Simulating Organogenesis in COMSOL: Phase-Field Based Simulations of Embryonic Lung Branching Morphogenesis

Organogenesis has been studied for decades, but fundamental questions regarding the control of growth and shape remain unsolved. We have recently shown that of all proposed mathematical models only ligand-receptor based Turing models successfully reproduce the experimentally determined growth fields of the embryonic lung and thus provide a mechanism for growth control during embryonic lung development. Turing models are based on at least two coupled non-linear reaction-diffusion equations. In case of the lung model, at least two distinct layers (mesenchyme and epithelium) need to be considered that express different components (ligand and receptor, respectively). The Arbitrary Lagrangian-Eulerian (ALE) method has previously been used to solve this Turing system on growing and deforming (branching) domains, where outgrowth occurs proportional to the strength of ligand-receptor signalling. However, the ALE method requires mesh deformations that eventually limit its use. Therefore, we incorporate the phase field method to simulate 3D embryonic lung branching with COMSOL.

[1]  Nobuyuki Itoh,et al.  Fgf10 is essential for limb and lung formation , 1999, Nature Genetics.

[2]  B. Spencer‐Dene,et al.  An important role for the IIIb isoform of fibroblast growth factor receptor 2 (FGFR2) in mesenchymal-epithelial signalling during mouse organogenesis. , 2000, Development.

[3]  Xiangrong Li,et al.  SOLVING PDES IN COMPLEX GEOMETRIES: A DIFFUSE DOMAIN APPROACH. , 2009, Communications in mathematical sciences.

[4]  Dagmar Iber,et al.  Digit patterning during limb development as a result of the BMP-receptor interaction , 2012, Scientific Reports.

[5]  A. Turing.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[6]  Dagmar Iber,et al.  Simulating Organogenesis in COMSOL: Image-based Modeling , 2014, ArXiv.

[7]  Dagmar Iber,et al.  The control of branching morphogenesis , 2013, Open Biology.

[8]  H. Meinhardt,et al.  A theory of biological pattern formation , 1972, Kybernetik.

[9]  B. Hogan,et al.  Fibroblast growth factor 10 (FGF10) and branching morphogenesis in the embryonic mouse lung. , 1997, Development.

[10]  J. Waals.  The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density , 1979 .

[11]  Dagmar Iber,et al.  Image-based Modelling of Organogenesis , 2015, Briefings Bioinform..

[12]  A. M. Turing,et al.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[13]  I. Epstein,et al.  Pattern formation in a tunable medium: the Belousov-Zhabotinsky reaction in an aerosol OT microemulsion. , 2001, Physical review letters.

[14]  J. Azaïs,et al.  A Role for Mesenchyme Dynamics in Mouse Lung Branching Morphogenesis , 2012, PloS one.

[15]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[16]  Dagmar Iber,et al.  Simulating Organogenesis in COMSOL , 2011 .

[17]  Dagmar Iber,et al.  Simulation Organogenesis in COMSOL: Deforming and Interacting Domains , 2012, 1210.0810.

[18]  Ophir D. Klein,et al.  The branching programme of mouse lung development , 2008, Nature.

[19]  Terence Hwa,et al.  Predicting the spatiotemporal dynamics of hair follicle patterns in the developing mouse , 2014, Proceedings of the National Academy of Sciences.

[20]  Peng Song,et al.  A diffuse-interface method for two-phase flows with soluble surfactants , 2011, J. Comput. Phys..

[21]  István Szalai,et al.  An Experimental Design Method Leading to Chemical Turing Patterns , 2009, Science.

[22]  M. Akam,et al.  Drosophila development: making stripes inelegantly. , 1989, Nature.

[23]  A. Voigt,et al.  Adaptive diffuse domain approach for calculating mechanically induced deformation of trabecular bone , 2014, Computer methods in biomechanics and biomedical engineering.

[24]  Axel Voigt,et al.  A DIFFUSE-INTERFACE APPROACH FOR MODELING TRANSPORT, DIFFUSION AND ADSORPTION/DESORPTION OF MATERIAL QUANTITIES ON A DEFORMABLE INTERFACE. , 2009, Communications in mathematical sciences.

[25]  Guillermo Sapiro,et al.  Variational Problems and Partial Differential Equations on Implicit Surfaces: Bye Bye Triangulated Surfaces? , 2003 .

[26]  Dagmar Iber,et al.  An interplay of geometry and signaling enables robust lung branching morphogenesis , 2014, Development.

[27]  Blagoy Blagoev,et al.  Functional proteomics defines the molecular switch underlying FGF receptor trafficking and cellular outputs. , 2013, Molecular cell.

[28]  John Lowengrub,et al.  Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules , 2016, J. Comput. Phys..

[29]  Dagmar Iber,et al.  Inter-dependent tissue growth and Turing patterning in a model for long bone development , 2013, Physical biology.

[30]  G. Kreiss,et al.  A conservative level set method for two phase flow II , 2005, Journal of Computational Physics.

[31]  Dagmar Iber,et al.  Dynamic Image-Based Modelling of Kidney Branching Morphogenesis , 2013, CMSB.

[32]  Dagmar Iber,et al.  Branch Mode Selection during Early Lung Development , 2012, PLoS Comput. Biol..

[33]  I. Prigogine,et al.  Symmetry Breaking Instabilities in Dissipative Systems. II , 1968 .

[34]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[35]  B. Hogan,et al.  Bmp4 and Fgf10 play opposing roles during lung bud morphogenesis. , 2000, Development.

[36]  S. Werner,et al.  Targeted expression of a dominant negative FGF receptor blocks branching morphogenesis and epithelial differentiation of the mouse lung. , 1994, The EMBO journal.

[37]  Dagmar Iber,et al.  Kidney branching morphogenesis under the control of a ligand–receptor-based Turing mechanism , 2013, Physical biology.

[38]  I. Prigogine,et al.  On symmetry-breaking instabilities in dissipative systems , 1967 .

[39]  A. Voigt,et al.  PDE's on surfaces---a diffuse interface approach , 2006 .

[40]  Axel Voigt,et al.  A continuum model of colloid-stabilized interfaces , 2011 .

[41]  Dagmar Iber,et al.  Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.