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Research Papers

Bending of the Looping Heart: Differential Growth Revisited

[+] Author and Article Information
Yunfei Shi

Department of Biomedical Engineering,
Washington University,
Saint Louis, MO 63130
e-mail: yunfei.shi@wustl.edu

Jiang Yao

Dassault Systemes Simulia Corp.,
166 Valley Street,
Providence, RI 02902-2499
e-mail: jiang.yao@3ds.com

Gang Xu

Department of Engineering and Physics,
University of Central Oklahoma,
Edmond, OK 73034
e-mail: gxu@uco.edu

Larry A. Taber

Department of Biomedical Engineering,
Washington University,
Saint Louis, MO 63130
e-mail: lat@wustl.edu

1Corresponding author.

*All supplemental material for this paper can be accessed in the “SUPPLEMENTAL DATA” tab in the online version of this paper on the ASME digital collection.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received October 15, 2013; final manuscript received January 20, 2014; accepted manuscript posted February 6, 2014; published online June 2, 2014. Assoc. Editor: Hai-Chao Han.

J Biomech Eng 136(8), 081002 (Jun 02, 2014) (15 pages) Paper No: BIO-13-1491; doi: 10.1115/1.4026645 History: Received October 15, 2013; Revised January 20, 2014; Accepted February 06, 2014

In the early embryo, the primitive heart tube (HT) undergoes the morphogenetic process of c-looping as it bends and twists into a c-shaped tube. Despite intensive study for nearly a century, the physical forces that drive looping remain poorly understood. This is especially true for the bending component, which is the focus of this paper. For decades, experimental measurements of mitotic rates had seemingly eliminated differential growth as the cause of HT bending, as it has commonly been thought that the heart grows almost exclusively via hyperplasia before birth and hypertrophy after birth. Recently published data, however, suggests that hypertrophic growth may play a role in looping. To test this idea, we developed finite-element models that include regionally measured changes in myocardial volume over the HT. First, models based on idealized cylindrical geometry were used to simulate the bending process in isolated hearts, which bend without the complicating effects of external loads. With the number of free parameters in the model reduced to the extent possible, stress and strain distributions were compared to those measured in embryonic chick hearts that were isolated and cultured for 24 h. The results show that differential growth alone yields results that agree reasonably well with the trends in our data, but adding active changes in myocardial cell shape provides closer quantitative agreement with stress measurements. Next, the estimated parameters were extrapolated to a model based on realistic 3D geometry reconstructed from images of an actual chick heart. This model yields similar results and captures quite well the basic morphology of the looped heart. Overall, our study suggests that differential hypertrophic growth in the myocardium (MY) is the primary cause of the bending component of c-looping, with other mechanisms possibly playing lesser roles.

FIGURES IN THIS ARTICLE
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Copyright © 2014 by ASME
Topics: Stress , Geometry , Shapes , Tension
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References

Figures

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Fig. 1

Cardiac c-looping of chick embryo. ((a) and (b)) SEM images of embryonic chick hearts during c-looping (ventral view). The originally straight HT at HH10 (a) bends ventrally and rotates rightward, transforming into a c-shaped tube at HH12 (b). To help visualize rotation, artificial labels (dots) along the ventral midline of the HT at HH10 move to the outer curvature of the HH12 heart. The splanchnopleure membrane was removed to reveal the HT. ((a′) and (b′)) Rotation of the HT is shown by the orientation of the elliptical lumen (arrowheads) in OCT cross sections taken midway along the length of the HT (dashed lines in (a) and (b)). A = atrium, AIP = anterior intestinal portal, C = conotruncus, CJ = cardiac jelly, DM = dorsal mesocardium, EN = endocardium, IC = inner curvature, LU = lumen, HT = heart tube, MY = myocardium, SPL = splanchnopleure, OC = outer curvature, OT = outflow tract, OV = omphalomesenteric veins, V = ventricle. Scale bars: 200 μm.

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Fig. 2

Schematic of configurations in computational modeling. Intermediate states (B, BR) are defined between the initial unstressed (β) and the current stressed (b) configurations. The total deformation gradient tensor (F) is decomposed into morphogenetic (M) and elastic (F*) deformations. The Cauchy stress (σ) only depends on the elastic deformation (F*).

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Fig. 3

Finite-element models for bending of the isolated heart. ((a)–(c)) Idealized cylinder model. Due to symmetry, only the top half of the model is shown, i.e., the heart is actually about 1 mm long. ((a′)–(c′)) Model based on realistic geometry. The undeformed geometries and meshes are shown in lateral ((a), (a′)), ventral ((b), (b′)), and cross-sectional views ((c), (c′)). In both models, the heart tube consists of ventral myocardium (VMY), dorsal myocardium (DMY), dorsal mesocardium (DM), and cardiac jelly (CJ). The outflow tract and the remnant omphalomesenteric veins are considered part of the heart tube in the cylinder model, but they are included as passive structures in the realistic geometry model. The lumen is included in the realistic model but not in the cylinder model. Shown separately in (b) and (b′), a global cylindrical coordinate system {R,Θ,Z} and principal directions (eR,eΘ,eZ) are defined in the undeformed configurations. Symmetry planes of the cylinder model are shown as dashed-dot lines in (b) and (c).

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Fig. 4

Bending of isolated hearts in different culture conditions. (a) Ventral view of a representative HH10 chick embryo before heart dissection. (b) Lateral views and OCT cross sections of hearts isolated at HH10 (0 h) and cultured for 24 h in various conditions: control, 30 μM blebbistatin (Bleb), 20 UTR/mL hyaluronidase (Hyal), and 100 nM cytochalasin D (CytoD). Bending occurred in all cases except the CytoD-treated hearts. Significant thickening of the myocardial wall was observed in the cross sections of bent hearts (solid arrowheads), while the myocardium thickened less in the CytoD-treated heart (hollow arrowheads). DM = remnant dorsal mesocardium, IC = inner curvature, OC = outer curvature. Scale bar: 200 μm in (a) (the same for (b)).

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Fig. 5

Morphogenetic strains measured during bending of the isolated heart. (a) Fluorescent labels were injected on the ventral (v) and dorsal (d) sides of the HT to measure longitudinal strains. (b) Longitudinal stretch ratios (λzv > 1,λzd < 1) indicate ventral elongation and dorsal shortening in both control hearts and hearts treated with 30 μM blebbistatin (Bleb). Linear regressions (solid lines) suggest longitudinal stretch ratios change linearly with time (for control and Bleb-treated hearts, R2 = 0.9839, 0.9157 for λzv and R2 = 0.7831, 0.8409 for λzd, respectively). (c) Summary of all myocardial stretch ratios after 24 h culture: radial λr, circumferential λθ, longitudinal on the ventral side λzv, and longitudinal on the dorsal side λzd. The myocardial wall thickened less in Bleb-treated hearts than that in control, and even less in hearts treated with 100 nM cytochalasin D (CytoD;  *p < 0.001, one-way ANOVA). Note that longitudinal stretch ratios were not measured in CytoD-treated hearts, where bending was inhibited. Scale bar: 200 μm.

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Fig. 6

Residual stresses in the myocardium as revealed by microsurgical cuts. (a) Linear cut in heart tube cultured for 24 h. Opening of the circumferential cut indicates tensile longitudinal stress. Cut aspect ratio (α), defined as opening width (w) divided by cut length (l) in the local myocardial plane (see panel (c)), characterizes tension in the myocardium. (b) Aspect ratios for cuts made near the OC or IC of control hearts before (0 h) or after (24 h) culture. Subscripts z and θ denote longitudinal and circumferential tensions, respectively ( *p < 0.001, **p = 0.011). (c) Opening (dashed ellipses) and closure (dashed lines) of representative cuts show residual stress states in control hearts before (0 h) and after (24 h) culture. Outward and inward arrows indicate tension and compression, respectively. Since cuts made near the IC of bent hearts usually do not open, aspect ratios were reported as 0 in (b). Scale bars: 200 μm.

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Fig. 7

Single-mechanism cylinder models for bending of blebbistatin-treated heart. (a) Deformed shapes and stress distributions shown in lateral and cross-sectional views. Because of symmetry, only the top half of the model is shown. The initial configuration for each model includes CJ growth that occurs prior to HH10. Simulations then include one of the following mechanisms: additional CJ growth with DM constraint; DM tension; active cell-shape changes in the MY; or MY differential growth. Only the differential growth model produces deformation and stresses comparable to experimental results (DM = dorsal mesocardium, DMY = dorsal myocardium, VMY = ventral myocardium, IC = inner curvature, OC = outer curvature). (b) Experimental and numerical stretch ratios in the MY: radial λr, circumferential λθ, longitudinal on ventral side λzv, and longitudinal on dorsal side λzd. The differential growth model yields the closest agreement with experiment.

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Fig. 8

Baseline cylinder model for bending of the isolated heart. (a) This model includes five steps: CJ growth, DM dissection, MY contraction, MY differential growth, and active MY cell-shape change. Deformed shape and longitudinal stress distribution after each step in simulation are shown (lateral view; DM = dorsal mesocardium, DMY = dorsal myocardium, VMY = ventral myocardium, IC = inner curvature, OC = outer curvature). (b) MY contraction is turned off to simulate bending of hearts treated with blebbistatin (Bleb). (The scale and legend are the same as in (a).) ((c) and (d)) Stress distributions after each step along the MY circumference at center of the heart tube. (e) Experimental and numerical stretch ratios in the MY for control and Bleb-treated hearts: radial λr, circumferential λθ, longitudinal on ventral side λzv, and longitudinal on dorsal side λzv. Model results are shown after the differential growth and cell-shape change steps. (f) Decrease in MY tension after 24 h culture as characterized by decrease in aspect ratios of cut (Δα = α(0 h)-α(24 h)). Although most bending is produced by differential growth, cell-shape change significantly lowers the circumferential stress (σθ), especially near the IC (panels (d) and (f)).

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Fig. 9

Model for bending of control heart based on realistic geometry. Lagrangian strains (EZ,EΘ) and myocardial stresses (σz,σθ) are shown in the initial (0 h) and final (24 h) shapes of the heart (lateral view). To help visualize the bending deformation, the passive outflow tract and remnant omphalomesenteric veins are separated from the rest of the heart tube by dashed lines. When growth of CJ occurs, the lumen decreases significantly, as shown in cross-sectional view. (CJ = cardiac jelly, DM = dorsal mesocardium, MY = myocardium, DMY = dorsal myocardium, VMY = ventral myocardium)

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