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Assessing the variability in respiratory acoustic thoracic imaging (RATHI)
Computers in Biology and Medicine 45 (2014) 58–66
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Assessing the variability in respiratory acoustic thoracic imaging (RATHI) S. Charleston-Villalobos a,n, A. Torres-Jiménez a, R. González-Camarena b, G. Chi-Lem c, T. Aljama-Corrales a a
Electrical Engineering Department, Universidad Autonoma Metropolitana, Mexico City 09340, Mexico Department of Health Science, Universidad Autonoma Metropolitana, Mexico City 09340, Mexico c National Institute of Respiratory Diseases, Mexico City 14080, Mexico b
art ic l e i nf o
a b s t r a c t
Article history: Received 3 October 2012 Accepted 18 November 2013
Multichannel analysis of lung sounds (LSs) has enabled the generation of a functional image for the temporal and spatial study of LS intensities in healthy and diseased subjects; this method is known as respiratory acoustic thoracic imaging (RATHI). This acoustic imaging technique has been applied to diverse pulmonary conditions, but it is important to contribute to the understanding of RATHI characteristics, such as acoustic spatial distribution, dependence on airflow and variability. The purpose of the current study is to assess the intra-subject and inter-subject RATHI variabilities in a cohort of 12 healthy male subjects (24.371.5 years) using diverse quantitative indices. The indices were obtained directly from the acoustic image and did not require scores from human raters, which helps to prevent inter-observer variability. To generate the acoustic image, LSs were acquired at 25 positions on the posterior thoracic surface by means of airborne sound sensors with a wide frequency band from 75 up to 1000 Hz under controlled airflow conditions at 1.0, 1.5 and 2.0 L/s. To assess intra-subject variability, the degree of similitude between inspiratory acoustic images was evaluated through quadratic mutual information based on the Cauchy–Schwartz inequality (ICS). The inter-subject variability was assessed by an image registration procedure between RATHIs and X-ray images to allow the computation of average and variance acoustic image in the same coordinate space. The results indicated that intra-subject RATHI similitude, reflected by I CSglobal , averaged 0.960 70.008, 0.958 70.008 and 0.960 70.007 for airflows of 1.0, 1.5, and 2 L/s, respectively. As for the inter-subject variability, the variance image values for three airflow conditions indicated low image variability as they ranged from 0.01 to 0.04. In conclusion, the assessment of intra-subject and inter-subject variability by similitude indices indicated that the acoustic image pattern is repeatable along different respiratory cycles and across different subjects. Therefore, RATHI could be used to explore different aspects of spatial distribution and its association with regional pulmonary ventilation. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Acoustic thoracic imaging Breathing sounds Intra-subject variability Inter-subject variability Mutual information
1. Introduction As lung sounds (LSs) contain relevant information related to pulmonary structure and function, they have been the focus of interest for decades [1,2]. Physicians have looked for peculiar LSs using the classical auscultation procedure to diagnose lung disorders. To achieve a diagnosis, a physician needs to integrate all of the available spatial and temporal acoustic information qualitatively using a single stethoscope at different positions on the thoracic surface. Recently, several studies have obtained systematic quantitative LS measures in healthy and diseased subjects
n
Corresponding author. Tel.: þ 52 555804 4600x1171. E-mail address: [email protected] (S. Charleston-Villalobos).
0010-4825/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiomed.2013.11.007
[3–5]. In an earlier study by Dosani and Kraman [6], LSs were analyzed over different regions on the thoracic surface by the use of one to four microphones, but the acoustic information was not acquired simultaneously. Kompis et al. went a step further and studied the LS spatial distribution during inspiratory and expiratory phases using LS intensity values on the posterior thoracic surface with a 2 4 microphone array [7]. Sound intensities were mapped with a grayscale color palette, but the maps exhibited low spatial resolution due to the low number of sensors; therefore, association of the acoustic activity with anatomic regions was difficult. In 2004, Charleston et al. used a 5 5 microphone array to propose the concept of respiratory acoustic thoracic imaging (RATHI) by evaluating different deterministic interpolating functions to generate 2D acoustic thoracic images [8]. Some research
S. Charleston-Villalobos et al. / Computers in Biology and Medicine 45 (2014) 58–66
has been performed on multichannel analysis of LSs [3,9,10], and applications of the acoustic image have been evaluated and reported previously [11,12], which promotes its usefulness in a clinical environment. The imaging of LSs by their 2D representation on the thoracic surface is suitable for the study of LS distribution; in clinical settings, the consensus is that intense LSs are associated with well-ventilated pulmonary regions [13,14]. Due to the relevance of acoustic imaging for studying pulmonary function, efforts have been made to understand its repeatability, i.e., it is desirable that the acoustic information remains similar for a subject among different respiratory cycles and across subjects with comparable pulmonary function at the same airflow value. In this sense, there are contributions focused on assessing the interand intra-subject variability of the acoustic image as reported by Maher et al. [15] and Bartziokas et al. [16]. In these studies, the authors used trained raters to analyze images recorded during one complete breathing cycle. Notably, the raters provided a qualitative assessment of the acoustic image by the dynamic appearance attribute, among others, that was coded for intra-rater reliability and inter-rater agreement categories. Additionally, the reproducibility was assessed by computing a global index based on the average energy values of the acoustic image; Maher et al. reported a reproducibility of 90% in 98% of the studied cases [15]. Using a different approach to previous studies, this study attempts to give a quantitative and accurate estimation of the inter- and intrasubject RATHI variability using diverse quantitative indices obtained directly from the acoustic image. This approach avoids inter-observer rater variability. The novelty of our study is to add knowledge about RATHI by assessing its variability taking advantage of image processing techniques to obtain quantitative figures of merit that indicate (a) the similitude of RATHI within-subjects for diverse inspiratory phases and (b) the average and variance acoustic images between subjects. The similitude between images was evaluated using mutual information, which is a robust and high accuracy technique that has been successfully used in medical imaging [17], and takes into account the probability density function of the pixels in the whole image. The intersubject RATHI variability was assessed by estimating the average and variance images as a measure of change across the tested population. A variance image was proposed instead of mutual information, which requires a base image that could not be appropriately selected from the cohort of healthy subjects included in this study. In particular, the variance acoustic image provides information about the pulmonary sites with more variability compared with the average image. Image registration between the acoustic and X-ray images was required to align the acoustic information of different subjects in the same coordinate space. The assessment of RATHI was achieved with multichannel measurements acquired by airborne sound sensors using a wide frequency band of LSs, ranging from 75 Hz to 1000 Hz. Additionally, RATHI variability was assessed in this study at different airflows to study possible alterations under different airflow conditions [18].
2. Theoretical framework
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reflected in diverse performance indices as the maximum squared residual error. The procedure for mapping the multichannel acoustic intensity LS information to a 2D space can be stated as follows. Considering that SðP; f ðPÞÞ represents the original intensity acoustic values matrix, the interpolation procedure transforms I SðP; f ðPÞÞ into an acoustic image denoted by SI ðP I ; f Þ, incrementing the original discretization level of S. The variable P represents a finite set of coordinates ðpk ; pl Þ, f ðPÞ is the intensity function that produces different color palette values, and I stands for the interpolated image. In the case of the 1D Hermite interpolating I function, f ðpk Þ is obtained from f ðPÞ and from its first derivative, evaluating both at pk and pk þ 1 [8]. The 2D extension of the interpolation procedure can be carried out by applying the separability property of the interpolation function, i.e., the data columns are interpolated first followed by the rows [19]. 2.2. Mutual Information (MI) In some studies, measurement of the information content in a single image or between two images of the same or different modalities is necessary. The Shannon entropy has been used to quantify the degree of information and is defined as HðXÞ ¼ ∑ pi ðXÞ logðpi ðXÞÞ;
ð1Þ
i
where pi ðXÞ is the probability density function of the random variable X. For the case of two random variables X 1 and X 2 , the mutual information (MI) between them is stated as MIðX 1 ; X 2 Þ ¼ HðX 1 Þ þ HðX 2 Þ HðX 1 ; X 2 Þ;
ð2Þ
where HðX 1 ; X 2 Þ is the joint entropy; MI can be interpreted as the reduction of uncertainty in X 1 when X 2 is known. If HðX 1 ; X 2 Þ is minimized, MI is maximized, i.e., X 1 and X 2 are highly correlated. An alternative expression of MI can be obtained by the Kullback– Leibler distance between the joint probability density function (pdf) and the product of the marginal pdfs [20]: MI ¼ ∑∑f X 1 X 2 ðx1 ; x2 Þlog
f X 1 X 2 ðx1 ; x2 Þ ; f X 1 ðx1 Þf X 2 ðx2 Þ
ð3Þ
where f X 1 ðx1 Þ and f X 2 ðx2 Þ represent the marginal pdfs and f X 1 X 2 ðx1 ; x2 Þ is the joint pdf. It has been reported, however, that MI based on Shannon entropy experiences problems with images of low structural content [21,22]. To overcome the limitation, Xu [23] suggested computing MI between images by simplifying the calculus of the joint pdf as I CS ðX 1 ; X 2 Þ ¼ DCS ðf X 1 X 2 ðx1 ; x2 Þ; f X 1 ðx1 Þf X 2 ðx2 ÞÞ;
ð4Þ
where DCS is the Cauchy–Schwartz distance [23,24]. In the current study, the acoustic image comparison was based on Eq. (4) considering the estimation of the marginal and joint pdfs. The pdfs were estimated by the Parzen window method using a Gaussian function with zero mean and unitary variance [26]. The “optimum value” of the window size requires knowledge of the true data pdf, which is unknown [25]. However, the window size can be estimated based on the spread of the data as well as the number of pixels as in [27], i.e., using a data-driven estimation.
2.1. Respiratory acoustic thoracic imaging (RATHI) 2.3. Image registration An acoustic image is formed by interpolating a matrix obtained by averaging LS intensity values in a window centered at a particular airflow value. The selection of the optimal deterministic interpolating function was accomplished in [8] by measuring the differences between the acoustic information acquired by additional microphones to pick up LSs in between the fixed microphones of the 5 5 sensor array and the interpolated information
Image registration is used to obtain spatial alignment of images of the same or different modalities acquired from the same subject or from different subjects; in this study, the procedure was applied to the X-ray and acoustic images of each subject. To register images, a transformation Tð U Þ that relates the position of certain features in a base image to the position of the corresponding
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features in another image is necessary TðpAk ; pAl Þ ¼ ðpBm ; pBn Þ; where A represents the base image and B is the image to be aligned, ðpAk ; pAl Þ represents the position of features in A, and ðpBm ; pBn Þ represents the transformed position in B [28]. Furthermore, AðpAk ; pAl Þ and BðpBm ; pBn Þ represent the intensity values in the
PLX PLC PM
corresponding images where ðpAk ; pAl Þ A ΩA , ðpBm ; pBn Þ A ΩB , and ΩA , ΩB indicate the related fields of view, which are normally different. To compare the images A and B in the same coordinate space, it is necessary to transform B to obtain a comparison between AðpAk ; pAl Þ and BT ðpAk ; pAl Þ. In this study, an affine transformation Tð UÞ was used in which parallel lines were mapped to parallel lines and the rotation matrix (R) was unrestricted; additionally, the
PRC PRX
1 2 3 4 5
PRC4
Fig. 1. The acoustic sensor array: (a) Acoustic sensor nomenclature where P indicates posterior surface, L means left side, R means right side, M indicates middle vertebral line, C means midclavicular line and X indicates axillary line and (b) The actual array location on the posterior thoracic surface.
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Cauchy-Schwartz Mutual Information (Ics) Fig. 2. Intra-subject variability assessment by mutual information. The entire inspiratory acoustic images (upper panel) are divided into 16 sub-images (middle panel), and sixteen similitude indices Ics are calculated between matching sub-images. The letters R and L stand for the right and left sides of the subject's back.
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transformation was global to avoid discontinuities in BT , i.e.,
pmB pnB
R
pkA
t
plA
T
! where t represents a translation vector. The values in the R ! matrix and t vector were estimated by the least square procedure from selected landmark positions ðpAk ; pAl Þ and ðpBm ; pBn Þ. To define landmarks in the images that need to be aligned, it is possible to use objects attached to the subjects that are visible in the image space (extrinsic registration) or anatomical points (intrinsic registration) [28]. In this study, a combination of extrinsic and intrinsic landmarks was used.
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The acquisition protocol included 12 clinically healthy nonsmoker male subjects with an average age of 24.3 71.5 years, an average weight of 77.87 11.0 kg, an average height of 174.8 77.8 cm, and an average body mass index of 25.47 2.7. During the acquisition, the subjects were standing up with their hands on the back of their neck and their elbows slightly towards the front to avoid scapular anatomic interference [18]. The subjects were asked to breathe at airflows of 1.0, 1.5 and 2.0 L/s for a period of 15 s. The airflow was acquired with a calibrated Fleisch pneumotachometer and visually controlled through a monitor localized in front of the subject for feedback purposes [3,18]. All subjects were residents of Mexico City (2240 m above sea level) and provided a signed informed consent according to the principles of the Declaration of Helsinki; this study was approved by the ethical review board of the National Institute of Respiratory Diseases. The multichannel LSs and the airflow information were digitized with a 12-bit A/D card with a sampling frequency of 10 kHz. For the analysis of the inter-subject RATHI variability, the acquisition protocol included a posteroanterior thoracic X-ray image of each subject. Three small metallic objects were attached to the subject's back to provide distance references.
3. Methodology 3.2. LS digital signal processing and imaging 3.1. Microphone array and acquisition protocol The microphone array consisted of 25 microphones aligned in five rows and five columns (see Fig. 1) as originally proposed in [8] except that the distance between microphones was adapted to completely cover the pulmonary zone on the posterior surface of each subject's thorax [12]. To obtain a regular microphone distribution, the array included microphones on the middle line, and the first row was located 6 cm below the spinous process of the seventh cervical vertebra; all sensors were attached with double-sided adhesive tape according to anatomical positions [8,3]; see Fig. 1. Furthermore, the acoustic sensors were assembled with subminiature electret microphones coupled in air bells, i.e., the sensors are airborne sound type instead of structured-borne sound type. The sensors have a flat frequency response in the range of 0.05–3.0 kHz, and they were submitted to a calibration procedure.
A band-pass digital filter was applied to the 25 LS information channels to reduce heart sound interference and high-frequency noise. The cut-off frequencies were set at 75–1000 Hz as suggested by previous studies [1,29], which found that normal chest wall breath sound contains information at frequencies below 100 Hz and frequencies up to 1000 Hz. To generate the intensity-type RATHI, the Hilbert transform of the acoustic signal of each channel of the sensor array was calculated to obtain the corresponding envelope. Afterwards, an average value was obtained at each sensor by 1000 LS envelope samples selected on the inspiratory airflow plateau at four respiratory phases. Finally, the 2D data array of averaged values was interpolated with the Hermite interpolating function to generate normalized RATHIs of size 1444 1988 pixels; in the normalized color palette, red implies the largest intensity and black represents acoustic silence.
Anatomical Images Base Image
T12 ( ) T2 ( ) T1 ( ) Functional Images
Registered Functional Images
Average and variance images
T12 ( ) T2 ( ) T1 ( ) Fig. 3. Inter-subject variability assessment using average and variance images. The anatomical X-ray images are registered to obtain T 1 ð U Þ to T 12 ð U Þ, and the transformations are applied to RATHIs to obtain registered functional images. Afterwards, average and variance acoustic images are calculated.
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3.3. Intra-subject variability assessment To assess the intra-subject variability, i.e., to estimate the degree of similitude between RATHI images, four RATHIs were selected for each subject during inspiratory phases along different
Fig. 4. Landmarks on the X-ray image to assess inter-subject variability. The four gray circles correspond to metallic objects attached to the subject's back, the white squares indicate the positions of the acoustic sensors and the green dots represent the selected landmarks for image registration.
L/s
respiratory cycles. The RATHI of the first inspiratory phase was treated as the base image. Furthermore, to analyze the LS spatial distribution with a finer resolution, the entire RATHIs were divided into 16 sub-images: four were used to compare lung apical areas, eight were used for middle areas including the lung basal zones and four were used for lung edge areas; see Fig. 2. The assessment of the similitude between the four RATHIs was obtained by averaging three ICS values of the matching sub-images at airflows of 1, 1.5 and 2 L/s and for two recordings. The described procedure was applied for the cohort of 12 subjects included in this study. Finally, the assessment of the intra-subject variability was performed in two ways: a) by averaging ICS for each sub-image (I CS local ) and b) by averaging the sub-images I CS local to obtain a global mean ICS (I CS global ) for each airflow value. The intra-subject RATHI variability is considered low when the sixteen I CS local values or the I CS global approach one. Additionally, an ICS value was calculated for whole images, without dividing the RATHI, but the results indicated that the RATHI spatial distribution is best captured by extracting local similitude information. 3.4. Inter-subject variability assessment The inter-subject variability of RATHI was assessed using a twostep procedure. First, a transformation was obtained to register acoustic information for each subject by registering his own X-ray image to a base X-ray image. Then, average and variance images were computed from all the aligned RATHIs (see Fig. 3). The intersubject variability is reported in this study as a variance image because that picture provides information about the pulmonary zones with smaller or larger dispersions of the LS intensity values among the subjects. For anatomical image registration, 16 landmarks were placed throughout the X-ray image of each subject that took as references the points defined in Section 3.1 and four anatomical landmarks at the lung apical and basal zones (see Fig. 4).
4. Results
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Fig. 5. RATHIs from a healthy subject for four inspiratory phases. (a) Acquired airflow signal at 1.0 L/s, (b) RATHIs obtained from multichannel LSs around the red vertical dashed lines, and (c) Average RATHI computed from RATHIs in (b).
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The spatial distribution of RATHI for a healthy subject breathing at 1 L/s is shown in Fig. 5. The airflow signal is depicted in Fig. 5 (a) with red vertical dashed lines indicating the airflow value around which RATHI was built for four inspiratory phases. The corresponding normalized inspiratory RATHIs are displayed in Fig. 5(b). In Fig. 5(c), the mean RATHI is displayed by averaging the RATHIs images in Fig. 5(b). In the color palette of RATHIs, the more intense sound is represented with more intense red color while the acoustic silence is represented with black color. As observed, the inspiratory RATHIs in Fig. 5(b) and the mean RATHI in Fig. 5(c) display a spatial distribution that reveals two intense red blobs and darker zones at the middle line, towards the posterior axillary lines, and at the edge of the basal pulmonary
1
0 Fig. 6. Dependence of RATHI on the airflow value. (a) Average inspiratory RATHI from one subject breathing at 1.0 L/s, (b) RATHI at 1.5 L/s, and (c) RATHI at 2.0 L/s. The RATHI has increased magnitude as the airflow value increases.
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region, i.e., RATHI for a healthy subject evidences intense LS in the middle and basal regions of the lung with a decrement in LS magnitude towards the lung apices.
Table 2 I CS local values for one healthy subject for different airflows. Sub-image
Airflow value
4.1. Dependence of RATHI on airflow value The dependence of RATHI on the airflow value was also analyzed in this study. In Fig. 6, the normalized RATHIs at airflows of 1, 1.5 and 2 L/s for one healthy subject are displayed. As can be observed, the spatial distribution in the RATHI is maintained but the magnitude of the blobs increases as the airflow increases. Specifically, the norm values of RATHI were 91 for 1.0 L/s, 98 for 1.5 L/s and 112 for 2.0 L/s. It is feasible that the former condition may owe to the addition of pulmonary sources contributing to ventilation as described above. 4.2. Intra-subject variability assessment Regarding the assessment of the intra-subject variability of RATHI, Table 1 shows the ICS and I CS local values of the 16 subRATHIs for one subject in a comparison of the first inspiratory phase with three subsequent phases for two recordings at an airflow of 1 L/s. The I CS local values per sub-image exhibit low intra-subject RATHI variability as their range goes from 0.906 to 0.970 with a mean value of 0.941 and standard deviation of 0.022. The dependency of the intra-subject variability on the airflow value is reported in Table 2 through the I CS local values of the acoustic images for a subject at 1, 1.5 and 2 L/s. As seen the mean of the ICS values for these three conditions is approximately 0.965, which supports the idea that RATHI possesses low intra-subject variability even for different airflows. The I CS local values are listed Table 1 Ics for one subject including two recordings. Subimage
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Average Ics I CS local
Airflow 1.0 L/s Recording number
Ics
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
0.902 0.960 0.955 0.943 0.976 0.970 0.951 0.901 0.946 0.929 0.931 0.944 0.884 0.877 0.964 0.947 0.964 0.907 0.959 0.952 0.913 0.931 0.884 0.890 0.963 0.963 0.952 0.967 0.978 0.930 0.957 0.958
Average
0.998 0.864 0.939 0.991 0.947 0.998 0.913 0.939 0.963 0.929 0.957 0.941 0.875 0.942 0.940 0.986 0.963 0.955 0.922 0.931 0.946 0.889 0.932 0.876 0.968 0.947 0.938 0.967 0.941 0.945 0.988 0.971
0.914 0.879 0.990 0.979 0.973 0.983 0.917 0.881 0.904 0.919 0.943 0.962 0.912 0.986 0.994 0.975 0.922 0.922 0.936 0.921 0.958 0.893 0.992 0.864 0.990 0.919 0.966 0.962 0.940 0.962 0.977 0.971
0.938 0.901 0.961 0.971 0.965 0.983 0.927 0.907 0.937 0.925 0.943 0.949 0.890 0.935 0.966 0.969 0.949 0.928 0.939 0.934 0.939 0,904 0.936 0.876 0.973 0.943 0.952 0.965 0.953 0.945 0.974 0.966
0.919 0.966
63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 L/s
1.5 L/s
2 L/s
0.953 0.963 0.959 0.934 0.934 0.959 0.960 0.970 0.943 0.961 0.954 0.970 0.968 0.981 0.963 0.946
0.971 0.991 0.961 0.971 0.955 0.984 0.978 0.975 0.959 0.985 0.976 0.977 0.964 0.984 0.975 0.981
0.967 0.978 0.949 0.952 0.981 0.972 0.967 0.978 0.950 0.981 0.954 0.974 0.955 0.965 0.956 0.983
Table 3 Global average Ics for twelve subjects at different airflows. Sub-image
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 I CSglobal 7 SD
Average Ics (I CS local ) 1 L/s
1.5 L/s
2 L/s
0.956 0.964 0.967 0.954 0.967 0.965 0.957 0.964 0.969 0.959 0.947 0.943 0.962 0.975 0.957 0.958 0.960 70.008
0.956 0.953 0.959 0.970 0.964 0.956 0.959 0.964 0.961 0.953 0.943 0.944 0.966 0.968 0.949 0.963 0.958 7 0.008
0.968 0.956 0.960 0.964 0.959 0.962 0.963 0.954 0.956 0.961 0.950 0.948 0.958 0.971 0.960 0.972 0.9607 0.007
0,974 0.917 0.931 0.946 0.912 0.967 0.938 0.936 0.921 0.906 0.958 0.958 0.949 0.970
in Table 3 for the cohort of 12 subjects considering the 16 subRATHIs and three airflow values. At the bottom of the table, the I CS global values and standard deviations for the 1, 1.5 and 2 L/s flow rates are 0.960 70.008, 0.95870.008 and 0.960 70.007, respectively. Because theI CS local and I CS global values approach one, it is plausible to state that RATHI has a low variability among different inspiratory phases, i.e., this study validates the low intrasubject variability of RATHI through a quantitative and accurate methodology. It is pertinent to mention here that the present results are in agreement with the results obtained for the acoustic image generated by vibration sensors wherein the authors reported values of reproducibility using qualitative indices and a global quantitative index based on the acoustic energy of approximately 90% [15]. 4.3. Inter-subject variability assessment For the cohort of 12 subjects, the average images of normalized RATHIs for airflow rates between 1 L/s and 2 L/s and the corresponding variance images are shown on the left and right sides of Fig. 7, respectively. The average RATHIs were computed after an anatomical image registration procedure and affine transformation
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Average RATHI at 1.0 L/s
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Fig. 7. Inter-subject variability assessment for three different airflows. From top to bottom, the average RATHI and its corresponding variance image are displayed at 1, 1.5 and 2.0 L/s. The average and variance images were obtained from a cohort of twelve healthy subjects.
of normalized RATHIs. As seen in Fig. 7, the average RATHIs for the three airflow rates reveal common acoustic information across the subjects for different inspiratory phases. In fact, the spatial distribution of the average images appears to be comparable with the distribution of the average RATHI within a subject as depicted in Fig. 5(c), which suggests a low inter-subject variability. The former statement is confirmed by the variance images, which exhibit values below 4% with respect to the average RATHIs for the three airflow values; see Fig. 7.
5. Discussion and conclusion The aim of this study was to assess the intra- and intersubject RATHI variabilities by means of quantitative indices that were obtained directly from the acoustic images. RATHI was formed using
multichannel LSs acquired by airborne sound sensors with a wide LS frequency band ranging from 75 Hz to 1000 Hz. RATHI variability was evaluated at three airflow rates. For the intra- and inter-subject variabilities, the similitude among RATHIs was evaluated by quadratic Cauchy–Schwartz mutual information and by a variance image, respectively. The results showed that for intra-subject RATHI variability, the similitude index I CS global was 0.96070.008, 0.95870.008 and 0.96070.007 for airflow rates of 1.0, 1.5, and 2 L/s, respectively. For the inter-subject variability, the variance image indicated, at most, 4% acoustic variation with respect to the mean RATHIs. The main findings of this study can be summarized as follows:
RATHI has low intra-subject variability because the I CS global index approached the optimum value of 1. RATHI can be considered as a reliable image for different inspiratory phases and different airflow rates.
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RATHI has low inter-subject variability as the variance image of
registered normalized RATHIs showed low values of less than 4%. RATHI intensity is influenced by the airflow rate because the norm of RATHI increased from 91 to 112 as the airflow rate was increased from 1 to 2 L/s. However, the intra- and inter-subject variabilities remained low as reflected by the proposed indices.
In future studies, it may be interesting to assess the effect of gender and age on RATHI variability because only healthy young males were included in the present study. Regarding gender influence, it is expected that RATHI would maintain its low variability for healthy female subjects with a similar average age as in the present study considering that their pulmonary anatomies and functions are similar to those of males [30]. In contrast, inter-subject RATHI variability may increase with age because healthy elderly subjects exhibit anatomical alterations, such as chest wall and thoracic spine deformities, among other physiological changes [31]. In summary, the intra- and inter-subject RATHI variabilities were assessed, and the results validated high intra-subject RATHI similitude and low inter-subject RATHI variability. The results are in agreement with other research efforts using vibration sensors, which sustains the reliability of the acoustic image in the clinical environment. The main implication of the present study is that RATHI is a trustworthy acoustic representation of the pulmonary function that could be used to explore different aspects of LS spatial distribution and its associations with regional pulmonary ventilation.
Summary Multichannel analysis of lung sounds (LSs) has enabled the generation of a functional image for temporal and spatial study of LS intensities in healthy and pathological subjects known as respiratory acoustic thoracic imaging (RATHI). In contrast with other studies, this study provides a quantitative and accurate estimation of the inter- and intra-subject RATHI variabilities using diverse indices obtained directly from the acoustic image, therefore avoiding the variability of human raters. The assessment of acoustic image variability was performed with a cohort of 12 healthy male subjects (24.3 71.5 years). To generate the acoustic image, LSs were acquired at 25 positions on the posterior thoracic surface by means of airborne sound sensors with a wide frequency band from 75 Hz to 1000 Hz under controlled airflow conditions at 1.0, 1.5 and 2.0 L/s. To explore intra-subject variability, the degree of similitude between inspiratory acoustic images was evaluated by quadratic mutual information based on the Cauchy–Schwartz inequality (ICS) at different inspiratory phases. Furthermore, the entire RATHIs were divided into 16 sub-images to analyze LS spatial distribution with finer resolution. The inter-subject variability of RATHI was assessed using a two-step procedure. First, a transformation was obtained to register acoustic information for each subject by registering his own X-ray image to a base X-ray image. Second, average and variance images were computed from all of the aligned RATHIs. The results indicated that the intrasubject RATHI variability has an average ICS value of approximately 0.96 for 1.0, 1.5, and 2 L/s; these values approach the unitary ideal value. For inter-subject variability, the variance image values for three airflow conditions exhibited low image variability as they ranged from 0.01 to 0.04, which indicates at most 4% acoustic variation with respect to the RATHI average value. In conclusion, the assessment of intra-subject and inter-subject variabilities revealed that the acoustic image pattern is repeatable for multiple respiratory cycles and across different subjects.
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Conflict of Interest Statement None Declared.
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Contents lists available at ScienceDirect
Computers in Biology and Medicine journal homepage: www.elsevier.com/locate/cbm
Assessing the variability in respiratory acoustic thoracic imaging (RATHI) S. Charleston-Villalobos a,n, A. Torres-Jiménez a, R. González-Camarena b, G. Chi-Lem c, T. Aljama-Corrales a a
Electrical Engineering Department, Universidad Autonoma Metropolitana, Mexico City 09340, Mexico Department of Health Science, Universidad Autonoma Metropolitana, Mexico City 09340, Mexico c National Institute of Respiratory Diseases, Mexico City 14080, Mexico b
art ic l e i nf o
a b s t r a c t
Article history: Received 3 October 2012 Accepted 18 November 2013
Multichannel analysis of lung sounds (LSs) has enabled the generation of a functional image for the temporal and spatial study of LS intensities in healthy and diseased subjects; this method is known as respiratory acoustic thoracic imaging (RATHI). This acoustic imaging technique has been applied to diverse pulmonary conditions, but it is important to contribute to the understanding of RATHI characteristics, such as acoustic spatial distribution, dependence on airflow and variability. The purpose of the current study is to assess the intra-subject and inter-subject RATHI variabilities in a cohort of 12 healthy male subjects (24.371.5 years) using diverse quantitative indices. The indices were obtained directly from the acoustic image and did not require scores from human raters, which helps to prevent inter-observer variability. To generate the acoustic image, LSs were acquired at 25 positions on the posterior thoracic surface by means of airborne sound sensors with a wide frequency band from 75 up to 1000 Hz under controlled airflow conditions at 1.0, 1.5 and 2.0 L/s. To assess intra-subject variability, the degree of similitude between inspiratory acoustic images was evaluated through quadratic mutual information based on the Cauchy–Schwartz inequality (ICS). The inter-subject variability was assessed by an image registration procedure between RATHIs and X-ray images to allow the computation of average and variance acoustic image in the same coordinate space. The results indicated that intra-subject RATHI similitude, reflected by I CSglobal , averaged 0.960 70.008, 0.958 70.008 and 0.960 70.007 for airflows of 1.0, 1.5, and 2 L/s, respectively. As for the inter-subject variability, the variance image values for three airflow conditions indicated low image variability as they ranged from 0.01 to 0.04. In conclusion, the assessment of intra-subject and inter-subject variability by similitude indices indicated that the acoustic image pattern is repeatable along different respiratory cycles and across different subjects. Therefore, RATHI could be used to explore different aspects of spatial distribution and its association with regional pulmonary ventilation. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Acoustic thoracic imaging Breathing sounds Intra-subject variability Inter-subject variability Mutual information
1. Introduction As lung sounds (LSs) contain relevant information related to pulmonary structure and function, they have been the focus of interest for decades [1,2]. Physicians have looked for peculiar LSs using the classical auscultation procedure to diagnose lung disorders. To achieve a diagnosis, a physician needs to integrate all of the available spatial and temporal acoustic information qualitatively using a single stethoscope at different positions on the thoracic surface. Recently, several studies have obtained systematic quantitative LS measures in healthy and diseased subjects
n
Corresponding author. Tel.: þ 52 555804 4600x1171. E-mail address: [email protected] (S. Charleston-Villalobos).
0010-4825/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiomed.2013.11.007
[3–5]. In an earlier study by Dosani and Kraman [6], LSs were analyzed over different regions on the thoracic surface by the use of one to four microphones, but the acoustic information was not acquired simultaneously. Kompis et al. went a step further and studied the LS spatial distribution during inspiratory and expiratory phases using LS intensity values on the posterior thoracic surface with a 2 4 microphone array [7]. Sound intensities were mapped with a grayscale color palette, but the maps exhibited low spatial resolution due to the low number of sensors; therefore, association of the acoustic activity with anatomic regions was difficult. In 2004, Charleston et al. used a 5 5 microphone array to propose the concept of respiratory acoustic thoracic imaging (RATHI) by evaluating different deterministic interpolating functions to generate 2D acoustic thoracic images [8]. Some research
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has been performed on multichannel analysis of LSs [3,9,10], and applications of the acoustic image have been evaluated and reported previously [11,12], which promotes its usefulness in a clinical environment. The imaging of LSs by their 2D representation on the thoracic surface is suitable for the study of LS distribution; in clinical settings, the consensus is that intense LSs are associated with well-ventilated pulmonary regions [13,14]. Due to the relevance of acoustic imaging for studying pulmonary function, efforts have been made to understand its repeatability, i.e., it is desirable that the acoustic information remains similar for a subject among different respiratory cycles and across subjects with comparable pulmonary function at the same airflow value. In this sense, there are contributions focused on assessing the interand intra-subject variability of the acoustic image as reported by Maher et al. [15] and Bartziokas et al. [16]. In these studies, the authors used trained raters to analyze images recorded during one complete breathing cycle. Notably, the raters provided a qualitative assessment of the acoustic image by the dynamic appearance attribute, among others, that was coded for intra-rater reliability and inter-rater agreement categories. Additionally, the reproducibility was assessed by computing a global index based on the average energy values of the acoustic image; Maher et al. reported a reproducibility of 90% in 98% of the studied cases [15]. Using a different approach to previous studies, this study attempts to give a quantitative and accurate estimation of the inter- and intrasubject RATHI variability using diverse quantitative indices obtained directly from the acoustic image. This approach avoids inter-observer rater variability. The novelty of our study is to add knowledge about RATHI by assessing its variability taking advantage of image processing techniques to obtain quantitative figures of merit that indicate (a) the similitude of RATHI within-subjects for diverse inspiratory phases and (b) the average and variance acoustic images between subjects. The similitude between images was evaluated using mutual information, which is a robust and high accuracy technique that has been successfully used in medical imaging [17], and takes into account the probability density function of the pixels in the whole image. The intersubject RATHI variability was assessed by estimating the average and variance images as a measure of change across the tested population. A variance image was proposed instead of mutual information, which requires a base image that could not be appropriately selected from the cohort of healthy subjects included in this study. In particular, the variance acoustic image provides information about the pulmonary sites with more variability compared with the average image. Image registration between the acoustic and X-ray images was required to align the acoustic information of different subjects in the same coordinate space. The assessment of RATHI was achieved with multichannel measurements acquired by airborne sound sensors using a wide frequency band of LSs, ranging from 75 Hz to 1000 Hz. Additionally, RATHI variability was assessed in this study at different airflows to study possible alterations under different airflow conditions [18].
2. Theoretical framework
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reflected in diverse performance indices as the maximum squared residual error. The procedure for mapping the multichannel acoustic intensity LS information to a 2D space can be stated as follows. Considering that SðP; f ðPÞÞ represents the original intensity acoustic values matrix, the interpolation procedure transforms I SðP; f ðPÞÞ into an acoustic image denoted by SI ðP I ; f Þ, incrementing the original discretization level of S. The variable P represents a finite set of coordinates ðpk ; pl Þ, f ðPÞ is the intensity function that produces different color palette values, and I stands for the interpolated image. In the case of the 1D Hermite interpolating I function, f ðpk Þ is obtained from f ðPÞ and from its first derivative, evaluating both at pk and pk þ 1 [8]. The 2D extension of the interpolation procedure can be carried out by applying the separability property of the interpolation function, i.e., the data columns are interpolated first followed by the rows [19]. 2.2. Mutual Information (MI) In some studies, measurement of the information content in a single image or between two images of the same or different modalities is necessary. The Shannon entropy has been used to quantify the degree of information and is defined as HðXÞ ¼ ∑ pi ðXÞ logðpi ðXÞÞ;
ð1Þ
i
where pi ðXÞ is the probability density function of the random variable X. For the case of two random variables X 1 and X 2 , the mutual information (MI) between them is stated as MIðX 1 ; X 2 Þ ¼ HðX 1 Þ þ HðX 2 Þ HðX 1 ; X 2 Þ;
ð2Þ
where HðX 1 ; X 2 Þ is the joint entropy; MI can be interpreted as the reduction of uncertainty in X 1 when X 2 is known. If HðX 1 ; X 2 Þ is minimized, MI is maximized, i.e., X 1 and X 2 are highly correlated. An alternative expression of MI can be obtained by the Kullback– Leibler distance between the joint probability density function (pdf) and the product of the marginal pdfs [20]: MI ¼ ∑∑f X 1 X 2 ðx1 ; x2 Þlog
f X 1 X 2 ðx1 ; x2 Þ ; f X 1 ðx1 Þf X 2 ðx2 Þ
ð3Þ
where f X 1 ðx1 Þ and f X 2 ðx2 Þ represent the marginal pdfs and f X 1 X 2 ðx1 ; x2 Þ is the joint pdf. It has been reported, however, that MI based on Shannon entropy experiences problems with images of low structural content [21,22]. To overcome the limitation, Xu [23] suggested computing MI between images by simplifying the calculus of the joint pdf as I CS ðX 1 ; X 2 Þ ¼ DCS ðf X 1 X 2 ðx1 ; x2 Þ; f X 1 ðx1 Þf X 2 ðx2 ÞÞ;
ð4Þ
where DCS is the Cauchy–Schwartz distance [23,24]. In the current study, the acoustic image comparison was based on Eq. (4) considering the estimation of the marginal and joint pdfs. The pdfs were estimated by the Parzen window method using a Gaussian function with zero mean and unitary variance [26]. The “optimum value” of the window size requires knowledge of the true data pdf, which is unknown [25]. However, the window size can be estimated based on the spread of the data as well as the number of pixels as in [27], i.e., using a data-driven estimation.
2.1. Respiratory acoustic thoracic imaging (RATHI) 2.3. Image registration An acoustic image is formed by interpolating a matrix obtained by averaging LS intensity values in a window centered at a particular airflow value. The selection of the optimal deterministic interpolating function was accomplished in [8] by measuring the differences between the acoustic information acquired by additional microphones to pick up LSs in between the fixed microphones of the 5 5 sensor array and the interpolated information
Image registration is used to obtain spatial alignment of images of the same or different modalities acquired from the same subject or from different subjects; in this study, the procedure was applied to the X-ray and acoustic images of each subject. To register images, a transformation Tð U Þ that relates the position of certain features in a base image to the position of the corresponding
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features in another image is necessary TðpAk ; pAl Þ ¼ ðpBm ; pBn Þ; where A represents the base image and B is the image to be aligned, ðpAk ; pAl Þ represents the position of features in A, and ðpBm ; pBn Þ represents the transformed position in B [28]. Furthermore, AðpAk ; pAl Þ and BðpBm ; pBn Þ represent the intensity values in the
PLX PLC PM
corresponding images where ðpAk ; pAl Þ A ΩA , ðpBm ; pBn Þ A ΩB , and ΩA , ΩB indicate the related fields of view, which are normally different. To compare the images A and B in the same coordinate space, it is necessary to transform B to obtain a comparison between AðpAk ; pAl Þ and BT ðpAk ; pAl Þ. In this study, an affine transformation Tð UÞ was used in which parallel lines were mapped to parallel lines and the rotation matrix (R) was unrestricted; additionally, the
PRC PRX
1 2 3 4 5
PRC4
Fig. 1. The acoustic sensor array: (a) Acoustic sensor nomenclature where P indicates posterior surface, L means left side, R means right side, M indicates middle vertebral line, C means midclavicular line and X indicates axillary line and (b) The actual array location on the posterior thoracic surface.
Inspiratory phase 1
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Cauchy-Schwartz Mutual Information (Ics) Fig. 2. Intra-subject variability assessment by mutual information. The entire inspiratory acoustic images (upper panel) are divided into 16 sub-images (middle panel), and sixteen similitude indices Ics are calculated between matching sub-images. The letters R and L stand for the right and left sides of the subject's back.
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transformation was global to avoid discontinuities in BT , i.e.,
pmB pnB
R
pkA
t
plA
T
! where t represents a translation vector. The values in the R ! matrix and t vector were estimated by the least square procedure from selected landmark positions ðpAk ; pAl Þ and ðpBm ; pBn Þ. To define landmarks in the images that need to be aligned, it is possible to use objects attached to the subjects that are visible in the image space (extrinsic registration) or anatomical points (intrinsic registration) [28]. In this study, a combination of extrinsic and intrinsic landmarks was used.
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The acquisition protocol included 12 clinically healthy nonsmoker male subjects with an average age of 24.3 71.5 years, an average weight of 77.87 11.0 kg, an average height of 174.8 77.8 cm, and an average body mass index of 25.47 2.7. During the acquisition, the subjects were standing up with their hands on the back of their neck and their elbows slightly towards the front to avoid scapular anatomic interference [18]. The subjects were asked to breathe at airflows of 1.0, 1.5 and 2.0 L/s for a period of 15 s. The airflow was acquired with a calibrated Fleisch pneumotachometer and visually controlled through a monitor localized in front of the subject for feedback purposes [3,18]. All subjects were residents of Mexico City (2240 m above sea level) and provided a signed informed consent according to the principles of the Declaration of Helsinki; this study was approved by the ethical review board of the National Institute of Respiratory Diseases. The multichannel LSs and the airflow information were digitized with a 12-bit A/D card with a sampling frequency of 10 kHz. For the analysis of the inter-subject RATHI variability, the acquisition protocol included a posteroanterior thoracic X-ray image of each subject. Three small metallic objects were attached to the subject's back to provide distance references.
3. Methodology 3.2. LS digital signal processing and imaging 3.1. Microphone array and acquisition protocol The microphone array consisted of 25 microphones aligned in five rows and five columns (see Fig. 1) as originally proposed in [8] except that the distance between microphones was adapted to completely cover the pulmonary zone on the posterior surface of each subject's thorax [12]. To obtain a regular microphone distribution, the array included microphones on the middle line, and the first row was located 6 cm below the spinous process of the seventh cervical vertebra; all sensors were attached with double-sided adhesive tape according to anatomical positions [8,3]; see Fig. 1. Furthermore, the acoustic sensors were assembled with subminiature electret microphones coupled in air bells, i.e., the sensors are airborne sound type instead of structured-borne sound type. The sensors have a flat frequency response in the range of 0.05–3.0 kHz, and they were submitted to a calibration procedure.
A band-pass digital filter was applied to the 25 LS information channels to reduce heart sound interference and high-frequency noise. The cut-off frequencies were set at 75–1000 Hz as suggested by previous studies [1,29], which found that normal chest wall breath sound contains information at frequencies below 100 Hz and frequencies up to 1000 Hz. To generate the intensity-type RATHI, the Hilbert transform of the acoustic signal of each channel of the sensor array was calculated to obtain the corresponding envelope. Afterwards, an average value was obtained at each sensor by 1000 LS envelope samples selected on the inspiratory airflow plateau at four respiratory phases. Finally, the 2D data array of averaged values was interpolated with the Hermite interpolating function to generate normalized RATHIs of size 1444 1988 pixels; in the normalized color palette, red implies the largest intensity and black represents acoustic silence.
Anatomical Images Base Image
T12 ( ) T2 ( ) T1 ( ) Functional Images
Registered Functional Images
Average and variance images
T12 ( ) T2 ( ) T1 ( ) Fig. 3. Inter-subject variability assessment using average and variance images. The anatomical X-ray images are registered to obtain T 1 ð U Þ to T 12 ð U Þ, and the transformations are applied to RATHIs to obtain registered functional images. Afterwards, average and variance acoustic images are calculated.
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3.3. Intra-subject variability assessment To assess the intra-subject variability, i.e., to estimate the degree of similitude between RATHI images, four RATHIs were selected for each subject during inspiratory phases along different
Fig. 4. Landmarks on the X-ray image to assess inter-subject variability. The four gray circles correspond to metallic objects attached to the subject's back, the white squares indicate the positions of the acoustic sensors and the green dots represent the selected landmarks for image registration.
L/s
respiratory cycles. The RATHI of the first inspiratory phase was treated as the base image. Furthermore, to analyze the LS spatial distribution with a finer resolution, the entire RATHIs were divided into 16 sub-images: four were used to compare lung apical areas, eight were used for middle areas including the lung basal zones and four were used for lung edge areas; see Fig. 2. The assessment of the similitude between the four RATHIs was obtained by averaging three ICS values of the matching sub-images at airflows of 1, 1.5 and 2 L/s and for two recordings. The described procedure was applied for the cohort of 12 subjects included in this study. Finally, the assessment of the intra-subject variability was performed in two ways: a) by averaging ICS for each sub-image (I CS local ) and b) by averaging the sub-images I CS local to obtain a global mean ICS (I CS global ) for each airflow value. The intra-subject RATHI variability is considered low when the sixteen I CS local values or the I CS global approach one. Additionally, an ICS value was calculated for whole images, without dividing the RATHI, but the results indicated that the RATHI spatial distribution is best captured by extracting local similitude information. 3.4. Inter-subject variability assessment The inter-subject variability of RATHI was assessed using a twostep procedure. First, a transformation was obtained to register acoustic information for each subject by registering his own X-ray image to a base X-ray image. Then, average and variance images were computed from all the aligned RATHIs (see Fig. 3). The intersubject variability is reported in this study as a variance image because that picture provides information about the pulmonary zones with smaller or larger dispersions of the LS intensity values among the subjects. For anatomical image registration, 16 landmarks were placed throughout the X-ray image of each subject that took as references the points defined in Section 3.1 and four anatomical landmarks at the lung apical and basal zones (see Fig. 4).
4. Results
L
0
R
1
Fig. 5. RATHIs from a healthy subject for four inspiratory phases. (a) Acquired airflow signal at 1.0 L/s, (b) RATHIs obtained from multichannel LSs around the red vertical dashed lines, and (c) Average RATHI computed from RATHIs in (b).
L
R
The spatial distribution of RATHI for a healthy subject breathing at 1 L/s is shown in Fig. 5. The airflow signal is depicted in Fig. 5 (a) with red vertical dashed lines indicating the airflow value around which RATHI was built for four inspiratory phases. The corresponding normalized inspiratory RATHIs are displayed in Fig. 5(b). In Fig. 5(c), the mean RATHI is displayed by averaging the RATHIs images in Fig. 5(b). In the color palette of RATHIs, the more intense sound is represented with more intense red color while the acoustic silence is represented with black color. As observed, the inspiratory RATHIs in Fig. 5(b) and the mean RATHI in Fig. 5(c) display a spatial distribution that reveals two intense red blobs and darker zones at the middle line, towards the posterior axillary lines, and at the edge of the basal pulmonary
1
0 Fig. 6. Dependence of RATHI on the airflow value. (a) Average inspiratory RATHI from one subject breathing at 1.0 L/s, (b) RATHI at 1.5 L/s, and (c) RATHI at 2.0 L/s. The RATHI has increased magnitude as the airflow value increases.
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region, i.e., RATHI for a healthy subject evidences intense LS in the middle and basal regions of the lung with a decrement in LS magnitude towards the lung apices.
Table 2 I CS local values for one healthy subject for different airflows. Sub-image
Airflow value
4.1. Dependence of RATHI on airflow value The dependence of RATHI on the airflow value was also analyzed in this study. In Fig. 6, the normalized RATHIs at airflows of 1, 1.5 and 2 L/s for one healthy subject are displayed. As can be observed, the spatial distribution in the RATHI is maintained but the magnitude of the blobs increases as the airflow increases. Specifically, the norm values of RATHI were 91 for 1.0 L/s, 98 for 1.5 L/s and 112 for 2.0 L/s. It is feasible that the former condition may owe to the addition of pulmonary sources contributing to ventilation as described above. 4.2. Intra-subject variability assessment Regarding the assessment of the intra-subject variability of RATHI, Table 1 shows the ICS and I CS local values of the 16 subRATHIs for one subject in a comparison of the first inspiratory phase with three subsequent phases for two recordings at an airflow of 1 L/s. The I CS local values per sub-image exhibit low intra-subject RATHI variability as their range goes from 0.906 to 0.970 with a mean value of 0.941 and standard deviation of 0.022. The dependency of the intra-subject variability on the airflow value is reported in Table 2 through the I CS local values of the acoustic images for a subject at 1, 1.5 and 2 L/s. As seen the mean of the ICS values for these three conditions is approximately 0.965, which supports the idea that RATHI possesses low intra-subject variability even for different airflows. The I CS local values are listed Table 1 Ics for one subject including two recordings. Subimage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Average Ics I CS local
Airflow 1.0 L/s Recording number
Ics
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
0.902 0.960 0.955 0.943 0.976 0.970 0.951 0.901 0.946 0.929 0.931 0.944 0.884 0.877 0.964 0.947 0.964 0.907 0.959 0.952 0.913 0.931 0.884 0.890 0.963 0.963 0.952 0.967 0.978 0.930 0.957 0.958
Average
0.998 0.864 0.939 0.991 0.947 0.998 0.913 0.939 0.963 0.929 0.957 0.941 0.875 0.942 0.940 0.986 0.963 0.955 0.922 0.931 0.946 0.889 0.932 0.876 0.968 0.947 0.938 0.967 0.941 0.945 0.988 0.971
0.914 0.879 0.990 0.979 0.973 0.983 0.917 0.881 0.904 0.919 0.943 0.962 0.912 0.986 0.994 0.975 0.922 0.922 0.936 0.921 0.958 0.893 0.992 0.864 0.990 0.919 0.966 0.962 0.940 0.962 0.977 0.971
0.938 0.901 0.961 0.971 0.965 0.983 0.927 0.907 0.937 0.925 0.943 0.949 0.890 0.935 0.966 0.969 0.949 0.928 0.939 0.934 0.939 0,904 0.936 0.876 0.973 0.943 0.952 0.965 0.953 0.945 0.974 0.966
0.919 0.966
63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 L/s
1.5 L/s
2 L/s
0.953 0.963 0.959 0.934 0.934 0.959 0.960 0.970 0.943 0.961 0.954 0.970 0.968 0.981 0.963 0.946
0.971 0.991 0.961 0.971 0.955 0.984 0.978 0.975 0.959 0.985 0.976 0.977 0.964 0.984 0.975 0.981
0.967 0.978 0.949 0.952 0.981 0.972 0.967 0.978 0.950 0.981 0.954 0.974 0.955 0.965 0.956 0.983
Table 3 Global average Ics for twelve subjects at different airflows. Sub-image
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 I CSglobal 7 SD
Average Ics (I CS local ) 1 L/s
1.5 L/s
2 L/s
0.956 0.964 0.967 0.954 0.967 0.965 0.957 0.964 0.969 0.959 0.947 0.943 0.962 0.975 0.957 0.958 0.960 70.008
0.956 0.953 0.959 0.970 0.964 0.956 0.959 0.964 0.961 0.953 0.943 0.944 0.966 0.968 0.949 0.963 0.958 7 0.008
0.968 0.956 0.960 0.964 0.959 0.962 0.963 0.954 0.956 0.961 0.950 0.948 0.958 0.971 0.960 0.972 0.9607 0.007
0,974 0.917 0.931 0.946 0.912 0.967 0.938 0.936 0.921 0.906 0.958 0.958 0.949 0.970
in Table 3 for the cohort of 12 subjects considering the 16 subRATHIs and three airflow values. At the bottom of the table, the I CS global values and standard deviations for the 1, 1.5 and 2 L/s flow rates are 0.960 70.008, 0.95870.008 and 0.960 70.007, respectively. Because theI CS local and I CS global values approach one, it is plausible to state that RATHI has a low variability among different inspiratory phases, i.e., this study validates the low intrasubject variability of RATHI through a quantitative and accurate methodology. It is pertinent to mention here that the present results are in agreement with the results obtained for the acoustic image generated by vibration sensors wherein the authors reported values of reproducibility using qualitative indices and a global quantitative index based on the acoustic energy of approximately 90% [15]. 4.3. Inter-subject variability assessment For the cohort of 12 subjects, the average images of normalized RATHIs for airflow rates between 1 L/s and 2 L/s and the corresponding variance images are shown on the left and right sides of Fig. 7, respectively. The average RATHIs were computed after an anatomical image registration procedure and affine transformation
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Average RATHI at 1.0 L/s
0
0.2
0.4
0.6
0.8
Variance image at 1.0 L/s
1
0.01
Average RATHI at 1.5 L/s
0
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
0.03
0.04
0.05
Variance image at 1.5 L/s
1
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Average RATHI at 2.0 L/s
0
0.02
Variance image at 2.0 L/s
1
0.01
0.02
0.03
0.04
0.05
0.06
Fig. 7. Inter-subject variability assessment for three different airflows. From top to bottom, the average RATHI and its corresponding variance image are displayed at 1, 1.5 and 2.0 L/s. The average and variance images were obtained from a cohort of twelve healthy subjects.
of normalized RATHIs. As seen in Fig. 7, the average RATHIs for the three airflow rates reveal common acoustic information across the subjects for different inspiratory phases. In fact, the spatial distribution of the average images appears to be comparable with the distribution of the average RATHI within a subject as depicted in Fig. 5(c), which suggests a low inter-subject variability. The former statement is confirmed by the variance images, which exhibit values below 4% with respect to the average RATHIs for the three airflow values; see Fig. 7.
5. Discussion and conclusion The aim of this study was to assess the intra- and intersubject RATHI variabilities by means of quantitative indices that were obtained directly from the acoustic images. RATHI was formed using
multichannel LSs acquired by airborne sound sensors with a wide LS frequency band ranging from 75 Hz to 1000 Hz. RATHI variability was evaluated at three airflow rates. For the intra- and inter-subject variabilities, the similitude among RATHIs was evaluated by quadratic Cauchy–Schwartz mutual information and by a variance image, respectively. The results showed that for intra-subject RATHI variability, the similitude index I CS global was 0.96070.008, 0.95870.008 and 0.96070.007 for airflow rates of 1.0, 1.5, and 2 L/s, respectively. For the inter-subject variability, the variance image indicated, at most, 4% acoustic variation with respect to the mean RATHIs. The main findings of this study can be summarized as follows:
RATHI has low intra-subject variability because the I CS global index approached the optimum value of 1. RATHI can be considered as a reliable image for different inspiratory phases and different airflow rates.
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RATHI has low inter-subject variability as the variance image of
registered normalized RATHIs showed low values of less than 4%. RATHI intensity is influenced by the airflow rate because the norm of RATHI increased from 91 to 112 as the airflow rate was increased from 1 to 2 L/s. However, the intra- and inter-subject variabilities remained low as reflected by the proposed indices.
In future studies, it may be interesting to assess the effect of gender and age on RATHI variability because only healthy young males were included in the present study. Regarding gender influence, it is expected that RATHI would maintain its low variability for healthy female subjects with a similar average age as in the present study considering that their pulmonary anatomies and functions are similar to those of males [30]. In contrast, inter-subject RATHI variability may increase with age because healthy elderly subjects exhibit anatomical alterations, such as chest wall and thoracic spine deformities, among other physiological changes [31]. In summary, the intra- and inter-subject RATHI variabilities were assessed, and the results validated high intra-subject RATHI similitude and low inter-subject RATHI variability. The results are in agreement with other research efforts using vibration sensors, which sustains the reliability of the acoustic image in the clinical environment. The main implication of the present study is that RATHI is a trustworthy acoustic representation of the pulmonary function that could be used to explore different aspects of LS spatial distribution and its associations with regional pulmonary ventilation.
Summary Multichannel analysis of lung sounds (LSs) has enabled the generation of a functional image for temporal and spatial study of LS intensities in healthy and pathological subjects known as respiratory acoustic thoracic imaging (RATHI). In contrast with other studies, this study provides a quantitative and accurate estimation of the inter- and intra-subject RATHI variabilities using diverse indices obtained directly from the acoustic image, therefore avoiding the variability of human raters. The assessment of acoustic image variability was performed with a cohort of 12 healthy male subjects (24.3 71.5 years). To generate the acoustic image, LSs were acquired at 25 positions on the posterior thoracic surface by means of airborne sound sensors with a wide frequency band from 75 Hz to 1000 Hz under controlled airflow conditions at 1.0, 1.5 and 2.0 L/s. To explore intra-subject variability, the degree of similitude between inspiratory acoustic images was evaluated by quadratic mutual information based on the Cauchy–Schwartz inequality (ICS) at different inspiratory phases. Furthermore, the entire RATHIs were divided into 16 sub-images to analyze LS spatial distribution with finer resolution. The inter-subject variability of RATHI was assessed using a two-step procedure. First, a transformation was obtained to register acoustic information for each subject by registering his own X-ray image to a base X-ray image. Second, average and variance images were computed from all of the aligned RATHIs. The results indicated that the intrasubject RATHI variability has an average ICS value of approximately 0.96 for 1.0, 1.5, and 2 L/s; these values approach the unitary ideal value. For inter-subject variability, the variance image values for three airflow conditions exhibited low image variability as they ranged from 0.01 to 0.04, which indicates at most 4% acoustic variation with respect to the RATHI average value. In conclusion, the assessment of intra-subject and inter-subject variabilities revealed that the acoustic image pattern is repeatable for multiple respiratory cycles and across different subjects.
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Conflict of Interest Statement None Declared.
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