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      A method to quantify mechanobiologic forces during zebrafish cardiac development using 4-D light sheet imaging and computational modeling

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          Abstract

          Blood flow and mechanical forces in the ventricle are implicated in cardiac development and trabeculation. However, the mechanisms of mechanotransduction remain elusive. This is due in part to the challenges associated with accurately quantifying mechanical forces in the developing heart. We present a novel computational framework to simulate cardiac hemodynamics in developing zebrafish embryos by coupling 4-D light sheet imaging with a stabilized finite element flow solver, and extract time-dependent mechanical stimuli data. We employ deformable image registration methods to segment the motion of the ventricle from high resolution 4-D light sheet image data. This results in a robust and efficient workflow, as segmentation need only be performed at one cardiac phase, while wall position in the other cardiac phases is found by image registration. Ventricular hemodynamics are then quantified by numerically solving the Navier-Stokes equations in the moving wall domain with our validated flow solver. We demonstrate the applicability of the workflow in wild type zebrafish and three treated fish types that disrupt trabeculation: (a) chemical treatment using AG1478, an ErbB2 signaling inhibitor that inhibits proliferation and differentiation of cardiac trabeculation; (b) injection of gata1a morpholino oligomer ( gata1aMO) suppressing hematopoiesis and resulting in attenuated trabeculation; (c) weak-atrium m58 mutant ( wea) with inhibited atrial contraction leading to a highly undeveloped ventricle and poor cardiac function. Our simulations reveal elevated wall shear stress (WSS) in wild type and AG1478 compared to gata1aMO and wea. High oscillatory shear index (OSI) in the grooves between trabeculae, compared to lower values on the ridges, in the wild type suggest oscillatory forces as a possible regulatory mechanism of cardiac trabeculation development. The framework has broad applicability for future cardiac developmental studies focused on quantitatively investigating the role of hemodynamic forces and mechanotransduction during morphogenesis.

          Author summary

          We present a novel computational workflow for quantifying hemodynamic forces in developing zebrafish embryos by coupling high resolution 4-D light sheet imaging with a moving domain blood flow solver. Our framework employs deformable image registration to extract the motion of the ventricle from high resolution image data. This produces a robust and efficient workflow, as segmentation is performed at only one cardiac phase, while the wall position in other cardiac phases is found from the displacement field obtained during image registration. This approach avoids a laborious process of manual segmentation in all cardiac phases, and minimizes spurious errors arising from manual processing. Our validated flow solver is optimized for cardiac hemodynamics with backflow stabilization, efficient data management and dynamic remeshing algorithms for moving domains. We demonstrate the utility of the framework in wild type zebrafish and three treated variants in which the formation of cardiac trabeculations is disrupted. In this study, we then quantify the relationship between oscillatory shear forces and the presence or absence of ventricular trabeculation during cardiac development. Our framework has broad applicability in cardiac developmental studies focused on quantitatively investigating the mechanobiology during morphogenesis.

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          IMMERSED BOUNDARY METHODS

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            Digital particle image velocimetry

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              Point set registration: coherent point drift.

              Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown nonrigid spatial transformation, large dimensionality of point set, noise, and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and nonrigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the Gaussian mixture model (GMM) centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by reparameterization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the nonrigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and nonrigid transformations in the presence of noise, outliers, and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods.
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                Author and article information

                Contributors
                Role: Formal analysisRole: InvestigationRole: MethodologyRole: SoftwareRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: InvestigationRole: MethodologyRole: Writing – review & editing
                Role: InvestigationRole: Writing – review & editing
                Role: ConceptualizationRole: SupervisionRole: Writing – review & editing
                Role: ConceptualizationRole: Funding acquisitionRole: MethodologyRole: Project administrationRole: ResourcesRole: Writing – review & editing
                Role: ConceptualizationRole: MethodologyRole: Project administrationRole: ResourcesRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                October 2017
                30 October 2017
                : 13
                : 10
                : e1005828
                Affiliations
                [1 ] Department of Pediatrics (Cardiology), Stanford University, Stanford, California, United States of America
                [2 ] Department of Bioengineering, University of California, Los Angeles, Los Angeles, California, United States of America
                [3 ] Department of Electrical Engineering, University of Southern California, Los Angeles, California, United States of America
                [4 ] Department of Medicine, Division of Cardiology, University of California, Los Angeles, Los Angeles, California, United States of America
                [5 ] Department of Bioengineering, Stanford University, Stanford, California, United States of America
                [6 ] Institute for Computational and Mathematical Engineering (ICME), Stanford University, Stanford, California, United States of America
                University of Pennsylvania, UNITED STATES
                Author notes

                The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0001-9474-5035
                http://orcid.org/0000-0003-1902-171X
                Article
                PCOMPBIOL-D-17-00923
                10.1371/journal.pcbi.1005828
                5679653
                29084212
                83510ad2-7ccf-41eb-af8b-ddba675b3242
                © 2017 Vedula et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 9 June 2017
                : 15 October 2017
                Page count
                Figures: 9, Tables: 0, Pages: 24
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/100000050, National Heart, Lung, and Blood Institute;
                Award ID: 5R01HL129727-02
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100000050, National Heart, Lung, and Blood Institute;
                Award ID: R01HL111437
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100007523, Division of Advanced Cyberinfrastructure;
                Award ID: 1339824
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100000968, American Heart Association;
                Award ID: 15PRE21400019
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100000001, National Science Foundation;
                Award ID: XSEDE TG-CTS30034
                Award Recipient :
                The authors acknowledge financial support through NIH NHLBI R01 grant 5R01HL129727-02. VV & ALM would also like to acknowledge computing resources received through NSF XSEDE grant TG-CTS30034 and software resources provided by the SimVascular project ( www.simvascular.org) under NSF ACI 1339824. JL would like to acknowledge funding received through AHA pre-doctoral grant 15PRE21400019. TKH also acknowledges support through NIH NHLBI R01 grant R01HL111437. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Research and Analysis Methods
                Experimental Organism Systems
                Model Organisms
                Zebrafish
                Research and Analysis Methods
                Model Organisms
                Zebrafish
                Research and Analysis Methods
                Experimental Organism Systems
                Animal Models
                Zebrafish
                Biology and Life Sciences
                Organisms
                Eukaryota
                Animals
                Vertebrates
                Fish
                Osteichthyes
                Zebrafish
                Research and Analysis Methods
                Imaging Techniques
                Biology and Life Sciences
                Developmental Biology
                Embryology
                Embryos
                Biology and Life Sciences
                Anatomy
                Body Fluids
                Blood
                Blood Flow
                Medicine and Health Sciences
                Anatomy
                Body Fluids
                Blood
                Blood Flow
                Biology and Life Sciences
                Physiology
                Body Fluids
                Blood
                Blood Flow
                Medicine and Health Sciences
                Physiology
                Body Fluids
                Blood
                Blood Flow
                Medicine and Health Sciences
                Hematology
                Hemodynamics
                Biology and Life Sciences
                Anatomy
                Cardiovascular Anatomy
                Heart
                Cardiac Ventricles
                Medicine and Health Sciences
                Anatomy
                Cardiovascular Anatomy
                Heart
                Cardiac Ventricles
                Physical Sciences
                Chemistry
                Chemical Properties
                Viscosity
                Physical Sciences
                Chemistry
                Physical Chemistry
                Chemical Properties
                Viscosity
                Physical Sciences
                Materials Science
                Materials Physics
                Viscosity
                Physical Sciences
                Physics
                Materials Physics
                Viscosity
                Biology and Life Sciences
                Anatomy
                Cardiovascular Anatomy
                Heart
                Endocardium
                Medicine and Health Sciences
                Anatomy
                Cardiovascular Anatomy
                Heart
                Endocardium
                Custom metadata
                vor-update-to-uncorrected-proof
                2017-11-09
                All image segmentation, cardiac model construction and finite element software is available as part of the SimVascular open source project at www.simvascular.org. The registration toolkit is available at https://sites.google.com/site/myronenko/research/mirt. Image data and simulation results has been incorporated at vascular model repository at http://www.vascularmodel.com/sandbox/doku.php.

                Quantitative & Systems biology
                Quantitative & Systems biology

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