Bayesian multi-modal model comparison: a case study on the generators of the spike and the wave in generalized spike–wave complexes

We present a novel approach to assess the networks involved in the generation of spontaneous pathological brain activity based on multi-modal imaging data. We propose to use probabilistic fMRI-constrained EEG source reconstruction as a complement to EEG-correlated fMRI analysis to disambiguate between networks that co-occur at the fMRI time resolution. The method is based on Bayesian model comparison, where the different models correspond to different combinations of fMRI-activated (or deactivated) cortical clusters. By computing the model evidence (or marginal likelihood) of each and every candidate source space partition, we can infer the most probable set of fMRI regions that has generated a given EEG scalp data window. We illustrate the method using EEG-correlated fMRI data acquired in a patient with ictal generalized spike–wave (GSW) discharges, to examine whether different networks are involved in the generation of the spike and the wave components, respectively. To this effect, we compared a family of 128 EEG source models, based on the combinations of seven regions haemodynamically involved (deactivated) during a prolonged ictal GSW discharge, namely: bilateral precuneus, bilateral medial frontal gyrus, bilateral middle temporal gyrus, and right cuneus. Bayesian model comparison has revealed the most likely model associated with the spike component to consist of a prefrontal region and bilateral temporal–parietal regions and the most likely model associated with the wave component to comprise the same temporal–parietal regions only. The result supports the hypothesis of different neurophysiological mechanisms underlying the generation of the spike versus wave components of GSW discharges

Inverse Problems in data-driven multi-scale Systems Medicine: application to cancer physiology

Systems Medicine is an interdisciplinary framework involving reciprocal feedback between clinical investigation and mathematical modeling/analysis. Its aim is to improve the understanding of complex diseases by integrating knowledge and data across multiple levels of biological organization. This Thesis focuses on three inverse problems, arising from three kinds of data and related to cancer physiology, at different scales: tissues, cells, molecules. The general assumption of this piece of research is that cancer is associated toa path ological glucose consumption and, in fact, its functional behavior can be assessed by nuclear medicine experiments using [18F]-fluorodeoxyglucose (FDG) as a radioactive tracer mimicking the glucose properties. At tissue-scale, this Thesis considers the Positron Emission Tomography (PET) imaging technique, and deals with two distinct issues within compartmental analysis. First, this Thesis presents a compartmental approach, referred to as reference tissue model, for the estimation of FDG kinetics inside cancer tissues when the arterial blood input of the system is unknown. Then, this Thesis proposes an efficient and reliable method for recovering the compartmental kinetic parameters for each PET image pixel in the context of parametric imaging, exploiting information on the tissue physiology. Standard models in compartmental analysis assume that phosphorylation and dephosphorylation of FDG occur in the same intracellular cytosolic volume. Advances in cell biochemistry have shown that the appropriate location of dephosphorylation is the endoplasmic reticulum (ER). Therefore, at cell-scale, this Thesis formalizes a biochemically-driven compartmental model accounting for the specific role played by the ER, and applies it to the analysis of in vitro experiments on FDG uptake by cancer cell cultures obtained with a LigandTracer (LT) device. Finally, at molecule-scale, this Thesis provides a preliminary mathematical investigation of a chemical reaction network (CRN), represented by a huge Molecular Interaction Map (MIM), describing the biochemical interactions occurring between signaling proteins in specific pathways within a cancer cell. The main issue addressed in this case is the network parameterization problem, i.e. how to determine the reaction rate coefficients from protein concentration data

Constructing mean electron distributions from hard X-ray spectra of solar flares

The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) mission provides information on high resolution X-ray spectra emitted by collisional bremsstrahlung of thermal and non-thermal electrons with ions in solar flares. One of the aims of the mission is to infer information about the acceleration and transport mechanisms of hard X-ray emitting electrons and 7-ray emitting ions in solar flares. I investigate events observed during distinct attenuator states of the satellite, which have unique characteristics in their photon and mean electron distributions. Such characteristics include evidence of low energy cutoff features and other such physically real bump and dip features. In the framework of a colli-sionally thin bremsstrahlung model and an adjustable thermal function I forward fit these to the background-removed count flux data, using least squares minimization via OSPEX (Object Spectroscopy Executive). Along with Chi-Square Tests, I present random and non- systematic residuals to show goodness of fit. Conversion from count rate to count flux and then to photon flux spectra is a traditional approach to modelling hard X-ray spectra, but is significantly unreliable due to its dependence on parametric electron distribution approximations. Model independent hard X-ray spectra can be non-trivially calculated using the Detector Response Matrix (DRM) and are computed using a sequence of algorithms solving a linear system of equations, which present an inversion problem characterized by numerical instability due to the non-diagonal nature of the DRM. The extent of such instability is unique for different DRM configurations, hence different under each attenuator state. We then address the solution of this inversion problem- by using a regularization algorithm with the aim of inferring accurate and useful electron distribution spectra. Adjustment of this procedure to convert directly between counts and electrons, which is a one step rather than two step process, presents more robust and detailed information about features of electron dynamics during flares. Significant features such as low and high energy cutoffs tell us much about electron acceleration properties and energy losses in the flare evolution. Comparing regularized solutions in each event through different approaches will allow for confirmation of the existence or non-existence of such features. This innovative regularization technique is capable of portraying a truer interpretation of both hard X-ray and mean electron spectra

Functional magnetic resonance imaging : an intermediary between behavior and neural activity

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging is a non-invasive technique used to trace changes in neural dynamics in reaction to mental activity caused by perceptual, motor or cognitive tasks. The BOLD response is a complex signal, a consequence of a series of physiological events regulated by increased neural activity. A method to infer from the BOLD signal onto underlying neuronal activity (hemodynamic inverse problem) is proposed in Chapter 2 under the assumption of a previously proposed mathematical model on the transduction of neural activity to the BOLD signal. Also, in this chapter we clarify the meaning of the neural activity function used as the input for an intrinsic dynamic system which can be viewed as an advanced substitute for the impulse response function. Chapter 3 describes an approach for recovering neural timing information (mental chronometry) in an object interaction decision task via solving the hemodynamic inverse problem. In contrast to the hemodynamic level, at the neural level, we were able to determine statistically significant latencies in activation between functional units in the model used. In Chapter 4, two approaches for regularization parameter tuning in a regularized-regression analysis are compared in an attempt to find the optimal amount of smoothing to be imposed on fMRI data in determining an empirical hemodynamic response function. We found that the noise autocorrelation structure can be improved by tuning the regularization parameter but the whitening-based criterion provides too much smoothing when compared to cross-validation. Chapter~5 illustrates that the smoothing techniques proposed in Chapter 4 can be useful in the issue of correlating behavioral and hemodynamic characteristics. Specifically, Chapter 5, based on the smoothing techniques from Chapter 4, seeks to correlate several parameters characterizing the hemodynamic response in Broca's area to behavioral measures in a naming task. In particular, a condition for independence between two routes of converting print to speech in a dual route cognitive model was verified in terms of hemodynamic parameters

Tomographic imaging of combustion zones using tunable diode laser absorption spectroscopy (TDLAS)

This work concentrates on enabling the usage of a specific variant of tunable diode laser absorption spectroscopy (abbr. TDLAS) for tomogaphically reconstructing spatially varying temperature and concentrations of gases with as few reconstruction artifacts as possible. The specific variant of TDLAS used here is known as wavelength modulation with second harmonic detection (abbr. WMS-2f) which uses the wavelength dependent absorbance information of two different spectroscopic transitions to determine temperature and concentration values. Traditionally, WMS-2f has generally been applied to domains where temperature although unknown, was spatially largely invariant while concentration was constant and known to a reasonable approximation (_x0006_+/- 10% ). In case of unknown temperatures and concentrations with large variations in space such techniques do not hold good since TDLAS is a “line-of-sight” (LOS) technique. To alleviate this problem, computer tomographic methods were developed and used to convert LOS projection data measured using WMS-2f TDLAS into spatially resolved local measurements. These locally reconstructed measurements have been used to determine temperature and concentration of points inside the flame following a new temperature and concentration determination strategy for WMS-2f that was also developed for this work. Specifically, the vibrational transitions (in the 1.39 microns to 1.44 microns range) of water vapor (H2O) in an axi-symmetric laminar flame issuing from a standard flat flame burner (McKenna burner) was probed using telecom grade diode lasers. The temperature and concentration of water vapor inside this flame was reconstructed using axi-symmetric Abel de-convolution method. The two different sources of errors in Abel’s deconvolution - regularization errors and perturbation errors, were analyzed and strategies for their mitigation were discussed. Numerical studies also revealed the existence of a third kind of error - tomographic TDLAS artifact. For 2D tomography, studies showing the required number of views, number of rays per view, orientation of the view and the best possible algorithm were conducted. Finally, data from 1D tomography was extrapolated to 2D and reconstructions were benchmarked with the results of 1D tomography

Differential Models, Numerical Simulations and Applications

This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems