Mechanism-Driven Modeling to Aid Non-invasive Monitoring of Cardiac Function via Ballistocardiography

Figures

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  Figure 1. (A) Schematic representation of the closed-loop model utilized to simulate blood flow through the cardiovascular system. With respect to the version of the model described in (29), two ideal switches (sw1 and sw2) and a capacitor (Cstore) have been added upstream of the right ventricle in order to simulate the experimental procedure performed on swine to acquire data of left-ventricular pressure and volume. (B) Basic model components for ventricles and valves. The subscript i is used to distinguish between left (i = L) and right (i = R) ventricles; Pi is the ventricular pressure; R1,i, R2,i, and R3,i are hydraulic resistances assumed to be constant; Ui and Ei characterize ventricular pumping, Ei representing the variable ventricular elastance. (Bottom) Large arteries; the subscript j is used to distinguish among different arterial segments, specifically aortic arch (j = 3), thoracic aorta (j = 4), abdominal aorta (j = 5), and iliac arteries (j = 6); Pj is the pressure of the specific arterial segment; Ra,j and Rb,j are the hydraulic resistances; Lj is the inductance; Cj and γj represent elastic and viscoleastic properties of the arterial wall, respectively. (C) Basic model…

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  Figure 2. (A) Time recordings of pressure and volume in the left ventricle (LV) under conditions of reducing pre-load, achieved through transient occlusion of the inferior vena cava via inflation of a balloon catheter. (B) Pressure-Volume (P-V) loops in the left ventricle (LV) under conditions of reducing pre-load. The end-systolic and end-diastolic P-V relationships (ESPVR and EDPVR) are also shown. (C) Relationship between stroke work (SW) and end-diastolic volume (EDV) under conditions of reducing pre-load. The slope of the line approximating the SW-EDV relationship is the pre-load recruitable stroke work (PRSW).

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  Figure 3. Angiography pre-(Left) and post-(Right) occlusion of the Left Anterior Descending Coronary artery.

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  Figure 4. Schematic of the sensor placement for the synchronous acquisition of ECG and BCG signals. A three axis accelerometer positioned under the swine neck with the indicated axis orientation is utilized to acquire the BCG signal (Left). The three leads for ECG acquisition are positioned as illustrated (Right).

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  Figure 5. Model-simulated pressure PL(t) and volume VL(t) in the left ventricle (LV), along with their ratio PL(t)/VL(t) representing the actual istantaneous elastance (A). The value of E~L is independent of the loading conditions (black dashed line), whereas the actual instantaneous elastance varies as the load changes. The times at which the actual instantaneous elastance attains its maximum within a cardiac cycle are noted (red crosses) and mark the end-systolic points in the P-V loops whose interpolation gives the end-systolic pressure-volume relationship (ESPVR) (B). The stroke work (SW) computed for each cardiac cycle is reported against the end-diastolic volume (EDV), whose interpolation determines the pre-load recruitable stroke work (PRSW) (C).

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  Figure 6. Model simulated end-systolic pressure-volume relationship (ESPVR) (left) and pre-load recruitable stroke work (PRSW) (right) for ELS at baseline (blue line) and for ELS reductions of 10, 30, and 50% from baseline (red, yellow, and purple curves, respectively). The numerical values of the ESPVR slopes and PRSW are also reported.

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  Figure 7. Model-predicted BCG waveforms fA for different values of the ELS parameter. The vertical dashed lines represent the beginning of the systole and the circles indicate the J peaks in the BCG.

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  Figure 8. Ten s sample of ECG (top) and BCG (bottom) signals recorded synchronously in swine before inducing myocardial infarction (Subject A2). The vertical black dashed lines mark the R peaks in the ECG. The red circles mark the J peak in the BCG.

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  Figure 9. Ten s sample of ECG (top) and BCG (bottom) signals recorded synchronously in swine after inducing myocardial infarction (Subject A2). The vertical black dashed lines mark the R peaks in the ECG. The red circles mark the J peak in the BCG.

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  Figure 10. Comparison between BCG waveforms measure before (blue) and after (red) myocardial infarction on a swine. The curves have been aligned with respect to the preceding R peaks in the ECG (vertical dashed line).

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  Figure 11. Bar chart summarizing the values of TEB and BCG amplitude for the three swine (Subjects A2, A3, and A4) measured pre- and post-MI. The height of the bars correspond to the medians, whereas the black brackets mark the 25th and 75th percentiles. * P < 0.05 pre-MI vs. post-MI.

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  Figure 12. Bar chart summarizing the values of TEB and BCG amplitude measured on three subjects during three consecutive sessions of data acquisition, each lasting 3 min. The bar height correspond to the medians, the black lines correspond to the 25th and 75th percentiles.* P < 0.05 among sessions.