Affiliations: [a] Department of Biochemistry and Biophysics, University of Rochester, Rochester, New York, USA | [b] Department of Pharmacology and Physiology, University of Rochester, Rochester, New York, USA
Note: [*] Reprint requests to: Giles Cokelet, Department of Pharmacology and Physiology, University of Rochester, 601 Elmwood Avenue, Rochester, NY 14642, USA; Fax: (716) 244-9283; E-mail: [email protected]
Abstract: Computational fluid dynamics (CFD) and large scale model experiments were used to analyze the hemodynamic impact of leukocytes adherent to the wall of post-capillary venules. Using a large scale model and, with the aid of a finite element package, solving the Navier Stokes equations for low Reynolds number flow in a cylinder past an adherent sphere, we have developed a dimensionless correlation which permits the estimation of the pressure drop across an adherent leukocyte in an in vivo vessel. This relationship is:
f·Re=exp[2.877+4.630(dD)4]
where f is the Fanning friction factor, Re is the Reynolds number and d/D is the leukocyte to vessel diameter ratio. The friction factor is proportional to the pressure drop across the leukocyte, and does not significantly increase until d/D is greater than 0.5, and then increases rapidly with increasing d/D. Computations indicate that the length of the disturbed flow region generated by an adherent leukocyte increases with decreasing vessel size. The average wall stress in the disturbed flow region remains constant, and equal to the wall stress in the undisturbed region for d/D less than approximately 0.5. For d/D greater than 0.5, the average wall stress in the disturbed flow region increases rapidly with increasing d/D. There is an even larger increase, up to five times greater than the average disturbed stress, in the peak wall stress in the disturbed flow region. This indicates that significant wall stress gradients can be generated by an adherent leukocyte in post-capillary size vessels.
