title: Emerging Brain Morphologies from Axonal Elongation.
abstract: Understanding the characteristic morphology of our brain remains a challenging, yet important task in human evolution, developmental biology, and neurosciences. Mathematical modeling shapes our understanding of cortical folding and provides functional relations between cortical wavelength, thickness, and stiffness. Yet, current mathematical models are phenomenologically isotropic and typically predict non-physiological, periodic folding patterns. Here we establish a mechanistic model for cortical folding, in which macroscopic changes in white matter volume are a natural consequence of microscopic axonal growth. To calibrate our model, we consult axon elongation experiments in chick sensory neurons. We demonstrate that a single parameter, the axonal growth rate, explains a wide variety of in vitro conditions including immediate axonal thinning and gradual thickness restoration. We embed our axonal growth model into a continuum model for brain development using axonal orientation distributions motivated by diffusion spectrum imaging. Our simulations suggest that white matter anisotropy-as an emergent property from directional axonal growth-intrinsically induces symmetry breaking, and predicts more physiological, less regular morphologies with regionally varying gyral wavelengths and sulcal depths. Mechanistic modeling of brain development could establish valuable relationships between brain connectivity, brain anatomy, and brain function.
authors.affiliation: Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA, mholla@stanford.edu.
authors.forename: Maria A
authors.initials: MA
authors.lastname: Holland
authors.forename: Kyle E
authors.initials: KE
authors.lastname: Miller
authors.forename: Ellen
authors.initials: E
authors.lastname: Kuhl
mesh_terms: D000818:Animals; D001369:Axons / Q000502:physiology*; D001921:Brain / Q000254:growth & development*; D002645:Chickens; D020342:Finite Element Analysis; D008959:Models, Neurological; D011984:Sensory Receptor Cells / Q000502:physiology
references.citation: Science. 1975 Jul 4;189(4196):18-21
references.pmid: 1135626
references.citation: Am J Psychiatry. 2003 Sep;160(9):1606-13
references.pmid: 12944334
references.citation: Neuroimage. 2004 Jul;22(3):1302-14
references.pmid: 15219602
references.citation: J Neurosci. 2004 Sep 8;24(36):7978-83
references.pmid: 15356212
references.citation: Psychiatry Res. 2004 Sep 15;131(3):263-8
references.pmid: 15465295
references.citation: Cereb Cortex. 2005 Dec;15(12):1900-13
references.pmid: 15758198
references.citation: J R Soc Interface. 2006 Feb 22;3(6):15-35
references.pmid: 16849214
references.citation: Semin Fetal Neonatal Med. 2006 Dec;11(6):415-22
references.pmid: 16962836
references.citation: J Neurosci. 2007 Oct 24;27(43):11725-35
references.pmid: 17959814
references.citation: Biophys J. 2008 Apr 1;94(7):2610-20
references.pmid: 18178646
references.citation: Biomech Model Mechanobiol. 2009 Aug;8(4):253-62
references.pmid: 18651186
references.citation: J Theor Biol. 2008 Dec 21;255(4):369-77
references.pmid: 18845167
references.citation: Nat Rev Neurosci. 2009 Oct;10(10):724-35
references.pmid: 19763105
references.citation: Dev Neurobiol. 2010 Feb 15;70(3):135-49
references.pmid: 19950193
references.citation: J Mech Behav Biomed Mater. 2010 Feb;3(2):158-66
references.pmid: 20129415
references.citation: J Biomech Eng. 2010 Jul;132(7):071013
references.pmid: 20590291
references.citation: Cereb Cortex. 2011 Jul;21(7):1674-94
references.pmid: 21127018
references.citation: Prog Neurobiol. 2011 Jul;94(2):91-101
references.pmid: 21527310
references.citation: J Mech Phys Solids. 2011 Apr 1;59(4):863-883
references.pmid: 21532929
references.citation: J Neurotrauma. 2011 Nov;28(11):2389-403
references.pmid: 21663384
references.citation: Neuroimage. 2012 Feb 1;59(3):2255-65
references.pmid: 21985910
references.citation: Nature. 2012 Mar 21;483(7390):394-6
references.pmid: 22437591
references.citation: Mech Res Commun. 2012 Jun 1;42:1-14
references.pmid: 22919118
references.citation: PLoS One. 2012;7(10):e45661
references.pmid: 23049683
references.citation: J Biomech. 2013 Mar 15;46(5):863-70
references.pmid: 23352648
references.citation: Phys Biol. 2013 Feb;10(1):016005
references.pmid: 23357794
references.citation: J Mech Behav Biomed Mater. 2014 Jan;29:568-81
references.pmid: 23566768
references.citation: J Mech Behav Biomed Mater. 2013 Dec;28:495-509
references.pmid: 23623569
references.citation: Annu Rev Biomed Eng. 2013;15:227-51
references.pmid: 23642242
references.citation: J Mech Behav Biomed Mater. 2013 Jul;23:117-32
references.pmid: 23680651
references.citation: Neuroradiology. 2013 Sep;55 Suppl 2:23-40
references.pmid: 23832006
references.citation: Development. 2013 Aug;140(15):3069-77
references.pmid: 23861056
references.citation: Nat Rev Neurosci. 2014 Apr;15(4):217-32
references.pmid: 24646670
references.citation: JAMA Psychiatry. 2014 Jul 1;71(7):751-60
references.pmid: 24740586
references.citation: J Cell Sci. 2014 Aug 15;127(Pt 16):3593-602
references.pmid: 24951117
references.citation: Sci Rep. 2014 Jul 10;4:5644
references.pmid: 25008163
references.citation: Proc Natl Acad Sci U S A. 2014 Sep 2;111(35):12667-72
references.pmid: 25136099
references.citation: J Mech Phys Solids. 2014 Dec 1;72:75-92
references.pmid: 25202162
references.citation: Biomech Model Mechanobiol. 2015 Oct;14(5):931-65
references.pmid: 25716305
references.citation: J Mech Behav Biomed Mater. 2015 Jun;46:318-30
references.pmid: 25819199
references.citation: J Cell Biol. 1989 Dec;109(6 Pt 1):3073-83
references.pmid: 2592415
references.citation: Prog Neurobiol. 1989;32(2):137-58
references.pmid: 2645619
references.citation: Philos Mag (Abingdon). 2015;95(28-30):3208-3224
references.pmid: 26752977
references.citation: Child Dev. 1987 Jun;58(3):601-22
references.pmid: 3608641
references.citation: J Anat. 1986 Jun;146:141-52
references.pmid: 3693054
references.citation: Dev Biol. 1984 Apr;102(2):379-89
references.pmid: 6706005
references.citation: J Biomech. 1994 Apr;27(4):455-67
references.pmid: 8188726
references.citation: Nature. 1997 Jan 23;385(6614):313-8
references.pmid: 9002514