Mass partitioning effects in diffusion transport

Computers in Biology and Medicine

Milošević²,

Simić³

et al. 2018

One of the basic and vital processes in living organisms is mass exchange, which occurs on several levels: it goes from blood vessels to cells and organelles within cells. On that path, molecules, as oxygen, metabolic products, drugs, etc. Traverse different macro and micro environments - blood, extracellular/intracellular space, and interior of organelles; and also biological barriers such as walls of blood vessels and membranes of cells and organelles. Many aspects of this mass transport remain unknown, particularly the biophysical mechanisms governing drug delivery. The main research approach relies on laboratory and clinical investigations. In parallel, considerable efforts have been directed to develop computational tools for additional insight into the intricate process of mass exchange and transport. Along these lines, we have recently formulated a composite smeared finite element (CSFE) which is composed of the smeared continuum pressure and concentration fields of the capillary and lymphatic system, and of these fields within tissue. The element offers an elegant and simple procedure which opens up new lines of inquiry and can be applied to large systems such as organs and tumors models. Here, we extend this concept to a multiscale scheme which concurrently couples domains that span from large blood vessels, capillaries and lymph, to cell cytosol and further to organelles of nanometer size. These spatial physical domains are coupled by the appropriate connectivity elements representing biological barriers. The composite finite element has "degrees of freedom" which include pressures and concentrations of all compartments of the vessels-tissue assemblage. The overall model uses the standard, measurable material properties of the continuum biological environments and biological barriers. It can be considered as a framework into which we can incorporate various additional effects (such as electrical or biochemical) for transport through membranes or within cells. This concept and the developed FE software within our package PAK offers a computational tool that can be applied to whole-organ systems, while also including specific domains such as tumors. The solved examples demonstrate the accuracy of this model and its applicability to large biological systems.

Section: Basic Equations For Modeling Transport In Blood Vessels and mentioning

confidence: 99%

Multiscale smeared finite element model for mass transport in biological tissue: From blood vessels to cells and cellular organelles

Computers in Biology and Medicine

Milošević²,

Simić³

et al. 2018

Phys. Chem. Chem. Phys.

“…All these applications consider and use the ability of these three-dimensional polymeric systems to regulate and control the transport of solutes through their three-dimensional network [11][12][13] . Indeed, effective solute transport is one of the most critical design parameters [14][15][16][17][18] . Mass transport parameters determine how nutrients, gasses, waste products, and bioactive agents, such as growth factors and drugs are exchanged within gels or are delivered by them.…”

Section: Introductionmentioning

confidence: 99%

On the parallelism between the mechanisms behind chromatography and drug delivery: the role of interactions with a stationary phase

Rossi

Castiglione

Salvalaglio

et al. 2017

A huge number of studies and works in drug delivery literature are focused on understanding and modeling transport phenomena, the pivotal point for a good device design. The rationalization of all phenomena involved is fundamental, but several concerns arise leaving many issues unsolved. In order to change point of view we decided to focus our attention on parallelisms between two fields that seem to be very far each other: chromatography and drug release. Taking advantages on the studies conducted by many researchers with chromatographic columns we decided to explain all the phenomena involved in drug delivery considering sodium ibuprofen molecules (IP) as analytes and hydrogel as stationary phase. In particular we considered not only diffusion, but also drug-polymer interactions as adsorption on the stationary phase and drug-drug interactions as analytes aggregation. Hydrogel investigated is a promising formulation made of agarose and carbomer 974p (AC) loaded with IP, a non-steroidal common anti-inflammatory drugs. The self-diffusion coefficient of IP in AC formulations was measured by using an innovative method based on Magic Angle Spinning NMR spectroscopic technique to produce High Resolution (liquid-like) spectra.This method (HR-MAS NMR) is used in combination with pulsed field gradient spin echo (PGSE) liquid-state techniques. The model predictions satisfactorily match with experimental data obtained in water and the gel environment, indicating that the model presented here, despite its simplicity, is able to describe the key phenomena governing the device behavior and could be used to rationalize the experimental activity.!

“…It occurs when transported particles display hydrophobicity with respect to certain solvents, as, for example in case of drug molecules which are hydrophobic and prefer organic phase over water [53,54]. Then, the transport law based on concentration gradient is violated.…”

Section: Computational Proceduresmentioning

confidence: 99%

“…The partitioning effects within the FE computational scheme can be included as follows [53]. Namely, the ratio between the number of particles passing the boundary between two media during a time step is a constant P, …”

Section: Computational Proceduresmentioning

confidence: 99%

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

Milošević²,

Computers in Biology and Medicine

et al. 2018

In diffusion governed by Fick's 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.