A mechanical model of cardiovascular system for blood pressure estimation

The Non-invasive Physiological Activity Monitoring System (NiPAMS) project is being developed by the research group of Prof. Plant at McGill University. The system is based on vibrations detected by a six-degree of freedom MEMS accelerometer, placed at the xiphoid process of the sternum, using Vibrational Cardiography (VCG) technique. The aim is to build a non-invasive, continue and central system for blood pressure estimation using VCG data acquired experimentally. This thesis describes my contribution to the project, which is based on a lumped parameter model for cardiovascular system (CVS). A simple hydraulic CVS model was selected from literature. An equivalent electric model is obtained correlating blood flow rate to the current “through” electric elements, and blood pressure drop to the voltage drop “across” each element. Hydraulic capacitances are correlated to inertial effects, resistances to damping and inductances to stiffness. This approach implies Firestone analogy to transform the electric CVS model into the equivalent mechanical one. Finally, a linear mass-damper-spring model (MCK) with 12 degrees of freedom (DOF) is obtained, where each DOF represents a significant compartment of the cardiovascular system, including four heart chambers. Some springs connected to ground are added to ensure static state for the model; then, mass, damping and stiffness matrices are derived. In this CVS model, damping is not classical, i.e. not proportional; therefore, complex modal analysis is implemented in the numerical analyses. Complex eigenvectors and eigenvalues are obtained, hence 24 natural frequencies and damping ratios are calculated. LUPOS FEM code is used to evaluate and to visualise vibrational modes. Assuming non-classical damping, the system performs two modes of rigid body motion, sixteen underdamped modes and six overdamped modes. The two rigid body modes can be interpreted as two moments when blood flow through vessels looks like rigid body motion. The frequency range for CVS model goes from 1.3 Hz to 21 Hz. That confirms model validity because time-frequency spectrograms of VCG signals show a high frequency contribution in the same range. Furthermore, heart rate measured in NiPAMS tests corresponds to frequencies around 1.3 Hz. Besides, some HR super harmonics correspond to significant frequencies in VCG Continuous Wavelet Transformation graphs. To confirm the robustness of the simple lumped model, heart excitation is included. Pulsating heart action is assumed to depend only on left and right ventricles contractility. It implies to define two pressure functions over time for the two ventricles, which correspond to velocities, according to analogies used. Displacement and acceleration come from velocity integration and derivation, hence imposed kinematics is applied on left and right ventricular DOFs. The model is implemented in LUPOS and Simulink to solve the new time-dependent dynamic problem. Finally, time response is obtained with displacement, velocity and acceleration over time for each DOF. Resulting pressure waveforms can be directly compared with invasive pressure recordings. Heart chambers pressure curves show a straightforward correspondence; more investigation is required to assess waveforms for the other DOFs. Moreover, a CVS model without rigid body modes is proposed adding two springs connecting masses to ground. It generates more reliable time responses. Discussion on reference data concludes this work.