For more than a century, it has been known that the body recoils each time the heart ejects blood into the arteries. These subtle cardiogenic body movements have been measured with increasingly convenient ballistocardiography (BCG) instruments over the years. A typical BCG measurement shows several waves, most notably the "I", "J", and "K" waves. However, the mechanism for the genesis of these waves has remained elusive. We formulated a simple mathematical model of the BCG waveform. We showed that the model could predict the BCG waves as well as physiologic timings and amplitudes of the major waves. The validated model reveals that the principal mechanism for the genesis of the BCG waves is blood pressure gradients in the ascending and descending aorta. This new mechanistic insight may be exploited to allow BCG to realize its potential for unobtrusive monitoring and diagnosis of cardiovascular health and disease. It has long been known that the body moves with each heartbeat 1 . These subtle movements represent the body's recoil to cardiac expulsion of blood into the arteries. Various "ballistocardiography (BCG)" instruments have been developed (ranging from tables to wearables 2-4 ) to measure the periodic, reactionary forces experienced by the body. Figure 1 illustrates an example of a measured BCG waveform for one heartbeat. The example shows several waves such as the "I", "J", and "K" waves, which are typical of BCG recordings. Current understanding of the curious BCG waves is based mainly upon empirical correlations with other measurements such as the electrocardiogram, phonocardiogram, and blood pressure (BP) waveform 5, 6 . However, theoretical efforts to explain the underlying mechanism have been relatively rare. Further, while a few mathematical models of the BCG waveform have been proposed, these models have either failed to reproduce the key BCG waves 7 or were too complicated to glean any mechanistic insight 8 . Hence, despite increasing interest in BCG 9 , the origin of the BCG waves has remained mysterious. In this study, we formulated and validated a simple mathematical model of the BCG waveform. The model reveals the primary mechanism of the BCG waves as well as their meaning in terms of cardiovascular parameters of clinical significance. This discovery reveals the potential of BCG for unobtrusive monitoring and diagnosis of cardiovascular health and disease. Simple Mathematical Model of the BCG Waveform. We mathematically modeled the BCG waveform as an instantaneous force in the head-to-foot direction (F BCG (t)) by analyzing the equilibrium of forces exerted on the blood in the main artery of the body, the aorta (see Fig. 2 and Materials and Methods for details). A simple model resulted as follows: Here, A A and A D represent the average cross-sectional areas of the ascending and descending aorta; P 0 (t) represents BP at the inlet of the ascending aorta; P 1 (t) represents BP at the outlet of the ascending aorta or inlet of the descending aorta; and P 2 (t) represents BP at the outlet of the descending aorta. Note that δP 01 (t) = P 0 (t) − P 1 (t) 1
Many approaches have been developed for analyzing the BCG signal for heartbeat detection and heart rate monitoring. REF investigates the mechanism for the genesis of BCG waveforms and verifies the proposed model surgically, providing more theoretical foundation for unobtrusive monitoring of heart rate and diagnosis of cardiovascular disease.
Ballistocardiogram: Mechanism and Potential for Unobtrusive Cardiovascular Health Monitoring
Scientific Reports
Scientific Reports
Medicine