## 1 Introduction  
Soft tissue elastic properties change in various pathological tissues, such as malignant tumors and inflammatory processes. Strain elastography can be used to quantify this physical feature based on ultrasound imaging. Tissue hardness can be assessed across tissue images describing the Elastic modulus (\(E\)), defined as the relationship between the application of local stress and the resulting strain. This can be expressed as:  
\[E=\frac{\Delta\text{strain}}{\Delta\text{stress}} \tag{1}\]Since the stress is not recorded as it travels from the stress source through the tissue as it gradually attenuates, calculating the Elastic modulus from strain data alone is not possible. This phenomenon is sometimes referred to as the \"inverse problem\" of strain elastography [1]. Under similar stress, strain in harder tissue is lower than strain in softer tissue [2; 3]. Thus, a comparison between strain in the reference tissue and lesion produces a ratio that increases above one when the focal lesion is harder than the reference tissue. Strain ratio (\(SR\)) represents the relative difference in tissue hardness [4]. The definition of \(SR\) is:  
\[Strain\ Ratio\ (SR)=\frac{Mean\ strain\ B\ (reference\ area)}{Mean\ strain\ A\ ( lesion\ area)} \tag{2}\]  
[PERSON]'s law states that for small deformations in elastic media, the strain is linearly proportional with the force (stress) applied. However, this is true for isotropic and homogeneous media with near infinite or free border conditions. These conditions are rarely present in biological tissues, which exhibit non-linear elastic properties of different magnitudes due to differences in tissue structure and function. This may be of importance for the accuracy of strain elastography. By restricting the pre-compression and range of compressions (\(\Delta\)-stress) to a limited interval, the stress-strain relation of the tissues involved may still be regarded as linear. Vital tissue contains ducts and veins that act as stress dampers, as well as connective tissue and sliding anatomical surfaces that limit and enhance tissue movement, respectively. Unintended movements may cause strain concentration and reduce the accuracy of \(SR\) evaluation. Hence, in vivo conditions often do not meet the preconditions of [PERSON]'s law for elasticity calculation, and may therefore represent limitations and cause strain-imaging artefacts that increase variability and reduce the reproducibility of \(SR\) measurements. \(SR\) expresses a momentarily and relative difference in compressibility in two user-selected areas within selected regions of interest in a strain elastogram. \(SR\) is dependent on similar stress applications in the two areas compared, and similar stress attenuation in the tissue between the stress source (probe) and the area of interest. The \(SR\) measurement method was first introduced as the \"fat-lesion ratio\" in breast imaging, where an area of subcutaneous fat was used as the reference to mean strain in the lesion under investigation. Using the subcutaneous fat as reference was perhaps as close to a standardized reference tissue as one can get. However, the same preconditions apply, as the tissue constitution between the probe and target lesion, and the probe distance may influence the strain distribution in reference area fat tissue. The variations in elasticity of biological tissues is not linear with varying pre-compression or stretch of the tissue. For breast and pancreatic tissues, this has been evaluated by force indentation and deformation studies under increasing strength. This implies that the amount of pre-compression and the range of the stress applied influences the strain result and thereby the elastogram. In one study, the authors recommended a pre-compression level less than 0.2-0.4 kPa for breast imaging [5]. Another physical condition that complicates the reproducibility of strain ratios is the temporal variability in a live strain cine-loop.