Tidal volume estimation using the blanket fractal dimension of the tracheal sounds acquired by smartphone

Abstract

In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days.

Figure 1

Simultaneous recordings of the tracheal sound (using a smartphone) and the volume signal (using Respibands). (a) The participant is breathing through 800 mL bag; (b) The participant is breathing through a tube while performing the respiratory maneuver.

Figure 2

The flowchart showing the steps for tracheal sounds’ and Respitrace signal’s processing.

Figure 3

Filtered, detrended and aligned tracheal sounds and volume signal during the respiratory maneuver. Tracheal sound (in volts) is represented in blue, while volume signal (in liters) is in orange.

Figure 4

The flowchart showing the computation of the fitting models.

Figure 5

An example of the volume estimation from smartphone acquired tracheal sounds using BFD features and exponential model of one subject. The true volumes while breathing through a tube (green circles) are limited to a range from 0.2 to 1 L. (a) The inspiration phase; (b) The expiration phase.

Figure 6

Top: Reference and estimated volumes for the same example as in Figure 5. Bottom: The corresponding NRMSE errors.

Figure 7

NRMSE errors (represented with its mean and standard error of the mean) when: BFD and exponential model (red circles), BFD and linear model (green downward triangles), SE and exponential model (blue squares), and SE and linear model (black triangles) are used. (a) No tube and inspiration; (b) No tube and expiration; (c) Tube and inspiration; (d) Tube and expiration.

Figure 8

Bland-Altman plot for BFD feature with the exponential model, for expiratory phase, while the participants (N = 5) were breathing without a tube during the first day of experiments. (a) The regression plot: The unitary line is shown as gray dashed line, while the regression line is represented as black solid line; (b) Bland-Altman plot: The bias is represented as a solid black line and the 95% limits of agreement as gray dashed lines.