### Article

## Adaptive Slice Method to determine the dynamic respiratory mechanics

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Published: | September 10, 2008 |
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### Outline

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#### Introduction

The online estimation of respiratory system mechanics at the bedside might lead to new diagnostic insights about the mechanically ventilated patient. Since the parameters of the respiratory system mechanics change during a breathing cycle, i.e. resistance and compliance depend on volume, flow and respiratory frequency [Ref. 1], [Ref. 2], nonlinearity has to be taken into account to analyze the mechanical behaviour of the lung under dynamic conditions.

The aim of the study was to develop a method, which -though based on the linear first order equation of motion- is capable to capture the nonlinearity of the lung mechanics.

#### Methods and Material

The Adaptive Slice Method (ASM) was developed to assess lung mechanics. It is derived from the slice method [Ref. 3], which divides a breathing cycle into several fixed volume slices. For each slice, one compliance value and one resistance value are calculated by applying a least-squares-fit (LSF) method. Since compliance and resistance values are not constant, the calculated values will be changing if the width of the corresponding slice is changed. Please note that there are two conflicting influence factors: nonlinearity demands smaller slices while noise requires larger slices. Therefore in ASM, instead of applying a fixed width, the width of each slice is determined according to a quality measure based on the confidence interval (CI) of the parameter estimation.

The determination of the slices’ width is done iteratively. Starting with a small slice in every step the width is increased. During the growth of the slice width, the relative CI of parameters (CI divided by parameter value) is usually decreasing. Once the relative CI is smaller than a preset threshold, the growth process stops, and the current slice width is returned. After the widths of every slice are set, sequences of R and C can be obtained.

Data of a lung simulation and of animal experiments (6 sheep, 2 rats) were included into this study for evaluation purpose. Pressure, flow and volume data provided by a ventilator (Evita XL, Dräger, Lübeck Germany) were sampled at 125 Hz and subsequently analysed.

In order to evaluate the Adaptive Slice Method, it was compared with some existing methods (SLICE [Ref. 3], GSM [Ref. 4], APVNL [Ref. 5], and LSF [Ref. 6]) on the data mentioned above.

#### Results

Table 1 [Tab. 1] summarizes a comparison using animal data. The MSE is given i.e. the mean of squared differences between data and model prediction for every method. All numbers are in the range of 10^{-6}.

The variation of the parameters calculated by GSM and APVNL are larger than those calculated by ASM (Figure 1 [Fig. 1]).

#### Discussion

Applying a linear regression for the equation of motion, R, 1/C and PEEP as the regression parameters are obtained (Paw is dependent variable; Flow and Volume are independent variables; α is error).

Paw(t) = R*Flow(t) + Volume(t)*(1/C) + PEEP + α

It is assumed that the errors are independent and identically normally distributed. Based on this assumption, the confidence intervals (CI) can be used to express the uncertainty in the parameters estimation with respect to the noise level.

As seen in Figure 1 [Fig. 1], the variation of the results calculated by APVNL and GSM are large. Since the noise level of the signals in the rat data is high, APVNL method fails to deliver enough values to depict the nonlinearity of the parameters. At the same time Figure 1 [Fig. 1] also suggests that the results provided by ASM are more stable and rational.

This study shows that online analysis of nonlinear respiratory mechanics may profit from an adaptive selection of interval size.

The fitted parameter values of ASM are more consistent and the overall error measure (sum of squared error, SSE) is smaller. In addition, the fitting process is equally robust as the LSF i.e. in the worst case it reduces to a LSF of the whole cycle, thus neglecting nonlinearity. On the other hand if noise is low, nonlinear parameters are better approximated by creating more and smaller intervals.

#### Acknowledgment

This work is partially supported by grants of the MWK Baden-Württemberg, DFG (Gu561/6-1) and Dräger medical, Lübeck.

### References

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