A Mathematical Model Representing the Cortical Folding Disorder Hemimegalencephaly
Poster No:
2136
Submission Type:
Abstract Submission
Authors:
Monica Hurdal1, Sarah Kim2
Institutions:
1Florida State University, Tallahassee, FL, 2Univeristy of Florida, Orlando, FL
First Author:
Co-Author:
Introduction:
The complexity of brain folding patterns make it extremely challenging to study brain diseases since there is such variability in the folding patterns across healthy individuals. There is considerable debate among biologists as to how folding patterns develop, including biochemical [1], biomechanical [2], and differential growth hypotheses. In previous work we developed a combined biochemical-biomechanical model to elucidate the mechanisms of cortical folding development [3]. In this research, we alter various model parameters and demonstrate how disorders of cortical formations such as hemimegalencephaly can be explained by parameters in our model.
Methods:
The intermediate progenitor (IP) model is a biochemical biological hypothesis to explain pre-patterning of cortical folding in early development [1]. Several genes have been shown to regulate cortical folding via modulating IP cell development in mice. Our biochemical model [3] uses a dynamically growing domain Turing reaction-diffusion system [4] where the morphogens regulate IP cell patterning. A chemical morphogen activates IP cell proliferation in specific regions, resulting in folding patterns on the cerebral cortex caused by irregular distributions of cell populations throughout the surface. The concentration of neurons from the Turing model are used to govern the magnitude of the applied axonal tension forces in our biomechanical model. We use a linear stress-strain-elasticity model with biophysical parameters to determine displacements due to external forces. The deformation of a two-dimensional semi-circular domain representing the cerebral cortex is implemented computationally using a finite element formulation. External forces corresponding to the axonal tension-forces are applied on the boundary of the model cortex.
The lateral ventricle of a brain with hemimegalencephaly is enlarged, so it may contain more IP cells as compared to a healthy brain, resulting in the production of excessive number of neurons. We model the asymmetrically increased cell proliferation with irregular Turing patterns. The cortex of a brain with hemimegalencephaly also has a thickened cortex [5], which is captured by one of the model parameters.
The lateral ventricle of a brain with hemimegalencephaly is enlarged, so it may contain more IP cells as compared to a healthy brain, resulting in the production of excessive number of neurons. We model the asymmetrically increased cell proliferation with irregular Turing patterns. The cortex of a brain with hemimegalencephaly also has a thickened cortex [5], which is captured by one of the model parameters.
Results:
The morphogens evolve and change rapidly during domain growth and converge when growth stops. We assume the morphogen concentration is correlated to the concentration of neurons and determine the magnitude of the applied axonal tension force in our biomechanical model (Fig. 1).
Irregular Turing patterns can be generated by changing the initial conditions of the model. These irregular patterns lead to asymmetric forces. When applied to the semi-circular model cortex, the asymmetric forces pull together, resulting in a deformed configuration corresponding to an enlarged hemisphere. Increasing the thickness of the cortex reduces the elongation of the asymmetric development (Fig. 2).
Irregular Turing patterns can be generated by changing the initial conditions of the model. These irregular patterns lead to asymmetric forces. When applied to the semi-circular model cortex, the asymmetric forces pull together, resulting in a deformed configuration corresponding to an enlarged hemisphere. Increasing the thickness of the cortex reduces the elongation of the asymmetric development (Fig. 2).
Conclusions:
MR images of brains with hemimegalencephaly show one hemisphere to be enlarged. The hemisphere grows asymmetrically and the cortex is thicker [6]. Modifying model parameters and initial conditions allow us to explore possible mechanisms involved in disorders of cortical formations. Irregular Turing patterns are used to represent asymmetric IP cells in the lateral ventricle of a hemimegalencephalic brain. The corresponding asymmetric forces and increased cortical thickness parameter result in an enlarged cortex configuration in one hemisphere.
Our model is the first model to explore how different IP cell patterns can lead to unusual cortex configurations that can be correlated to cortical patterning disorders. This modeling and simulation research represents an important step in improving our understanding of cortical folding pattern formation.
Our model is the first model to explore how different IP cell patterns can lead to unusual cortex configurations that can be correlated to cortical patterning disorders. This modeling and simulation research represents an important step in improving our understanding of cortical folding pattern formation.
Modeling and Analysis Methods:
Methods Development 2
Other Methods
Neuroanatomy, Physiology, Metabolism and Neurotransmission:
Anatomy and Functional Systems
Cortical Anatomy and Brain Mapping 1
Neuroanatomy Other
Keywords:
Development
DISORDERS
Modeling
STRUCTURAL MRI
Other - Hemimegalencaphaly; Brain Mapping; Cortical Folding; Sulcus
1|2Indicates the priority used for review
Provide references using author date format
[2] Van Essen, D.C. (1997), Nature, 385: 313-318.
[3] Striegel, D.A. & Hurdal, M.K. (2009), PLoS Computational Biology, 5: e1000524.
[4] Turing, A.M. (1952), Philosophical Transactions of the Royal Society of London B., 237: 37-72.
[5] Abdel Razek, A.A.K. et al. (2009), American Journal of Radiology, 30:4-11.
[6] Kim, S. (2015), Florida State University, PhD Dissertation.