Estimation of invasive physiological parameters from non invasive parameters using dimensionless numbers and Monte Carlo cross-validation

According to NCEP-ATPIII criterion, metabolic syndrome (MS) diagnosis is based in the measurement of invasive (triglycerides, HDL, glucose) and non invasive variables (height, weight, waist circumference). The aim of this work is find, since dimensionless numbers design from physiological (π 1IS , π 2IS ) and heart rate variability (π 1HRV , π 2HRV ) parameters, three polynomial equations (π 1IS =f(π 2HRV ), π 2IS =f(π 1HRV ), π 2IS =f(π 2HRV )) that relate invasive with non invasive variables. In this sense, a fitting using Monte Carlo cross validation (MCCV) was performed. A database of 40 subjects (25 control subjects and 15 subjects with MS) was employed. The results suggest that MCCV improves the coefficient of determination (R 2 ), compared to the application of the least squares method only, in each polynomial: π 1IS =f(π 2HRV ) (R 2 =0.62 vs. 0.21), π 2IS =f(π 1HRV ) (R 2 =0.62 vs. 0.36) and π 2IS =f(π 2HRV ) (R 2 =0.56 vs. 0.19). The fitting by MCCV allows the estimation of invasive from non invasive parameters.