Christoph Schranz

Structural Identifiability and Practical Applicability of an Alveolar Recruitment Model for ARDS Patients

Patient-specific mathematical models of respiratory mechanics can offer substantial insight into patient state and pulmonary dynamics that are not directly measurable. Thus, they offer significant potential to evaluate and guide patient-specific lung protective ventilator strategies for acute respiratory distress syndrome (ARDS) patients. To assure bedside applicability, the model must be computationally efficient and identifiable from the limited available data, while also capturing dominant dynamics and trends observed in ARDS patients. In this study, an existing static recruitment model is enhanced by considering alveolar distension and implemented in a novel time-continuous dynamic respiratory mechanics model. The model was tested for structural identifiability and a hierarchical gradient descent approach was used to fit the model to low-flow test responses of 12 ARDS patients. Finally, a comprehensive practical identifiability analysis was performed to evaluate the impact of data quality on the model parameters. Identified parameter values were physiologically plausible and very accurately reproduced the measured pressure responses. Structural identifiability of the model was proven, but practical identifiability analysis of the results showed a lack of convexity on the error surface indicating that successful parameter identification is currently not assured in all test sets. Overall, the model presented is physiologically and clinically relevant, captures ARDS dynamics, and uses clinically descriptive parameters. The patient-specific models show the ability to capture pulmonary dynamics directly relevant to patient condition and clinical guidance. These characteristics currently cannot be directly measured or established without such a validated model.

Iterative integral parameter identification of a respiratory mechanics model

BackgroundPatient-specific respiratory mechanics models can support the evaluation of optimal lung protective ventilator settings during ventilation therapy. Clinical application requires that the individual’s model parameter values must be identified with information available at the bedside. Multiple linear regression or gradient-based parameter identification methods are highly sensitive to noise and initial parameter estimates. Thus, they are difficult to apply at the bedside to support therapeutic decisions.MethodsAn iterative integral parameter identification method is applied to a second order respiratory mechanics model. The method is compared to the commonly used regression methods and error-mapping approaches using simulated and clinical data. The clinical potential of the method was evaluated on data from 13 Acute Respiratory Distress Syndrome (ARDS) patients.ResultsThe iterative integral method converged to error minima 350 times faster than the Simplex Search Method using simulation data sets and 50 times faster using clinical data sets. Established regression methods reported erroneous results due to sensitivity to noise. In contrast, the iterative integral method was effective independent of initial parameter estimations, and converged successfully in each case tested.ConclusionThese investigations reveal that the iterative integral method is beneficial with respect to computing time, operator independence and robustness, and thus applicable at the bedside for this clinical application.

Physiological relevance and performance of a minimal lung model – an experimental study in healthy and acute respiratory distress syndrome model piglets

BackgroundMechanical ventilation (MV) is the primary form of support for acute respiratory distress syndrome (ARDS) patients. However, intra- and inter- patient-variability reduce the efficacy of general protocols. Model-based approaches to guide MV can be patient-specific. A physiological relevant minimal model and its patient-specific performance are tested to see if it meets this objective above.MethodsHealthy anesthetized piglets weighing 24.0 kg [IQR: 21.0-29.6] underwent a step-wise PEEP increase manoeuvre from 5cmH2O to 20cmH2O. They were ventilated under volume control using Engström Care Station (Datex, General Electric, Finland), with pressure, flow and volume profiles recorded. ARDS was then induced using oleic acid. The data were analyzed with a Minimal Model that identifies patient-specific mean threshold opening and closing pressure (TOP and TCP), and standard deviation (SD) of these TOP and TCP distributions. The trial and use of data were approved by the Ethics Committee of the Medical Faculty of the University of Liege, Belgium.Results and discussions3 of the 9 healthy piglets developed ARDS, and these data sets were included in this study. Model fitting error during inflation and deflation, in healthy or ARDS state is less than 5.0% across all subjects, indicating that the model captures the fundamental lung mechanics during PEEP increase. Mean TOP was 42.4cmH2O [IQR: 38.2-44.6] at PEEP = 5cmH2O and decreased with PEEP to 25.0cmH2O [IQR: 21.5-27.1] at PEEP = 20cmH2O. In contrast, TCP sees a reverse trend, increasing from 10.2cmH2O [IQR: 9.0-10.4] to 19.5cmH2O [IQR: 19.0-19.7]. Mean TOP increased from average 21.2-37.4cmH2O to 30.4-55.2cmH2O between healthy and ARDS subjects, reflecting the higher pressure required to recruit collapsed alveoli. Mean TCP was effectively unchanged.ConclusionThe minimal model is capable of capturing physiologically relevant TOP, TCP and SD of both healthy and ARDS lungs. The model is able to track disease progression and the response to treatment.

Utility of a novel error-stepping method to improve gradient-based parameter identification by increasing the smoothness of the local objective surface

Accurate model parameter identification relies on accurate forward model simulations to guide convergence. However, some forward simulation methodologies lack the precision required to properly define the local objective surface and can cause failed parameter identification. The role of objective surface smoothness in identification of a pulmonary mechanics model was assessed using forward simulation from a novel error-stepping method and a proprietary Runge-Kutta method. The objective surfaces were compared via the identified parameter discrepancy generated in a Monte Carlo simulation and the local smoothness of the objective surfaces they generate. The error-stepping method generated significantly smoother error surfaces in each of the cases tested (p<0.0001) and more accurate model parameter estimates than the Runge-Kutta method in three of the four cases tested (p<0.0001) despite a 75% reduction in computational cost. Of note, parameter discrepancy in most cases was limited to a particular oblique plane, indicating a non-intuitive multi-parameter trade-off was occurring. The error-stepping method consistently improved or equalled the outcomes of the Runge-Kutta time-integration method for forward simulations of the pulmonary mechanics model. This study indicates that accurate parameter identification relies on accurate definition of the local objective function, and that parameter trade-off can occur on oblique planes resulting prematurely halted parameter convergence.

A Time-Continuous Model of Respiratory Mechanics of ARDS Patients

Predictions of individualized models of respiratory mechanics provide insight into the patient state. Therefore, they may help to reduce the potentially harmful effects of ventilation therapy for Acute Respiratory Distress Syndrome (ARDS) patients. To assure bedside-applicability, the underlying model has to be computationally efficient while capturing dominant dynamics observed and also be identifiable from the available data. In this work, a recruitment model is enhanced by considering alveolar distension effects and implemented in a time-continuous respiratory mechanics model. The model is used to identify patient-specific models for 12 ARDS patients from a previous study using a gradient-based parameter identification method. Appropriate initial values for parameter identification are hierarchically derived by identifying simpler models first. The reported parameter values were physiologically plausible and capable of reproducing the measured pressure with high accuracy. The presented model provides timecontinuous simulations of airway pressure, is physiologically relevant term by term, uses clinically descriptive parameters and captures dominant ARDS dynamics. The patient-specific models also capture pulmonary dynamics for clinical guidance that are currently not directly measurable without such a validated model.

Traversing the Fuzzy Valley: Problems Caused by Reliance on Default Simulation and Parameter Identification Programs for Discontinuous Models

The Levenberg-Marquardt parameter identification method is often used in tandem with numerical Runge-Kutta model simulation to find optimal model parameter values to match measured data. However, these methods can potentially find erroneous parameter values. The problem is exacerbated when discontinuous models are analyzed. A highly parameterized respiratory mechanics model defines a pressure-volume response to a low flow experiment in an acute respiratory distress syndrome patient. Levenberg-Marquardt parameter identification is used with various starting values and either a typical numerical integration model simulation or a novel error-stepping method. Model parameter values from the error-stepping method were consistently located close to the error minima (median deviation: 0.4%). In contrast, model values from numerical integration were erratic and distinct from the error minima (median deviation: 1.4%). The comparative failure of Runge-Kutta model simulation was due to the methods poor handling of model discontinuities and the resultant lack of smoothness in the error surface. As the Levenberg-Marquardt identification system is an error gradient decent method, it depends on accurate measurement of the model-to-measured data error surface. Hence, the method failed to converge accurately due to poorly defined error surfaces. When the error surface is imprecisely identified, the parameter identification process can produce suboptimal results. Particular care must be used when gradient decent methods are used in conjunction with numerical integration model simulation methods and discontinuous models. Parameter identification, Physiological modelling, Numerical integration, Hickling model, Alveolar recruitment.

When the value of gold is zero

This manuscript presents the concerns around the increasingly common problem of not having readily available or useful “gold standard” measurements. This issue is particularly important in critical care where many measurements used in decision making are surrogates of what we would truly wish to use. However, the question is broad, important and applicable in many other areas.In particular, a gold standard measurement often exists, but is not clinically (or ethically in some cases) feasible. The question is how does one even begin to develop new measurements or surrogates if one has no gold standard to compare with?We raise this issue concisely with a specific example from mechanical ventilation, a core bread and butter therapy in critical care that is also a leading cause of length of stay and cost of care. Our proposed solution centers around a hierarchical validation approach that we believe would ameliorate ethics issues around radiation exposure that make current gold standard measures clinically infeasible, and thus provide a pathway to create a (new) gold standard.

Efficient computation of interacting model systems

Physiological processes in the human body can be predicted by mathematical models. Medical Decision Support Systems (MDSS) might exploit these predictions when optimizing therapy settings. In critically ill patients depending on mechanical ventilation, these predictions should also consider other organ systems of the human body. In a previously presented framework we combine elements of three model families: respiratory mechanics, cardiovascular dynamics and gas exchange. Computing combinations of moderately complex submodels showed to be computationally costly thus limiting the applicability of those model combinations in an MDSS. A decoupled computing approach was therefore developed, which enables individual evaluation of every submodel. Direct model interaction is not possible in separate calculations. Therefore, interface signals need to be substituted by estimates. These estimates are iteratively improved by increasing model detail in every iteration exploiting the hierarchical structure of the implemented model families. Simulation error converged to a minimum after three iterations. Maximum simulation error showed to be 1.44% compared to the original common coupled computing approach. Simulation error was found to be below measurement noise generally found in clinical data. Simulation time was reduced by factor 34 using one iteration and factor 13 using three iterations. Following the proposed calculation scheme moderately complex model combinations seem to be applicable for model based decision support.

Identifiability analysis of a pressure-depending alveolar recruitment model

Abstract Patient-specific physiological models of respiratory mechanics can offer insight into patient state and pulmonary dynamics that are not directly measurable. Thus, significant potential exists to evaluate and guide patient-specific lung protective ventilator strategies for Acute Respiratory Distress Syndrome (ARDS) patients. To assure bedside-applicability, the physiological model must be computationally efficient and identifiable from the limited available data, while also capturing dominant dynamics and trends observed in ARDS patients. In this work, an existing static recruitment model is enhanced by considering alveolar distension and implemented in a novel time-continuous dynamic respiratory mechanics model. A hierarchical gradient descent approach is used to fit the model to low-flow test responses of 12 ARDS patients. Identified parameter values were physiologically plausible and capable of reproducing the measured pressure responses with very high accuracy (Overall median percentage fitting error: MPE = 1.84% [IQR: 1.77% to 2.18%]). Structural identifiability of the model is proven, but a practical identifiability analysis of the results shows a lack of convexity on the error-surface for some patients due to reduced information content within the measured data set. Overall, the model presented is physiologically and clinically relevant, captures ARDS dynamics, and uses clinically descriptive parameters. The patient-specific models show their ability to capture pulmonary dynamics directly relevant to patient condition and clinical guidance. These characteristics cannot be directly measured without such a validated model.

Hierarchical individualization of a recruitment model with a viscoelastic component for ARDS patients

Patient-specific mathematical models of respiratory mechanics enable substantial insight into patient state and pulmonary dynamics that are not directly measurable. Thus they offer potential e.g. to predict the outcome of ventilator settings for Acute Respiratory Distress Syndrome (ARDS) patients. In this work, an existing static recruitment model is extended by viscoelastic components allowing model simulations in various ventilation scenarios. A hierarchical approach is used to identify the model with measured data of 12 ARDS patients under static and dynamic conditions. Identified parameter values were physiologically plausible and reproduced the measured pressure responses with a median Coefficient of Determination (CD) of 0.972 in the dynamic and 0.992 in the static maneuver. Overall, the model presented incorporates physiological mechanisms, captures ARDS dynamics and viscoelastic tissue properties and is valid under various ventilation patterns.