title: Intraoperative blood salvage: a mathematical perspective.
abstract: BACKGROUND
  Intraoperative blood salvage (IBS) is one of several blood-conservation strategies employed to limit the use of allogeneic blood. IBS with mathematical modeling was studied to gain a better understanding of its benefits and limitations.
  
  
  METHODS
  Equations, based on a convergent geometric series, allowed the assessment of maximum allowable blood losses to avoid allogeneic RBC exposure in relationship to the fractional recovery of IBS. Such equations allowed us to calculate the potential "savings" in allogeneic RBC volume and to define better the efficiency of IBS.
  
  
  RESULTS
  This model predicts that substantial amounts of RBCs (>2 units) can be recovered if there is large blood loss (e.g., >3000 mL) and if the minimal allowable Hct is low (e.g., 21%). As with other blood- conservation methods, this article shows that there are limits to the potential benefit of IBS for the avoidance of allogeneic RBC transfusion.
  
  
  CONCLUSIONS
  IBS can be modeled with a convergent geometric series, and the amount of blood loss is dependent on the difference between the patient's starting Hct, the minimum allowable Hct, and the fractional recovery of RBCs. Such modeling illustrates the limited utility of IBS as a sole blood-conservation strategy.
authors.affiliation: Department of Pathology, University of North Carolina and Transfusion Medicine Service, University of North Carolina Hospitals, Chapel Hill 27514, USA.
authors.forename: Shauna N
authors.initials: SN
authors.lastname: Hay
authors.forename: Terri G
authors.initials: TG
authors.lastname: Monk
authors.forename: Mark E
authors.initials: ME
authors.lastname: Brecher
mesh_terms: D016063:Blood Loss, Surgical; D001800:Blood Specimen Collection / Q000379:methods*; D003198:Computer Simulation; D006400:Hematocrit; D007430:Intraoperative Care; D008433:Mathematics; D008954:Models, Biological