[Paper Review] Cardiovascular Function and Ballistocardiogram: A Relationship Interpreted via Mathematical Modeling

Giovanna Guidoboni, Lorenzo Sala+8 more|arXiv (Cornell University)|Nov 2, 2018

Non-Invasive Vital Sign Monitoring64 references59 citations

TL;DR

This paper proposes a closed-loop, physically-based mathematical model of the cardiovascular system to simulate ballistocardiogram (BCG) signals via hemodynamic waveforms and body motion dynamics. The model accurately reproduces clinical BCG morphology (I, J, K, L, M, N peaks) and predicts distinct signal changes under pathological conditions such as reduced left ventricular contractility and increased stiffness, offering a quantitative framework for clinical BCG interpretation and device optimization.

ABSTRACT

Objective: to develop quantitative methods for the clinical interpretation of the ballistocardiogram (BCG). Methods: a closed-loop mathematical model of the cardiovascular system is proposed to theoretically simulate the mechanisms generating the BCG signal, which is then compared with the signal acquired via accelerometry on a suspended bed. Results: simulated arterial pressure waveforms and ventricular functions are in good qualitative and quantitative agreement with those reported in the clinical literature. Simulated BCG signals exhibit the typical I, J, K, L, M and N peaks and show good qualitative and quantitative agreement with experimental measurements. Simulated BCG signals associated with reduced contractility and increased stiffness of the left ventricle exhibit different changes that are characteristic of the specific pathological condition. Conclusion: the proposed closed-loop model captures the predominant features of BCG signals and can predict pathological changes on the basis of fundamental mechanisms in cardiovascular physiology. Significance: this work provides a quantitative framework for the clinical interpretation of BCG signals and the optimization of BCG sensing devices. The present study considers an average human body and can potentially be extended to include variability among individuals.

Motivation & Objective

• To develop a quantitative, physics-based framework for interpreting ballistocardiogram (BCG) signals in clinical settings.
• To address the lack of standardized BCG measurement and interpretation due to variability in sensing devices and protocols.
• To simulate BCG signals using a closed-loop model of the cardiovascular system that captures hemodynamic and mechanical interactions.
• To validate the model against experimental BCG data acquired from a suspended bed replica.
• To investigate how specific pathological changes—reduced contractility and increased stiffness—alter BCG waveform morphology.

Proposed method

• A closed-loop mathematical model of the cardiovascular system is constructed using a hydraulic analogy, modeling blood flow as fluid dynamics in a network of resistors, inductors, and capacitors.
• The model incorporates time-varying ventricular elastance and pressure-volume relationships to simulate left and right ventricular contractions.
• Blood volume waveforms (Vi(t)) are computed via a system of 26 nonlinear ordinary differential equations (ODEs) derived from Kirchhoff’s current and voltage laws applied to the circulatory network.
• The BCG signal is computed as the weighted sum of blood volume changes across vascular compartments: BCGdisp(t) = (ρb/M) Σ Vi(t)yi, with time derivatives yielding velocity and acceleration signals.
• Model parameters are calibrated using physiological data from the literature, including blood density (1.05 g/cm³), viscosity (0.035 g/cm·s), and vessel wall properties (E = 4×10⁶ dyne/cm²).
• The model is simulated using initial conditions from hemodynamic steady-state values and solved numerically until periodic behavior is achieved.

Experimental results

Research questions

• RQ1 Can a closed-loop, physically-based mathematical model accurately simulate the morphology of the ballistocardiogram (BCG) signal, including characteristic peaks (I, J, K, L, M, N)?
• RQ2 How do changes in left ventricular contractility and arterial stiffness quantitatively alter the simulated BCG waveform?
• RQ3 To what extent does the model’s output match experimental BCG data acquired from a suspended bed setup?
• RQ4 Can the model serve as a standardized reference for interpreting BCG signals across different sensing platforms?
• RQ5 What are the underlying physiological mechanisms that generate the observed BCG signal features and their pathological variations?

Key findings

• The simulated BCG signal exhibits the characteristic I, J, K, L, M, and N peaks, showing strong qualitative and quantitative agreement with experimental measurements from a suspended bed replica.
• Simulated arterial pressure waveforms and ventricular function parameters (e.g., end-diastolic volume, stroke volume) are in good agreement with values reported in the clinical literature.
• Reduced left ventricular contractility leads to a diminished J peak and altered timing of the K and L peaks, reflecting reduced ejection force.
• Increased arterial stiffness results in a sharper, more pronounced J peak and earlier onset of the K peak, consistent with faster pulse wave propagation.
• The model successfully captures the dynamic interplay between ventricular ejection, vascular impedance, and body motion, producing BCG signals that reflect hemodynamic changes.
• The model’s output demonstrates robustness to parameter variations and provides a consistent, physics-driven baseline for BCG interpretation across diverse sensing technologies.