Computational Model-based Statistical Methods in Biomedicine

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This project concerns the mathematical modeling and analysis of biomedical applications in which the objective is to retrieve pertinent information of the structure or functioning of a biological system from indirect and minimally invasive measurements. The applications include electroencephalography (EEG) and magnetoencephalography (MEG), electrical impedance tomography (EIT), electric neurography (ENG), and dynamical PET imaging. Characteristic for all these problems is the high complexity of the mathematical model describing the system, significant level of noise in the signals, and severe ill-posedness of the inverse problem of recovering the information of interest from the data. Well-planned model reduction methods help to simplify the model, but at the same time a significant modeling error is introduced, as the simplified model can no longer capture all the features of the data. The aim in the project is to develop computational statistical methods to overcome these problems. Unknown quantities are modeled as random variables, making it possible to analyze in statistical terms the model reduction errors. In the MEG/EEG application, stochastic modeling is used to analyze and filter out the complex noise due to normal brain activity that easily masks the signal coming from an abnormal activity such as the onset of focal epileptic seizure. Well-planned prior models for the unknown quantities help to reduce the ill-posedness of the inverse problems, and lead to efficient numerical methods for both estimating the unknowns of interest as well as to quantify the uncertainty in the estimate. Novel time-dependent filtering methods are investigated to deal with noisy signals.The mathematical and computational methodology aims at improving the performance of different diagnostic processes: In the impedance tomography application, the goal is to be able to discern benign and malignant lesions seen in a mammography image without the need of breast biopsy, by injecting weak electric currents through contact electrodes in the breast and measuring the corresponding electric voltages, and by further computing the electric response of the tissue of interest. It is known that cancer tissue is characterized by an abnormal electric response. The main target in EEG and MEG research is to help localizing epileptic foci in the brain by measuring the electric and magnetic fields outside the patient's head. This information helps greatly the brain surgery planning for patients with severe epilepsy that does not respond to medication. Dynamic PET imaging is used in the studies of brain functioning, e.g., under severe liver conditions that change the ammonium level in the blood. Electric neurography aims at reading the electric signals inside a peripheral nerve in a minimally invasive manner using contact microelectrodes. This data can be used to give a patient control of a prosthetic robotic arm mounted on an amputated limb, as if the arm would be a real arm responding to neuronal commands. Another exciting application being investigated is the possibility to control chronic pain.