1
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Henley L, Finch D, Mathews F, Jones O, Woolley TE. A simple and fast method for estimating bat roost locations. ROYAL SOCIETY OPEN SCIENCE 2024; 11:231999. [PMID: 38660598 PMCID: PMC11040240 DOI: 10.1098/rsos.231999] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Revised: 03/04/2024] [Accepted: 03/05/2024] [Indexed: 04/26/2024]
Abstract
Bats play a pivotal role in pest control, pollination and seed dispersal. Despite their ecological significance, locating bat roosts remains a challenging task for ecologists. Traditional field surveys are time-consuming, expensive and may disturb sensitive bat populations. In this article, we combine data from static audio detectors with a bat movement model to facilitate the detection of bat roosts. Crucially, our technique not only provides a point prediction for the most likely location of a bat roost, but because of the algorithm's speed, it can be applied over an entire landscape, resulting in a likelihood map, which provides optimal searching regions. To illustrate the success of the algorithm and highlight limitations, we apply our technique to greater horseshoe bat (Rhinolophus ferrumequinum) acoustic data acquired from six surveys from four different UK locations and over six different times in the year. Furthermore, we investigate what happens to the accuracy of our predictions in the case that the roost is not contained within the area spanned by the detectors. This innovative approach to searching rural environments holds the potential to greatly reduce the labour required for roost finding, and, hence, enhance the conservation efforts of bat populations and their habitats.
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Affiliation(s)
- Lucy Henley
- Cardiff School of Mathematics, Cardiff University, CardiffCF24 4AG, UK
| | - Domhnall Finch
- University of Sussex, John Maynard Smith Building, BrightonBN1 9RH, UK
- National Parks and Wildlife Service, North DublinD07 N7CV, Ireland
| | - Fiona Mathews
- University of Sussex, John Maynard Smith Building, BrightonBN1 9RH, UK
| | - Owen Jones
- Cardiff School of Mathematics, Cardiff University, CardiffCF24 4AG, UK
| | - Thomas E. Woolley
- Cardiff School of Mathematics, Cardiff University, CardiffCF24 4AG, UK
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2
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Henley L, Jones O, Mathews F, Woolley TE. Bat Motion can be Described by Leap Frogging. Bull Math Biol 2024; 86:16. [PMID: 38197980 PMCID: PMC10781826 DOI: 10.1007/s11538-023-01233-5] [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: 07/17/2023] [Accepted: 11/01/2023] [Indexed: 01/11/2024]
Abstract
We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our model to include non-autonomous parameters, or a leap frogging form of motion, where bats on the exterior move back first, we find we are able to accurately capture the bat's motion. We discuss ways of distinguishing between the two movement descriptions and, finally, consider how the different motion descriptions would impact a bat's hunting strategy.
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Affiliation(s)
- Lucy Henley
- Cardiff School of Mathematics Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK
| | - Owen Jones
- Cardiff School of Mathematics Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK
| | - Fiona Mathews
- University of Sussex, John Maynard Smith Building, Falmer, Brighton, BN1 9RH, UK
| | - Thomas E Woolley
- Cardiff School of Mathematics Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK.
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3
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Jørgensen ACS, Hill CS, Sturrock M, Tang W, Karamched SR, Gorup D, Lythgoe MF, Parrinello S, Marguerat S, Shahrezaei V. Data-driven spatio-temporal modelling of glioblastoma. ROYAL SOCIETY OPEN SCIENCE 2023; 10:221444. [PMID: 36968241 PMCID: PMC10031411 DOI: 10.1098/rsos.221444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 02/23/2023] [Indexed: 06/18/2023]
Abstract
Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.
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Affiliation(s)
| | - Ciaran Scott Hill
- Department of Neurosurgery, The National Hospital for Neurology and Neurosurgery, London WC1N 3BG, UK
- Samantha Dickson Brain Cancer Unit, UCL Cancer Institute, London WC1E 6DD, UK
| | - Marc Sturrock
- Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin D02 YN77, Ireland
| | - Wenhao Tang
- Department of Mathematics, Faculty of Natural Sciences, Imperial College London, London SW7 2AZ, UK
| | - Saketh R. Karamched
- Division of Medicine, Centre for Advanced Biomedical Imaging, University College London (UCL), London WC1E 6BT, UK
| | - Dunja Gorup
- Division of Medicine, Centre for Advanced Biomedical Imaging, University College London (UCL), London WC1E 6BT, UK
| | - Mark F. Lythgoe
- Division of Medicine, Centre for Advanced Biomedical Imaging, University College London (UCL), London WC1E 6BT, UK
| | - Simona Parrinello
- Samantha Dickson Brain Cancer Unit, UCL Cancer Institute, London WC1E 6DD, UK
| | - Samuel Marguerat
- Genomics Translational Technology Platform, UCL Cancer Institute, University College London, London WC1E 6DD, UK
| | - Vahid Shahrezaei
- Department of Mathematics, Faculty of Natural Sciences, Imperial College London, London SW7 2AZ, UK
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4
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Woolley TE, Hill W, Hogan C. Accounting for dimensional differences in stochastic domain invasion with applications to precancerous cell removal. J Theor Biol 2022; 541:111024. [PMID: 35108550 DOI: 10.1016/j.jtbi.2022.111024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Revised: 01/06/2022] [Accepted: 01/10/2022] [Indexed: 11/26/2022]
Abstract
We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, highlighting unforeseen nonlinear dependencies on the dimension of the solution domain. Specifically, stochastically simulated populations invade with a dimension dependent wave speed that can be over twice as fast as their deterministic analogues. Although the wave speed can be analytically derived in the cases of small domains, the probabilistic state space grows exponentially and, thus, we use numeric simulation and curve fitting to predict limiting dynamics.
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Affiliation(s)
- Thomas E Woolley
- Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK.
| | - William Hill
- Cancer Evolution and Genome Instability Laboratory, The Francis Crick Institute, London, NW1 1AT, UK; European Cancer Stem Cell Research Institute, School of Biosciences, Cardiff University, Hadyn Ellis Building, Maindy Road, Cardiff, CF24 4HQ, UK
| | - Catherine Hogan
- European Cancer Stem Cell Research Institute, School of Biosciences, Cardiff University, Hadyn Ellis Building, Maindy Road, Cardiff, CF24 4HQ, UK
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5
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Krause AL, Gaffney EA, Maini PK, Klika V. Modern perspectives on near-equilibrium analysis of Turing systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200268. [PMID: 34743603 PMCID: PMC8580451 DOI: 10.1098/rsta.2020.0268] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/18/2021] [Indexed: 05/02/2023]
Abstract
In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
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Affiliation(s)
- Andrew L. Krause
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
- Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Rd, Durham DH1 3LE, UK
| | - Eamonn A. Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Philip K. Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Václav Klika
- Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova, 13, 12000 Praha, Czech Republic
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6
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Suarez-Berumen K, Collins-Hooper H, Gromova A, Meech R, Sacco A, Dash PR, Mitchell R, Shestopalov VI, Woolley TE, Vaiyapuri S, Patel K, Makarenkova HP. Pannexin 1 Regulates Skeletal Muscle Regeneration by Promoting Bleb-Based Myoblast Migration and Fusion Through a Novel Lipid Based Signaling Mechanism. Front Cell Dev Biol 2021; 9:736813. [PMID: 34676213 PMCID: PMC8523994 DOI: 10.3389/fcell.2021.736813] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 09/13/2021] [Indexed: 12/12/2022] Open
Abstract
Adult skeletal muscle has robust regenerative capabilities due to the presence of a resident stem cell population called satellite cells. Muscle injury leads to these normally quiescent cells becoming molecularly and metabolically activated and embarking on a program of proliferation, migration, differentiation, and fusion culminating in the repair of damaged tissue. These processes are highly coordinated by paracrine signaling events that drive cytoskeletal rearrangement and cell-cell communication. Pannexins are a family of transmembrane channel proteins that mediate paracrine signaling by ATP release. It is known that Pannexin1 (Panx1) is expressed in skeletal muscle, however, the role of Panx1 during skeletal muscle development and regeneration remains poorly understood. Here we show that Panx1 is expressed on the surface of myoblasts and its expression is rapidly increased upon induction of differentiation and that Panx1-/- mice exhibit impaired muscle regeneration after injury. Panx1-/- myoblasts activate the myogenic differentiation program normally, but display marked deficits in migration and fusion. Mechanistically, we show that Panx1 activates P2 class purinergic receptors, which in turn mediate a lipid signaling cascade in myoblasts. This signaling induces bleb-driven amoeboid movement that in turn supports myoblast migration and fusion. Finally, we show that Panx1 is involved in the regulation of cell-matrix interaction through the induction of ADAMTS (Disintegrin-like and Metalloprotease domain with Thrombospondin-type 5) proteins that help remodel the extracellular matrix. These studies reveal a novel role for lipid-based signaling pathways activated by Panx1 in the coordination of myoblast activities essential for skeletal muscle regeneration.
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Affiliation(s)
- Katia Suarez-Berumen
- Department of Molecular Medicine, The Scripps Research Institute, La Jolla, CA, United States.,West Anaheim Medical Center, Anaheim, CA, United States
| | | | - Anastasia Gromova
- Department of Molecular Medicine, The Scripps Research Institute, La Jolla, CA, United States.,Development, Aging and Regeneration Program, Center for Genetic Disorders and Aging Research, Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA, United States
| | - Robyn Meech
- Department of Clinical Pharmacology, Flinders University, Adelaide, SA, Australia
| | - Alessandra Sacco
- Development, Aging and Regeneration Program, Center for Genetic Disorders and Aging Research, Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA, United States
| | - Phil R Dash
- School of Biological Sciences, University of Reading, Reading, United Kingdom
| | - Robert Mitchell
- School of Biological Sciences, University of Reading, Reading, United Kingdom
| | - Valery I Shestopalov
- Bascom Palmer Eye Institute, University of Miami School of Medicine, Miami, FL, United States.,Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
| | - Thomas E Woolley
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | | | - Ketan Patel
- School of Biological Sciences, University of Reading, Reading, United Kingdom
| | - Helen P Makarenkova
- Department of Molecular Medicine, The Scripps Research Institute, La Jolla, CA, United States
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7
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Chulián S, Martinez-Rubio Á, Gandarias ML, Rosa M. Lie point symmetries for generalised Fisher's equations describing tumour dynamics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:3291-3312. [PMID: 34198386 DOI: 10.3934/mbe.2021164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem for both applied mathematics and physics. Multiple integration methods have been developed to the day to solve particular types of differential equations, specially those focused on physical or biological phenomena. In this work, we review several applications of the Lie method to obtain solutions of reaction-diffusion equations describing cell dynamics and tumour invasion.
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Affiliation(s)
- Salvador Chulián
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
| | - Álvaro Martinez-Rubio
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
| | | | - María Rosa
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
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8
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Krause AL, Klika V, Woolley TE, Gaffney EA. From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ. J R Soc Interface 2020; 17:20190621. [PMID: 31937231 DOI: 10.1098/rsif.2019.0621] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction-diffusion system, and derive conditions for instability which are local versions of the classical Turing conditions. We find that the structure of unstable modes differs substantially from the typical trigonometric functions seen in the spatially homogeneous setting. Modes of different growth rates are localized to different spatial regions. This localization helps explain common amplitude modulations observed in simulations of Turing systems in heterogeneous settings. We numerically demonstrate this theory, giving an illustrative example of the emergent instabilities and the striking complexity arising from spatially heterogeneous reaction-diffusion systems. Our results give insight both into systems driven by exogenous heterogeneity, as well as successive pattern forming processes, noting that most scenarios in biology do not involve symmetry breaking from homogeneity, but instead consist of sequential evolutions of heterogeneous states. The instability mechanism reported here precisely captures such evolution, and extends Turing's original thesis to a far wider and more realistic class of systems.
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Affiliation(s)
- Andrew L Krause
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Václav Klika
- Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
| | - Thomas E Woolley
- Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
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9
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Budia I, Alvarez-Arenas A, Woolley TE, Calvo GF, Belmonte-Beitia J. Radiation protraction schedules for low-grade gliomas: a comparison between different mathematical models. J R Soc Interface 2019; 16:20190665. [PMID: 31822220 DOI: 10.1098/rsif.2019.0665] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
We optimize radiotherapy (RT) administration strategies for treating low-grade gliomas. Specifically, we consider different tumour growth laws, both with and without spatial effects. In each scenario, we find the optimal treatment in the sense of maximizing the overall survival time of a virtual low-grade glioma patient, whose tumour progresses according to the examined growth laws. We discover that an extreme protraction therapeutic strategy, which amounts to substantially extending the time interval between RT sessions, may lead to better tumour control. The clinical implications of our results are also presented.
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Affiliation(s)
- I Budia
- Department of Mathematics and MôLAB-Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - A Alvarez-Arenas
- Department of Mathematics and MôLAB-Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - T E Woolley
- School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
| | - G F Calvo
- Department of Mathematics and MôLAB-Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - J Belmonte-Beitia
- Department of Mathematics and MôLAB-Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
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10
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Debussche A, Nguepedja Nankep MJ. A Law of Large Numbers in the Supremum Norm for a Multiscale Stochastic Spatial Gene Network. Int J Biostat 2019; 15:ijb-2017-0091. [DOI: 10.1515/ijb-2017-0091] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2017] [Accepted: 04/10/2019] [Indexed: 11/15/2022]
Abstract
Abstract
We study the asymptotic behavior of multiscale stochastic spatial gene networks. Multiscaling takes into account the difference of abundance between molecules, and captures the dynamic of rare species at a mesoscopic level. We introduce an assumption of spatial correlations for reactions involving rare species and a new law of large numbers is obtained. According to the scales, the whole system splits into two parts with different but coupled dynamics. The high scale component converges to the usual spatial model which is the solution of a partial differential equation, whereas the low scale component converges to the usual homogeneous model which is the solution of an ordinary differential equation. Comparisons are made in the supremum norm.
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Affiliation(s)
- Arnaud Debussche
- Institut de Recherche Mathematique de Rennes , Rennes , Bretagne , France
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11
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Yurk BP, Cobbold CA. Homogenization techniques for population dynamics in strongly heterogeneous landscapes. JOURNAL OF BIOLOGICAL DYNAMICS 2018; 12:171-193. [PMID: 29228877 DOI: 10.1080/17513758.2017.1410238] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Accepted: 11/17/2017] [Indexed: 06/07/2023]
Abstract
An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction-diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic environment. We find that population persistence and the large-scale population carrying capacity is influenced by patch residence times that depend on patch preference, as well as movement rates in adjacent patches. The forms of the homogenized coefficients yield key theoretical insights into how large-scale dynamics arise from the small-scale features.
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Affiliation(s)
- Brian P Yurk
- a Department of Mathematics , Hope College , Holland , MI , USA
| | - Christina A Cobbold
- b School of Mathematics and Statistics , University of Glasgow , Glasgow , UK
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12
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Rockne RC, Adhikarla V, Tsaturyan L, Li Z, Masihi MB, Aboody KS, Barish ME, Gutova M. Long-term stability and computational analysis of migration patterns of L-MYC immortalized neural stem cells in the brain. PLoS One 2018; 13:e0199967. [PMID: 30071048 PMCID: PMC6071994 DOI: 10.1371/journal.pone.0199967] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Accepted: 06/18/2018] [Indexed: 12/23/2022] Open
Abstract
Background Preclinical studies indicate that neural stem cells (NSCs) can limit or reverse central nervous system (CNS) damage through delivery of therapeutic agents for cell regeneration. Clinical translation of cell-based therapies raises concerns about long-term stability, differentiation and fate, and absence of tumorigenicity of these cells, as well as manufacturing time required to produce therapeutic cells in quantities sufficient for clinical use. Allogeneic NSC lines are in growing demand due to challenges inherent in using autologous stem cells, including production costs that limit availability to patients. Methods/Principal findings We demonstrate the long-term stability of L-MYC immortalized human NSCs (LM-NSC008) cells in vivo, including engraftment, migration, and absence of tumorigenicity in mouse brains for up to nine months. We also examined the distributions of engrafted LM-NSC008 cells within brain, and present computational techniques to analyze NSC migration characteristics in relation to intrinsic brain structures. Conclusions/Significance This computational analysis of NSC distributions following implantation provides proof-of-concept for the development of computational models that can be used clinically to predict NSC migration paths in patients. Previously, models of preferential migration of malignant tumor cells along white matter tracts have been used to predict their final distributions. We suggest that quantitative measures of tissue orientation and white matter tracts determined from MR images can be used in a diffusion tensor imaging tractography-like approach to describe the most likely migration routes and final distributions of NSCs administered in a clinical setting. Such a model could be very useful in choosing the optimal anatomical locations for NSC administration to patients to achieve maximum therapeutic effects.
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Affiliation(s)
- Russell C. Rockne
- Department of Information Sciences, Division of Mathematical Oncology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
| | - Vikram Adhikarla
- Department of Information Sciences, Division of Mathematical Oncology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
| | - Lusine Tsaturyan
- Department of Developmental and Stem Cell Biology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
| | - Zhongqi Li
- Department of Developmental and Stem Cell Biology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
| | - Meher B. Masihi
- Department of Developmental and Stem Cell Biology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
| | - Karen S. Aboody
- Department of Developmental and Stem Cell Biology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
| | - Michael E. Barish
- Department of Developmental and Stem Cell Biology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
| | - Margarita Gutova
- Department of Developmental and Stem Cell Biology, Beckman Research Institute of City of Hope, Duarte, California, United States of America
- * E-mail:
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13
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Massey SC, Rockne RC, Hawkins-Daarud A, Gallaher J, Anderson ARA, Canoll P, Swanson KR. Simulating PDGF-Driven Glioma Growth and Invasion in an Anatomically Accurate Brain Domain. Bull Math Biol 2017; 80:1292-1309. [PMID: 28842831 DOI: 10.1007/s11538-017-0312-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2016] [Accepted: 06/16/2017] [Indexed: 10/19/2022]
Abstract
Gliomas are the most common of all primary brain tumors. They are characterized by their diffuse infiltration of the brain tissue and are uniformly fatal, with glioblastoma being the most aggressive form of the disease. In recent years, the over-expression of platelet-derived growth factor (PDGF) has been shown to produce tumors in experimental rodent models that closely resemble this human disease, specifically the proneural subtype of glioblastoma. We have previously modeled this system, focusing on the key attribute of these experimental tumors-the "recruitment" of oligodendroglial progenitor cells (OPCs) to participate in tumor formation by PDGF-expressing retrovirally transduced cells-in one dimension, with spherical symmetry. However, it has been observed that these recruitable progenitor cells are not uniformly distributed throughout the brain and that tumor cells migrate at different rates depending on the material properties in different regions of the brain. Here we model the differential diffusion of PDGF-expressing and recruited cell populations via a system of partial differential equations with spatially variable diffusion coefficients and solve the equations in two spatial dimensions on a mouse brain atlas using a flux-differencing numerical approach. Simulations of our in silico model demonstrate qualitative agreement with the observed tumor distribution in the experimental animal system. Additionally, we show that while there are higher concentrations of OPCs in white matter, the level of recruitment of these plays little role in the appearance of "white matter disease," where the tumor shows a preponderance for white matter. Instead, simulations show that this is largely driven by the ratio of the diffusion rate in white matter as compared to gray. However, this ratio has less effect on the speed of tumor growth than does the degree of OPC recruitment in the tumor. It was observed that tumor simulations with greater degrees of recruitment grow faster and develop more nodular tumors than if there is no recruitment at all, similar to our prior results from implementing our model in one dimension. Combined, these results show that recruitment remains an important consideration in understanding and slowing glioma growth.
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Affiliation(s)
- Susan Christine Massey
- Precision Neurotherapeutics Innovation Program, Mayo Clinic, 5777 E Mayo Blvd, Phoenix, AZ, 85054, USA.
| | - Russell C Rockne
- Division of Mathematical Oncology, Department of Information Sciences, City of Hope, Duarte, CA, USA
| | - Andrea Hawkins-Daarud
- Precision Neurotherapeutics Innovation Program, Mayo Clinic, 5777 E Mayo Blvd, Phoenix, AZ, 85054, USA
| | - Jill Gallaher
- Integrative Mathematical Oncology, Moffitt Cancer Research Center, Tampa, FL, USA
| | | | - Peter Canoll
- Division of Neuropathology, Department of Pathology and Cell Biology, Columbia University School of Medicine, New York, NY, USA
| | - Kristin R Swanson
- Precision Neurotherapeutics Innovation Program, Mayo Clinic, 5777 E Mayo Blvd, Phoenix, AZ, 85054, USA
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A Patient-Specific Anisotropic Diffusion Model for Brain Tumour Spread. Bull Math Biol 2017; 80:1259-1291. [DOI: 10.1007/s11538-017-0271-8] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2016] [Accepted: 03/15/2017] [Indexed: 02/01/2023]
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Kaznatcheev A, Scott JG, Basanta D. Edge effects in game-theoretic dynamics of spatially structured tumours. J R Soc Interface 2016; 12:20150154. [PMID: 26040596 DOI: 10.1098/rsif.2015.0154] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Cancer dynamics are an evolutionary game between cellular phenotypes. A typical assumption in this modelling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard for local neighbourhood structure. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go versus grow game. We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary--such as a blood vessel, organ capsule or basement membrane--we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (epithelial-mesenchymal transition-positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Our results caution that pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. Although we concentrate on applications in mathematical oncology, we expect our approach to extend to other evolutionary game models where interaction neighbourhoods change at fixed system boundaries.
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Affiliation(s)
- Artem Kaznatcheev
- School of Computer Science and Department of Psychology, McGill University, Montreal, Quebec, Canada Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Jacob G Scott
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK
| | - David Basanta
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
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Bengfort M, Malchow H, Hilker FM. The Fokker-Planck law of diffusion and pattern formation in heterogeneous environments. J Math Biol 2016; 73:683-704. [PMID: 26803768 DOI: 10.1007/s00285-016-0966-8] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2015] [Revised: 11/12/2015] [Indexed: 11/29/2022]
Abstract
We analyze the influence of spatially inhomogeneous diffusion on several common ecological problems. Diffusion is modeled with Fick's law and the Fokker-Planck law of diffusion. We discuss the differences between the two formalisms and when to use either the one or the other. In doing so, we start with a pure diffusion equation, then turn to a reaction-diffusion system with one logistically growing component which invades the spatial domain. We also look at systems of two reacting components, namely a trimolecular oscillating chemical model system and an excitable predator-prey model. Contrary to Fickian diffusion, spatial inhomogeneities promote spatial and spatiotemporal pattern formation in case of Fokker-Planck diffusion.
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Affiliation(s)
- Michael Bengfort
- Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany.
| | - Horst Malchow
- Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany
| | - Frank M Hilker
- Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076, Osnabrück, Germany
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The “edge effect” phenomenon: deriving population abundance patterns from individual animal movement decisions. THEOR ECOL-NETH 2015. [DOI: 10.1007/s12080-015-0283-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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