A model of anaerobic tissue perfusion during trauma—Lactate trajectory curvature can determine recovery

Hypovolemic shock and hemorrhage continue to shape healthcare delivery and incur a heavy burden on public health and wellbeing. Many healthcare organizations have specific transfusion protocols that are referenced when a patient meets certain physiological criteria. These protocols are shaped around best practices and nuanced understanding of the physiology of the patient. Despite their importance, these protocols are extremely difficult to change or challenge and, to date, there does not exist a sufficient mathematical model that may be employed towards investigating simulated patient hemorrhage. We show that once constructed, we can consider the health of the patient in phase-space rather than traditional time-series representations, quantifying the recovery of the patient due to the geometry of the trajectories. We construct a whole-body physiology model of hemorrhagic shock and trauma that encompasses multiple organ systems, non-linear feedback mechanisms and patient variability. We validate this model by constructing a major hemorrhage scenario, that includes transit time and associated mass transfusion resuscitation of the patient. We then use this model to create phase-plane diagrams of patient trajectories as a function of lactate blood pH and volumes, among other relevant physiological metrics. Exploring these patient trajectories amongst a varied patient population yields a series of high curvature points associated with the transition from deterioration to recovery of the patient. We then construct a convex hull, covering the high curvature regions of a diverse simulated patient population. These hulls, constructed by simulated numerous patients, exposed to three distinct hemorrhagic severities, are then used to validate the model by comparing experimental serum lactate levels as a function of blood volume to these regions in phase-space. In conclusion, we show that the model is highly accurate and accounts for distinct lactate trajectories amongst the simulated patient cohorts. Finally, we fit a logistic curve to the resulting data for a quick patient severity tool and denote the standard error of parameterization based on the delta method.