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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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Mostofinejad A, Romero DA, Brinson D, Marin-Araujo AE, Bazylak A, Waddell TK, Haykal S, Karoubi G, Amon CH. In silico model development and optimization of in vitro lung cell population growth. PLoS One 2024; 19:e0300902. [PMID: 38748626 PMCID: PMC11095723 DOI: 10.1371/journal.pone.0300902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 03/04/2024] [Indexed: 05/19/2024] Open
Abstract
Tissue engineering predominantly relies on trial and error in vitro and ex vivo experiments to develop protocols and bioreactors to generate functional tissues. As an alternative, in silico methods have the potential to significantly reduce the timelines and costs of experimental programs for tissue engineering. In this paper, we propose a methodology to formulate, select, calibrate, and test mathematical models to predict cell population growth as a function of the biochemical environment and to design optimal experimental protocols for model inference of in silico model parameters. We systematically combine methods from the experimental design, mathematical statistics, and optimization literature to develop unique and explainable mathematical models for cell population dynamics. The proposed methodology is applied to the development of this first published model for a population of the airway-relevant bronchio-alveolar epithelial (BEAS-2B) cell line as a function of the concentration of metabolic-related biochemical substrates. The resulting model is a system of ordinary differential equations that predict the temporal dynamics of BEAS-2B cell populations as a function of the initial seeded cell population and the glucose, oxygen, and lactate concentrations in the growth media, using seven parameters rigorously inferred from optimally designed in vitro experiments.
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Affiliation(s)
- Amirmahdi Mostofinejad
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada
| | - David A. Romero
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada
| | - Dana Brinson
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
| | - Alba E. Marin-Araujo
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
- Latner Research Laboratories, Division of Thoracic Surgery, University Health Network, Toronto, Ontario, Canada
| | - Aimy Bazylak
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada
| | - Thomas K. Waddell
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
- Latner Research Laboratories, Division of Thoracic Surgery, University Health Network, Toronto, Ontario, Canada
| | - Siba Haykal
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
- Division of Plastic Surgery, University Health Network, Toronto, Ontario, Canada
| | - Golnaz Karoubi
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
- Latner Research Laboratories, Division of Thoracic Surgery, University Health Network, Toronto, Ontario, Canada
| | - Cristina H. Amon
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
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Walsh CL, Berg M, West H, Holroyd NA, Walker-Samuel S, Shipley RJ. Reconstructing microvascular network skeletons from 3D images: What is the ground truth? Comput Biol Med 2024; 171:108140. [PMID: 38422956 DOI: 10.1016/j.compbiomed.2024.108140] [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] [Received: 10/18/2023] [Revised: 01/29/2024] [Accepted: 02/12/2024] [Indexed: 03/02/2024]
Abstract
Structural changes to microvascular networks are increasingly highlighted as markers of pathogenesis in a wide range of disease, e.g. Alzheimer's disease, vascular dementia and tumour growth. This has motivated the development of dedicated 3D imaging techniques, alongside the creation of computational modelling frameworks capable of using 3D reconstructed networks to simulate functional behaviours such as blood flow or transport processes. Extraction of 3D networks from imaging data broadly consists of two image processing steps: segmentation followed by skeletonisation. Much research effort has been devoted to segmentation field, and there are standard and widely-applied methodologies for creating and assessing gold standards or ground truths produced by manual annotation or automated algorithms. The Skeletonisation field, however, lacks widely applied, simple to compute metrics for the validation or optimisation of the numerous algorithms that exist to extract skeletons from binary images. This is particularly problematic as 3D imaging datasets increase in size and visual inspection becomes an insufficient validation approach. In this work, we first demonstrate the extent of the problem by applying 4 widely-used skeletonisation algorithms to 3 different imaging datasets. In doing so we show significant variability between reconstructed skeletons of the same segmented imaging dataset. Moreover, we show that such a structural variability propagates to simulated metrics such as blood flow. To mitigate this variability we introduce a new, fast and easy to compute super metric that compares the volume, connectivity, medialness, bifurcation point identification and homology of the reconstructed skeletons to the original segmented data. We then show that such a metric can be used to select the best performing skeletonisation algorithm for a given dataset, as well as to optimise its parameters. Finally, we demonstrate that the super metric can also be used to quickly identify how a particular skeletonisation algorithm could be improved, becoming a powerful tool in understanding the complex implication of small structural changes in a network.
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Affiliation(s)
- Claire L Walsh
- Department of Mechanical Engineering, University College London, United Kingdom
| | - Maxime Berg
- Department of Mechanical Engineering, University College London, United Kingdom.
| | - Hannah West
- Department of Mechanical Engineering, University College London, United Kingdom
| | - Natalie A Holroyd
- Centre for Computational Medicine, Division of Medicine, University College London, United Kingdom
| | - Simon Walker-Samuel
- Centre for Computational Medicine, Division of Medicine, University College London, United Kingdom
| | - Rebecca J Shipley
- Department of Mechanical Engineering, University College London, United Kingdom; Centre for Computational Medicine, Division of Medicine, University College London, United Kingdom
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Berg M, Eleftheriadou D, Phillips JB, Shipley RJ. Mathematical modelling with Bayesian inference to quantitatively characterize therapeutic cell behaviour in nerve tissue engineering. J R Soc Interface 2023; 20:20230258. [PMID: 37669694 PMCID: PMC10480012 DOI: 10.1098/rsif.2023.0258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 08/15/2023] [Indexed: 09/07/2023] Open
Abstract
Cellular engineered neural tissues have significant potential to improve peripheral nerve repair strategies. Traditional approaches depend on quantifying tissue behaviours using experiments in isolation, presenting a challenge for an overarching framework for tissue design. By comparison, mathematical cell-solute models benchmarked against experimental data enable computational experiments to be performed to test the role of biological/biophysical mechanisms, as well as to explore the impact of different design scenarios and thus accelerate the development of new treatment strategies. Such models generally consist of a set of continuous, coupled, partial differential equations relying on a number of parameters and functional forms. They necessitate dedicated in vitro experiments to be informed, which are seldom available and often involve small datasets with limited spatio-temporal resolution, generating uncertainties. We address this issue and propose a pipeline based on Bayesian inference enabling the derivation of experimentally informed cell-solute models describing therapeutic cell behaviour in nerve tissue engineering. We apply our pipeline to three relevant cell types and obtain models that can readily be used to simulate nerve repair scenarios and quantitatively compare therapeutic cells. Beyond parameter estimation, the proposed pipeline enables model selection as well as experiment utility quantification, aimed at improving both model formulation and experimental design.
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Affiliation(s)
- Maxime Berg
- Centre for Nerve Engineering, University College London, WC1E 6BT London, UK
- Department of Mechanical Engineering, University College London, WC1E 6BT London, UK
| | - Despoina Eleftheriadou
- Centre for Nerve Engineering, University College London, WC1E 6BT London, UK
- School of Pharmacy, University College London, WC1N 1AX London, UK
| | - James B. Phillips
- Centre for Nerve Engineering, University College London, WC1E 6BT London, UK
- School of Pharmacy, University College London, WC1N 1AX London, UK
| | - Rebecca J. Shipley
- Centre for Nerve Engineering, University College London, WC1E 6BT London, UK
- Department of Mechanical Engineering, University College London, WC1E 6BT London, UK
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Laranjeira S, Roberton VH, Phillips JB, Shipley RJ. Perspectives on optimizing local delivery of drugs to peripheral nerves using mathematical models. WIREs Mech Dis 2023; 15:e1593. [PMID: 36624330 PMCID: PMC10909486 DOI: 10.1002/wsbm.1593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Revised: 12/05/2022] [Accepted: 12/15/2022] [Indexed: 01/11/2023]
Abstract
Drug therapies for treating peripheral nerve injury repair have shown significant promise in preclinical studies. Despite this, drug treatments are not used routinely clinically to treat patients with peripheral nerve injuries. Drugs delivered systemically are often associated with adverse effects to other tissues and organs; it remains challenging to predict the effective concentration needed at an injured nerve and the appropriate delivery strategy. Local drug delivery approaches are being developed to mitigate this, for example via injections or biomaterial-mediated release. We propose the integration of mathematical modeling into the development of local drug delivery protocols for peripheral nerve injury repair. Mathematical models have the potential to inform understanding of the different transport mechanisms at play, as well as quantitative predictions around the efficacy of individual local delivery protocols. We discuss existing approaches in the literature, including drawing from other research fields, and present a process for taking forward an integrated mathematical-experimental approach to accelerate local drug delivery approaches for peripheral nerve injury repair. This article is categorized under: Neurological Diseases > Molecular and Cellular Physiology Neurological Diseases > Computational Models Neurological Diseases > Biomedical Engineering.
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Affiliation(s)
- Simao Laranjeira
- UCL Mechanical EngineeringUCL Centre for Nerve EngineeringLondonLondonUK
| | | | - James B. Phillips
- UCL School of PharmacyUCL Centre for Nerve EngineeringLondonLondonUK
| | - Rebecca J. Shipley
- UCL Mechanical EngineeringUCL Centre for Nerve EngineeringLondonLondonUK
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