Two-step hybrid virtual array ray (VAR) technique for focusing through the rib cage.

A new methodology for focusing ultrasonic beams noninvasively in the presence of the rib cage is investigated. This investigation is motivated by the need to employ high intensity focused ultrasound (HIFU) using phased array applicators for the treatment of liver tumors partially shadowed by the rib obstacles. This approach enables us to efficiently perform the ultrasound computational analysis and pattern synthesis in the interior region of the rib cage. The proposed technique consists of two main steps. First, a virtual array is introduced along the intercostal spacings between the solid ribs to generate the prespecified intensity levels at a set of control points within the target region. The second step involves the design of the actual feed array that induces the virtual sources between the intercostal spacings. This design optimization is carried out via the pseudo-inverse technique (minimum norm least squares solution) and by enforcing a constrained preconditioned pseudo-inverse method. The proposed procedure calculates the required primary sources (feed array) while maintaining minimal power deposition over the solid obstacles.