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Abstracts: Meeting of the Society in Europe for Simulation Applied to Medicine (SESAM), 10-11 May 2002: Santander, Spain

Graphical and mathematical representation of congenital heart disease

Sá Couto, D.*; van Meurs, W. L.*†¶; Goodwin, J. A.¶‡

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European Journal of Anaesthesiology: October 2003 - Volume 20 - Issue 10 - p 841-842
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The aim of this work is to represent congenital heart diseases graphically and mathematically for use in educational simulations of the neonate and infant. This work is based on a previously published model for the adult cardiovascular system [1](Fig. 1).

Figure 1
Figure 1:
Hydraulic analog of the Beneken model.

Methods: A model for the term fetus [2] contains structural elements representing a patent ductus arteriosus and an open foramen ovale. These structures, as well as those necessary for the simulation of a ventricular septal defect were incorporated in the Beneken model (Fig. 2).

Figure 2
Figure 2:
Hydraulic analog of the cardiovascular model reflecting congenital heart diseases.

As an example of how the mathematical model is derived from the graphical representations, we present the equations for the patent ductus arteriosus (PDA). The flow rate trough the PDA is a new state variable:

where F(t): flow rate; P(t): pressures; R: resistances; L: inertia; da: ductus arteriosus; itha: intrathoracic arteries; pa: pulmonary arteries. Fda(t) is positive in the systemic → pulmonary direction.

Conservation of mass in the intrathoracic and pulmonary arteries is reformulated as follows:

where V: volumes; lv: left ventricle; rv: right ventricle. Flow rates are compartment outflow rates.

This model was simulated with the parameters reflecting a 6-month-old infant [3].

Results:Table 1 shows preliminary simulation results with and without a moderate PDA. The relative pressure changes are similar to the ones reported for neonates in [4]. We are currently pursuing a specific reference for infants.

Table 1
Table 1:
Simulation results: Normal infant and an infant with a moderate PDA.

Acknowledgements: This work was funded in part by a grant from Medical Education Technologies, Inc., Sarasota, Florida, USA. The Fundação para a Ciência e a Tecnologia of the Portuguese Ministry of Science and Technology provided funds for participation in this conference.


1. Beneken JEW. A mathematical approach to cardiovascular function. The uncontrolled human system. Utrecht, The Netherlands: Ph.D. thesis, 1965.
2. Huikeshoven F, et al. Mathematical model of the fetal cardiovascular system: the uncontrolled case. Am J Physiol 1980; 239: R317-325.
3. Goodwin JA, et al. Modeling infant cardiovascular physiology for educational simulations. In preparation, 2002.
4. Klaus MH, et al. Care of the high-risk neonate, 5th edn. Philadelphia, USA: W.B. Saunders Company, 2001.

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The senior author of each article has confirmed that the ethical aspects of these studies have been approved (a) for clinical studies by the Institution or an Ethics Committee and, if applicable, that informed patient consent has been obtained, (b) for experimental studies, involving the use of animals, by the institution and that the animals have been treated according to good practice.

© 2003 European Academy of Anaesthesiology