Solubility, diffusivity and permeability of gases in glassy polymers

Gas separation membranes of high CO2 permeability and selectivity have great potential in both natural gas sweetening and carbon dioxide capture. Many modified PIM membranes results permselectivity above Robinson upper bound. The big problem that should be solved for these polymers to be commercialized is their aging through time. In high glassy polymeric membrane such as PIM-1 and its modifications, solubility selectivity has more contribution towards permselectivity than diffusivity selectivity. So in this thesis work pure and mixed gas sorption behavior of carbon dioxide and methane in three PIM-based membranes (PIM-1, TZPIM-1 and AO-PIM-1) and Polynonene membrane is rigorously studied. Sorption experiment is performed at different temperatures and molar fraction. Sorption isotherms found from the experiment shows that there is a decrease of solubility as the temperature of the experiment increases for both gases in all polymers. There is also a decrease of solubility due to the presence of the other gas in the system in the mixed gas experiments due to competitive sorption effect. Variation of solubility is more visible in methane sorption than carbon dioxide, which will make the mixed gas solubility selectivity higher than that of pure gas solubility selectivity. Modeling of the system using NELF and Dual mode sorption model estimates the experimental results correctly Sorption of gases in heat treated and untreated membranes show that the sorption isotherms don’t vary due to the application of heat treatment for both carbon dioxide and methane. But there is decrease in the diffusivity coefficient and permeability of pure gases due to heat treatment. Both diffusivity coefficient and permeability decreases with increasing of heat treatment temperature. Diffusivity coefficient calculated from transient sorption experiment and steady state permeability experiment is also compared in this thesis work. The results reveal that transient diffusivity coefficient is higher than steady state diffusivity selectivity.

Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.

MR in vivo tractography for the reconstruction of cranial nerves course

Aim The aim of my Ph.D. was to implement a diffusion tensor tractography (DTT) pipeline to reconstruct cranial nerve I (olfactory) to study COVID-19 patients, and anterior optic pathway (AOP, including optic nerve, chiasm, and optic tract) to study patients with sellar/parasellar tumors, and with Leber’s Hereditary Optic Neuropathy (LHON). Methods We recruited 23 patients with olfactory dysfunction after COVID-19 infection (mean age 37±14 years, 12 females); 27 patients with sellar/parasellar tumors displacing the optic chiasm eligible for endonasal endoscopic surgery (mean age 53. ±16.4 years, 13 female) and 6 LHON patients (mutation 11778/MT-ND4, mean age 24.9±15.7 years). Sex- and age-matched healthy control were also recruited. In LHON patients, optical coherence tomography (OCT) was performed. Acquisitions were performed on a clinical high field 3-T MRI scanner, using a multi-shell HARDI (High Angular Resolution Diffusion Imaging) sequence (b-values 0-300-1000-2000 s/mm2, 64 maximum gradient directions, 2mm3 isotropic voxel). DTT was performed with a multi-tissue spherical deconvolution approach and mean diffusivity (MD) DTT metrics were compared with healthy controls using an unpaired t-test. Correlations of DTT metrics with clinical data were sought by regression analysis. Results In all 23 hypo/anosmic patients with previous COVID-19 infection the CN I was successfully reconstructed with no DTT metrics alterations, thus suggesting the pathogenetic role of central olfactory cortical system dysfunction. In all 27 patients with sellar/parasellar tumors the AOP was reconstructed, and in 11/13 (84.7%) undergoing endonasal endoscopic surgery the anatomical fidelity of the reconstruction was confirmed; a significant decrease in MD within the chiasma (p<0.0001) was also found. In LHON patients a reduction of MD in the AOP was significantly associated with OCT parameters (p=0.036). Conclusions Multi-shell HARDI diffusion-weighted MRI followed by multi-tissue spherical deconvolution for the DTT reconstruction of the CN I and AOP has been implemented, and its utility demonstrated in clinical practice.