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Kojic M, Milosevic M, Simic V, Milicevic B, Terracciano R, Filgueira CS. On the generality of the finite element modeling physical fields in biological systems by the multiscale smeared concept (Kojic transport model). Heliyon 2024; 10:e26354. [PMID: 38434281 PMCID: PMC10907537 DOI: 10.1016/j.heliyon.2024.e26354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Revised: 02/09/2024] [Accepted: 02/12/2024] [Indexed: 03/05/2024] Open
Abstract
The biomechanical and biochemical processes in the biological systems of living organisms are extremely complex. Advances in understanding these processes are mainly achieved by laboratory and clinical investigations, but in recent decades they are supported by computational modeling. Besides enormous efforts and achievements in this modeling, there still is a need for new methods that can be used in everyday research and medical practice. In this report, we give a view of the generality of the finite element methodology introduced by the first author and supported by his collaborators. It is based on the multiscale smeared physical fields, termed as Kojic Transport Model (KTM), published in several journal papers and summarized in a recent book (Kojic et al., 2022) [1]. We review relevant literature to demonstrate the distinctions and advantages of our methodology and indicate possible further applications. We refer to our published results by a selection of a few examples which include modeling of partitioning, blood flow, molecular transport within the pancreas, multiscale-multiphysics model of coupling electrical field and ion concentration, and a model of convective-diffusive transport within the lung parenchyma. Two new examples include a model of convective-diffusive transport within a growing tumor, and drug release from nanofibers with fiber degradation.
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Affiliation(s)
- Milos Kojic
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- 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
| | - Miljan Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
- Institute of Information Technologies, University of Kragujevac, Department of Technical- Technological Sciences, Jovana Cvijica bb, 34000, Kragujevac, Serbia
- Belgrade Metropolitan University, Tadeusa Koscuska 63, 11000, Belgrade, Serbia
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
- Institute of Information Technologies, University of Kragujevac, Department of Technical- Technological Sciences, Jovana Cvijica bb, 34000, Kragujevac, Serbia
| | - Bogdan Milicevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
- Faculty of Engineering, University of Kragujevac, Kragujevac, 34000, Serbia
| | - Rossana Terracciano
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy
| | - Carly S. Filgueira
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- Department of Cardiovascular Surgery, Houston Methodist Research Institute, Houston, TX, 77030, USA
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Akalın AA, Dedekargınoğlu B, Choi SR, Han B, Ozcelikkale A. Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty. Pharm Res 2023; 40:501-523. [PMID: 35650448 PMCID: PMC9712595 DOI: 10.1007/s11095-022-03298-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 05/17/2022] [Indexed: 01/18/2023]
Abstract
Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.
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Affiliation(s)
- Ali Aykut Akalın
- Department of Mechanical Engineering, Middle East Technical University, 06531, Ankara, Turkey
| | - Barış Dedekargınoğlu
- Department of Mechanical Engineering, Middle East Technical University, 06531, Ankara, Turkey
| | - Sae Rome Choi
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, Indiana, 47907, USA
| | - Bumsoo Han
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, Indiana, 47907, USA.
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana, USA.
- Center for Cancer Research, Purdue University, 585 Purdue Mall, West Lafayette, Indiana, 47907, USA.
| | - Altug Ozcelikkale
- Department of Mechanical Engineering, Middle East Technical University, 06531, Ankara, Turkey.
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Prochor P, Gryko A. Numerical Analysis of the Influence of Porosity and Pore Geometry on Functionality of Scaffolds Designated for Orthopedic Regenerative Medicine. Materials (Basel) 2020; 14:ma14010109. [PMID: 33383866 PMCID: PMC7796183 DOI: 10.3390/ma14010109] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Revised: 12/22/2020] [Accepted: 12/24/2020] [Indexed: 02/06/2023]
Abstract
BACKGROUND Scaffolds are vital for orthopedic regenerative medicine. Therefore, comprehensive studies evaluating their functionality with consideration of variable parameters are needed. The research aim was to evaluate pore geometry and scaffold porosity influence on first, cell culture efficiency in a perfusion bioreactor and second, osteogenic cell diffusion after its implantation. METHODS For the studies, five pore geometries were selected (triangular prism with a rounded and a flat profile, cube, octagonal prism, sphere) and seven porosities (up to 80%), on the basis of which 70 models were created for finite element analyses. First, scaffolds were placed inside a flow channel to estimate growth medium velocity and wall shear stress. Secondly, scaffolds were placed in a bone to evaluate osteogenic cell diffusion. RESULTS In terms of fluid minimal velocity (0.005 m/s) and maximal wall shear stress (100 mPa), only cubic and octagonal pores with 30% porosity and spherical pores with 20% porosity fulfilled the requirements. Spherical pores had the highest osteogenic cell diffusion efficiency for porosities up to 30%. For higher porosities, the octagonal prism's pores gave the best results up to 80%, where no differences were noted. CONCLUSIONS The data obtained allows for the appropriate selection of pore geometry and scaffold porosity for orthopedic regenerative medicine.
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Silva-Vera W, Ramírez C, Pinto M, Simpson R, Almonacid S. Anisotropic diffusion assessment in salmon (salmo salar) composite muscle tissue: Theoretical and image-processing experimental approaches. Food and Bioproducts Processing 2020. [DOI: 10.1016/j.fbp.2020.06.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Arabi Bulaghi Z, Habibi Zad Navin A, Hosseinzadeh M, Rezaee A. SENET: A novel architecture for IoT-based body sensor networks. Informatics in Medicine Unlocked 2020. [DOI: 10.1016/j.imu.2020.100365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022] Open
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Milosevic M, Simic V, Milicevic B, Koay E, Ferrari M, Ziemys A, Kojic M. Correction function for accuracy improvement of the Composite Smeared Finite Element for diffusive transport in biological tissue systems. Comput Methods Appl Mech Eng 2018; 338:97-116. [PMID: 30555187 PMCID: PMC6292687 DOI: 10.1016/j.cma.2018.04.012] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Modeling of drug transport within capillaries and tissue remains a challenge, especially in tumors and cancers where the capillary network exhibits extremely irregular geometry. Recently introduced Composite Smeared Finite Element (CSFE) provides a new methodology of modeling complex convective and diffusive transport in the capillary-tissue system. The basic idea in the formulation of CSFE is in dividing the FE into capillary and tissue domain, coupled by 1D connectivity elements at each node. Mass transport in capillaries is smeared into continuous fields of pressure and concentration by introducing the corresponding Darcy and diffusion tensors. Despite theoretically correct foundation, there are still differences in the overall mass transport to (and from) tissue when comparing smeared model and a true 3D model. The differences arise from the fact that the smeared model cannot take into account the detailed non-uniform pressure and concentration distribution in the vicinity of capillaries. We introduced a field of correction function for diffusivity through the capillary walls of smeared models, in order to have the same mass accumulation in tissue as in case of true 3D models. The parameters of the numerically determined correction function are: ratio of thickness and diameter of capillary wall, ratio of diffusion coefficient in capillary wall and surrounding tissue; and volume fraction of capillaries within tissue domain. Partitioning at the capillary wall - blood interface can also be included. It was shown that the correction function is applicable to complex configurations of capillary networks, providing improved accuracy of our robust smeared models in computer simulations of real transport problems, such as in tumors or human organs.
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Affiliation(s)
- M. Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia
- Belgrade Metropolitan University, Tadeusa Koscuska 63, 11000 Belgrade, Serbia
| | - V. Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia
| | - B. Milicevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia
| | - E.J. Koay
- Department of Radiation 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
| | - A. Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030
| | - M. Kojic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030
- Serbian Academy of Sciences and Arts, Knez Mihailova 35,11000 Belgrade
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Kojic M, Milosevic M, Simic V, Koay EJ, Kojic N, Ziemys A, Ferrari M. Multiscale smeared finite element model for mass transport in biological tissue: From blood vessels to cells and cellular organelles. Comput Biol Med 2018; 99:7-23. [PMID: 29807251 DOI: 10.1016/j.compbiomed.2018.05.022] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2018] [Revised: 05/19/2018] [Accepted: 05/19/2018] [Indexed: 11/16/2022]
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.
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Affiliation(s)
- M Kojic
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA; 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
| | - V Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia
| | - E J Koay
- Department of Radiation Oncology, MD Anderson Cancer Center, Houston, TX, 77030, USA
| | - N Kojic
- Center for Engineering in Medicine and Surgical Services, Massachusetts General Hospital, Harvard Medical School, Boston, MA, 02114, USA
| | - A Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA
| | - M Ferrari
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA
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Kojic M, Milosevic M, Simic V, Koay E, Fleming J, Nizzero S, Kojic N, Ziemys A, Ferrari M. A composite smeared finite element for mass transport in capillary systems and biological tissue. Comput Methods Appl Mech Eng 2017; 324:413-437. [PMID: 29200531 PMCID: PMC5703437 DOI: 10.1016/j.cma.2017.06.019] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
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.
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Affiliation(s)
- M. Kojic
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030
- 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
- Corresponding author: Milos Kojic, Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030, , phone: 713 441 7355; fax: 713 441 7438
| | - M. Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia
| | - V. Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia
| | - E.J. Koay
- Department of Radiation Oncology, MD Anderson Cancer Center, Houston, TX 77030
| | - J.B. Fleming
- Department of Surgical Oncology, MD Anderson Cancer Center, Houston, TX 77030
| | - S. Nizzero
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030
- Applied Physics Graduate Program, Rice University, Houston, TX 77005
| | - N. Kojic
- Center for Engineering in Medicine and Surgical Services, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114
| | - A. Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030
| | - M. Ferrari
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX 77030
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