A Mathematical Model for Simulation of Vasoplegic Shock and Vasopressor Therapy

Yi Ming Kao, Catherine Sampson, Syed A. Shah, John R. Salsbury, Ali Tivay, Ramin Bighamian, Christopher G. Scully, Michael Kinsky, George Kramer, Jin Oh Hahn

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Objective: To develop a high-fidelity mathematical model intended to replicate the cardiovascular (CV) responses of a critically ill patient to vasoplegic shock-induced hypotension and vasopressor therapy. Methods: The mathematical model consists of a lumped-parameter CV physiology model with baroreflex modulation feedback and a phenomenological dynamic dose-response model of a vasopressor. The adequacy of the proposed mathematical model was investigated using an experimental dataset acquired from 10 pigs receiving phenylephrine (PHP) therapy after vasoplegic shock induced via sodium nitroprusside (SNP). Results: Upon calibration, the mathematical model could (i) faithfully replicate the effects of PHP on dynamic changes in blood pressure (BP), cardiac output (CO), and systemic vascular resistance (SVR) (root-mean-squared errors between measured and calibrated mathematical responses: mean arterial BP 2.5+/-1.0 mmHg, CO 0.2+/-0.1 lpm, SVR 2.4+/-1.5 mmHg/lpm; r value: mean arterial BP 0.96+/-0.01, CO 0.65+/-0.45, TPR 0.92+/-0.10) and (ii) predict physiologically plausible behaviors of unmeasured internal CV variables as well as secondary baroreflex modulation effects. Conclusion: This mathematical model is perhaps the first of its kind that can comprehensively replicate both primary (i.e., direct) and secondary (i.e., baroreflex modulation) effects of a vasopressor drug on an array of CV variables, rendering it ideally suited to pre-clinical virtual evaluation of the safety and efficacy of closed-loop control algorithms for autonomous vasopressor administration once it is extensively validated. Significance: This mathematical model architecture incorporating both direct and baroreflex modulation effects may generalize to serve as part of an effective platform for high-fidelity in silico simulation of CV responses to vasopressors during vasoplegic shock.

Original languageEnglish (US)
Pages (from-to)1565-1574
Number of pages10
JournalIEEE Transactions on Biomedical Engineering
Issue number5
StatePublished - May 1 2023
Externally publishedYes


  • Vasopressor
  • autonomous critical care
  • digital twin
  • phenylephrine
  • physiological closed-loop control
  • vasoplegia

ASJC Scopus subject areas

  • Biomedical Engineering


Dive into the research topics of 'A Mathematical Model for Simulation of Vasoplegic Shock and Vasopressor Therapy'. Together they form a unique fingerprint.

Cite this