Assessing clot lysis strategies using a simplified mathematical model

Abstract

This paper attempts to describe lysis of a clot by infusion of lytic agent using a simple geometrical approach, in which the rate of clot lysis is assumed proportional to the exposed surface of the clot and the concentration of lytic agent. Six simple realizations (a)-(f) of this basic model are developed which account for the dependence of clot lysis time on five different clot geometries. In all six cases the clot is initially described as a uniform cylinder which totally occludes a vessel. In model (a) lysis proceeds as an advancing front at the proximal face of the clot. In model (b) lysis proceeds radially outwards from the central axis of the vessel while in model (c) lysis occurs radially inwards from the surface adjacent the wall, of the cylinder. In models (d) and (e) it is assumed that the clot breaks into n uniform spherical and cylindrical fragments, respectively, while model (f) uses the spherical fragment model combined with a lytic agent concentration which decreases with time. The validity of the models was assessed using previously published data from 76 patients in whom lysis time and clot size were recorded. Least squares linear regression analysis based on the six model equations yielded highly significant correlation coefficients r² of 0.457, 0.412, 0.412, 0.495, 0.469, 0.663 for models (a)-(f), respectively. The results suggest that when a constant lytic agent concentration is assumed, no single geometry accounts for significantly more variation than any other, but that a combination of varying lytic agent concentration and clot geometry significantly influences clot lysis time and accounts for much of the observed variation.