## 1 Introduction  
Ultrasound has been commonly used for medical purposes owing to its safety, effective penetration, and radiation-free characteristics [1, 2]. Focused ultrasound (FUS) is one of the emerging technologies in the biomedical field. FUS concentrates acoustic energy to the focal spot, thereby heating or ablating the target issue [3]. FUS waves targeted at a tissue cause a vibration of the biomolecules, which results in the generation of frictional heat [4]. The rise in temperature of a tissue beyond a certain threshold causes the coagulative necrosis of the tissue [5]. Conventional high-intensity FUS performs non-intrusively, delivering ultrasound waves from the outer side of the body [6, 7]. The conventional modality is still attractive as a noninvasive medical treatment. However, non-intrusive FUS techniques should be performed with care, as FUS delivered in an indirect manner may cause unwanted damage to healthy tissue and complications after the treatment [8]. Moreover, some bio-organs that lie behind a media with a high acoustic impedance, such as bones, are challengingto treat with the noninvasive FUS method [9]. Therefore, precise monitoring of the target lesion, such as with MRI or CT imaging, may be required during noninvasive FUS ultrasound treatment [9; 10]. In recent years, interstitial FUS has been actively studied to overcome the technical restrictions in the noninvasive FUS [11; 12; 13]. Miniaturized FUS transducers, generally directed through catheters, are capable of heating and directly ablating the target tissue by transmitting acoustic waves near the target [14; 15; 16]. The direct application of acoustic waves can minimize the potential of damage in unwanted tissues compared to the typical noninvasive FUS modality. However, the geometric restriction of the aperture of the device is one of its most challenging issues as the aperture size directly affects the efficiency of the acoustic transmission. Piezoelectric materials, such as PZT, are most commonly used as active layers of FUS devices owing to their effective energy conversion and the fast response time [17]. PZT materials, due to the benefits, have been commonly used in various engineering fields, including sound and vibration control, biomedical imaging, structural health monitoring, and so on [18; 19; 20; 21]. The thickness and the piezoelectric property of the active layer determine the operating frequency of the device when the vibration modes along the thickness and the lateral directions are decoupled [22]. However, as for interstitial, miniaturized, FUS transducers, in the case where the lateral dimension becomes similar to the thickness, the vibration mode along the thickness direction is coupled with the lateral mode, resulting in an inefficient transmission of acoustic waves. The composite type of the active element may not have the geometric restrictions of the single-phase piezoelectric transducers. For example, a 1-3 composite (1-D connection of the piezoelectric element and a 3-D connection of polymer matrix) piezoelectric material comprises small-width piezoelectric columns combined with a passive media such as epoxy [23]. All the individual active elements have a relatively small width compared to the thickness of the device; thus, it exhibits a distinguished thickness vibration mode [11; 23]. In addition, the 1-3 composite structure normally decreases the overall acoustic impedance level, reducing the acoustic mismatch between the transducer and the target acoustic medium such as blood, water, and bio tissues [23; 24; 25]. As such, due to its potential benefits, 1-3 piezocomposites have been widely employed for the industrial [26; 27; 28] and the biomedical applications [29; 30; 31]. For decades, there have been some engineering efforts to analyze the characteristics of 1-3 piezoelectric composite through numerical simulations.