In the past few decades, the number of people diagnosed with neurodegenerative diseases has increased. If digital biomarkers and machine learning algorithms could be used to predict structural brain characteristics, it would significantly reduce the strain on patients. In this thesis, the feasibility of using speech biomarkers to predict the cortical thickness of brain regions is investigated. Acoustic and linguistic features are extracted from recordings of spontaneous speech and their transcriptions. Disvoice library with additional changes was used to extract acoustic features. For linguistic features, the Part-of-speech tagging from the stanza toolkit was used. For the non-interpretable features, the semantic vectors were extracted from different layers of the BERT and CzeGPT-2 models. Three types of models were tested: models trained on interpretable features only, models trained on non-interpretable features only, and models trained on both interpretable and non-interpretable features using early or late fusion. Neural networks, linear regression, and XGBoost were the architectures tested in this thesis. To evaluate the best models, Stratified K-Fold cross-validation was used. After the initial results, the best-performing models were then tested using Leave-one-out cross-validation on five brain regions. Among the evaluated regions, the models achieved the best results when predicting the insula in both the left and right hemispheres. The best results for the early fusion model were achieved using an XGBoost regressor trained on selected principal component analysis-derived features from the 12th layer of the CzeGPT-2 model, interpretable biomarkers, and demographic features including age, education, and gender. This model achieved a mean percentage error (MAPE) of 0.0403, R-squared (R2) of 0.1105, and estimation error rate (EER) of 0.1188. For late fusion, the models did not outperform those trained only on interpretable features. The best results were achieved by a model trained using a selection of interpretable features, age, and education, with MAPE of 0.0383, R2 of 0.1444, and EER of 0.0991.