Public defence: Marco Antonio Pinto Orellana

Background 

The brain is a highly complex system that self-regulates while it receives,
processes, and reacts to external stimuli. 

The central functions in this intricate structure reside in the neurovascular units, which undergo numerous electro-vascular interactions that, at a macroscopic level, produce signals at the scalp that can be measured by functional near infrared spectroscopy (fNIRS) and electroencephalograms (EEGs). 

These biomedical signals provide complementary knowledge about the underlying physiological and cognitive processes encoded through variations in their spectral properties. 

Due to their nature, both recorded signals have different spectral characteristics: fNIRS signals are located in the range 0-2 Hz (with primary neurological-associated waves in 0.003-0.015 Hz), and EEGs lie in the interval 0-50 Hz mainly. 

Therefore, several mathematical models can be formulated to capture the dynamics of such a complex system in terms of their time-varying spectral characteristics and their interrelationships (under reasonable assumptions). 

Signal interactions, in particular, can also be modelled under the Granger-causality framework, where time-causality is described as the effect that a signal has on another in order to reduce its prediction error.

Aims 

Develop interpretable and robust mathematical models and computationally efficient algorithms that describe the spectral characteristics and interactions within EEG and fNIRS to ultimately understand the control mechanisms inside the brain.

Methods 

We formulated a set of methods for representing associations and interactions at various levels of representation in biomedical signals:

• Complex filter representation (COFRE) enables precise estimation of stationary spectrum response at any desired frequency with calibratable frequency resolution and transient response along with real-time execution capabilities.
• Dyadic aggregated autoregressive (DASAR) model offers a compact and smooth time frequency representation where time-varying transitions are captured by a dyadic decomposition.
• Maximum cross-lag magnitude (MCLM) is a computationally efficient metric derived from a vector autoregressive model that measures time-domain dependences.
• Spectral causality (SCAU) captures modulatory interactions between frequency components of signals.

Highlighted results

• Very low-frequency oscillations (0.007, 0.030-0.050 Hz) estimated with COFRE appeared to be a significant biomarker in tinnitus.
• DASAR spectral modelling provided higher prediction accuracies to identify modulation strategies while improving the differentiation between arithmetic tasks and a baseline in EEG and fNIRS.
• DASAR was the only technique capable of identifying potential Mayer waves as narrow-band artifacts between 97.4 MHz and 97.5 MHz.
• Motion imagery and mental arithmetic tasks shared a background MCLM net-work structure.
• The right prefrontal cortex, around the electrode AFp8, seemed to be an invariable destination for information flows in cross-stimuli and cross-subject MCLM connectivity networks.
• In lexical activities, connections estimated with SCAU networks had smaller variance than links estimated with VAR networks.
• SCAU connections denoted delta-originated and theta-induced links in the frontotemporal brain network configuration.

Discussion 

The introduced methods covered various degrees of representation of biomedical signals, with a particular emphasis on modelling spectral characteristics and inter-signal interactions. 

We use the association between frequency characteristics and psychophysiological conditions to provide an interpretative basis for our mathematical model findings. 

As a result, we contributed rigorous statistical and computational approaches and data-driven biomarkers that can be used to describe cognitive mechanisms and analyse different dimensions of diseases with neurological implications.