title: A mathematical model relating cortical oxygenated and deoxygenated hemoglobin flows and volumes to neural activity.
abstract: OBJECTIVE
  To describe a toolkit of components for mathematical models of the relationship between cortical neural activity and space-resolved and time-resolved flows and volumes of oxygenated and deoxygenated hemoglobin motivated by optical intrinsic signal imaging (OISI).
  
  
  METHODS
  Both blood flow and blood volume and both oxygenated and deoxygenated hemoglobin and their interconversion are accounted for. Flow and volume are described by including analogies to both resistive and capacitive electrical circuit elements. Oxygenated and deoxygenated hemoglobin and their interconversion are described by generalization of Kirchhoff's laws based on well-mixed compartments.
  
  
  RESULTS
  Mathematical models built from this toolkit are able to reproduce experimental single-stimulus OISI results that are described in papers from other research groups and are able to describe the response to multiple-stimuli experiments as a sublinear superposition of responses to the individual stimuli.
  
  
  CONCLUSIONS
  The same assembly of tools from the toolkit but with different parameter values is able to describe effects that are considered distinctive, such as the presence or absence of an initial decrease in oxygenated hemoglobin concentration, indicating that the differences might be due to unique parameter values in a subject rather than different fundamental mechanisms.
authors.affiliation: Department of Biomedical Engineering, Weill Hall, Cornell University, Ithaca, NY 14853, USA.
authors.forename: Nathan R
authors.initials: NR
authors.lastname: Cornelius
authors.forename: Nozomi
authors.initials: N
authors.lastname: Nishimura
authors.forename: Minah
authors.initials: M
authors.lastname: Suh
authors.forename: Theodore H
authors.initials: TH
authors.lastname: Schwartz
authors.forename: Peter C
authors.initials: PC
authors.lastname: Doerschuk
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001783:Blood Flow Velocity / Q000502:physiology; D001810:Blood Volume / Q000502:physiology; D002560:Cerebrovascular Circulation / Q000502:physiology; D003198:Computer Simulation; D006454:Hemoglobins / Q000737:chemistry / Q000378:metabolism*; D006801:Humans; D008955:Models, Cardiovascular; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D000069336:Neurovascular Coupling / Q000502:physiology*; D010100:Oxygen / Q000737:chemistry* / Q000378:metabolism
chemical_list: D006454:Hemoglobins; D010100:Oxygen