A Simple Cardiovascular Model for the Study of Hemorrhagic Shock

Hemorrhagic shock is the number one cause of death on the battlefield and in civilian trauma as well. Mathematical modeling has been applied in this context for decades; however, the formulation of a satisfactory model that is both practical and effective has yet to be achieved. This paper introduces an upgraded version of the 2007 Zenker model for hemorrhagic shock termed the ZenCur model that allows for a better description of the time course of relevant observations. Our study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. This model is capable of replicating the changes in mean arterial pressure, heart rate, and cardiac output after the onset of bleeding (as observed in four experimental laboratory animals) and achieves a reasonable compromise between an overly detailed depiction of relevant mechanisms, on the one hand, and model simplicity, on the other. The former would require considerable simulations and entail burdensome interpretations. From a clinical standpoint, the goals of the new model are to predict survival and optimize the timing of therapy, in both civilian and military scenarios.

[1]  A. Kerwin,et al.  An analysis of shock index as a correlate for outcomes in trauma by age group. , 2013, Surgery.

[2]  V. Convertino,et al.  Integrated Compensatory Responses in a Human Model of Hemorrhage. , 2016, Journal of visualized experiments : JoVE.

[3]  R. Wytch,et al.  Validation of a computer model of haemorrhage and transcapillary refill. , 1995, Medical engineering & physics.

[4]  J. Demuro,et al.  Application of the Shock Index to the prediction of need for hemostasis intervention. , 2013, The American journal of emergency medicine.

[5]  C. Wade,et al.  Normal physiological values for conscious pigs used in biomedical research. , 1990, Laboratory animal science.

[6]  D. Prough,et al.  Isoflurane Inhibits Compensatory Intravascular Volume Expansion After Hemorrhage in Sheep , 2006, Anesthesia and analgesia.

[7]  D. Gann,et al.  Restitution of blood volume after hemorrhage: role of the adrenal cortex. , 1976, The American journal of physiology.

[8]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[9]  Biswadev Mitra,et al.  Long-Term Outcomes of Patients Receiving a Massive Transfusion After Trauma , 2014, Shock.

[10]  Sabir Ali,et al.  Correlation of Shock Index and Modified Shock Index with the Outcome of Adult Trauma Patients: A Prospective Study of 9860 Patients , 2014, North American journal of medical sciences.

[11]  S. Malpas,et al.  Slow oscillations in blood pressure via a nonlinear feedback model. , 2001, American journal of physiology. Regulatory, integrative and comparative physiology.

[12]  J. Levick,et al.  Microvascular fluid exchange and the revised Starling principle. , 2010, Cardiovascular research.

[13]  D. Prough,et al.  Volume Turnover Kinetics of Fluid Shifts after Hemorrhage, Fluid Infusion, and the Combination of Hemorrhage and Fluid Infusion in Sheep , 2005, Anesthesiology.

[14]  E. Starling.  On the Absorption of Fluids from the Connective Tissue Spaces , 1896, The Journal of physiology.

[15]  R. Bellamy.  The causes of death in conventional land warfare: implications for combat casualty care research. , 1984, Military medicine.

[16]  C. Michel,et al.  Understanding and extending the Starling principle , 2020, Acta anaesthesiologica Scandinavica.

[17]  Jeremy W. Cannon,et al.  Resuscitative Endovascular Balloon Occlusion of the Aorta (REBOA) for Hemorrhagic Shock. , 2018, Military medicine.

[18]  R. Hahn,et al.  The Extended Starling principle needs clinical validation , 2020, Acta anaesthesiologica Scandinavica.

[19]  D. Gann,et al.  Role of cortisol in the restitution of blood volume after hemorrhage. , 1975, American journal of surgery.

[20]  Bernadette A. Thomas,et al.  Global and regional mortality from 235 causes of death for 20 age groups in 1990 and 2010: a systematic analysis for the Global Burden of Disease Study 2010 , 2012, The Lancet.

[21]  E. Uhl,et al.  A porcine polytrauma model with two different degrees of hemorrhagic shock: outcome related to trauma within the first 48 h , 2015, European Journal of Medical Research.

[22]  C. Rothe,et al.  Reflex control of veins and vascular capacitance. , 1983, Physiological reviews.

[23]  N. Silverman,et al.  Cardiac ventricular diastolic and systolic duration in children with heart failure secondary to idiopathic dilated cardiomyopathy. , 2006, The American journal of cardiology.

[24]  K. Baker,et al.  Venous return and clinical hemodynamics: how the body works during acute hemorrhage. , 2015, Advances in physiology education.

[25]  Matthias Münzberg,et al.  The Shock Index revisited – a fast guide to transfusion requirement? A retrospective analysis on 21,853 patients derived from the TraumaRegister DGU® , 2013, Critical Care.

[26]  G. Thind,et al.  Recent advances in the understanding of endothelial barrier function and fluid therapy , 2018, Postgraduate Medical Journal.

[27]  L. Harsányi,et al.  Experimental Models of Hemorrhagic Shock: A Review , 2013, European Surgical Research.

[28]  Pierre Baconnier,et al.  SAPHIR: a physiome core model of body fluid homeostasis and blood pressure regulation , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[29]  G. Clermont,et al.  Development of hemorrhage identification model using non-invasive vital signs , 2020, Physiological measurement.

[30]  Gilles Clermont,et al.  Towards a model-based medicine: integration of probabilistic inference with mechanistic knowledge , 2006 .

[31]  Daniel A Beard,et al.  A computational analysis of the long-term regulation of arterial pressure. , 2013, F1000Research.

[32]  R White,et al.  A computer model of major haemorrhage and resuscitation. , 1996, Medical engineering & physics.

[33]  D. Glower,et al.  Linearity of the Frank-Starling relationship in the intact heart: the concept of preload recruitable stroke work. , 1985, Circulation.

[34]  J. P. Hannon.  Hemorrhage and Hemorrhagic Shock in Swine: A Review , 1989 .

[35]  D. Gann,et al.  Transcapillary refill in hemorrhage and shock. , 1981, Archives of surgery.

[36]  Koji Kashihara,et al.  A derivative-sigmoidal model reproduces operating point-dependent baroreflex neural arc transfer characteristics. , 2004, American journal of physiology. Heart and circulatory physiology.

[37]  S. Weinbaum,et al.  A new view of Starling's hypothesis at the microstructural level. , 1999, Microvascular research.

[38]  M. Feneley,et al.  Comparison of preload recruitable stroke work, end-systolic pressure-volume and dP/dtmax-end-diastolic volume relations as indexes of left ventricular contractile performance in patients undergoing routine cardiac catheterization. , 1992, Journal of the American College of Cardiology.

[39]  Gilles Clermont,et al.  Correction: From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses , 2019, PLoS Comput. Biol..

[40]  Kjell Titlestad,et al.  Epidemiology of Massive Transfusion: A Binational Study From Sweden and Denmark* , 2016, Critical care medicine.

[41]  G. Mcgwin,et al.  Identifying risk for massive transfusion in the relatively normotensive patient: utility of the prehospital shock index. , 2011, The Journal of trauma.

[42]  T. Woodcock,et al.  Revised Starling equation and the glycocalyx model of transvascular fluid exchange: an improved paradigm for prescribing intravenous fluid therapy. , 2012, British journal of anaesthesia.

[43]  M. Fitzgerald,et al.  Prediction of critical haemorrhage following trauma: A narrative review , 2016 .

[44]  João Paulo Souza,et al.  A Systematic Review of the Relationship between Blood Loss and Clinical Signs , 2013, PloS one.

[45]  D. Hoyt,et al.  Hemorrhagic shock , 1997 .

[46]  Gilles Clermont,et al.  From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses , 2007, PLoS Comput. Biol..

[47]  Jeremy W. Cannon,et al.  Damage control resuscitation in patients with severe traumatic hemorrhage: A practice management guideline from the Eastern Association for the Surgery of Trauma , 2017, The journal of trauma and acute care surgery.

[48]  I. F. McNeill,et al.  TRANSCAPILLARY REFILLING AFTER HEMORRHAGE IN NORMAL MAN: BASAL RATES AND VOLUMES; EFFECT OF NOREPINEPHRINE. , 1963, Annals of surgery.

[49]  Biswadev Mitra,et al.  The utility of a shock index ≥ 1 as an indication for pre-hospital oxygen carrier administration in major trauma. , 2014, Injury.

[50]  P. Radermacher,et al.  Modeling traumatic-hemorrhagic shock--nothing is simple and easy. , 2012, Shock.

[51]  B J TenVoorde,et al.  A baroreflex model of short term blood pressure and heart rate variability. , 2000, Studies in health technology and informatics.

[52]  G. A. Braga,et al.  A QUANTITATIVE ANALYSIS OF TRANSCAPILLARY REFILL IN SEVERE HEMORRHAGIC HYPOTENSION IN DOGS , 1994, Shock.