Improved PRF-based MR thermometry using k-space energy spectrum analysis

Abstract

Purpose: Proton resonance frequency (PRF) thermometry encodes information in the phase of MRI signals. A multiplicative factor converts phase changes into temperature changes, and this factor includes the TE. However, phase variations caused by B₀ and/or B₁ inhomogeneities can effectively change TE in ways that vary from pixel to pixel. This work presents how spatial phase variations affect temperature maps and how to correct for corresponding errors.

Methods: A method called "k-space energy spectrum analysis" was used to map regions in the object domain to regions in the k-space domain. Focused ultrasound heating experiments were performed in tissue-mimicking gel phantoms under two scenarios: with and without proper shimming. The second scenario, with deliberately de-adjusted shimming, was meant to emulate B₀ inhomogeneities in a controlled manner. The TE errors were mapped and compensated for using k-space energy spectrum analysis, and corrected results were compared with reference results. Furthermore, a volunteer was recruited to help evaluate the magnitude of the errors being corrected.

Results: The in vivo abdominal results showed that the TE and heating errors being corrected can readily exceed 10%. In phantom results, a linear regression between reference and corrected temperatures results provided a slope of 0.971 and R² of 0.9964. Analysis based on the Bland-Altman method provided a bias of -0.0977°C and 95% limits of agreement that were 0.75°C apart.

Conclusion: Spatially varying TE errors, such as caused by B₀ and/or B₁ inhomogeneities, can be detected and corrected using the k-space energy spectrum analysis method, for increased accuracy in proton resonance frequency thermometry.

Keywords: KESA algorithm; MR thermometry; PRF temperature measurements; TE errors.

Fig. 1:

The k-space energy spectrum analysis (KESA) algorithm is depicted here. An increasing number of lines in a given k-space matrix (a) were replaced with zeros in (b-d) while the strength of the signal at the location indicated by a small red circle in (e-g) was monitored. As a result, the plot in (h) was obtained that shows signal strength as a function of the number of k-space lines being zeroed. A sharp transition occurs in (h) at the effective k-space center for the particular spatial region marked in red in (e-g). In the presence of a linear gradient k-space was shifted in (i), as detected through KESA in (j). In more complicated cases where spatial field variations may lead to a ‘broadening’ of the k-space signal distribution, as opposed to a simple shift as in (i), KESA could still detect the effective k-space center location for given spatial regions/locations. The frequency-encoding (FE) direction is indicated with an arrow in (a) and (e) in k-space and image space, respectively.

Fig. 2:

(a) The experimental set-up is depicted, see text for more details. Field maps are shown for both the good-shim (b) and bad-shim (d) scenarios. Associated k-space center offsets are readily seen in (c,e). The red ‘o’ symbols in (b) and (d) mark the hottest locations at focus, for which plots were generated in (f) and (g). The presence of background phase gradients did affect the temperature measurements, as shown in (f). The size of the error depends on the acquisition bandwidth, as expected from Eq. 4.

Fig. 3:

(a.1-a.4) Maps are shown for the k-space shift and the associated TE error. The top row represents preheating data, while the bottom row represents the hottest time frame. The process of heating introduces its own spatial field variations, which lead to time-varying TE errors. These TE errors can be appreciated looking near the focus in (a.4), inside the area marked by a gray rectangle. The median size of the shift and TE error was roughly 30 pixels and 2.5 ms, respectively. (b.1,b.2) Non-heated in vivo results are shown, where background phase gradients created TE errors. Two particular locations are highlighted with black boxes in (b.2) where errors were about +0.8 ms and −0.4 ms, near the tissue/air transitions. With respect to the nominal TE of 7 ms these represent errors of 11% and 5.7%, respectively, and these relative errors would directly transfer to heating measurements. (c.1-c.4) Heating results with and without correction were compared, for two separate time points.

Fig. 4:

(a) The data obtained with de-adjusted shimming, as shown with an orange dashed line here and in Fig. 2f, was corrected using the proposed algorithm, see the full orange line. The corrected data is very similar to the reference data acquired with proper shimming, see blue line. More generally, the agreement between corrected and reference results is shown for all time points at focus in (b) and (c), using a scatter plot and a Bland-Altman analysis, respectively (slope/intercept = 0.971/0.0665, R² = 0.9964, bias = 0.06 ^oC, 95% confidence interval of ±0.37 ^oC).

Fig. 5:

The present method was compared to a previously-published method in terms of robustness to noise. For all tested levels, the proposed approach (orange bars) led to smaller levels of temperature noise than the prior method (blue bars). The difference became more meaningful in lower-SNR situations.