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Published February 1, 2001 | public
Journal Article Open

Mechanical haemolysis in shock wave lithotripsy (SWL): I. Analysis of cell deformation due to SWL flow-fields


This work analyses the interaction of red blood cells (RBCs) with shock-induced and bubble-induced flows in shock wave lithotripsy (SWL), and calculates, in vitro, the lytic effects of these two flows. A well known experimentally observed fact about RBC membranes is that the lipid bilayer disrupts when subjected to an areal strain (ΔA/A)c of 3%, and a corresponding, critical, isotropic tension, Tc, of 10 mN m-1 (1 mN m-1 = 1 dyne cm-1). RBCs suspended in a fluid medium tend to deform in accordance with the deformation of the surrounding fluid medium. The fluid flow-field is lytically effective if the membrane deformation exceeds the above threshold value. From kinematic analysis, motion of an elementary fluid particle can always be decomposed into a uniform translation, an extensional flow (e.g. vec u∞(x,y,z) = (k(t)x,-k(t)y,0)) along three mutually perpendicular axes, and a rigid rotation of these axes. However, only an extensional flow causes deformation of a fluid particle, and consequently deforms the RBC membrane. In SWL, a fluid flow-field, induced by a non-uniform shock wave, as well as radial expansion/implosion of a bubble, has been hypothesized to cause lysis of cells. Both the above flow-fields constitute an unsteady, extensional flow, which exerts inertial as well as viscous forces on the RBC membrane. The transient inertial force (expressed as a tension, or force/length), is given by Tiner~ρrc3k/τ, where τ is a timescale of the transient flow and rc is a characteristic cell size. When the membrane is deformed due to inertial effects, membrane strain is given by ΔA/A~kτ. The transient viscous force is given by Tvisc~ρ(ν/τ)1/2rc2k, where ρ and ν are the fluid density and kinematic viscosity. For the non-uniform shock, the extensional flow exerts an inertial force, Tinerapprox64 mN m-1, for a duration of 3 ns, sufficient to induce pores in the RBC membrane. For a radial flow-field, induced by bubble expansion/implosion, the inertial forces are of a magnitude 100 mN m-1, which last for a duration of 1 µs, sufficient to cause rupture. Bubble-induced radial flow is predicted to be lytically more effective than shock-induced flow in typical in vitro experimental conditions.

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© Institute of Physics 2001. Received 5 September 2000, in final form 13 November 2000; Print publication: Issue 2 (February 2001) We thank Ganesh Subramanian of California Institute of Technology and Dr Jim Williams of Indiana University School of Medicine for their valuable comments on the ideas discussed in this work. This work was supported by NIH Grant P01 DK43881.


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