A mathematical model for the dissolution of non-occlusive blood clots in fast tangential blood flow.

Our aim was to study the effect of an axially directed blood plasma flow on the dissolution rate of cylindrical non-occlusive blood clots in an in vitro flow system and to derive a mathematical model for the process. The model was based on the hypothesis that clot dissolution dynamics is proportional not only to the biochemical proteolysis of fibrin but also to the power of the flowing blood plasma dissipated along the clot. The predicted rate of thrombolysis is then proportional to the square of the average blood plasma velocity for laminar flow and to the third power of the average velocity for turbulent flow. To verify the model, the time dependence of the clot cross-sectional area was measured by dynamic magnetic resonance microscopy during fast (turbulent) and slow (laminar) flow of plasma through an axially directed channel along the clot. The flowing plasma contained a magnetic resonance imaging contrast agent (Gd-DTPA) and a thrombolytic agent (recombinant tissue-type plasminogen activator). The experimental data fitted well to the model, and confirmed the predicted increase in the dissolution rate when blood flow changed from a laminar to a turbulent flow regime.