title: A statistical model of the penetrating arterioles and venules in the human cerebral cortex.
abstract: Models of the cerebral microvasculature are required at many different scales in order to understand the effects of microvascular topology on CBF. There are, however, no data-driven models at the arteriolar/venular scale. In this paper, we develop a data-driven algorithm based on available data to generate statistically accurate penetrating arterioles and venules.
  
  
  
  A novel order-based density-filling algorithm is developed based on the statistical data including bifurcating angles, LDRs, and area ratios. Three thousand simulations are presented, and the results validated against morphological data. These are combined with a previous capillary network in order to calculate full vascular network parameters.
  
  
  
  Statistically accurate penetrating trees were successfully generated. All properties provided a good fit to experimental data. The k exponent had a median of 2.5 and an interquartile range of 1.75-3.7. CBF showed a standard deviation ranging from ±18% to ±34% of the mean, depending on the penetrating vessel diameter.
  
  
  
  Small CBF variations indicate that the topology of the penetrating vessels plays only a small part in the large regional variations of CBF seen in the brain. These results open up the possibility of efficient oxygen and blood flow simulations at MRI voxel scales which can be directly validated against MRI data.
authors.affiliation: Department of Engineering, Institute of Biomedical Engineering, University of Oxford, Oxford, UK. wahbi.el-bouri@eng.ox.ac.uk.
authors.forename: Wahbi K
authors.identifier: 0000-0002-2732-5927
authors.initials: WK
authors.lastname: El-Bouri
authors.affiliation: Department of Engineering, Institute of Biomedical Engineering, University of Oxford, Oxford, UK.
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Payne
mesh_terms: D000465:Algorithms; D001160:Arterioles / Q000033:anatomy & histology* / Q000502:physiology; D002540:Cerebral Cortex / Q000098:blood supply; D002560:Cerebrovascular Circulation / Q000502:physiology*; D003198:Computer Simulation; D006439:Hemodynamics; D006801:Humans; D055806:Microvessels / Q000033:anatomy & histology; D015233:Models, Statistical; D014699:Venules / Q000033:anatomy & histology* / Q000502:physiology
keywords: Murray's law; cerebral blood flow; microcirculation; microvasculature; vascular resistance