Generating 24-Hour ECG, BP and Respiratory Signals with Realistic Linear and Nonlinear Clinical Characteristics Using a Nonlinear Model GD Clifford , PE McSharry Harvard-MIT Division of Health Sciences & Technology, Cambridge MA, USA Department of Engineering Science, University of Oxford, Oxford, UK Mathematical Institute, University of Oxford, Oxford, UK Centre for the Analysis of Time Series, London School of Economics, London, UK Abstract A nonlinear model for generating lifelike human ECG, blood pressure and respiratory signals is described. Each cycle of the model corresponds to one heart beat and the signals therefore exhibit beat-to-beat ﬂuctuations by driv- ing the model with a sequence of RR intervals. By using a modiﬁed version of entry no.201 of the CinC 2002 24-hour RR interval generator challenge, (such that the user can specify the probability of ectopy or artefact) and coupling it to three ordinary differential equations, the model gen- erates a 24-hour ECG signal. Using both standard linear metrics, and nonlinear long range statistics, the signal is shown to exhibit many of the known characteristics such as Respiratory Sinus Arrhythmia, Mayer waves and an over- all diurnal rhythm. The RR interval time series is modelled as a set of sta- tionary states (joined by a transient heart rate overshoot) of differing lengths, mean heart rates (HR), LF/HF ratios and standard deviations. The length of time in each state is governed by a power law distribution with marked dif- ferences between waking and sleep states. The statistics of each RR time series segment (a state) can be fully speciﬁed by its mean (HR) and spectral distribution (LF/HF ratio). The resultant ECG is shown to exhibit realistic QRS- and QT-dispersions, R-S amplitude modulation and Res- piratory Sinus Arrhythmia in the short term and normal values for nonlinear statistics (such as entropy) in the long term. By altering the parameters of the ECG model, in- troducing a heart-rate dependent delay (to simulate pulse transit time), and coupling the baseline to the long-term ﬂuctuations of the 24 hour RR interval generator, realis- tic short and long range blood pressure ﬂuctuations are shown to result. Together with seeded RR interval dynam- ics, the morphology of the signals can be fully speciﬁed by three parameters per feature and therefore a large range of different (deterministic) signals can be generated with fully known characteristics, to facilitate the testing of sig- nal processing algorithms. Open source C, Matlab and Java programs for generating the model are available from Physionet. 1. Introduction In order to effectively test the performance of signal processing algorithms for analysing biomedical signals, a noise-free signal is often desired [1]. A realistic artiﬁcial biomedical signal generator that is able to encompass the range of signals observed for both normal and abnormal subjects is therefore a useful tool. Furthermore, the abil- ity to rapidly create a regenerateable time series enables a researcher to quickly prototype applications and test theo- ries such as signal mixing and as a function of the model parameters such as sampling rate [1, 2]. Modiﬁcations of our published models for generating artiﬁcial 24-hour RR intervals [3] and ECG, blood pres- sure (BP) and respiration waveforms [1, 2] for generating 24-hour versions of these waveforms are presented. They are shown to have realistic properties; the signal possesses oscillations in morphological features and clinical param- eters (such as QRS width, RS amplitude, RR and QT- intervals) as well as statistical similarities with real data on many scales. Furthermore, the signals possess morpho- logical appearances similar to that of a real waveforms and have a realistic inter-signal relationship. 2. Methods 2.1. RR interval sequence During a 24 hour period, the HR tends to jump between different quantised states, relating to different physical and mental activity [4, 5], with different means , and vari- ances, . The 24 hour tachogram is therefore built from a