Modelling, analysis and simulation of spatial patterning on evolving surfaces

Lead Research Organisation: University of Sussex
Department Name: Sch of Mathematical & Physical Sciences

Abstract

For many centuries, the problem of pattern formation has fascinated experimentalists and theoreticians alike. Understanding how spatial pattern arises during growth development is a central but still unresolved issue in developmental biology. It is clear that genes play a crucial role in embryology but the study of genetics alone cannot explain how the complex mechanical and chemical spatio-temporal signalling cues which determine cell fate are set up and regulated in the early embryo. These signals are a consequence of many nonlinear interactions and mathematical modelling and numerical computation have an important role to play in understanding and predicting the outcome of such complex interactions during growth development.

Several studies have shown that reaction-diffusion type models appear to be excellent for describing gross patterning behaviour in developmental biology. Since the seminal work of Turing in 1952, which showed that a system of reacting and diffusing chemical morphogens could evolve from an initially uniform spatial distribution to concentration profiles that vary spatially - a spatial pattern - many models have been proposed exploiting the generalised patterning principle of short-range activation, long-range inhibition elucidated by Meinhardt of which the Turing model is an example, and which in fact is common to many patterning paradigms based on different biological hypotheses. Turing's hypothesis was that one or more of the morphogens played the role of a signaling chemical, such that cell fate is determined by levels of morphogen concentration. Although invalid on stationary domains, our recent results prove that in the presence of domain growth, short-range inhibition, long-range activation as well as activator-activator mechanisms have the potential of giving rise to the formation of patterns only during growth development of the organism. These results offer us a unique opportunity to model, analyse and simulate new non-standard mechanisms for pattern formation on evolving surfaces, a largely unchartered research area. Furthermore, experimental biochemists are now able to design new experiments involving non-standard mechanisms to validate our theoretical predictions. This study offers to address one of the main objections to the Turing mechanism, namely that it operates only under very restrictive and biologically unrealistic conditions.

Hence, we propose to derive mathematical models, carry-out theoretical stability analysis and compute numerical solutions on realistic, geometrically accurate complex evolving surfaces as well as carrying-out applications in developmental biology and cell motility. More specifically we want to (a) derive models for pattern formation on evolving surfaces, (b) derive non-standard mechanisms capable of generating patterns only during surface evolution, (c) derive diffusion-driven instability conditions on evolving surfaces, (d) derive bifurcation theory to study partial differential equations on evolving domains and surfaces, (e) numerically compute solutions of the models and (f) to use biological, chemical and biomedical data to validate our theoretical predictions. The results obtained will have wider implications in the areas of developmental biology, cell motility, biomedicine, textiles, ecology, semiconductor physics, material science, hydrodynamics, astrophysics, chemistry, meteorology, economics, cancer biology, mathematics, numerical analysis as well as other non-traditional fields such as languages where such mechanisms are readily applicable. For examples, one could study (as competition models)the survival or extinction of languages due to migration where the inhabitants' environment continuously changes.

Planned Impact

The proposed research will impact four critical research areas: (i) modelling and analysis, (ii) numerical analysis, (iii) computations and (iv) applications to spatial pattern formation on evolving surfaces during growth development in developmental biology and to cell movement and deformation in cell motility. The derivation of the mathematical models in non-homogeneous environments on evolving surfaces will necessitate significant extension of prevailing mathematical techniques for analysing partial differential equations on evolving surfaces. Numerical analysis will benefit from the development of innovative numerical methods to solve the model equations on evolving surfaces. The surface finite element method is a natural candidate for solving partial differential equations on complex real-world evolving biological surfaces. On the other hand, particle methods coupled with generalised level set methods are perfect for treating splitting and reconnecting evolving surfaces; fundamental to understanding models for cell movement and deformation in cell motility.

The main impact of this proposal lies in its applications to biomedical, chemical and biological systems. For example, in cell motility, the modelling and simulations of cell movement will give rise to the possibility of experimentalists being able to introduce mutation within part of the cell population to study how it affects cell behaviour. For the first time, biochemists, bio-engineers and neurologists will be able to study how mutated cells behave in virtual experiments without the complications of in vivo experiments. On the other hand, it will be possible to predict cell population behaviour in the presence of obstacles on a substrate, as well as competition for food (prey).

In developmental biology, new insights on non-standard reaction kinetic models will offer experimentalists avenues to test in experiments the evolution of patterns only during growth development. Madzvamuse and his group have established collaborations with several experimentalists in developmental biology. Profs. Sekimura and Kondo in Japan will be able to test such hypotheses to study the emergence of patterns on evolving fish surfaces. Prof. Cheong's group in California is interested in models that could describe zebra stripe formation during growth development. Prof. Marle at IMPAS in Manaus Brazil has accumulated a huge amount of data on characterising chemical molecules that could be associated with Turing morphogens which could give rise to evolving patterns on the Brazilian Amazon fish known locally as Tambaqui.

The results of this research will be disseminated through: (i) Publications in peer-reviewed journals across the numerical analysis, mathematical and biological communities. (ii) Software packages will be uploaded to Madzvamuse's website which is accessible to the academic research community, either in the public sector, commercial private sector, third sector or the wider public in general. (iii) Delivery of lectures at conferences, seminars and workshops. (iv) Delivery of special seminars/presentations at public sector events such as the Brighton Science Festival or meetings between universities (public) and the private sector (industries).

The University of Sussex and the Medical Research Council, through the School of Mathematics and Physical Sciences has committed and recruited a 3.5-year DTA student to start work on atherosclerosis where reaction-diffusion equations describe the formation of carotid plaque during growth development. The PI (main advisor), the surgeon (Dr Jibawi) and the cardiologist (Dr Cheal), both at Sussex Hospitals, will co-supervise the student. This project has direct impact on modelling blood flow in arteries coupled with the formation of plaque as free moving boundaries. Therefore the PI will explore the possibilities of collaborating with medical companies via the Knowledge Transfer Partnership programme.

Publications

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Blank L (2013) Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints in Numerical Methods for Partial Differential Equations

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Blank L (2014) Relating phase field and sharp interface approaches to structural topology optimization in ESAIM: Control, Optimisation and Calculus of Variations

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Blank L (2013) Nonlocal Allen-Cahn systems: analysis and a primal-dual active set method in IMA Journal of Numerical Analysis

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Blazakis Konstantinos N. (2015) Whole cell tracking through the optimal control of geometric evolution laws in ArXiv e-prints

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Blazakis K (2015) Whole cell tracking through the optimal control of geometric evolution laws in Journal of Computational Physics

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Campillo-Funollet E (2019) Bayesian Parameter Identification for Turing Systems on Stationary and Evolving Domains. in Bulletin of mathematical biology

 
Description 1. Analysis and simulations of reaction-diffusion systems with cross-diffusion on stationary and evolving domains. By employing appropriately asymptotic theory, we derived and proved cross-diffusion-driven instability conditions for a reaction-diffusion system with linear cross-diffusion for the case of slow, isotropic domain growth. Our analytical results reveal that unlike the restrictive diffusion-driven instability conditions on stationary domains, in the presence of cross-diffusion coupled with domain evolution, it is no longer necessary to enforce cross nor pure kinetic conditions. The restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Reaction-cross-diffusion models with equal diffusion coefficients in the principal components as well as those of the short-range inhibition, long-range activation and activator-activator form can generate patterns only in the presence of cross-diffusion coupled with domain evolution. To confirm our theoretical findings, we exhibited detailed parameter spaces for the special cases of isotropic exponential, linear and logistic growth profiles. In support of our theoretical predictions, we presented evolving or moving finite element solutions exhibiting patterns generated by a short-range inhibition, long-range activation reaction-diffusion model with linear cross-diffusion in the presence of domain evolution. This is a substantial extension of the theory for pattern formation during growth development.

2. Development of particle and whole cell tracking algorithms. In this project we develop some novel in-house computational techniques for particle and whole cell tracking. Cell tracking is becoming increasingly important in cell biology as it provides a valuable tool for analysing experimental data and hence furthering our understanding of dynamic cellular phenomena. The advent of high-throughput, high-resolution microscopy and imaging techniques means that a wealth of large data is routinely generated in many laboratories. Due to the sheer magnitude of the data involved manual tracking is often cumbersome and the development of computer algorithms for automated cell tracking is thus highly desirable. In this work, we developed two approaches for automated cell tracking. Firstly,
we consider particle tracking. We propose a few segmentation techniques for the detection of cells migrating in a non-uniform background, centroids of the segmented cells are then calculated and linked from frame to frame via a nearest neighbour approach. Secondly, we consider the problem of whole cell tracking in which one wishes to reconstruct in time whole cell morphologies. Our approach is based on fitting a mathematical model to the experimental imaging data with the goal being that the physics encoded in the model is reflected
in the reconstructed data. The resulting mathematical problem involves the optimal control of a phase-field formulation of a geometric evolution law. Efficient approximation of this challenging optimal control problem is achieved via
advanced numerical methods for the solution of semilinear parabolic partial differential equations coupled with parallelisation and adaptive resolution techniques. Along with a detailed description of our algorithms, a number of simulation
results are reported on. We focus on illustrating the effectivity of our approaches by applying the algorithms to the tracking of migrating cells in a industrial inspired-dataset (from one of our collaborating companies) which reflects many of the challenges typically encountered in microscopy data.

3. Development of a robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws. In our efforts to solve complex partial differential equations on complex evolving surfaces, we have developed new numerical solution procedures to help us tackle complex problems in 2- and 3-dimensions. In this research, we proposed and investigated a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focussing on the optimal control of phase field formulations of geometric evolution laws.
The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility.
Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focused on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problem is computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work was to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An in-house two-grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptive-step gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3-D which would be computationally infeasible without the solution strategies proposed in the present work.

4. Mathematical modelling of plant cell invasion by the rice blast
fungus. In the last three years, we have iterated between modelling and experimental validation with our collaborators in the plant biology laboratory of Professor Nick Talbot at the University of Exeter. Although this work has not been published yet, we have made enormous progress in both modelling and experimental manipulations of how the rice blast disease penetrates to destroy the leaf cuticle in a process that destroys crop harvest across the globe. In this research, we formulated from first principles surface geometric PDEs describing how the rice blast disease, fungus Magnaporthe oryzae, develops a pressurised dome-shaped cell (40 times the pressure of a car tyre) called an appressorium, which physically ruptures the leaf cuticle to gain entry to plant tissue. Rice blast is the most devastating prevalent disease of cultivated rice and a constant threat to global food security; it is of paramount importance to find an effective way to control it. In our research, we have systematically iterated between modeling, experiments and refinement resulting in a robust predictive model and new experiments that help explain how rice fungus damages plant leaf cuticles. The results of this research will be submitted to high impact journal shortly.

5. Commercialisation of software algorithms for particle and whole cell tracking. This project focused on the development of new geometric models for particle cell tracking based on experimental images (static). From this data, our models are able to reconstruct the continuous trajectory pathways taken by cells migrating on two dimensional substrates. In order to deal with shape morphology during cell migration, a robust and efficient multigrid method was developed to solve an optimal control using phase fields that tracks whole cell migration. Both algorithms are currently being commercialised and will be made available to customers within the next month or so.
Exploitation Route 1. Commercialisation and/or open source packages for particle and whole cell tracking in multi-dimensions. Our software algorithms are currently being trailed in Netherlands and Germany as well as by industrial partners with a view to commercialisation. We have since, successfully collaborated with TissueGnostics in Vienna to commercialise our software algorithms.

2. Our research offers other researchers new mathematical and computational frameworks for studying coupled bulk-surface dynamics in the area of cell migration as well as how cells interact and migrate through non-isotropic environments such as tissue or collagen fibres.
Sectors Agriculture, Food and Drink,Chemicals,Communities and Social Services/Policy,Digital/Communication/Information Technologies (including Software),Education,Environment,Healthcare,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology

URL http://www.sussex.ac.uk/profiles/136962
 
Description Our primary findings are the development of new mathematics driven by experimental observations. The models we have developed have been taken up by theoretical mathematicians to study the existence and uniqueness of solutions for such problems. Also, new techniques are being developed such and mass lumping in order to make sure that the numerical solvers preserve properties (such as positivity, invariant regions, etc.) of the the continuous problem. In mathematical and computational biology, our model outcomes and predictions are being tested and validated by experimentalists. Furthermore, we have been able to commercialise some of our algorithms for whole and particle cell tracking in collaboration with TissueGnostics in Vienna Austria.
First Year Of Impact 2017
Sector Agriculture, Food and Drink,Education,Environment,Healthcare,Pharmaceuticals and Medical Biotechnology
Impact Types Societal,Economic

 
Description Associate Editor: In Silico Tissue and Cell Science
Geographic Reach Multiple continents/international 
Policy Influence Type Participation in advisory committee
Impact In 2014, we launched a Springer International Journal on In Silico Tissue and Cell Science in order to bring to the international forum new research outputs associated with cell motility, migration and tissue science. Already, at least 4 articles have been published in 2014 soon after its launch.
URL http://www.in-silico-cell-and-tissue-science.com/
 
Description Editorial Board Member of the international journal: Mathematical Biology and Systems Biology (MBSB)
Geographic Reach Multiple continents/international 
Policy Influence Type Participation in advisory committee
 
Description Steering Committee Member: MASAMU Program
Geographic Reach Multiple continents/international 
Policy Influence Type Membership of a guidance committee
Impact The primary goal of the Masamu (masamu means mathematics in Southern Africa) Program is to enhance research in mathematical sciences within Southern Africa Mathematical Sciences Association (SAMSA) institutions through promotion of international research collaboration. A key component of the Masamu Program is the Advanced Study Institute and Workshop Series in mathematical sciences that provides a platform for such collaboration. Other activities include Research Workshop, Career Development Workshop, Department Heads and Chairs and Senior Research Scientists Workshop, Colloquia and Webinar Series, and AfricaMath. The target audiences of the Advanced Study Institute are graduate students and early career faculty (rank less than associate professor) while the workshops are open to students, faculty, and other researchers in the mathematical sciences.
URL https://masamu.auburn.edu/
 
Description The University of Sussex Environment and Health Advisory Group Board Member
Geographic Reach Local/Municipal/Regional 
Policy Influence Type Participation in advisory committee
Impact Development of interdisciplinary research between different departments and schools at Sussex through organised workshops such as blind-dating, research meetings etc.
 
Description African Diaspora Mathematicians Program (ADMP), University of Sussex - University of Zimbabwe
Amount € 14,000 (EUR)
Organisation International Mathematical Union 
Start 04/2017 
End 03/2019
 
Description Algorithm development for use in commercial cell tracking software.
Amount £3,500 (GBP)
Organisation University of Sussex 
Department School of Mathematical and Physical Sciences Sussex
Sector Academic/University
Country United Kingdom
Start 12/2013 
End 07/2014
 
Description Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation
Amount £256,000 (GBP)
Organisation Isaac Newton Institute for Mathematical Sciences 
Sector Academic/University
Country United Kingdom
Start 07/2015 
End 12/2016
 
Description From experiments to mathematics: Unearthing mathematical models for cell adhesion.
Amount £60,000 (GBP)
Organisation University of Sussex 
Department Chancellor’s International Research Scholarship (CIRC)
Sector Academic/University
Country United Kingdom
Start 09/2014 
End 08/2017
 
Description HEIF KICKSTART PROJECT: Software and algorithm development for cell tracking
Amount £4,500 (GBP)
Organisation University of Sussex 
Sector Academic/University
Country United Kingdom
Start 11/2014 
End 07/2015
 
Description High Performance Computing Equipment
Amount £104,000 (GBP)
Organisation University of Sussex 
Department School of Mathematical and Physical Sciences Sussex
Sector Academic/University
Country United Kingdom
Start 05/2013 
End 04/2018
 
Description International Conference Travel Grant.
Amount £1,000 (GBP)
Organisation Institute of Mathematics and its Applications 
Sector Learned Society
Country United Kingdom
Start 12/2018 
End 01/2019
 
Description International Conference Travel Grant.
Amount £300 (GBP)
Organisation Institute of Mathematics and its Applications 
Sector Learned Society
Country United Kingdom
Start 09/2018 
End 10/2018
 
Description Research Training Network on Integrated Component Cycling in Epithelial Cell Motility
Amount € 3,884,019 (EUR)
Funding ID InCeM 
Organisation European Commission 
Department Horizon 2020
Sector Public
Country European Union (EU)
Start 01/2015 
End 12/2019
 
Description SA-DISCNet: A collaborative data science training network across southern Africa and southern UK
Amount £98,000 (GBP)
Funding ID ST/R002746/1 
Organisation Science and Technologies Facilities Council (STFC) 
Sector Academic/University
Country United Kingdom
Start 01/2018 
End 12/2018
 
Description SA-UK University Staff Doctoral Programme (USDP)- Phase 2 Collaboration and Scoping Grant
Amount £10,000 (GBP)
Organisation British Council 
Sector Charity/Non Profit
Country United Kingdom
Start 03/2019 
End 06/2019
 
Description US-Africa Collaborative Research Network
Amount $415,000 (USD)
Organisation National Science Foundation (NSF) 
Sector Public
Country United States
Start 09/2013 
End 08/2018
 
Description Unearthing new models for Dynein transport mechanisms from the cell membrane to the nucleus
Amount £60,000 (GBP)
Organisation University of Sussex 
Department Genome Damage and Stability Centre
Sector Academic/University
Country United Kingdom
Start 09/2012 
End 08/2016
 
Description Unravelling new mathematics for 3D cell migration
Amount £258,593 (GBP)
Funding ID RPG-2014-149 
Organisation The Leverhulme Trust 
Sector Academic/University
Country United Kingdom
Start 10/2014 
End 09/2017
 
Title Software development for cell tracking 
Description This is a proof-of-concept software development for cell tracking using optimal control. The software is based on open sources codes (ALBERTA) and proposes a physical evolution law for two-dimensional image data provided as a discrete sequences of cell locations. We are currently developing this package in collaboration with our industrial partners. 
Type Of Material Technology assay or reagent 
Provided To Others? No  
Impact Commercial assay systems for cell tracking are a hot topic with almost 90% of the market interested in two-dimensional cell tracking algorithms. Because of the relevance of cellular migration for many active research fields in medicine and biotechnology, there is a high demand for commercially available assaying systems. Automated cell tracking is revolutionalising research in medicine and biology, dramatically reducing the time it takes to interrogate large experimental datasets. Current tracking algorithms are inherently slow with limited tracking pathways (e.g. centroid) and lack complete descriptions of cell morphology and shape changes. Our aim is to develop fast, reliable and efficient cell tracking packages that will yield results in minutes rather than hours or days. The end goal is to develop a commercially viable business providing bespoke cell tracking software thereby enhancing the reputation of University in the development of entrepreneurial activities from academic research. It also has the potential to have lasting social impact by contributing to important research in the life-sciences in fields such as cancer treatment and synthetic biology. It will advance the goals of the research themes such as Environment and Health and Mind and Brain. 
 
Title Optimal control model for cell tracking 
Description The software developed allows us to track the evolution of cells on a two-dimensional substrate. The package is able to predict whole cell morphological changes and evolution unlike current models which track only the centroid. This new algorithm is a proof-of-concept for future and more robust cell tracking algorithms that might help experimentalists to track not only particles but shape changes and other geometric and physical quantities associated with cell tracking. The package has the potential of replacing animals for experimentation. 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact This is a proof-of-concept package that is under trial with our industrial collaborators, IBIDI, Gradientech etc. 
 
Description Algorithms for particle and whole cell tracking in multi-dimensions 
Organisation Ibidi
Country Germany 
Sector Private 
PI Contribution My research group have developed research collaboration with IBIDI. The primary focus of the collaborations is to develop software algorithms for particle and whole cell tracking of static images from experimental observations. The results of this collaboration has resulted in one publication and two under preparation.
Collaborator Contribution IBIDI provided experimental images on which the mathematical models were based. This has resulted in a robust and efficient algorithm for particle and whole cell tracking.
Impact This research is multi-disciplinary, it involves mathematics, numerical analysis, HPC scientific computing, image analysis, and cell biology. The research outcomes are the development of an efficient and robust algorithm for cell tracking and a publication in high impact journal of Biomechanics. Further research outcomes are expected since this collaboration is still active.
Start Year 2014
 
Description Commercialisation of software algoritms for partical and whole cell tracking 
Organisation TissueGnostics GmbH
PI Contribution We have successfully collaborated with TissueGnostics (TG) to translate our research outcomes on particle and whole cell tracking into viable commercial products within TG. TG has partnered with the University of Sussex in a formal agreement to commercialise the software. To-date, we have implement the particle cell tracking onto TG's StrataQuest platform for direct sale to customers and the whole cell tracking package will be provided as an in-house service for TG customers from Sussex.
Collaborator Contribution TsissueGnostics has given us the platform and access to customers to sell our algorithms. In return we will share revenue through a formal contractual agreement.
Impact Early to state the outputs.
Start Year 2016
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Andor Technology
Country United Kingdom 
Sector Private 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Gradientech AB
Country Sweden 
Sector Private 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Ibidi
Country Germany 
Sector Private 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Julich Research Centre
Country Germany 
Sector Public 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation RWTH Aachen University
Country Germany 
Sector Academic/University 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Royal Netherlands Academy of Arts and Sciences
Country Netherlands 
Sector Learned Society 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Software Competence Center Hagenberg
Country Austria 
Sector Charity/Non Profit 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Tel Aviv University
Country Israel 
Sector Academic/University 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation University Duisburg-Essen
Country Germany 
Sector Academic/University 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description Horizon2020-MSCA-ITN-2014 
Organisation Weizmann Institute of Science
Country Israel 
Sector Academic/University 
PI Contribution 1. H2020-MSCA-ITN-2014 grant application (I was one of two pioneers of the research network comprising 11 Universities, 4 Research Institutes and 4 Industrial Companies). 2. I hosted the first pre-grant meeting here at Sussex in 2012 3. I identified and visited all industrial companies to engage with them and get their approval to join the network.
Collaborator Contribution My collaborators helped with the grant application. Professor Rudolf Leube agreed to be the coordinator of the network.
Impact 1. H2020-MSCA-ITN-2014 (SEP-210161846), Research Training Network on Integrated Component Cycling in Epithelial Cell Motility (InCeM): Funded: Euros 3,8 million. 4 Year grant. (Multi-disciplinary - Cell motility, Cell migration, Mathematics, Image Analysis, BioPhysics, Cell Biology, Scientific Computing, etc.) 2. Isaac Newton Institute for Mathematical Sciences: 6 Months Research Programme. Funded (more than £300K allocated). Organisers: A. Madzvamuse ( Principal Organiser), R. Merkel, R. Leube and H.G. Othmer. Coupling geometric PDEs for cell motility, morphology and pattern formation. 3. The Leverhulme Trust Research Project Grant (RPG-2014-149). Unravelling new mathematics for 3D cell motility. A. Madzvamuse, V. Styles and C. Venkataraman. 3 Years. £258.593. Advisory Board: C.M. Elliott, R. Leube, and H.G. Othmer.
Start Year 2014
 
Description SA-DISCNet: A collaborative data science training network across southern Africa and southern UK 
Organisation African Institute for Mathematical Sciences
PI Contribution Our contributions were to provide support for PhD students during their internships in terms of modelling, numerical methods and simulation.
Collaborator Contribution The partners made a significant contribution to knowledge primarily for organisations in South Africa (SA) engaged in activities related to economic development, welfare, and SDGs, and secondarily for academics in SA and the UK. The training scheme we proposed was intrinsically multi-disciplinary, using insights from data science as used by physicists from cosmology, particle physics and solid state physics; this multidisciplinary synthesis was of great value to the students. For our partner organisations in SA, the contributions of the internship students provided solutions to significant SDGrelated questions. In particular, for Transport for Cape Town, they contributed to the improved integration of Cape Town transport and land use planning. For Siyavula, the intern explored their massive student progress data for new insights, and for Zoona, the intern estimated key risks based on micro-loans. For Ekaya, the intern analysed data to build a better picture of clients and hence help make this small startup more sustainable.
Impact Not yet
Start Year 2018
 
Description SA-DISCNet: A collaborative data science training network across southern Africa and southern UK 
Organisation Open University
Department Faculty of Science, Technology, Engineering & Mathematics
Country United Kingdom 
Sector Academic/University 
PI Contribution Our contributions were to provide support for PhD students during their internships in terms of modelling, numerical methods and simulation.
Collaborator Contribution The partners made a significant contribution to knowledge primarily for organisations in South Africa (SA) engaged in activities related to economic development, welfare, and SDGs, and secondarily for academics in SA and the UK. The training scheme we proposed was intrinsically multi-disciplinary, using insights from data science as used by physicists from cosmology, particle physics and solid state physics; this multidisciplinary synthesis was of great value to the students. For our partner organisations in SA, the contributions of the internship students provided solutions to significant SDGrelated questions. In particular, for Transport for Cape Town, they contributed to the improved integration of Cape Town transport and land use planning. For Siyavula, the intern explored their massive student progress data for new insights, and for Zoona, the intern estimated key risks based on micro-loans. For Ekaya, the intern analysed data to build a better picture of clients and hence help make this small startup more sustainable.
Impact Not yet
Start Year 2018
 
Description SA-DISCNet: A collaborative data science training network across southern Africa and southern UK 
Organisation Queen Mary University of London
Country United Kingdom 
Sector Academic/University 
PI Contribution Our contributions were to provide support for PhD students during their internships in terms of modelling, numerical methods and simulation.
Collaborator Contribution The partners made a significant contribution to knowledge primarily for organisations in South Africa (SA) engaged in activities related to economic development, welfare, and SDGs, and secondarily for academics in SA and the UK. The training scheme we proposed was intrinsically multi-disciplinary, using insights from data science as used by physicists from cosmology, particle physics and solid state physics; this multidisciplinary synthesis was of great value to the students. For our partner organisations in SA, the contributions of the internship students provided solutions to significant SDGrelated questions. In particular, for Transport for Cape Town, they contributed to the improved integration of Cape Town transport and land use planning. For Siyavula, the intern explored their massive student progress data for new insights, and for Zoona, the intern estimated key risks based on micro-loans. For Ekaya, the intern analysed data to build a better picture of clients and hence help make this small startup more sustainable.
Impact Not yet
Start Year 2018
 
Description SA-DISCNet: A collaborative data science training network across southern Africa and southern UK 
Organisation University of Essex
Department School of Computer Science and Electronic Engineering
Country United Kingdom 
Sector Academic/University 
PI Contribution Our contributions were to provide support for PhD students during their internships in terms of modelling, numerical methods and simulation.
Collaborator Contribution The partners made a significant contribution to knowledge primarily for organisations in South Africa (SA) engaged in activities related to economic development, welfare, and SDGs, and secondarily for academics in SA and the UK. The training scheme we proposed was intrinsically multi-disciplinary, using insights from data science as used by physicists from cosmology, particle physics and solid state physics; this multidisciplinary synthesis was of great value to the students. For our partner organisations in SA, the contributions of the internship students provided solutions to significant SDGrelated questions. In particular, for Transport for Cape Town, they contributed to the improved integration of Cape Town transport and land use planning. For Siyavula, the intern explored their massive student progress data for new insights, and for Zoona, the intern estimated key risks based on micro-loans. For Ekaya, the intern analysed data to build a better picture of clients and hence help make this small startup more sustainable.
Impact Not yet
Start Year 2018
 
Description SA-DISCNet: A collaborative data science training network across southern Africa and southern UK 
Organisation University of Portsmouth
Department Institute of Cosmology and Gravitation (ICG)
Country United Kingdom 
Sector Academic/University 
PI Contribution Our contributions were to provide support for PhD students during their internships in terms of modelling, numerical methods and simulation.
Collaborator Contribution The partners made a significant contribution to knowledge primarily for organisations in South Africa (SA) engaged in activities related to economic development, welfare, and SDGs, and secondarily for academics in SA and the UK. The training scheme we proposed was intrinsically multi-disciplinary, using insights from data science as used by physicists from cosmology, particle physics and solid state physics; this multidisciplinary synthesis was of great value to the students. For our partner organisations in SA, the contributions of the internship students provided solutions to significant SDGrelated questions. In particular, for Transport for Cape Town, they contributed to the improved integration of Cape Town transport and land use planning. For Siyavula, the intern explored their massive student progress data for new insights, and for Zoona, the intern estimated key risks based on micro-loans. For Ekaya, the intern analysed data to build a better picture of clients and hence help make this small startup more sustainable.
Impact Not yet
Start Year 2018
 
Description SA-DISCNet: A collaborative data science training network across southern Africa and southern UK 
Organisation University of Southampton
Department Physics and Astronomy
Country United Kingdom 
Sector Academic/University 
PI Contribution Our contributions were to provide support for PhD students during their internships in terms of modelling, numerical methods and simulation.
Collaborator Contribution The partners made a significant contribution to knowledge primarily for organisations in South Africa (SA) engaged in activities related to economic development, welfare, and SDGs, and secondarily for academics in SA and the UK. The training scheme we proposed was intrinsically multi-disciplinary, using insights from data science as used by physicists from cosmology, particle physics and solid state physics; this multidisciplinary synthesis was of great value to the students. For our partner organisations in SA, the contributions of the internship students provided solutions to significant SDGrelated questions. In particular, for Transport for Cape Town, they contributed to the improved integration of Cape Town transport and land use planning. For Siyavula, the intern explored their massive student progress data for new insights, and for Zoona, the intern estimated key risks based on micro-loans. For Ekaya, the intern analysed data to build a better picture of clients and hence help make this small startup more sustainable.
Impact Not yet
Start Year 2018
 
Description SA-UK USDP Phase 2 Doctoral Training Centre 
Organisation University of Johannesburg
Country South Africa 
Sector Academic/University 
PI Contribution The aim of this partnership is to establish a university capacity development programme collaborative project to establish a four year university staff doctoral training programme in South Africa at a historically disadvantaged institution, in this case, the University of Limpopo. The partnership is working of a larger research proposal worth 5 million rands and will support up to 10 University Staff to be trained over a period of four years.
Collaborator Contribution Our partners contribute with both infrastructure and resources for phd training as well as venues and students to be trained.
Impact Not yet
Start Year 2019
 
Description SA-UK USDP Phase 2 Doctoral Training Centre 
Organisation University of Limpopo
Country South Africa 
Sector Academic/University 
PI Contribution The aim of this partnership is to establish a university capacity development programme collaborative project to establish a four year university staff doctoral training programme in South Africa at a historically disadvantaged institution, in this case, the University of Limpopo. The partnership is working of a larger research proposal worth 5 million rands and will support up to 10 University Staff to be trained over a period of four years.
Collaborator Contribution Our partners contribute with both infrastructure and resources for phd training as well as venues and students to be trained.
Impact Not yet
Start Year 2019
 
Description SA-UK USDP Phase 2 Doctoral Training Centre 
Organisation University of Stellenbosch
Country South Africa 
Sector Academic/University 
PI Contribution The aim of this partnership is to establish a university capacity development programme collaborative project to establish a four year university staff doctoral training programme in South Africa at a historically disadvantaged institution, in this case, the University of Limpopo. The partnership is working of a larger research proposal worth 5 million rands and will support up to 10 University Staff to be trained over a period of four years.
Collaborator Contribution Our partners contribute with both infrastructure and resources for phd training as well as venues and students to be trained.
Impact Not yet
Start Year 2019
 
Title Software for cell tracking 
Description We developed a robust and efficient algorithm for single and population cell tracking that could help experimentalists characterise cell tracking statistical measures. 
IP Reference  
Protection Copyrighted (e.g. software)
Year Protection Granted 2018
Licensed Yes
Impact The software for cell tracking has been licenced to TissuGnostics and will be released in their next version and rolled out to customers.
 
Title Software and algorithm development for cell tracking 
Description We have successfully developed a cell tracking algorithm for single and population cell migration and the software has been licenced with TissueGnostics. The current status is that the software will be moved from a demo version to a commercial version in the next few months and hopefully it will be released in the next version. By using optimal control theory, we have developed a proof-of-concept software package for cell tracking with the potential of tracking whole cell morphology. The software has undergone trials with IBIDI with an eye of embedding the package into their commercial packages. In particular it has the potential to help biologists automatically quantify proliferation rates which are currently done manually, i.e. counting cell division rates. 
Type Of Technology Software 
Year Produced 2018 
Impact Although there are no notable impacts to date, this software is currently being developed as part of the REF impact case for 2020. 
 
Description SIANM Conference on Nonlinear Waves and Coherent Structures (NW14-SIAM) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact I was invited to give a talk at the SIAM-NW14 conference in Cambridge. During and after the talk, participants asked questions about the new models whereby we couple bulk and surface dynamics with applications to cell motility. After the talk, researchers at Bristol found our methodology appealing to their current research and have since invited us to visit their laboratories to explore avenues on applying our models to plant biology.

After the talk, a research group from Bristol would like to apply our model system to plant biology.
Year(s) Of Engagement Activity 2014
 
Description Symposium speaker and Forum Panelist at the Association of International Education Administrators (AIEA) annual conference in New Orleans, US 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? Yes
Geographic Reach International
Primary Audience Policymakers/politicians
Results and Impact My presentation on multi-lateral partnerships between the UK, the US and Sub-Saharan Africa generated a lot of debate and discussions beyond those envisaged by the British Council.

After the panel presentation and the conference, I have received numerous emails with requests on modes for developing multi-lateral partnerships. The current EU Horizon2020 MSCA-ITN-2014 grant was inspired by such an activity involving international collaborators.
Year(s) Of Engagement Activity 2013
 
Description The University of Sussex Environment and Health Advisory Group 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? Yes
Geographic Reach Local
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact (1) Leadership in developing interdisciplinary research
(2) Securing internal and external funding to support interdisciplinary research between different schools and the Brighton and Sussex University Hospitals.
(3) Development of human infrastructure through the appointment of research personnel.

After each workshop, the participants were able to foster interdisciplinary research groups between schools with several researchers submitting funding proposals were interdisciplinarity was a core requirement.
Year(s) Of Engagement Activity 2014