Bioengineering Research and Development Center Bio Kragujevac

Kragujevac, Serbia

Bioengineering Research and Development Center Bio Kragujevac

Kragujevac, Serbia
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Kojic M.,Houston Methodist Research Institute | Kojic M.,Serbian Academy of Science and Arts | Milosevic M.,Bioengineering Research and Development Center Bio Kragujevac | Simic V.,Bioengineering Research and Development Center Bio Kragujevac | And 7 more authors.
Computer Methods in Applied Mechanics and Engineering | Year: 2017

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 Darcy's 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. © 2017 Elsevier B.V.


Kojic M.,Houston Methodist Research Institute TMHRI | Kojic M.,Serbian Academy of Science and Arts | Milosevic M.,Houston Methodist Research Institute TMHRI | Isailovic V.,Bioengineering Research and Development Center Bio Kragujevac | And 3 more authors.
2015 IEEE 15th International Conference on Bioinformatics and Bioengineering, BIBE 2015 | Year: 2015

In this report we summarize computational models for convective and diffusive drug transport within small blood vessels (capillaries) and tissue. The presented methodology is primarily focused on drug transport via micro-nanoparticles designed for nanotherapeutics in cancer. Our original multiscale hierarchical models couple nanoscale molecular dynamics (MD) and macroscale continuum finite element (FE) discretization. The convective part relies on a FE solution of the solid-fluid interaction problem of moving bodies within fluid, with a remeshing procedure. In diffusion, MD is used to evaluate the effective diffusivity of a porous continuum, where the physico-chemical interaction between transported molecules and microstructural surface is included, and the mass release curves are considered as the constitutive curves. Several representative examples illustrate effectiveness of our methodology and developed software PAK. © 2015 IEEE.

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