Subject-specific model estimation of cardiac output and blood volume during hemorrhage

Abstract

We have developed a novel method for estimating subject-specific hemodynamics during hemorrhage. First, a mathematical model representing a closed-loop circulation and baroreceptor feedback system was parameterized to match the baseline physiology of individual experimental subjects by fitting model results to 1 min of pre-injury data. This automated parameterization process matched pre-injury measurements within 1.4 +/- 1.3% SD. Tuned parameters were then used in similar open-loop models to simulate dynamics post-injury. Cardiac output (CO) estimates were obtained continuously using post-injury measurements of arterial blood pressure (ABP) and heart rate (HR) as inputs to the first open-loop model. Secondarily, total blood volume (TBV) estimates were obtained by summing the blood volumes in all the circulatory segments of a second open-loop model that used measured CO as an additional input. We validated the estimation method by comparing model CO results to flowprobe measurements in 14 pigs. Overall, CO estimates had a Bland-Altman bias of -0.30 l/min with upper and lower limits of agreement 0.80 and -1.40 l/min. The negative bias is likely due to overestimation of the peripheral resistance response to hemorrhage. There was no reference measurement of TBV; however, the estimates appeared reasonable and clearly predicted survival versus death during the post-hemorrhage period. Both open-loop models ran in real time on a computer with a 2.4 GHz processor, and their clinical applicability in emergency care scenarios is discussed.

Fig. 1

Block diagram of the open-loop models used to estimate cardiac output and total blood volume. The cardiac output estimation model uses heart rate and arterial blood pressure as inputs and generates a nonpulsatile aortic flow estimate that sets the overall cardiac output estimate. The total blood volume estimation model uses heart rate, arterial blood pressure and measured cardiac output as inputs, and does not use the baroreceptor functions to set peripheral resistance in the systemic circulation (double slashes). See Model Description for details

Fig. 2

Electrical analog schematic of the circulatory model used for cardiac output estimation. Symbols for components are at bottom

Fig. 3

Comparisons between model-estimated and measured cardiac output (CO) for the best fitted subject P132 and the worst, P168. (A) Model (line) and measured (circles) cardiac output versus time. Root mean square (RMS) error values are indicated. (B) Model versus measured cardiac output. Arrows indicate temporal direction. R² is the square of the correlation coefficient. (C) Bland-Altman plots. CO difference = (model cardiac output - measured cardiac output) versus CO average = (model cardiac output + measured cardiac output)/2. Biases (average CO difference) and limits of agreement are indicated

Fig. 4

Cardiac output estimation: Bland-Altman plot for the combined cardiac output estimation results of all 14 study animals. Bias and upper and lower limits of agreement are −0.30, 0.80 and −1.40 l/min, respectively. CO difference = (model cardiac output – measured cardiac output), CO average = (model cardiac output + measured cardiac output)/2

Fig. 5

Model-estimated percent total blood volume loss following hemorrhage vs. time to death. (A) Total blood volume estimation model: percent total blood volume lost. Survivors had significantly lower model-predicted blood loss than nonsurvivors (t-test, P < 0.0001). (B) Cardiac output estimation model: percent total blood volume lost. Survivors had significantly lower model-predicted blood loss than nonsurvivors (t-test, P < 0.0001)