Modeling of nonlinear and time-varying dynamic systems: Development of methods for the identification of non linear and/or time-varying (nonstationary) systems, acategory which subsumes the vast majority of biological/ physiological systems. We are focusing mostly on data-driven approaches (e.g. Volterra models) that do not place strictassumptions on system structure. We are using techniques such as basis expansions, neural networks and Bayesian estimation in order to achieve more efficient estimation and reduce the number of required free parameters, which may pose significant challenge in the case of nonlinear systems. We are also using recursive techniques in order to track the possibly time-varying characteristics of such systems.
Cerebral hemodynamics and autoregulation: The cerebrovascular bed is able to maintain a relatively constant cerebral blood flow (CBF) in response to fluctuations of several physiological signals, particularly arterial blood pressure (ABP). Specifically, the regulation of ABP changes in order to maintain a relatively constant CBF is termed cerebral autoregulation and is a very important homeostatic mechanism as the brain accounts for around 20% of the body’s total O2 consumption, while accounting for only 2% of its mass. We are interested in modeling cerebral autoregulation using multivariate, nonlinear/nonstationary approaches as well as noninvasive measurements of ABP, CBF velocity and arterial CO2.TWe are interested both in systemic autoregulation, which can be assessed with transcranial Doppler ultrasound and regional autoregulation, which can be assessed by functional magnetic resonance imaging (fMRI). Cerebral hemodynamics play a central role in the interpretation of task-related and resting-state fMRI experiments, which are closely linked to the intricate coupling between neural activity and the resulting hemodynamic fMRI signal (neurovascular coupling). In this context, we are interested in modeling the fMRI hemodynamics response function and the effect of physiological noise and nonstationarities on resting state network analyses.
Computational oncology: We are investigating the development of deterministic and stochastic mathematical models that describe the dynamic evolution of cancerous tumours, as well as the effect of therapy using pharmacokinetic/pharmacodynamic models. We are also investigating the use of control strategies to design optimal therapies that utilize the aforementioned models, taking into account drug toxicity and the emergence of drug resistance. Along with our experimental collaborators (Laboratory of Tumour Virology, University of Cyprus, Dr. K. Strati) we are validating these models and evaluating the effect of optimally designed therapies in animal models (double transgenic mice).
Glucose metabolism and control: We are interested in data-driven models of glucose metabolism and their relation to widely used parametric (differential equation) models of glucose metabolism. Data-driven models provide more flexibility and may be used in practical settings in combination with the recently developed technology of continuous glucose sensors and programmable insulin micropumps in order to (i) quantify the dynamics of glucose variability and its relation to other signals of interest such as insulin and extract indices of diagnostic importance (e.g. insulin resistance, glucose sensitivity) and (ii) obtain adaptive patient-specific models between glucose and other variables (insulin, glucagon), which can be used to implement model-predictive glucose regulation algorithms.