eCommons

 

Mathematical Modeling And Statistical Analysis Of The Cortical Microvasculature And Hemodynamic Response

Other Titles

Abstract

Mathematical models can serve as useful tools to better understand physiology and biological phenomena. This work outlines several mathematical models and their connection with various types of cortical microvascular topology and blood flow data obtained with various imaging modalities. Three models are proposed. The first is a model based on electrical circuit ideas that describes the relationship between cortical neural activity and space-resolved and time-resolved blood flows in the ensuing hemodynamic response. The second model, also based on electrical circuits, seeks to predict blood flows in a network of blood vessels based on topological network data and experimental blood flow measurements taken on a subset of vessels in the network. Finally, random graph ideas are used to propose two related models to represent the cortical microvasculature topology. The first is a Poisson process approach in which a vessel network is modeled by randomly positioning nodes in a three-dimensional space and randomly placing an edge between pairs of nodes based on various hard and soft constraints. The second related model is based on a Gibbsian Markov Random Field approach in which a vessel network is created using a Hamiltonian that favors or penalizes certain network features according to physiologic observations of vessel network topology. A wide range of applications of these types of models are demonstrated.

Journal / Series

Volume & Issue

Description

Sponsorship

Date Issued

2014-01-27

Publisher

Keywords

Location

Effective Date

Expiration Date

Sector

Employer

Union

Union Local

NAICS

Number of Workers

Committee Chair

Doerschuk, Peter

Committee Co-Chair

Committee Member

Schaffer, Chris
Molnar, Alyosha Christopher

Degree Discipline

Biomedical Engineering

Degree Name

Ph. D., Biomedical Engineering

Degree Level

Doctor of Philosophy

Related Version

Related DOI

Related To

Related Part

Based on Related Item

Has Other Format(s)

Part of Related Item

Related To

Related Publication(s)

Link(s) to Related Publication(s)

References

Link(s) to Reference(s)

Previously Published As

Government Document

ISBN

ISMN

ISSN

Other Identifiers

Rights

Rights URI

Types

dissertation or thesis

Accessibility Feature

Accessibility Hazard

Accessibility Summary

Link(s) to Catalog Record