Almost every living thing exhibits daily cycles in behavior and physiology known as circadian rhythms. In humans, disrupted circadian rhythms have been implicated in a spectrum of both mental and physical health maladies including cancer, diabetes, addiction, depression and sleep disorders. Therefore, it is a matter of vital importance to understand and predict human circadian rhythms. In previous work we have derived and fit a low dimensional dynamical model for human circadian rhythms. However, the heterogeneity of circadian behaviors (early birds/night owls) in the human population must be accounted for in the model. In this work we investigate how data collected by wearable devices (apple watch, fitbit, etc) can be used to personalize the circadian parameters and improve forecasting accuracy.
"Data driven model for detecting insomnia from multi-night actigraphy time series data"
Sleep is an important part of human existence as we spend 1/3 of our lives sleeping. It is a complex multi-dimensional cycle that reflects developmental changes in mental and physical health, along with the day-to-day state fluctuations. Insomnia is characterised by the inability to fall asleep or stay asleep and/or waking too early and being unable to fall back asleep. Insomnia is a sleep disorder that remains under-diagnosed. We propose a new data driven model for classification of nocturnal awakenings in acute and chronic insomnia and normal sleep from nocturnal actigraphy collected from pre-medicated individuals with insomnia and normal sleep controls. Our model does not require sleep diaries or any other subjective information from the individuals. We derive dynamical and statistical features from the actigraphy time series data. These features are then combined in machine learning model to classify individuals with insomnia from healthy sleepers. The model includes a classifier followed by optimization algorithm that incorporates the predicted quality of each night of sleep for an individual to classify into acute/chronic insomnia or healthy group. The developed model provides a signature of acute/chronic insomnia obtained from actigraphy only and is very promising as a pre-screening tool to detect the condition in home environment. M Angelova, C Karmakar, Y Zhu, SP Drummond, J Ellis. (2020). Automated Method for Detecting Acute Insomnia Using Multi-Night Actigraphy Data. IEEE Access, 8, 74413-74422.
"A mathematical model of 'wanting', 'liking, and brain reward circuitry in drug addiction"
We propose a mathematical model combining the so-called opponent process theory and the reward prediction error (RPE) in the context of drug addiction. Using this model, we investigate the different dynamics towards addiction and provide a possible description of the process of detoxification. The opponent processes are modeled by introducing a response kernel that integrates dopamine-induced neuronal activity to form a sense of reward. The shape of the kernel, which might be associated with physical and biological characteristics of neurocircuits of the brain reward system, plays a key role in determining the overall experience of consumption of addictive substances and the mismatch between the expected reward and the actual eward, the reward prediction error (RPE). With time and repeated exposures to drugs of abuse, the response kernel will change based on the value of the RPE and on the process of neuroadaptation. The dynamics of this change represents the evolution towards addiction and is mathematically described as a trajectory in a three-dimensional parameter space representing the RPE. In our framework, the surface representing the RPE is divided in two regions representing positive and negative values of value of the RPE, respectively. We show that the dynamics associated with naïve drug users is represented by a trajectory lying in the first, positive-RPE region but, with time and repeated exposure to drugs of abuse, the trajectory will enter into the second, negative-RPE region. After transition to addiction, the subsequent dynamics is largely confined within the negative-RPE region. We finally propose models for exiting the negative-RPE parameter regions and connect it to a description of a detoxification protocols, such as the use of methadone to address heroin addiction.
University of Sussex
"Using mathematics to investigate the mechanisms behind vision loss"
The retina is a tissue layer at the back of the eye that uses photoreceptor cells to detect light. Photoreceptors can be characterised as either rods or cones. Rods provide achromatic vision under low light conditions, while cones provide high-acuity colour vision under well-lit conditions. The term Retinitis Pigmentosa (RP) refers to a range of genetically mediated retinal diseases that cause the loss of photoreceptors and hence visual function. RP leads to a patchy degeneration of photoreceptors and typically directly affects either rods or cones, but not both. During the course of the disease, degenerate patches spread and the photoreceptor type unaffected by the mutation also begins to degenerate. The cause underlying these phenomena is currently unknown; however, several key mechanisms have been hypothesised: oxygen toxicity, trophic factor depletion and the release of toxic substances by dying cells. Here we present mathematical models, formulated as systems of PDEs, to investigate the trophic factor hypothesis. Using a combination of numerical simulations and mathematical analysis, we determine the geographic variation in retinal susceptibility to degeneration, evaluate the degree to which in vivo spatio-temporal patterns of degeneration can be replicated by our models and predict the effects of various clinically-relevant treatment strategies.