Journal of Biomechanics 32 (1999) 1107}1112 A discussion on the threshold limit for hemolysis related to Reynolds shear stress M. Grigioni*, C. Daniele, G. D'Avenio, V. Barbaro Istituto Superiore di Sanita % , Laboratory of Biomedical Engineering, Viale Regina Elena 299, 00161 Roma, Italy Received 16 July 1998; accepted 8 March 1999 Abstract Turbulence-related damage to blood is a major problem with the use of prosthetic devices, such as mechanical heart valves. An often-cited paper by Sallam and Hwang (1984). Biorheology 21, 783}797) quanti"ed the threshold for hemolysis to be about 400 Nm, a value that has hitherto contributed to the evaluation of the potential dangerousness of a medical implantable device. We propose a discussion of the mentioned experiment, based on the application of stress analysis concepts to the original measurements: this is necessary to assess the peak turbulence shear stress value that could have been found in Sallam and Hwangs experiment, with a suitable orientation of the measurement axes. The result of our theoretical discussion is that the threshold value of 400 N m could probably be considerably underestimated: following this point of view, a 3-D stress analysis shows that the peak turbulence shear stress at the inception of hemolysis should be at least 600 N m. This result, obtained on the basis of the study of RBCs' response to a turbulent environment, indicates that blood particles are probably more resistant to short-time shear stresses than it was thought.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Reynolds shear stress; Hemolysis; Implantable devices 1. Introduction A common concern about the use of prosthetic devices in the human body is the minimization of the possible damage that can arise from an implanted arti"cial struc- ture. In particular, prosthetic heart valves (PHVs) are known to a!ect the local hemodynamic conditions, with a possible thrombogenic behavior (Stein and Sabbah, 1974; Edmunds, 1982; Arom et al., 1987): in fact, the patient has to follow a strict anticoagulant therapy, after arti"cial heart valve replacement (Czer et al., 1985). A major problem with devices directly exposed to blood is the possibility of hemolysis they can produce, due to the shear stresses in the #ow through them (Blackshear, 1972). An experiment made by Sallam and Hwang (1984) quanti"ed the value of Reynolds shear stress (RSS) uv (that is, the turbulence-related shear stress) respon- * Corresponding author. Tel.: # 39-6-49902855; fax: # 39-6- 49387079. E-mail address: Grigioni@SUN.ISS.IT (M. Grigioni) sible for the inception of hemolysis to be 400 N m, and this value has been considered in several works in litera- ture the threshold for lethal damage to erythrocytes, for an exposure time of about 1 ms (Hasenkam et al., 1988; Hanle et al., 1989; Nygaard et al., 1990). However, since the measured turbulence shear stress, as any other kind of shear stress, is a quantity dependent on the orientation of the measurement system (Malvern, 1969; Baldwin et al., 1993; Fontaine et al., 1996; Barbaro et al., 1997), it can be shown that the value uv "400 N m, in the condi- tions of the mentioned experiment, was not the max- imum value (as far as all orientations of a generic surface element are considered) of the measurable Reynolds shear stress, to which blood was actually exposed, at the inception of hemolysis. With simple assumptions on the #ow used by Sallam and Hwang (1984) to study the hemolytic behavior of turbulence, the threshold limit of RSS for hemolysis can be recalculated to be 600 N m or higher. In fact, using the information taken from the mentioned study, we can propose the following dis- cussion, based on the application of stress analysis to turbulence measurements (Fontaine et al., 1996; Barbaro et al., 1997). 0021-9290/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 0 6 3 - 9