The aim of the project is to develop new computational tools for solving inverse problems arising in biomedical applications. The computational framework is based on the Bayesian statistical paradigm, in which the inverse problem is reformulated as a statistical inference problem, and information complementing the scarce and noisy data is imported in the form of prior probability distribution. The methodological emphasis of this project is the development of structural, hierarchical and dynamic prior models. Structural prior models make it possible to combine different imaging modalities, an approach often referred to as data assimilation. The closely related hierarchical models, on the other hand, allow uncertainties in the prior model itself, letting the data guide the prior. In particular, the approach facilitates the implementation of prior information that is qualitative in nature, important examples being sparsity or locality of the solution. Dynamic prior models are essential in time dependent problems, and they often involve structural elements. Another central question addressed in this project is the development of efficient computational strategies to explore the posterior probability distributions. In particular, sequential methods based on the use of fast reduced forward models will be explored. The visualization of uncertainties drawn from a Monte Carlo sample in imaging applications will also be addressed. The resulting algorithms will be applied to biomedical inverse problems, including Electrical Impedance Tomography (EIT), MagnetoEncephaloGraphy (MEG), Positron Emission Tomography (PET) and ElectroNeuroGraphy (ENG), using data provided by an already established network of collaborators.
The current trend in biomedical research is to develop new imaging modalities, clinical procedures and technologies that are minimally invasive. Instead of using ionizing radiation that may constitute a health risk, methods that use weak electric currents or the electromagnetic fields of the body itself are preferable. Electric current/voltage measurements can be used to identify potential malignant tumors in breast tissue; localization of the onset loci of epileptic seizures, an essential procedure before brain surgery to gain control of refractive epilepsy, can be done by measuring the weak magnetic fields due to the brain activity. Similarly, in designing technologies that help patients with spinal cord trauma to regain control of their muscles, or patients with an amputated limb to control a prosthetic arm, new methods of recording non-invasively the nerve signals are developed. A common feature of these methods is that the signals that they rely on are weak, cluttered by noise, and hard to identify. In addition, the computational models are incomplete, since several details describing the setting are unknown. The investigator, together with his colleagues, develops computational methods to overcome the aforementioned difficulties. The methodology relies on probabilistic modeling of the signal and uncertainties within the model. The incomplete data is augmented by complementary information, and a particular emphasis is on the question, how to translate qualitative information about the unknowns into a quantitative form so that it can be entered in the computational model.
Normal 0 false false false EN-US X-NONE X-NONE The goal of this project was to develop new computational methods for various biomedical applications that help to interpret the measured output, extract pertinent and clinically useful information out of the data using sophisticated mathematical models, and visualize the results. The proposed methodology uses tools from mathematical modeling, numerical analysis and computational statistics. Successful implementation of the methodology also requires a good understanding of the underlying application and the biological background of the data acquisition. In magnetoencephalograpy (MEG), the goal is to map the electric activity of the brain by measuring the magnetic field outside the head. In this project, the focus was on finding efficient ways of localizing spiking activity in the brain, a precursor of a seizure in some epilepsy patients. Localizing the onset activity may help to plan efficient surgery for patients that are not responsive to medication, in order to get the seizures under control. Electrical impedance tomography (EIT) is an imaging modality in which the electric conductivity distribution inside a body is estimated computationally from the data obtained by injecting very low electric currents into the body and by measuring the resulting voltages. It has been demonstrated that the electromagnetic response of cancerous tissue differs from that of healthy and benign tumor tissue. Therefore, the modality could potentially help identifying malignant lesions from benign ones inside breast tissue, thus reducing the need of needle biopsies. Electroneurography (ENG) is an emerging modality to read in a minimally invasive way the nerve signals in peripheral nerves. These signals can then be used, e.g., to regain control the muscles of a patient with a spinal cord injury, or make it possible for an amputee to control a robotic prosthetic arm through the intact nerves. The computational challenge is to find a way to extract specific signals from a peripheral nerve fascicle by measuring electric fields outside the nerve without the need of penetrating it. All of the described applications involve the solutions of an inverse problem, in which one needs to estimate the unknown cause of a measured effect. Such problems are known to be very challenging, since small errors in data or in the mathematical model usually propagate into the estimated solutions and get amplified, potentially making the estimate useless. To mitigate these effects, the data need to be augmented by complementary information that excludes unrealistic solutions. Understandably, one needs a way to describe and recognize a realistic solution in a quantitative way, at the same time leaving enough degrees of freedom so that useful data are not filtered out. How this can be done in practice, and what kind of complementary information can be used, were the central questions in this project. Probabilistic and statistical methods, combined with detailed modeling of the underlying biophysics are the key components in the proposed solutions. In the MEG application, two new approaches were suggested. Both of the algorithms are based on the separation of the brain activity into focal activity and non-focal activity, based on the different statistical characteristics of the activities. The attached Figure 1 visualizes one computed solution, in which the electric activity is calculated from the magnetic field and based on a probabilistic modeling of the activity, it is split into a focal part and a part that represents non-focal cerebral processes. In the EIT application, a new way of identifying cancerous tissue was proposed. The idea is to augment the EIT modality by the structural information coming from mammography images, and to use a supervised learning algorithm to classify the tissue into cancerous or non-cancerous pool. Finally, in the ENG application, a method for filtering out and identifying the signals from different nerve fascicles inside a peripheral nerve was proposed. The difficulty is that the ENG data is very noisy, and the nerve signals themselves look remarkably like noise, too, so distinguishing between the signal and noise is a challenge. The proposed method is based on the idea that while the nerve signal may look like noise, its variance may serve as a good fingerprint to be estimated from the data. Figure 2 shows to computed examples in which the simulated noisy signals (left) are processed using a statistical model and the informative part of nerve activation is extracted from it (right).
