State estimation problems in PRF-shift magnetic resonance thermometry

Abstract

Purpose The purpose of this paper is to apply the Steady State Kalman Filter for temperature measurements of tissues via magnetic resonance thermometry. Instead of using classical direct inversion, a methodology is proposed that couples the magnetic resonance thermometry with the bioheat transfer problem and the local temperatures can be identified through the solution of a state estimation problem. Design/methodology/approach Heat transfer in the tissues is given by Pennes’ bioheat transfer model, while the Proton Resonance Frequency (PRF)-Shift technique is used for the magnetic resonance thermometry. The problem of measuring the transient temperature field of tissues is recast as a state estimation problem and is solved through the Steady-State Kalman filter. Noisy synthetic measurements are used for testing the proposed methodology. Findings The proposed approach is more accurate for recovering the local transient temperatures from the noisy PRF-Shift measurements than the direct data inversion. The methodology used here can be applied in real time due to the reduced computational cost. Idealized test cases are examined that include the actual geometry of a forearm. Research limitations/implications The solution of the state estimation problem recovers the temperature variations in the region more accurately than the direct inversion. Besides that, the estimation of the temperature field in the region was possible with the solution of the state estimation problem via the Steady-State Kalman filter, but not with the direct inversion. Practical implications The recursive equations of the Steady-State Kalman filter can be calculated in computational times smaller than the supposed physical times, thus demonstrating that the present approach can be used for real-time applications, such as in control of the heating source in the hyperthermia treatment of cancer. Originality/value The original and novel contributions of the manuscript include: formulation of the PRF-Shift thermometry as a state estimation problem, which results in reduced uncertainties of the temperature variation as compared to the classical direct inversion; estimation of the actual temperature in the region with the solution of the state estimation problem, which is not possible with the direct inversion that is limited to the identification of the temperature variation; solution of the state estimation problem with the Steady-State Kalman filter, which allows for fast computations and real-time calculations.

Estimation of the temperature field in laser-induced hyperthermia experiments with a phantom

“…However, in practice they could have been taken with any other measurement technique. For example, synthetic magnetic resonance thermometry measurements were used for the solution of the state estimation problem in reference [11].…”

“…Noninvasive techniques are generally contact free, do not require the sensors to be inserted into the body and can provide a three-dimensional map of the temperature field. Currently, magnetic resonance temperature imaging (MRTI) via proton resonance frequency shift is the most advanced non-invasive temperature measurement technique, but its widespread use in clinics is still limited [8][9][10][11]. In contrast, the sensors are inserted into the body in invasive techniques.…”

Magnetic Resonance Thermometry During the Localized Heating of Biological Tissues

“…is constant for a wide range of temperatures (in special those for hyperthermia treatment applications) and practically independent of the tissue, except for fat [2,7,13,16,17]. Therefore, the local phase shift from a reference angular value, ( , ) T ∆Φ r , can be obtained for the precession movement as:…”

“…Several techniques have been developed for the measurement of the temperature inside the human body, including the Magnetic Resonance Thermometry (MRT) [1,2,7,8]. Although this technique has been successfully used in practice, related uncertainties can be reduced by coupling this kind of measurement with the mathematical model of the physical problem and by solving a state estimation problem [9][10][11][12], as demonstrated for an arbitrary heating in [13]. In this paper, we extend our previous work [13] and couple the bioheat transfer problem to the heating problem imposed by the external application of waves in the radiofrequency range.…”

“…Although this technique has been successfully used in practice, related uncertainties can be reduced by coupling this kind of measurement with the mathematical model of the physical problem and by solving a state estimation problem [9][10][11][12], as demonstrated for an arbitrary heating in [13]. In this paper, we extend our previous work [13] and couple the bioheat transfer problem to the heating problem imposed by the external application of waves in the radiofrequency range. The state estimation problem is solved with an asymptotic version of the Kalman filter, referred to as the Steady-State Kalman filter [12], which provides a significant reduction on the required computational effort.…”