title: Blunt trauma to large vessels: a mathematical study.
abstract: BACKGROUND
  Blunt trauma causes short-term compression of some or all parts of the chest, abdomen or pelvis and changes hemodynamics of the blood. Short-term compression caused by trauma also results in a short-term decrease in the diameter of blood vessels. It has been shown that with a sudden change in the diameter of a tube or in the direction of the flow, the slower-moving fluid near the wall stops or reverses direction, which is known as boundary layer separation (BLS). We hypothesized that a sudden change in the diameter of elastic vessel that results from compression may lead not only to BLS but also to other hemodynamic changes that can damage endothelium.
  
  
  METHODS
  We applied Navier-Stokes, multiphase and boundary layer equations to examine such stress. The method of approximation to solve the BL equations was used. Experiments were conducted in an aerodynamic tube, where incident flow velocity and weight of carriage with particles before and after blowing were measured.
  
  
  RESULTS
  We found that sudden compression resulting from trauma leads to (1) BLS on the curved surface of the vessel wall; (2) transfer of laminar boundary layer into turbulent boundary layer. Damage to the endothelium can occur if compression is at least 25% and velocity is greater than 2.4 m/s or if compression is at least 10% and velocity is greater than 2.9 m/s.
  
  
  CONCLUSIONS
  Our research may point up new ways of reducing the damage from blunt trauma to large vessels. It has the potential for improvement of safety features of motor vehicles. This work will better our understanding of the precise mechanics and critical variables involved in diagnosis and prevention of blunt trauma to large vessels.
authors.affiliation: Department of Epidemiology, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA 15213, USA. rmi1@pitt.edu
authors.forename: Rovshan M
authors.initials: RM
authors.lastname: Ismailov
authors.forename: Nikolai A
authors.initials: NA
authors.lastname: Shevchuk
authors.forename: Joseph
authors.initials: J
authors.lastname: Schwerha
authors.forename: Lawrence
authors.initials: L
authors.lastname: Keller
authors.forename: Higmat
authors.initials: H
authors.lastname: Khusanov
mesh_terms: D001011:Aorta / Q000293:injuries / Q000473:pathology / Q000503:physiopathology; D001783:Blood Flow Velocity; D001808:Blood Vessels / Q000293:injuries* / Q000473:pathology / Q000503:physiopathology; D004730:Endothelium, Vascular / Q000293:injuries / Q000473:pathology; D006439:Hemodynamics; D006801:Humans; D008433:Mathematics; D008955:Models, Cardiovascular; D033081:Shear Strength