The primary diagnosis of thyroid tumors based on histopathological patterns can be ambiguous in some cases, so proper classification of thyroid diseases might be improved if molecular biomarkers support cytological and histological assessment. In this work, tissue microarrays representative for major types of thyroid malignancies—papillary thyroid cancer (classical and follicular variant), follicular thyroid cancer, anaplastic thyroid cancer, and medullary thyroid cancer—and benign thyroid follicular adenoma and normal thyroid were analyzed by mass spectrometry imaging (MSI), and then different computation approaches were implemented to test the suitability of the registered profiles of tryptic peptides for tumor classification. Molecular similarity among all seven types of thyroid specimens was estimated, and multicomponent classifiers were built for sample classification using individual MSI spectra that corresponded to small clusters of cells. Moreover, MSI components showing the most significant differences in abundance between the compared types of tissues detected and their putative identity were established by annotation with fragments of proteins identified by liquid chromatography-tandem mass spectrometry in corresponding tissue lysates. In general, high accuracy of sample classification was associated with low inter-tissue similarity index and a high number of components with significant differences in abundance between the tissues. Particularly, high molecular similarity was noted between three types of tumors with follicular morphology (adenoma, follicular cancer, and follicular variant of papillary cancer), whose differentiation represented the major classification problem in our dataset. However, low level of the intra-tissue heterogeneity increased the accuracy of classification despite high inter-tissue similarity (which was exemplified by normal thyroid and benign adenoma). We compared classifiers based on all detected MSI components (n = 1536) and the subset of the most abundant components (n = 147). Despite relatively higher contribution of components with significantly different abundance and lower overall inter-tissue similarity in the latter case, the precision of classification was generally higher using all MSI components. Moreover, the classification model based on individual spectra (a single-pixel approach) outperformed the model based on mean spectra of tissue cores. Our result confirmed the high feasibility of MSI-based approaches to multi-class detection of cancer types and proved the good performance of sample classification based on individual spectra (molecular image pixels) that overcame problems related to small amounts of heterogeneous material, which limit the applicability of classical proteomics.

The objective of the studies described here was the development of a mathematical model which would fit experimental data for the repair of single and double strand breaks induced in DNA in living cells by exposure to ionizing radiation, and which would allow to better understand the processes of DNA repair. DNA breaks are believed to play the major role in radiation-induced lethality and formation of chromosome deletions, and are therefore crucial to the response of cells to radiotherapy. In an initial model which we reported on the basis of data for the repair of Epstein-Barr minichromosomes in irradiated Raji cells, we assumed that DNA breaks are induced only at the moment of irradiation and are later removed by repair systems. This work gives a development of that mathematical model which fits the experimental results more precisely and suggests strongly that DNA breaks are generated not only by direct irradiation but also later, probably by systems engaged in repair of oxidative damage.

This article presents a method for sensitivity analysis of non-linear continuous-time models with delays and its application to parameter estimation. The method is universal and may be used for sensitivity analysis of any system given as a block diagram with arbitrary structure and any number of delays. The method gives sensitivity functions of model trajectories with respect to all model parameters, including delay times, and both forward and adjoint sensitivity analysis may be performed. Two examples application of the method are presented: identification of a Wiener model with delay and identification of a model of JAK-STAT cell signal transduction mechanism.

We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.

Since the very beginning of the COVID-19 pandemic, control policies and restrictions have been the hope for containing the rapid spread of the virus. However, the psychological and economic toll they take on society entails the necessity to develop an optimal control strategy. Assessment of the effectiveness of these interventions aided with mathematical modelling remains a non-trivial issue in terms of numerical conditioning due to the high number of parameters to estimate from a highly noisy dataset and significant correlations between policy timings. We propose a solution to the problem of parameter non-estimability utilizing data from a set of European countries. Treating a subset of parameters as common for all countries and the rest as country-specific, we construct a set of individualized models incorporating 13 different pandemic control measures, and estimate their parameters without prior assumptions. We demonstrate high predictive abilities of these models on an independent validation set and rank the policies by their effectiveness in reducing transmission rates. We show that raising awareness through information campaigns, providing income support, closing schools and workplaces, cancelling public events, and maintaining an open testing policy have the highest potential to mitigate the pandemic.