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

Daniel Romero1, Jesus Lazaro2, Raquel Bailón3
1Institute for Bioengineering of Catalonia (IBEC), 2University of Zaragoza, 3I3A, IIS, Universidad de Zaragoza, CIBER-BBN


Aims: This work presents an electrocardiogram-derived respiration (EDR) approach to efficiently estimate the respiratory rate from the vectorcardiogram (VCG). It exploits and combines the spatial rotations and magnitude variations occurring in the heart’s electrical vector due to the subject’s respiration.

Methods: Orthogonal leads X, Y and Z from 10 volunteers were acquired and analyzed during a tilt-up table test. The largest vector magnitude (VM) within each QRS loop was assessed, and its 3D coordinates were converted into unit quaternion qb, which provides a compact notation for 3D orientations. Angular distances between these normalized quaternions and each axis of the reference coordinate system, θX, θY, and θZ, were computed on a beat-to-beat basis to track their relative variations caused by respiration (see Figure). 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 signals obtained by principal component analysis (PCA). Moreover, combinations of the EDR signals spectra were considered in order to obtain more robust respiratory rate estimates.

Results: Relative errors (eR) referred to the reference respiratory signal, computed for our method, exhibited relatively low values. In particular, the combination of signals’ spectrum {θX, θY, θZ, VM} (eR=1.3±12%) and individual signals derived from θX (eR=0.32±13%) and θZ (eR=0.62±14%) achieved the overall best results, as compared to those obtained for PCA-derived signals.

Conclusions: The proposed EDR method represents a computationally efficient alternative to other rotation-based approaches such as rotation matrices and Euler-angles, although its robustness should be further investigated. Nonetheless, this could be enhanced if combined with other non-rotational features tracking morphological changes induced by respiration.