Rheology of colloidal suspensions in confined flow: Treatment of hydrodynamic interactions in particle-based simulations inspired by dynamical density functional theory

Multiphysics pharmacokinetic model for targeted nanoparticles

Nanoparticles (NP) are being increasingly explored as vehicles for targeted drug delivery because they can overcome free therapeutic limitations by drug encapsulation, thereby increasing solubility and transport across cell membranes. However, a translational gap exists from animal to human studies resulting in only several NP having FDA approval. Because of this, researchers have begun to turn toward physiologically based pharmacokinetic (PBPK) models to guide in vivo NP experimentation. However, typical PBPK models use an empirically derived framework that cannot be universally applied to varying NP constructs and experimental settings. The purpose of this study was to develop a physics-based multiscale PBPK compartmental model for determining continuous NP biodistribution. We successfully developed two versions of a physics-based compartmental model, models A and B, and validated the models with experimental data. The more physiologically relevant model (model B) had an output that more closely resembled experimental data as determined by normalized root mean squared deviation (NRMSD) analysis. A branched model was developed to enable the model to account for varying NP sizes. With the help of the branched model, we were able to show that branching in vasculature causes enhanced uptake of NP in the organ tissue. The models were solved using two of the most popular computational platforms, MATLAB and Julia. Our experimentation with the two suggests the highly optimized ODE solver package DifferentialEquations.jl in Julia outperforms MATLAB when solving a stiff system of ordinary differential equations (ODEs). We experimented with solving our PBPK model with a neural network using Julia's Flux.jl package. We were able to demonstrate that a neural network can learn to solve a system of ODEs when the system can be made non-stiff via quasi-steady-state approximation (QSSA). Our model incorporates modules that account for varying NP surface chemistries, multiscale vascular hydrodynamic effects, and effects of the immune system to create a more comprehensive and modular model for predicting NP biodistribution in a variety of NP constructs.

Migration and Morphology of Colloidal Gel Clusters in Cylindrical Channel Flow

We report the cluster-level structural parameters of colloidal thermogelling nanoemulsions in channel flow as a function of attractive interactions and local shear stress. The spatiotemporal evolution of the gel microstructure is obtained by directly visualizing the dispersed phase near the edge of a cylindrical channel. We observe the flow of the nanoemulsion gels in a range of radial positions (r) and shear stresses between 70 and 220 Pa, finding that the r-dependent cluster sizes are due to a balance between shear forces that yield bonds and attractive interactions that rebuild the inter-colloid bonds. In addition, the largest clusters appear to be affected by confinement and accumulate toward the central axis of the channel, resulting in a volume fraction gradient. Cluster size and volume fraction variabilities are most prominent when the attractive interactions are the strongest. Specifically, a distinct transition from sparse, fluidized clusters near the walls to concentrated, large clusters toward the center is observed. These two structural states coincide with a velocity-based transition from higher shear rates near the walls to lower shear rates toward the center of the channel. We find a compounding effect where larger gel clusters, formed under strong attractions and low shear stresses, are susceptible to shear-induced migration that intensifies r-dependent heterogeneity and deviations in the flow behavior from predictive models.

Microrheology of thermoresponsive poly(N-isopropylacrylamide) microgel dispersions near a substrate surface

HYPOTHESIS

Relative to the bulk systems, the near-wall (<500 nm) rheological responses of soft poly(N-isopropylacrylamide) (PNIPAM) microgel dispersions may exhibit distinct dependence on the frequency (ω), temperature (T), and effective volume fraction (ϕ_eff) during the volume phase transitions. The microrheological behaviors are expected to be governed by the near-wall microstructure and its spatial heterogeneity.

EXPERIMENTS

The combination of active microrheometry (multipole magnetic tweezers) and total internal reflection microscopy (TIRM) was employed to probe the structure-rheology relationships of microgel dispersions near a substrate surface. The ω, T, and ϕ_eff-dependences of the storage modulus (G'), loss modulus (G"), and softness (J) were analyzed by power-law and Arrhenius-like scaling theories. The fluctuation of J was further analyzed to give a quantitative description of the inhomogeneity in the near-wall regions.

FINDINGS

(1) Remarkable differences in the rheological behaviors between the bulk and near-wall cases are revealed, where the latter shows a segmented overlap behavior in ϕ_eff; (2) Five regimes of ϕ_eff that correspond to distinct physical states of the microgel dispersions are determined; (3) The near-wall local structures exhibit more heterogeneity in the glass and colloidal gel regimes as compared to the liquid regime.

A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects

Research problems in the domains of physical, engineering, biological sciences often span multiple time and length scales, owing to the complexity of information transfer underlying mechanisms. Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A paradigm shift in MSM implementations is being fueled by the rapid advances and emerging paradigms in HPC at the dawn of exascale computing. Moreover, amidst the explosion of data science, engineering, and medicine, machine learning (ML) integrated with MSM is poised to enhance the capabilities of standard MSM approaches significantly, particularly in the face of increasing problem complexity. The potential to blend MSM, HPC, and ML presents opportunities for unbound innovation and promises to represent the future of MSM and explainable ML that will likely define the fields in the 21st century.

Multiscale modeling of protein membrane interactions for nanoparticle targeting in drug delivery

Nanoparticle (NP)-based imaging and drug delivery systems for systemic (e.g. intravenous) therapeutic and diagnostic applications are inherently a complex integration of biology and engineering. A broad range of length and time scales are essential to hydrodynamic and microscopic molecular interactions mediating NP (drug nanocarriers, imaging agents) motion in blood flow, cell binding/uptake, and tissue accumulation. A computational model of time-dependent tissue delivery, providing in silico prediction of organ-specific accumulation of NPs, can be leveraged in NP design and clinical applications. In this article, we provide the current state-of-the-art and future outlook for the development of predictive models for NP transport, targeting, and distribution through the integration of new computational schemes rooted in statistical mechanics and transport. The resulting multiscale model will comprehensively incorporate: (i) hydrodynamic interactions in the vascular scales relevant to NP margination; (ii) physical and mechanical forces defining cellular and tissue architecture and epitope accessibility mediating NP adhesion; and (iii) subcellular and paracellular interactions including molecular-level targeting impacting NP uptake.

Viscosity Estimation of a Suspension with Rigid Spheres in Circular Microchannels Using Particle Tracking Velocimetry

Suspension flows are ubiquitous in industry and nature. Therefore, it is important to understand the rheological properties of a suspension. The key to understanding the mechanism of suspension rheology is considering changes in its microstructure. It is difficult to evaluate the influence of change in the microstructure on the rheological properties affected by the macroscopic flow field for non-colloidal particles. In this study, we propose a new method to evaluate the changes in both the microstructure and rheological properties of a suspension using particle tracking velocimetry (PTV) and a power-law fluid model. Dilute suspension (0.38%) flows with fluorescent particles in a microchannel with a circular cross section were measured under low Reynolds number conditions (Re ≈ 10^-4). Furthermore, the distribution of suspended particles in the radial direction was obtained from the measured images. Based on the power-law index and dependence of relative viscosity on the shear rate, we observed that the non-Newtonian properties of the suspension showed shear-thinning. This method will be useful in revealing the relationship between microstructural changes in a suspension and its rheology.

Nanoparticle transport phenomena in confined flows

Nanoparticles submerged in confined flow fields occur in several technological applications involving heat and mass transfer in nanoscale systems. Describing the transport with nanoparticles in confined flows poses additional challenges due to the coupling between the thermal effects and fluid forces. Here, we focus on the relevant literature related to Brownian motion, hydrodynamic interactions and transport associated with nanoparticles in confined flows. We review the literature on the several techniques that are based on the principles of non-equilibrium statistical mechanics and computational fluid dynamics in order to simultaneously preserve the fluctuation-dissipation relationship and the prevailing hydrodynamic correlations. Through a review of select examples, we discuss the treatments of the temporal dynamics from the colloidal scales to the molecular scales pertaining to nanoscale fluid dynamics and heat transfer. As evident from this review, there, indeed has been little progress made in regard to the accurate modeling of heat transport in nanofluids flowing in confined geometries such as tubes. Therefore the associated mechanisms with such processes remain unexplained. This review has revealed that the information available in open literature on the transport properties of nanofluids is often contradictory and confusing. It has been very difficult to draw definitive conclusions. The quality of work reported on this topic is non-uniform. A significant portion of this review pertains to the treatment of the fluid dynamic aspects of the nanoparticle transport problem. By simultaneously treating the energy transport in ways discussed in this review as related to momentum transport, the ultimate goal of understanding nanoscale heat transport in confined flows may be achieved.

Stiffness can mediate balance between hydrodynamic forces and avidity to impact the targeting of flexible polymeric nanoparticles in flow

We report computational investigations of deformable polymeric nanoparticles (NPs) under colloidal suspension flow and adhesive environment. We employ a coarse-grained model for the polymeric NP and perform Brownian dynamics (BD) simulations with hydrodynamic interactions and in the presence of wall-confinement, particulate margination, and wall-adhesion for obtaining NP microstructure, shape, and anisotropic and inhomogeneous transport properties for different NP stiffness. These microscopic properties are utilized in solving the Fokker-Planck equation to obtain the spatial distribution of NP subject to shear, margination due to colloidal microparticles, and confinement due to a vessel wall. Comparing our computational results for the amount of NP margination to the near-wall adhesion regime with those of our binding experiments in cell culture under shear, we found quantitative agreement on shear-enhanced binding, the effect of particulate volume fraction, and the effect of NP stiffness. For the experimentally realized polymeric NP, our model predicts that the shear and volume fraction mediated enhancement in targeting has a hydrodynamic transport origin and is not due to a multivalent binding effect. However, for ultrasoft polymeric NPs, our model predicts a substantial increase in targeting due to multivalent binding. Our results are also in general agreement with experiments of tissue targeting measurements in vivo in mice, however, one needs to exercise caution in extending the modeling treatment to in vivo conditions owing to model approximations. The reported combined computational approach and results are expected to enable fine-tuning of design and optimization of flexible NP in targeted drug delivery applications.