A mathematical model of cardiovascular dynamics for the diagnosis and prognosis of hemorrhagic shock

Laura D'Orsi, Luciano Curcio, Fabio Cibella, Alessandro Borri, Lilach Gavish, Arik Eisenkraft, Andrea De Gaetano

Research output: Contribution to journalArticlepeer-review


A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-Algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.

Original languageAmerican English
Pages (from-to)417-441
Number of pages25
JournalMathematical Medicine and Biology
Issue number4
StatePublished - 15 Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.


  • Cardiovascular dynamics
  • Hemorrhagic shock
  • Mathematical modelling


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