Poster U1 - Quantitative assessment of compensatory and decompensatory mechanisms during hemorrhage through mathematical modeling of acute hemodynamics

Introduction: Hemorrhagic shock is the leading cause of potentially preventable deaths from injury in people aged 1-44 years. Substantial blood loss results in insufficient oxygen delivery to key organs and triggers compensatory mechanisms. Without quick and effective lifesaving interventions to minimize blood loss and restore systemic pressures and blood volume, one’s condition can deteriorate to decompensated shock. Large animal models, particularly swine, have been the gold standard for studying the pathophysiology of hemorrhagic shock and optimizing resuscitation strategies. However, their high financial cost and the necessity for technical and surgical expertise have limited their use among trauma and shock researchers. There is a need for alternative platforms that can provide insights into acute physiologic responses post-hemorrhage.

Physiology-based and experimentally validated in-silico models of hemorrhagic shock can provide a cost-effective method to investigate hemodynamic adaptations to sustained blood loss and to optimize resuscitation and other life-saving strategies. Currently, there is a need to develop mathematical models that can adequately describe the complex adaptations of the cardiovascular system during hemorrhage. As a critical step towards developing a mathematical framework of hemorrhagic shock and resuscitation, we developed a model of blood flow during hemorrhage using a closed-loop lumped parameter network and calibrated it using rich experimental data collected in swine. Model parameters were calibrated at multiple time points as blood volume was removed from the closed-loop circuit, facilitating interpretable and meaningful insight into the regulatory response of the cardiovascular system to hemorrhage.

Materials and

Methods: Yorkshire swine (preliminary data on n=4), under an approved IACUC protocol, were anesthetized and instrumented with flow and pressure probes along the aorta and with a pressure-volume catheter in the left ventricle (Figure 1). Once instrumented, 30% of the animal’s blood volume was removed through the femoral vein over a 30-minute period to induce a class III hemorrhage. Changes in cardiac and vascular hemodynamics were recorded in real-time.

Hemodynamics were simulated through a closed-loop lumped parameter network, shown in Figure 1, developed using the open-source software CRIMSON. A time-varying elastance function was imposed to model the heart contractility, determined from the left ventricle pressure-volume catheter data. Target flow distributions among aortic branches were determined from the flow probes, supplemented by assumptions on mass conservation and anatomy-based flow splits when necessary. Total blood volume was initialized in volume-tracking pressure elements and was estimated as 60 mL/kg.

Using data from a single pig, time-averaged experimental flow and pressure waveforms were generated for various branches at baseline (i.e., T(0)) and at multiple time points during hemorrhage. At baseline, model parameters were tuned to match the mean and amplitude of flow and pressure waveforms. Following baseline, a subset of parameters of the closed-loop network were calibrated to match the flow and pressure waveforms as blood volume was removed from the circuit. Tunable parameters included: total arterial compliance (C), total arterial resistance (R_Proximal+R_Distal) and ratio of proximal to distal resistance (RProximal/RDistal) for each branch, venule resistance (R_V3), venous unstressed volume (V_u), and venous elastance (E_V).

Results, Conclusions, and Discussions: We observed a clear flow distribution shift in the main aortic branches following 30% blood loss, suggesting differential regulatory control between the vascular beds (Figure 2). Notably, the proportion of cardiac output (CO) to the intercostal arteries increases substantially during hemorrhage, while the proportion to the carotid and visceral arteries is maintained. The remaining arteries experienced a decrease in the proportion of CO.

Three distinct stages are apparent in the moving average of the hemodynamic data over the 30-minute experiment (Figure 3A), likely representing different physiological control mechanisms. In the first stage [T(0)-T(12)], pressure and CO continuously decrease as blood volume is removed. In the second stage [T(12)-T(20)], compensatory mechanisms stabilize the mean arterial pressure (MAP) and CO, resulting in increased flow to the brain via the left carotid artery. Lastly, in the third stage [T(20)-T(30)], there is a shift from compensatory to decompensatory mechanisms; CO and MAP cannot be maintained and decrease. In this work, we focused our efforts on simulating the hemodynamic adaptations during the first stage of hemorrhage.

The calibrated model parameters are evidence that physiological control is important in mitigating decreased blood perfusion during the first stage of hemorrhage. Vascular beds vary their total resistance at different rates to accommodate the measured changes in blood flow distribution (Figure 3B). For example, the increase in carotid artery distal resistance is 50% smaller than that of the subclavian arteries, prioritizing carotid artery flow. The total arterial compliance increases over stage one, consistent with the decrease in blood pressure. The venous unstressed volume decreases by 6% from baseline to raise MAP, changing slowly at first but accelerating as hemorrhage continues. Furthermore, our model effectively captures the leftward shift in the left ventricle pressure-volume loops and the decrease in systolic ventricle pressure (Figure 3C) during hemorrhage. Simulated flow and pressure waveforms match within 5% values of mean and amplitude of the measured data throughout the first stage of hemorrhage (Figure 3C).

This work is a critical step for developing novel mathematical frameworks of hemorrhage, which will be foundational for accelerating hemorrhagic shock research and the development of next-generation treatment strategies.

Acknowledgements (Optional): Funding provided by NIH/NHLBI: R01HL162633