The BCG Model: A Solved Problem?

Ramon Casanella
Universitat Politecnica de Catalunya


Abstract

In 1958, A.Noordergraaf proposed a mathematical model for the ballistocardiogram (BCG) that, considering the instrumentation and measurement accuracy of the time, provided a reasonably accurate explanation of the recorded waveforms and was widely accepted as the definitive interpretation of the BCG for several decades. However, in recent years, alternative models have been introduced by Kim et al.(2016), Yousefian et al.(2019), Guidoboni et al.(2019), and Rabineau et al.(2021), thereby reopening the question of whether the BCG model can truly be considered a solved problem. Although these models stem from a common conceptual framework, they represent sufficiently distinct approaches, such that certain models offer advantages not present in others, while also presenting inherent limitations that, in the author's view, preclude any from offering a fully satisfactory and comprehensive explanation of experimentally observed BCG signals. As an illustrative case, the figure displays a Woody's averaged BCG waveform obtained from a healthy 28-year-old male subject over a two-minute period using a weighing scale. Initially, the subject maintained a relaxed posture with arms alongside the body, followed by a posture with arms fully extended horizontally to the sides. In these experimental results, also reproduced in four other subjects, we observe, on the one hand, a typical prominent I wave that is not satisfactorily reproduced by Guidoboni's model. On the other hand, Rabineau's model predicts a notch between the J and K waves that is not observed—neither in this signal nor in any scale-based recordings. Finally, Kim's simplified model, which attributes the BCG primarily to aortic motion transmitted, according to Yousefian's model, almost unaltered to the scale, does not seem able to account for the peak changes observed due to arm repositioning. These findings suggest that, despite the significant and valuable contributions of existing models, a conclusive and unified model of the BCG remains elusive.