Modulation of ATP/ADP Concentration at the Endothelial Surface by Shear Stress: Effect of Flow Recirculation HYO WON CHOI, 1 KATHERINE W. FERRARA, 2 and ABDUL I. BARAKAT 1 1 Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA, 95616, USA; and 2 Department of Biomedical Engineering, University of California, Davis, CA, 95616, USA (Received 21 February 2006; accepted 5 December 2006; published online 26 January 2007) Abstract—The extracellular presence of the adenine nucleo- tides ATP and ADP induces calcium mobilization in vascular endothelial cells (ECs). ATP/ADP concentration at the EC surface is determined by a balance of convective-diffusive transport to and from the EC surface, hydrolysis by ectonucleotidases at the cell surface, and flow-induced ATP release from ECs. Our previous numerical simulations in a parallel plate geometry had demonstrated that flow-induced ATP release has a profound effect on nucleotide concentra- tion at the EC surface. In the present study, we have extended the modeling to probe the impact of flow separation and recirculation downstream of a backward facing step (BFS) on ATP/ADP concentration at the EC surface. The results show that for both steady and pulsatile flow over a wide range of wall shear stresses, the ATP + ADP concentration at the EC surface is considerably lower within the flow recirculation region than in areas of undisturbed flow outside the recirculation zone. Pulsatile flow also leads to sharp temporal gradients in nucleotide concentration. If confirmed experimentally, the present findings suggest that disturbed and undisturbed flow may affect EC calcium mobilization differently. Such differences might, in turn, contribute to the observed endothelial dysfunction in regions of disturbed flow. Keywords—Endothelium, ATP, ADP, Adenine nucleotides, Shear stress, Atherosclerosis, Mechanotransduction, Flow recirculation, Backward facing step. INTRODUCTION The extracellular presence of the adenine nucleo- tides ATP and ADP stimulates the production of vasoactive agents and mobilizes intracellular calcium in vascular endothelial cells (ECs). 7,30 Both of these responses are also modulated by fluid mechanical shear stress on the cell surface. 1,14,33,35 Therefore, determin- ing the effect of shear stress on adenine nucleotide concentration at the EC surface is essential for understanding flow-mediated vasoregulation and cal- cium signaling. Nollert et al. 26,27 had previously developed mathe- matical models that demonstrated that the ATP con- centration at the EC surface increases with the magnitude of applied shear stress. Because ADP is virtually as potent as ATP in mobilizing EC intracel- lular calcium, Shen et al. 34 extended the modeling to include ADP and showed that the combined nucleotide (ATP + ADP) cell-surface concentration increases only slightly over a wide range of shear stress. These results were used to argue that shear stress affects EC intracellular calcium directly rather than through the more indirect pathway of altering nucleotide concen- tration at the EC surface. Subsequently, motivated by experimental data demonstrating that flow elicits ATP release in ECs, 22 John and Barakat 19 incorporated shear stress-induced ATP release into the model. Their simulations revealed that for sufficiently rapid ATP release, the ATP + ADP concentration at the EC surface is strongly dependent on the applied shear stress, suggesting that transport of nucleotides to and from the EC surface may indeed contribute signifi- cantly to flow-induced calcium mobilization. Most of the previous numerical results were obtained in parallel plate flow chambers where the velocity profile and wall shear stress distribution are known a priori and thus need not be determined as part of the solution. In large arteries, curvature and branching often lead to regions of flow separation and recirculation that are associated with sharp spatial variations in wall shear stress. 3,20,21,24 These complex flow patterns correlate with the endothelial dysfunc- tion occurring during the early development of ath- erosclerosis. 4,11,25 Therefore, there is a need for elucidating the effect of complex flows on EC-surface ATP/ADP concentration. David 10 and Plank et al. 31,32 used a similarity formulation to derive an analytical solution for the ATP/ADP concentration at the EC Address correspondence to Abdul I. Barakat, Department of Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, Davis, CA, 95616, USA. Electronic mail: abarakat@ucdavis.edu Annals of Biomedical Engineering, Vol. 35, No. 4, April 2007 (Ó 2007) pp. 505–516 DOI: 10.1007/s10439-006-9247-9 0090-6964/07/0400-0505/0 Ó 2007 Biomedical Engineering Society 505