A general method to correct non-linear spatial and temporal phase deformations for measurement of temperature by proton resonance shift at low field

Purpose/Introduction: The proton resonance frequency shift provides a means of measuring temperature changes during food processing [1-2]. Unfortunately, this method is very sensitive to phase drift induced by the instability of the scanner. In this study we propose a method to correct errors in temperature mapping induced by phase drift for specific food applications. Both the spatial and temporal continuity of the phase drift phenomena were considered. Subjects and Methods: The experiments were performed on an experimental device composed of the object under study surrounded with a thermal insulated reference phantom (25.4 °C), both filled with a gel and equipped with thermocouples for temperature control. The phase drift (δf) for about four hours was studied by keeping the temperature in the object under study constant. Images were acquired using a 0.2 T MR scanner (Open System, Siemens) with a RF spoiled gradient echo sequence (TR=150 ms, TE=30 ms, angle = 40°, matrix =128², FOV=250 mm², slice thickness = 5 mm). The mean main magnetic field drift was estimated by following the derivation of the automatically adjusted emission frequency (f0) for each scan. The phase difference images, calculated with reference to the image at reference time, were used for modelling. The data in the reference phantom was fitted with 3D equations, using TableCurve software. The phase in the object under study was then corrected for phase drift using the best-obtained model equation. Results: The experiences were performed for different uniform temperatures: 4.6, 25.4 and 40.0 °C. For all experiences, regardless of the acquisition time, the best model determined in respect of the best correlation coefficient (r²) was a polynomial equation: δf=a+bx+cx²+dy+ey²+fy3 (r² >0.99). This demonstrated that our model is time-independent. The mean difference between the thermocouple measurement and MRI temperature data corrected with the model was 1.7 °C. For each of the experiences, all polynomial parameters excepted for f have a linear behaviour according to time over the measurement period. This can be correlated with the observed linear relation between f0 and time. Discussion/Conclusion: This study demonstrated the feasibility of modelling the phase drift surface using the data from the reference temperature phantom permitting the accurate temperature measurements under relatively long acquisition times.