# Ultrasound Elastography: Methods, Clinical Applications, and Limitations: A Review Article
## 2 Elastography Physics  
Elastography is a technique used to evaluate the elasticity of tissue. Elasticity refers to the ability of tissue to resist deformation when a force is applied and to return to its original shape once the force is removed. If a material is completely elastic and its deformation does not depend on time (i.e., it is not viscous), then its elasticity can be explained by [PERSON]'s Law:  
\[\sigma=\Gamma\cdot\varepsilon \tag{1}\]  
where stress (\(\sigma\)) is the force per unit area with units of kilopaccals (i.e., N/m\({}^{2}\)), strain (\(\varepsilon\)) is the expansion per unit length, which is dimensionless, and the elastic modulus (\(\Gamma\)) relates stress to strain with units of kilopaccals. [PERSON]'s law, an elasticity principle formulated by the English scientist [PERSON] in 1660, asserts that the displacement or size of the deformation of an item is precisely proportionate to the applied force or load, as long as the deformations are relatively modest [22; 23]. Under these circumstances, the object reverts to its initial shape and dimensions once the load is removed. The elastic behavior of solids, as described by [PERSON]'s law, can be attributed to the proportionate relationship between the force applied to the solid and the resulting displacement of its constituent molecules, atoms, or ions from their normal positions. See Figure 1.  
One can exert various types of deforming forces on a solid, such as stretching, compressing, squeezing, bending, or twisting. Therefore, when subjected to a doubled force, a metal wire exhibits elastic behavior in accordance with [PERSON]'s law, as its length increases proportionally. [PERSON]'s law can be expressed mathematically as F = kx, where F is the applied force, k is a constant, and x is the displacement or change in length. The value of k is contingent upon not just the type of elastic material being examined, but also its dimensions and shape. The significance of elastography physics lies in its ability to employ several methodologies to measure tissue stiffness, a physical attribute known as Young's modulus (E). Young's modulus, a constant, establishes the relationship between the force per unit area, known as stress, and the resulting change in tissue dimensions, known as strain. As mentioned before, the principle of elastography depends heavily on the assessment of tissue elasticity, which is defined as the tendency of the tissue to return to its original shape and resist disfiguration following the application of force. Deformations of tissue elasticity can be characterized by strain, stress, and elastic moduli, according to [PERSON]'s law. Based on their static deformation and the speed of wave propagation, we can classify multiple types of elastic moduli. Young's modulus, shear modulus, and bulk modulus provide an indication of the difficulty of soft tissue deformation following compression and shear. These three types of elastic moduli vary in their method of deformation due to the different production of strain. Young's modulus, for example, produces a normal perpendicular strain on the tissue, whereas shear modulus produces a shear strain tangentially, and bulk modulus involves a normal inward pressure that results in a volume change, also known as bulk strain [6; 8; 10; 14; 18; 24; 25; 26; 27; 28]. Shear waves and longitudinal waves define the types of wave propagation in ultrasound. Shear waves, which are also sometimes called transverse waves, cause particles to move in a way that is perpendicular to the direction of the wave. This motion is directly correlated with the shear modulus G and exhibits a rapid and subtle weakening effect (reduced amplitude). Compared to longitudinal waves, which show particle movement in the same direction as the wave's propagation and are directly affected by the bulk modulus, K employs longitudinal waves. However, these waves do not offer sufficient tissue contrast due to the relatively minor variations in wave speed and bulk modulus.