This is the most common mechanical test method and involves controlled stretching of a regular shaped sample in a single direction, often until failure. Dimensions of the sample are precisely measured beforehand particularly in the gauge length (i.e. the length over which data will be extracted). The force and displacement in the direction of elongation is measured throughout the test and used to infer behaviour of the tissue. The techniques used to test cardiovascular tissue have evolved from international industry standards used to test rubber (ASTM International 2013).

Typically, the sample is cut into dumbbell or rectangular shapes, selecting areas of uniform thickness, and mounted in the jaws of the tensile testing system. All dimensions are measured at least three times using either callipers or optical methods (see O’Leary et al. (2013) for the influence of thickness measurement error on data). The samples are mounted to the test machine using flat clamps at both ends of the specimen so as to exert a uniform force over the clamped area. To account for anisotropy (i.e. tissue can behaviour differently in both the circumferential and longitudinal direction), the orientation of the sample’s origin is noted. The sample is preconditioned until repeatable mechanical behaviour is observed (e.g. 10 cycles), then elongated until failure. The applied force is measured by the test machine using a load cell. The tissue displacements are measured, either by taking the displacement of the machine head or gauge region markers, or optically via marker tracking (Shazly et al. 2015) or digital image correlation techniques (Zhang et al. 2002; Zhang and Arola 2004). Optical tracking is the preferred option as it measures the true strain of the sample.

The resulting data is a plot of the stress versus the stretch. In mathematical terms, the stretch λ is defined as the fractional change in length of the sample in the unloaded, l _o , and loaded, l, configurations:

The stress can be found with reference to the undeformed geometry, known as the first Piola-Kirchoff stress, P, (or often called the ‘engineering stress’) or with reference to the deformed geometry, known as the Cauchy stress, σ, (often called the ‘true stress’). In the case of uniform deformation, these stresses can be found via:

where f _x is the applied load, t and w are the reference thickness and width of the specimen in the gauge region, and Eq. 13.3 is derived from the assumed incompressibility of vascular tissue (Chuong and Fung 1984).

The most common parameter describing the mechanical behaviour is the Young’ modulus, which is the ratio of stress over strain. This is applicable when the stress-strain behaviour is linear. However, it was noted in Chap. 1 that many biological materials exhibit a non-linear stress-strain relationship. The mechanical behaviour can be characterised by the incremental Young’s modulus, which is the slope of the stress/strain curve. More commonly, the stress-strain behaviour is characterised by a non-linear constitutive model containing two or more parameters (the details of such models are beyond the scope of this book; however see Chap. 1 for a brief description).

Uniaxial extension is the most common measurement undertaken to measure mechanical properties related to stiffness. There is measurement of displacement in only one direction (as opposed to two directions in the biaxial system described in the next section); hence, the instrumentation costs are relatively low. For materials, which are anisotropic the stress-strain behaviour will be different depending on the orientation of the material. For example, in arteries the mechanical behaviour is different in the longitudinal and circumferential directions.

This involves stress-strain measurements in a single plane. Simple biaxial testing involves stretching in two directions (x, y) at 90° to each other. More complex systems have the capability of stretching along multiple different directions. Figure 13.1 shows a simple schematic of this test, whereas Fig. 13.2 shows an actual image of a sample of intraluminal thrombus (ILT) under equi-biaxial extension (O’Leary et al. 2013).

Typically, a square specimen is cut from a larger tissue sample. The sample dimensions are measured; sample dimensions are typically much bigger than in uniaxial tests (e.g. 14 × 14 mm in Fig. 13.2). The sample is mounted to the biaxial test machine. Instead of clamps used in uniaxial tests, hooks, barbs and tines are often used. Hooks and barbs can damage the tissue, especially under high strain, and samples can be lost due to failure at the boundaries. Evenly spread tines are the preferred option (as in Fig. 13.2). Loading is applied along each axis and is independently controlled, enabling variable loading rates or different stretch ratios in each direction. The displacement of marks on the central region of the specimen surface is tracked optically (see Fig. 13.2) or by using full-field methods like Electronic Speckle Pattern Interferometry (ESPI) or Digital Image Correlation (DIC). It is important to only examine the central region to avoid the effects present from the attachment area. This is known as Saint-Venant’s principle and become negligible beyond a critical distance (decay length) from the grips. For cardiovascular tissue, this central area varies from 16 (Sun et al. 2005) to 25 % (O’Leary et al. 2013, 2014b). The measured positions are expressed in a coordinate system (x1, x2) and the axial forces are measured using load cells.

The principles for estimation of elastic moduli are similar to that for uniaxial testing in that these are ratios of stress/strain; however, the mathematics is more complex involving tensor equations and hence is provided in the appendix. The reader is referred to Macrae et al. (2016) for more detail.

Biaxial testing is used to obtain data on mechanical properties, which exhibit anisotropy. While planar biaxial testing enables some characterisation of anisotropic behaviour, it does not provide full 3D characterisation; Holzapfel and Ogden (2009) discusses the issue of full 3D characterisation of mechanical properties in detail.

Biaxial testing systems are more expensive that uniaxial testing (in 2016 around £100 k as opposed to £15 k for uniaxial testing), so are less commonly used.

Inflation testing is an alternative to tensile testing on excised samples of tissues. The whole vessel is inflated under a controlled pressure and the resulting change in dimensions is measured (Fig. 13.3). This method allows the vessel to maintain the same overall shape as it had in the body, including any pre-stressing, and therefore provides a measurement environment more similar to that in vivo than is possible using tensile testing. The widely cited work on the mechanical properties of whole arteries by Learoyd and Taylor (1966) and Bergel (1961a, b) involved an inflation methodology.

The method involves excising a whole artery and incorporating this into a pressurisation system. Any side branches are tied off to prevent leakage. The artery is stretched to its in vivo length and filled with a fluid such as isotonic saline. Pressure and force measurements are continuously recorded by transducers as the pressure increases/decreases, and the changes in geometry are measured with non-contact methods, such as a Charged Coupled Device (CCD) camera, DIC or by measuring the outer diameter with a precise laser micrometer. The wall thickness can be measured by cutting the vessel into slices after testing or by performing Computed Tomography (CT) imaging on the whole sample prior to testing (Doyle et al. 2010). The incremental Young’s modulus, E _inc can be found from the following equation (from Learoyd and Taylor 1966) which is based on a thin-walled model:
where σ is the Poisson ratio taken as 0.5; P is the pressure, R _O the outer radius, R _I the inner radius. The subscripts 1, 2, 3 refer to successive measurements at equal pressure differences (e.g. 10 mmHg).

It is important to note that in many cardiovascular applications the sample will be inhomogeneous, thick-walled and anisotropic in behaviour, which leads to significantly more complicated mathematics.

Bioreactors enable the study of vascular response to transmural pressure, flow rate and axial extension, and often employ inflation-extension tests within a bioreactor chamber. Early experiments involved culturing artery segments in a custom rig, where wall tension was applied via steel wires or by being cultured around a needle (De Mey et al. 1989; Lindqvist et al. 1997) before being subjected to mechanical testing. However, designs have since evolved (McFetridge et al. 2007; Tondreau et al. 2015) and can now accommodate cylindrical specimens (Zaucha et al. 2009) and even much more complicated geometries (e.g. tissue engineered heart valves (Engelmayr et al. 2003)).