Correction of spectral distortions in nanothermometry using machine learning

Abstract

Accurate temperature measurements are crucial in various fields, particularly in nanomedicine, where the early diagnosis of diseases and the development of effective treatments can be achieved. Traditional thermometers, however, have reduced applicability in measurements within internal organs due to their invasiveness. In that sense, luminescence thermometry has emerged as a promising solution. Yet, its clinical application is hindered by challenges inherent to the presence of tissues—one of them being the wavelength dependence of the optical coefficients (i.e. scattering and absorption) of the tissue, leading to spectral distortions that result in a higher thermal uncertainty. A promising solution to enhance the accuracy of luminescence thermometry involves the application of machine learning (ML). To investigate the viability of using ML for spectral corrections of luminescent nanothermometers, we simulated spectral distortions in the emissions of titanium dioxide nanocrystals doped with 10.0 wt% of Nd${}^{3+}$ ions (TiO₂:10Nd${}^{3+}$). These simulations utilized the Beer–Lambert Law, along with the absorption and reduced scattering coefficients of brain gray matter, breast pre-menopause tissue, liver, skin, and water. We tested six ML models: multiple linear regression (MLR), decision tree (DT), random forest (RF), adaptive boosting (Adaboost), k-nearest neighbor (kNN), and artificial neural network multilayer perceptron (MLP). The results demonstrate that traditional models like MLR, Adaboost, and MLP fail to adequately correct these distortions, leading to substantial errors in temperature determination. In contrast, models such as DT, RF, and kNN are highly effective in correcting these distortions, thereby ensuring accurate temperature measurements. These latter models consistently achieved $\Delta T_{effective}\approx 0$, indicating precise temperature measurements even in the presence of significant spectral distortions. Therefore, these results underscore the potential of DT, RF, and kNN models in enhancing the accuracy of luminescent nanothermometers, opening new possibilities for more reliable and precise applications in biological systems.