Hemostasis is the process of sealing a vascular injury with a thrombus to arrest bleeding. The type of thrombus that forms depends on the nature of the injury and hemodynamics. There are many models of intravascular thrombus formation whereby blood is exposed to prothrombotic molecules on a solid substrate. However, there are few models of extravascular thrombus formation whereby blood escapes into the extravascular space through a hole in the vessel wall. Here, we describe a microfluidic model of hemostasis that includes vascular, vessel wall, and extravascular compartments. Type I collagen and tissue factor, which support platelet adhesion and initiate coagulation, respectively, were adsorbed to the wall of the injury channel and act synergistically to yield a stable thrombus that stops blood loss into the extravascular compartment in ~7.5 min. Inhibiting factor VIII to mimic hemophilia A results in an unstable thrombus that was unable to close the injury. Treatment with a P2Y12 antagonist to reduce platelet activation prolonged the closure time two-fold compared to controls. Taken together, these data demonstrate a hemostatic model that is sensitive to both coagulation and platelet function and can be used to study coagulopathies and platelet dysfunction that result in excessive blood loss.

Upon injury to a blood vessel, flowing platelets will aggregate at the injury site, forming a plug to prevent blood loss. Through a complex system of biochemical reactions, a stabilizing mesh forms around the platelet aggregate forming a blood clot that further seals the injury. Computational models of clot formation have been developed to a study intravascular thrombosis, where a vessel injury does not cause blood leakage outside the blood vessel but blocks blood flow. To model scenarios in which blood leaks from a main vessel out into the extravascular space, new computational tools need to be developed to handle the complex geometries that represent the injury. We have previously modeled intravascular clot formation under flow using a continuum approach wherein the transport of platelet densities into some spatial location is limited by the platelet fraction that already reside in that location, i.e., the densities satisfy a maximum packing constraint through the use of a hindered transport coefficient. To extend this notion to extravascular injury geometries, we have modified a finite element method flux‐corrected transport (FEM‐FCT) scheme by prelimiting antidiffusive nodal fluxes. We show that our modified scheme, under a variety of test problems, including mesh refinement, structured vs unstructured meshes, and for a range of reaction rates, produces numerical results that satisfy a maximum platelet‐density packing constraint.

No abstract

No abstract

We present a theoretical description of the flow of a thin polymeric film on the inner wall of a rotating horizontal cylinder. We account for polymer elasticity with the quasi-linear Oldroyd-B constitutive relation. We apply several simplifications to derive analytical solutions to this otherwise analytically intractable problem. Because the film is thin and the Reynolds number is small, we can implement a lubrication approximation. Furthermore, if we consider weakly elastic polymers, we can expand perturbation series in the limit of a small Deborah number. The analytical approximation for the steady-state free surface shows qualitative agreement with previous numerical simulation. Numerical solutions of the approximate evolution equation demonstrate the destabilizing effect of elasticity on the film's perturbed steady-state profile. Keywords Rimming flow · Visco-elastic fluid · Approximate model List of symbols De Deborah number De = λ 1 Ω C B Inverse to the Bond number C B = δ 2 σ/r 0 μΩ e r , e θ Radial and azimuthal unit vectors g Gravity vector g = (−gsinθ, −gcosθ) h Thickness of the liquid layer h(θ, t) η 0 Characteristic thickness of the liquid layer h * = η 0 h K Ratio of solvent viscosity to solution viscosity, K = μ s /μ n Normal to the free surface p Pressure φ Mass flux through liquid layer φ (θ, t) = h 0 ν θ d R r Radial coordinate r 0 Radius of the cylinder R Non-dimensional radial coordinate t Time Communicated by Tim Phillips.

We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODE) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes-Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical ADP hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool.