Endocavitary thermal therapy by MRI-guided phased-array contact ultrasound: experimental and numerical studies on the multi-input single-output PID temperature controller's convergence and stability

Abstract

Purpose: Endocavitary high intensity contact ultrasound (HICU) may offer interesting therapeutic potential for fighting localized cancer in esophageal or rectal wall. On-line MR guidance of the thermotherapy permits both excellent targeting of the pathological volume and accurate preoperatory monitoring of the temperature elevation. In this article, the authors address the issue of the automatic temperature control for endocavitary phased-array HICU and propose a tailor-made thermal model for this specific application. The convergence and stability of the feedback loop were investigated against tuning errors in the controller's parameters and against input noise, through ex vivo experimental studies and through numerical simulations in which nonlinear response of tissue was considered as expected in vivo.

Methods: An MR-compatible, 64-element, cooled-tip, endorectal cylindrical phased-array applicator of contact ultrasound was integrated with fast MR thermometry to provide automatic feedback control of the temperature evolution. An appropriate phase law was applied per set of eight adjacent transducers to generate a quasiplanar wave, or a slightly convergent one (over the circular dimension). A 2D physical model, compatible with on-line numerical implementation, took into account (1) the ultrasound-mediated energy deposition, (2) the heat diffusion in tissue, and (3) the heat sink effect in the tissue adjacent to the tip-cooling balloon. This linear model was coupled to a PID compensation algorithm to obtain a multi-input single-output static-tuning temperature controller. Either the temperature at one static point in space (situated on the symmetry axis of the beam) or the maximum temperature in a user-defined ROI was tracked according to a predefined target curve. The convergence domain in the space of controller's parameters was experimentally explored ex vivo. The behavior of the static-tuning PID controller was numerically simulated based on a discrete-time iterative solution of the bioheat transfer equation in 3D and considering temperature-dependent ultrasound absorption and blood perfusion.

Results: The intrinsic accuracy of the implemented controller was approximately 1% in ex vivo trials when providing correct estimates for energy deposition and heat diffusivity. Moreover, the feedback loop demonstrated excellent convergence and stability over a wide range of the controller's parameters, deliberately set to erroneous values. In the extreme case of strong underestimation of the ultrasound energy deposition in tissue, the temperature tracking curve alone, at the initial stage of the MR-controlled HICU treatment, was not a sufficient indicator for a globally stable behavior of the feedback loop. Our simulations predicted that the controller would be able to compensate for tissue perfusion and for temperature-dependent ultrasound absorption, although these effects were not included in the controller's equation. The explicit pattern of acoustic field was not required as input information for the controller, avoiding time-consuming numerical operations.

Conclusions: The study demonstrated the potential advantages of PID-based automatic temperature control adapted to phased-array MR-guided HICU therapy. Further studies will address the integration of this ultrasound device with a miniature RF coil for high resolution MRI and, subsequently, the experimental behavior of the controller in vivo.