The Utility and Potential of Mathematical Models in Predicting Fibrinolytic Outcomes

Internal fibrinolysis of fibrin clots is driven by pore expansion

Blood clots, which are composed of blood cells and a stabilizing mesh of fibrin fibers, are critical in cessation of bleeding following injury. However, their action is transient and after performing their physiological function they must be resolved through a process known as fibrinolysis. Internal fibrinolysis is the degradation of fibrin by the endogenous or innate presence of lytic enzymes in the bloodstream; under healthy conditions, this process regulates hemostasis and prevents bleeding or clotting. Fibrin-bound tissue plasminogen activator (tPA) converts nearby plasminogen into active plasmin, which is bound to the fibrin network, breaking it down into fibrin degradation products and releasing the entrapped blood cells. It is poorly understood how changes in the fibrin structure and lytic protein ratios influence the biochemical regulation and behavior of internal fibrinolysis. We used turbidity kinetic tracking and microscopy paired with mathematical modeling to study fibrin structure and lytic protein ratios that restrict internal fibrinolysis. Analysis of simulations and experiments indicate that fibrinolysis is driven by pore expansion of the fibrin network. We show that this effect is strongly influenced by the ratio of fibrin:tPAwhen compared to absolute tPA concentration. Thus, it is essential to consider relative protein concentrations when studying internal fibrinolysis both experimentally and in the clinic. An improved understanding of effective internal lysis can aid in development of better therapeutics for the treatment of bleeding and thrombosis.

A simplified mesoscale 3D model for characterizing fibrinolysis under flow conditions

One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient's bloodstream, which breaks down the thrombi's fibrin fibers: intravenous or intravascular thrombolysis. However, this procedure is not without risk for the patient; the worst circumstances can cause a brain hemorrhage or embolism that can be fatal. Improvement in patient management drastically reduced these risks, and patients who benefited from thrombolysis soon after the onset of the stroke have a significantly better 3-month prognosis, but treatment success is highly variable. The causes of this variability remain unclear, and it is likely that some fundamental aspects still require thorough investigations. For that reason, we conducted in vitro flow-driven fibrinolysis experiments to study pure fibrin thrombi breakdown in controlled conditions and observed that the lysis front evolved non-linearly in time. To understand these results, we developed an analytical 1D lysis model in which the thrombus is considered a porous medium. The lytic cascade is reduced to a second-order reaction involving fibrin and a surrogate pro-fibrinolytic agent. The model was able to reproduce the observed lysis evolution under the assumptions of constant fluid velocity and lysis occurring only at the front. For adding complexity, such as clot heterogeneity or complex flow conditions, we propose a 3-dimensional mesoscopic numerical model of blood flow and fibrinolysis, which validates the analytical model's results. Such a numerical model could help us better understand the spatial evolution of the thrombi breakdown, extract the most relevant physiological parameters to lysis efficiency, and possibly explain the failure of the clinical treatment. These findings suggest that even though real-world fibrinolysis is a complex biological process, a simplified model can recover the main features of lysis evolution.

Microscale structural changes of individual fibrin fibers during fibrinolysis

Fibrinolysis is the enzymatic digestion of fibrin, the primary structural component in blood clots. Mechanisms of fibrin fiber digestion during lysis have long been debated and obtaining detailed structural knowledge of these processes is important for developing effective clinical approaches to treat ischemic stroke and pulmonary embolism. Using dynamic fluorescence microscopy, we studied the time-resolved digestion of individual fibrin fibers by the fibrinolytic enzyme plasmin. We found that plasmin molecules digest fibers along their entire lengths, but that the rates of digestion are non-uniform, resulting in cleavage at a single location along the fiber. Using mathematical modeling we estimated the rate of plasmin arrival at the fiber surface and the number of digestion sites on a fiber. We also investigated correlations between local fiber digestion rates, cleavage sites, and fiber properties such as initial thickness. Finally, we uncovered a previously unknown tension-dependent mechanism that pulls fibers apart during digestion. Taken together these results promote a paradigm shift in understanding mechanisms of fibrinolysis and underscore the need to consider fibrin tension when assessing fibrinolytic approaches. STATEMENT OF SIGNIFICANCE: We developed a method for interrogating lysis of individual fibrin fibers, enabling the time-resolved observation of individual fiber digestion for the first time. Our results resolve longstanding disagreements about fibrinolytic processes and reveal previously unknown mechanisms that also play a role. Also, we developed the first microscale mathematical model of plasmin-fibrin interaction, which predicts the number of plasmin molecules on each fiber and can serve as a framework for investigating novel therapeutics.