers remain relatively unchanged from 0.11 to 0.13. Our moving domain simulations highlights hemodynamic changes in relation to cardiac morphogenesis; thereby, providing a 2-D quantitative approach to complement imaging analysis.

Figure 1. Dorsal view of zebrafish embryos illustrated cardiac system prior to and after pigmentation removal.

(a) Pigmentation opacifies internal organ systems at 120 hpf. (b) Treatments with PTU beginning at 10 hpf prevented pigment formation, allowing for clear organ visualization. (c) PTU-treated zebrafish heart observed under bright field microscope at 120 hpf. Despite visualization of outer wall, inner wall is poorly demarcated. (d) The use of transgenic Tg(fli1a:EGFP)y1 embryos allows for clear delineation of inner wall for reconstructing the CFD model. (e) Tg(gata1:dsRed)sd2 transgenic zebrafish allows to visualize the blood particle in order to take velocity by particle tracking technique. A, atrium; V, ventricle; B, bulbus arteriosus.

Figure 2. Schematic drawing of cardiac development in each stages.

At the early embryonic stage, heart shape is a tube-like structure. At about 20 hours, zebrafish heart is undergoing looping. After completion of cardiac looping, AV cushion starts to develop into a AV valve.

Figure 3. CFD simulation data was obtained at AV canal at three different developmental stages; namely, 20-30 hpf, 60-70 hpf, and 110-120 hpf.

The velocity profiles were validated by comparing with those of particle image velocimetry (PIV) via the Matlab-coded PIV tool. The CFD simulations overlapped reasonably with those of PIV. Noticeable are the increase in both the blood velocities and heart rates at later stages in development.

Figure 4. At 20-30 hpf, zebrafish heart is morphologically a tube-like structure with a AV canal (AV) separating the atrium (A) and ventricle (V).

(a) Atrial contraction, the first peak, engenders an increase in shear stress profiles through the AV canal. (b) Diastasis between atrial and ventricular contraction result in a decrease in shear stress across the AV canal. (c) Ventricular contraction, the second peak, results in flow reversal or regurgitation through the AV canal. The magnitude of wall shear stress (WSS) across the AV canal is about half of the forward blood flow at AV canal. (d) The green fluorescent protein (GFP) delineated the tubular structure. Unidirectional forward flow from the contracting atrium into the ventricle develops through the AV canal. (e) The GFP image reveals movement of peristaltic wave to the end of tubular heart structure. (f) Flow reversal develops in response to the contraction of tubular structure. (g) Velocity profiles show the maximal magnitude through the AV canal. (h) The magnitude of velocity is minimal at AV canal. (i) The magnitude of flow reversal or regurgitation is about half of the forward blood flow at AV canal. Contoured velocity profiles confirm the observed result (g–i). Red bars in (a–c) represent the time points at which the corresponding velocity profiles were reconstructed. A, atrium; V, ventricle.

Figure 5. At 40-50 hpf, the zebrafish heart begins to undergo looping.

(a–c) Compared to 20-30 hpf, WSS across the AV canal is increased by ~9-fold during atrial contraction. However, the magnitude of flow reversal or regurgitation-induced WSS during ventricular contraction decreases by ~33% in comparison with the earlier stages as the AV canal is developing into a valvular structure. (d–i) The ventricle has increased in size when compared to the atrium and absolute values of velocity have increased by 33%, A, atrium; V, ventricle.

Figure 6. At 110-120 hpf, the morphologic AV valve is distinct and left ventricle is enlarging.

(a–c) WSS across AV valve in response to atrium contraction is significantly higher than that of ventricular contraction. (d–i) Complete formation of the AV valve and bulbus arteriosus was observed at this stage, and amount of flow reversal reduced. The ventricle has become larger than the atrium in size, and the flow reversal through the AV canal during ventricular contraction is reduced due to small size of AV canal. A, atrium; V, ventricle; B, bulbus arteriosus.

Figure 7. Statistical data for average peak shear stress and pressure gradient.

(a) Average peak shear stress increases during developmental stages. At 50 hpf, the heart has undergone cardiac looping, which corresponds to an increase in magnitude of shear stress by 5-fold from 30 to 50 hpf (^* p < 0.01, n = 6) (b). In corollary, average peak pressure gradient across morphological AV canal increased from early to later developmental stages (^* p < 0.01, n = 6).

Figure 8. Instantaneous streamlines from early to the later stages.

(A–B) At the early stage (20hpf-30hpf), vortices in the morphological atrium is present in response to flow reversal during contraction of the morphological ventricle. (C–D) At 110 to 120 hpf, vortices are present downstream from the AV valve during atrial contraction and upstream (in the atrium) during ventricular contraction.