An internal reference model–based PRF temperature mapping method with Cramer‐Rao lower bound noise performance analysis

Abstract

The conventional phase difference method for MR thermometry suffers from disturbances caused by the presence of lipid protons, motion-induced error, and field drift. A signal model is presented with multi-echo gradient echo (GRE) sequence using a fat signal as an internal reference to overcome these problems. The internal reference signal model is fit to the water and fat signals by the extended Prony algorithm and the LevenbergMarquardt algorithm to estimate the chemical shifts between water and fat which contain temperature information. A noise analysis of the signal model was conducted using the CramerRao lower bound to evaluate the noise performance of various algorithms, the effects of imaging parameters, and the influence of the water:fat signal ratio in a sample on the temperature estimate. Comparison of the calculated temperature map and thermocouple temperature measurements shows that the maximum temperature estimation error is 0.614°C, with a standard deviation of 0.06°C, confirming the feasibility of this modelbased temperature mapping method. The influence of sample water:fat signal ratio on the accuracy of the temperature estimate is evaluated in a water-fat mixed phantom experiment with an optimal ratio of approximately 0. Quantitative MRI thermometry has become an attractive method to noninvasively monitor the evolution of tissue temperatures and to guide tumor ablation based on local thermal therapy, such as high-intensity focused ultrasound surgery (1,2). Temperature imaging based on the temperature dependence of the water proton resonance frequency (PRF) (3,4) is currently the main choice for many applications, especially for high magnetic fields above 1 T, because there exists a linear relationship between PRF and temperature that is independent of the physiologic effects of hyperthermia (5). Typically, a temperature map from PRF is generated using phase-difference images from a single long gradient echo sequence (4,6). Despite many advantages, the conventional phasedifference method still has several problems that may influence the precision of the quantitative temperature mapping, such as the presence of lipid protons (7,8), inter-and intrascan motion (9), and frequency drift due to an unstable magnetic field (10). The presence of lipids modifies the phase difference because the lipid resonance frequencies are not temperature dependent, which leads to temperature estimation errors. Fat-suppressed slice-selective excitation or spectral-spatial pulses (7,11) have been proposed by several research groups to overcome this problem. However, these techniques are sensitive to field inhomogeneities and typically yield nonuniform suppression over the field of view (12,13).The motion artifacts and field drift associated with the traditional phase-difference approach have been reduced using an internal frequency reference that has a temperature-insensitive resonance. Magnetic resonance spectroscopic imaging (14) can trace the changes in the water resonance frequency, using a non-temperature-dependent c...

Accelerated model-based proton resonance frequency shift temperature mapping using echo-based GRAPPA reconstruction

“…As fat protons do not show a temperature-dependent frequency change, they can be used as a reference to provide more accurate temperature estimation. A multi-echo signal model which combines the fat signal and water signal has been established in a previous study [7,8]: where i is the type of tissue composition, n is number of echoes, ρ is relative proton density, Φ is the initial phase of each composition, and ω is the off-resonance angular frequency of each composition.…”

“…This technique avoids the use of baseline images. It has been demonstrated to be relatively insensitive to inter-frame motion, as compared to other MR temperature estimation methods [7,8]. A previous study shows the accuracy of this method is 0.7 ± 0.5°C during ex vivo HIFU-heating experiment of a goose liver as …”

“…A model-based PRF method was proposed in 2009 [7,8]. This method uses the frequency difference between fat and water to calculate the absolute temperature based on multi-echo GRE images.…”

Comprehensive analysis of the Cramer–Rao bounds for magnetic resonance temperature change measurement in fat–water voxels using multi-echo imaging

“…Several methods have been proposed to deal with the errors caused by fat signal, including fat suppression [9–11], spectroscopy [12–14], and multi-echo fitting [15–17]. Multi-echo fitting methods (such as IDEAL [18]) have been used to create water-only images that can then be used to calculate temperature changes using normal PRFS techniques [15].…”

“…CRLB analyses have been performed for multi-echo fitting techniques [17,23]. In the case of Li et al, a temperature noise CRLB value can be determined.…”