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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:e3832. [PMID: 38770788 DOI: 10.1002/cnm.3832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [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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2
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Borau C, Wertheim KY, Hervas-Raluy S, Sainz-DeMena D, Walker D, Chisholm R, Richmond P, Varella V, Viceconti M, Montero A, Gregori-Puigjané E, Mestres J, Kasztelnik M, García-Aznar JM. A multiscale orchestrated computational framework to reveal emergent phenomena in neuroblastoma. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 241:107742. [PMID: 37572512 DOI: 10.1016/j.cmpb.2023.107742] [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: 04/27/2023] [Revised: 07/19/2023] [Accepted: 07/31/2023] [Indexed: 08/14/2023]
Abstract
Neuroblastoma is a complex and aggressive type of cancer that affects children. Current treatments involve a combination of surgery, chemotherapy, radiotherapy, and stem cell transplantation. However, treatment outcomes vary due to the heterogeneous nature of the disease. Computational models have been used to analyse data, simulate biological processes, and predict disease progression and treatment outcomes. While continuum cancer models capture the overall behaviour of tumours, and agent-based models represent the complex behaviour of individual cells, multiscale models represent interactions at different organisational levels, providing a more comprehensive understanding of the system. In 2018, the PRIMAGE consortium was formed to build a cloud-based decision support system for neuroblastoma, including a multi-scale model for patient-specific simulations of disease progression. In this work we have developed this multi-scale model that includes data such as patient's tumour geometry, cellularity, vascularization, genetics and type of chemotherapy treatment, and integrated it into an online platform that runs the simulations on a high-performance computation cluster using Onedata and Kubernetes technologies. This infrastructure will allow clinicians to optimise treatment regimens and reduce the number of costly and time-consuming clinical trials. This manuscript outlines the challenging framework's model architecture, data workflow, hypothesis, and resources employed in its development.
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Affiliation(s)
- C Borau
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Mechanical Engineering Department, University of Zaragoza, Zaragoza, Spain.
| | - K Y Wertheim
- Department of Computer Science and InsigneoInstitute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom; Centre of Excellence for Data Science, Artificial Intelligence and Modelling and School of Computer Science, University of Hull, Kingston upon Hull, United Kingdom
| | - S Hervas-Raluy
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Mechanical Engineering Department, University of Zaragoza, Zaragoza, Spain
| | - D Sainz-DeMena
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Mechanical Engineering Department, University of Zaragoza, Zaragoza, Spain
| | - D Walker
- Department of Computer Science and InsigneoInstitute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - R Chisholm
- Department of Computer Science and InsigneoInstitute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - P Richmond
- Department of Computer Science and InsigneoInstitute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - V Varella
- Department of Industrial Engineering, Alma Mater Studiorum - University of Bologna, Bologna, Italy; Medical Technology Lab, IRCCS Istituto Ortopedico Rizzoli, Bologna, Italy
| | - M Viceconti
- Department of Industrial Engineering, Alma Mater Studiorum - University of Bologna, Bologna, Italy; Medical Technology Lab, IRCCS Istituto Ortopedico Rizzoli, Bologna, Italy
| | - A Montero
- Chemotargets SL, Baldiri Reixac 4, Parc Cientific de Barcelona (PCB), Barcelona, Spain
| | - E Gregori-Puigjané
- Chemotargets SL, Baldiri Reixac 4, Parc Cientific de Barcelona (PCB), Barcelona, Spain
| | - J Mestres
- Chemotargets SL, Baldiri Reixac 4, Parc Cientific de Barcelona (PCB), Barcelona, Spain
| | - M Kasztelnik
- ACC Cyfronet, AGH University of Science and Technology, Kraków, Poland
| | - J M García-Aznar
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Mechanical Engineering Department, University of Zaragoza, Zaragoza, Spain
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Vinje V, Zapf B, Ringstad G, Eide PK, Rognes ME, Mardal KA. Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation. Fluids Barriers CNS 2023; 20:62. [PMID: 37596635 PMCID: PMC10439559 DOI: 10.1186/s12987-023-00459-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2023] [Accepted: 07/21/2023] [Indexed: 08/20/2023] Open
Abstract
Whether you are reading, running or sleeping, your brain and its fluid environment continuously interacts to distribute nutrients and clear metabolic waste. Yet, the precise mechanisms for solute transport within the human brain have remained hard to quantify using imaging techniques alone. From multi-modal human brain MRI data sets in sleeping and sleep-deprived subjects, we identify and quantify CSF tracer transport parameters using forward and inverse subject-specific computational modelling. Our findings support the notion that extracellular diffusion alone is not sufficient as a brain-wide tracer transport mechanism. Instead, we show that human MRI observations align well with transport by either by an effective diffusion coefficent 3.5[Formula: see text] that of extracellular diffusion in combination with local clearance rates corresponding to a tracer half-life of up to 5 h, or by extracellular diffusion augmented by advection with brain-wide average flow speeds on the order of 1-9 [Formula: see text]m/min. Reduced advection fully explains reduced tracer clearance after sleep-deprivation, supporting the role of sleep and sleep deprivation on human brain clearance.
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Affiliation(s)
- Vegard Vinje
- Simula Research Laboratory, Kristian Augusts gate 23, 0164, Oslo, Norway
- Expert Analytics AS, Møllergata 8, 0179, Oslo, Norway
| | - Bastian Zapf
- Department of Mathematics, University of Oslo, Oslo, Norway
| | - Geir Ringstad
- Department of Radiology, Oslo University Hospital - Rikshospitalet, Oslo, Norway
- Department of Geriatrics and Internal Medicine, Sørlandet Hospital, Arendal, Norway
| | - Per Kristian Eide
- Department of Neurosurgery, Oslo University Hospital - Rikshospitalet, Oslo, Norway
| | - Marie E Rognes
- Simula Research Laboratory, Kristian Augusts gate 23, 0164, Oslo, Norway
| | - Kent-Andre Mardal
- Simula Research Laboratory, Kristian Augusts gate 23, 0164, Oslo, Norway.
- Department of Mathematics, University of Oslo, Oslo, Norway.
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Poulain A, Riseth J, Vinje V. Multi-compartmental model of glymphatic clearance of solutes in brain tissue. PLoS One 2023; 18:e0280501. [PMID: 36881576 PMCID: PMC9990927 DOI: 10.1371/journal.pone.0280501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 01/02/2023] [Indexed: 03/08/2023] Open
Abstract
The glymphatic system is the subject of numerous pieces of research in biology. Mathematical modelling plays a considerable role in this field since it can indicate the possible physical effects of this system and validate the biologists' hypotheses. The available mathematical models that describe the system at the scale of the brain (i.e. the macroscopic scale) are often solely based on the diffusion equation and do not consider the fine structures formed by the perivascular spaces. We therefore propose a mathematical model representing the time and space evolution of a mixture flowing through multiple compartments of the brain. We adopt a macroscopic point of view in which the compartments are all present at any point in space. The equations system is composed of two coupled equations for each compartment: One equation for the pressure of a fluid and one for the mass concentration of a solute. The fluid and solute can move from one compartment to another according to certain membrane conditions modelled by transfer functions. We propose to apply this new modelling framework to the clearance of 14C-inulin from the rat brain.
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Affiliation(s)
- Alexandre Poulain
- Laboratoire Paul Painlevé, UMR 8524 CNRS, Université de Lille, Lille, France
- Department for Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
- * E-mail:
| | - Jørgen Riseth
- Department of Mathematics, University of Oslo, Oslo, Norway
- Department for Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
| | - Vegard Vinje
- Department for Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
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Vaghi C, Fanciullino R, Benzekry S, Poignard C. Macro-scale models for fluid flow in tumour tissues: impact of microstructure properties. J Math Biol 2022; 84:27. [DOI: 10.1007/s00285-022-01719-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Revised: 01/04/2022] [Accepted: 01/20/2022] [Indexed: 11/28/2022]
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Nagesetti A, Dulikravich GS, Orlande HRB, Colaco MJ, McGoron AJ. Computational model of silica nanoparticle penetration into tumor spheroids: Effects of methoxy and carboxy PEG surface functionalization and hyperthermia. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3504. [PMID: 34151543 DOI: 10.1002/cnm.3504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Revised: 06/02/2021] [Accepted: 06/12/2021] [Indexed: 06/13/2023]
Abstract
Drug delivery to tumors suffers from poor solubility, specificity, diffusion through the tumor micro-environment and nonoptimal interactions with components of the extracellular matrix and cell surface receptors. Nanoparticles and drug-polymer complexes address many of these problems. However, large size exasperates the problem of slow diffusion through the tumor. Three-dimensional tumor spheroids are good models to evaluate approaches to mitigate these difficulties and aid in design strategies to improve the delivery of drugs to treat cancer effectively. Diffusion of drug carriers is highly dependent on cell uptake rate parameters (association/dissociation) and temperature. Hyperthermia increases molecular transport and is known to act synergistically with chemotherapy to improve treatment. This study presents a new inverse estimation approach based on Bayesian probability for estimating nanoparticle cell uptake rates from experiments. The parameters were combined with a finite element computational model of nanoparticle transport under hyperthermia conditions to explore its effect on tumor porosity, diffusion and particle binding (association and dissociation) at cell surfaces. Carboxy-PEG-silane (cPEGSi) nanoparticles showed higher cell uptake compared to methoxy-PEG-silane (mPEGSi) nanoparticles. Simulations were consistent with experimental results from Skov-3 ovarian cancer spheroids. Amorphous silica (cPEGSi) nanoparticles (58 nm) concentrated at the periphery of the tumor spheroids at 37°C but mild hyperthermia (43°C) increased nanoparticle penetration. Thus, hyperthermia may enhance cancer treatment by improving blood delivery to tumors, enhancing extravasation and penetration into tumors, trigger release of drug from the carrier at the tumor site and possibly lead to synergistic anti-cancer activity with the drug.
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Affiliation(s)
- Abhignyan Nagesetti
- Department of Biomedical Engineering, Florida International University, Miami, Florida, USA
| | - George S Dulikravich
- Department of Mechanical and Materials Engineering, Florida International University, Miami, Florida, USA
| | - Helcio R B Orlande
- Department of Mechanical Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
| | - Marcelo J Colaco
- Department of Mechanical Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
| | - Anthony J McGoron
- Department of Biomedical Engineering, Florida International University, Miami, Florida, USA
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Hormuth DA, Phillips CM, Wu C, Lima EABF, Lorenzo G, Jha PK, Jarrett AM, Oden JT, Yankeelov TE. Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data. Cancers (Basel) 2021; 13:3008. [PMID: 34208448 PMCID: PMC8234316 DOI: 10.3390/cancers13123008] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Revised: 06/07/2021] [Accepted: 06/13/2021] [Indexed: 01/03/2023] Open
Abstract
Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.
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Affiliation(s)
- David A. Hormuth
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
- Livestrong Cancer Institutes, Dell Medical School, The University of Texas at Austin, Austin, TX 78712, USA
| | - Caleb M. Phillips
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
| | - Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
| | - Ernesto A. B. F. Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
- Texas Advanced Computing Center, The University of Texas at Austin, Austin, TX 78758, USA
| | - Guillermo Lorenzo
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
- Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy
| | - Prashant K. Jha
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
| | - Angela M. Jarrett
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA;
| | - J. Tinsley Oden
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
- Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Computer Science, The University of Texas at Austin, Austin, TX 78712, USA
| | - Thomas E. Yankeelov
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA; (C.M.P.); (C.W.); (E.A.B.F.L.); (G.L.); (P.K.J.); (J.T.O.); (T.E.Y.)
- Livestrong Cancer Institutes, Dell Medical School, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA;
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Oncology, The University of Texas at Austin, Austin, TX 78712, USA
- Department of Imaging Physics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA
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