Scattering of high-intensity focused ultrasound by the ribs: Constrained optimization with a complex surface impedance boundary condition

Abstract

One of the challenges of trans-rib high-intensity focused ultrasound (HIFU) treatment is the need to transmit sufficient energy through the ribcage to ablate tissue whilst minimizing the formation of side lobes, and sparing healthy tissue. Ribs strongly absorb and reflect ultrasound. This may result in overheating of bone and overlying tissue during treatment, leading to skin burns. Successful treatment of a patient with tumors of the liver or the pancreas therefore requires a thorough understanding of the way acoustic and thermal energy is deposited. A boundary element approach was developed to predict the field of a multi-element HIFU array scattered by human ribs in 3D. This forward model has been reformulated as a constrained least squares optimization problem where the velocity of each individual element on the array is an optimization variable. A locally reacting complex surface impedance condition at the surface of the ribs has been implemented. The methodology has been tested at an excitation frequency of 1 MHz on a spherical section multi-element array and a total of six array-rib configurations have been investigated. The results were compared against other focusing and rib-sparing approaches, demonstrating the efficacy and flexibility of the constrained optimization approach.