Miljan Milosevic

A robust nanofluidic membrane with tunable zero-order release for implantable dose specific drug delivery

This manuscript demonstrates a mechanically robust implantable nanofluidic membrane capable of tunable long-term zero-order release of therapeutic agents in ranges relevant for clinical applications. The membrane, with nanochannels as small as 5 nm, allows for the independent control of both dosage and mechanical strength through the integration of high-density short nanochannels parallel to the membrane surface with perpendicular micro- and macrochannels for interfacing with the ambient solutions. These nanofluidic membranes are created using precision silicon fabrication techniques on silicon-on-insulator substrates enabling exquisite control over the monodispersed nanochannel dimensions and surface roughness. Zero-order release of analytes is achieved by exploiting molecule to surface interactions which dominate diffusive transport when fluids are confined to the nanoscale. In this study we investigate the nanofluidic membrane performance using custom diffusion and gas testing apparatuses to quantify molecular release rate and process uniformity as well as mechanical strength using a gas based burst test. The kinetics of the constrained zero-order release is probed with molecules presenting a range of sizes, charge states, and structural conformations. Finally, an optimal ratio of the molecular hydrodynamic diameter to the nanochannel dimension is determined to assure zero-order release for each tested molecule.

Hierarchical modeling of diffusive transport through nanochannels by coupling molecular dynamics with finite element method

We present a successful hierarchical modeling approach which accounts for interface effects on diffusivity, ignored in classical continuum theories. A molecular dynamics derived diffusivity scaling scheme is incorporated into a finite element method to model transport through a nanochannel. In a 5nm nanochannel, the approach predicts 2.2 times slower mass release than predicted by Ficks law by comparing time spent to release 90% of mass. The scheme was validated by predicting experimental glucose diffusion through a nanofluidic membrane with a correlation coefficient of 0.999. Comparison with experiments through a nanofluidic membrane showed interface effects to be crucial. We show robustness of our discrete continuum model in addressing complex diffusion phenomena in biomedical and engineering applications by providing flexible hierarchical coupling of molecular scale effects and preserving computational finite element method speed.

Capillary-Wall Collagen as a Biophysical Marker of Nanotherapeutic Permeability into the Tumor Microenvironment

The capillary wall is the chief barrier to tissue entry of therapeutic nanoparticles, thereby dictating their efficacy. Collagen fibers are an important component of capillary walls, affecting leakiness in healthy or tumor vasculature. Using a computational model along with in vivo systems, we compared how collagen structure affects the diffusion flux of a 1-nm chemotherapeutic molecule [doxorubicin (DOX)] and an 80-nm chemotherapy-loaded pegylated liposome (DOX-PLD) in tumor vasculature. We found a direct correlation between the collagen content around a tumor vessel to the permeability of that vessel permeability to DOX-PLD, indicating that collagen content may offer a biophysical marker of extravasation potential of liposomal drug formulations. Our results also suggested that while pharmacokinetics determined the delivery of DOX and DOX-PLD to the same tumor phenotype, collagen content determined the extravasation of DOX-PLD to different tumor phenotypes. Transport physics may provide a deeper view into how nanotherapeutics cross biological barriers, possibly helping explain the balance between biological and physical aspects of drug delivery.

Computational analysis of drug transport in tumor microenvironment as a critical compartment for nanotherapeutic pharmacokinetics

Abstract Over the last decade, nanotherapeutics gained increasingly important role in drug delivery because of their frequently beneficial pharmacokinetics (PK) and lower toxicity when compared to classical systemic drug delivery. In view of therapeutic payload delivery, convective transport is crucial for systemic distribution via circulatory system, but the target domain is tissue outside vessels where transport is governed by diffusion. Here, we have computationally investigated the understudied interplay of physical transports to characterize PK of payload of nanotherapeutics. The analysis of human vasculature tree showed that convective transport is still 5 times more efficient than diffusion suggesting that circulating and payload releasing drug vectors can contribute mostly to systemic delivery. By comparing payload delivery using systemic circulation and drug vectors to microenvironment, internalized vectors were the most efficient and showed Area under the Curve almost 100 higher than in systemic delivery. The newly introduced zone of influence parameter indicated that vectors, especially internalized, lead to the largest tissue fraction covered with therapeutically significant payload concentration. The internalization to microenvironment minimizes effects of plasma domain on payload extravasation from nanotherapeutics. The computed results showed that classical PK, which mostly relies on concentration profiles in plasma, sometimes might be inadequate or not sufficient in explaining therapeutic efficacy of nanotherapeutics. These results provide a deeper look into PK of drug vectors and can help in the design of better drug delivery strategies.

A computational study of circulating large tumor cells traversing microvessels

Circulating tumor cells (CTCs) are known to be a harbinger of cancer metastasis. The CTCs are known to circulate as individual cells or as a group of interconnected cells called CTC clusters. Since both single CTCs and CTC clusters have been detected in venous blood samples of cancer patients, they needed to traverse at least one capillary bed when crossing from arterial to venous circulation. The diameter of a typical capillary is about 7µm, whereas the size of an individual CTC or CTC clusters can be greater than 20µm and thus size exclusion is believed to be an important factor in the capillary arrest of CTCs - a key early event in metastasis. To examine the biophysical conditions needed for capillary arrest, we have developed a custom-built viscoelastic solid-fluid 3D computational model that enables us to calculate, under physiological conditions, the maximal CTC diameter that will pass through the capillary. We show that large CTCs and CTC clusters can successfully cross capillaries if their stiffness is relatively small. Specifically, under physiological conditions, a 13µm diameter CTC passes through a 7µm capillary only if its stiffness is less than 500Pa and conversely, for a stiffness of 10Pa the maximal passing diameter can be as high as 140µm, such as for a cluster of CTCs. By exploring the parameter space, a relationship between the capillary blood pressure gradient and the CTC mechanical properties (size and stiffness) was determined. The presented computational platform and the resulting pressure-size-stiffness relationship can be employed as a tool to help study the biomechanical conditions needed for capillary arrest of CTCs and CTC clusters, provide predictive capabilities in disease progression based on biophysical CTC parameters, and aid in the rational design of size-based CTC isolation technologies where CTCs can experience large deformations due to high pressure gradients.

Mass partitioning effects in diffusion transport

Frequent mass exchange takes place in a heterogeneous environment among several phases, where mass partitioning may occur at the interface of phases. Analytical and computational methods for diffusion do not usually incorporate molecule partitioning masking the true picture of mass transport. Here we present a computational finite element methodology to calculate diffusion mass transport with a partitioning phenomenon included and the analysis of the effects of partitioning. Our numerical results showed that partitioning controls equilibrated mass distribution as expected from analytical solutions. The experimental validation of mass release from drug-loaded nanoparticles showed that partitioning might even dominate in some cases with respect to diffusion itself. The analysis of diffusion kinetics in the parameter space of partitioning and diffusivity showed that partitioning is an extremely important parameter in systems, where mass diffusivity is fast and that the concentration of nanoparticles can control payload retention inside nanoparticles. The computational and experimental results suggest that partitioning and physiochemical properties of phases play an important, if not crucial, role in diffusion transport and should be included in the studies of mass transport processes.

A composite smeared finite element for mass transport in capillary systems and biological tissue

One of the key processes in living organisms is mass transport occurring from blood vessels to tissues for supplying tissues with oxygen, nutrients, drugs, immune cells, and - in the reverse direction - transport of waste products of cell metabolism to blood vessels. The mass exchange from blood vessels to tissue and vice versa occurs through blood vessel walls. This vital process has been investigated experimentally over centuries, and also in the last decades by the use of computational methods. Due to geometrical and functional complexity and heterogeneity of capillary systems, it is however not feasible to model in silico individual capillaries (including transport through the walls and coupling to tissue) within whole organ models. Hence, there is a need for simplified and robust computational models that address mass transport in capillary-tissue systems. We here introduce a smeared modeling concept for gradient-driven mass transport and formulate a new composite smeared finite element (CSFE). The transport from capillary system is first smeared to continuous mass sources within tissue, under the assumption of uniform concentration within capillaries. Here, the fundamental relation between capillary surface area and volumetric fraction is derived as the basis for modeling transport through capillary walls. Further, we formulate the CSFE which relies on the transformation of the one-dimensional (1D) constitutive relations (for transport within capillaries) into the continuum form expressed by Darcys and diffusion tensors. The introduced CSFE is composed of two volumetric parts - capillary and tissue domains, and has four nodal degrees of freedom (DOF): pressure and concentration for each of the two domains. The domains are coupled by connectivity elements at each node. The fictitious connectivity elements take into account the surface area of capillary walls which belongs to each node, as well as the wall material properties (permeability and partitioning). The overall FE model contains geometrical and material characteristics of the entire capillary-tissue system, with physiologically measurable parameters assigned to each FE node within the model. The smeared concept is implemented into our implicit-iterative FE scheme and into FE package PAK. The first three examples illustrate accuracy of the CSFE element, while the liver and pancreas models demonstrate robustness of the introduced methodology and its applicability to real physiological conditions.

Transport Phenomena: Computational Models for Convective and Diffusive Transport in Capillaries and Tissue

A review of computational procedures for convective and diffusive transport, developed by the authors, is presented in this chapter. The presented finite element computational framework is directed to transport within capillaries and tissue. The convective transport includes modeling of motion of deformable bodies within fluid flow. It is based on a strong coupling concept and remeshing procedure. It was found by the authors that this approach has advantages in reliability and accuracy with respect to others available in literature, although it is not computationally efficient. A hierarchical multiscale model for diffusion couples molecular dynamics and continuum FE method by evaluating equivalent continuum diffusive parameters; these parameters include commonly used diffusion coefficients, but also parameters which account for physicochemical interactions between diffusing molecules and microstructural solid surfaces. A numerical homogenization is used in this multiscale model. Coupled convective and diffusive transport is also considered. A number of typical solved examples illustrate generality, robustness, and accuracy of the presented computational methodology.

Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

In diffusion governed by Ficks law, the diffusion coefficient represents the phenomenological material parameter and is, in general, a constant. In certain cases of diffusion through porous media, the diffusion coefficient can be variable (i.e. non-constant) due to the complex process of solute displacements within microstructure, since these displacements depend on porosity, internal microstructural geometry, size of the transported particles, chemical nature, and physical interactions between the diffusing substance and the microstructural surroundings. In order to provide a simple and general approach of determining the diffusion coefficient for diffusion through porous media, we have introduced mass release curves as the constitutive curves of diffusion. The mass release curve for a selected direction represents cumulative mass (per surface area) passed in that direction through a small reference volume, in terms of time. We have developed a methodology, based on numerical Finite Element (FE) and Molecular Dynamics (MD) methods, to determine simple mass release curves of solutes through complex media from which we calculate the diffusion coefficient. The diffusion models take into account interactions between solute particles and microstructural surfaces, as well as hydrophobicity (partitioning). We illustrate the effectiveness of our approach on several examples of complex composite media, including an imaging-based analysis of diffusion through pancreatic cancer tissue. The presented work offers an insight into the role of mass release curves in describing diffusion through porous media in general, and further in case of complex composite media such as biological tissue.

Tumor progression effects on drug vector access to tumor-associated capillary bed

Abstract Over the last decade, the benefits of drug vectors to treat cancer have been well recognized. However, drug delivery and vector distribution differences in tumor‐associated capillary bed at different stages of disease progression are not well understood. To obtain further insights into drug vector distribution changes in vasculature during tumor progression, we combined intra‐vital imaging of metastatic tumors in mice, microfluidics‐based artificial tumor capillary models, and Computational Fluid Dynamics (CFD) modeling. Microfluidic and CFD circulation models were designed to mimic tumor progression by escalating flow complexity and chaoticity. We examined flow of 0.5 and 2 &mgr;m spherical particles, and tested the effects of hematocrit on particle local accessibility to flow area of capillary beds by co‐circulating red blood cells (RBC). Results showed that tumor progression modulated drug vector distribution in tumor‐associated capillaries. Both particles shared 80–90% common flow area, while 0.5 and 2 &mgr;m particles had 2–9% and 1–2% specific flow area, respectively. Interestingly, the effects of hematocrit on specific circulation area was opposite for 0.5 and 2 &mgr;m particles. Dysfunctional capillaries with no flow, a result of tumor progression, limited access to all particles, while diffusion was shown to be the only prevailing transport mechanism. In view of drug vector distribution in tumors, independent of formulation and other pharmacokinetic aspects, our results suggest that the evolution of tumor vasculature during progression may influence drug delivery efficiency. Therefore, optimized drug vectors will need to consider primary vs metastatic tumor setting, or early vs late stage metastatic disease, when undergoing vector design. Graphical abstract Figure. No Caption available.