Revealing the Finer Details of Thermal Heterogeneity: Decryption of the Statistics Encoded in Thermometric MR Spectra

All methods discussed in the four preceding subsections and the following seven subsections have in common that they determine one temperature value (or one temperature difference value) per volume or voxel measured. As a result, any temperature map generated with a phase-based or a spectroscopic MRT technique will only convey one temperature value for each image pixel. Consequently, although these maps are able to reveal temperature gradients between voxels, they cannot detect or even quantify intra-voxel temperature gradients. However, in hyperthermia treatment and cryotherapy, significant temperature gradients may occur not only between but also within selected tissue volumes or voxels. In other words, such a volume or voxel is likely to be characterized by a finite distribution of temperature values within a particular temperature range.

Very recently, a new paradigm for spectroscopic evaluation of the water ¹H resonance line shape has been suggested, aimed at overcoming these limitations (Lutz and Bernard, 2017, 2018a); see also Table S1. This new method is based on the fact that, in the presence of thermal heterogeneity (i.e., temperature gradients) within a given volume, the broad water ¹H resonance representing that volume is in fact composed of overlapping individual lines with varying chemical shifts, the latter being defined by the local temperatures at the nuclei detected. However, the resulting envelope line shapes are not simply broadened but actually encode quantitative information on the statistical distribution of temperature values within the thermally heterogeneous volume. The authors suggested to decode this information by statistical line shape analysis, thus integrating established NMR line shape analysis and statistical curve shape analysis (Lutz and Bernard, 2017). This analysis results in at least eight statistical parameters, aka “descriptors,” that quantitatively describe the statistical distribution of temperature values within the measured volume or voxel (for details of descriptors see Table S1). In other words, the classical spectroscopic MRT measurement only extracts one average value from each single volume or voxel-based MR spectrum as stated above, whereas the new approach exploits the entire water proton MRS line shape encoding the total distribution of temperature values existing within the volume/voxel in question. As this new technique allows one to quantitatively analyze thermal heterogeneity, it is termed quantitative heterogeneity MRT (qhMRT), a particular variant from the group of qhMRS (quantitative heterogeneity MRS) methods (Lutz et al., 2013; Lutz and Bernard, 2019a, 2019b, 2018a, 2018b, 2018c, 2017).

This new technique has been validated by computer simulations in silico, by gel sample studies in vitro, and by investigations of muscle tissue ex vivo. Thanks to the strong NMR signal of water protons occurring in the 10¹–10² molar concentration range, fast spectra were obtainable from specially designed agarose hydrogel samples exhibiting temperature gradients of approximately 50°C within the phantom at the start of each measurement series (Lutz and Bernard, 2018a). This permitted the acquisition of complete temperature profiles at sub-second temporal resolution during the subsequent thermal equilibration, with at least one profile every 400 ms. The statistical descriptors obtained from each temperature profile give unprecedented quantitative access to the statistical temperature distribution of the samples in question (see Table S1 for the temperature sensitivity of this method). An overview of the entire thermal process as a function of time can be obtained by visualizing the temperature profiles in a 3D presentation (Figure 3) facilitating the detection of critical changes during thermal equilibration, whereas the time course of the calculated descriptors provides quantitative time-dependent data on statistical temperature distribution (Figure 4). Like other qhMRS applications, qhMRT can be integrated with MRSI and thus generate maps presenting the spatial organization of tissue or hydrogel areas with different statistical descriptors of temperature distribution (Lutz and Bernard, 2018a). If successfully translated to practical applications, this approach would add novel, detailed information on thermal behavior in the context of thermotherapy and other clinical applications, and in the production and use of hydrogel biomaterials.

Experimental Validation of qhMRT

Graphic presentation of temperature profiles derived from an experiment for monitoring the evolution of heat exchange in a thermally heterogeneous gel sample surrounded by an air stream at a constant temperature (see Table S1). Temperature gradients within the sample were largest at the start of the experiment (after placing a narrow tube filled with cold gel into a wider tube filled with hot gel). Toward the end of the experiment, thermal equilibrium was reached throughout the combined sample, at the temperature of the air stream.

(A) Selected height-normalized temperature profiles for different time points after the first measurement. The first temperature profile, derived from a spectrum that had been acquired when heat exchange between the tubes had only begun to evolve, clearly shows two partially resolved peaks; the origin of the lower (higher) peak was the narrow (wide) tube. As heat exchange progressed, the two peaks coalesced progressively and became very narrow after several minutes. The final temperature of the gel in both tubes was defined by the temperature of the hot air stream around the outer tube (about 55°C, as indicated by the peak derived from the spectrum measured about 3 h after the first acquisition).

(B) 3D rendering of stacked plot of all temperature profiles after area-normalization. (a) Oblique view of profiles. (b) Oblique view of profiles presented as a surface plot to facilitate inspection of the overall evolution of temperature profiles over time. (c) View of the entire 3D surface plot from top. (d) and (e) View of portions of (c) to facilitate inspection of finer details at the start (d) and the end (e) of the experiment.

Reproduced from Lutz and Bernard (2018a), no permission required.

Experimental Validation of qhMRT

Statistical descriptors of temperature distributions as a function of time, derived from temperature profiles shown in Figure 3A (see also Table S1). Weighted mean and median temperatures remain rather stable as long as heat exchange between the two gel compartments dominates thermal behavior (i.e., during the first 30 s); then, means and medians increase to the final value (top left). This is confirmed by the coalescence of the two modes (peak maxima) and their approaching the final temperature (bottom left). Progressive narrowing of the temperature profiles is reflected by decreasing range and standard deviation values (top left and right). Among other descriptors, kurtosis (peakedness), skewness (symmetry), and entropy (evenness, smoothness) offer quantitative measures of the shapes of temperature distribution curves (top right). Two partially separate areas can be distinguished below some of the temperature distribution profiles shown in Figure 3A; for each of these profiles, two separate areas (area1 and area2) below the curve can be quantified, and the temporal evolution of the area1/area2 ratio can be followed as a function of time (bottom right). This also applies to the heights of the individual peaks over these areas (height1 and height2).

Reproduced from Lutz and Bernard (2018a), no permission required.