Modeling the transport phenomena within arterial wall: porous media approach

The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.

Chelating Adsorbents in Purification of Hydrometallurgical Solutions

In this thesis, equilibrium and dynamic sorption properties of weakly basic chelating adsorbents were studied to explain removal of copper, nickel from a concentrated zinc sulfate solution in a hydrometallurgical process. Silica-supported chelating composites containing either branched poly(ethyleneimine) (BPEI) or 2-(aminomethyl)pyridine (AMP) as a functional group were used. The adsorbents are commercially available from Purity Systems Inc, USA as WP-1® and CuWRAM®, respectively. The fundamental interactions between the adsorbents, sulfuric acid and metal sulfates were studied in detail and the results were used to find the best conditions for removal of copper and nickel from an authentic ZnSO4 process solution. In particular, the effect of acid concentration and temperature on the separation efficiency was considered. Both experimental and modeling aspectswere covered in all cases. Metal sorption is considerably affected by the chemical properties of the studied adsorbents and by the separation conditions. In the case of WP-1, acid affinity is so high that column separation of copper, nickel and zinc has to be done using the adsorbent in base-form. On the other hand, the basicity of CuWRAM is significantly lower and protonated adsorbent can be used. Increasing temperature decreases the basicity and the metals affinity of both adsorbents, but the uptake capacities remain practically unchanged. Moreover, increasing temperature substantially enhances intra-particle mass transport and decreases viscosities thus allowing significantly higher feed flow rates in the fixed-bed separation. The copper selectivity of both adsorbents is very high even in the presence of a 250-fold excess of zinc. However, because of the basicity of WP-1, metal precipitation is a serious problem and therefore only CuWRAM is suitable for the practical industrial application. The optimum temperature for copper removal appears to be around 60 oC and an alternative solution purification method is proposed. The Ni/Zn selectivity of both WP-1 and CuWRAM is insufficient for removal of the very small amounts of nickel present in the concentrated ZnSO4 solution.

Modeling of electrolyte sorption – from phase equilibria to dynamic separation systems

In this thesis, general approach is devised to model electrolyte sorption from aqueous solutions on solid materials. Electrolyte sorption is often considered as unwanted phenomenon in ion exchange and its potential as an independent separation method has not been fully explored. The solid sorbents studied here are porous and non-porous organic or inorganic materials with or without specific functional groups attached on the solid matrix. Accordingly, the sorption mechanisms include physical adsorption, chemisorption on the functional groups and partition restricted by electrostatic or steric factors. The model is tested in four Cases Studies dealing with chelating adsorption of transition metal mixtures, physical adsorption of metal and metalloid complexes from chloride solutions, size exclusion of electrolytes in nano-porous materials and electrolyte exclusion of electrolyte/non-electrolyte mixtures. The model parameters are estimated using experimental data from equilibrium and batch kinetic measurements, and they are used to simulate actual single-column fixed-bed separations. Phase equilibrium between the solution and solid phases is described using thermodynamic Gibbs-Donnan model and various adsorption models depending on the properties of the sorbent. The 3-dimensional thermodynamic approach is used for volume sorption in gel-type ion exchangers and in nano-porous adsorbents, and satisfactory correlation is obtained provided that both mixing and exclusion effects are adequately taken into account. 2-Dimensional surface adsorption models are successfully applied to physical adsorption of complex species and to chelating adsorption of transition metal salts. In the latter case, comparison is also made with complex formation models. Results of the mass transport studies show that uptake rates even in a competitive high-affinity system can be described by constant diffusion coefficients, when the adsorbent structure and the phase equilibrium conditions are adequately included in the model. Furthermore, a simplified solution based on the linear driving force approximation and the shrinking-core model is developed for very non-linear adsorption systems. In each Case Study, the actual separation is carried out batch-wise in fixed-beds and the experimental data are simulated/correlated using the parameters derived from equilibrium and kinetic data. Good agreement between the calculated and experimental break-through curves is usually obtained indicating that the proposed approach is useful in systems, which at first sight are very different. For example, the important improvement in copper separation from concentrated zinc sulfate solution at elevated temperatures can be correctly predicted by the model. In some cases, however, re-adjustment of model parameters is needed due to e.g. high solution viscosity.

Quantum transport phenomena and shallow impurity states in CdSb

This work is dedicated to investigation of the energy spectrum of one of the most anisotropic narrow-gap semiconductors, CdSb. At the beginning of the present studies even the model of its energy band structure was not clear. Measurements of galvanomagnetic effects in wide temperature range (1.6 - 300 K) and in magnetic fields up to 30 T were chosen for clarifying of the energy spectrum in the intentionally undoped CdSb single crystals and doped with shallow impurities (In, Ag). Detection of the Shubnikov - de Haas oscillations allowed estimating the fundamental energy spectrum parameters. The shapes of the Fermi surfaces of electrons (sphere) and holes (ellipsoid), the number of the equivalent extremums for valence band (2) and their positions in the Brillouin zone were determined for the first time in this work. Also anisotropy coefficients, components of the tensor of effective masses of carriers, effective masses of density of states, nonparabolicity of the conduction and valence bands, g-factor and its anisotropy for n- and p-CdSb were estimated for the first time during these studies. All the results obtained are compared with the cyclotron resonance data and the corresponding theoretical calculations for p-CdSb. This is basic information for the analyses of the complex transport properties of CdSb and for working out the energy spectrum model of the shallow energy levels of defects and impurities in this semiconductor. It was found out existence of different mechanisms of hopping conductivity in the presence of metal - insulator transition induced by magnetic field in n- and p-CdSb. Quite unusual feature opened in CdSb is that different types of hopping conductivity may take place in the same crystal depending on temperature, magnetic field or even orientation of crystal in magnetic field. Transport properties of undoped p-CdSb samples show that the anisotropy of the resistivity in weak and strong magnetic fields is determined completely by the anisotropy of the effective mass of the holes. Temperature and magnetic field dependence of the Hall coefficient and magnetoresistance is attributed to presence of two groups of holes with different concentrations and mobilities. The analysis demonstrates that below Tcr ~ 20 K and down to ~ 6 - 7 K the low-mobile carriers are itinerant holes with energy E2 ≈ 6 meV. The high-mobile carriers, at all temperatures T < Tcr, are holes activated thermally from a deeper acceptor band to itinerant states of a shallower acceptor band with energy E1 ≈ 3 meV. Analysis of temperature dependences of mobilities confirms the existence of the heavy-hole band or a non-equivalent maximum and two equivalent maxima of the light-hole valence band. Galvanomagnetic effects in n-CdSb reveal the existence of two groups of carriers. These are the electrons of a single minimum in isotropic conduction band and the itinerant electrons of the narrow impurity band, having at low temperatures the energies above the bottom of the conduction band. It is found that above this impurity band exists second impurity band of only localized states and the energy of both impurity bands depend on temperature so that they sink into the band gap when temperature is increased. The bands are splitted by the spin, and in strong magnetic fields the energy difference between them decreases and redistribution of the electrons between the two impurity bands takes place. Mobility of the conduction band carriers demonstrates that scattering in n-CdSb at low temperatures is strongly anisotropic. This is because of domination from scattering on the neutral impurity centers and increasing of the contribution to mobility from scattering by acoustic phonons when temperature increases. Metallic conductivity in zero or weak magnetic field is changed to activated conductivity with increasing of magnetic field. This exhibits a metal-insulator transition (MIT) induced by the magnetic field due to shift of the Fermi level from the interval of extended states to that of the localized states of the electron spectrum near the edge of the conduction band. The Mott variablerange hopping conductivity is observed in the low- and high-field intervals on the insulating side of the MIT. The results yield information about the density of states, the localization radius of the resonant impurity band with completely localized states and about the donor band. In high magnetic fields this band is separated from the conduction band and lies below the resonant impurity bands.

Particle transport method for convection-diffusion-reaction problems

Convective transport, both pure and combined with diffusion and reaction, can be observed in a wide range of physical and industrial applications, such as heat and mass transfer, crystal growth or biomechanics. The numerical approximation of this class of problemscan present substantial difficulties clue to regions of high gradients (steep fronts) of the solution, where generation of spurious oscillations or smearing should be precluded. This work is devoted to the development of an efficient numerical technique to deal with pure linear convection and convection-dominated problems in the frame-work of convection-diffusion-reaction systems. The particle transport method, developed in this study, is based on using rneshless numerical particles which carry out the solution along the characteristics defining the convective transport. The resolution of steep fronts of the solution is controlled by a special spacial adaptivity procedure. The serni-Lagrangian particle transport method uses an Eulerian fixed grid to represent the solution. In the case of convection-diffusion-reaction problems, the method is combined with diffusion and reaction solvers within an operator splitting approach. To transfer the solution from the particle set onto the grid, a fast monotone projection technique is designed. Our numerical results confirm that the method has a spacial accuracy of the second order and can be faster than typical grid-based methods of the same order; for pure linear convection problems the method demonstrates optimal linear complexity. The method works on structured and unstructured meshes, demonstrating a high-resolution property in the regions of steep fronts of the solution. Moreover, the particle transport method can be successfully used for the numerical simulation of the real-life problems in, for example, chemical engineering.

Modeling of non-isothermalvapor membrane separation with thermodynamic models and generalized mass transfer equations

A rigorous unit operation model is developed for vapor membrane separation. The new model is able to describe temperature, pressure, and concentration dependent permeation as wellreal fluid effects in vapor and gas separation with hydrocarbon selective rubbery polymeric membranes. The permeation through the membrane is described by a separate treatment of sorption and diffusion within the membrane. The chemical engineering thermodynamics is used to describe the equilibrium sorption of vapors and gases in rubbery membranes with equation of state models for polymeric systems. Also a new modification of the UNIFAC model is proposed for this purpose. Various thermodynamic models are extensively compared in order to verify the models' ability to predict and correlate experimental vapor-liquid equilibrium data. The penetrant transport through the selective layer of the membrane is described with the generalized Maxwell-Stefan equations, which are able to account for thebulk flux contribution as well as the diffusive coupling effect. A method is described to compute and correlate binary penetrant¿membrane diffusion coefficients from the experimental permeability coefficients at different temperatures and pressures. A fluid flow model for spiral-wound modules is derived from the conservation equation of mass, momentum, and energy. The conservation equations are presented in a discretized form by using the control volume approach. A combination of the permeation model and the fluid flow model yields the desired rigorous model for vapor membrane separation. The model is implemented into an inhouse process simulator and so vapor membrane separation may be evaluated as an integralpart of a process flowsheet.

JNK, a versatile regulator of kinesin-1 transport and cytoskeleton dynamics

C-Jun N-terminal kinase (JNK) is traditionally recognized as a crucial factor in stress response and inducer of apoptosis upon various stimulations. Three isoforms build the JNK subfamily of MAPK; generally expressed JNK1 and JNK2 and brain specific JNK3. Degenerative potency placed JNK in the spotlight as potential pharmacological option for intervention. Unfortunately, adverse effects of potential drugs and observation that expression of only JNK2 and JNK3 are induced upon stress, restrained initial enthusiasm. Notably, JNK1 demonstrated atypical high constitutive activity in neurons that is not responsive to cellular stresses and indicated existence of physiological activity. This thesis aimed at revealing the physiological functions of JNK1 in actin homeostasis through novel effector MARCKS-Like 1 (MARCKSL1) protein, neuronal trafficking mediated by major kinesin-1 motor protein and microtubule (MT) dynamics via STMN2/SCG10. The screen for novel physiological JNK substrates revealed specific phosphorylation of C-terminal end of MARCKSL1 at S120, T148 and T183 both ex vivo and in vitro. By utilizing site-specific mutagenesis, various actin dynamics and migrations assays we were able to demonstrate that JNK1 phosphorylation specifically facilitates F-actin bundling and thus filament stabilisation. Consecutively, this molecular mechanism was proved to enhance formation of filopodia; cell surface projections that allow cell sensing surrounding environment and migrate efficiently. Our results visualize JNK dependent and MARCKSL1 executed induction of filopodia in neurons and fibroblast indicating general mechanism. Subsequently, inactivation of JNK action on MARCKSL1 shifts cellular actin machinery into lamellipodial dynamic arrangement. Tuning of actin cytoskeleton inevitably melds with cell migration. We observed that both active JNK and JNK pseudo-phosphorylated form of MARCKSL1 reduce actin turnover in intact cells leading to overall diminished cell motility. We demonstrate that tumour transformed cells from breast, prostate, lung and muscle-derived cancers upregulate MARCKSL1. We showed on the example of prostate cancer PC-3 cell line that JNK phosphorylation negatively controls MARCKSL1 ability to induce migration, which precedes cancer cell metastasis. The second round of identification of JNK physiological substrates resulted in detection of predominant motor protein kinesin-1 (Kif5). Mass spectrometry detailed analysis showed evident endogenous phosphorylation of kinesin-1 on S176 within motor domain that interacts with MT. In vitro phosphorylation of bacterially expressed kinesin heavy chain by JNK isoforms displayed higher specificity of JNK1 when compared to JNK3. Since, JNK1 is constitutively active in neurons it signified physiological aspect of kinesin-1 regulation. Subsequent biochemical examination revealed that kinesin-1, when not phosphorylated on JNK site, exhibits much higher affinity toward MTs. Expression of the JNK non-phosphorable kinesin-1 mutant in intact cells as well as in vitro single molecule imaging using total internal reflection fluorescence microscopy indicated that the mutant loses normal speed and is not able to move processively into proper cellular compartments. We identify novel kinesin-1 cargo protein STMN2/SCG10, which along with known kinesin-1 cargo BDNF is showing impaired trafficking when JNK activity is inhibited. Our data postulates that constitutive JNK activity in neurons is crucial for unperturbed physiologically relevant transport of kinesin-1 dependant cargo. Additionally, my work helps to validate another novel physiological JNK1 effector STMN2/SCG10 as determinant of axodendritic neurites dynamics in the developing brain through regulation of MT turnover. We show successively that this increased MT dynamics is crucial during developmental radial migration when brain layering occurs. Successively, we are able to show that introduction of JNK phosphorylation mimicking STMN2/SCG10 S62/73D mutant rescues completely JNK1 genetic deletion migration phenotype. We prove that STMN2/SCG10 is predominant JNK effector responsible for MT depolymerising activity and neurite length during brain development. Summarizing, this work describes identification of three novel JNK substrates MARCKSL1, kinesin-1 and STMN2/SCG10 and investigation of their roles in cytoskeleton dynamics and cargo transport. This data is of high importance to understand physiological meaning of JNK activity, which might have an adverse effect during pharmaceutical intervention aiming at blocking pathological JNK action.