A dynamical model of influenza A virus infection: clinical and epidemiological relevance

Abstract

measured every minute in a PDMS system (Metavision, iMD-Soft, Needham, MA), for a set of 30 ICU patients, with lengths of stay varying from a couple of hours to several days. These time series are compressed to obtain a measurement every hour. The following variables are selected as inputs for the Gaussian process algorithm because of their clinical relevance in prediction of temperature: blood temperature, peripheral temperature, oxygen blood saturation, heart frequency, mean blood pressure, systolic blood pressure, pH, cardiac output, urine output, frequency of respiration (measured automatically by the respirator), white blood cell count, and arterial CO2 tension. A fraction of the data from each patient is used to train the Gaussian process model and the remaining data are used for testing the model’s predictive performance. A window of 15 previous time points per physiological variable is used to predict the patient’s blood temperature of the following hour. This one-step ahead process is iterated to obtain predictions multiple time steps ahead. To deal with the large amount of data a sparse method (pseudoinput Gaussian process) is used. Results: Predictions 4 and 10 time steps ahead were bounded to an mean squared error (MSE) below 0:21 and 0:83, respectively, for all patients. Predicted SDs remained below 0:63. Using the current value as a predictor of the future temperature resulted in upper bounds for MSE of 0:63 and 3:24 for 4 and 10 time steps ahead respectively. Using the average temperature as a predictor, the upper bound was 2:77. For all patients, Gaussian processes outperformed the other 2 predictors within the 10-hour-ahead prediction range. Predictions for 1 example patient are shown in Fig. 1, with performance (MSE) shown in Table 1. Conclusion: Gaussian process when used for forecasting an ICU patient’s blood temperature, result in predictions with small MSE (within the studied range), when compared with using the mean value or the current value as predictors. The range of prediction must be further extended before these models can be used in prediction of inflammatory states several days in advance.