A Mathematical Model for the Prediction of Fluid Responsiveness BENNO LANSDORP, 1,2 MICHEL VAN PUTTEN, 1 ANDER DE KEIJZER, 1 PETER PICKKERS, 2 and JOHANNES VAN OOSTROM 3 1 MIRA Institute for Biomedical Technology and Technical Medicine, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands; 2 Department of Intensive Care Medicine, Radboud University Nijmegen Medical Centre, Nijmegen, The Netherlands; and 3 J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, USA (Received 25 July 2012; accepted 15 January 2013; published online January 24, 2013) Associate Editor Ajit P. Yoganathan oversaw the review of this article. Abstract—Fluid therapy is commonly used to improve cardiac output in hemodynamically instable patients in the intensive care unit. However, to predict whether patients will benefit from this intervention (i.e. are volume responsive), is difficult. Dynamic indices, that rely on heart-lung interactions, have shown to be good predictors of fluid responsiveness under strict clinical conditions, but clinical use is still limited. This is due to the lack of understanding of the complex underlying physiology since multiple quantities are involved. We present a physiolog- ically based mathematical model of the interaction between the respiratory and cardiovascular systems incorporating dynamic indices and fluid responsiveness. Our model is based on existing models of the cardiovascular system, its control, and the respiratory system during mechanical ventilation. The model of the cardiovascular system is expanded by including non-linear cardiac elastances to improve simulation of the Frank-Starling mechanism. An original model including five mechanisms for interaction between mechanical ventilation and the circulation is also presented. This model allows for the simulation of these complex relationships and may predict the effect of volume infusion in specific patients in the future. The presented model must be seen as a first step to a bedside clinical decision support system, and can be used as an educational model. Keywords—Simulation, Modeling, Cardiovascular system, Hemodynamics, Heart-lung interaction. INTRODUCTION Volume resuscitation is one of the most common therapeutic procedures in intensive care units to improve cardiac output (CO) or stroke volume index (SVI) and thus hemodynamics in critically ill patients. However, to identify patients who might benefit from this therapy by an increase in cardiac output (volume responders), is a clinical challenge. Both clinical examination and static indicators of cardiac preload (e.g. central venous pres- sure) have been shown to be of minimal predictive value in distinguishing volume responders from non-respond- ers. 8,16 Over the last decade, dynamic indices that rely on cardiopulmonary interactions are used to assess fluid responsiveness in ventilated patients. Examples of dynamic indices are pressure or flow fluctuations that can be observed within the peripheral arteries. They are caused by mechanical ventilation when the heart operates on the steep portion of the Frank–Starling curve instead of on the flat portion of the curve and changes in preload cause variations in stroke volume. 11,15 Although dynamic indices have shown to be good predictors of volume responsiveness, 12,16 , their use is limited to selected populations of patients and requires specific conditions for its application. 9 The reason for this limited applicability is the complex underlying physiology in which many quantities are involved (e.g. tidal volume, lung compliance, chest wall compliance and volume status), which makes the dynamic indices difficult to interpret. It is our contention that by a better understanding of the complex relationships between the involved quantities, this use can be expanded. It is our goal to develop a mathematical model that captures the dynamics of heart-lung interactions and their relation to a patient’s volume status. Such a model, that is able to simulate the highly interrelated processes of this com- plex physiology, could also be used for educational simulations. 24,25 . When adaptable to the individual patient, the model could form the basis of a decision support system by predicting the effect of any considered volume infusion in specific patients. 10–26 A first, and to our knowledge only step towards the identification of factors that influence the arterial Address correspondence to Benno Lansdorp, MIRA Institute for Biomedical Technology and Technical Medicine, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. Elec- tronic mail: b.lansdorp@utwente.nl Cardiovascular Engineering and Technology, Vol. 4, No. 1, March 2013 (Ó 2013) pp. 53–62 DOI: 10.1007/s13239-013-0123-0 1869-408X/13/0300-0053/0 Ó 2013 Biomedical Engineering Society 53