Model-Based Decision Support Algorithm to Guide Fluid Resuscitation**This work was supported by the French Community of Belgium, the Belgian Funds for Scientific Research (F.R.S.-FNRS) and EU Marie Curie Actions (FP7-PEOPLE-2012-IRSES)

Preserving multi-dimensional information: A hypersphere method for parameter space analysis

Background

Physiological modelling often involves models described by large numbers of variables and significant volumes of clinical data. Mathematical interpretation of such models frequently necessitates analysing data points in high-dimensional spaces. Existing algorithms for analysing high-dimensional points either lose important dimensionality or do not describe the full position of points. Hence, there is a need for an algorithm which preserves this information.

Methods

The most-distant uncovered point (MDUP) hypersphere method is a binary classification approach which defines a collection of equidistant N-dimensional points as the union of hyperspheres. The method iteratively generates hyperspheres at the most distant point in the interest region not yet contained within any hypersphere, until the entire region of interest is defined by the union of all generated hyperspheres. This method is tested on a 7-dimensional space with up to 35.8 million points representing feasible and infeasible spaces of model parameters for a clinically validated cardiovascular system model.

Results

For different numbers of input points, the MDUP hypersphere method tends to generate large spheres away from the boundary of feasible and infeasible points, but generates the greatest number of relatively much smaller spheres around the boundary of the region of interest to fill this space. Runtime scales quadratically, in part because the current MDUP implementation is not parallelised.

Conclusions

The MDUP hypersphere method can define points in a space of any dimension using only a collection of centre points and associated radii, making the results easily interpretable. It can identify large continuous regions, and in many cases capture the general structure of a region in only a relative few hyperspheres. The MDUP method also shows promise for initialising optimisation algorithm starting conditions within pre-defined feasible regions of model parameter spaces, which could improve model identifiability and the quality of optimisation results.

Parameter estimation in a minimal model of cardio-pulmonary interactions

Mechanical ventilation is a widely used breathing support for patients in intensive care. Its effects on the respiratory and cardiovascular systems are complex and difficult to predict. This work first presents a minimal mathematical model representing the mechanics of both systems and their interaction, in terms of flows, pressures and volumes. The aim of this model is to get insight on the two systems' status when mechanical ventilation settings, such as positive end-expiratory pressure, are changing. The parameters of the model represent cardiac elastances and vessel compliances and resistances. As a second step, these parameters are estimated from 16 experimental datasets. The data come from three pig experiments reproducing intensive care conditions, where a large range of positive end-expiratory pressures was imposed by the mechanical ventilator. The data used for parameter estimation is limited to information available in the intensive care unit, such as stroke volume, central venous pressure and systemic arterial pressure. The model is able to satisfactorily reproduce this experimental data, with mean relative errors ranging from 1 to 26%. The model also reproduces the dynamics of the cardio-vascular and respiratory systems, and their interaction. By looking at the estimated parameter values, one can quantitatively track how the two coupled systems mechanically react to changes in external conditions imposed by the ventilator. This work thus allows real-time, model-based management of ventilator settings.

Mathematical modeling of extracorporeal CO2 removal therapy : A validation carried out on ten pigs

The extracorporeal CO₂ removal device (ECCO₂RD) is used in clinics to treat patients suffering from respiratory failures like acute respiratory distress syndrome (ARDS) or chronic obstructive pulmonary disease (COPD). The aim of this device is to decarboxylate blood externally with low blood flow. A mathematical model is proposed to describe protective ventilation, ARDS, and an extracorporeal CO₂ removal therapy (ECCO₂RT). The simulations are compared with experimental data carried out on ten pigs. The results show a good agreement between the mathematical simulations and the experimental data, which provides a nice validation of the model. This model is thus able to predict the decrease of PCO₂ during ECCO₂RT for different blood flows across the extracorporeal lung support.