Drug diffusion from polymeric delivery devices: a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective

Hi-Fidelity Simulation of the Self-Assembly and Dynamics of Colloids and Polymeric Solutions with Long Range Interactions

Modeling the equilibrium properties and dynamic response of the colloidal and polymeric solutions provides valuable insight into numerous biological and industrial processes and facilitates development of novel technologies. To this end, the centerpiece of this research is to incorporate the long range electrostatic or hydrodynamic interactions via computationally efficient algorithms and to investigate the effect of these interactions on the self-assembly of colloidal particles and dynamic properties of polymeric solutions. Specifically, self-assembly of a new class of materials, namely bipolar Janus nano-particles, is investigated via molecular dynamic simulation in order to establish the relationship between individual particle characteristics, such as surface charge density, particle size, etc., and the final structure formation. Furthermore, the importance of incorporating the long range electrostatic interaction in achieving the corresponding final morphology is discussed. The dynamic properties of polymeric solutions are investigated via two parallel pathways. In the first approach, force-extension behavior of the flexible polyelectrolytes is probed via fine-grained Brownian dynamics simulation of the bead-rod model. The presented model accurately incorporates the excluded volume interaction in order to capture the effect of salt concentration on the force-extension response of polyelectrolyte chain as observed in the single chain experiments. It is shown that accurate incorporation of the excluded volume effect on a long chain of more than 500 Kuhn segments is necessary to reach the universal scaling both for equilibrium properties and force-extension response. Next, a new force law is extracted using a novel discrete Pade approximant from the constant-force ensemble result of the bead-rod model. The new force law is implemented in the coarse-grained meso-scale bead-spring model with hydrodynamic interactions in order to investigate the dynamics of flexible macromolecules in the athermal solvent. In the second approach the computational cost of the long range hydrodynamic interaction in dilute solution of polymeric chains with constrains is reduced via development of a new computational technique based on the conjugate gradient and Krylov subspace methods. Moreover, an algorithm for estimating the contribution of various forces to the transient polymeric stress tensor is introduced and employed in order to investigate transient dynamics of the solution of the flexible polymeric chains

MULTISCALE SIMULATION OF POLYMER NANOPARTICLES PRECIPITATION FOR PHARMACEUTICAL APPLICATIONS

This work focuses on the development and use of a multiscale computational tool for the simulation of the process of precipitation of polymeric nanoparticles in micro-mixers. This process, as will be shown through the rest of the thesis, is not very easy to model with single scale model (i.e., Computational Fluid Dy- namics, Population Balances, Molecular Dynamics). The main reason stands in the complex behaviour of the system investigated (the polymer); the behaviour at atomistic scale influences the macro-scale. With micro-scale (which is equivalent in our notation to the atomistic scale) we refer to all the phenomena occurring at length-scales of nanometres (1 nm = 10−9 m) and time-scales of picoseconds (1 ps = 10−12 s), whereas with macroscale we intend all the phenomena occur- ring at length-scale of meters and at time-scale of seconds. There are different models used to describes these (apparently) uncorrelated phenomena. Computa- tional Fluid Dynamics (CFD) which describes at the macroscale the motion of a fluid in a given domain often coupled with Population Balance Model (PBM) to describe the presence of a dispersed colloidal phase, and Molecular Dynamics (MD) which describes the motion of a collection of atoms in an interval of time. The coupling of these methods in a unique description of the problem is called multiscale modelling, a research area which has raised much interests in the last few years. In this work, precipitation of nanoparticles occurs in a micromixer, is investigated trough CFD-PBM, whilst the precipitation process is described by extracting some information from MD simulations, hence, coupling these differ- ent models in one description. The thesis is structured as follows: 1. The First Chapter is an introduction to the investigated problem. A brief description of the use of polymer nanoparticles in the pharmaceutical in- dustry is given, with the current state of the art. A brief overview of the different production processes and devices used will be also given 2. The Second Chapter in intended to give all the theoretical background re- quired for the understanding of the subsequent chapters. Starting from the very beginning, the governing equations for the generic N-body prob- lem are derived together with the description of the theoretical tools for the molecular dynamics. By using the Boltzmann Equation we show how to move from a description of the problem a the micro-scale (here repre- sented by the MD) to a description of the problem at the macro-scale (rep- resented by the CFD). The introduction of the Boltzmann equation (and the mesoscale) is also useful since the PBM is a kinetic equation very similar to the Boltzmann equation 3. The Third Chapter involves the description of the CFD model of the micro- mixer used in this study. The polymeric nanoparticles precipitation model is presented along with its intrinsic limitations highlighting the need of a more fundamental approach 4. In the Fourth Chapter we discuss the improvement of the CFD model by developing a nucleation theory adequate to the description of the polymer particle formation. The parameters appearing in this theory are estimated by using the standard full atoms MD simulations. Eventually the nucle- ation theory is integrated into the CFD-PBM and used to simulate the entire process 5. The Fifth Chapter is devoted to the extension of the MD framework. In fact, in order to further investigate the polymer particle formation process, larger systems, involving many polymeric chains have to be described. This requires some form of partial coarse-graining, resulting in hybrid atomistic/coarse-grained model. The framework to do this is in this chapter described, showing how the model allows to speed up the simulation by ne- glecting some Degrees of Freedom of the original problem but maintaining the necessary details where needed 6. In the last Chapter some conclusions from the simulations presented are draw

Corner and finger formation in Hele--Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic

Molecular dynamics simulations of cRGD-conjugated PEGylated TiO2_2 nanoparticles for targeted photodynamic therapy

The conjugation of high-affinity cRGD-containing peptides is a promising approach in nanomedicine to efficiently reduce off-targeting effects and enhance the cellular uptake by integrin-overexpressing tumor cells. Herein we utilize atomistic molecular dynamics simulations to evaluate key structural-functional parameters of these targeting ligands for an effective binding activity towards $\alpha_V\beta_3$ integrins. An increasing number of cRGD ligands is conjugated to PEG chains grafted to highly curved TiO$_2$ nanoparticles to unveil the impact of cRGD density on the ligand's presentation, stability, and conformation in an explicit aqueous environment. We find that a low density leads to an optimal spatial presentation of cRGD ligands out of the "stealth" PEGylated layer around the nanosystem, favoring a straight upward orientation and spaced distribution of the targeting ligands in the bulk-water phase. On the contrary, high densities favor clustering and internalization of cRGD ligands in the inner region of the PEGylated layer, driven by a concerted mechanism of enhanced ligand-ligand interactions and reduced water accessibility over the ligand's molecular surface. These findings strongly suggest that the ligand density modulation is a key factor in the design of cRGD-targeting nanodevices to maximize their binding efficiency into over-expressed $\alpha_V\beta_3$ integrin receptors

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy