Physiological Vital Time Series Forecasting using Fractional Calculus and Deep Neural Network

Abstract

Sama Nemati, Seyed Amin Seyed Jafari, Mostafa Fakhri, Kosar Seraji, Farzane Vosoughi-Motlagh and Mojtaba Hajihasani

Continuous physiological monitoring integrated with time series analysis and multi-step forecasting is vital when encountering postoperative cases either hospitalized in intensive care units (ICU) or given home health care will experience adverse cardiac events. The low-cost common vital signs, i.e., heart rate and arterial blood pressure are captured and predicted with adjustable horizons up to 30 minutes in advance to achieve punctual clinical decision-making to prevent the events of bradycardia, tachycardia, hypo-tension, and hypertension. Scaling properties of physiological stationary/non-stationary signals are necessarily determined and drastically affected by the selection and architecture design of time series forecasting models. In contrast to integer-order difference that achieves stationary memory-erased series, fractional order difference ensures the stationary of the data while preserving as much memory as possible. The deep learning architecture for multi- step forecasting is the combination of two direct and iterative methods which utilizes the convolutional neural networks with skip connections inspired by the concepts of U-Net convolutional networks and multi-layer bi-directional long short-term memories (Bi-LSTMs). Various scenarios of observe-target windows e.g. (20, 30, 60, or 120) - (7, 15, 20, or 30) minutes are trained using hyper-parameter tuning and evaluated by mean absolute percentage error (MAPE). The results of the proposed method indicate that crucial vital signs such as heart rate, systolic blood pressure and mean arterial blood pressure will be predictable in an adjustable observe-target window size from 20-7 to 120-30 minutes with narrow ranges of MAPE values between [2.78%, 4.17%], [4.69%, 6.47%] and [4.45%, 6.86%], respectively.

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