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Jayathungage Don TD, Safaei S, Maso Talou GD, Russell PS, Phillips ARJ, Reynolds HM. Computational fluid dynamic modeling of the lymphatic system: a review of existing models and future directions. Biomech Model Mechanobiol 2024; 23:3-22. [PMID: 37902894 PMCID: PMC10901951 DOI: 10.1007/s10237-023-01780-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 10/02/2023] [Indexed: 11/01/2023]
Abstract
Historically, research into the lymphatic system has been overlooked due to both a lack of knowledge and limited recognition of its importance. In the last decade however, lymphatic research has gained substantial momentum and has included the development of a variety of computational models to aid understanding of this complex system. This article reviews existing computational fluid dynamic models of the lymphatics covering each structural component including the initial lymphatics, pre-collecting and collecting vessels, and lymph nodes. This is followed by a summary of limitations and gaps in existing computational models and reasons that development in this field has been hindered to date. Over the next decade, efforts to further characterize lymphatic anatomy and physiology are anticipated to provide key data to further inform and validate lymphatic fluid dynamic models. Development of more comprehensive multiscale- and multi-physics computational models has the potential to significantly enhance the understanding of lymphatic function in both health and disease.
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Affiliation(s)
| | - Soroush Safaei
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Gonzalo D Maso Talou
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Peter S Russell
- School of Biological Sciences, The University of Auckland, Auckland, New Zealand
- Surgical and Translational Research Centre, Department of Surgery, Faculty of Medical and Health Sciences, The University of Auckland, Auckland, New Zealand
| | - Anthony R J Phillips
- School of Biological Sciences, The University of Auckland, Auckland, New Zealand
- Surgical and Translational Research Centre, Department of Surgery, Faculty of Medical and Health Sciences, The University of Auckland, Auckland, New Zealand
| | - Hayley M Reynolds
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand.
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Gyllingberg L, Birhane A, Sumpter DJT. The lost art of mathematical modelling. Math Biosci 2023:109033. [PMID: 37257641 DOI: 10.1016/j.mbs.2023.109033] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Revised: 05/24/2023] [Accepted: 05/24/2023] [Indexed: 06/02/2023]
Abstract
We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of an pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.
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Affiliation(s)
| | - Abeba Birhane
- Mozilla Foundation, 2 Harrison Street, Suite 175, San Francisco, CA 94105, USA
| | - David J T Sumpter
- Department of Information Technology, Uppsala University, Box 337, Uppsala, SE-751 05, Sweden.
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Shahidi N, Pan M, Tran K, Crampin EJ, Nickerson DP. SBML to bond graphs: From conversion to composition. Math Biosci 2022; 352:108901. [PMID: 36096376 DOI: 10.1016/j.mbs.2022.108901] [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: 05/29/2022] [Revised: 08/15/2022] [Accepted: 09/05/2022] [Indexed: 11/29/2022]
Abstract
The Systems Biology Markup Language (SBML) is a popular software-independent XML-based format for describing models of biological phenomena. The BioModels Database is the largest online repository of SBML models. Several tools and platforms are available to support the reuse and composition of SBML models. However, these tools do not explicitly assess whether models are physically plausible or thermodynamically consistent. This often leads to ill-posed models that are physically impossible, impeding the development of realistic complex models in biology. Here, we present a framework that can automatically convert SBML models into bond graphs, which imposes energy conservation laws on these models. The new bond graph models are easily mergeable, resulting in physically plausible coupled models. We illustrate this by automatically converting and coupling a model of pyruvate distribution to a model of the pentose phosphate pathway.
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Affiliation(s)
- Niloofar Shahidi
- Auckland Bioengineering Institute, University of Auckland, Auckland, 1010, New Zealand.
| | - Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, 3010, Victoria, Australia; School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Melbourne, 3010, Victoria, Australia
| | - Kenneth Tran
- Auckland Bioengineering Institute, University of Auckland, Auckland, 1010, New Zealand
| | - Edmund J Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Melbourne, 3010, Victoria, Australia; School of Mathematics and Statistics, Faculty of Science, University of Melbourne, Melbourne, 3010, Victoria, Australia; ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Faculty of Engineering and Information Technology, University of Melbourne, Melbourne, 3010, Victoria, Australia; School of Medicine, University of Melbourne, Melbourne, 3010, Victoria, Australia
| | - David P Nickerson
- Auckland Bioengineering Institute, University of Auckland, Auckland, 1010, New Zealand
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Gawthrop PJ, Pan M. Network thermodynamics of biological systems: A bond graph approach. Math Biosci 2022; 352:108899. [PMID: 36057321 DOI: 10.1016/j.mbs.2022.108899] [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: 05/04/2022] [Revised: 08/26/2022] [Accepted: 08/26/2022] [Indexed: 10/14/2022]
Abstract
Edmund Crampin (1973-2021) was at the forefront of Systems Biology research and his work will influence the field for years to come. This paper brings together and summarises the seminal work of his group in applying energy-based bond graph methods to biological systems. In particular, this paper: (a) motivates the need to consider energy in modelling biology; (b) introduces bond graphs as a methodology for achieving this; (c) describes extensions to modelling electrochemical transduction; (d) outlines how bond graph models can be constructed in a modular manner and (e) describes stoichiometric approaches to deriving fundamental properties of reaction networks. These concepts are illustrated using a new bond graph model of photosynthesis in chloroplasts.
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Affiliation(s)
- Peter J Gawthrop
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Victoria 3010, Australia.
| | - Michael Pan
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Victoria 3010, Australia; School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
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