Axel Riedlinger

A simple gas exchange model predicting arterial oxygen content for various FiO 2 levels

The application of mechanical ventilation is a life-saving routine therapy that allows the patient to overcome the physiological impact of surgeries, trauma or critical illness by ensuring vital oxygenation and carbon dioxide removal. Above a certain level of minute ventilation (usually set to ensure acceptable carbon dioxide removal and oxygenation) oxygenation is only marginally affected by a further increase in minute ventilation. Thus, oxygenation is predominantly influenced by inspiratory oxygen fraction (FiO2) Usually, finding the appropriate setting is a trial-and-error procedure, as the clinician is unaware of the exact value that needs to be set in order to reach the desired arterial oxygen partial pressures (PaO2) in the patient. Mathematical models of physiological processes in the human body may be used to predict patient reactions towards alterations in the therapy regime. These predictions can be exploited by Medical Decision Support Systems to find optimal therapy settings. A simple mathematical model is presented, that allows calculation of a patients shunt fraction, i.e. the percentage of blood that is not participating in lung gas exchange. On this basis, it predicts PaO2 at various FiO2-levels and thus allows reaching desired PaO2 in just one step. Due to its simple design it does not require complicated - and possibly error-prone - parameter identification procedures, thus allowing its application at the bedside. Retrospective analysis of oxygenation data from a patient data management system showed that the presented model predicted PaO2 with less than 10% deviation in 23 out of 29 measurements, proving the practical applicability of the presented model approach.

A Family of Physiological Models to Simulate Human Gas Exchange.

Mathematical models are a widely accepted tool to simulate physiological processes in the human body and to predict patient response towards changes in the therapy regime. These results might be exploited for medical decision support with the goal of finding optimal settings for an individual patient. To allow for an optimal reproduction of patient physiology in all possible situations, rather complex model descriptions are necessary. However, these all-embracing models require an extensive amount of measurements for robust parameter identification and might be computationally costly. Therefore, it would be beneficial to provide multiple model versions each differing in simulation focus and complexity which the decision support system can choose from. We are thus presenting a hierarchically ordered family of gas exchange models and we are showing examples of applications for some of these.

Evaluation of an algorithm to choose between competing models of respiratory mechanics

Abstract Model based decision support helps in optimizing therapy settings for individual patients while providing additional insight into a patient’s disease state through the identified model parameters. Using multiple models with different simulation focus and complexity allows adapting decision support to the current clinical situation and the available data. A previously presented set of numerical criteria allows selecting the best model based on fit quality, model complexity, and how well the parameter values are defined by the presented data. To systematically evaluate those criteria in an algorithm we have created insilico data sets using four different respiratory mechanics models with three different parameter settings each. Each of those artificial patients was ventilated with three different manoeuvres and the resulting data was used to identify the same models used to create the data. The selection algorithm was then presented with the results to select the best model. Not considering determinateness of the identified model parameters, the algorithm chose the same model that was used to create the data in 78%, a more complex model in 5% and a less complex model in 18% of all cases. When including the determinateness of model parameters in the decision process, the algorithm chose the same model in 42% of the cases and a less complex model in 56% of all cases. In 2% of the presented cases, no model complied with the required criteria.

Robustness Analysis of a Mathematical Gas Exchange Model.

Mathematical gas exchange models can support decision making for clinicians in mechanical ventilation. F or example individually optimized inspired oxygen frac- tion (Fi,O2) may be determined using patient specific pre- diction of blood gas oxygenation (Pa,O2). Before using a model for prediction purposes, the model parameters have to be adapted to the individual patient characteris- tics. Successful parameter identification depends on the required initial guess of the parameter values to be identi- fied. The robustness of the identification process of a mathematical gas exchange model that considers shunt and ventilation/perfusion-mismatch ( V˙ /Q-mismatch) is analysed in this work using simulation data. Results show that parameter identification of the data sets tested is robust for fs and fA smaller than 0.8 and 0.9. This analysis provides an overview on the convergence of parameter identification of a two-compartment gas-exchange model.

Evaluating different approaches to identify a three parameter gas exchange model

Abstract Mathematical models can be employed to simulate a patient’s individual physiology and can therefore be used to predict reactions to changes in the therapy. To be clinically useful, those models need to be identifiable from data available at the bedside. Gradient based methods to identify the values of the model parameters that represent the recorded data highly depend on the initial estimates. The proposed work implements a previously developed method to overcome those dependencies to identify a three parameter model of gas exchange. The proposed hierarchical method uses models of lower order related to the three parameter model to calculate valid initial estimates for the parameter identification. The presented approach was evaluated using 12 synthetic patients and compared to a traditional direct approach as well as a global search method. Results show that the direct approach is highly dependent on how well the initial estimates are selected, while the hierarchical approach was able to find correct parameter values in all tested patients.

Komplexe Modellsysteme in der automatisierten Beatmung

Zusammenfassung Die künstliche Beatmung stellt eine etablierte Therapie in der Intensivmedizin dar. Trotz der routinemäßigen Anwendung kann es bei schwerkranken Patienten zu Komplikationen kommen. Die modellbasierte Entscheidungsunterstützung erlaubt eine Verbesserung der Therapie, indem an den Patienten angepasste Modelle für Prädiktionen genutzt und damit Therapieeinstellungen individuell optimiert werden. Die eingesetzten Modelle sollten dabei an den Krankheitszustand des Patienten, an die vorliegenden Daten sowie an die aktuelle klinische Fragestellung anpassbar sein und neben der Atemmechanik ebenfalls die wichtigen Bereiche Gasaustausch und Hämodynamik umfassen. Die gezeigten hierarchisch geordneten Modellfamilien erlauben eine flexible Anpassung an die aktuelle klinische Situation, eine robuste Identifikation der Modellparameter sowie eine umfassende Abbildung des Patienten.

Hierarchical structure of human gas exchange models to improve parameter identification

Mathematical models can be used to simulate a patients respiratory system and thus predict the outcome of a change in therapy settings. Therefore, mathematical models might be exploited to support therapeutic decision making in mechanical ventilation. In interaction with models of respiratory mechanics and cardiovascular dynamics, gas exchange models may help to find optimal ventilator settings achieving sufficient oxygenation of the patient along with avoiding further lung damage due to high peak inspiratory pressures. Considering the risk of oxygen toxicity, gas exchange models may calculate optimal inspired oxygen fraction (Fi, 02) to achieve a desired goal for blood gas oxygenation (Pa, 02). In general, physiological models should be kept as simple as possible to reduce the number of model parameters that have to be identified for adaptation to the individual patient. However, in case of severe lung disease simple gas exchange models often are not able to simulate patient physiology adequately. More complex models are necessary and identification may be intractable due to a higher number of model parameters. Thus, depending on the complexity of the employed model a different amount of information is required for identification. A hierarchical structure of different gas exchange models is presented that might be exploited to simplify parameter identification of complex models. A stepwise identification of the model parameters may lead to an accelerated and robust identification process as shown in a retrospective analysis of patient data.

Selection Criteria for Competing Models of Respiratory Mechanics

Mathematical models of respiratory mechanics are useful for assessing the mechanical properties of the respiratory system. The application of models in therapy requires robust identification methods and criteria to quantify the quality of the estimated model parameters. These criteria should support the selection of the best model amongst a collection of competing models to describe the given mechanical behaviour. In this work, three selection criteria were tested on two respiratory mechanics models in various lung conditions using experimental data of 11 mechanically ventilated subjects. Different lung conditions lead to different model preferences as indicated by the Coefficient of Determination, Akaikes Information Criterion and reported confidence intervals. The combination of the presented selection criteria provides a clear preference to select an appropriate model for a given situation to be implemented in a model-based ventilation monitoring.

Predicting etCO2 Response in a Model of Ventilation-Perfusion Mismatch.

Mathematical models are a popular tool to simulate physiological processes in the human body. This ability can be exploited to predict patient response towards changes in the therapy regime. Results of these predictions might be exploited for medical decision support with the goal of finding optimal settings for an individual patient. One possible application would be to identify the optimal minute ventilation to achieve a defined carbon dioxide removal in the patient. Purely titration based optimization methods need to identify the optimal minute ventilation by a trial-and-error approach whereas model based methods can identify the correct setting directly. The proposed model comprises two alveolar compartments that are ventilated and perfused differently. Additionally, the model contains a dead space and a shunt compartment with constant size as well as a body compartment, where oxygen is consumed and carbon dioxide is produced. The model was evaluated using real patient data and showed results mostly within 10% deviation of the measured etCO2 values.

On the practical identifiability of a two-parameter model of pulmonary gas exchange

BackgroundSuccessful application of mechanical ventilation as a life-saving therapy implies appropriate ventilator settings. Decision making is based on clinicians’ knowledge, but can be enhanced by mathematical models that determine the individual patient state by calculating parameters that are not directly measurable. Evaluation of models may support the clinician to reach a defined treatment goal. Bedside applicability of mathematical models for decision support requires a robust identification of the model parameters with a minimum of measuring effort. The influence of appropriate data selection on the identification of a two-parameter model of pulmonary gas exchange was analyzed.MethodsThe model considers a shunt as well as ventilation-perfusion-mismatch to simulate a variety of pathologic pulmonary gas exchange states, i.e. different severities of pulmonary impairment. Synthetic patient data were generated by model simulation. To incorporate more realistic effects of measurement errors, the simulated data were corrupted with additive noise. In addition, real patient data retrieved from a patient data management system were used retrospectively to confirm the obtained findings. The model was identified to a wide range of different FiO2 settings. Just one single measurement was used for parameter identification. Subsequently prediction performance was obtained by comparing the identified model predicted oxygen level in arterial blood either to exact data taken from simulations or patients measurements.ResultsStructural identifiability of the model using one single measurement for the identification process could be demonstrated. Minimum prediction error of blood oxygenation depends on blood gas level at the time of system identification i.e. the measurement situation. For severe pulmonary impairment, higher FiO2 settings were required to achieve a better prediction capability compared to less impaired pulmonary states. Plausibility analysis with real patient data could confirm this finding.Discussion and conclusionsDependent on patients’ pulmonary state, the influence of ventilator settings (here FiO2) on model identification of the gas exchange model could be demonstrated. To maximize prediction accuracy i.e. to find the best individualized model with as few data as possible, best ranges of FiO2-settings for parameter identification were obtained. A less effort identification process, which depends on the pulmonary state, can be deduced from the results of this identifiability analysis.