# Analytical interpretation of hemodynamic data in patients with intracardiac shunts: Role of mathematical modeling

## TL;DR

This paper uses a mathematical model to better understand how blood flow is affected in heart patients with specific types of shunts.

## Contribution

The study introduces a lumped parameters model to analytically interpret hemodynamic changes in intracardiac shunts.

## Key findings

- A twofold rise in pulmonary vascular resistance significantly reduces Qp/Qs in VSD and VSD+ASD models but not in isolated ASD.
- In isolated ASD models, Qp/Qs reduction is linked to changes in right ventricular elastance and relaxation time.
- Pulmonary vasodilators' effects in ASD patients may be influenced by ventricular stiffness.

## Abstract

Shunt lesions are categorized into pre- and post-tricuspid. Although it is well recognized that these two entities have a different pathophysiology, hemodynamic variables involved are still poorly understood. This paper aims to analytically appraise shunt physiology exploiting a lumped parameters mathematical model.

Circulatory system was split into arterial and venous compartments, each of them being described by resistive, capacitive and inductive components. The model was modified including communication between atria and ventricles. Predicted changes in the ratio between pulmonary blood flow and systemic blood flow (Qp/Qs), obtained by manipulating pulmonary resistances (PVR) and ventricular stiffness were computed.

A twofold rise of pulmonary vascular resistance resulted in a significant reduction of Qp/Qs in the setting of isolated ventricular septal defect (VSD) and VSD associated with atrial septal defect (ASD) but did not produce a sizable effect in case of isolated ASD. In the model describing an isolated ASD, a similar magnitude of Qp/Qs reduction was predicted by simulating an increase of right ventricular passive elastance and relaxation time. In this type of shunt, the dependence of Qp/Qs from PVR and ventricular elastance appeared analytically linked.

This model analytically illustrates that shunt through an ASD is minimally affected by PVRs. The marginal change of pulmonary flow produced by large variations of PVR appeared mediated by changes in right ventricular elastance. The effect of pulmonary vasodilators in patients with ASD can be concealed or enhanced by increased stiffness of the right or left ventricle, respectively.