Mathematical principles of ultrasound.

Although ultrasound cannot be heard by humans, it has been produced and used for a vast number of applications in many different fields. In industry, ultrasound has been used as a technique to assess the structural integrity of materials. The interaction between ultrasound and live systems has been studied since the 1920s. During the 1960s, it was used in medicine, initially as a therapeutic option and then later as a diagnostic resource. In the twenty-first century, ultrasound is a major medical imaging technology widely used in clinical facilities around the world because it causes no harm to the human body and results can be achieved in real time, besides the fact it is considerably cheap and easy to use. The available technologies using ultrasound are in constant development. Every new application depends on the advance of computer sciences that work with many concepts of physics and the solution of mathematical problems in this field seems inexhaustible.