The differential-algebraic Windkessel model with power as input

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The lack of methods to evaluate mechanical function of donated hearts in the context of transplantation imposes large precautionary margins, translating into a low utilization rate of donor organs. This has spawned research into cyber-physical models constituting artificial afterloads (arterial trees), that can serve to evaluate the contractile capacity of the donor heart.

The Windkessel model is an established linear time-invariant afterload model, that researchers committed to creating a cyber-physical afterload have used as a template. With aortic volumetric flow as input and aortic pressure as output, it is not directly obvious how a Windkessel model will respond to changes in heart contractility.

We transform the classic Windkessel model to relate power, rather than flow, to pressure. This alters the model into a differential-algebraic equation, albeit one that is straightforward to simulate. We then propose a power signal model, that is based on pressure and flow measurements and optimal in a Bayesian sense within the class of C2 signals. Finally, we show how the proposed signal model can be used to create relevant simulation scenarios, and use this to illustrate why it is problematic to use the Windkessel model as a basis for designing a clinically relevant artificial afterload.
Original languageEnglish
Title of host publication2022 American Control Conference (ACC)
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Number of pages6
Publication statusPublished - 2022
EventAmerican Control Conference, 2022 - Atlanta, GA, United States
Duration: 2022 Jun 82022 Jun 10


ConferenceAmerican Control Conference, 2022
Abbreviated titleACC
Country/TerritoryUnited States
Internet address

Subject classification (UKÄ)

  • Other Medical Engineering
  • Control Engineering


  • Modelling and simulation
  • cardiac afterload
  • heart evaluation
  • differential-algebraic equation


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