Fig 1.
A schematic representation of the cardiovascular model.
The model is a serial circuit and contains one heart chamber which acts like a pump, organs, and arterial and venous compartments. Heart rate, contractility, vascular resistance and unstressed venous volume are affected by the baroreflex (Sb) which is determined by the arterial pressure, and by S which is an independent component that does not depend on the current physiological state. In addition, intra-vascular volume can change through Iex and the vascular resistance is also modulated by MSVR. Created with BioRender.com.
Fig 2.
Overview of the estimation process.
A. Arterial and venous pressure waveforms are recorded via arterial and central venous catheters that are connected to pressure transducers. Specifically, in this paper waveforms are sampled from critically-ill children hospitalized in an intensive care unit and recorded at 125Hz. B. The raw data is analyzed and five measurements are extracted—the observables. C. The observables are used as an input for the full model (iCVS) estimation and using constrained nonlinear optimization we obtain the set of parameter values that best fit observables. Created with BioRender.com.
Table 1.
List of estimated parameters.
Table 2.
List of measurements.
Fig 3.
Simulations of the iCVS model for different shock conditions.
Each column presents a simulation of one artificial patient with a given shock state: A-H—hypovolemic shock state, I-P—distributive shock state and Q-X—combined hypovolemic and distributive shock state. The hidden parameters are fixed, and the observables are simulated accordingly (see Methods). Two of the hidden parameters are presented for each patient: A, I, Q Time dependent intra vascular volume change (Iex). In A, Q liquid withdrawal occurs over a period of 15 minutes. B, J, R Time course of MSVR. In J, R a reduction in MSVR occurs over a period of 15 minutes. C-H, K-P, S-X—the resulting observables: C, K, S Arterial pressure (Pa), D, L, T Venous pressure (Pv), E, M, U Peripheral resistance multiplied by arterial compliance (RC), F, N, V Heart rate (Hr), G, O, W Pulse pressure (Pp). H, P, X The time dependent magnitude of the baro-reflex (Sb).
Fig 4.
Extraction of slow and fast time scales features from venous and arterial blood pressure recordings.
A,B. An example of the raw data, sampled at 125 Hz frequency by the bedside patient monitor. A. Arterial blood pressure, B. Venous blood pressure. Note how these real-life data are noisy, fluctuating, and riddled with artifacts related to patient movement and care. C-G. Features that are extracted from the raw data. C,D. Mean arterial and venous pressures (slow time scale features), E-G. Heart rate, peripheral resistance and pulse pressure (fast time scale features).
Table 3.
For each patient, age, weight, cause of admission to the intensive care unit and the cardio-vascular state as determined by an expert clinician are given.
Fig 5.
Demonstration of iCVS model inference results for a neonate patient (body weight < 5 Kg), in a hypovolemic shock state.
iCVS results for patient number 1 (see Table 3) are presented. A-E.—The observables: mean arterial pressure (A), mean venous pressure (B), heart rate (C.), RC—the peripheral resistance multiplied by the arterial compliance (D) and pulse pressure (E). F-H. Gray circles—optimal parameters which are achieved in each segment of 300 sec. Black line—a smoothed version of the estimated parameters (see Material and methods). F. Relative intra vascular volume change (). G. Non autonomic vascular resistance (MSVR). H. Maximal relative contractility (
). Note that in this patient which suffers from a hypovolemic shock state is identified as having negative
by the model.
Fig 6.
iCVS model inference results for an adolescent patient (body weight ∼ 60 Kg), in a distributive shock state.
iCVS results for patient number 5 (see Table 3) are presented. A-E. The observables: Mean arterial pressure (A), mean venous pressure (B), heart rate (C), RC—the peripheral resistance multiplied by the arterial compliance (D) and pulse pressure (E). F-H. Gray circles—optimal parameters which are achieved in each segment of 300 sec. Black line—a smoothed version of the estimated parameters (see Material and methods). F. Relative intra vascular volume change (). G. Non autonomic vascular resistance (MSVR). H. Maximal relative contractility (
). Note that this patient, suffering from a distributive shock state, is correctly identified as having negative MSVR by the model.
Fig 7.
iCVS model inference results for a neonate patient (body weight < 5 Kg), in a combined hypovolemic, cardiogenic and distributive shock state.
iCVS results for patient number 4 (see Table 3) are presented. Dots mark chest opening. A-E.—The observables: mean arterial pressure (A), mean venous pressure (B), heart rate (C), RC—the peripheral resistance multiplied by the arterial compliance (D) and pulse pressure (E). F-H. Gray circles—optimal parameters which are achieved in each segment of 300 sec. Black line—a smoothed version of the estimated parameters (see Material and methods). F. Relative intra vascular volume change (). G. Non autonomic vascular resistance (MSVR). H. Maximal relative contractility (
). Note that in this patient
becomes non-negative and the contractility increases after the chest opening procedure, compatible with an improving in cardiac function and bleeding cessation as a result of the chest opening procedure. We note that in panel H a single point with an extremely large value is not plotted, at 9.66 minutes after chest opening (
mmHg). This point correlates with a short transient increase in the venous and arterial pressures, possibly resulting from a bolus of a vasoactive drug given to the patient at the time.
Fig 8.
Illustration of the estimation process for a neonate patient (body weight < 5 Kg) control patient, post cardiac surgery.
iCVS results for patient number 9 (see Table 3) are presented. A-E. The observables: mean arterial pressure (A), mean venous pressure (B), heart rate (C), RC—the peripheral resistance multiplied by the arterial compliance (D) and pulse pressure (E). F-H. Gray circles—optimal parameters which are achieved in each segment of 300 sec. Black line—a smoothed version of the estimated parameters (see Material and methods). F. Relative intravascular volume change (). G. Non autonomic vascular resistance (MSVR). H. Maximal relative contractility (
).
Fig 9.
Estimated and MSVR for ten subjects.
For each subject, the model is applied for a time window of 25 minutes (see Methods). The analysis is done over segments of 300 seconds and the average values of (panel A) and MSVR (panel B) are presented. A. The average
value is presented for all sample patients. Blue—patients which are documented with post-operative bleeding, black—no post operative bleeding is documented (average value of the hypovolemic group is −0.016 min−1, average value of the non-hypovolemic group is 0.0003 min−1, Pvalue = 0.026). B. The average MSVR value of all sample patients is presented, ordered differently than in A. As there is no objective criteria for a distributive state, unlike blood loss, we resort to identifying such patients by either expert opinion or indirect evidence from the electronic medical record. In red—patients who were identified by clinical experts as suffering from distributive shock states, in pink—patients who were treated by vaso-constrictors (drugs that directly affect vascualr smooth muscle to increase systemic vascular resistance), in black—patients who were not documented with distributive shock states (average value of the distributive group (red) is −0.43, average value of the non-distributive group is −0.07, Pvalue = 0.077). Error bars in A and B represent standard error of the mean.
Table 4.
Minimal and maximal values of Pset are the 10th and 90th percentile of the mean arterial pressure respectively, adapted from [11]. Bounds of minimal heart rate are the 5th percentile and 25th percentile (adapted from [10]). Bounds of maximal heart rate are the 75th percentile and 95th percentile (adapted from [10]). In addition, and
are the values of minimal and maximal arterial compliance, respectively. See [24].