A closed form solution of convective mass transfer model for intracellular calcium response of endothelial cells

Mathematical Problems in Engineering

Volumn 4, Issue 5, 1998, Pages 437-459

  Kumar, Vineet ^a,b   Pandey, R N ^a   Upadhyay, S N ^a  

^a BANARAS HINDU UNIVERSITY   (India)

^b School of Biochemical Engineering ^*

Author keywords

ATP; Calcium response; Endothelium; Mass transfer; Shear stress

Indexed keywords

EID: 0343084490     PISSN: 1024123X     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1024123x9800091x     Document Type: Article

References (41)

1. Pappenheimer, J.R., "Passase of molecules through capillary wall", Physiol. Rev., 33 (1953), 387-423.
2. Landis, E.M. and Pappenheimer, J.R., "Exchange of substance through the capillary walls", Handbook of Physiology (Am. Physiol. Soc., Washington), Section 2: Circulation, Vol. II (1963), pp. 961-1034.
3. Stemerman, M.B., Baumgartner, H.R. and Spaet, T.H., "The subendothelial microfibril and platelet adhesion", Lab. Invest., 24 (1971), 179-186.
4. Vander, A.J., Sherman, J.H. and Luciano, D.S., Human Physiology: The Mechanisms of Body Function, Tata-McGraw Hill, New Delhi (1981).
5. Yuan, F., Chien, S. and Weinbaum, S., "A new view of convective-diffusive transport processes in the arterial intima", Trans. ASME (J. Biomech. Eng.), 113 (1991), 314-329.
6. Furchgott, R.F. and Vanhoutte, P.M., "Endothelium derived relaxing and contracting factors", FASEB J., 3 (1989), 2007-2018.
7. Hong, S.L., McLaughlin, N.J., Tzeng, C. and Patton, G., "Prostacyclin synthesis and deacylation of phospholipids in human endothelial cells: comparison of thrombin, histamine and ionophore A23187", Thromb. Res., 38 (1985), 1-10.
8. Hallam, T.J., Pearson, J.D. and Needham, L.A., "Thrombin-stimulated elevation of human endothelial cell cytoplasmic free calcium concentration causes prostacyclin production", Biochem. J., 251 (1988), 243-249.
9. Pearson, J.D., Carleton, J.S. and Gordon, J.L., "Metabolism of adenine nucleotides by ectoenzymes of vascular endothelial and smooth muscle cells in culture", Biochem. J., 190 (1980), 421-429.
10. Pearson, J.D. and Gordon, J.L., "Nucleotide metabolism by endothelium", Annu. Rev. Physiol., 47 (1985), 617-627.
11. Nollert, M.U. and McIntire, L.V., "Convective mass transfer effects on the intracellular calcium response of endothelial cells", Trans. ASME (J. Biomech. Eng.), 114 (1992), 321-326.
12. Mo, M., Eskin, S.G. and Schilling, W.P., "Flow induced changes in calcium signaling of vascular endothelial cells: effect of shear stress and ATP", Am. J. Physiol., 260 (Heart Circ. Physiol. 29) (1991), H1698-H1707.
13. Frangos, J.A., Eskin, S.G., McIntire, L.V. and Ives, C.L., "Flow effects on prostacyclin production by culture human endothelial cell", Science, 227 (1985), 1477-1479.
14. Diamond, S.L., Eskin, S.G. and McIntire, L.V., "Fluid flow stimulates tissue plasminogen activator secration by cultured human endothelial cells", Science, 243 (1989), 1483-1485.
15. Grabowski, E.F., Jaffe, E.A. and Weksler, B.B., "Prostacyclin production by cultured endothelial cell monolayers exposed to step increases in shear stress", J. Lab. Clin. Med., 105 (1985), 36-43.
16. Fry, D.L., "Effect of pressure and stirring on in vitro aortic transmural I-albumin transport", Am. J. Physiol., 260 (Heart Circ. Physiol. 14) (1983), H977-H991.
17. Olesen, S.P., Clapham, D.E. and Davies, P.P., "Haemodynamic shear stress activates a K. current in vascular endothelial cells", Nature, 331 (1988), 168-170.
18. Davies, P.F., "How do vascular endothelial cells respond to flow?", News Physiol. Sci., 4 (1989), 22-25.
19. ++) coupling in vascular endothelial cells", Am. J. Physiol., 261(1) (1991), H149-H154.
20. Friedman, M.H., Bargeron, C.B., Duncan, D.D., Hutchins, G.M. and Mark, F.F., "Effects of arterial compliance and non-Newtonian rheology on correlations between intimai thickness and wall shear", Trans. ASME (J. Biomech. Eng.), 114 (1992), 317-320.
21. Nerem, R.M., "Vascular fluid mechanics, the arterial wall and atherosclerosis", Trans. ASME (J. Biomech. Eng.), 114 (1992), 274-282.
22. Okano, M. and Yoshida, Y., "Endothelial cell morphometry of atherosclerotic lesions and flow profiles at aortic bifurcations in cholesterol fed rabbits", Trans. ASME (J. Biomech. Eng.), 114 (1992), 301-308.
23. Satcher, R.L. Jr., Bussolri, S.R., Gimbrone, M.A. Jr. and Dewey, C.F. Jr., "The distribution of fluid forces on model arterial endothelium using computational fluid dynamics", Trans. ASME (J. Biomech. Eng.), 114 (1992), 309-316.
24. Holtz, J., Forstermann, U., Pohl, U., Geisler, M. and Bassenge, E., "Flow dependent endothelium-mediated dilation of epicardial coronary arteries in conscious dogs: Effects of cyclooxygenase inhibition", J. Cardiovasc. Pharmacol., 6 (1984), 1161-1169.
25. Pohl, U.J., Holtz, R.B. and Bassenge, E., "Crucial role of endothelium in the vasodilator response to increased flow in vivo", Hypertension Dallas, 7 (1986), 37-44.
26. Rubanyi, G.M., Romero, J.C. and Vanhoutte, P.M., "Flow induced release of endothelium-derived relxing factor", Am. J. Physiol., 250 (Heart Circ. Physiol. 19) (1986), H1145-H1149.
27. Kreutzberg, G., Reddington, M. and Zimmermann, H. (eds.), Cellular Biology of Ectoenzymes, Springer-Verlag: Berlin (1986).
28. Friedli, B., Kent, G. and Olley, P.M., "Inactivation of bradykinin in the pulmonary vascular bed of new born fetal Iambs", Circ. Res., 33 (1973), 421-427.
29. Burnstock, G., Physiological and Regulatory Functions of Adenosine and Adenine Nucleotides, Bassel: Karger (1978), pp. 278-284.
30. Lieberman, G.E., Lewis, G.P. and Peters, T.J., "A membrane bound enzyme in rabbit aorta capable of inhibiting adenosine-diphosphate induced platelet aggregation", Lancet, 2 (1977), 330-332.
31. Berridge, M.J., "Inositol trisphosphate and diacylglycerol: two interacting second messengers", Ann. Rev. Biochem., 59 (1987), 159-193.
32. Berridge, M.J. and Irvine, R.F., "Inositol phosphates and cell signaling", Nature, 341 (1989), 197-205.
33. Jans, D.A. and Hubner, S., "Regulation of protein transport to the nucleus: central role of phosporylation", Physiol. Rev., 76 (1996), 651-685.
34. Grimsrud, L. and Babb, A.L., "Velocity and concentration profiles for laminar flow of a Newtonian fluid in dialyzer", Chem. Eng. Prog. Symp. Ser., 62(66) (1966), 19-31.
35. Colton, C.K., Smith, K.A., Stroeve, P. and Merril, E.W., "Laminar flow mass transfer in a flat duct with permeable walls", AIChE J., 17 (1971), 773-780.
36. Coade, S.B. and Pearson, J.D., "Metabolism of adenine nucleotides in human blood", Circulation Research, 65(3) (1989), 531-537.
37. Berman, A.S., "Laminar flow in channels with porous walls", J. Appl. Phys., 24 (1953), 1232-1235.
38. Kozinski, A.A., Schmidt, F.P. and Lightfoot, E.N., "Velocity profile in porous walled duct", Ind. Eng. Chem. Fund., 9 (1970), 502-505.
39. Kleinstreuer, C. and Palier, M.S., "Laminar dilute suspension flow in plate-and-frame ultrafiltration units", AIChE J., 29 (1983), 529-533.
40. Kumar, V., "Mathematical modelling and computer simulation of membrane processes involving synthetic and natural membranes", Ph.D. Thesis, Dept. of Chem. Eng., Banaras Hindu University, Varanasi (1995).
41. Slater, L.J., Confluent Hypergeometric Functions, The Synodics of the Cambridge University Press (1960).