A Quaternion-based Approach to Estimate Respiratory Rate from the Vectorcardiogram

A novel ECG-derived respiration (EDR) approach is presented to efficiently estimate the respiratory rate. It combines spatial rotations and magnitude variations occurring in the heart’s electrical vector due to respiration. Orthogonal leads X, Y and Z from 10 volunteers were analyzed during a tilt table test. The largest vector magnitude (VM) within each QRS loop was assessed, and its 3D coordinates were converted into unit quaternion q_b. Angular distances between these quaternions and the axes of the reference coordinate system, θ_x, θ_y and θ_z, were then computed as EDR signals to track their relative variations caused by respiration. The respiratory rate was estimated on the spectrum of individual EDR signals obtained from the angular distances and VM time-series, but also on transformed EDR signals obtained by principal component analysis (PCA). Relative errors (e_R) to the reference respiratory signal exhibited relatively low values. In particular, the combination of EDR signals’ spectrum {θ_X, θ_Y , θ_Z, VM} (e_R=0.63±4.15%) and individual signals derived from θ_X (e_R=0.46±8.22%) and PCA (e_R=0.36±6.58%) achieved the overall best results. The proposed EDR method represents a computationally efficient alternative to other EDR approaches, although its robustness should be further investigated. The method could be enhanced if combined with other features tracking morphological changes induced by respiration