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Acute Respiratory Distress Syndrome (ARDS) is a major cause of morbidity and has a high rate of mortality. ARDS patients in the intensive care unit (ICU) require mechan-ical ventilation (MV) for breathing support, but inappropriate settings of MV can lead to ventilator induced lung injury (VILI). Those complications may be avoided by carefully optimizing ventilation parameters through model-based approaches. In this study we introduced a new model of lung mechanics (mNARX) which is a variation of the NARX model by Langdon et al. A multivariate process was undertaken to deter-mine the optimal parameters of the mNARX model and hence, the final structure of the model fit 25 patient data sets and successfully described all parts of the breathing cycle. The model was highly successful in predicting missing data and showed minimal error. Thus, this model can be used by the clinicians to find the optimal patient specific ventilator settings.

Acute Respiratory Distress syndrome (ARDS) is a major cause of morbidity and has a high mortality (between 20% and 50%) [

The data were measured between 2000 and 2002 in the intensive care units of eight German hospitals [_{2} < 55 mmHg were maintained before the measurements. The patients were ventilated with zero end expiratory pressure (ZEEP) for 5 minutes, having an end-inspira- tory pause of ≥0.2 seconds and afterwards the PEEP level was increased in steps of 2 cm H_{2}O―each PEEP level was kept constant for 10 breathing cycles. The volume was calculated through continuous integration of the flow with adjustment for volume creep. The data sampling rate was 62.5 Hz. Full details of the original study can be found in Stahl et al. (2006) [

The simplest pulmonary model to describe the human lungs is a first order model (FOM). The FOM simplifies the lung as being one compartment with a constant airway resistance and constant lung compliance. The behavior of the FOM can be expressed by Equation (1).

where P_{aw} is airway pressure, _{0} is the offset pressure.

Langdon et al. (2015) proposed a non-linear autoregressive model (NARX) of the pulmonary mechanics, based on an FOM. This NARX model determines the input-output relationship of the system and thus can predict the pressure volume relationship, based on previous inputs. It consists of a pressure dependent elastance term and a multi-valued resistance term that captures changes in pressure.

where a_{i}, b_{j} and c are parameters to be identified, M the number of basis-functions Φ_{i}_{,d} (P_{aw}(t)) of degree d, V(t) is the inspired volume, L is the length of the resistance vector, j is the index of the resistance vector and

Zeroth and higher order basis functions are defined as:

The modified NARX (mNARX) model was built on the basis of the NARX model by replacing the multi-valued resistance term by a pressure dependent resistance via the use of basis functions. The modified NARX model was defined as:

where a_{i} are the coefficients for the basis functions that represents the elastance terms, M the number of elastance basis functions Φ_{i}_{,d}(P_{aw}(t)) of degree d, b_{j} are the resistance coefficients that represent the resistance terms, L the number of the pressure dependent resistance basis functions ∏_{j}_{,d}(P_{aw}(t)) of degree d.

Zeroth and higher order basis functions are defined as:

Though the final goal was to identify the parameters a_{i} (elastance coefficients), b_{j} (resistance coefficients) and c (offset or initial pressure), first the optimum number (M) of basis functions for the elastance term, the number (L) of basis functions for the resistance term and their order (d) had to be determined. Therefore the mNARX model was applied to 25 data sets and by varying the values of M, L and d, this parameters were determined via analyzing the fit of the model. First, the optimal value of L was selected, followed by d and finally M. To get the optimal value for L, it was varied until convergence of the root mean squared (RMS) residuals was achieved. In the case of d, cumulative distribution function (CDF) plots were determine to find significant differences between the residuals. Finally, the optimal value of M was determined as a tradeoff between improving residuals and avoidance of over fitting.

The value of L was varied from 1 (in steps of 10) until a convergence was achieved, with constant values for M = 5 and d = 1. Convergence was assumed when the root mean squared residual stopped improving by more than 0.5% of the previous value.

_{i} coefficients for patient 1, the elastance coefficients in ARDS patients are expected to be smooth and curve due to lung characteristics (such as recruitment phases and overdistention during different PEEP levels).

The parameters of the NARX and the mNARX model were identified by using the first 4 and the last 4 different PEEP levels―the remaining data (approx. 5 different PEEP levels) was used to evaluate the model performance assuming missing data.

The NARX model and mNARX model fit all the 25 patients successfully and both the models were able to describe all the parts of the breathing cycle. The outcomes of the NARX and mNARX models were compared with the outcome of the FOM. The model fit during the inspiratory pause and expiratory relation were promising in NARX and mNARX, while the FOM failed to describe all parts of the breathing cycle in higher PEEP-levels.

Model | L | d | M |
---|---|---|---|

NARX | 350 (length of the resistance vector) | 1 | 5 |

mNARX | 20 (number of basis functions) | 1 | 5 |

residuals showed improved results between zeroth and first order basis functions, while the usage of second order basis functions didn’t show worthwhile improvements. Hence, first order basis functions were sufficient for both models. The elastance coefficients in ARDS patients are expected to be smooth and curve due to the lung characteristics of ARDS patients such as recruitment phases and overdistention during different PEEP levels. _{i} coefficients becomes unstable and doesn’t allow predicting the future and past PEEP levels. Hence, the number of basis function for both the models was set to M = 5.

A limitation for the prediction behavior of NARX and mNARX is that the range of identification pressure should cover the entire range of interpolation. A multiple and broad range of steps were undertaken to evaluate both models to find the optimal values of their final structure. A broad range of clinical conditions and ventilation modes were applied to both models to capture the different behavior and the obtained results enabled us to interpret and compare the models.

In this study a new lung mechanics model was introduced. The multivariate process was undertaken to determine the optimal parameters for the final structure of the mNARX model. The model was able to fit all 25 patient data sets and successfully describe all the parts of the breathing cycle. The model was highly successful in predicting missing data with minimal error compared to the FOM. Hence, this model could be

used by the clinicians to optimize patient specific ventilator settings. Further improvements of the model could be done by investigating the order of the basis functions of the resistance term which was not evaluated in this study.

Jayaramaiah, M., Laufer, B., Kretschmer, J. and Möller, K. (2016) A New Lung Mechanics Model and Its Evaluation with Clinical Data. J. Biomedical Science and Engineering, 9, 107-115. http://dx.doi.org/10.4236/jbise.2016.910B014