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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 of 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 qb. Angular distances between these quaternions and the axes of the reference coordinate system, θx, θy and θz, 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 EDR signals obtained by principal component analysis (PCA). Relative errors (eR) to the reference respiratory signal exhibited relatively low values. The combination of EDR signals' spectrum {θX,θY,θZ, VM} (eR=0.63±4.15%) and individual signals derived from θX (eR =0.46±8.22%) and PCA (eR=0.36±6.58%) achieved the overall best results. The proposed method represents a computationally efficient alternative to other EDR approaches, but its robustness should be further investigated. The method could be enhanced if combined with other features tracking morphological changes induced by respiration.