Modelling fibrinolysis: 1D continuum models

Abstract

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.Keywords: fibrin; enzymatic degradation; lysis front. B. E. BANNISH ET AL. Fig. 1. Cartoon of fibrinolysis (not to scale): PLG and tPA diffuse in the plasma and can bind to fibrin. If tPA and PLG bind in close proximity to one another, the tPA can convert the plasminogen to plasmin (PLi). PLi then degrades the fibrin by cutting across the fibre. New binding sites for tPA and PLG are exposed as plasmin cleaves fibrin. Plasma concentration of PLG ≈2 µM, and plasma concentration of tPA ≈70 pM.

Physical Determinants of Fibrinolysis in Single Fibrin Fibers

“…Together, our experimental and modeling data indicate that fiber diameter determines the prestrain induced by fibrin polymerization, and the pre-strain, in part, governs a fiber’s susceptibility to plasmin. Combining our models involving fiber strain during lysis, with other recently published models of lysis involving stochastic reactions and enzyme diffusion may be required for a complete picture of fibrinolysis [ 37 , 38 ].…”

Circulating Microparticles Alter Formation, Structure and Properties of Fibrin Clots

“…These results are in line with the observation that the number of fibres per volume determines resistance to the enzymatic lysis rather than an individual fibre diameter 43 . The delay in fibrinolysis rates in densely packed clots with thinner fibres is likely due to the greater number of fibres in the clot that need to be cleaved and other differences in spatio-temporal protein distributions 44 45 . There are a number of other factors that influence lysis speeds in clots of varying structure 46 .…”

Basic mechanisms and regulation of fibrinolysis

“…An issue with some fibrinolysis models was the approximation that fibrin was distributed homogenously rather than in fibers, which does not permit any investigation of the effects of fibrin architecture. Bannish et al [58] approached this problem by developing a one-dimensional reaction-diffusion model that included a concentration of fibrin that was fixed but heterogeneously distributed into fiber patterns. As the lysis front travelled through the clot, the model was able to replicate some features seen in in vitro clot lysis experiments, including concentration of tPA and plasminogen at the lysis front (reported to be up to 30-fold increased for plasminogen in aggregates in the 3 lm lysis front [11]).…”