Computational Modeling of Intravascular and Perivascular Transport of Active Nanoparticles to Target Sites

Introduction: : Targeted drug delivery using nano-sized carriers is a multi-faceted problem that aims to maximize therapeutic efficacy while minimizing systemic dosage and side effects of medicine. This technology leverages the unique properties of nanoparticles (NPs) to improve delivery specificity, cellular uptake, and targeting of therapeutic agents. This work presents a novel multiscale computational framework that simulates the coupled intravascular and perivascular transport of NPs to the target site. The intravascular model is based on convective transport of viscous, incompressible fluid (blood) coupled with advection-diffusion equations for drug concentration gradients in the blood flow and the buildup of NP concentration at the target site. In addition, the framework is equipped with multiscale stochastic models that capture ligand-receptor binding and the effect of dislodging hydrodynamic forces on particle adhesion and retention. Special interface conditions were developed for transvascular movement of NPs from intravascular space to perivascular tissue through a leaky endothelium. Flow in the perivascular space is modeled via a mixture-theory-based homogenized porous media flow model with anisotropic diffusion tensor for the heterogenous permeability in the biological tissues. Validation of this integrated computational framework is carried out using in vitro transwell tests. Simulations unraveled the complex interplay between ligand-receptor binding strength, shear rates, and porosity of endothelium on targeting efficiency of NPs.

Materials and

Methods: : The intravascular nanoparticle transport framework integrates several multiscale models. It includes (i) momentum–balance equations for vascular hemodynamics; (ii) advection–diffusion equations governing dispersion and diffusion of nanoparticle in bloodstream; (iii) an asperity model of endothelial surface roughness; (iv) a Taylor–Aris–based for boundary layer dispersion; and (v) an experimentally calibrated stochastic adhesion model to predict nanoparticle binding and retention at the target site.

Transvacuolar transport across the leaky endothelium is governed by Robin boundary conditions that model permeative resistance. Once across the endothelial barrier, perivascular transport is simulated using a time-dependent Darcy flow model, where convective velocity is derived from local pressure gradients. NP distribution in tissue is modeled via Fick’s law of diffusion, with spatially varying diffusion coefficients reflecting heterogeneity of the extracellular matrix structure (such as tumors or fibrotic tissues).

Model validation for intravascular and perivascular transport of drug-carrying nanoparticles (NPs) is carried out on carefully designed transwell tests. In these tests, 5 ml solutions of 200 nm PLGA and PLGA-HA NPs at 0.05 mg/ml were perfused at Reynolds numbers of 10 and 50 over a 3 µm polycarbonate membrane seeded with C166 endothelial cells inflamed by 20 nm/mL TNF-alpha.

Results, Conclusions, and Discussions:: The intravascular and perivascular transport of drug-carrying nanoparticles aims to enhance drug delivery by targeting specific injured/ diseased sites in the body and optimizing therapeutic efficacy and safety. To simulate these spatiotemporal dynamics, we developed a novel computational model for transvascular transport of active nanoparticles. Our model combines principles from fluid dynamics, diffusion theory, and pharmacokinetics to describe the complex interactions of NPs within both bloodstream and in the perivascular space. The multiscale approach, combining both macroscopic intravascular transport and microscopic transendothelial transport of NPs, is a powerful approach for gaining more accurate and detailed insights into nanoparticle behavior in human-relevant biological systems.

We simulated transport of 200 nm PLGA nanoparticles targeting C166 mouse endothelium cells across a 3 µm porous membrane at different physiological shear rates (between 10 – 150 s-1). The kinetic transport rate of NPs (0.4 mg/hr) across the porous membrane aligned closely with the in vitro experiments thus validating the computational framework. To quantify the effect of porosity on transvascular transport, we also simulated transport across a healthy endothelium with a porosity of 0.02 µm. Almost all of the NPs were quickly washed away over the healthy endothelium at higher shear rates. In addition, we mapped drug distribution within extracellular matrix domains to capture the influence of tissue-level heterogenous permeability with the values ranging from 10-4 to 10-7 mm2.

Our results indicated that porosity of the endothelium layer influences transvascular movement of NPs more than the shear rate or ligand-receptor binding strength. Enhanced retention of particles at the endothelium under lower shear rates highlighted the importance of the stochastic adhesion model in predicting intravascular binding. Perivascular distribution results revealed that tissue heterogeneity strongly influences NP dispersion; higher diffusion into low-density regions suggests that matrix porosity is a critical design parameter for targeting applications.

We envision that such first-principles-based simulations can inform and optimize the design of nanocarriers within human-relevant vascular microenvironments, enhancing efficacy and safety while substantially reducing in vivo experimentation and lowering development costs.

Acknowledgements and/or References (Optional):: 1. Goraya, S.A., Ding, S., Miller, R.C., Arif, M.K., Kong, H. and Masud, A., 2024. Modeling of spatiotemporal dynamics of ligand-coated particle flow in targeted drug delivery processes. Proceedings of the National Academy of Sciences, 121(22), p.e2314533121.

2. Goraya, S.A., Ding, S., Arif, M.K., Kong, H. and Masud, A., 2024. Effect of circadian rhythm modulated blood flow on nanoparticle based targeted drug delivery in virtual in vivo arterial geometries. Brain Multiphysics, 7, p.100105.

3. Anguiano, M., Gajendran, H., Hall, R.B., Rajagopal, K.R. and Masud, A., 2020. Chemo-mechanical coupling and material evolution in finitely deforming solids with advancing fronts of reactive fluids. Acta Mechanica, 231, pp.1933-1961.