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

Systematic derivation of hybrid coarse-grained models

Molecular dynamics represents a key enabling technology for applications ranging from biology to the development of new materials. However, many real-world applications remain inaccessible to fully-resolved simulations due their unsustainable computational costs and must therefore rely on semi-empirical coarse-grained models. Significant efforts have been devoted in the last decade towards improving the predictivity of these coarse-grained models and providing a rigorous justification of their use, through a combination of theoretical studies and data-driven approaches. One of the most promising research effort is the (re)discovery of the Mori-Zwanzig projection as a generic, yet systematic, theoretical tool for deriving coarse-grained models. Despite its clean mathematical formulation and generality, there are still many open questions about its applicability and assumptions. In this work, we propose a detailed derivation of a hybrid multi-scale system, generalising and further investigating the approach developed in [Español, P., EPL, 88, 40008 (2009)]. Issues such as the general coexistence of atoms (fully-resolved degrees of freedom) and beads (larger coarse-grained units), the role of the fine-to-coarse mapping chosen, and the approximation of effective potentials are discussed. The theoretical discussion is supported by numerical simulations of a monodimensional nonlinear periodic benchmark system with an open-source parallel Julia code, easily extensible to arbitrary potential models and fine-to-coarse mapping functions. The results presented highlight the importance of introducing, in the macroscopic model, non-constant fluctuating and dissipative terms, given by the Mori-Zwanzig approach, to correctly reproduce the reference fine-grained results, without requiring ad-hoc calibration of interaction potentials and thermostats

Molecules as building blocks for a CFD-PBE model to describe the effect of fluid dynamics on nanoparticle formation

Recently research efforts have focused on the effect of fluid dynamics on particle formation processes, by using special mixing devices, that allow to perform controlled experiments, and complex models, that allow to quantify its influence on the final particle size. The standard modelling approach consists in considering three different steps: nucleation, molecular growth and aggregation. This is usually done by simulating the process with a population balance equation (PBE) coupled with computational fluid dynamics (CFD), in which these three different steps are considered separately. The PBE is often written using as internal coordinate the actual particle size or volume; here, we propose a new modelling strategy that overcomes the concepts of nucleation and molecular growth, by using as internal coordinate the number of molecules which aggregate, or self-assemble, together forming a nanoparticle. The novel modelling approach is therefore defined as a purely-aggregative model

Constant Chemical Potential-Quantum Mechanical-Molecular Dynamics simulations of the Graphene-electrolyte double layer

We present the coupling of two frameworks -- the pseudo-open boundary simulation method known as constant potential Molecular Dynamics simulations (C$\mu$MD), combined with QMMD calculations -- to describe the properties of graphene electrodes in contact with electrolytes. The resulting C$\mu$QMMD model was then applied to three ionic solutions (LiCl, NaCl and KCl in water) at bulk solution concentrations ranging from 0.5 M up to 6 M in contact with a charged graphene electrode. The new approach we are describing here provides a simulation protocol to control the concentration of the electrolyte solutions while including the effects of a fully polarizable electrode surface. Thanks to this coupling, we are able to accurately model both the electrode and solution side of the double layer and provide a thorough analysis of the properties of electrolytes at charged interfaces, such as the screening ability of the electrolyte and the electrostatic potential profile. We also report the calculation of the integral electrochemical double layer capacitance in the whole range of concentrations analysed for each ionic species, while the QM simulations provide access to the differential and integral quantum capacitance. We highlight how subtle features, such as the adsorption of potassium at the interface or the tendency of the ions to form clusters, emerge from our simulations, contribute to explaining the ability of graphene to store charge and suggest implications for desalination.Comment: 28 pages, 10 figure

A systematic analysis of the memory term in coarse-grained models: The case of the Markovian approximation

The systematic development of coarse-grained (CG) models via the Mori–Zwanzig projector operator formalism requires the explicit description of a deterministic drift term, a dissipative memory term and a random fluctuation term. The memory and fluctuating terms are related by the fluctuation–dissipation relation and are more challenging to sample and describe than the drift term due to complex dependence on space and time. This work proposes a rational basis for a Markovian data-driven approach to approximating the memory and fluctuating terms. We assumed a functional form for the memory kernel and under broad regularity hypothesis, we derived bounds for the error committed in replacing the original term with an approximation obtained by its asymptotic expansions. These error bounds depend on the characteristic time scale of the atomistic model, representing the decay of the autocorrelation function of the fluctuating force; and the characteristic time scale of the CG model, representing the decay of the autocorrelation function of the momenta of the beads. Using appropriate parameters to describe these time scales, we provide a quantitative meaning to the observation that the Markovian approximation improves as they separate. We then proceed to show how the leading-order term of such expansion can be identified with the Markovian approximation usually considered in the CG theory. We also show that, while the error of the approximation involving time can be controlled, the Markovian term usually considered in CG simulations may exhibit significant spatial variation. It follows that assuming a spatially constant memory term is an uncontrolled approximation which should be carefully checked. We complement our analysis with an application to the estimation of the memory in the CG model of a one-dimensional Lennard–Jones chain with different masses and interactions, showing that even for such a simple case, a non-negligible spatial dependence for the memory term exists

Population Balance Models for Particulate Flows in Porous Media: Breakage and Shear-Induced Events

Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from nonlinear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows

Significance of serum Myostatin in hemodialysis patients

Background: Malnutrition and muscle wasting are common in haemodialysis (HD) patients. Their pathogenesis is complex and involves many molecules including Myostatin (Mstn), which acts as a negative regulator of skeletal muscle. The characterisation of Mstn as a biomarker of malnutrition could be useful in the prevention and management of this condition. Previous studies have reported no conclusive results on the actual relationship between serum Mstn and wasting and malnutrition. So, in this study, we evaluated Mstn profile in a cohort of regular HD patients. Methods: We performed a cross-sectional study, enrolling 37 patients undergoing bicarbonate-HD (BHD) or haemodiafiltration (HDF) at least for six months. 20 sex-matched healthy subjects comprised the control group. Mstn serum levels were evaluated by ELISA before and after HD. We collected clinical and biochemical data, evaluated insulin resistance, body composition, malnutrition [by Malnutrition Inflammation Score (MIS)] and tested muscle function (by hand-grip strength, six-minute walking test and a questionnaire on fatigue). Results: Mstn levels were not significantly different between HD patients and controls (4.7 \ub1 2.8 vs 4.5 \ub1 1.3 ng/ml). In addition, while a decrease in Mstn was observed after HD treatment, there were no differences between BHD and HDF. In whole group of HD patients Mstn was positively correlated with muscle mass (r = 0.82, p < 0.001) and inversely correlated with age (r = - 0.63, p < 0.01) and MIS (r = - 0.39, p = 0.01). No correlations were found between Mstn and insulin resistance, such as between Mstn levels and parameters of muscle strength and fatigue. In multivariate analysis, Mstn resulted inversely correlated with fat body content (\u3b2 = - 1.055, p = 0.002). Conclusions: Circulating Mstn is related to muscle mass and nutritional status in HD patients, suggesting that it may have a role in the regulation of skeletal muscle and metabolic processes. However, also considering the lack of difference of serum Mstn between healthy controls and HD patients and the absence of correlations with muscle function tests, our findings do not support the use of circulating Mstn as a biomarker of muscle wasting and malnutrition in HD