Dynamic Estimation of Cardiovascular State From Arterial Blood Pressure Recordings

Fig. 1.. Illustration of physiological model. (a) The two-element Windkessel model, which models arterial blood pressure (ABP) as an RC-circuit receiving blood flow from the heart, and its physiological parallels in humans (figure graphic created with BioRender.com). Components of this model include aortic flow (AF) into the system as f(t), ABP as p(t), arterial resistance from the microcirculation as R and compliance of large arteries, with primary contributions from the aorta, as C. The time constant of this model is τ=RC. We highlight three locations of arterial catheterization (femoral, brachial and central), as analog locations were used in the experimental swine dataset. (b) In vivo swine central ABP (top) and AF (bottom) with τ≈1. (c) In vivo swine central ABP (top) and AF (bottom) with τ≈.5. (d) (Top) Simulation of the Windkessel Model forward in time with R=1 and C=1 from 0≤t<10 and then C=1 and R=.5 from 10≤t<20 where t is time. (bottom) Comparison of the exponential decay of one beat for C=1 and R=1 (light green) versus C=1 and R=.5 (dark green).

Fig. 2.. Method to estimate τ from aortic flow (AF) and arterial blood pressure (ABP). (a) We used the dynamic equation from the two-element Windkessel model to generate estimates of τ using AF, ABP and an approximate derivative of pressure. (b) Example in vivo swine AF (f(t)). (c) Example in vivo swine ABP (p(t)). (d) Example in vivo derivative of swine ABP (p˙(t)).

Fig. 3.. Method to estimate τ from arterial blood pressure (ABP). We built a graphical model of τ in relation to samples of ABP and then built a Kalman filter around this model to learn τ at each beat k. (a) Modeled ABP from the two-element Windkessel Model. (b) Modeled aortic flow as impulses of stroke volume, ΔVk. (c) Graphical model of τk related to ABP (p(t)) observations, vk. (d) Example in vivo ABP observations. (e) Modeled ABP observations.

Fig. 4.. Benefits of Kalman filter for estimation of τ. (a) (Top) Segment of central ABP waveform from experiment 1. (bottom) Corresponding Kalman τ estimates, along with exponential fit τ estimates lacking history dependence. (b) Zoomed in segment of (a) emphasizing Kalman τ estimates’ resistance to breathing artifacts with τ≈.6. (c) Zoomed in segment of (a) emphasizing Kalman τ estimates’ responsiveness to rapid changes. (d) Zoomed in segment of (a) emphasizing Kalman τ estimates’ resistance to breathing artifacts with τ≈.8. (e) (Top) Segment of brachial ABP with potential prominent backward reflected pressure waves from experiment 2. (Bottom) Corresponding Kalman τ estimates, along with exponential fit τ estimates lacking history dependence.

Fig. 5.. Experiment 1: Proportional R (τ) estimation results. Accompanying each estimate using arterial blood pressure (ABP) is the calculated 95% credibility interval of τk at beat k. (a) Comparison of the beat-by-beat estimate of τ using femoral ABP versus the beat-by-beat estimate of τ using femoral ABP and aortic flow. (b) Same as (a) but using central ABP. Areas of lighter blue indicate that the estimate using ABP was derived from a central ABP pulse with a prominent dicrotic notch. (c) Same as (a) but using brachial ABP. (d) Agreement of our Kalman estimates using central, brachial or femoral ABP. Once again, areas of lighter blue indicate that the estimate using ABP was derived from a central ABP pulse with a prominent dicrotic notch.

Fig. 6.. Experiment 1: Proportional CO (CO/C) estimation results. Accompanying each estimate using arterial blood pressure (ABP) is the calculated 95% credibility interval of CO/C at beat k. (a) Comparison of the beat-by-beat estimate of CO/C using femoral ABP and τ estimates versus the beat-by-beat estimate of CO/C using central ABP and aortic flow. (b) Same as (a) but using central ABP. (c) Same as (a) but using brachial ABP. (d) Agreement of our Kalman estimates using central, brachial or femoral ABP with corresponding central, brachial or femoral τ estimates.

Fig. 7.. Effects of common cardiovascular drugs on femoral mean arterial pressure (MAP) and femoral ABP-derived estimates of proportional R and CO. Here, k indexes the beat, and ki indicates the initial beat of a segment. (a) Direct (i.e., change in R or CO from change in drug concentrations) and indirect (i.e., change in MAP as a result of change in R or CO) effects of cardiovascular drugs phenylephrine (PE), dobutamine (DB), esmolol (ES), nitroglycerin (NI) and fentanyl (FT). Proportional R and CO estimates were normalized to the first estimate of the segment. (b) Direct changes in estimates of τ and estimates of CO/C causing indirect changes in MAP from a PE infusion. Segment is from Experiment 1. (c) Same as (b) but from a DB infusion with background PE. Segment is from Experiment 3. (d) Same as B. but from an ES infusion with background PE. Segment is from Experiment 3. (e) Same as (b) but from an NI infusion with background PE. Segment is from Experiment 5. (f) Same as (b) but from FT boluses with background DB and PE. Vertical lines indicate drug boluses. Segment is from Experiment 6.