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Kojic M, Milosevic M, Kojic N, Koay EJ, Fleming JB, Ferrari M, Ziemys A. Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue. Comput Biol Med 2016; 92:156-167. [PMID: 29182964 DOI: 10.1016/j.compbiomed.2016.06.026] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2016] [Revised: 06/15/2016] [Accepted: 06/24/2016] [Indexed: 11/17/2022]
Abstract
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.
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Affiliation(s)
- M Kojic
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030, United States; Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia; Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000 Belgrade, Serbia.
| | - M Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia
| | - N Kojic
- Center for Engineering in Medicine and Surgical Services, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114, United States
| | - E J Koay
- Department of Radiation Oncology, MD Anderson Cancer Center, Houston, TX 77030, United States
| | - J B Fleming
- Department of Surgical Oncology, MD Anderson Cancer Center, Houston, TX 77030, United States
| | - M Ferrari
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030, United States
| | - A Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030, United States
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