Biomechanics of cardiovascular development

Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.

Alteration of mechanical stresses in the murine brain by age and hemorrhagic stroke

Residual mechanical stresses, also known as solid stresses, emerge during rapid differential growth or remodeling of tissues, as observed in morphogenesis and tumor growth. While residual stresses typically dissipate in most healthy adult organs, as the growth rate decreases, high residual stresses have been reported in mature, healthy brains. However, the origins and consequences of residual mechanical stresses in the brain across health, aging, and disease remain poorly understood. Here, we utilized and validated a previously developed method to map residual mechanical stresses in the brains of mice across three age groups: 5-7 days, 8-12 weeks, and 22 months. We found that residual solid stress rapidly increases from 5-7 days to 8-12 weeks and remains high in mature 22 months mice brains. Three-dimensional mapping revealed unevenly distributed residual stresses from the anterior to posterior coronal brain sections. Since the brain is rich in negatively charged hyaluronic acid, we evaluated the contribution of charged extracellular matrix (ECM) constituents in maintaining solid stress levels. We found that lower ionic strength leads to elevated solid stresses, consistent with its unshielding effect and the subsequent expansion of charged ECM components. Lastly, we demonstrated that hemorrhagic stroke, accompanied by loss of cellular density, resulted in decreased residual stress in the murine brain. Our findings contribute to a better understanding of spatiotemporal alterations of residual solid stresses in healthy and diseased brains, a crucial step toward uncovering the biological and immunological consequences of this understudied mechanical phenotype in the brain.

Engineers in Medicine: Foster Innovation by Traversing Boundaries

Engineers play a critical role in the advancement of biomedical science and the development of diagnostic and therapeutic technologies for human well-being. The complexity of medical problems requires the synthesis of diverse knowledge systems and clinical experiences to develop solutions. Therefore, engineers in the healthcare and biomedical industries are interdisciplinary by nature to innovate technical tools in sophisticated clinical settings. In academia, engineering is usually divided into disciplines with dominant characteristics. Since biomedical engineering has been established as an independent curriculum, the term "biomedical engineers" often refers to the population from a specific discipline. In fact, engineers who contribute to medical and healthcare innovations cover a broad range of engineering majors, including electrical engineering, mechanical engineering, chemical engineering, industrial engineering, and computer sciences. This paper provides a comprehensive review of the contributions of different engineering professions to the development of innovative biomedical solutions. We use the term "engineers in medicine" to refer to all talents who integrate the body of engineering knowledge and biological sciences to advance healthcare systems.

Mechano-regulated cell-cell signaling in the context of cardiovascular tissue engineering

Cardiovascular tissue engineering (CVTE) aims to create living tissues, with the ability to grow and remodel, as replacements for diseased blood vessels and heart valves. Despite promising results, the (long-term) functionality of these engineered tissues still needs improvement to reach broad clinical application. The functionality of native tissues is ensured by their specific mechanical properties directly arising from tissue organization. We therefore hypothesize that establishing a native-like tissue organization is vital to overcome the limitations of current CVTE approaches. To achieve this aim, a better understanding of the growth and remodeling (G&R) mechanisms of cardiovascular tissues is necessary. Cells are the main mediators of tissue G&R, and their behavior is strongly influenced by both mechanical stimuli and cell-cell signaling. An increasing number of signaling pathways has also been identified as mechanosensitive. As such, they may have a key underlying role in regulating the G&R of tissues in response to mechanical stimuli. A more detailed understanding of mechano-regulated cell-cell signaling may thus be crucial to advance CVTE, as it could inspire new methods to control tissue G&R and improve the organization and functionality of engineered tissues, thereby accelerating clinical translation. In this review, we discuss the organization and biomechanics of native cardiovascular tissues; recent CVTE studies emphasizing the obtained engineered tissue organization; and the interplay between mechanical stimuli, cell behavior, and cell-cell signaling. In addition, we review past contributions of computational models in understanding and predicting mechano-regulated tissue G&R and cell-cell signaling to highlight their potential role in future CVTE strategies.

Of form and function: Early cardiac morphogenesis across classical and emerging model systems

The heart is the earliest organ to develop during embryogenesis and is remarkable in its ability to function efficiently as it is being sculpted. Cardiac heart defects account for a high burden of childhood developmental disorders with many remaining poorly understood mechanistically. Decades of work across a multitude of model organisms has informed our understanding of early cardiac differentiation and morphogenesis and has simultaneously opened new and unanswered questions. Here we have synthesized current knowledge in the field and reviewed recent developments in the realm of imaging, bioengineering and genetic technology and ex vivo cardiac modeling that may be deployed to generate more holistic models of early cardiac morphogenesis, and by extension, new platforms to study congenital heart defects.

Hypertrophic Cardiomyopathy in Infants from the Perspective of Cardiomyocyte Maturation

Hypertrophic cardiomyopathy (HCM) in infancy is rare and many fulminant cases are fatal. Infantile HCM shows a rapid progressive clinical course and different characteristics compared with late-onset HCM presenting during the prepubertal age. There are also spontaneously resolving phenotypes of HCM that are diagnosed in neonates being treated for bronchopulmonary dysplasia with corticosteroids or in those with other problems related to maternal endocrine diseases. The pathophysiology of infantile HCM has not been well described. Therefore, this review updates the pathophysiology of infantile HCM and includes molecular studies on maturation of cardiomyocytes from a clinician's point of view.

Hypertrophic cardiomyopathy (HCM) is characterized by ventricular wall hypertrophy with diastolic dysfunction. Pediatric HCM is distinguished from the adult in many aspects. Most children with HCM do not present clinically until the adolescent period, even when they are born with genetic mutations. Some infants with early-onset HCM present with massive progressive myocardial hypertrophy in the first few months of life, which is often fatal. The mortality of pediatric HCM peaks during the infantile and adolescent periods. These periods roughly correlate with children's growth spurt. Non-sarcomeric causes of HCM are more frequent in pediatric HCM, while sarcomeric causes are more common in adults. From the perspective of cardiac development, the fetal heart has immature cardiomyocytes, which are characterized by proliferation and exit their cell cycles with a decreased regenerative property after birth. In the perinatal period, there is a dynamic change in maturation of cardiomyocytes from immature to mature cells. Infants who are treated with steroids or born to mothers with diabetes or hyperthyroidism often show phenotypes of HCM, which gradually resolve. With remarkable advancement of molecular biology, understanding on maturation of cardiomyocytes has increased. Neonates undergo abrupt environmental changes during the transitional circulation, which is affected by oxygen, metabolic and hormonal fluctuations. Derangement in physiological transition to the normal postnatal environment may influence maturation of proliferative immature cardiomyocytes during early infancy. This article reviews updates of infantile HCM and recent molecular studies related to maturation of cardiomyocytes from the clinical point of view of identifying distinct characteristics of infantile HCM.

Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

Growth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the "opening-angle" in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.

Developmental origins of mechanical homeostasis in the aorta

BACKGROUND

Mechanical homeostasis promotes proper aortic structure and function. Pathological conditions may arise, in part, from compromised or lost homeostasis. There is thus a need to quantify the homeostatic state and when it emerges. Here we quantify changes in mechanical loading, geometry, structure, and function of the murine aorta from the late prenatal period into maturity.

RESULTS

Our data suggest that a homeostatic set-point is established by postnatal day P2 for the flow-induced shear stress experienced by endothelial cells; this value deviates from its set-point from P10 to P21 due to asynchronous changes in mechanical loading (flow, pressure) and geometry (radius, wall thickness), but is restored thereafter consistent with homeostasis. Smooth muscle contractility also decreases during this period of heightened matrix deposition but is also restored in maturity. The pressure-induced mechanical stress experienced by intramural cells initially remains low despite increasing blood pressure, and then increases while extracellular matrix accumulates.

CONCLUSIONS

These findings suggest that cell-level mechanical homeostasis emerges soon after birth to allow mechanosensitive cells to guide aortic development, with deposition of matrix after P2 increasingly stress shielding intramural cells. The associated tissue-level set-points that emerge for intramural stress can be used to assess and model the aorta that matures biomechanically by P56.

Design of synthetic microenvironments to promote the maturation of human pluripotent stem cell derived cardiomyocytes

Cardiomyocyte like cells derived from human pluripotent stem cells (hPSC-CMs) have a good application perspective in many fields such as disease modeling, drug screening and clinical treatment. However, these are severely hampered by the fact that hPSC-CMs are immature compared to adult human cardiomyocytes. Therefore, many approaches such as genetic manipulation, biochemical factors supplement, mechanical stress, electrical stimulation and three-dimensional culture have been developed to promote the maturation of hPSC-CMs. Recently, establishing in vitro synthetic artificial microenvironments based on the in vivo development program of cardiomyocytes has achieved much attention due to their inherent properties such as stiffness, plasticity, nanotopography and chemical functionality. In this review, the achievements and deficiency of reported synthetic microenvironments that mainly discussed comprehensive biological, chemical, and physical factors, as well as three-dimensional culture were mainly discussed, which have significance to improve the microenvironment design and accelerate the maturation of hPSC-CMs.

Uncertainty quantification reveals the physical constraints on pumping by peristaltic hearts

Most biological functional systems are complex, and this complexity is a fundamental driver of diversity. Because input parameters interact in complex ways, a holistic understanding of functional systems is key to understanding how natural selection produces diversity. We present uncertainty quantification (UQ) as a quantitative analysis tool on computational models to study the interplay of complex systems and diversity. We investigate peristaltic pumping in a racetrack circulatory system using a computational model and analyse the impact of three input parameters (Womersley number, compression frequency, compression ratio) on flow and the energetic costs of circulation. We employed two models of peristalsis (one that allows elastic interactions between the heart tube and fluid and one that does not), to investigate the role of elastic interactions on model output. A computationally cheaper surrogate of the input parameter space was created with generalized polynomial chaos expansion to save computational resources. Sobol indices were then calculated based on the generalized polynomial chaos expansion and model output. We found that all flow metrics were highly sensitive to changes in compression ratio and insensitive to Womersley number and compression frequency, consistent across models of peristalsis. Elastic interactions changed the patterns of parameter sensitivity for energetic costs between the two models, revealing that elastic interactions are probably a key physical metric of peristalsis. The UQ analysis created two hypotheses regarding diversity: favouring high flow rates (where compression ratio is large and highly conserved) and minimizing energetic costs (which avoids combinations of high compression ratios, high frequencies and low Womersley numbers).

Cardiomyocyte Maturation: New Phase in Development

Maturation is the last phase of heart development that prepares the organ for strong, efficient, and persistent pumping throughout the mammal's lifespan. This process is characterized by structural, gene expression, metabolic, and functional specializations in cardiomyocytes as the heart transits from fetal to adult states. Cardiomyocyte maturation gained increased attention recently due to the maturation defects in pluripotent stem cell-derived cardiomyocyte, its antagonistic effect on myocardial regeneration, and its potential contribution to cardiac disease. Here, we review the major hallmarks of ventricular cardiomyocyte maturation and summarize key regulatory mechanisms that promote and coordinate these cellular events. With advances in the technical platforms used for cardiomyocyte maturation research, we expect significant progress in the future that will deepen our understanding of this process and lead to better maturation of pluripotent stem cell-derived cardiomyocyte and novel therapeutic strategies for heart disease.

Enhanced structural maturation of human induced pluripotent stem cell-derived cardiomyocytes under a controlled microenvironment in a microfluidic system

The lack of a fully developed human cardiac model in vitro hampers the progress of many biomedical research fields including pharmacology, developmental biology, and disease modeling. Currently, available methods may only differentiate human induced pluripotent stem cells (iPSCs) into immature cardiomyocytes. To achieve cardiomyocyte maturation, appropriate modulation of cellular microenvironment is needed. This study aims to optimize a microfluidic system that enhances maturation of human iPSC-derived cardiomyocytes (iPSC-CMs) through cyclic pulsatile hemodynamic forces. Human iPSC-CMs cultured in the microfluidic system show increased alignment and contractility and appear more rod-like shaped with increased cell size and increased sarcomere length when compared to static cultures. Increased complexity and density of the mitochondrial network in iPSC-CMs cultured in the microfluidic system are in line with expression of mitochondrial marker genes MT-CO1 and OPA1. Moreover, the optimized microfluidic system is capable of stably maintaining controlled oxygen levels and inducing hypoxia, revealed by increased expression of HIF1α and EGLN2 as well as changes in contraction parameters in iPSC-CMs. In summary, this microfluidic system boosts the structural maturation of iPSC-CM culture and could serve as an advanced in vitro cardiac model for biomedical research in the future. STATEMENT OF SIGNIFICANCE: The availability of in vitro human cardiomyocytes generated from induced pluripotent stem cells (iPSCs) opens the possibility to develop human in vitro heart models for disease modeling and drug testing. However, iPSC-derived cardiomyocytes remain structurally and functionally immature, which hinders their application. In this manuscript, we present an optimized and complete microfluidic system that enhances maturation of iPSC-derived cardiomyocytes through physiological cyclic pulsatile hemodynamic forces. Furthermore, we improved our microfluidic system by using a closed microfluidic recirculation and oxygen exchangers to achieve and maintain low oxygen in the culture chambers, which is suitable for mimicking the hypoxic condition and studying the pathophysiological mechanisms of human diseases in vitro. In the future, a variety of technologies including 3D tissue engineering could be integrated into our system, which may greatly extend the use of iPSC-derived cardiac models in drug development and disease modeling.

The role of topology and mechanics in uniaxially growing cell networks

In biological systems, the growth of cells, tissues and organs is influenced by mechanical cues. Locally, cell growth leads to a mechanically heterogeneous environment as cells pull and push their neighbours in a cell network. Despite this local heterogeneity, at the tissue level, the cell network is remarkably robust, as it is not easily perturbed by changes in the mechanical environment or the network connectivity. Through a network model, we relate global tissue structure (i.e. the cell network topology) and local growth mechanisms (growth laws) to the overall tissue response. Within this framework, we investigate the two main mechanical growth laws that have been proposed: stress-driven or strain-driven growth. We show that in order to create a robust and stable tissue environment, networks with predominantly series connections are naturally driven by stress-driven growth, whereas networks with predominantly parallel connections are associated with strain-driven growth.

An actuatable soft reservoir modulates host foreign body response

The performance of indwelling medical devices that depend on an interface with soft tissue is plagued by complex, unpredictable foreign body responses. Such devices-including breast implants, biosensors, and drug delivery devices-are often subject to a collection of biological host responses, including fibrosis, which can impair device functionality. This work describes a milliscale dynamic soft reservoir (DSR) that actively modulates the biomechanics of the biotic-abiotic interface by altering strain, fluid flow, and cellular activity in the peri-implant tissue. We performed cyclical actuation of the DSR in a preclinical rodent model. Evaluation of the resulting host response showed a significant reduction in fibrous capsule thickness (P = 0.0005) in the actuated DSR compared with non-actuated controls, whereas the collagen density and orientation were not changed. We also show a significant reduction in myofibroblasts (P = 0.0036) in the actuated group and propose that actuation-mediated strain reduces differentiation and proliferation of myofibroblasts and therefore extracellular matrix production. Computational models quantified the effect of actuation on the reservoir and surrounding fluid. By adding a porous membrane and a therapy reservoir to the DSR, we demonstrate that, with actuation, we could (i) increase transport of a therapy analog and (ii) enhance pharmacokinetics and time to functional effect of an inotropic agent. The dynamic reservoirs presented here may act as a versatile tool to further understand, and ultimately to ameliorate, the host response to implantable biomaterials.

Trabecular Architecture Determines Impulse Propagation Through the Early Embryonic Mouse Heart

Most embryonic ventricular cardiomyocytes are quite uniform, in contrast to the adult heart, where the specialized ventricular conduction system is molecularly and functionally distinct from the working myocardium. We thus hypothesized that the preferential conduction pathway within the embryonic ventricle could be dictated by trabecular geometry. Mouse embryonic hearts of the Nkx2.5:eGFP strain between ED9.5 and ED14.5 were cleared and imaged whole mount by confocal microscopy, and reconstructed in 3D at 3.4 μm isotropic voxel size. The local orientation of the trabeculae, responsible for the anisotropic spreading of the signal, was characterized using spatially homogenized tensors (3 × 3 matrices) calculated from the trabecular skeleton. Activation maps were simulated assuming constant speed of spreading along the trabeculae. The results were compared with experimentally obtained epicardial activation maps generated by optical mapping with a voltage-sensitive dye. Simulated impulse propagation starting from the top of interventricular septum revealed the first epicardial breakthrough at the interventricular grove, similar to experimentally obtained activation maps. Likewise, ectopic activation from the left ventricular base perpendicular to dominant trabecular orientation resulted in isotropic and slower impulse spreading on the ventricular surface in both simulated and experimental conditions. We conclude that in the embryonic pre-septation heart, the geometry of the A-V connections and trabecular network is sufficient to explain impulse propagation and ventricular activation patterns.

Transcriptional regulation of cell shape during organ morphogenesis

The emerging field of transcriptional regulation of cell shape changes aims to address the critical question of how gene expression programs produce a change in cell shape. Together with cell growth, division, and death, changes in cell shape are essential for organ morphogenesis. Whereas most studies of cell shape focus on posttranslational events involved in protein organization and distribution, cell shape changes can be genetically programmed. This review highlights the essential role of transcriptional regulation of cell shape during morphogenesis of the heart, lungs, gastrointestinal tract, and kidneys. We emphasize the evolutionary conservation of these processes across different model organisms and discuss perspectives on open questions and research avenues that may provide mechanistic insights toward understanding birth defects.

Maturation of Cardiomyocytes Derived from Human Pluripotent Stem Cells: Current Strategies and Limitations

The capacity of differentiation of human pluripotent stem cells (hPSCs), which include both embryonic stem cells and induced pluripotent stem cells, into cardiomyocytes (CMs) in vitro provides an unlimited resource for human CMs for a wide range of applications such as cell based cardiac repair, cardiac drug toxicology screening, and human cardiac disease modeling. However, their applicability is significantly limited by immature phenotypes. It has been well known that currently available CMs derived from hPSCs (hPSC-CMs) represent immature embryonic or fetal stage CMs and are functionally and structurally different from mature human CMs. To overcome this critical issue, several new approaches aiming to generate more mature hPSC-CMs have been developed. This review describes recent approaches to generate more mature hPSC-CMs including their scientific principles, advantages, and limitations.

Soft robotic sleeve supports heart function

There is much interest in form-fitting, low-modulus, implantable devices or soft robots that can mimic or assist in complex biological functions such as the contraction of heart muscle. We present a soft robotic sleeve that is implanted around the heart and actively compresses and twists to act as a cardiac ventricular assist device. The sleeve does not contact blood, obviating the need for anticoagulation therapy or blood thinners, and reduces complications with current ventricular assist devices, such as clotting and infection. Our approach used a biologically inspired design to orient individual contracting elements or actuators in a layered helical and circumferential fashion, mimicking the orientation of the outer two muscle layers of the mammalian heart. The resulting implantable soft robot mimicked the form and function of the native heart, with a stiffness value of the same order of magnitude as that of the heart tissue. We demonstrated feasibility of this soft sleeve device for supporting heart function in a porcine model of acute heart failure. The soft robotic sleeve can be customized to patient-specific needs and may have the potential to act as a bridge to transplant for patients with heart failure.

Organ Dynamics and Fluid Dynamics of the HH25 Chick Embryonic Cardiac Ventricle as Revealed by a Novel 4D High-Frequency Ultrasound Imaging Technique and Computational Flow Simulations

Past literature has provided evidence that a normal mechanical force environment of blood flow may guide normal development while an abnormal environment can lead to congenital malformations, thus warranting further studies on embryonic cardiovascular flow dynamics. In the current study, we developed a non-invasive 4D high-frequency ultrasound technique, and use it to analyze cardiovascular organ dynamics and flow dynamics. Three chick embryos at stage HH25 were scanned with high frequency ultrasound in cine-B-mode at multiple planes spaced at 0.05 mm. 4D images of the heart and nearby arteries were generated via temporal and spatial correlation coupled with quadratic mean ensemble averaging. Dynamic mesh CFD was performed to understand the flow dynamics in the ventricle of the 2 hearts. Our imaging technique has sufficiently high resolution to enable organ dynamics quantification and CFD. Fine structures such as the aortic arches and details such as the cyclic distension of the carotid arteries were captured. The outflow tract completely collapsed during ventricular diastole, possible serving the function of a valve to prevent regurgitation. CFD showed that ventricular wall shear stress (WSS) were in the range of 0.1-0.5 Pa, and that the left side of the common ventricle experienced lower WSS than the right side. The pressure gradient from the inlet to the outlet of the ventricle was positive over most of the cardiac cycle, and minimal regurgitation flow was observed, despite the absence of heart valves. We developed a new image-based CFD method to elucidate cardiac organ dynamics and flow dynamics of embryonic hearts. The embryonic heart appeared to be optimized to generate net forward flow despite the absence of valves, and the WSS environment appeared to be side-specific.

Steps toward Maturation of Embryonic Stem Cell-Derived Cardiomyocytes by Defined Physical Signals

Cardiovascular disease remains a leading cause of mortality and morbidity worldwide. Embryonic stem cell-derived cardiomyocytes (ESC-CMs) may offer significant advances in creating in vitro cardiac tissues for disease modeling, drug testing, and elucidating developmental processes; however, the induction of ESCs to a more adult-like CM phenotype remains challenging. In this study, we developed a bioreactor system to employ pulsatile flow (1.48 mL/min), cyclic strain (5%), and extended culture time to improve the maturation of murine and human ESC-CMs. Dynamically-cultured ESC-CMs showed an increased expression of cardiac-associated proteins and genes, cardiac ion channel genes, as well as increased SERCA activity and a Raman fingerprint with the presence of maturation-associated peaks similar to primary CMs. We present a bioreactor platform that can serve as a foundation for the development of human-based cardiac in vitro models to verify drug candidates, and facilitates the study of cardiovascular development and disease.

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Custom-made bioreactor exposes ESC-CMs to defined shear stress and cyclic stretch

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Physical signals and extended culture significantly improve maturation of ESC-CMs

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Biochemical fingerprint of dynamically cultured ESC-CMs is similar to primary CMs

Naturally Engineered Maturation of Cardiomyocytes

Ischemic heart disease remains one of the most prominent causes of mortalities worldwide with heart transplantation being the gold-standard treatment option. However, due to the major limitations associated with heart transplants, such as an inadequate supply and heart rejection, there remains a significant clinical need for a viable cardiac regenerative therapy to restore native myocardial function. Over the course of the previous several decades, researchers have made prominent advances in the field of cardiac regeneration with the creation of in vitro human pluripotent stem cell-derived cardiomyocyte tissue engineered constructs. However, these engineered constructs exhibit a functionally immature, disorganized, fetal-like phenotype that is not equivalent physiologically to native adult cardiac tissue. Due to this major limitation, many recent studies have investigated approaches to improve pluripotent stem cell-derived cardiomyocyte maturation to close this large functionality gap between engineered and native cardiac tissue. This review integrates the natural developmental mechanisms of cardiomyocyte structural and functional maturation. The variety of ways researchers have attempted to improve cardiomyocyte maturation in vitro by mimicking natural development, known as natural engineering, is readily discussed. The main focus of this review involves the synergistic role of electrical and mechanical stimulation, extracellular matrix interactions, and non-cardiomyocyte interactions in facilitating cardiomyocyte maturation. Overall, even with these current natural engineering approaches, pluripotent stem cell-derived cardiomyocytes within three-dimensional engineered heart tissue still remain mostly within the early to late fetal stages of cardiomyocyte maturity. Therefore, although the end goal is to achieve adult phenotypic maturity, more emphasis must be placed on elucidating how the in vivo fetal microenvironment drives cardiomyocyte maturation. This information can then be utilized to develop natural engineering approaches that can emulate this fetal microenvironment and thus make prominent progress in pluripotent stem cell-derived maturity toward a more clinically relevant model for cardiac regeneration.

Endothelial Plasticity: Shifting Phenotypes through Force Feedback

The endothelial lining of the vasculature is exposed to a large variety of biochemical and hemodynamic stimuli with different gradients throughout the vascular network. Adequate adaptation requires endothelial cells to be highly plastic, which is reflected by the remarkable heterogeneity of endothelial cells in tissues and organs. Hemodynamic forces such as fluid shear stress and cyclic strain are strong modulators of the endothelial phenotype and function. Although endothelial plasticity is essential during development and adult physiology, proatherogenic stimuli can induce adverse plasticity which contributes to disease. Endothelial-to-mesenchymal transition (EndMT), the hallmark of endothelial plasticity, was long thought to be restricted to embryonic development but has emerged as a pathologic process in a plethora of diseases. In this perspective we argue how shear stress and cyclic strain can modulate EndMT and discuss how this is reflected in atherosclerosis and pulmonary arterial hypertension.

Systems biology and mechanics of growth

In contrast to inert systems, living biological systems have the advantage to adapt to their environment through growth and evolution. This transfiguration is evident during embryonic development, when the predisposed need to grow allows form to follow function. Alterations in the equilibrium state of biological systems breed disease and mutation in response to environmental triggers. The need to characterize the growth of biological systems to better understand these phenomena has motivated the continuum theory of growth and stimulated the development of computational tools in systems biology. Biological growth in development and disease is increasingly studied using the framework of morphoelasticity. Here, we demonstrate the potential for morphoelastic simulations through examples of volume, area, and length growth, inspired by tumor expansion, chronic bronchitis, brain development, intestine formation, plant shape, and myopia. We review the systems biology of living systems in light of biochemical and optical stimuli and classify different types of growth to facilitate the design of growth models for various biological systems within this generic framework. Exploring the systems biology of growth introduces a new venue to control and manipulate embryonic development, disease progression, and clinical intervention.

Biomechanics of Cardiac Function

The heart pumps blood to maintain circulation and ensure the delivery of oxygenated blood to all the organs of the body. Mechanics play a critical role in governing and regulating heart function under both normal and pathological conditions. Biological processes and mechanical stress are coupled together in regulating myocyte function and extracellular matrix structure thus controlling heart function. Here, we offer a brief introduction to the biomechanics of left ventricular function and then summarize recent progress in the study of the effects of mechanical stress on ventricular wall remodeling and cardiac function as well as the effects of wall mechanical properties on cardiac function in normal and dysfunctional hearts. Various mechanical models to determine wall stress and cardiac function in normal and diseased hearts with both systolic and diastolic dysfunction are discussed. The results of these studies have enhanced our understanding of the biomechanical mechanism in the development and remodeling of normal and dysfunctional hearts. Biomechanics provide a tool to understand the mechanism of left ventricular remodeling in diastolic and systolic dysfunction and guidance in designing and developing new treatments.

Right ventricular function in preterm and term neonates: reference values for right ventricle areas and fractional area of change

BACKGROUND

Right ventricular (RV) fractional area of change (FAC) is a quantitative two-dimensional echocardiographic measurement of RV function. RV FAC expresses the percentage change in the RV chamber area between end-diastole (RV end-diastolic area [RVEDA]) to end-systole (RV end-systolic area [RVESA]). The objectives of this study were to determine the maturational (age- and weight-related) changes in RV FAC and RV areas and to establish reference values in healthy preterm and term neonates.

METHODS

A prospective longitudinal study was conducted in 115 preterm infants (23-28 weeks' gestational age at birth, 500-1,500 g). RV FAC was measured at 24 hours of age, 72 hours of age, and 32 and 36 weeks' postmenstrual age (PMA). The maturational patterns of RVEDA, RVESA, and RV FAC were compared with those in 60 healthy full-term infants in a cross-sectional study (≥37 weeks, 3.5 ± 1 kg), who underwent echocardiography at birth (n = 25) and 1 month of age (n = 35). RVEDA and RVESA were traced in the RV-focused apical four-chamber view, and FAC was calculated using the formula 100 × [(RVEDA - RVESA)/RVEDA)]. Premature infants who developed chronic lung disease or had clinically and hemodynamically significant patent ductus arteriosus were excluded (n = 55) from the reference values. Intra- and interobserver reproducibility analysis was performed.

RESULTS

RV FAC ranged from 26% at birth to 35% by 36 weeks' PMA in preterm infants (n = 60) and increased almost 2 times faster in the first month of age compared with healthy term infants (n = 60). Similarly, RVEDA and RVESA increased throughout maturation in both term and preterm infants. RV FAC and RV areas were correlated with weight (r = 0.81, P < .001) but were independent of gestational age at birth (r = 0.3, P = .45). RVEDA and RVESA were correlated with PMA in weeks (r = 0.81, P < .001). RV FAC trended lower in preterm infants with bronchopulmonary dysplasia (P = .04) but was not correlated with size of patent ductus arteriosus (P = .56). There was no difference in RV FAC based on gender or need for mechanical ventilation.

CONCLUSIONS

This study establishes reference values of RV areas (RVEDA and RVESA) and RV FAC in healthy term and preterm infants and tracks their maturational changes during postnatal development. These measures increase from birth to 36 weeks' PMA, and this is reflective of the postnatal cardiac growth as a contributor to the maturation of cardiac function These measures are also linearly associated with increasing weight throughout maturation. This study suggests that two-dimensional RV FAC can be used as a complementary modality to assess global RV systolic function in neonates and facilitates its incorporation into clinical pediatric and neonatal guidelines.

Physical developmental cues for the maturation of human pluripotent stem cell-derived cardiomyocytes

Human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) are the most promising source of cardiomyocytes (CMs) for experimental and clinical applications, but their use is largely limited by a structurally and functionally immature phenotype that most closely resembles embryonic or fetal heart cells. The application of physical stimuli to influence hPSC-CMs through mechanical and bioelectrical transduction offers a powerful strategy for promoting more developmentally mature CMs. Here we summarize the major events associated with in vivo heart maturation and structural development. We then review the developmental state of in vitro derived hPSC-CMs, while focusing on physical (electrical and mechanical) stimuli and contributory (metabolic and hypertrophic) factors that are actively involved in structural and functional adaptations of hPSC-CMs. Finally, we highlight areas for possible future investigation that should provide a better understanding of how physical stimuli may promote in vitro development and lead to mechanistic insights. Advances in the use of physical stimuli to promote developmental maturation will be required to overcome current limitations and significantly advance research of hPSC-CMs for cardiac disease modeling, in vitro drug screening, cardiotoxicity analysis and therapeutic applications.

Studying dynamic events in the developing myocardium

Differentiation and conduction properties of the cardiomyocytes are critically dependent on physical conditioning both in vitro and in vivo. Historically, various techniques were introduced to study dynamic events such as electrical currents and changes in ionic concentrations in live cells, multicellular preparations, or entire hearts. Here we review this technological progress demonstrating how each improvement in spatial or temporal resolution provided answers to old and provoked new questions. We further demonstrate how high-speed optical mapping of voltage and calcium can uncover pacemaking potential within the outflow tract myocardium, providing a developmental explanation of ectopic beats originating from this region in the clinical settings.

A computational model that predicts reverse growth in response to mechanical unloading

Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure-volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.

Growth and residual stresses of arterial walls

Growth, residual stresses and mechanical responses of arterial walls under the inner pressure are investigated within the framework of a finite deformation hyper-elasticity theory. A biomechanical model for a two-layer thick-walled circular cylindrical tube is proposed to address the mechanical effects of finite volumetric growth and residual stresses of arterial walls. The active stress due to smooth muscle tone in the media and the dispersion of collagen fiber orientations in the adventitia are also considered. The fields of displacements and stress distributions of arterial walls with growth are solved analytically. Analysis of axial, radial and circumferential growth is considered and residual stress distributions of arterial walls in different cases of growth are compared.

Computational and experimental study of the mechanics of embryonic wound healing

Wounds in the embryo show a remarkable ability to heal quickly without leaving a scar. Previous studies have found that an actomyosin ring (purse string) forms around the wound perimeter and contracts to close the wound over the course of several dozens of minutes. Here, we report experiments that reveal an even faster mechanism which remarkably closes wounds by more than 50% within the first 30s. Circular and elliptical wounds (~100μm in size) were made in the blastoderm of early chick embryos and allowed to heal, with wound area and shape characterized as functions of time. The closure rate displayed a biphasic behavior, with rapid constriction lasting about a minute, followed by a period of more gradual closure to complete healing. Fluorescent staining suggests that both healing phases are driven by actomyosin contraction, with relatively rapid contraction of fibers at cell borders within a relatively thick ring of tissue (several cells wide) around the wound followed by slower contraction of a thin supracellular actomyosin ring along the margin, consistent with a purse string mechanism. Finite-element modeling showed that this idea is biophysically plausible, with relatively isotropic contraction within the thick ring giving way to tangential contraction in the thin ring. In addition, consistent with experimental results, simulated elliptical wounds heal with little change in aspect ratio, and decreased membrane tension can cause these wounds to open briefly before going on to heal. These results provide new insight into the healing mechanism in embryonic epithelia.

Alterations in pulse wave propagation reflect the degree of outflow tract banding in HH18 chicken embryos

Hemodynamic conditions play a critical role in embryonic cardiovascular development, and altered blood flow leads to congenital heart defects. Chicken embryos are frequently used as models of cardiac development, with abnormal blood flow achieved through surgical interventions such as outflow tract (OFT) banding, in which a suture is tightened around the heart OFT to restrict blood flow. Banding in embryos increases blood pressure and alters blood flow dynamics, leading to cardiac malformations similar to those seen in human congenital heart disease. In studying these hemodynamic changes, synchronization of data to the cardiac cycle is challenging, and alterations in the timing of cardiovascular events after interventions are frequently lost. To overcome this difficulty, we used ECG signals from chicken embryos (Hamburger-Hamilton stage 18, ∼3 days of incubation) to synchronize blood pressure measurements and optical coherence tomography images. Our results revealed that, after 2 h of banding, blood pressure and pulse wave propagation strongly depend on band tightness. In particular, while pulse transit time in the heart OFT of control embryos is ∼10% of the cardiac cycle, after banding (35% to 50% band tightness) it becomes negligible, indicating a faster OFT pulse wave velocity. Pulse wave propagation in the circulation is likewise affected; however, pulse transit time between the ventricle and dorsal aorta (at the level of the heart) is unchanged, suggesting an overall preservation of cardiovascular function. Changes in cardiac pressure wave propagation are likely contributing to the extent of cardiac malformations observed in banded hearts.

Stress and strain adaptation in load-dependent remodeling of the embryonic left ventricle

Altered pressure in the developing left ventricle (LV) results in altered morphology and tissue material properties. Mechanical stress and strain may play a role in the regulating process. This study showed that confocal microscopy, three-dimensional reconstruction, and finite element analysis can provide a detailed model of stress and strain in the trabeculated embryonic heart. The method was used to test the hypothesis that end-diastolic strains are normalized after altered loading of the LV during the stages of trabecular compaction and chamber formation. Stage-29 chick LVs subjected to pressure overload and underload at stage 21 were reconstructed with full trabecular morphology from confocal images and analyzed with finite element techniques. Measured material properties and intraventricular pressures were specified in the models. The results show volume-weighted end-diastolic von Mises stress and strain averaging 50-82 % higher in the trabecular tissue than in the compact wall. The volume-weighted-average stresses for the entire LV were 115, 64, and 147 Pa in control, underloaded, and overloaded models, while strains were 11, 7, and 4 %; thus, neither was normalized in a volume-weighted sense. Localized epicardial strains at mid-longitudinal level were similar among the three groups and to strains measured from high-resolution ultrasound images. Sensitivity analysis showed changes in material properties are more significant than changes in geometry in the overloaded strain adaptation, although resulting stress was similar in both types of adaptation. These results emphasize the importance of appropriate metrics and the role of trabecular tissue in evaluating the evolution of stress and strain in relation to pressure-induced adaptation.

Perspectives on the advanced control of bioreactors for functional vascular tissue engineering in vitro

Tissue engineering aims to produce tissues using cells and materials. The action of designing tissues involves observing the process of growth to understand its underlying mechanisms. It requires manipulation of the critical parameters for cell growth and remodeling to produce structured tissues and functional organs. Tissue engineers face the challenge of orchestrating the signals in a cell's microenvironment to efficiently grow an anisotropic and hierarchical tissue. It can be performed in vivo through the design of bioactive scaffolds and manipulation of biological signals using growth factors. It can also be performed in vitro in a controlled environment called the bioreactor. This article addresses the matter of finding the optimal dynamic sequence of culture conditions in a bioreactor for the maturation of tissues. Artificial intelligence and optimal control are accelerating technologies towards an understanding of tissue regeneration. The particular example of the functional engineering of small-diameter blood vessels has been chosen to illustrate this idea.

The contribution of cellular mechanotransduction to cardiomyocyte form and function

Myocardial development is regulated by an elegantly choreographed ensemble of signaling events mediated by a multitude of intermediates that take a variety of forms. Cellular differentiation and maturation are a subset of vertically integrated processes that extend over several spatial and temporal scales to create a well-defined collective of cells that are able to function cooperatively and reliably at the organ level. Early efforts to understand the molecular mechanisms of cardiomyocyte fate determination focused primarily on genetic and chemical mediators of this process. However, increasing evidence suggests that mechanical interactions between the extracellular matrix (ECM) and cell surface receptors as well as physical interactions between neighboring cells play important roles in regulating the signaling pathways controlling the developmental processes of the heart. Interdisciplinary efforts have made it apparent that the influence of the ECM on cellular behavior occurs through a multitude of physical mechanisms, such as ECM boundary conditions, elasticity, and the propagation of mechanical signals to intracellular compartments, such as the nucleus. In addition to experimental studies, a number of mathematical models have been developed that attempt to capture the interplay between cells and their local microenvironment and the influence these interactions have on cellular self-assembly and functional behavior. Nevertheless, many questions remain unanswered concerning the mechanism through which physical interactions between cardiomyocytes and their environment are translated into biochemical cellular responses and how these signaling modalities can be utilized in vitro to fabricate myocardial tissue constructs from stem cell-derived cardiomyocytes that more faithfully represent their in vivo counterpart. These studies represent a broad effort to characterize biological form as a conduit for information transfer that spans the nanometer length scale of proteins to the meter length scale of the patient and may yield new insights into the contribution of mechanotransduction into heart development and disease.

On integrating experimental and theoretical models to determine physical mechanisms of morphogenesis

Researchers in developmental biology are increasingly recognizing the value of theoretical models in studies of morphogenesis. However, creating and testing realistic quantitative models for morphogenetic processes can be an extremely challenging task. The focus of this paper is on models for the mechanics of morphogenesis. Models for these problems often must include large changes in geometry, leading to highly nonlinear problems with the possibility of multiple solutions that must be sorted out using experimental data. Here, we illustrate our approach to these problems using the specific example of head fold formation in the early chick embryo. The interplay between experimental and theoretical results is emphasized throughout, as the model is gradually refined. Some of the limitations inherent in theoretical/computational modeling of biological systems are also discussed.

On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration

Alteration of the native mitral valve (MV) shape has been hypothesized to have a profound effect on the local tissue stress distribution, and is potentially linked to limitations in repair durability. The present study was undertaken to elucidate the relation between MV annular shape and central mitral valve anterior leaflet (MVAL) strain history, using flat annuloplasty in an ovine model. In addition, we report for the first time the presence of residual in vivo leaflet strains. In vivo leaflet deformations were measured using sonocrystal transducers sutured to the MVAL (n = 10), with the 3D positions acquired over the full cardiac cycle. In six animals a flat ring was sutured to the annulus and the transducer positions recorded, while in the remaining four the MV was excised from the exsanguinated heart and the stress-free transducer positions obtained. In the central region of the MVAL the peak stretch values, referenced to the minimum left ventricular pressure (LVP), were 1.10 ± 0.01 and 1.31 ± 0.03 (mean ± standard error) in the circumferential and radial directions, respectively. Following flat ring annuloplasty, the central MVAL contracted 28% circumferentially and elongated 16% radially at minimum LVP, and the circumferential direction was under a negative strain state during the entire cardiac cycle. After valve excision from the exsanguinated heart, the MVAL contracted significantly (18 and 30% in the circumferential and radial directions, respectively), indicating the presence of substantial in vivo residual strains. While the physiological function of the residual strains (and their associated stresses) are at present unknown, accounting for their presence is clearly necessary for accurate computational simulations of MV function. Moreover, we demonstrated that changes in annular geometry dramatically alter valvular functional strains in vivo. As levels of homeostatic strains are related to tissue remodeling and homeostasis, our results suggest that surgically introduced alterations in MV shape could lead to the long term MV mechanobiological and microstructural alterations that could ultimately affect MV repair durability.

Assessment of Minimally Invasive Device That Provides Simultaneous Adjustable Cardiac Support and Active Synchronous Assist in an Acute Heart Failure Model

One of the major maladaptive changes after a major heart attack or cardiac event is an initial decline in pumping capacity of the heart leading to activation of a variety of compensatory mechanisms, and subsequently a phenomenon known as cardiac or left ventricular remodeling, i.e., a geometrical change in the architecture of the left ventricle. Evidence suggests that the local mechanical environment governs remodeling processes. Thus, in order to control two important mechanical parameters, cardiac size and cardiac output, we have developed a minimally invasive direct cardiac contact device capable of providing two actions simultaneously: (1) adjustable cardiac support to modulate cardiac size and (2) synchronous active assist to modulate cardiac output. As a means of enabling experiments to determine the role of these mechanical parameters in reverse remodeling or ventricular recovery, the device was further designed to (1) be deployed via minimally invasive surgical procedures, (2) allow uninhibited motion of the heart, (3) remain in place about the heart via an intrinsic pneumatic attachment, and (4) provide direct cardiac compression without aberrantly inverting the curvature of the heart. These actions and features are mapped to particular design solutions and assessed in an acute implantation in an ovine model of acute heart failure (esmolol overdose). The passive support component was used to effectively shift the EDPVR leftward, i.e., counter to the effects of disease. The active assist component was used to effectively decompress the constrained heart and restore lost cardiac output and stroke work in the esmolol failure model. It is expected that such a device will provide better control of the mechanical environment and thereby provide cardiac surgeons a broader range of therapeutic options and unique intervention possibilities.

On the growth and form of the gut

The developing vertebrate gut tube forms a reproducible looped pattern as it grows into the body cavity. Here we use developmental experiments to eliminate alternative models and show that gut looping morphogenesis is driven by the homogeneous and isotropic forces that arise from the relative growth between the gut tube and the anchoring dorsal mesenteric sheet, tissues that grow at different rates. A simple physical mimic, using a differentially strained composite of a pliable rubber tube and a soft latex sheet is consistent with this mechanism and produces similar patterns. We devise a mathematical theory and a computational model for the number, size and shape of intestinal loops based solely on the measurable geometry, elasticity and relative growth of the tissues. The predictions of our theory are quantitatively consistent with observations of intestinal loops at different stages of development in the chick embryo. Our model also accounts for the qualitative and quantitative variation in the distinct gut looping patterns seen in a variety of species including quail, finch and mouse, illuminating how the simple macroscopic mechanics of differential growth drives the morphology of the developing gut.

Consistent formulation of the growth process at the kinematic and constitutive level for soft tissues composed of multiple constituents

Previous studies have investigated the possibilities of modelling the change in volume and change in density of biomaterials. This can be modelled at the constitutive or the kinematic level. This work introduces a consistent formulation at the kinematic and constitutive level for growth processes. Most biomaterials consist of many constituents and can be approximated as being incompressible. These two conditions (many constituents and incompressibility) suggest a straightforward implementation in the context of the finite element (FE) method which could now be validated more easily against histological measurements. Its key characteristic variable is the normalised partial mass change. Using the concept of homeostatic equilibrium, we suggest two complementary growth laws in which the evolution of the normalised partial mass change is governed by an ordinary differential equation in terms of either the Piola-Kirchhoff stress or the Green-Lagrange strain. We combine this approach with the classical incompatibility condition and illustrate its algorithmic implementation within a fully nonlinear FE approach. This approach is first illustrated for a simple uniaxial tension and extension test for pure volume change and pure density change and is validated against previous numerical results. Finally, a physiologically based example of a two-phase model is presented which is a combination of volume and density changes. It can be concluded that the effect of hyper-restoration may be due to the systemic effect of degradation and adaptation of given constituents.

Mechanotransduction: the role of mechanical stress, myocyte shape, and cytoskeletal architecture on cardiac function

Mechanotransduction refers to the conversion of mechanical forces into biochemical or electrical signals that initiate structural and functional remodeling in cells and tissues. The heart is a kinetic organ whose form changes considerably during development and disease, requiring cardiac myocytes to be mechanically durable and capable of fusing a variety of environmental signals on different time scales. During physiological growth, myocytes adaptively remodel to mechanical loads. Pathological stimuli can induce maladaptive remodeling. In both of these conditions, the cytoskeleton plays a pivotal role in both sensing mechanical stress and mediating structural remodeling and functional responses within the myocyte.

Perspectives on biological growth and remodeling

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

A POROELASTIC MODEL FOR CELL CRAWLING INCLUDING MECHANICAL COUPLING BETWEEN CYTOSKELETAL CONTRACTION AND ACTIN POLYMERIZATION

Much is known about the biophysical mechanisms involved in cell crawling, but how these processes are coordinated to produce directed motion is not well understood. Here, we propose a new hypothesis whereby local cytoskeletal contraction generates fluid flow through the lamellipodium, with the pressure at the front of the cell facilitating actin polymerization which pushes the leading edge forward. The contraction, in turn, is regulated by stress in the cytoskeleton. To test this hypothesis, finite element models for a crawling cell are presented. These models are based on nonlinear poroelasticity theory, modified to include the effects of active contraction and growth, which are regulated by mechanical feedback laws. Results from the models agree reasonably well with published experimental data for cell speed, actin flow, and cytoskeletal deformation in migrating fish epidermal keratocytes. The models also suggest that oscillations can occur for certain ranges of parameter values.

Mechanics of head fold formation: investigating tissue-level forces during early development

During its earliest stages, the avian embryo is approximately planar. Through a complex series of folds, this flat geometry is transformed into the intricate three-dimensional structure of the developing organism. Formation of the head fold (HF) is the first step in this cascading sequence of out-of-plane tissue folds. The HF establishes the anterior extent of the embryo and initiates heart, foregut and brain development. Here, we use a combination of computational modeling and experiments to determine the physical forces that drive HF formation. Using chick embryos cultured ex ovo, we measured: (1) changes in tissue morphology in living embryos using optical coherence tomography (OCT); (2) morphogenetic strains (deformations) through the tracking of tissue labels; and (3) regional tissue stresses using changes in the geometry of circular wounds punched through the blastoderm. To determine the physical mechanisms that generate the HF, we created a three-dimensional computational model of the early embryo, consisting of pseudoelastic plates representing the blastoderm and vitelline membrane. Based on previous experimental findings, we simulated the following morphogenetic mechanisms: (1) convergent extension in the neural plate (NP); (2) cell wedging along the anterior NP border; and (3) autonomous in-plane deformations outside the NP. Our numerical predictions agree relatively well with the observed morphology, as well as with our measured stress and strain distributions. The model also predicts the abnormal tissue geometries produced when development is mechanically perturbed. Taken together, the results suggest that the proposed morphogenetic mechanisms provide the main tissue-level forces that drive HF formation.