A mathematical model of evolving mechanical properties of intraluminal thrombus

Abstract

Quantifying mechanical properties of blood clots is fundamental to understanding many aspects of cardiovascular disease and its treatment. Nevertheless, there has been little attention to quantifying the evolving composition, structure, and properties when a clot transforms from an initial fibrin-based mesh to a predominantly collagenous mass. Although more data are needed to formulate a complete mathematical model of the evolution of clot properties, we propose a general constrained mixture model based on diverse data available from in vitro tests on fibrinogenesis, the stiffness of fibrin gels, and fibrinolysis as well as histological and mechanical data from clots retrieved from patients at surgery or autopsy. In particular, albeit resulting from complex kinetics involving many clotting factors, we show that the rapid (minutes) in vitro production of fibrin from fibrinogen can be modeled well by an Avrami-type relation and similarly that the fast (tens of minutes) in vitro degradation of fibrin in response to different concentrations of plasmin can be captured via a single “master function” parameterized by appropriate half-times that can be inferred from laboratory or clinical data. Accounting simultaneously for the production and removal of fibrin as well as chemo-mechano-stimulated production of fibrillar collagens yields predictions of changing mass fractions and bulk mechanical properties that correspond well to experimentally available data. Constrained mixture models thus hold considerable promise for modeling the biomechanics of clot evolution and can guide the design and interpretation of needed experiments and stress analyses.

A constitutive model for developing blood clots with various compositions and their nonlinear viscoelastic behavior

“…Models for the intraluminal thrombus in abdominal aortic aneurysms have been developed (van Dam et al. 2008 ; Karšaj and Humphrey 2009 ) that describe the mechanical properties of the clot during the long time scale of years. The goal of this study is to develop a model that describes the mechanical properties of the developing clot, with a typical time scale of hours.…”

FEM Simulation of Subintimal Angioplasty for the Treatment of Chronic Total Occlusions

“…Therefore, we considered more reasonable using values of coefficients C ij reported in [24] for calcified plaques (see Table 2 ). Direct measurements of core properties were not available, but for shear modulus of thrombus values in the range 14-21 kPa were reported [25]. Since the coefficients C ji in the strain energy function reported in (1) are related to the initial shear modulus, by properly scaling their values a suitable equivalent shear stiffness can be obtained for the core while keeping the same constitutive law.…”

“…As a first estimate, we assumed yield stress value to be 0.3 MPa, which according to [26] is the threshold stress value that induces plaque rupture (most used within FE studies). To include permanent damage of the core, plastic yield stress was set to 30 kPa, i.e., slightly lower than tensile strength between 50 and 150 kPa reported in [25]. Following [24], a hyperelastic behavior was assumed for the arterial wall.…”

A loosely-coupled scheme for the interaction between a fluid, elastic structure and poroelastic material

“…Blood clots contain different types of blood [1], cells [32] and extracellular matrix constituents. Near the vessel wall, they show a considerable amount of collagen [44], forming a core with a low permeability. The layers around the core contain mainly fibers, overlaid by a micro-structure of pores and cavities filled by a fluid [1,36] whose dimensions vary strongly.…”