Modelling fibrinolysis: 1D continuum models

Fibrinolysis is the enzymatic degradation of the fibrin mesh that stabilizes blood clots. Experiments have shown that coarse clots made of thick fibres sometimes lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. This paper aims at using a 1D continuum reaction-diffusion model of fibrinolysis to elucidate the mechanism by which coarse clots lyse more quickly than fine clots. Reaction-diffusion models have been the standard tool for investigating fibrinolysis, and have been successful in capturing the wave-like behaviour of lysis seen in experiments. These previous models treat the distribution of fibrin within a clot as homogeneous, and therefore cannot be used directly to study the lysis of fine and coarse clots. In our model, we include a spatially heterogeneous fibrin concentration, as well as a more accurate description of the role of fibrin as a cofactor in the activation of the lytic enzyme. Our model predicts spatio-temporal protein distributions in reasonable quantitative agreement with experimental data. The model also predicts observed behaviour such as a front of lysis moving through the clot with an accumulation of lytic proteins at the front. In spite of the model improvements, however, we find that 1D continuum models are unable to accurately describe the observed differences in lysis behaviour between fine and coarse clots. Features of the problems that lead to the inaccuracy of 1D continuum models are discussed. We conclude that higher-dimensional, multiscale models are required to investigate the effect of clot structure on lysis behaviour.

Modelling fibrinolysis: a 3D stochastic multiscale model

Fibrinolysis, the proteolytic degradation of the fibrin fibres that stabilize blood clots, is initiated when tissue-type plasminogen activator (tPA) activates plasminogen to plasmin, the main fibrinolytic enzyme. Many experiments have shown that coarse clots made of thick fibres lyse more quickly than fine clots made of thin fibres, despite the fact that individual thick fibres lyse more slowly than individual thin fibres. The generally accepted explanation for this is that a coarse clot with fewer fibres to transect will be degraded faster than a fine clot with a higher fibre density. Other experiments show the opposite result. The standard mathematical tool for investigating fibrinolysis has been deterministic reaction-diffusion models, but due to low tPA concentrations, stochastic models may be more appropriate. We develop a 3D stochastic multiscale model of fibrinolysis. A microscale model representing a fibre cross section and containing detailed biochemical reactions provides information about single fibre lysis times, the number of plasmin molecules that can be activated by a single tPA molecule and the length of time tPA stays bound to a given fibre cross section. Data from the microscale model are used in a macroscale model of the full fibrin clot, from which we obtain lysis front velocities and tPA distributions. We find that the fibre number impacts lysis speed, but so does the number of tPA molecules relative to the surface area of the clot exposed to those molecules. Depending on the values of these two quantities (tPA number and surface area), for given kinetic parameters, the model predicts coarse clots lyse faster or slower than fine clots, thus providing a possible explanation for the divergent experimental observations.