Filtering and Prediction of Blood Flow and Oxygen Consumption for Patient Monitoring

Abstract

Suppose data is to be electronically acquired at discrete times Δ, 2Δ, 3Δ,..., tΔ,... (starting from an arbitrary origin) on arterial and venous oxygen concentration as well as an independent variable which is either blood flow rate or oxygen consumption, and that the remaining dependent variable (O₂ consumption or blood flow) is to be predicted from the data. We refer to “time tΔ” merely as “time t”. Let y _1t be the observed value of the independent variable at time t and let y_2t, y_3t. be the observed values of the arterial and venous O₂ concentrations respectively at time t. The observations are physiological state values corrupted by noise or observation error. For j = 1,2,3 corresponding to the observation subscripts, let x̃j (t) be the jth physiological state (existing in continuous time) and let v_jt be the noise or observation error of the jth observation at time t.