## 1 Introduction  
The diagnosis of thyroid nodules usually happens when the patient notices their presence, when clinically examined by a doctor or, more and more commonly, when an incidental imaging procedure is performed, such as carotid ultrasonography (US), computed tomography (CT) or magnetic resonance imaging (MRI) of the neck [1, 2, 3]. The diagnostic goal is to estimate the malignancy risk of each nodule at the time of the initial diagnosis in order to make an accurate, individualized therapeutic decision [1, 4, 5] in order to avoid an unnecessary fine-needle aspiration (FNA), or surgical treatments. Oversurveillance is often made responsible for the rising prevalence of thyroid cancer, with an increasing detection of particularly small, differentiated tumors [5], such as microacarcinomas. Ultrasound evaluation selects the nodules that need to be evaluated by FNA. Molecular testing in additional to FNA cytology is useful in nondiagnostic or indeterminate cytological results [4]. Nevertheless, it is not a routine procedure, not widely available, and a certain panel of genetic rearrangements and mutations are not well-established [6, 7]. The imaging evaluation remains the main component for guiding the medical approach. Thyroid scintigraphy is not routinely recommended in the evaluation of thyroid nodules by most authorities, but rather in selected cases, when autonomous function is suspected [8]. High-resolution neck ultrasound (US) provides excellent images for thyroid morphology, and is considered the golden standard in thyroid imaging [9; 10]. There is no single ultrasound characteristic predictive for malignancy, but rather, a combination of multiple US characteristics that generate different risk categories. In this regard, various stratification systems have been proposed [4; 8; 11; 12; 13]. They are continuously being improved, given the crucial role of imaging in the correct identification of the small percentage of thyroid cancers (up to 7-8%) in all thyroid nodules [14]. Elastography has been a helpful additional tool that enhances the diagnostic quality of classic ultrasound evaluation [15]. The technique provides complementary US information by detecting differences in the elastic properties of the thyroid tissue, adding stiffness as the extra quantifiable parameter to the ultrasound evaluation. Strain elastography (SE) assesses the tissue elasticity by applying an external or internal compression (stress) and measuring the normal strain. In shear-wave elastography (SWE), a dynamic stress is applied by the device, generating perpendicular (point-SWE and 2D-SWE) or parallel (transient SWE) shear waves (SW). The measurement of shear-wave (SW) speed provides a quantitative measurement of the tissue elasticity [14]. The first 2D-SWE technique was developed by Supersonic Imagine (France) and was extensively used for the evaluation of liver fibrosis [16; 17]. The operator must understand the limitations of each technique, which may affect the interpretation of the results [15]. Most clinical guidelines for thyroid pathology acknowledge elastography as an important additional tool for greyscale evaluation [4; 8]. Moreover, the World Federation of Societies for Ultrasound in Medicine and Biology (WFUMB) has provided guidelines for the use of thyroid US elastography [18]. SE offers convincing evidence for detecting high-risk thyroid focal lesions [19; 20; 21], whereas SWE techniques still need more research to provide confidence in thyroid imaging [22; 23; 24]. The main aim of this paper is to assess if there are any differences in the elastography information delivered by two high-end techniques for 2D-SWE and SE in predicting the risk of malignancy of thyroid nodules, with histology as a reference. We chose to perform a head-to-head comparison of the two elastography techniques in order to demonstrate if either one of them has a general advantage, given that the vast majority of previously published comparative studies analyze different study groups, introducing evaluation biases.