Type of Document Dissertation Author Striegel, Deborah A. Author's Email Address firstname.lastname@example.org URN etd-11092009-184905 Title Modeling the Folding Pattern of the Cerebral Cortex Degree Doctor of Philosophy Department Mathematics, Department of Advisory Committee
Advisor Name Title Monica K. Hurdal Committee Chair DeWitt Sumners Committee Member Jack Quine Committee Member Richard Bertram Committee Member Oliver Steinbock University Representative Keywords
- Cerebral Cortex
- Prolate Spheroid
- Turing System
- Cortical Folding Pattern
Date of Defense 2009-10-08 Availability unrestricted AbstractThe mechanism for cortical folding pattern formation is not fully understood. Current
models represent scenarios that describe pattern formation through local interactions and one
recent model is the intermediate progenitor model. The intermediate progenitor (IP) model
describes a local chemically-driven scenario, where an increase in intermediate progenitor
cells in the subventricular zone (an area surrounding the lateral ventricles) correlates to gyral
formation. This dissertation presents the Global Intermediate Progenitor (GIP) model, a
theoretical biological model that uses features of the IP model and further captures global
characteristics of cortical pattern formation. To illustrate how global features can eect the
development of certain patterns, a mathematical model that incorporates a Turing system
is used to examine pattern formation on a prolate spheroidal surface.
Pattern formation in a biological system can be studied with a Turing reaction-diusion
system which utilizes characteristics of domain size and shape to predict which pattern will
form. The GIP model approximates the shape of the lateral ventricle with a prolate spheroid.
This representation allows the capture of a key shape feature, lateral ventricular eccentricity,
in terms of the focal distance of the prolate spheroid.
A formula relating domain scale and focal distance of a prolate spheroidal surface to
specic prolate spheroidal harmonics is developed. This formula allows the prediction of
pattern formation with solutions in the form of prolate spheroidal harmonics based on the
size and shape of the prolate spheroidal surface.
By utilizing this formula a direct correlation between the size and shape of the lateral
ventricle, which drives the shape of the ventricular zone, and cerebral cortical folding pattern formation is found. This correlation is illustrated in two dierent applications: (i) how the
location and directionality of the initial cortical folds change with respect to evolutionary
development and (ii) how the initial folds change with respect to certain diseases, such as
Microcephalia Vera and Megalencephaly Polymicrogyria Polydactyly with Hydrocephalus.
The signicance of the GIP model, presented in this dissertation, is that it elucidates the
consistency of cortical patterns among healthy individuals within a species and addresses
inter-species variability based on global characteristics. This model provides a critical piece
to the puzzle of cortical pattern formation.
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