Oxygen Tension Profiles In Tumors Predicted By A Diffusion With Absorption Model Involving A Moving Free Boundary

The dynamic behavior of the oxygen tension distribution in tumors during radiotherapy is studied by the development and solution of a diffusion with absorption model involving a moving free boundary. The oxygen uptake rates within the tumor are considered to be functions of the oxygen concentration and results are presented for zeroth-, half-, first- and second-order rates of absorption, as well as when the rate of oxygen absorption is described by the Michaelis-Menten expression. The results presented in this work may be used together with the data from the oxygen radiosensitivity curve of a tumor, in order to determine the proper radiation dosage that should be applied to the tumor during radiotherapy, so as to compensate for the lost killing effectiveness resulting from oxygen consumption by the tumor. The model used in this study may also be employed in examining the role of oxygen and hypoxia in chemotherapy, when cycle-specific chemotherapeutic agents are used. The numerical procedure developed for the solution of the equations of the model may become applicable to problems encountered in such diverse areas as statistical decision theory, heat transfer with changes of phase, thermal explosions, optimal control and fluid flow in porous media. © 1988

Modeling the Construction of Polymeric Adsorbent Media: Effects of Counter-Ions on Ligand Immobilization and Pore Structure

Molecular dynamics modeling and simulations are employed to study the effects of counter-ions on the dynamic spatial density distribution and total loading of immobilized ligands as well as on the pore structure of the resultant ion exchange chromatography adsorbent media. The results show that the porous adsorbent media formed by polymeric chain molecules involve transport mechanisms and steric resistances which cause the charged ligands and counter-ions not to follow stoichiometric distributions so that (i) a gradient in the local nonelectroneutrality occurs, (ii) non-uniform spatial density distributions of immobilized ligands and counter-ions are formed, and (iii) clouds of counter-ions outside the porous structure could be formed. The magnitude of these counter-ion effects depends on several characteristics associated with the size, structure, and valence of the counter-ions. Small spherical counter-ions with large valence encounter the least resistance to enter a porous structure and their effects result in the formation of small gradients in the local nonelectroneutrality, higher ligand loadings, and more uniform spatial density distributions of immobilized ligands, while the formation of exterior counter-ion clouds by these types of counter-ions is minimized. Counter-ions with lower valence charges, significantly larger sizes, and elongated shapes, encounter substantially greater steric resistances in entering a porous structure and lead to the formation of larger gradients in the local nonelectroneutrality, lower ligand loadings, and less uniform spatial density distributions of immobilized ligands, as well as substantial in size exterior counter-ion clouds. The effects of lower counter-ion valence on pore structure, local nonelectroneutrality, spatial ligand density distribution, and exterior counter-ion cloud formation are further enhanced by the increased size and structure of the counter-ion. Thus, the design, construction, and functionality of polymeric porous adsorbent media will significantly depend, for a given desirable ligand to be immobilized and represent the adsorption active sites, on the type of counter-ion that is used during the ligand immobilization process. Therefore, the molecular dynamics modeling and simulation approach presented in this work could contribute positively by representing an engineering science methodology to the design and construction of polymeric porous adsorbent media which could provide high intraparticle mass transfer and adsorption rates for the adsorbate biomolecules of interest which are desired to be separated by an adsorption process

A Molecular Dynamics Study on the Transport of a Charged Biomolecule in a Polymeric Adsorbent Medium and Its Adsorption onto a Charged Ligand

The transport of a charged adsorbate biomolecule in a porous polymeric adsorbent medium and its adsorption onto the covalently immobilized ligands have been modeled and investigated using molecular dynamics modeling and simulations as the third part of a novel fundamental methodology developed for studying ion-exchange chromatography based bioseparations. To overcome computational challenges, a novel simulation approach is devised where appropriate atomistic and coarse grain models are employed simultaneously and the transport of the adsorbate is characterized through a number of locations representative of the progress of the transport process. The adsorbate biomolecule for the system studied in this work changes shape, orientation, and lateral position in order to proceed toward the site where adsorption occurs and exhibits decreased mass transport coefficients as it approaches closer to the immobilized ligand. Furthermore, because the ligands are surrounded by counterions carrying the same type of charge as the adsorbate biomolecule, it takes the biomolecule repeated attempts to approach toward a ligand in order to displace the counterions in the proximity of the ligand and to finally become adsorbed. The formed adsorbate-ligand complex interacts with the counterions and polymeric molecules and is found to evolve slowly and continuously from one-site (monovalent) interaction to multisite (multivalent) interactions. Such a transition of the nature of adsorption reduces the overall adsorption capacity of the ligands in the adsorbent medium and results in a type of surface exclusion effect. Also, the adsorption of the biomolecule also presents certain volume exclusion effects by not only directly reducing the pore volume and the availability of the ligands in the adjacent regions, but also causing the polymeric molecules to change to more compact structures that could further shield certain ligands from being accessible to subsequent adsorbate molecules. These findings have significant practical implications to the design and construction of polymeric porous adsorbent media for effective bioseparations and to the synthesis and operation of processes employed in the separation of biomolecules. The modeling and analysis methods presented in this work could also be suitable for the study of biocatalysis where an enzyme is immobilized on the surface of the pores of a porous medium

An Analysis Of The Lyophilization Process Using A Sorption‐sublimation Model And Various Operational Policies

The freeze‐drying process is studied under various operational policies through the use of a sorption‐sublimation model. The operational policy that provides the shortest drying times keeps the pressure at its lowest value. The upper and lower heating plates are independently controlled so that the material constraints are encountered and held throughout the free water removal phase. Under certain conditions, and for the case of samples of small thickness, the sorbed water profiles may have segments whose bound water concentrations are higher than those at the start of the free water removal phase. It is shown that the criterion used in terminating the freeze‐drying process is of extreme importance, since it may lead to an undesirable sorbed water profile which may deteriorate the quality of the dried product. Copyright © 1985 American Institute of Chemical Engineer

Expression for the Film Mass-Transfer Coefficient of Charged Solutes in a Liquid Stream Flowing in Packed Beds of Charged Particles and Charged Porous Monoliths

Numerous biochemical and chemical separation and reaction systems have low Reynolds and high Peclet numbers and involve mass transfer of charged solutes between a pressure-driven flowing liquid stream and packed beds of charged particles or charged porous monoliths. For such systems, an expression for determining the film mass-transfer coefficient of a charged solute in a pore (channel) was derived from fundamental expressions of physics. In the derivation of the expression for the film mass-transfer coefficient, mass transport by the mechanisms of convection, diffusion, and electrophoretic migration was taken into account. by considering geometrical (physical) similarity between all pores in a packed bed of charged particles or in a charged porous monolith and the existence of a macroscopic pressure field with uniform gradient, the film mass-transfer coefficient is found to be the same over all pores regardless of size. The values of the parameters in the derived expression for the film mass-transfer coefficient depend on the value of the size of the electrical double layer (Debye length), the magnitude of the zeta potential on the surface of the pores, the relative concentrations of the cations and anions of the supporting electrolyte and of the charged solute, the interaction (adsorption) isotherm of the charged analyte with the charged pore surface, and the values of the charge and Peclet numbers of the charged analyte and the cations and anions of the background/buffer electrolyte. The expression for the film mass-transfer coefficient presented in this work could be used to analyze and correlate experimental data on the rate of mass transfer between charged porous monoliths or packed beds of particles having charged pore surfaces and a flowing liquid stream containing charged species

Theoretical Aspects Of Affinity Chromatography

There is significant interest in the biochemical industry in the use of affinity-chromatography processes for the purification, separation, and analysis of enzymes, hormones, antibodies, proteins and other macromolecules. Appropriate theories are needed in order to predict the dynamic behavior, to design, to scale-up, to optimize, and to control affinity-chromatography systems. This review presents the mass transfer mechanisms and rate steps involved in the formation and dissociation of the adsorbate-ligand complex, and suggests models which can be used to predict the performance characteristics of affinity-chromatography processes. Procedures are also presented with which the parameters characterizing the mass transfer and interaction mechanisms of the models can be estimated, and theoretical and experimental areas and directions are suggested for future research in affinity-chromatography systems. Results and their implications for batch, fixed bed, periodic countercurrent bed, and radial flow systems are discussed. The need for continuous affinity-chromatography separations is also considered. © 1989

Adsorption in a Stratified Column Bed Packed with Porous Particles Having Partially Fractal Structures and a Distribution of Particle Diameters

Stratified column bed systems whose sections are formed by packing adsorbent particles with a partially fractal structure are proposed and studied. The simulation results clearly show that the breakthrough times and the shape of the breakthrough curves obtained from stratified column beds are significantly larger and sharper than those obtained from conventional columns. The stratified column beds provide, to the designer and user of chromatographic column systems, more degrees of freedom with respect to the number of parameters and variables that could be controlled in the design, construction, and operation of efficient chromatographic adsorption systems. Furthermore, the results suggest that the stratified column beds could provide a higher dynamic adsorptive capacity than conventional columns when it is required to increase the column throughput

A Theory for the Primary and Secondary Drying Stages of the Freeze-Drying of Pharmaceutical Crystalline and Amorphous Solutes: Comparison Between Experimental Data and Theory

A theory is constructed to describe quantitatively the dynamic behavior of the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes. Experimental data for the freeze-drying of cloxacillin monosodium salt and skim milk are obtained using a pilot freeze-dryer. The comparison of the theoretical results with the experimental data shows that the agreement between experiment and theory is good

The Dynamic Behavior of a Stratified Column Bed Packed with Porous Adsorbent Particles Having Partially Fractal Structures and a Nonuniform Ligand Density Distribution

The dynamic behavior of adsorption in a single column and in stratified column beds packed with porous adsorbent particles having partially fractal structures is studied when all columns have the same total length and the spatial ligand density distribution in the porous microspheres from which the porous adsorbent particles are made, is either uniform or nonuniform and such that the concentration of the immobilized ligands (active sites) increases monotonically from the center of the microspheres to their outer surface. The total number of immobilized ligands in the porous adsorbent particles has the same value whether the spatial ligand density distribution is uniform or nonuniform. The results in this study clearly show that for a given value of the superficial velocity of the flowing fluid stream in the column (for a given value of throughput) the breakthrough time is significantly increased when the radius of the microspheres is decreased, the total number of sections of the stratified column bed is increased, and the spatial ligand density distribution employed in the microspheres is nonuniform. Furthermore, when the superficial velocity of the flowing fluid stream in the column is increased (throughput is increased) the effect that (i) the reduction in the radius of the microspheres and (ii) the increase in the number of sections of the stratified column bed have on providing robust and effective dynamic adsorptive capacity and smaller reductions on the breakthrough time is substantially larger than that realized through the use of the nonuniform ligand density distribution. Similar trends are also observed in the dynamic behavior of adsorption in the systems studied here when the value of the concentration of the adsorbate in the flowing fluid stream entering the column (inlet concentration) has such a high magnitude that the value of the equilibrium concentration of the adsorbate in the adsorbed phase determined from the equilibrium Langmuir isotherm that would correspond to the inlet concentration of the adsorbate in the flowing fluid stream is, for all practical purposes, at its saturation limit