Effect of Circadian Rhythm Modulated Blood Flow on Nanoparticle based Targeted Drug Delivery in Virtual In Vivo Arterial Geometries.

Delivery of drug using nanocarriers tethered with vasculature-targeting epitopes aims to maximize the therapeutic efficacy of the drug while minimizing the drug side effects. Circadian rhythm which is governed by the central nervous system has implications for targeted drug delivery due to sleep-wake cycle changes in blood flow dynamics. This paper presents an advanced fluid dynamics modeling method that is based on viscous incompressible shear-rate fluid (blood) coupled with an advection-diffusion equation to simulate the formation of drug concentration gradients in the blood stream and buildup of concentration at the targeted site. The method is equipped with an experimentally calibrated nanoparticle-endothelial cell adhesion model that employs Robin boundary conditions to describe nanoparticle retention based on probability of adhesion, a friction model accounting for surface roughness of endothelial cell layer, and a dispersion model based on Taylor-Aris expression for effective diffusion in the boundary layer. The computational model is first experimentally validated and then tested on engineered bifurcating arterial systems where impedance boundary conditions are applied at the outflow to account for the downstream resistance at each outlet. It is then applied to a virtual geometric model of an in vivo arterial tree developed through MRI-based image processing techniques. These simulations highlight the potential of the computational model for drug transport, adhesion, and retention at multiple sites in virtual in vivo models. The model provides a virtual platform for exploring circadian rhythm modulated blood flow for targeted drug delivery while minimizing the in vivo experimentation.

Modeling of spatiotemporal dynamics of ligand-coated particle flow in targeted drug delivery processes.

Nanoparticles tethered with vasculature-binding epitopes have been used to deliver the drug into injured or diseased tissues via the bloodstream. However, the extent that blood flow dynamics affects nanoparticle retention at the target site after adhesion needs to be better understood. This knowledge gap potentially underlies significantly different therapeutic efficacies between animal models and humans. An experimentally validated mathematical model that accurately simulates the effects of blood flow on nanoparticle adhesion and retention, thus circumventing the limitations of conventional trial-and-error-based drug design in animal models, is lacking. This paper addresses this technical bottleneck and presents an integrated mathematical method that derives heavily from a unique combination of a mechanics-based dispersion model for nanoparticle transport and diffusion in the boundary layers, an asperity model to account for surface roughness of endothelium, and an experimentally calibrated stochastic nanoparticle-cell adhesion model to describe nanoparticle adhesion and subsequent retention at the target site under external flow. PLGA-b-HA nanoparticles tethered with VHSPNKK peptides that specifically bind to vascular cell adhesion molecules on the inflamed vascular wall were investigated. The computational model revealed that larger particles perform better in adhesion and retention at the endothelium for the particle sizes suitable for drug delivery applications and within physiologically relevant shear rates. The computational model corresponded closely to the in vitro experiments which demonstrates the impact that model-based simulations can have on optimizing nanocarriers in vascular microenvironments, thereby substantially reducing in vivo experimentation as well as the development costs.

Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations.

Physics Informed Neural Networks (PINNs) are shown to be a promising method for the approximation of partial differential equations (PDEs). PINNs approximate the PDE solution by minimizing physics-based loss functions over a given domain. Despite substantial progress in the application of PINNs to a range of problem classes, investigation of error estimation and convergence properties of PINNs, which is important for establishing the rationale behind their good empirical performance, has been lacking. This paper presents convergence analysis and error estimates of PINNs for a multi-physics problem of thermally coupled incompressible Navier-Stokes equations. Through a model problem of Beltrami flow it is shown that a small training error implies a small generalization error. Posteriori convergence rates of total error with respect to the training residual and collocation points are presented. This is of practical significance in determining appropriate number of training parameters and training residual thresholds to get good PINNs prediction of thermally coupled steady state laminar flows. These convergence rates are then generalized to different spatial geometries as well as to different flow parameters that lie in the laminar regime. A pressure stabilization term in the form of pressure Poisson equation is added to the PDE residuals for PINNs. This physics informed augmentation is shown to improve accuracy of the pressure field by an order of magnitude as compared to the case without augmentation. Results from PINNs are compared to the ones obtained from stabilized finite element method and good properties of PINNs are highlighted.

Physics-Constrained Data-Driven Variational Method for Discrepancy Modeling.

This paper presents a data-driven discrepancy modeling method that variationally embeds measured data in the modeling and analysis framework. The proposed method exploits the residual between the first-principles theory and sensor-based measurements from the dynamical system, and it augments the physics-based model with a variationally derived loss function that is comprised of this residual. The method was first developed in the context of linear elasticity (Masud and Goraya, J. Appl. Mech. 89 (11), 111001 (2022)) wherein the relation between the discrepancy model and loss terms was derived to show that the data embedding terms behave like residual-based least-squares regression functions. An interpretation of the stabilization tensor as a kernel function was formally established and its role in assimilating a-priori knowledge of the problem in the modeling method was highlighted. The present paper employs linear elastodynamics as a model problem where the Data-Driven Variational (DDV) method incorporates high-fidelity data into the forward simulations, thereby driving the problem with not only the boundary and initial conditions, but also by measurement data that is taken at only a small subset of the total domain. The effect of the loss function on the time-dependent response of the system is investigated under a variety of loading conditions and model discrepancies. The energy and Morlet wavelet analyses reveal that the problem with embedded data recovers the energy and the fundamental frequency band of the target system. Time histories of strain energy and kinetic energy of a cantilever beam undergoing damped oscillations are recovered by including known data in an undamped model to highlight the data-driven discrepancy modeling feature of the method under the combined effect of parameter and model discrepancy.