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Dyck C, Isaac KV, Edelstein-Keshet L. Models for Implant-Induced Capsular Contracture Post Breast Cancer Surgery. Bull Math Biol 2023; 86:7. [PMID: 38091110 PMCID: PMC10719149 DOI: 10.1007/s11538-023-01236-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 11/09/2023] [Indexed: 12/17/2023]
Abstract
Capsular contracture is a painful deformation of scar-tissue that may form around an implant in post-breast cancer reconstruction or cosmetic surgery. Inflammation due to surgical trauma or contamination in the tissue around the implant could account for recruitment of immune cells, and transdifferentiation of resident fibroblasts into cells that deposit abnormally thick collagen. Here we examine this hypothesis using a mathematical model for interacting macrophages, fibroblasts, myofibroblasts, and collagen. Our model demonstrates that cellular response can, together with inflammatory cell recruitment, account for prognoses.
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Affiliation(s)
- Cheryl Dyck
- Insight Math Unincorporated, Port Moody, BC, Canada
| | - Kathryn V Isaac
- Department of Surgery, Faculty of Medicine, University of British Columbia, Vancouver, BC, Canada
| | - Leah Edelstein-Keshet
- Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada.
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2
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Egberts G, Vermolen F, van Zuijlen P. Stability of a two-dimensional biomorphoelastic model for post-burn contraction. J Math Biol 2023; 86:59. [PMID: 36964257 PMCID: PMC10038978 DOI: 10.1007/s00285-023-01893-w] [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: 10/11/2022] [Revised: 02/24/2023] [Accepted: 02/27/2023] [Indexed: 03/26/2023]
Abstract
We consider the stability analysis of a two-dimensional model for post-burn contraction. The model is based on morphoelasticity for permanent deformations and combined with a chemical-biological model that incorporates cellular densities, collagen density, and the concentration of chemoattractants. We formulate stability conditions depending on the decay rate of signaling molecules for both the continuous partial differential equations-based problem and the (semi-)discrete representation. We analyze the difference and convergence between the resulting spatial eigenvalues from the continuous and semi-discrete problems.
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Affiliation(s)
- Ginger Egberts
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
- Research Group Computational Mathematics (CMAT), Department of Mathematics and Statistics, University of Hasselt, Hasselt, Belgium.
| | - Fred Vermolen
- Research Group Computational Mathematics (CMAT), University of Hasselt, Hasselt, Belgium
- Data Science Institute (DSI), University of Hasselt, Hasselt, Belgium
| | - Paul van Zuijlen
- Burn Centre and Department of Plastic, Reconstructive and Hand Surgery, Red Cross Hospital, Beverwijk, The Netherlands
- Department of Plastic, Reconstructive and Hand Surgery, Amsterdam UMC, location VUmc, Amsterdam Movement Sciences, Amsterdam, The Netherlands
- Pediatric Surgical Centre, Emma Children's Hospital, Amsterdam UMC, location AMC and VUmc, Amsterdam, The Netherlands
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3
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Egberts G, Desmoulière A, Vermolen F, van Zuijlen P. Sensitivity of a two-dimensional biomorphoelastic model for post-burn contraction. Biomech Model Mechanobiol 2023; 22:105-121. [PMID: 36229698 PMCID: PMC9957927 DOI: 10.1007/s10237-022-01634-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 09/05/2022] [Indexed: 11/02/2022]
Abstract
We consider a two-dimensional biomorphoelastic model describing post-burn scar contraction. This model describes skin displacement and the development of the effective Eulerian strain in the tissue. Besides these mechanical components, signaling molecules, fibroblasts, myofibroblasts, and collagen also play a significant role in the model. We perform a sensitivity analysis for the independent parameters of the model and focus on the effects on features of the relative surface area and the total strain energy density. We conclude that the most sensitive parameters are the Poisson's ratio, the equilibrium collagen concentration, the contraction inhibitor constant, and the myofibroblast apoptosis rate. Next to these insights, we perform a sensitivity analysis where the proliferation rates of fibroblasts and myofibroblasts are not the same. The impact of this model adaptation is significant.
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Affiliation(s)
- Ginger Egberts
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands. .,Research Group Computational Mathematics (CMAT), Department of Mathematics and Statistics, University of Hasselt, Hasselt, Belgium.
| | - Alexis Desmoulière
- grid.9966.00000 0001 2165 4861Department of Physiology, and EA 6309, Faculty of Pharmacy, University of Limoges, Limoges, France
| | - Fred Vermolen
- grid.12155.320000 0001 0604 5662Research Group Computational Mathematics (CMAT), Department of Mathematics and Statistics, University of Hasselt, Hasselt, Belgium
| | - Paul van Zuijlen
- grid.415746.50000 0004 0465 7034Burn Centre and Department of Plastic, Reconstructive and Hand Surgery, Red Cross Hospital, Beverwijk, The Netherlands ,grid.509540.d0000 0004 6880 3010Department of Plastic, Reconstructive and Hand Surgery, Amsterdam UMC, location VUmc, Amsterdam Movement Sciences, Amsterdam, The Netherlands ,grid.5650.60000000404654431Pediatric Surgical Centre, Emma Children’s Hospital, Amsterdam UMC, location AMC and VUmc, Amsterdam, The Netherlands
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4
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van Zuijlen PPM, Korkmaz HI, Sheraton VM, Haanstra TM, Pijpe A, de Vries A, van der Vlies CH, Bosma E, de Jong E, Middelkoop E, Vermolen FJ, Sloot PMA. The future of burn care from a complexity science perspective. J Burn Care Res 2022; 43:1312-1321. [PMID: 35267022 DOI: 10.1093/jbcr/irac029] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Healthcare is undergoing a profound technological and digital transformation and has become increasingly complex. It is important for burns professionals and researchers to adapt to these developments which may require new ways of thinking and subsequent new strategies. As Einstein has put it: 'We must learn to see the world anew'. The relatively new scientific discipline "Complexity science" can give more direction to this and is the metaphorical open door that should not go unnoticed in view of the burn care of the future. Complexity sciences studies 'why the whole is more than the sum of the parts'. It studies how multiple separate components interact with each other and their environment and how these interactions lead to 'behavior of the system'. Biological systems are always part of smaller and larger systems and exhibit the behavior of adaptivity, hence the name complex adaptive systems. From the perspective of complexity science, a severe burn injury is an extreme disruption of the 'human body system'. But this disruption also applies to the systems at the organ and cellular level. All these systems follow principles of complex systems. Awareness of the scaling process at multilevel helps to understand and manage the complex situation when dealing with severe burn cases. The aim of this paper is to create awareness of the concept of complexity and to demonstrate the value and possibilities of complexity science methods and tools for the future of burn care through examples from preclinical, clinical, and organizational perspective in burn care.
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Affiliation(s)
- Paul P M van Zuijlen
- Burn Center, Red Cross Hospital, Beverwijk, The Netherlands.,Department of Plastic and Reconstructive Surgery, Red Cross Hospital, Beverwijk, The Netherlands.,Department of Plastic Reconstructive and Hand Surgery, Amsterdam Movement Sciences (AMS) Institute, Amsterdam UMC, Location VUmc, Amsterdam, The Netherlands.,Paediatric Surgical Centre, Emma Children's Hospital, Amsterdam UMC, location AMC, Amsterdam, The Netherlands
| | - H Ibrahim Korkmaz
- Burn Center, Red Cross Hospital, Beverwijk, The Netherlands.,Department of Plastic Reconstructive and Hand Surgery, Amsterdam Movement Sciences (AMS) Institute, Amsterdam UMC, Location VUmc, Amsterdam, The Netherlands.,Department of Molecular Cell Biology and Immunology, Amsterdam UMC, Location VUmc, Amsterdam, The Netherlands.,Association of Dutch Burn Centres (ADBC), Beverwijk, The Netherlands
| | - Vivek M Sheraton
- Institute for Advanced Study, University of Amsterdam, Amsterdam, The Netherlands
| | | | - Anouk Pijpe
- Burn Center, Red Cross Hospital, Beverwijk, The Netherlands
| | - Annebeth de Vries
- Burn Center, Red Cross Hospital, Beverwijk, The Netherlands.,Paediatric Surgical Centre, Emma Children's Hospital, Amsterdam UMC, location AMC, Amsterdam, The Netherlands.,Department of Surgery, Red Cross Hospital, Beverwijk, The Netherlands
| | - Cornelis H van der Vlies
- Burn Centre, Maasstad Ziekenhuis, Rotterdam, The Netherlands.,Trauma Research Unit, Department of Surgery, Erasmus MC, University Medical Centre Rotterdam, Rotterdam, The Netherlands
| | - Eelke Bosma
- Burn Centre and Department of Surgery, Martini Ziekenhuis, Groningen, The Netherlands
| | - Evelien de Jong
- Burn Center, Red Cross Hospital, Beverwijk, The Netherlands.,Intensive Care Unit, Red Cross Hospital, Beverwijk, The Netherlands
| | - Esther Middelkoop
- Burn Center, Red Cross Hospital, Beverwijk, The Netherlands.,Department of Plastic Reconstructive and Hand Surgery, Amsterdam Movement Sciences (AMS) Institute, Amsterdam UMC, Location VUmc, Amsterdam, The Netherlands.,Association of Dutch Burn Centres (ADBC), Beverwijk, The Netherlands
| | - Fred J Vermolen
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.,Computational Mathematics, Hasselt University, Diepenbeek, Belgium
| | - Peter M A Sloot
- Institute for Advanced Study, University of Amsterdam, Amsterdam, The Netherlands.,Complexity Institute, Nanyang Technological University, Singapore.,ITMO University, Saint Petersburg, Russian Federation
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5
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Egberts G, Schaaphok M, Vermolen F, Zuijlen PV. A Bayesian finite-element trained machine learning approach for predicting post-burn contraction. Neural Comput Appl 2022; 34:8635-8642. [PMID: 35125668 PMCID: PMC8801043 DOI: 10.1007/s00521-021-06772-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 11/21/2021] [Indexed: 11/29/2022]
Abstract
Burn injuries can decrease the quality of life of a patient tremendously, because of esthetic reasons and because of contractions that result from them. In severe case, skin contraction takes place at such a large extent that joint mobility of a patient is significantly inhibited. In these cases, one refers to a contracture. In order to predict the evolution of post-wounding skin, several mathematical model frameworks have been set up. These frameworks are based on complicated systems of partial differential equations that need finite element-like discretizations for the approximation of the solution. Since these computational frameworks can be expensive in terms of computation time and resources, we study the applicability of neural networks to reproduce the finite element results. Our neural network is able to simulate the evolution of skin in terms of contraction for over one year. The simulations are based on 25 input parameters that are characteristic for the patient and the injury. One of such input parameters is the stiffness of the skin. The neural network results have yielded an average goodness of fit (\documentclass[12pt]{minimal}
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\begin{document}$$R^2$$\end{document}R2) of 0.9928 (± 0.0013). Further, a tremendous speed-up of 19354X was obtained with the neural network. We illustrate the applicability by an online medical App that takes into account the age of the patient and the length of the burn.
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Affiliation(s)
- Ginger Egberts
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
- Research Group Computational Mathematics(CMAT),Department of Mathematics and Statistics, University of Hasselt, Hasselt, Belgium
| | - Marianne Schaaphok
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
| | - Fred Vermolen
- Research Group Computational Mathematics(CMAT),Department of Mathematics and Statistics, University of Hasselt, Hasselt, Belgium
| | - Paul van Zuijlen
- Burn Centre and Department of Plastic,Reconstructive & Hand Surgery, Red Cross Hospital, Beverwijk, Netherlands
- Department of Plastic, Reconstructive & Hand Surgery, Amsterdam UMC, location VUmc, Amsterdam Movement Sciences, Amsterdam, The Netherlands
- Pediatric Surgical Centre, Emma Children’s Hospital, Amsterdam UMC, location AMC and VUmc, Amsterdam, Netherlands
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