A model of fibrinolysis was developed using multicomponent convection-diffusion equations with homogeneous reaction and heterogeneous adsorption and reaction. Fibrin is the dissolving stationary phase and plasminogen, tissue plasminogen activator (tPA), urokinase (uPA), and plasmin are the soluble mobile species. The model is based on an accurate molecular description of the fibrin fiber and protofibril structure and contains no adjustable parameters and one phenomenological parameter estimated from experiment. The model can predict lysis fronts moving across fibrin clots (fine or coarse fibers) of various densities under different administration regimes using uPA and tPA. We predict that pressure-driven permeation is the major mode of transport that allows for kinetically significant thrombolysis during clinical situations. Without permeation, clot lysis would be severely diffusion limited and would require hundreds of minutes. Adsorption of tPA to fibrin under conditions of permeation was a nonequilibrium process that tended to front load clots with tPA. Protein engineering efforts to design optimal thrombolytics will likely be affected by the permeation processes that occur during thrombolysis.

A numerical model based on the convective-diffusive transport of reacting and adsorbing proteolytic enzymes within erodible fibrous biopolymers was used to predict lysis fronts moving across biogels such as fibrin or collagen. The fiber structure and the transport properties of solutes in fibrin (or collagen) were related to the local extent of dissolution within the dissolving structure. An accounting for solubilization of adsorbed species into solution from the eroding fiber phase provided for complete conservation of mass in reacting systems containing over 10 species. At conditions of fibrinolysis typical of clinical situations, the model accurately predicted the dynamic rate of lysis front movement for plasmin, urokinase, and tissue plasminogen activator (tPA)-mediated lysis of fibrin gels measured in vitro. However, under conditions of extremely fast fibrinolysis using high enzyme concentrations, fibrinolytic fronts moved very rapidly (>0.1 mm/mm)-faster than predicted for diffusionlimited reactions-at nearly constant velocity for over 2 h, indicating non-Fickian behavior. This was due to proteolysis-mediated retraction of dissolving fibrin fibers that resulted in fiber convection and front-sharpening within 3 mum of the reaction front, as observed by digitally enhanced microscopy. In comparing the model to fibrinolysis measurements using human lys(77)-plasmin, the average first order rate constant for non-crosslinked fibrin bond cleavage by fibrin-bound plasmin was calculated to be 5s(-1) assuming that 10 cleavages per fibrin monomer were required to solubilize each monomer. The model accurately predicted lysis front movement using pressure-driven permeation of plasmin or urokinase into fibrin as well as literature data obtained under well- mixed conditions for tPA-mediated fibrinolysis. This numerical formulation provides predictive capability for optimization of proteolytic systems which include thrombolytic therapy, wound healing, controlled drug release, and tissue engineering applications. (c) 1995 John Wiley & Sons, Inc.

Pressure-driven permeation greatly enhances and is a primary determinant of the overall rate of clot lysis and creates a complex local reaction environment at the plasma/clot interface. With simulation of reaction and transport, it becomes possible to quantitatively link the administration regimen, plasminogena activator properties, and thrombolytic outcome.

A transport-reaction model describing penetration of plasmin by diffusion and permeation into a dissolving fibrin gel was solved numerically to explore mechanisms that lead to the formation and growth of dissolution fingers through blood clots during thrombolytic therapy. Under conditions of fluid permeation driven by arterial pressures, small random spatial variations in the initial fibrin density within clots (+/-4 to 25% peak variations) were predicted by the simulation to result in dramatic dissolution fingers that grew in time. With in vitro experiments, video microscopy revealed that the shape of the proximal face of a fibrin gel, when deformed by pressure-driven permeation, led to lytic breakthrough in the center of the clot, consistent with model predictions of increased velocities in this region leading to cannulation. Computer simulation of lysis of fibrin retracted by platelets (where more permeable regions are expected in the middle of the clot due to retraction) predicted cannulation of the clot during thrombolysis. This residual, annular thrombus was predicted to lyse more slowly, because radial pressure gradients to drive inner clot permeation were quite small. In conjunction with kinetic models of systemic pharmacodynamics and plasminogen activation biochemistry, a two-dimensional transport-reaction model can facilitate the prediction of the time and causes of clot cannulation, poor reperfusion, and embolism during thrombolysis.

A transport-reaction model describing penetration of plasmin by diffusion and permeation into a dissolving fibrin gel was solved numerically to explore mechanisms that lead to the formation and growth of dissolution fingers through blood clots during thrombolytic therapy. Under conditions of fluid permeation driven by arterial pressures, small random spatial variations in the initial fibrin density within clots (+/-4 to 25% peak variations) were predicted by the simulation to result in dramatic dissolution fingers that grew in time. With in vitro experiments, video microscopy revealed that the shape of the proximal face of a fibrin gel, when deformed by pressure-driven permeation, led to lytic breakthrough in the center of the clot, consistent with model predictions of increased velocities in this region leading to cannulation. Computer simulation of lysis of fibrin retracted by platelets (where more permeable regions are expected in the middle of the clot due to retraction) predicted cannulation of the clot during thrombolysis. This residual, annular thrombus was predicted to lyse more slowly, because radial pressure gradients to drive inner clot permeation were quite small. In conjunction with kinetic models of systemic pharmacodynamics and plasminogen activation biochemistry, a two-dimensional transport-reaction model can facilitate the prediction of the time and causes of clot cannulation, poor reperfusion, and embolism during thrombolysis.