Research paperMechano-rheological properties of the murine thrombus determined via nanoindentation and finite element modeling
Introduction
Nanoindentation is a locally high resolution (micron scale) technique capable of characterizing the mechanical properties of many biomaterials, including cortical and trabecular bone (Wang et al., 2006). In a typical nanoindentation test, an indenter probe with known mechanical properties, usually much stiffer than the sample, is pressed into a small volume of sample whose mechanical properties are unknown. Though it is often used for indenting hard materials, many researchers have nanoindented soft materials (elastic modulus on the order of MPa or kPa). Huang et al. (2008) nanoindented the human tympanic membrane using a spherical tip with a radius of 10 μm, and reported elastic modulus values ranging between 7 and 13 MPa. Simha et al. (2007) nanoindented bovine patellar cartilage using flat-ended cone tips with diameters ranging between 5 and 1000 μm and also with flat cylindrical tips having diameters of 1, 2, and 4 mm. The reported elastic modulus values ranged between 1 and 4 MPa (Simha et al., 2007). Ebenstein and Pruitt (2004) nanoindented agarose gels using a 1000 μm radius spherical tip, and reported reduced elastic modulus values ranging between 0.5 and 1 MPa. Lee et al. (2008) indented contact lenses using a 3 mm diameter cylindrical probe having a 7.78 mm radius spherical tip, and reported elastic modulus values ranging from 50 to 160 kPa. Liu et al. (2009) nanoindented Kraton polymer gels using a cylindrical flat punch indenter tip with diameters of 750 and 1750 μm, and reported elastic modulus values ranging between 36.6 and 168.3 kPa.
Based on the aforementioned studies, there are several common issues that should be addressed when nanoindenting soft materials. Special considerations should be taken to choose the appropriate nanoindenter tip, based on the relative stiffness of the test sample. The surface of the specimen should also be as flat as possible, especially when using flat punch tips. Since nanoindentation has been adapted for use on various soft materials, this technique is suitable for determining the mechanical properties of numerous soft biomaterials.
A thrombus, or blood clot, may form in a vein or artery, often without warning, and result in sudden death due either to dissociation and relocation of the thrombus (which may obstruct a small vein), or aortic rupture. The formation of thrombi is a complicated biological process. While researchers have studied many aspects of this process, there is still a great deal to be learned. The effects of mechanical properties on thrombi dissociation and aortic rupture are not well characterized. This lack of knowledge may have hampered improvements in preventative treatment and management of many blood-related diseases, as well as the development of novel drug therapies. Accurate determination of the mechanical properties of thrombi can be used as inputs to fluid-structure simulations of thrombus-related disorders, such as fracture and dissociation. This will provide a means to unravel the key factors that result in the dissociation of a thrombus, or to more accurately identify an individual’s risk of aortic rupture.
One common method to determine the mechanical properties of thrombi is rheometry. van Dam et al. (2006) used a shear rheometer with parallel plate geometry () to calculate the storage modulus () and loss modulus () of two different types of thrombi. However, parallel plate shear rheometry requires flat specimens that have the same diameter as the plates () in order to properly shear the entire surface and obtain accurate results.
Schmitt et al. (2011) employed a method using dynamic ultrasound elastography to calculate the storage and loss moduli of porcine thrombi. Dynamic elastography studies the mechanical behavior of soft tissue via its motion response to propagating shear waves. The specimen volume in this study was , considerably larger than the specimen size used in this study.
Another method for determining the mechanical properties of thrombi is to create a custom measurement device. Xie et al. (2005) developed a system that compresses the entire cylindrical thrombus while measuring force and displacement. A strain gage measures the compression force while the rectangular pressing stamp compresses the specimen. Using this device, each test requires a new specimen since the entire diameter of the specimen () is compressed. In nanoindentation, multiple tests can be performed on the same specimen.
Nanoindentation has several advantages over other testing methods, including a small scale of measurements (i.e., loads and displacements in the nN and nm range, respectively), indenter tips that can be customized (i.e., size, shape, material, surface coating, etc.), and high resolution sensitivity for both load and displacement.
A comprehensive literature review of the evaluation of thrombi mechanical properties was conducted, and nanoindentation testing has not been utilized as a candidate methodology. Therefore, this investigation is the first to utilize nanoindentation to determine the mechanical properties of thrombi.
The purpose of this study is three-fold. First, the mechanical behavior of murine (rat) thrombi will be measured via nanoindentation testing. Second, elastic contact theory will be used to determine an approximate elastic modulus. Finally, the approximate elastic modulus value will be used as an initial input to a finite element (FE) optimization program, where the elastic modulus and viscosity will be further refined through a parameter optimization routine.
Section snippets
Materials and methods
Platelet-rich plasma (PRP) clots are widely used in literature to study properties of thrombi because their structure and mechanical properties are similar to whole blood clots (Fukada et al., 1984, Gennisson et al., 2006, Huang et al., 2007, Riha et al., 1999, Semeraro et al., 2007, Weisel, 2004, Weisel, 2007). The process used to create PRP clots (i.e., centrifugation) results in a high concentration of activated platelets that bind clotting factors and protect them from being inhibited by
Results
The indentation tests performed on a specimen () were averaged to create an average load–displacement curve for that specimen (i.e., one curve was obtained for each specimen). A representative plot of the mean load–displacement curve for one specimen tested under a maximum load of 250 μN is displayed in Fig. 4. The slope () of the entire loading curve from each mean load–displacement plot was used to calculate the elastic modulus for each specimen via elastic contact theory (Eq. (1)).
Discussion
Elastic modulus values of thrombi reported in the literature vary widely from 1.7x10−6 kPa to 5134 kPa (Table 5). As one would expect, the testing method greatly affects the modulus values. Using a rheometer or viscometer results in modulus values less than 10 kPa (Henderson and Thurston, 1993, Riha et al., 1999, Ryan et al., 1999, van Dam et al., 2006). Custom-made instruments and compression testing yield modulus values between 10 and 1000 kPa (Hinnen et al., 2007, Xie et al., 2005). Finally,
Conclusions
Nanoindentation is a locally high resolution (micron scale) technique used in this investigation to determine the elastic modulus and viscosity of thrombi. This was accomplished using the mean load–displacement nanoindentation curve for each specimen, elastic contact theory, and inverse finite element modeling. The maximum testing load (250 μN) was determined via a sequential search method. Indentation tests were successfully performed on 8 specimens at the maximum load, with 7 indents per
References (30)
The hemodynamic forces acting on thrombi, from incipient attachment of single cells to maturity and embolization
Journal of Biomechanics
(1984)- et al.
Biomechanics of abdominal aortic aneurysm in the presence of endoluminal thrombus: experimental characterization and structural static computational analysis
European Journal of Vascular and Endovascular Surgery
(1998) - et al.
Assessment by transient elastography of the viscoelastic properties of blood during clotting
Ultrasound in Medicine and Biology
(2006) - et al.
Development of fibrinous thrombus analogue for in-vitro abdominal aortic aneurysm studies
Journal of Biomechanics
(2007) - et al.
Cinnamaldehyde reduction of platelet aggregation and thrombosis in rodents
Thrombosis Research
(2007) - et al.
Mechanical characterization of contact lenses by microindentation: constant velocity and relaxation testing
Acta Biomaterialia
(2008) - et al.
Mechanical characterization of soft viscoelastic gels via indentation and optimization-based inverse finite element analysis
Journal of the Mechanical Behavior of Biomedical Materials
(2009) - et al.
Structural origins of fibrin clot rheology
Biophysical Journal
(1999) - et al.
Characterization of blood clot viscoelasticity by dynamic ultrasound elastography and modeling of the rheological behavior
Journal of Biomechanics
(2011) - et al.
Elastic modulus and hardness of cortical and trabecular bovine bone measured by nanoindentation
Transactions of Nonferrous Metals Society of China
(2006)
The mechanical properties of fibrin for basic scientists and clinicians
Biophysical Chemistry
Structure of fibrin: impact on clot stability
Journal of Thrombosis and Haemostasis
Correspondence of ultrasound elasticity imaging to direct mechanical measurement in aging DVT in rats
Ultrasound in Medicine and Biology
Measurement and analysis of ultimate mechanical properties, stress–strain curve fit, and elastic modulus formula of human abdominal aortic aneurysm and nonaneurysmal abdominal aorta
Journal of Vascular Surgery
Nanoindentation of soft hydrated materials for application to vascular tissues
Journal of Biomedical Materials Research
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2020, Journal of the Mechanical Behavior of Biomedical MaterialsCitation Excerpt :Some relevant studies in the literature will be mentioned here but more may be found in a recent review of research on the mechanical behavior of clots and thrombi based on experimental, analytical, and computational methods (Johnson et al., 2017). Uniaxial and biaxial tensile tests on thrombi have been reported (Di Martino et al., 1998; Vande Geest et al., 2006; Teng et al., 2015; Gasser et al., 2008; Rausch and Humphrey, 2016), comparisons of ex vivo thrombi and in vitro thrombus models (Johnson et al., 2017; Brown et al., 2009; Saldivar et al., 2002), shear testing of ex vivo thrombi (van Dam et al., 2008), in vitro thrombus models (van Kempen et al., 2014), and compression testing of in vitro thrombus models (Kim et al., 2016; Chueh et al., 2011; Ashton et al., 2009; Noailly et al., 2008; Slaboch et al., 2012), and for ex vivo thrombi (Ashton et al., 2009; Chueh et al., 2011; Xie et al., 2005). Linear models (van Dam et al., 2008; Gasser et al., 2008; Kim et al., 2014), nonlinear continuum models (Vande Geest et al., 2006; van Dam et al., 2008; Noailly et al., 2008; van Kempen et al., 2014), and computational methods (Di Martino et al., 1998; Rausch and Humphrey, 2016; Slaboch et al., 2012) have been used to interpret data from various experiments.
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