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

Abstract

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.

Overcoming Biological Barriers in Neuroblastoma Therapy: The Vascular Targeting Approach with Liposomal Drug Nanocarriers

“…On the other hand, various biobarriers may limit the extravasation of nanodrugs into solid tumor, and in certain cases, such as in the case of liposomal nanocarriers, the gain in the therapeutic index is primarily related to reduction of toxicity rather than to efficacy increase . Indeed, nanodrugs, including liposomes, must overcome various and sequential biobarriers to reach their targets, such as the endothelial barrier, the membrane of tumor cells, and subcellular organelles (e.g., nucleus and lysosomes); they must resist to enzymatic degradation in the blood, should avoid sequestration by phagocytes of the reticuloendothelial system (RES) and molecular efflux pumps, and must migrate against adverse oncotic and interstitial pressures in the tumor . Some of these barriers are related (or consequent) to the abnormal structure of the tumor vasculature, which is typically characterized by highly disorganized architecture, by vessels with dilated and excessive branching, shunts, and fenestrations, and by vessels lacking basement membrane or with fewer pericytes, compared to normal vessels .…”

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics

“…The surface areas entering into matrices of the connectivity elements are as given in Equation (21). The above concept has been implemented for diffusion and fluid transport through complex systems consisting of capillary network and tissue, with inclusion of the hydrophobicity effects in the connectivity elements (Kojic et al, 2014(Kojic et al, , 2017a(Kojic et al, , 2018, and with improvements of accuracy of the smeared methodology achieved by the correction function introduced in Milosevic et al (2018a). The robustness and applicability of the smeared model are demonstrated (Milosevic et al, 2018b), where the CSFE is extended for modeling drug release from a complex mesh of drug-loaded nanofibers.…”

Smeared Concept as a General Methodology in Finite Element Modeling of Physical Fields and Mechanical Problems in Composite Media

“…The above concept has been implemented to diffusion (including convection) and fluid transport through capillary network and tissue, with demonstration of accuracy of the smeared methodology (Kojic et al 2017a(Kojic et al , 2017b(Kojic et al , 2018. To improve the smeared model accuracy, a correction function was introduced in (Milosevic et al 2018a).…”

“…We have selected a small 50x50 micron size 2D tissue sample taken from images of cancerous tissue (E. J. Koay, MD Anderson Cancer Center, Houston, Kojic et al 2018) shown in Fig. 3a.…”

“…Here, we introduce a smeared FE formulation for mechanics in a way analogous to field problems described above and in our listed references, specifically in reference (Kojic et al 2018). The concept of the smeared finite element is shown in Fig.…”