Biology and medicine

Parkinson's disease

Parkinson's disease (PD) is a neurodegenerative disorder which is estimated that affects 1% of the population over the age 60. Given that the population is growing older the incidence rates are projected to increase in the near future. PD diagnosis is not 100% accurate because there are other neurological disorders with PD-like symptoms. PD symptom tracking is also required to optimize treatment; however, currently this requires the PD subject's physical presence in the clinic, which is awkward for patients, and the dedicated time of clinicians, which is logistically inconvenient for the national health systems.

There is empirical evidence linking PD with speech disorders at least as far back as the 60's. The challenge is to use signal processing method to extract clinically useful information from the speech signals in order to offer a robust decision support tool to clinicians aiding both in diagnosis and in quantifying PD symptom severity. Speech signals are particularly tricky time-series data, because they are non-stationary and inherently noisy. Novel signal processing and statistical machine learning algorithms have been developed in order to extract characteristic patterns from the the voice signals and map these patterns to the two outcomes: (1) differentiate PD subjects from healthy controls, (2) for those subjects already diagnosed with PD, replicate a clinical metric quantifying PD symptom severity.

These algorithms have been demonstrated to differentiate healthy controls and PD subjects with almost 99% accuracy, significantly improving previous state of the art results, which reached only 92% accuracy. They also manage to replicate the clinicians' symptom severity score with less that 5% deviation from the clinicians' estimates. Recently, it has been shown that this technology can be efficient using standard mobile phones through a simulation environment; the aim is to offer an automatic and objective screening test for PD over mobile phones. Future directions of research include extending this application to other neurological disorders which may have an imprint on speech. The technology can enable objective, remote, and accurate screening and follow-up of subjects who are unable or not willing to visit the clinic very frequently.

Key references in this area

  • A. Tsanas, M.A. Little, P.E. McSharry, L.O. Ramig (2010). Accurate telemonitoring of Parkinson's disease progression by non-invasive speech tests. IEEE Transactions on Biomedical Engineering 57: 884-893
  • A. Tsanas, M.A. Little, P.E. McSharry, L.O. Ramig (2011). Nonlinear speech analysis algorithms mapped to a standard metric achieve clinically useful quantification of average Parkinson’s disease symptom severity. Journal of the Royal Society Interface 8: 842-855.
  • A. Tsanas, M.A. Little, P.E. McSharry, J. Spielman, L.O. Ramig (2012). Novel speech signal processing algorithms for high-accuracy classification of Parkinson’s disease. IEEE Transactions on Biomedical Engineering 59(5).
  • A. Tsanas, M.A. Little, P.E. McSharry, B.K. Scanlon, S. Papapetropoulos (in press). Statistical analysis and mapping of the Unified Parkinson’s Disease Rating Scale to Hoehn and Yahr staging. Parkinsonism and Related Disorders.

For further information contact Athanasios Tsanas.


Predator-prey models of zooplankton-phytoplankton dynamics

Phytoplankton are primary producers that constitute the basis of the aquatic food chain. Phytoplankton, and the zooplankton that graze upon them, play a crucial role in the dynamics observed at higher levels of the ecosystem. We study models for predator-prey interaction where predators have a preferred prey type and switch to eat an alternative prey type when the preferred prey is low. We have constructed a model and compared it against available data in order to shed more light on mechanisms behind zooplankton-phytoplankton dynamics.

We are using a piecewise-smooth dynamical system to model prey switching. Piecewise-smooth systems show rich dynamics but their study is less developed than for smooth dynamical systems. They also have great potential utility for biological applications, but they seldom have been applied in these situations. Their investigation poses both analytical and conceptual challenges. We have begun a combined analytical and computational study to compare and contrast our piecewise-smooth representation with its smooth equivalent.

We have compared simulations of our piecewise-smooth model to data for two different phytoplankton prey groups collected from Lake Constance, a large, deep freshwater lake, with 536 km2 of surface area. Our model simulations capture the periodicity in the ratio between a more preferred and a less preferred phytoplankton prey type exhibited by the data collected during the spring, when the variability in the environmental conditions can be considered relatively low and thus modelled as constant. In the future we will adjust our model to be applicable to the sea environment. We will take seasonal change in the environment into account, explore different forms of predator conversion efficiency, and expand the food chain to include more species.

For more information please contact Mason Porter or Sofia Piltz.

Key references in this area

  • Katrin Tirok and Ursula Gaedke (2010). Internally driven alternation of functional traits in a multispecies predator-prey system. Ecology 91(6): 1748-1762.
  • Vlastimil Krivan (1996). Optimal foraging and predator-prey dynamics. Theoretical Population Biology 49: 265-290.
  • Alan R. Champneys and Mario di Bernardo (2008). Piecewise smooth dynamical systems. Scholarpedia 3(9):4041. (scholarpedia)


Network-based studies of infectious disease 

Infectious diseases are the second largest cause of death worldwide, accounting for 23% of all deaths. Mathematical studies are commonly used by both researchers and public health officials to better understand disease spread and predict and counteract epidemics. The traditional ways to model infectious diseases use differential equations, such as the SIR and force-of-infection models. More recently, scientists have attempted network-based approaches, such as describing disease as a dynamical process on a network of contacts. In this project, we investigate the applicability of a novel network science methodology, using community detection on time-dependent correlation networks to model the geographical spread of disease.

Using proprietary data on country-wide dengue fever, rubella, and H1N1 influenza occurrences for several years, we create networks with the provinces as nodes and correlation between the number of disease cases in each pair of provinces giving weights to the links between nodes. To study these temporally evolving networks, we use the framework of "multislice networks", which allows modelling the temporal aspect of the data with less data aggregation than with collections of ordinary (static) networks. We perform community detection, looking for groups of provinces in which disease patterns change in similar ways, and we analyse the properties of the communities over time. We also study the relations between epidemic spread and changes in different network and node statistics, to seek potential preepidemic signals.

Preliminary results (performed on static networks) suggest that there may be a drop in modularity around the epidemic start time, as well as changes in node statistics such as participation coefficient and geodesic betweenness.

We are currently investigating the statistical significance of the preliminary results by comparing their values to values observed in a random rewiring null model. We are looking at extending the definitions of the interesting statistics to multislice networks. We are also planning on changing the model to include time through using directed links and possibly a delay in the network creation.

For more information please contact Marta Sarzynska or Mason Porter.


Bipolar disorder

Bipolar disorder is a mental illness which causes an individual's mood to swing from one extreme to another, resulting in periods of depression and mania. The exact cause is not understood although genetic and environmental factors are known to play a part. The aim of this project is to use mathematical models to predict mood fluctuations and help in understanding and managing the disorder. The Department of Psychiatry in Oxford runs a scheme whereby patients can fill in a mood questionnaire each week and return the answer by text message. In this way, the weekly mood changes of 150 patients have been monitored continually over the last five years and provided a valuable database for analysis.

Some studies have applied dynamical systems theory to model mood in bipolar disorder (A. Gottschalk et al. 1995), while others have used non-linear time series approaches to develop measures for characterising mood changes (T. Glenn et al. 2006). For this project we are relatively rich in data and so have started by applying standard time series forecasting methods. However the mood time series are non-uniform in time while most time series methods assume uniformly spaced data. So we are developing measures of non-uniformity in order to characterise the data set and we have adopted some methods from spatial statistics to handle non-uniformity. For example, we use the variogram rather than the correlogram to examine correlation structure and we use Gaussian process regression (kriging) instead of trying to regularise the time series or imputing missing values.

Kriging leads to better results than linear smoothers that depend on uniformly sampled time series, although the difference in accuracy is marginal on our data set. We have found gender differences in mood dynamics, a result for which there is evidence in the psychiatric literature on bipolar disorder. There is also evidence of seasonality: some people get more depressed in the winter. There are no significant gender differences in time series uniformity, nor does the diagnostic subtype (the specific kind of bipolar disorder) affect the uniformity of response, a result that is unexpected since some subtypes can be associated with erratic behaviour.

The measures of non-uniformity may also be useful in a clinical setting because they relate to the reliability of the patient's response, a quality that is potentially informative. They are applicable more generally to any non-uniform time series and may find further applications in the burgeoning field of medical telemonitoring. Further work is planned on other regression methods and on optimal covariance functions and inference methods for this application.

For more information please contact Paul Moore.

Key references in this area

  • A. Gottschalk, M. S. Bauer, and P. C. Whybrow (1995). Evidence of chaotic mood variation in bipolar disorder. Archives of General Psychiatry 52(11): 947–959. (available here)
  • T. Glenn, P. C. Whybrow, N. Rasgon, P. Grof, M. Alda, C. Baethge and M. Bauer (2006). Approximate entropy of self-reported mood prior to episodes in bipolar disorder. Bipolar Disorders 8(5): 424–429. (available here).
  • P. J. Moore, M.A. Little, P. E. McSharry, J. R. Geddes and G. M. Goodwin (2012). Forecasting depression in bipolar disorder using cellphone telemonitoring. IEEE Transactions on Biomedical Engineering (submitted).
  • P.J. Moore, M. Little and P. McSharry (2011). Forecasting mood in bipolar disorder. International Symposium on Forecasting, Prague, 2011. (available here).


Oncolytic Virotherapy

Oncolytic virotherapy is the use of genetically modified viruses to selectively infect cancer cells and induce cell death. By targeting cancer cells specifically the aim is to drastically reduce the side effects of chemotherapy. The aim of this project is to model the infection mathematically to gain some insight into the key parameters associated with gene therapy treatments of solid tumours.

We have developed a continuum age-structured model describing the spatial distribution of a viral infection in a system of tumour cells on protein scaffolding; this model comprises a coupled set of partial differential equations (PDEs) for virus, infected and uninfected cells. In addition we have developed a corresponding stochastic discrete agent-based model, in which individual cells and virus particles are tracked. Analytic techniques have been used to derive an estimate for the speed of the infection wave in the continuum system, and numerical simulations have been performed. The discrete system has been modelled with a direct method stochastic simulation algorithm in two-dimensions. Numerical stability of the PDE solver as well as computational efficiency of the SSA implementation have been key challenges, which have resulted in a multi-resolution time discretization being used.

We have classified the effects of key experimentally-controlled variables on the likelihood of success and speed of spread of therapy in the two-dimensional discrete case. Currently, the system is being expanded to incorporate additional biological considerations such as macrophage obstacles, cell crowding and an immune response. Work is also in progress to extend the continuum numerical solver to two-dimensions, and combine these two approaches into a robust “in silico” model which could be used to predict the likelihood of success or failure based on the sensitivity to key experimental variables.

For more information please contact Alex Shabala, Jon Chapman, Chris Breward or Sarah Waters.

Conceptual schematic of gene therapy mechanisms. Pathway A represents immunotherapy, Pathway B represents gene transfer and Pathway C represents oncolytic virotherapy (adapted from Cross and Burmester, 2006).

Key references in this area  

  • Cross, D. & Burmester, J. (2006). Gene therapy for cancer treatment: past, present and future Clinical Medicine & Research 4 (3): 218–227.    
  • Wein, L., Wu, J. & Kirn, D. ( 2003). Validation and Analysis of a Mathematical Model of a Replication-competent Oncolytic Virus for Cancer Treatment.    Cancer Research 63: 1317-1324.