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Milanović Ž, Antonijević M, Avdović E, Simić V, Milošević M, Dolićanin Z, Kojić M, Marković Z. In silico evaluation of pharmacokinetic parameters, delivery, distribution and anticoagulative effects of new 4,7-dihydroxycoumarin derivative. J Biomol Struct Dyn 2024; 42:8343-8358. [PMID: 37545173 DOI: 10.1080/07391102.2023.2245071] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Accepted: 08/01/2023] [Indexed: 08/08/2023]
Abstract
In this study, pharmacological profiling and investigation of the anticoagulant activity of the newly synthesized coumarin derivative: (E)-3-(1-((4-hydroxy-3-methoxyphenyl)amino)ethylidene)-2,4-dioxochroman-7-yl acetate (L) were performed. The obtained results were compared with the parameters obtained for Warfarin (WF), which is a standard good oral anticoagulant. The estimated high binding affinity of L toward plasma proteins (PPS% value is > 90%) justifies the investigation of binding affinity and comparative analysis of L and WF to Human Serum Albumin (HSA) using the spectrofluorimetric method (296, 303 and 310 K) as well as molecular docking and molecular dynamics simulations. Compound L shows a very good binding affinity especially to the active site of WF (the active site I -subdomain IIA), quenching HSA fluorescence by a static process. Also, the finite element smeared model (Kojic Transport Model, KTM), which includes blood vessels and tissue, was implemented to compute the convective-diffusion transport of L and WF within the liver. Finally, compound L shows a high degree of inhibitory activity toward the VKOR receptor comparable to the inhibitory activity of WF. Stabilization and limited flexibility of amino acid residues in the active site of the VKOR after binding of L and WF indicates a very good inhibitory potential of compound L. The high affinity of the L for the VKOR enzyme (Vitamin K antagonist), as well as the structural similarity to commercial anticoagulants (WF), provide a basis for further studies and potential application in the treatment of venous thrombosis, pulmonary embolism and ischemic heart disease.Communicated by Ramaswamy H. Sarma.
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Affiliation(s)
- Žiko Milanović
- Institute for Information Technologies, University of Kragujevac, Kragujevac, Serbia
| | - Marko Antonijević
- Institute for Information Technologies, University of Kragujevac, Kragujevac, Serbia
| | - Edina Avdović
- Institute for Information Technologies, University of Kragujevac, Kragujevac, Serbia
| | - Vladimir Simić
- Institute for Information Technologies, University of Kragujevac, Kragujevac, Serbia
| | - Miljan Milošević
- Institute for Information Technologies, University of Kragujevac, Kragujevac, Serbia
- Bioengineering Research and Development Center (BioIRC), Kragujevac, Serbia
- Faculty of Information Technology, Belgrade Metropolitan University, Belgrade, Serbia
| | - Zana Dolićanin
- Department of Natural Science and Mathematics, State University of Novi Pazar, Novi Pazar, Serbia
| | - Miloš Kojić
- Bioengineering Research and Development Center (BioIRC), Kragujevac, Serbia
- Serbian Academy of Sciences and Arts, Belgrade, Serbia
- Houston Methodist Research Institute, Houston, TX, USA
| | - Zoran Marković
- Institute for Information Technologies, University of Kragujevac, Kragujevac, Serbia
- Department of Natural Science and Mathematics, State University of Novi Pazar, Novi Pazar, Serbia
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Sweeney PW, Walsh C, Walker-Samuel S, Shipley RJ. A three-dimensional, discrete-continuum model of blood pressure in microvascular networks. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024; 40:e3832. [PMID: 38770788 DOI: 10.1002/cnm.3832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Revised: 02/28/2024] [Accepted: 04/22/2024] [Indexed: 05/22/2024]
Abstract
We present a 3D discrete-continuum model to simulate blood pressure in large microvascular tissues in the absence of known capillary network architecture. Our hybrid approach combines a 1D Poiseuille flow description for large, discrete arteriolar and venular networks coupled to a continuum-based Darcy model, point sources of flux, for transport in the capillary bed. We evaluate our hybrid approach using a vascular network imaged from the mouse brain medulla/pons using multi-fluorescence high-resolution episcopic microscopy (MF-HREM). We use the fully-resolved vascular network to predict the hydraulic conductivity of the capillary network and generate a fully-discrete pressure solution to benchmark against. Our results demonstrate that the discrete-continuum methodology is a computationally feasible and effective tool for predicting blood pressure in real-world microvascular tissues when capillary microvessels are poorly defined.
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Affiliation(s)
- Paul W Sweeney
- Cancer Research UK Cambridge Institute, University of Cambridge, Cambridge, UK
- Department of Mechanical Engineering, University College London, London, UK
| | - Claire Walsh
- Department of Mechanical Engineering, University College London, London, UK
- Centre for Computational Medicine, University College London, London, UK
| | | | - Rebecca J Shipley
- Department of Mechanical Engineering, University College London, London, UK
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3
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Martino A, Terracciano R, Milićević B, Milošević M, Simić V, Fallon BC, Carcamo-Bahena Y, Royal ALR, Carcamo-Bahena AA, Butler EB, Willson RC, Kojić M, Filgueira CS. An Insight into Perfusion Anisotropy within Solid Murine Lung Cancer Tumors. Pharmaceutics 2024; 16:1009. [PMID: 39204354 PMCID: PMC11360231 DOI: 10.3390/pharmaceutics16081009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2024] [Revised: 07/15/2024] [Accepted: 07/24/2024] [Indexed: 09/04/2024] Open
Abstract
Blood vessels are essential for maintaining tumor growth, progression, and metastasis, yet the tumor vasculature is under a constant state of remodeling. Since the tumor vasculature is an attractive therapeutic target, there is a need to predict the dynamic changes in intratumoral fluid pressure and velocity that occur across the tumor microenvironment (TME). The goal of this study was to obtain insight into perfusion anisotropy within lung tumors. To achieve this goal, we used the perfusion marker Hoechst 33342 and vascular endothelial marker CD31 to stain tumor sections from C57BL/6 mice harboring Lewis lung carcinoma tumors on their flank. Vasculature, capillary diameter, and permeability distribution were extracted at different time points along the tumor growth curve. A computational model was generated by applying a unique modeling approach based on the smeared physical fields (Kojic Transport Model, KTM). KTM predicts spatial and temporal changes in intratumoral pressure and fluid velocity within the growing tumor. Anisotropic perfusion occurs within two domains: capillary and extracellular space. Anisotropy in tumor structure causes the nonuniform distribution of pressure and fluid velocity. These results provide insights regarding local vascular distribution for optimal drug dosing and delivery to better predict distribution and duration of retention within the TME.
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Affiliation(s)
- Antonio Martino
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
- Department of Materials Science and Engineering, University of Houston, Houston, TX 77024, USA
| | - Rossana Terracciano
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
- Department of Electronics and Telecommunications, Politecnico di Torino, 10129 Torino, Italy
| | - Bogdan Milićević
- Bioengineering Research and Development Center (BioIRC), 34000 Kragujevac, Serbia; (B.M.); (M.M.); (V.S.)
- Faculty of Engineering, University of Kragujevac, 34000 Kragujevac, Serbia
| | - Miljan Milošević
- Bioengineering Research and Development Center (BioIRC), 34000 Kragujevac, Serbia; (B.M.); (M.M.); (V.S.)
- Institute for Information Technologies, University of Kragujevac, 34000 Kragujevac, Serbia
- Faculty of Information Technology, Belgrade Metropolitan University, 11000 Belgrade, Serbia
| | - Vladimir Simić
- Bioengineering Research and Development Center (BioIRC), 34000 Kragujevac, Serbia; (B.M.); (M.M.); (V.S.)
- Institute for Information Technologies, University of Kragujevac, 34000 Kragujevac, Serbia
| | - Blake C. Fallon
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
| | - Yareli Carcamo-Bahena
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
| | - Amber Lee R. Royal
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
| | - Aileen A. Carcamo-Bahena
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
| | - Edward Brian Butler
- Department of Radiation Oncology, Houston Methodist Research Institute, Houston, TX 77030, USA;
| | - Richard C. Willson
- Department of Chemical and Biomolecular Engineering, University of Houston, Houston, TX 77024, USA;
| | - Miloš Kojić
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
- Bioengineering Research and Development Center (BioIRC), 34000 Kragujevac, Serbia; (B.M.); (M.M.); (V.S.)
- Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia
| | - Carly S. Filgueira
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; (A.M.); (R.T.); (B.C.F.); (Y.C.-B.); (A.L.R.R.); (A.A.C.-B.); (M.K.)
- Department of Cardiovascular Surgery, Houston Methodist Research Institute, Houston, TX 77030, USA
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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] [Abstract] [Key Words] [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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Yin S, Lu R, Li Y, Sun D, Liu C, Liu B, Li J. A microfluidic device inspired by leaky tumor vessels for hematogenous metastasis mechanism research. Analyst 2023; 148:1570-1578. [PMID: 36892183 DOI: 10.1039/d2an02081e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
Abstract
Endothelial intercellular pores of tumor vessels generally lead to enhanced interstitial flow and may facilitate the migration of tumor cells. The permeability of tumor vessels causes a concentration gradient of growth factors (CGGF) from blood vessels to tumor tissues, which is opposite to the direction of interstitial flow. In this work, exogenous chemotaxis under the CGGF is demonstrated as a mechanism of hematogenous metastasis. A bionic microfluidic device inspired by endothelial intercellular pores of tumor vessels has been designed to study the mechanism. A porous membrane vertically integrated into the device using a novel compound mold is utilized to mimic the leaky vascular wall. The formation mechanism of the CGGF caused by endothelial intercellular pores is numerically analyzed and experimentally verified. The migration behavior of U-2OS cells is studied in the microfluidic device. The device is divided into three regions of interest (ROI): primary site, migration zone, and tumor vessel. The number of cells in the migration zone increases significantly under the CGGF, but decreases under no CGGF, indicating tumor cells may be guided to the vascellum by exogenous chemotaxis. Transendothelial migration is subsequently monitored, demonstrating the successful replication of the key steps in vitro in the metastatic cascade by the bionic microfluidic device.
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Affiliation(s)
- Shuqing Yin
- Key Laboratory for Micro/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian, China.
| | - Ruoyu Lu
- Key Laboratory for Micro/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian, China.
| | - Yang Li
- Key Laboratory for Micro/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian, China.
| | - Dexian Sun
- Key Laboratory for Micro/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian, China.
| | - Chong Liu
- Key Laboratory for Micro/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian, China. .,Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian, China
| | - Bo Liu
- School of Biomedical Engineering, Liaoning Key Lab of Integrated Circuit and Biomedical Electronic System, Dalian University of Technology, Dalian, China.
| | - Jingmin Li
- Key Laboratory for Micro/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian, China.
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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] [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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Simic V, Milosevic M, Milicevic V, Filipovic N, Kojic M. A novel composite smeared finite element for mechanics (CSFEM): Some applications. Technol Health Care 2023; 31:719-733. [PMID: 36314177 DOI: 10.3233/thc-220414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
BACKGROUND Mechanical forces at the micro-scale level have been recognized as an important factor determining various biological functions. The study of cell or tissue mechanics is critical to understand problems in physiology and disease development. OBJECTIVE The complexity of computational models and efforts made for their development in the past required significant robustness and different approaches in the modeling process. METHOD For the purpose of modeling process simplifications, the smeared mechanics concept was introduced by M. Kojic as a general concept for modeling the deformation of composite continua. A composite smeared finite element for mechanics (CSFEM) was formulated which consists of the supporting medium and immersed subdomains of deformable continua with mutual interactions. Interaction is modeled using 1D contact elements (for both tangential and normal directions), where the interaction takes into account appropriate material parameters as well as the contact areas. RESULTS In this paper we have presented verification examples with applications of the CSFEMs that include the pancreatic tumor tissue, nano-indentation model and tumor growth model. CONCLUSION We have described CSFEM and contact elements between compartments that can interact. Accuracy and applicability are determined on two verification and tumor growth examples.
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Affiliation(s)
- Vladimir Simic
- Institute for Information Technologies, Department of Technological Sciences, University of Kragujevac, Kragujevac, Serbia
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia
| | - Miljan Milosevic
- Institute for Information Technologies, Department of Technological Sciences, University of Kragujevac, Kragujevac, Serbia
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia
- Belgrade Metropolitan University, Belgrade, Serbia
| | | | - Nenad Filipovic
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia
- Faculty for Engineering Sciences, University of Kragujevac, Kragujevac, Serbia
| | - Milos Kojic
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX, USA
- Serbian Academy of Sciences and Arts, Belgrade, Serbia
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Fritz M, Köppl T, Oden JT, Wagner A, Wohlmuth B, Wu C. A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3612. [PMID: 35522186 DOI: 10.1002/cnm.3612] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2022] [Revised: 03/30/2022] [Accepted: 04/27/2022] [Indexed: 06/14/2023]
Abstract
In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D-0D-3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D-0D-3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.
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Affiliation(s)
- Marvin Fritz
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Tobias Köppl
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - John Tinsley Oden
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA
| | - Andreas Wagner
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Barbara Wohlmuth
- Department of Mathematics, Technical University of Munich, Garching, Germany
| | - Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA
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Amiri M, Ayani MB, Ziolkowski P, Mikielewicz D. Numerical analysis of vacuum drying of a porous body in the integrated domain. J FOOD PROCESS ENG 2022. [DOI: 10.1111/jfpe.14006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Milad Amiri
- Department of Mechanical Engineering Ferdowsi University of Mashhad Mashhad Iran
- Faculty of Mechanical Engineering and Ship Technology, Institute of Energy Gdansk University of Technology Gdansk Poland
| | | | - Pawel Ziolkowski
- Faculty of Mechanical Engineering and Ship Technology, Institute of Energy Gdansk University of Technology Gdansk Poland
| | - Dariusz Mikielewicz
- Faculty of Mechanical Engineering and Ship Technology, Institute of Energy Gdansk University of Technology Gdansk Poland
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Deepa Maheshvare M, Raha S, Pal D. A Graph-Based Framework for Multiscale Modeling of Physiological Transport. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 1:802881. [PMID: 36925576 PMCID: PMC10013063 DOI: 10.3389/fnetp.2021.802881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 11/30/2021] [Indexed: 11/13/2022]
Abstract
Trillions of chemical reactions occur in the human body every second, where the generated products are not only consumed locally but also transported to various locations in a systematic manner to sustain homeostasis. Current solutions to model these biological phenomena are restricted in computability and scalability due to the use of continuum approaches in which it is practically impossible to encapsulate the complexity of the physiological processes occurring at diverse scales. Here, we present a discrete modeling framework defined on an interacting graph that offers the flexibility to model multiscale systems by translating the physical space into a metamodel. We discretize the graph-based metamodel into functional units composed of well-mixed volumes with vascular and cellular subdomains; the operators defined over these volumes define the transport dynamics. We predict glucose drift governed by advective-dispersive transport in the vascular subdomains of an islet vasculature and cross-validate the flow and concentration fields with finite-element-based COMSOL simulations. Vascular and cellular subdomains are coupled to model the nutrient exchange occurring in response to the gradient arising out of reaction and perfusion dynamics. The application of our framework for modeling biologically relevant test systems shows how our approach can assimilate both multi-omics data from in vitro-in vivo studies and vascular topology from imaging studies for examining the structure-function relationship of complex vasculatures. The framework can advance simulation of whole-body networks at user-defined levels and is expected to find major use in personalized medicine and drug discovery.
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Affiliation(s)
| | | | - Debnath Pal
- Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India
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Nikolić A, Topalović M, Simić V, Filipović N. Turbulent finite element model applied for blood flow calculation in arterial bifurcation. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2021; 209:106328. [PMID: 34407452 DOI: 10.1016/j.cmpb.2021.106328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 07/29/2021] [Indexed: 06/13/2023]
Abstract
BACKGROUND AND OBJECTIVE Due to the relatively low fluid velocities in major arteries and veins, blood flow is by default laminar, however, turbulence can occur as a result of stenosis or other obstacles. Hemodynamic parameters like Wall Shear Stress or Oscillatory Shear Index can be used for plaque formation prediction, and these parameters are depended on the nature of the flow. Implementation of the k-ω turbulent flow in the Finite Element solver aims to improve numerical analysis of cardio-vascular condition development and progression. Calculation of turbulent fluid flow in this paper is performed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer. METHODS Implicit integration of the equations is used for determining the fluid velocity, turbulent kinetic energy and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model with the customized generation of finite element meshes is used for calculating complex blood flow problems. RESULTS Turbulent model is verified on an example of fluid flow in the backward-facing step channel and analysis results correspond well with the experimental ones from the literature. Further, a turbulent model is applied for the simulation of blood flow through artery bifurcation. Verification of numerical examples obtained using different commercial software packages (Ansys, COMSOL Multiphysics) ensuring usage and accuracy of PAK in-house solver. CONCLUSIONS Analysis results show that turbulence cannot be neglected in the modelling of cardio-vascular conditions and that cardiologists can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries. Appropriate agreement between experimental results, and results obtained using commercial solutions and the k-ω turbulent flow in the Finite Element solver PAK, validate methodology presented in this paper. However, small deviations between the results underline the importance of the proper boundary condition prescription and mesh size and node distribution, which is also discussed in this paper. Due to the implicit integration implemented in PAK solver, time step size has an insignificant influence on the analysis results, assuming the initial time increments are sufficiently small to ensure proper discretization of velocity and pressure pulsatile functions.
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Affiliation(s)
- Aleksandar Nikolić
- Institute of Information Technologies, University of Kragujevac, Department of Technical- Technological Sciences, Jovana Cvijića bb, 34000 Kragujevac, Serbia.
| | - Marko Topalović
- Institute of Information Technologies, University of Kragujevac, Department of Technical- Technological Sciences, Jovana Cvijića bb, 34000 Kragujevac, Serbia
| | - Vladimir Simić
- Institute of Information Technologies, University of Kragujevac, Department of Technical- Technological Sciences, Jovana Cvijića bb, 34000 Kragujevac, Serbia
| | - Nenad Filipović
- Faculty of Engineering, University of Kragujevac, Sestre Janjic 6, 34000 Kragujevac, Serbia
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12
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Kremheller J, Brandstaeter S, Schrefler BA, Wall WA. Validation and parameter optimization of a hybrid embedded/homogenized solid tumor perfusion model. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3508. [PMID: 34231326 DOI: 10.1002/cnm.3508] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Revised: 06/21/2021] [Accepted: 07/02/2021] [Indexed: 06/13/2023]
Abstract
The goal of this paper is to investigate the validity of a hybrid embedded/homogenized in-silico approach for modeling perfusion through solid tumors. The rationale behind this novel idea is that only the larger blood vessels have to be explicitly resolved while the smaller scales of the vasculature are homogenized. As opposed to typical discrete or fully resolved 1D-3D models, the required data can be obtained with in-vivo imaging techniques since the morphology of the smaller vessels is not necessary. By contrast, the larger vessels, whose topology and structure is attainable noninvasively, are resolved and embedded as one-dimensional inclusions into the three-dimensional tissue domain which is modeled as a porous medium. A sound mortar-type formulation is employed to couple the two representations of the vasculature. We validate the hybrid model and optimize its parameters by comparing its results to a corresponding fully resolved model based on several well-defined metrics. These tests are performed on a complex data set of three different tumor types with heterogeneous vascular architectures. The correspondence of the hybrid model in terms of mean representative elementary volume blood and interstitial fluid pressures is excellent with relative errors of less than 4%. Larger, but less important and explicable errors are present in terms of blood flow in the smaller, homogenized vessels. We finally discuss and demonstrate how the hybrid model can be further improved to apply it for studies on tumor perfusion and the efficacy of drug delivery.
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Affiliation(s)
- Johannes Kremheller
- Institute for Computational Mechanics, Technical University of Munich, München, Germany
| | | | - Bernhard A Schrefler
- Institute for Advanced Study, Technical University of Munich, München, Germany
- Department of Civil, Environmental and Architectural Engineering, University of Padova, Padova, Italy
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, München, Germany
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13
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Akbarpour Ghazani M, Saghafian M, Jalali P, Soltani M. Mathematical simulation and prediction of tumor volume using RBF artificial neural network at different circumstances in the tumor microenvironment. Proc Inst Mech Eng H 2021; 235:1335-1355. [PMID: 34247529 PMCID: PMC8573697 DOI: 10.1177/09544119211028380] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Uncontrolled proliferation of cells in a tissue caused by genetic mutations inside a cell is referred to as a tumor. A tumor which grows rapidly encounters a barrier when it grows to a certain size in presence of preexisting vasculature. This is the time when it has to find a way to go on the growth. The tumor starts to secrete tumor angiogenic factors (TAFs) and stimulate preexisting vessels to grow new sprouts. These new sprouts will find their way to the tumor in the extracellular matrix (ECM) by the gradient of TAF. As these new capillaries anastomose and reach tumor, fresh oxygen is available for the tumor and it will reinitiate the growth. Number of initial sprouts, distance of initial tumor cells from the vessel(s) and initial density of the tumor at the time of sprout formation are questions which are to be investigated. In the present study, the aim is to find the response of tumor cells and vessels to the reciprocal effects of each other in different circumstances in the tissue. Together with a mathematical formulation, a radial basis function (RBF) neural network is established to predict the number of tumor cells at different circumstances including size and distance of initial tumors from the parent vessel. A final formulation is given for the final number of tumor cells as a function of initial tumor size and distance between a parent vessel and a tumor. Results of this simulation demonstrate that, increasing the distance between a tumor and a parent vessel decreases the number of final tumor cells. Specially, this decrement becomes faster beyond a certain distance. Moreover, initial tumors in bigger domains must become much bigger before inducing angiogenesis which makes it harder for them to survive.
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Affiliation(s)
- Mehran Akbarpour Ghazani
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran.,Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
| | - Mohsen Saghafian
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
| | - Peyman Jalali
- Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
| | - Madjid Soltani
- Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran.,Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada.,Centre for Biotechnology and Bioengineering (CBB), University of Waterloo, Waterloo, ON, Canada.,Advanced Bioengineering Initiative Center, Computational Medicine Center, K. N. Toosi University of Technology, Tehran, Iran
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14
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A hybrid modeling approach for assessing mechanistic models of small molecule partitioning in vivo using a machine learning-integrated modeling platform. Sci Rep 2021; 11:11143. [PMID: 34045592 PMCID: PMC8160209 DOI: 10.1038/s41598-021-90637-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 05/13/2021] [Indexed: 12/17/2022] Open
Abstract
Prediction of the first-in-human dosing regimens is a critical step in drug development and requires accurate quantitation of drug distribution. Traditional in vivo studies used to characterize clinical candidate’s volume of distribution are error-prone, time- and cost-intensive and lack reproducibility in clinical settings. The paper demonstrates how a computational platform integrating machine learning optimization with mechanistic modeling can be used to simulate compound plasma concentration profile and predict tissue-plasma partition coefficients with high accuracy by varying the lipophilicity descriptor logP. The approach applied to chemically diverse small molecules resulted in comparable geometric mean fold-errors of 1.50 and 1.63 in pharmacokinetic outputs for direct tissue:plasma partition and hybrid logP optimization, with the latter enabling prediction of tissue permeation that can be used to guide toxicity and efficacy dosing in human subjects. The optimization simulations required to achieve these results were parallelized on the AWS cloud and generated outputs in under 5 h. Accuracy, speed, and scalability of the framework indicate that it can be used to assess the relevance of other mechanistic relationships implicated in pharmacokinetic-pharmacodynamic phenomena with a lower risk of overfitting datasets and generate large database of physiologically-relevant drug disposition for further integration with machine learning models.
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15
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Numerical Modeling for the Photocatalytic Degradation of Methyl Orange from Aqueous Solution using Cellulose/Zinc Oxide Hybrid Aerogel: Comparison with Experimental Data. Top Catal 2021. [DOI: 10.1007/s11244-021-01451-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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16
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Ziemys A, Simic V, Milosevic M, Kojic M, Liu YT, Yokoi K. Attenuated Microcirculation in Small Metastatic Tumors in Murine Liver. Pharmaceutics 2021; 13:pharmaceutics13050703. [PMID: 34065867 PMCID: PMC8150276 DOI: 10.3390/pharmaceutics13050703] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 04/28/2021] [Accepted: 05/10/2021] [Indexed: 11/16/2022] Open
Abstract
Metastatic cancer disease is the major cause of death in cancer patients. Because those small secondary tumors are clinically hardly detectable in their early stages, little is known about drug biodistribution and permeation into those metastatic tumors potentially contributing to insufficient clinical success against metastatic disease. Our recent studies indicated that breast cancer liver metastases may have compromised perfusion of intratumoral capillaries hindering the delivery of therapeutics for yet unknown reasons. To understand the microcirculation of small liver metastases, we have utilized computational simulations to study perfusion and oxygen concentration fields in and around the metastases smaller than 700 µm in size at the locations of portal vessels, central vein, and liver lobule acinus. Despite tumor vascularization, the results show that blood flow in those tumors can be substantially reduced indicating the presence of inadequate blood pressure gradients across tumors. A low blood pressure may contribute to the collapsed intratumoral capillary lumen limiting tumor perfusion that phenomenologically corroborates with our previously published in vivo studies. Tumors that are smaller than the liver lobule size and originating at different lobule locations may possess a different microcirculation environment and tumor perfusion. The acinus and portal vessel locations in the lobule were found to be the most beneficial to tumor growth based on tumor access to blood flow and intratumoral oxygen. These findings suggest that microcirculation states of small metastatic tumors can potentially contribute to physiological barriers preventing efficient delivery of therapeutic substances into small tumors.
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Affiliation(s)
- Arturas Ziemys
- Houston Methodist Research Institute, Houston, TX 77030, USA; (M.K.); (Y.T.L.); (K.Y.)
- Correspondence:
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, 3400 Kragujevac, Serbia; (V.S.); (M.M.)
| | - Miljan Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, 3400 Kragujevac, Serbia; (V.S.); (M.M.)
| | - Milos Kojic
- Houston Methodist Research Institute, Houston, TX 77030, USA; (M.K.); (Y.T.L.); (K.Y.)
- Bioengineering Research and Development Center BioIRC Kragujevac, 3400 Kragujevac, Serbia; (V.S.); (M.M.)
| | - Yan Ting Liu
- Houston Methodist Research Institute, Houston, TX 77030, USA; (M.K.); (Y.T.L.); (K.Y.)
| | - Kenji Yokoi
- Houston Methodist Research Institute, Houston, TX 77030, USA; (M.K.); (Y.T.L.); (K.Y.)
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17
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Köppl T, Vidotto E, Wohlmuth B. A 3D-1D coupled blood flow and oxygen transport model to generate microvascular networks. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2020; 36:e3386. [PMID: 32659047 DOI: 10.1002/cnm.3386] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2020] [Revised: 05/18/2020] [Accepted: 07/05/2020] [Indexed: 06/11/2023]
Abstract
In this work, we introduce an algorithmic approach to generate microvascular networks starting from larger vessels that can be reconstructed without noticeable segmentation errors. Contrary to larger vessels, the reconstruction of fine-scale components of microvascular networks shows significant segmentation errors, and an accurate mapping is time and cost intense. Thus there is a need for fast and reliable reconstruction algorithms yielding surrogate networks having similar stochastic properties as the original ones. The microvascular networks are constructed in a marching way by adding vessels to the outlets of the vascular tree from the previous step. To optimise the structure of the vascular trees, we use Murray's law to determine the radii of the vessels and bifurcation angles. In each step, we compute the local gradient of the partial pressure of oxygen and adapt the orientation of the new vessels to this gradient. At the same time, we use the partial pressure of oxygen to check whether the considered tissue block is supplied sufficiently with oxygen. Computing the partial pressure of oxygen, we use a 3D-1D coupled model for blood flow and oxygen transport. To decrease the complexity of a fully coupled 3D model, we reduce the blood vessel network to a 1D graph structure and use a bi-directional coupling with the tissue which is described by a 3D homogeneous porous medium. The resulting surrogate networks are analysed with respect to morphological and physiological aspects.
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Affiliation(s)
- Tobias Köppl
- Chair for Numerics, University of Technology Munich, Garching, Germany
| | - Ettore Vidotto
- Chair for Numerics, University of Technology Munich, Garching, Germany
| | - Barbara Wohlmuth
- Chair for Numerics, University of Technology Munich, Garching, Germany
- Department of Mathematics, University of Bergen, Allegaten 41, 5020 Bergen, Norway, Germany
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18
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Drug delivery: Experiments, mathematical modelling and machine learning. Comput Biol Med 2020; 123:103820. [PMID: 32658778 DOI: 10.1016/j.compbiomed.2020.103820] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Revised: 04/22/2020] [Accepted: 05/10/2020] [Indexed: 01/28/2023]
Abstract
We address the problem of determining from laboratory experiments the data necessary for a proper modeling of drug delivery and efficacy in anticancer therapy. There is an inherent difficulty in extracting the necessary parameters, because the experiments often yield an insufficient quantity of information. To overcome this difficulty, we propose to combine real experiments, numerical simulation, and Machine Learning (ML) based on Artificial Neural Networks (ANN), aiming at a reliable identification of the physical model factors, e.g. the killing action of the drug. To this purpose, we exploit the employed mathematical-numerical model for tumor growth and drug delivery, together with the ANN - ML procedure, to integrate the results of the experimental tests and feed back the model itself, thus obtaining a reliable predictive tool. The procedure represents a hybrid data-driven, physics-informed approach to machine learning. The physical and mathematical model employed for the numerical simulations is without extracellular matrix (ECM) and healthy cells because of the experimental conditions we reproduce.
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19
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Milosevic M, Stojanovic DB, Simic V, Grkovic M, Bjelovic M, Uskokovic PS, Kojic M. Preparation and modeling of three-layered PCL/PLGA/PCL fibrous scaffolds for prolonged drug release. Sci Rep 2020; 10:11126. [PMID: 32636450 PMCID: PMC7341868 DOI: 10.1038/s41598-020-68117-9] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Accepted: 06/10/2020] [Indexed: 12/27/2022] Open
Abstract
The authors present the preparation procedure and a computational model of a three‐layered fibrous scaffold for prolonged drug release. The scaffold, produced by emulsion/sequential electrospinning, consists of a poly(d,l-lactic-co-glycolic acid) (PLGA) fiber layer sandwiched between two poly(ε-caprolactone) (PCL) layers. Experimental results of drug release rates from the scaffold are compared with the results of the recently introduced computational finite element (FE) models for diffusive drug release from nanofibers to the three-dimensional (3D) surrounding medium. Two different FE models are used: (1) a 3D discretized continuum and fibers represented by a simple radial one-dimensional (1D) finite elements, and (2) a 3D continuum discretized by composite smeared finite elements (CSFEs) containing the fiber smeared and surrounding domains. Both models include the effects of polymer degradation and hydrophobicity (as partitioning) of the drug at the fiber/surrounding interface. The CSFE model includes a volumetric fraction of fibers and diameter distribution, and is additionally enhanced by using correction function to improve the accuracy of the model. The computational results are validated on Rhodamine B (fluorescent drug l) and other hydrophilic drugs. Agreement with experimental results proves that numerical models can serve as efficient tools for drug release to the surrounding porous medium or biological tissue. It is demonstrated that the introduced three-layered scaffold delays the drug release process and can be used for the time-controlled release of drugs in postoperative therapy.
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Affiliation(s)
- Miljan Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, Kragujevac, 34000, Serbia.,Belgrade Metropolitan University, Tadeusa Koscuska 63, Belgrade, 11000, Serbia
| | - Dusica B Stojanovic
- Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, 11000, Serbia
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, Kragujevac, 34000, Serbia
| | - Mirjana Grkovic
- Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, 11000, Serbia
| | - Milos Bjelovic
- Department for Minimally Invasive Upper Digestive Surgery, Clinical Center of Serbia, Hospital for Digestive Surgery - First Surgical Hospital, Dr Koste Todorovica 66, Belgrade, 11000, Serbia
| | - Petar S Uskokovic
- Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, 11000, Serbia
| | - Milos Kojic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, Kragujevac, 34000, Serbia. .,The Department of Nanomedicine, Houston Methodist Research Institute, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA. .,Serbian Academy of Sciences and Arts, Knez Mihailova 35, Belgrade, 11000, Serbia.
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20
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Kojic M, Milosevic M, Simic V, Milicevic B, Geroski V, Nizzero S, Ziemys A, Filipovic N, Ferrari M. Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics. Front Bioeng Biotechnol 2020; 7:381. [PMID: 31921800 PMCID: PMC6914730 DOI: 10.3389/fbioe.2019.00381] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Accepted: 11/15/2019] [Indexed: 11/22/2022] Open
Abstract
Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.
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Affiliation(s)
- Milos Kojic
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX, United States.,Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia.,Serbian Academy of Sciences and Arts, Belgrade, Serbia
| | - Miljan Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia.,Faculty of Information Technologies, Belgrade Metropolitan University, Belgrade, Serbia
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia
| | - Bogdan Milicevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia
| | - Vladimir Geroski
- Bioengineering Research and Development Center BioIRC Kragujevac, Kragujevac, Serbia
| | - Sara Nizzero
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX, United States.,Applied Physics Graduate Program, Rice University, Houston, TX, United States
| | - Arturas Ziemys
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX, United States
| | - Nenad Filipovic
- Faculty for Engineering Sciences, University of Kragujevac, Kragujevac, Serbia
| | - Mauro Ferrari
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX, United States
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21
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Nizzero S, Shen H, Ferrari M, Corradetti B. Immunotherapeutic Transport Oncophysics: Space, Time, and Immune Activation in Cancer. Trends Cancer 2019; 6:40-48. [PMID: 31952780 DOI: 10.1016/j.trecan.2019.11.008] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2019] [Revised: 11/22/2019] [Accepted: 11/25/2019] [Indexed: 12/30/2022]
Abstract
Immuno-oncology has gained momentum thanks to the success of strategies aimed at enhancing immune-mediated antitumor response. The field of immunotherapeutic transport oncophysics investigates the physical processes that drive cancer immunotherapies. This review discusses three main aspects that determine the outcome of an immunotherapy-based treatment from a physical point of view; (i) space, the distribution of cancer and immune cells within tumor masses, (ii) time, the temporal dynamic of immune response against tumors, and (iii) activity, the ability of immune cell populations to suppress cancer. Upon introducing these topics with examples from the literature, we investigate in detail two cases where the interplay between space, time, and activation variables determines immune response: nanodendritic cell vaccines and immunosuppression in ovarian cancer.
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Affiliation(s)
- Sara Nizzero
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; Mathematics in Medicine, Houston Methodist Research Institute, Houston, TX 77030, USA.
| | - Haifa Shen
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA
| | - Mauro Ferrari
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; University of St. Thomas, Houston, TX 77006, USA
| | - Bruna Corradetti
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, TX 77030, USA; Swansea University Medical School, Singleton Park, Swansea, Wales, UK.
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22
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Kremheller J, Vuong AT, Schrefler BA, Wall WA. An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3253. [PMID: 31441222 DOI: 10.1002/cnm.3253] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2019] [Revised: 07/04/2019] [Accepted: 08/16/2019] [Indexed: 05/13/2023]
Abstract
The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology, and flow patterns in the neovasculature, which are challenging and computationally expensive to resolve with a discrete, 1D angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, 1D representation of the preexisting vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the thermodynamically constrained averaging theory. The new model enables us to study mass transport from the preexisting vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically.
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Affiliation(s)
- Johannes Kremheller
- Institute for Computational Mechanics, Technical University of Munich, Garching, Germany
| | - Anh-Tu Vuong
- Institute for Computational Mechanics, Technical University of Munich, Garching, Germany
| | - Bernhard A Schrefler
- Institute for Advanced Study, Technical University of Munich, Garching, Germany
- Department of Civil, Environmental and Architectural Engineering, University of Padova, Padua, Italy
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, Garching, Germany
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23
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Reconsidering Vasopressors for Cardiogenic Shock. Chest 2019; 156:392-401. [DOI: 10.1016/j.chest.2019.03.020] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2018] [Revised: 03/13/2019] [Accepted: 03/15/2019] [Indexed: 12/27/2022] Open
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24
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Qiu X, Sane N, Neogi P. Convection in a Krogh cylinder: Putting back fluid flow in the extravascular tissue. AIChE J 2019. [DOI: 10.1002/aic.16720] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Xianjie Qiu
- Chemical and Biochemical Engineering Missouri University of Science and Technology Rolla Missouri
| | - Nandini Sane
- Chemical and Biochemical Engineering Missouri University of Science and Technology Rolla Missouri
| | - Parthasakha Neogi
- Chemical and Biochemical Engineering Missouri University of Science and Technology Rolla Missouri
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25
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Riazy L, Schaeffter T, Olbrich M, Schueler J, von Knobelsdorff-Brenkenhoff F, Niendorf T, Schulz-Menger J. Porous medium 3D flow simulation of contrast media washout in cardiac MRI reflects myocardial injury. Magn Reson Med 2019; 82:775-785. [PMID: 30989720 DOI: 10.1002/mrm.27756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2018] [Revised: 02/07/2019] [Accepted: 03/08/2019] [Indexed: 11/06/2022]
Abstract
PURPOSE Myocardial blood-flow simulation based on laws of fluid mechanics is a valuable tool for understanding tissue behavior. Our aim is to evaluate the ability of a porous-media flow model approach to reflect disturbed washout of contrast media (CM) from the myocardium as observed by cardiovascular MR. METHODS A coupled advection-diffusion model is used to describe the CM flow in the vascular and extravascular space as separate compartments. Their exchange of CM is controlled by the exchange rate ExR , which in turn determines the washout behavior. We fitted simulations to CM concentration measurements, derived from T1 maps of the midventricular slice. The CM concentration was extracted from 18 patients with myocarditis in the acute phase and during follow-up after 6 months. The results were compared with 18 sex- and age-matched controls. For each subject, the measurements were acquired before and during the first 10 minutes at 5 time points after CM administration, representing CM washout. Image registration was applied to compensate for motion between different time points. RESULTS Eight matched data sets had to be excluded due to low registration quality. Processing was successful in n = 10 matched data sets of acute and healed myocarditis as well as controls. Significant differences in ExR were observed when comparing patients with acute myocarditis to controls (P < .001), to their follow-up (P < .05), and the follow-up to controls (P < .05). CONCLUSION Our study suggests the feasibility of using the proposed porous-medium flow framework for the simulation of pathologic myocardial tissue.
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Affiliation(s)
- Leili Riazy
- Berlin Ultrahigh Field Facility, Max-Delbrueck Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.,DZHK, German Center for Cardiovascular Research, Berlin, Germany.,Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, ECRC, Cardiology, Berlin, Germany
| | - Tobias Schaeffter
- Medical Physics and Metrological Information Technology, Physikalisch-Technische Bundesanstalt, Berlin, Germany
| | - Marc Olbrich
- Medical Physics and Metrological Information Technology, Physikalisch-Technische Bundesanstalt, Berlin, Germany.,Technical University Berlin, Berlin, Germany
| | - Johannes Schueler
- Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, ECRC, Cardiology, Berlin, Germany.,Department of Cardiology and Nephrology, HELIOS Klinikum Berlin Buch, Berlin, Germany
| | - Florian von Knobelsdorff-Brenkenhoff
- DZHK, German Center for Cardiovascular Research, Berlin, Germany.,Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, ECRC, Cardiology, Berlin, Germany.,Clinic Agatharied, Department of Cardiology, University of Munich, Hausham, Germany
| | - Thoralf Niendorf
- Berlin Ultrahigh Field Facility, Max-Delbrueck Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.,DZHK, German Center for Cardiovascular Research, Berlin, Germany
| | - Jeanette Schulz-Menger
- DZHK, German Center for Cardiovascular Research, Berlin, Germany.,Charité - Universitätsmedizin Berlin, corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, ECRC, Cardiology, Berlin, Germany.,Department of Cardiology and Nephrology, HELIOS Klinikum Berlin Buch, Berlin, Germany
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26
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Kojic M, Milosevic M, Simic V, Geroski V, Ziemys A, Filipovic N, Ferrari M. Smeared multiscale finite element model for electrophysiology and ionic transport in biological tissue. Comput Biol Med 2019; 108:288-304. [PMID: 31015049 DOI: 10.1016/j.compbiomed.2019.03.023] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2018] [Revised: 03/22/2019] [Accepted: 03/23/2019] [Indexed: 10/27/2022]
Abstract
Basic functions of living organisms are governed by the nervous system through bidirectional signals transmitted from the brain to neural networks. These signals are similar to electrical waves. In electrophysiology the goal is to study the electrical properties of biological cells and tissues, and the transmission of signals. From a physics perspective, there exists a field of electrical potential within the living body, the nervous system, extracellular space and cells. Electrophysiological problems can be investigated experimentally and also theoretically by developing appropriate mathematical or computational models. Due to the enormous complexity of biological systems, it would be almost impossible to establish a detailed computational model of the electrical field, even for only a single organ (e.g. heart), including the entirety of cells comprising the neural network. In order to make computational models feasible for practical applications, we here introduce the concept of smeared fields, which represents a generalization of the previously formulated multiscale smeared methodology for mass transport in blood vessels, lymph, and tissue. We demonstrate the accuracy of the smeared finite element computational models for the electric field in numerical examples. The electrical field is further coupled with ionic mass transport within tissue composed of interstitial spaces extracellularly and by cytoplasm and organelles intracellularly. The proposed methodology, which couples electrophysiology and molecular ionic transport, is applicable to a variety of 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; Belgrade Metropolitan University, Tadeuša Košćuška 63, 11000, Belgrade, Serbia
| | - V Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
| | - V Geroski
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400, Kragujevac, Serbia
| | - A Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA
| | - N Filipovic
- University of Kragujevac, Faculty for Engineering Sciences, Sestre Janic 6, 34000, Kragujevac, Serbia
| | - M Ferrari
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7-117, Houston, TX, 77030, USA
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Santagiuliana R, Milosevic M, Milicevic B, Sciumè G, Simic V, Ziemys A, Kojic M, Schrefler BA. Coupling tumor growth and bio distribution models. Biomed Microdevices 2019; 21:33. [PMID: 30906958 PMCID: PMC6686908 DOI: 10.1007/s10544-019-0368-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
We couple a tumor growth model embedded in a microenvironment, with a bio distribution model able to simulate a whole organ. The growth model yields the evolution of tumor cell population, of the differential pressure between cell populations, of porosity of ECM, of consumption of nutrients due to tumor growth, of angiogenesis, and related growth factors as function of the locally available nutrient. The bio distribution model on the other hand operates on a frozen geometry but yields a much refined distribution of nutrient and other molecules. The combination of both models will enable simulating the growth of a tumor in a whole organ, including a realistic distribution of therapeutic agents and allow hence to evaluate the efficacy of these agents.
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Affiliation(s)
- Raffaella Santagiuliana
- Department of Civil, Environmental and Architectural Engineering, University of Padova, via Marzolo 9, 35131, Padova, Italy.
| | - Miljan Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, Kragujevac, 34000, Serbia
- Belgrade Metropolitan University, Tadeuša Košćuška 63, Belgrade, 11000, Serbia
| | - Bogdan Milicevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, Kragujevac, 34000, Serbia
| | - Giuseppe Sciumè
- Institut de Mécanique et d'Ingénierie (I2M, CNRS UMR 5295), University of Bordeaux, Bordeaux, France
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, Kragujevac, 34000, Serbia
| | - Arturas Ziemys
- The Department of Nanomedicine, Houston Methodist Research Institute, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
| | - Milos Kojic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, Kragujevac, 34000, Serbia
- The Department of Nanomedicine, Houston Methodist Research Institute, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- Serbian Academy of Sciences and Arts, Knez Mihailova 35, Belgrade, 11000, Serbia
| | - Bernhard A Schrefler
- Department of Civil, Environmental and Architectural Engineering, University of Padova, via Marzolo 9, 35131, Padova, Italy
- The Department of Nanomedicine, Houston Methodist Research Institute, 6670 Bertner Ave., R7 117, Houston, TX, 77030, USA
- Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, D-85748, Garching b. München, Germany
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28
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Milosevic M, Stojanovic D, Simic V, Milicevic B, Radisavljevic A, Uskokovic P, Kojic M. A Computational Model for Drug Release from PLGA Implant. MATERIALS (BASEL, SWITZERLAND) 2018; 11:E2416. [PMID: 30501079 PMCID: PMC6316994 DOI: 10.3390/ma11122416] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2018] [Revised: 11/18/2018] [Accepted: 11/20/2018] [Indexed: 11/23/2022]
Abstract
Due to the relative ease of producing nanofibers with a core⁻shell structure, emulsion electrospinning has been investigated intensively in making nanofibrous drug delivery systems for controlled and sustained release. Predictions of drug release rates from the poly (d,l-lactic-co-glycolic acid) (PLGA) produced via emulsion electrospinning can be a very difficult task due to the complexity of the system. A computational finite element methodology was used to calculate the diffusion mass transport of Rhodamine B (fluorescent drug model). Degradation effects and hydrophobicity (partitioning phenomenon) at the fiber/surrounding interface were included in the models. The results are validated by experiments where electrospun PLGA nanofiber mats with different contents were used. A new approach to three-dimensional (3D) modeling of nanofibers is presented in this work. The authors have introduced two original models for diffusive drug release from nanofibers to the 3D surrounding medium discretized by continuum 3D finite elements: (1) A model with simple radial one-dimensional (1D) finite elements, and (2) a model consisting of composite smeared finite elements (CSFEs). Numerical solutions, compared to experiments, demonstrate that both computational models provide accurate predictions of the diffusion process and can therefore serve as efficient tools for describing transport inside a polymer fiber network and drug release to the surrounding porous medium.
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Affiliation(s)
- Miljan Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia.
- Belgrade Metropolitan University, Tadeuša Košćuška 63, 11000 Belgrade, Serbia.
| | - Dusica Stojanovic
- Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia.
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia.
| | - Bogdan Milicevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 34000 Kragujevac, Serbia.
| | - Andjela Radisavljevic
- Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia.
| | - Petar Uskokovic
- Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia.
| | - Milos 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, USA.
- Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000 Belgrade, Serbia.
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29
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Ziemys A, Yokoi K, Kai M, Liu YT, Kojic M, Simic V, Milosevic M, Holder A, Ferrari M. Progression-dependent transport heterogeneity of breast cancer liver metastases as a factor in therapeutic resistance. J Control Release 2018; 291:99-105. [PMID: 30332610 DOI: 10.1016/j.jconrel.2018.10.014] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Revised: 10/11/2018] [Accepted: 10/12/2018] [Indexed: 12/13/2022]
Abstract
Metastatic disease is a major cause of mortality in cancer patients. While many drug delivery strategies for anticancer therapeutics have been developed in preclinical studies of primary tumors, the drug delivery properties of metastatic tumors have not been sufficiently investigated. Therapeutic efficacy hinges on efficient drug permeation into the tumor microenvironment, which is known to be heterogeneous thus potentially making drug permeation heterogeneous, also. In this study, we have identified that 4 T1 liver metastases, treated with pegylated liposomal doxorubicin, have unfavorable and heterogeneous transport of doxorubicin. Our drug extravasation results differ greatly from analogous studies with 4 T1 tumors growing in the primary site. A probabilistic tumor population model was developed to estimate drug permeation efficiency and drug kinetics of liver metastases by integrating the transport and structural properties of tumors and delivered drugs. The results demonstrate significant heterogeneity in metastases with regard to transport properties of doxorubicin within the same animal model, and even within the same organ. These results also suggest that the degree of heterogeneity depends on the stage of tumor progression and that differences in transport properties can define transport-based tumor phenotypes. These findings may have valuable clinical implications by illustrating that therapeutic agents can permeate and eliminate metastases of "less resistant" transport phenotypes, while sparing tumors with more "resistant" transport properties. We anticipate that these results could challenge the current paradigm of drug delivery into metastases, highlight potential caveats for therapies that may alter tumor perfusion, and deepen our understanding of the emergence of drug transport-based therapeutic resistance.
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Affiliation(s)
- A Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, Houston, TX, USA.
| | - K Yokoi
- Houston Methodist Research Institute, The Department of Nanomedicine, Houston, TX, USA
| | - M Kai
- Houston Methodist Research Institute, The Department of Nanomedicine, Houston, TX, USA
| | - Y T Liu
- Houston Methodist Research Institute, The Department of Nanomedicine, Houston, TX, USA
| | - M Kojic
- Houston Methodist Research Institute, The Department of Nanomedicine, Houston, TX, 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
| | - V Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia
| | - M Milosevic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia
| | - A Holder
- Department of Surgery, Houston Methodist, Houston, TX, USA
| | - M Ferrari
- Houston Methodist Research Institute, The Department of Nanomedicine, Houston, TX, USA
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30
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Kremheller J, Vuong AT, Yoshihara L, Wall WA, Schrefler BA. A monolithic multiphase porous medium framework for (a-)vascular tumor growth. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2018; 340:657-683. [PMID: 33132456 PMCID: PMC7598028 DOI: 10.1016/j.cma.2018.06.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We present a dynamic vascular tumor model combining a multiphase porous medium framework for avascular tumor growth in a consistent Arbitrary Lagrangian Eulerian formulation and a novel approach to incorporate angiogenesis. The multiphase model is based on Thermodynamically Constrained Averaging Theory and comprises the extracellular matrix as a porous solid phase and three fluid phases: (living and necrotic) tumor cells, host cells and the interstitial fluid. Angiogenesis is modeled by treating the neovasculature as a proper additional phase with volume fraction or blood vessel density. This allows us to define consistent inter-phase exchange terms between the neovasculature and the interstitial fluid. As a consequence, transcapillary leakage and lymphatic drainage can be modeled. By including these important processes we are able to reproduce the increased interstitial pressure in tumors which is a crucial factor in drug delivery and, thus, therapeutic outcome. Different coupling schemes to solve the resulting five-phase problem are realized and compared with respect to robustness and computational efficiency. We find that a fully monolithic approach is superior to both the standard partitioned and a hybrid monolithic-partitioned scheme for a wide range of parameters. The flexible implementation of the novel model makes further extensions (e.g., inclusion of additional phases and species) straightforward.
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Affiliation(s)
- Johannes Kremheller
- Institute for Computational Mechanics, Technische Universität München, Boltzmannstrasse 15, D-85748 Garching b. München, Germany
| | - Anh-Tu Vuong
- Institute for Computational Mechanics, Technische Universität München, Boltzmannstrasse 15, D-85748 Garching b. München, Germany
| | - Lena Yoshihara
- Institute for Computational Mechanics, Technische Universität München, Boltzmannstrasse 15, D-85748 Garching b. München, Germany
| | - Wolfgang A. Wall
- Institute for Computational Mechanics, Technische Universität München, Boltzmannstrasse 15, D-85748 Garching b. München, Germany
| | - Bernhard A. Schrefler
- Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, D-85748 Garching b. München, Germany
- Department of Civil, Environmental and Architectural Engineering, University of Padova, Italy
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31
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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. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 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] [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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32
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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] [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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33
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Kojic M, Milosevic M, Simic V, Koay EJ, Kojic N, Ziemys A, Ferrari M. Extension of the composite smeared finite element (CSFE) to include lymphatic system in modeling mass transport in capillary systems and biological tissue. JOURNAL OF THE SERBIAN SOCIETY FOR COMPUTATIONAL MECHANICS 2017; 11:108-119. [PMID: 29782608 PMCID: PMC5957499 DOI: 10.24874/jsscm.2017.11.02.09] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We have recently introduced a composite smeared finite element (CSFE) to model gradient-driven mass transport in biological tissue. The transport from capillary system is smeared in a way to transform 1D transport to a continuum, while the tissue is considered as a continuum. Coupling between the smeared pressure and concentration field is achieved through 1D connectivity elements assigned at each FE node. Here we extend our smeared model to include the lymphatic system. The lymphatic vessels are treated in a way analogous to the capillaries, by introducing the corresponding Darcy and diffusion tensors. New connectivity elements are added. In the numerical examples we demonstrate accuracy of the smeared model and the effects of the lymph on the pressure and concentration within extracellular space are evaluated, assuming that there is no transport to the cell space.
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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
- Belgrade Metropolitan University, Tadeuša Košćuška 63, 11000 Belgrade, Serbia
| | - Vladimir Simic
- Bioengineering Research and Development Center BioIRC Kragujevac, Prvoslava Stojanovica 6, 3400 Kragujevac, Serbia
| | - Eugene J Koay
- Department of Radiation Oncology, MD Anderson Cancer Center, Houston, TX 77030
| | - Nikola Kojic
- Center for Engineering in Medicine and Surgical Services, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114
| | - Arturas Ziemys
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX 77030, USA
| | - Mauro Ferrari
- Houston Methodist Research Institute, The Department of Nanomedicine, 6670 Bertner Ave., R7 117, Houston, TX 77030, USA
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