Physics of non-autonomous systems in the life sciences: a new perspective on the time-variability of complex systems

Lead Research Organisation: Lancaster University
Department Name: Physics

Abstract

Despite the daunting complexity of living systems, great efforts have been made to describe aspects of their function in terms of phenomenological mathematical models. Once a quantitative understanding has been achieved in this way, one can hope to characterize the state of a system in terms of parameter values in the equation that describes it and to predict how it will evolve into the future. There are obvious potential applications in medicine, e.g. for the diagnosis of pathological conditions, prognosis, and assessment of the efficacy of treatment. However, almost all attempts to model the dynamics of living systems on other than very short timescales have run into the same fundamental problem: their time-variability.Living systems are in a state of continuous change, as they evolve from birth, through life, and finally to death. Throughout, they are in a state of continuous alteration, on many different timescales. For example, the heart rate varies in time, even for a healthy subject in repose - a phenomenon known as heart-rate variability (HRV). Because its amplitude and frequency content can be used as a measure of health, HRV has attracted enormous international attention. In view of the several underlying oscillatory processes now known to be responsible for HRV, one of the most promising pictures of the cardiovascular system is in terms of coupled oscillators, and a number of models have been proposed. But it is evident that the model parameters, e.g. characteristic frequencies, vary in time. This inevitably implies that conventional modeling is of strictly limited applicability, and must in many cases be doomed to failure. Thus it has become apparent that a radically different approach is needed. This is what we now propose, based on ideas and techniques developed in recent years for the treatment of nonautonomous systems.The notion of nonautonomous dynamical systems recognizes that a system under study is subject to outside influences that may e.g. cause its parameters to vary, and provides a way of characterising and quantifying the resultant phenomena. It is potentially ideal for the description of living systems which are thermodynamically open, subject to continuous exchange of matter and energy with their surroundings as well as internally between their different subsections. Every part and process within an organism to some extent influences every other subsystem, whence the extraordinary complexity of the observed behaviour when one measures one or two variables in attempting to understand a particular subsystem. For example HRV arises, not only from the influence of respiration on heart rate, but also through the influences of slower oscillatory processes corresponding to e.g. myogenic, neurogenic and endothelial activities. The theory of nonautonomous systems promises to quantify the degree of nonautonomicity and to describe resultant phenomena, e.g. extra attractors (steady states) created by the ``outside influences`` in question.What we propose amounts to a new approach to the inverse problem, seeking an answer to the question: given a signal (a sequence of measurements, or time series), what is the system that produced it? It is a conundrum found in many areas of science, but has been acutely difficult to tackle in the case of physiological signals on account of their time-variability. So the work we propose, if successful, is likely to have far-reaching consequences. Our team includes a biomedical engineer (PI) and 2 physicists (CI and RCI) who together have very extensive experience of autonomous dynamical systems in biomedicine, a mathematician (VR) who is a world-leading expert in the mathematical theory of non-autonomous systems, and clinical collaborators with expertise in the relevant physiology. We will thus bring relatively abstruse, topical, ideas from physics and mathematics to practical application in physiology, paving the way to innovation in clinical practice.

Planned Impact

We will exploit six impact pathways in parallel. Full details are given in the attached Impact Plan (pp 10-11) but, in summary they are - (a) Impact through collaborative research. Much of the group's research is already carried out in close collaboration with the clinicians who are potential users of the results. Thus potentially useful observations can be evaluated and exploited quickly. The main applications in progress are listed in the Impact Plan. Each and every one of them stands to be enhanced by finding better ways of creating phenomenological models to describe non-autonomous systems: (b) Impact through production of trained people. There will be a PDRA , the Project PhD Student requested, and also Mr T. Stankovski (existing PhD student) associated with the project. All will receive training in interdisciplinary scientific research. (c) Impact through scientific publications. Since 2000, the applicants have published over 200 scientific papers, of which 34 were joint papers often with clinical co-authors. We will continue this. (d) Impact though scientific presentations. We will make presentations at the standard scientific conferences in our field (see Impact Plan). We have given more that 50 talks on topics in biomedicine over the last ten years, mostly invited. (e) Impact through general scientific publications. We will make general scientific publication using a variety of media: (i) papers/articles for the general reader and (ii) use of non-standard media like You-Tube (see Impact Plan). (f) Impact through general scientific talks and presentations. We will continue using a diverse range of lectures, talks and interviews to bring our work to the general public (see Impact Plan).

Publications

10 25 50
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Barabash ML (2014) Homogeneous delays in the Kuramoto model with time-variable parameters. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Clemson P (2016) Reconstructing Time-Dependent Dynamics in Proceedings of the IEEE

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Clemson P (2014) Discerning non-autonomous dynamics in Physics Reports

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Clemson PT (2014) Inverse approach to chronotaxic systems for single-variable time series. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Iatsenko D (2015) Nonlinear mode decomposition: a noise-robust, adaptive decomposition method. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Iatsenko D (2013) Evolution of cardiorespiratory interactions with age. in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

 
Description The overarching aim of the research programme was to address the enduring problem of how to analyse data derived from biological (and other) systems that have time-variable parameters, i.e. that are nonautonomous on account of external influences. In particular, we were interested in the well-known 'inverse problem' in which a time series of data is analysed to infer information about the system that generated it, but under conditions such that the originating system is nonautonomous. The results described below are especially relevant to, but not restricted to, living systems -

1 . A wavelet-based coherence method was developed to evaluate the coherence of two oscillatory time series, applicable even when they have variable amplitudes and frequencies.

2. A method was introduced for analysis of the interactions between time-dependent coupled oscillators, based on the signals they generate. Based on Bayesian inference, it is capable of distinguishing genuinely unsynchronized dynamics from noise-induced phase slips between oscillators that are otherwise synchronised, and it enables the evolution of the coupling functions between the oscillators to be followed in time.

3. We have investigated how the cardiorespiratory interaction evolves with age, by the analysis of cardiac and respiratory time series recorded from 189 subjects of both genders,
aged 16-90. Treating the heart and respiration as coupled oscillators, we used Bayesian inference to find the underlying coupling parameters and their time dependence. We found
that the direct and indirect respiratory modulations of the heart rate both decrease with age, and that the cardiorespiratory coupling becomes less stable and more time-variable. This result can be interpreted as an indication that the cardiorespiratory system tends to function less well as a single entity as it gets older.

4. New approaches to the analysis of ensembles of coupled oscillators (like e.g those in the brain) were developed, based on the famous Kuramoto model, taking explicit account of deterministically time-varying parameters. The oscillators' natural frequencies and/or couplings were influenced by external forces with constant or distributed strengths. The dynamics of the collective rhythms was shown to consist of the external system superimposed on the autonomous one, a characteristic feature of many thermodynamically open systems. By analysis of a very general form of the Kuramoto model we found evidence for the long-predicted "oscillator glass" state - a kind of synchronous disorder - and studied its properties. We also discovered the new and intriguing phenomenon of super-relaxation where the oscillators feel no interaction at all while relaxing to incoherence.

5. We introduced the "mean-field variability index" (MFVI) to provide a way of characterizing an ensemble of interacting oscillators. It is defined as the variance of the oscillators' mean field divided by its mean square. Based on the assumption that the overall mean field is the sum of a very large number of oscillators, each giving a small contribution to the total signal, we showed that the MFVI depends on the mutual interactions between the oscillators, independently of their number or spectral properties. We used the MFVI to characterise electroencephalograph signals from the brains of human subjects under different conditions.

6. As a quite unexpected outcome of our studies of the time-varying nature of the cardiorespiratory interaction, we introduced a new class of secure communications that is highly resistant to conventional attacks. Unlike all earlier encryption procedures, this new cipher makes use of the coupling functions between interacting dynamical systems. It results in an unbounded number of encryption key possibilities, allows the transmission or reception of more than one signal simultaneously, and is robust against external noise. Thus, the information signals are encrypted as the time variations of linearly independent coupling functions.

7. Arguably, one of the most important outcomes of the research was the notion of chronotaxic system. These are oscillatory systems that are capable of stabilizing their own frequencies. They can be viewed as basic functional units of oscillatory systems far from thermodynamic equilibrium. They arise in many context, but are especially typical of living systems. Attempts are being made to create similar systems in robotics.
Exploitation Route The most promising direction for applications relates to the new method of secure encryption based on the modulation of coupling functions between interacting oscillators.

The theory of chronotaxic systems has broad applicability and may be used in biology, medicine, as well as in robotics, engineering, ecology and environmental science, and potentially astrophysics.
Sectors Digital/Communication/Information Technologies (including Software),Environment,Healthcare,Culture, Heritage, Museums and Collections,Pharmaceuticals and Medical Biotechnology,Security and Diplomacy,Other

 
Description The new method of secure encryption, based on the modulation of coupling functions, is being developed to prototype stage with DefineX Ltd and ExpertoCrede Ltd, with support from Lancaster University's EPSRC Impact Acceleration Account.
First Year Of Impact 2014
Sector Education,Healthcare,Security and Diplomacy,Other
Impact Types Cultural,Economic

 
Description Coupling functions secure communications for safety related and critical systems
Amount £10,000 (GBP)
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 09/2014 
End 09/2015
 
Description FST Research Impact Fund
Amount £5,000 (GBP)
Organisation Lancaster University 
Sector Academic/University
Country United Kingdom
Start 08/2016 
End 07/2017
 
Description Impact accleration account: Coupling functions encryption for emotion recognition
Amount £9,970 (GBP)
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 09/2014 
End 09/2015
 
Description LU Impact Fund
Amount £6,980 (GBP)
Organisation Lancaster University 
Sector Academic/University
Country United Kingdom
Start 08/2016 
End 07/2017
 
Description The physiological significance of cardiorespiratory interactions: bridging between data analysis, mathematical theory and physiological models. Catalyst Seeding
Amount $80,000 (NZD)
Organisation Royal Society of New Zealand 
Sector Learned Society
Country New Zealand
Start 11/2018 
End 11/2020
 
Title Extraction of ridges from 3-D amplitude or power spectra in time-frequency representations of measured signals 
Description The method enables adaptive, universal, extraction of ridge frequencies from time-frequency representations. Being based on dynamic path optimization and fixed point iteration, the method is very fast, and its superior accuracy is also demonstrated. The codes developed are freely available for download. 
Type Of Material Physiological assessment or outcome measure 
Year Produced 2016 
Provided To Others? Yes  
Impact The method has been used extensively by other scientists in a variety of different contexts. 
URL https://www.sciencedirect.com/science/article/pii/S0165168416000451
 
Title Measurement of coupling functions in networks of oscillators 
Description For analysis of the ASD/normal EEG brain wave dynamics we have developed a method based on dynamical Bayesian inference that is capable of detecting the effective phase connectivity within networks of time-evolving coupled phase oscillators subject to noise. It not only reconstructs pairwise, but also encompasses couplings of higher degree, including triplets and quadruplets of interacting oscillators. Thus inference of a multivariate network enables one to reconstruct the coupling functions that specify possible causal interactions, together with the functional mechanisms that underlie them. The characteristic features of the method are illustrated by the analysis of a numerically-generated network of phase oscillators with time-dependent coupling parameters and subject to noise, taken as an example. To demonstrate its potential, the method is also applied to neuronal coupling functions from single- and multi-channel electroencephalograph (EEG) recordings. The cross-frequency d,a to a coupling function, and the ?,a,? to ? triplet are computed, and their coupling strengths, forms of coupling function, and predominant coupling components, are analysed. The method is applicable to multivariate networks of oscillators, quite generally, but will be used here for our AMR project with Blackpool Victoria Hospital. 
Type Of Material Model of mechanisms or symptoms - human 
Year Produced 2015 
Provided To Others? Yes  
Impact No impact yet. 
 
Title Method to detect chronotaxicity from measured data 
Description Following the development of a new class of self-sustained oscillators with a time-varying but stable frequency, we have formulated an inverse approach to these systems . We have proposed a method that recognizes such systems from observed data arranged in a single-variable time series. The method makes use of time-frequency domain information based on the wavelet transform as well as the recently developed method of Bayesian-based inference. In addition, a set of methods, named phase fluctuation analysis, is introduced to detect the defining properties of the new class of systems by directly analyzing the statistics of the observed perturbations. The method can be used to study the chronotaxicisity of the brain waves and how it change with autism. 
Type Of Material Model of mechanisms or symptoms - human 
Year Produced 2014 
Provided To Others? Yes  
Impact We have applied the method to several important problems. It being noticed by other researchers and we expect a wider set of applications over the next few years. 
URL http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032904
 
Title Neuronal cross-frequency coupling functions 
Description We have introduced a method for the detection and characterisation of cross-frequency coupling functions between neuronal oscillations, suitable for analysing and seeking differences between the ASD/normal EEG data. Dynamical Bayesian inference of the time-evolving dynamics is used to estimate the effective couplings in the presence of noise. The approach is applied to the reconstruction of a phase dynamics model of five neuronal frequency intervals. The model encompasses not only pairwise, but also multivariate network interactions. By grouping partial functional contributions, it is shown how a coupling can be decomposed into its individual functional components and how its most important characteristics - its strength and form - can be quantified. The methodological aspects of the approach are illustrated by analyzing neuronal coupling functions from single- and multi-channel ectroencephalography (EEG) measurements. The delta-to-alpha and the triplet theta,alpha-to-gamma coupling functions are reconstructed, quantified, compared, and followed as they evolve in time. The method is expected to be very illuminating for the EEG data from ASD/normally-developing children in our AMR project. 
Type Of Material Model of mechanisms or symptoms - human 
Year Produced 2015 
Provided To Others? Yes  
Impact No impact so far. 
 
Title Nonlinear mode decomposition 
Description This is a numerical method that enables the separation of oscillatory components in complex signals measured either from living systems or more generally. It takes account of nonlinearities. 
Type Of Material Physiological assessment or outcome measure 
Year Produced 2015 
Provided To Others? Yes  
Impact There have been citation from scientists working in a diversity of fields. 
URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032916
 
Title Cardiovascular ageing and hypertension 
Description This dataset available on Pure contains simultaneous recordings of Electrocardiogram (ECG), Respiratory effort (RESP) and right wrist Laser Doppler Flowmetry (LDF) from 29 healthy young (Y, aged 24.4±3.4 years), 22 healthy aged (A, aged 71.1±6.6 years) and 29 treated hypertensive (H, aged 70.3±6.7 years) subjects. All the signals are re-sampled at 40Hz. The duration of the recordings differs between subjects and it is around 30 minutes. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
Impact The data file is embargoed until 2 May 2018, so no possibility for impact yet. 
 
Title Melanoma blood flow data 
Description This is a data set that contains blood flow data used in 'Dynamical markers based on blood perfusion fluctuations for selecting skin melanocytic lesions for biopsy'. Sci. Rep., article number: 12825 (2015) doi:10.1038/srep12825 
Type Of Material Database/Collection of data 
Year Produced 2015 
Provided To Others? Yes  
Impact Data have been used by other researcher and presented in publications, like 10.1109/BMEiCON.2016.7859638 published in December 2016. 
 
Title Nonlinear Biomedical Physics database 
Description The database contains data recorded from our previous EU-supported project BRACCIA and ESRC-supported project on "Dynamics of cardiovascular ageing". The BRACCIA data were analysed by members of the group to investigate the effects of general anesthesia with propofol and sevoflurane on cardiovascular and brain dynamics. The data collected during the ESRC-funded project were used to investigate the effect of healthy ageing on cardiovascular dynamics. Both data-sets were also utilized to develop and test new time-series analysis methods. 
Type Of Material Database/Collection of data 
Year Produced 2013 
Provided To Others? Yes  
Impact Subjects before and during general anesthesia were recorded in Lancaster Infirmary and in Oslo National Hospital. A classification analysis based on an optimal set of discriminatory parameters obtained from cardiovascular signals distinguished with 95% success between the awake and anesthetized states. 
URL http://py-biomedical.lancaster.ac.uk/
 
Description CRITICS 
Organisation Critical Transitions in Complex Systems
Country United Kingdom 
Sector Academic/University 
PI Contribution Possibilities to provide practical problems related to the CRITICS network.
Collaborator Contribution Possibilities to consult mathematical groups working in the area of complex, non-autonomous systems.
Impact In progress.
Start Year 2015
 
Description Collaboration on hypoxia 
Organisation University of Ljubljana
Department Medical Faculty
Country Slovenia 
Sector Academic/University 
PI Contribution Myself and my group contributed to the study design, the measurement set-up and the analysis of recorded data.
Collaborator Contribution The collaborators, Prof Damjan Osredkar and Prof Tadej Dobevec recruited the subjects, performed the measurements and contributed to the interpretation of results.
Impact A journal paper is drafted and is now being eddied between the co-authors.
Start Year 2017
 
Description Dr Megan Thomas and her team in Blackpool 
Organisation Blackpool Victoria Hospital
Country United Kingdom 
Sector Hospitals 
PI Contribution This is the partner in the collaborative project supported by our AMR grant. Our research team analyses data supplied by Blackpool Victoria Hospital. The initial Blackpool data have been used in Lancaster for developing new analysis methods to quantify the interactions between EEG waves. Although it is too early to draw definitive conclusions, these initial data appear to reveal clear differences in cerebral inter-oscillator interactions between the ASD and control groups. The next stage, once the analysis methods have been optimised and the data recording has been completed, will be analysis of the full set of data and then interpretation of the results through close Lancaster/Blackpool physics/clinical collaboration.
Collaborator Contribution Our Blackpool collaborators are diagnosing children on the ASD spectrum and measuring their EEG brain waves. They are also recording comparable data from normally developing children. In each case, the resultant time series data are being transferred to Lancaster for analysis. So far, the Blackpool team has recorded EEG data from 12 young ASD children, and a comparison group of 10 normally developing children. The aim is to increase each subject group to 20.
Impact The collaboration with this clinical group motivated development of several time-series analysis methods that were developed by the group and were published in 4 physics-related journals. A patent application "Autism scoring from EEG'" with Dr Thomas Megan, together with Valentna Ticcinelli, Prof Aneta Stefanovska and Prof Peter McClintock filed on 8 Deceber 2016. It is based on a highly multi-disciplinary work carried on within this collaboration. It includes neuro-pediatrics, physics and biomedical physics.
Start Year 2013
 
Description Dwain Ekberg 
Organisation Virginia Commonwealth University
Country United States 
Sector Academic/University 
PI Contribution Used our methods to analyze physiological data recorded by Prof Dwain L Eckberg and his collaborators.
Collaborator Contribution Prof Dwain L Eckberg visited Lancaster on several occasions to discuss results of analysis of data he provided, and to prepare joint publications.
Impact 1. Time-frequency methods and voluntary ramped-frequency breathing: a powerful combination for exploration of human neurophysiological mechanisms By: Stankovski, Tomislav; Cooke, William H.; Rudas, Laszlo; et al. JOURNAL OF APPLIED PHYSIOLOGY Volume: 115 Issue: 12 Pages: 1806-1821 Published: DEC 2013 2. Human sympathetic outflows to skin and muscle target organs fluctuate concordantly over a wide range of time-varying frequencies By: Bernjak, Alan; Cui, Jian; Iwase, Satoshi; et al. JOURNAL OF PHYSIOLOGY-LONDON Volume: 590 Issue: 2 Pages: 363-375 Published: JAN 2012
Start Year 2011
 
Description Marcin 
Organisation Medical University of Gdansk
Department Department of Radiology Informatics and Statistics
Country Poland 
Sector Hospitals 
PI Contribution Helped the collaborator to investigate the relationship between blood pressure and pial artery pulsation oscillations in human.
Collaborator Contribution The collaboration comes from a group that has developed a new device for non-invasive measurements of intracranial flow (NIRT). They are contributing signals that when analysed by our methods promise great impact.
Impact Papers in preparation.
Start Year 2015
 
Description Melanoma 
Organisation University of Pisa
Department Department of Clinical and Experimental Medicine
Country Italy 
Sector Academic/University 
PI Contribution Formulated problem and analysed the data, which was topic of Gemma Lancaster's PhD thesis on "Nonlinear dynamics of cancer".
Collaborator Contribution Recruited patients, performed the measurements and completed histological analysis.
Impact 1. Lancaster, G; Stefanovska, A ; Pesce, M ; Vezzoni, GM ; Loggini, B; Pingitore, R; Ghiara, F; Barachini, P; Cervadoro, G; Romanelli, M; Rossi, M, Dynamic markers based on blood perfusion fluctuations for selecting skin melanocytic lesions for biopsy, SCIENTIFIC REPORTS, 5: 12825 (2015) DOI: 10.1038/srep12825 2. DIAGNOSTIC METHODS AND DEVICE Publication number: 20160007907 Abstract: The present invention relates to a method of diagnosing, or providing a prognosis to, or for providing the likelihood of developing, malignant melanoma in a subject, the method comprising the steps of: (a) measuring two or more markers in blood perfusion dynamics at and/or around a skin lesion site; and (b) determining if the two or more markers is different to a normal value. The invention also relates to a device for diagnosing/providing a prognosis to/for malignant melanoma in a subject. Type: Application Filed: July 11, 2014 Publication date: January 14, 2016 Inventors: Gemma Lancaster, Aneta Stefanovska, Marco Rossi, Margherita Pesce
Start Year 2011
 
Description Prof Peter Kloeden 
Organisation Goethe University Frankfurt
Country Germany 
Sector Academic/University 
PI Contribution Expanded the mathematical theory of non-autonomous systems to include oscillatory systems.
Collaborator Contribution Prof Kloeden is a world leading expert in mathematical theory of non-autonomous systems who visited Lancaster on several occasions to discuss our progress in developing the theory of chronotaxic systems.
Impact The group contributed a chapter Clemson PT, Petkoski S, Stankovski T, Stefanovska A: Coupled Nonautonomous Oscillators in the book "Nonautonomous dynamical systems in the life sciences", edited by: Kloeden PE and Potzsche C, Lecture Notes in Mathematics 2102: 163-197, 2013 DOI: 10.1007/978-3-319-03080-7_5 Several mutual acknowledgements publications.
Start Year 2011
 
Description Tomislav Stankovski 
Organisation Saints Cyril and Methodius University of Skopje
Country Macedonia, the Former Yugoslav Republic of 
Sector Academic/University 
PI Contribution Aneta Stefanovska and Peter McClintock were PhD and PostDoc supervisors of Dr Tomislav Stankovski. During his stay in Lancaster (2008-2014) Tomislav mastered time series analysis methods and in particular Dynamical Bayesian inference.
Collaborator Contribution Dr Tomislav Stankovski expanded Dynamical Bayesian inference method to include multi-coupling analysis in collaboration with Valentina Ticcinelli, a PhD student funded by Physics Department to work on the project, who coded the algorithm. The method is very relevant for the data recorded during the study.
Impact Dr Tomislav Stankovski co-authored 5 journal papers relevant for our collaborative projects 1. G Nadzinski, M Dobrevski, C Anderson, PVE McClintock, A Stefanovska, M Stankovski, T Stankovski, Experimental Realization of the Coupling Function Secure Communications Protocol and Analysis of Its Noise Robustness, IEEE Transactions on Information Forensics and Security 13 (10), 2591-2601, 2018 2. T Stankovski, T Pereira, PVE McClintock, A Stefanovska, Coupling functions: universal insights into dynamical interaction mechanisms, Reviews of Modern Physics 89 (4), 045001, 2017 3. V Ticcinelli, T Stankovski, D Iatsenko, A Bernjak, AE Bradbury, AR Gallagher, P Clarkson, PVE McClintock, Aneta StefanovskaCoherence and coupling functions reveal microvascular impairment in treated hypertension, Frontiers in physiology 8, 749, 2017 4. T Stankovski, V Ticcinelli, PVE McClintock, A Stefanovska, Neural cross-frequency coupling functions, Frontiers in systems neuroscience 11, 33, 2017 5. T Stankovski, V Ticcinelli, PVE McClintock, A Stefanovska, Coupling functions in networks of oscillators, New Journal of Physics 17 (3), 035002, 2017 and a patent application T Stankovski, A Stefanovska, RJ Young, PVE McClintock, Encoding data using dynamic system coupling, US Patent App. 14/910,547, 2016.
Start Year 2014
 
Title Detecting ASD 
Description The discovery is based on the development of the theory of non-autonomous dynamical systems, methods to analyse time series that contain time-variable dynamics and several related applications where a similar rationale was applied to study e.g. nonlinear dynamics of cardiovascular ageing, or effects of anaesthesia. Our approach takes an explicit account of the intrinsically nonlinear, thermodynamically open, and time-variable nature of the living systems. We considered brain dynamics within this approach and hypothesized that using our methods to analyse EEG data recorded from a control group and children with clinically diagnosed ASD, we can extract bio-markers that are specific to ASD. In the Blackpool hospital, EEGs from 13 ASD (average age 50+-6 months) and 9 control (46+-7 months) males were measured, and 1 min of movement-artefact-free recordings were used in the analyses performed in the Nonlinear and Biomedical Physics Group at Lancaster University. We were able to confirm the hypothesis and extract a set of parameters based on spectral power, phase coherence and coupling functions, that enables a clear distinction between brain dynamics in ASD and control children. 
IP Reference WO 2018/104751 Al 
Protection Patent application published
Year Protection Granted
Licensed No
Impact No additional impact as yet.
 
Title Diagnostic methods and device 
Description The invention relates to a method of diagnosing, or providing a prognosis to, or for providing the likelihood of developing, malignant melanoma in a subject, the method comprising the steps of: (a) measuring two or more markers in blood perfusion dynamics at and/or around a skin lesion site; and (b) determining if the two or more markers is different to a normal value. The invention also relates to a device for diagnosing/providing a prognosis to/for malignant melanoma in a subject. 
IP Reference Patent number: 9907507 
Protection Patent granted
Year Protection Granted 2018
Licensed No
Impact Not yet.
 
Title Encoding Data using Dynamic System Coupling 
Description This is a method of encoding data at a computer, the computer storing data associated with a plurality of dynamical subsystems, each dynamical subsystem having a plurality of associated state variables, the plurality of dynamical subsystems being coupled by a plurality of coupling functions. The method comprises receiving, at the computer, data to be encoded; inputting, at the computer, the data to be encoded into the plurality of dynamical subsystems as a plurality of parameters of the coupling functions; and outputting, from the computer, a plurality of state variables associated with the plurality of dynamical subsystems, the plurality of state variables comprising at least one of the plurality of state variables associated with each of the dynamical subsystems, the plurality of state variables providing an encoding of the received data. 
IP Reference 20160182220 
Protection Patent application published
Year Protection Granted 2016
Licensed No
Impact Not yet.
 
Title MODA 
Description MODA is a toolbox that provides a set of methods to deal with signals affected by time variability. Currently, it contains 5 methods, including wavlet analysis, wavelet-based phase coherence analysis, wavelet-based bispectral analysis, ridge-extraction and coupling function analysis. It is intended to be very user friendly to be used by the wider scientific community. 
Type Of Technology Software 
Year Produced 2018 
Impact Too early. 
 
Title Nonlinear Biomedical Physics toolboxes 
Description Currently, it includes the following toolboxes: 1. Wavelet Phase Coherence, 2. TACTS Matlab toolbox, 3. TEDBI_Bayesian_Toolbox, 4. Time_Frequency_Representations and 5. Nonlinear_Mode_Decomposition 
Type Of Technology Software 
Year Produced 2013 
Open Source License? Yes  
Impact To date a total of 445 registered downloads. 
URL http://py-biomedical.lancaster.ac.uk/
 
Description Biological Oscillations conference 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Stefanovska and her group organised the 9th conference of the European Study Group on Cardiovascular Oscillations which took place in Lancaster from 10th to 14th April 2016. This was also the first International Conference on Biological Oscillations.
The aim of the conference was to provide an interdisciplinary forum for discussions of biological oscillations between researchers drawn from areas such as physics, mathematics, engineering, computer science, cardiovascular regulation, neuroscience, time-series analysis, theory of nonlinear oscillatory dynamics, information processing, cardiovascular and microvascular physiology, cell biology and clinical sciences.
In addition to the signal processing view of cardiovascular oscillations this conference expanded to incorporate a more physics-based approach. It also generalized the topic to include all biological oscillations.
Year(s) Of Engagement Activity 2016
URL http://www.physics.lancs.ac.uk/ESGCO2016/
 
Description Contribution to Headstart Programme 
Form Of Engagement Activity Participation in an open day or visit at my research institution
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact 30 Y12 Physics students from across the UK participated in the Headstart course. All students are studying A level Physics and another science in many cases and Mathematics and are high ability as indicated by their teachers. Our group organised a whole day event for the students and provided three workshop sessions: Physics of the Brain, Physics of the Cardiovascular System and Physics of the Cell. After a few introductory talks by members of the group students did either measurements or simulations, analysed their data and then presented the results to their audience.
Year(s) Of Engagement Activity 2017
URL http://www.etrust.org.uk/headstart/whatisheadstart
 
Description Data Science Institute workshop 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact Data Science Institute organized a Streaming Data workshop that was held in the Low Wood hotel 18-19 July 2016. I presented our work and participated in many activities of the workshop.The workshop was used to

• explore current Streaming Data research activities at Lancaster;
• identify challenges which can draw mutual interest;
• and develop ideas for future research and funding opportunities in this area.
Year(s) Of Engagement Activity 2016
 
Description Physics Department Colloquium, Royal Holloway, University of London, 18 May, 2018 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Other audiences
Results and Impact Delivered a talk "Understanding systems operating far from equilibrium from the perspective of time-varying dynamics" and enjoyed vigorous discussion about differences in living and non-living systems dynamics.
Year(s) Of Engagement Activity 2018
 
Description Physics Master Class: Waves and Oscillations featuring Biomedical Physics Research 
Form Of Engagement Activity Participation in an open day or visit at my research institution
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact 12 A-level students attended a whole day event which consisted of an introductory talk, two biomedical research taster projects and an oscillations and waves lab to complement their A-level studies. Students prepared group presentations and presented the results of their work. Several feedback - both from students and their A-level teachers indicate that students greatly enjoyed the day and developed an interest in the field.
Year(s) Of Engagement Activity 2017
 
Description Seminar (Reading) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Undergraduate students
Results and Impact Talk at the School of Biological Sciences Research Seminar Series, University of Reading, 16 October, 2018 to students of Biomedical Sciences and Biomedical Engineering and their lecturers interested in the filed of Biological Oscillators. Discussed examples related to ageing, dementia, ASD and the cell, cardiovascular system and brain oscillatory dynamics.
Year(s) Of Engagement Activity 2018
URL https://www.reading.ac.uk/biologicalsciences/SchoolofBiologicalSciences/Research/sbs-research-semina...