Assessing the Viscoelastic Properties of Thrombus Using a Solid-Sphere-Based Instantaneous Force Approach

Abstract

The viscoelastic properties of thrombus play a significant role when the clot closes a leak in a vessel of the blood circulation. The common method used to measure the viscoelastic properties of a clot employs a rheometer but this might be unsuitable due to the clot fiber network being broken up by excessive deformation. This study assessed the feasibility of using a novel acoustic method to assess the viscoelastic properties of blood clots. This method is based on monitoring the motion of a solid sphere in a blood clot induced by an applied instantaneous force. Experiments were performed in which a solid sphere was displaced by a 1 MHz single-element focused transducer, with a 20 MHz single-element focused transducer used to track this displacement. The spatiotemporal behavior of the sphere displacement was used to determine the viscoelastic properties of the clot. The experimental system was calibrated by measuring the viscoelastic modulus of gelatin using different types of solid spheres embedded in the phantoms and, then, the shear modulus and viscosity of porcine blood clots with hematocrits of 0% (plasma), 20% and 40% were assessed. The viscoelastic modulus of each clot sample was also measured directly by a rheometer for comparison. The results showed that the shear modulus increased from 173 ± 52 (mean ± SD) Pa for 40%-hematocrit blood clots to 619.5 ± 80.5 Pa for plasma blood clots, while the viscosity decreased from 0.32 ± 0.07 Pa∙s to 0.16 ± 0.06 Pa∙s, respectively, which indicated that the concentration of red blood cells and the amount of fibrinogen are the main determinants of the clot viscoelastic properties.

Introduction

The coagulation of blood is a complex process during which solid clots are formed in the blood. The conversion of fibrinogen into fibrin and the subsequent covalent cross-linking of fibrin play important roles in this process and can be induced by an imbalance between coagulant and anticoagulant factors (Murano and Bick 1980). Fibrin is the primary structural protein of the blood clot and its mechanical properties are essential to stop bleeding. Although clotting is vital to the preservation of life, blood clots can impede blood flow in the vessels. Thrombus formation is responsible for most heart attacks and strokes and complicates other pathologic conditions such as many types of cancer and peripheral vascular diseases (Kwaan and Samama 1989). In addition, deep vein thrombosis and its sequelae (pulmonary embolism and post-thrombotic syndrome) are some of the most common associated disorders and would lead to edema, interference with blood circulation and eventual death unless brought under control (Kuter and Rosenberg 1991). The blood clot is a viscoelastic polymer (Weisel 2008), which means that it exhibits the elastic properties of a spring combined with the viscous properties of a fluid. The clot deforms and may break up when its deformation exceeds a critical limit. In other words, the viscoelastic properties of a clot determine whether a thrombus will have a tendency to become occlusive or to break apart so that fragments block smaller vessels (Weisel 2008). It is therefore important to develop techniques for measuring the viscoelastic properties of thrombus (blood clot).

The most common technique used to measure the viscoelastic properties of a blood clot applies an amplitude oscillatory deformation to the clot during the coagulation process in rotational and capillary rheometers (Roberts et al. 1973). The clot viscoelastic properties can be quantified mechanically by measuring the clot elasticity as well as its viscous response to applied deformation. However, the storage and loss moduli measured with a rheometer cannot be related to the material properties since the presence of shear elasticity makes it impossible to relate an imposed steady load to the actual clot deformation (Riha et al. 1999) and, furthermore, the clot may be damaged and its viscoelasticity would not be linear as the applied deformation is too high (usually the strain less than 0.02) (Burghardt et al. 1995). In addition to direct mechanical methods for characterizing blood clots, rheological methods based on ultrasound have been developed due to their real-time capabilities and noninvasiveness (Jacobs et al., 1976, Grybauskas et al., 1978, Huang et al., 2011). Some ultrasonic methods characterize blood clots under a static condition based on acoustic streaming (Machado et al., 1991, Hartley, 1997, Shi et al., 2001), ultrasound shear waves (Alves and Machado 1994), transient elastography (Gennisson et al. 2006), ultrasound backscatter (Shung et al., 1975, Huang et al., 2005) and by measuring the velocity and attenuation of ultrasound (Shung et al., 1984, Huang et al., 2005). A pulsed Doppler ultrasound technique was used to evaluate the variation of clot structure in stirred blood during coagulation (Huang et al. 2006). Furthermore, the dynamic process of clot formation was also studied by analyzing the backscattering signals and its statistical behavior from coagulating blood under different flow shear rates (Huang and Wang, 2007, Huang et al., 2007).

While analyses based on the ultrasonic parameters of coagulating blood can be used to determine the elastic properties of clots indirectly, direct measurements of clot mechanical properties are needed. The age of deep vein thrombosis was evaluated by using quasistatic elastography to measure the mechanical properties of blood clots both in vivo and in vitro (Emelianov et al., 2002, Aglyamov et al., 2004). An animal model was also assessed using ultrasound elasticity imaging (Xie et al. 2004). In addition, the assessments of shear elasticity and viscosity of tissue by using the shearwave technology have been proposed (Chen et al., 2009, Mitri et al., 2011). Moreover, dynamic elastography based on an acoustic-radiation-force technique was developed to evaluate the viscoelastic properties of biologic tissue (Walker et al. 2000). It has been hypothesized that applying an acoustic radiation force will induce localized tissue displacement that can be directly correlated with localized variations of tissue viscoelastic properties (Nightingale et al. 2001). The relative elasticity and viscosity of blood clots were consequently assessed by this technique (Viola et al. 2004). This method was also used to investigate the dynamic process of clot formation (Viola et al. 2010). However, the applied force is unknown due to differences in the absorption coefficient and acoustic impedance of the tissues, which prevents absolute values of the elasticity and viscosity of a clot being obtained. To overcome this problem, a method based on measuring the displacement of a solid sphere or gas bubble embedded in viscoelastic gelatin induced by a radiation force was proposed (Ostreicher, 1951, Chen et al., 2002, Urban et al., 2010, Ilinskii et al., 2005, Aglyamov et al., 2007). The distinction between the terminologies of the “acoustic radiation force” and “instantaneous force” has been classified from previous studies (Mitri and Fellah, 2011a, Mitri and Fellah, 2011b). They indicated that the instantaneous force can be used to push a particle, whereas the static radiation force is shown to stabilize particle at an equilibrium position (Mitri and Fellah, 2011a, Mitri and Fellah, 2011b). Therefore, the shear elasticity and viscosity of the surrounding medium could be assessed by measuring the displacement of the sphere induced by the applied force. Since the temporal variations of the sphere displacement are independent of the applied instantaneous force, the viscoelastic properties of the medium can be measured without knowledge of the force magnitude (Karpiouk et al. 2009). A similar method has been used to characterize the viscoelastic properties of lens and cornea tissues (Erpelding et al. 2005). Therefore, it should be possible to apply this instantaneous force technique to measure the viscoelastic properties of blood clots.

The purpose of this study was to determine whether it is possible to assess the viscoelastic properties of blood clots using the instantaneous force approach, based on reconstructing the values of the shear elasticity and viscosity estimated from spatiotemporal measurements of the displacement of a solid sphere induced by an applied force. First, the experimental system was calibrated using solid spheres of different materials embedded in a gelatin phantom. Clotting experiments were then performed on porcine whole blood for hematocrits of 0% (plasma), 20% and 40%. Motion of the sphere embedded in the clot was induced by an instantaneous force from 1 MHz ultrasound transducer, with the sphere displacement detected using a 20 MHz transducer. The viscoelastic modulus of the blood clot was then assessed from the spatiotemporal behavior of the sphere displacement for applied forces with different durations. The accuracy of the measurement results in this acoustic method was determined by comparison with the elastic modulus of the clot measured directly by a rheometer. The feasibility of using an instantaneous force to characterize the viscoelastic properties of blood clots and the effects of hematocrit on clotting were both investigated.