Fibrin gel formation in a shear flow

Abstract

Blood clots are made up of platelets and fibrin gel, and the relative amount of fibrin is strongly influenced by the shear rate. In order to explore this phenomenon, this paper presents a model of fibrin gel formation over the surface of an injured blood vessel in a shear flow. A condition for gelation including source and sink terms of polymer is derived. A simplified model of coagulation, involving activation and inhibition of the enzyme thrombin and thrombinmediated production of fibrin monomer, is combined with the model of gelation to explore how the shear rate and other parameters control the formation of fibrin gel. The results show that the thrombin inhibition rate, the gel permeability, and the shear rate are key parameters in regulating the height of the fibrin gel.

On the predictions and limitations of the Becker–Döring model for reaction kinetics in micellar surfactant solutions

“…The third term is a slowly decaying exponential to represent the concentration of intermediate aggregates: the value of C can be used to control the ratio of maximum to minimum aggregate concentrations. The scaling of the second and third terms by m −3/2 and m −2 , respectively, ensures that the importance of these terms relative to each other and to the monomer concentration depends on the coefficients A, B and C and not on the most probable aggregation number, m. The distribution (15) captures the key features predicted by MT illustrated in figure 1. In particular, the largeness of m ensures the high relative concentration of monomer to aggregates, as well as a narrow Gaussian spread around n = m. We can fix two parameters, for example A and B, by requiring the righthand side of (15) to be equal to 1 when n = 1 and by specifying the net concentration:…”

“…We illustrate the dependence of the ratio ω = m/m on the dilution ratio D in figure 4, for the equilibrium distribution (15). The dashed curves show the leading-order approximations corresponding to (21) in the limit m → ∞, namely…”

“…In figure 5 we show the evolution of a typical distribution of aggregates, given by (15), with b = 10, β = 0.2, C = 0.5, d = 1, m = 100 and C b = 10, upon a two-fold dilution. We solve (20) to give ν ≈ 0.992 in this case, highlighting again the weak dependence of the equilibrium monomer concentration on the dilution factor provided the bulk concentration exceeds the CMC.…”

“…Coagulation theory has also been analysed in more complex situations, such as within a flowing fluid, with particular application to biological systems. For example, Band et al [4] combine the Becker-Döring theory with an advection-diffusion model to describe crystal aggregation in the lower urinary tract, while Guy et al [15] model the formation of a blood clot in a shearing flow.…”

“…In figure 2, we show a typical MD prediction for the surfactant C 6 E 3 alongside our ansatz (15), with chosen parameter values b = 4.7, β = 0.765, C = 3.47 × 10 −4 , d = 2.72, C b = 10 and m = 34 from which we infer that A ≈ 1 and B ≈ 2.26.…”