Figure 1.
The experimental set-up: (a) the patient’s desk had a large surface for the patient to lay on it, and it also had a stand for the patient’s legs, and a bar above on which the 3D camera was fixed; (b) the camera was fixed to the bar with a black self-adhesive band; (c) the side view of the patient’s legs and torso—the position of the patient was always standardized—the lower legs were put on the stand and thighs were put closely to the leg support stand that was adjustable in height and adapted to each patient; (d) in some cases, the pads were placed under the head to ensure the optimal position of head and neck. Patients were always placed and positioned by the physical therapist.
Figure 1.
The experimental set-up: (a) the patient’s desk had a large surface for the patient to lay on it, and it also had a stand for the patient’s legs, and a bar above on which the 3D camera was fixed; (b) the camera was fixed to the bar with a black self-adhesive band; (c) the side view of the patient’s legs and torso—the position of the patient was always standardized—the lower legs were put on the stand and thighs were put closely to the leg support stand that was adjustable in height and adapted to each patient; (d) in some cases, the pads were placed under the head to ensure the optimal position of head and neck. Patients were always placed and positioned by the physical therapist.
Figure 2.
The proposed algorithm flow diagram. The figure illustrates all the phases of the algorithm—image acquisition, point cloud processing, depth variation data extraction and analysis, and morphological cross-section (CS) extraction and analysis. To allow the derivation of depth variation data, point cloud processing was applied to an acquired sequence of RGB-D images. Each image underwent a consistent chain of rigid transformations and was searched for the depth values on the previously determined coordinates of the grid of channels. Since depth variation data was perceived as represent of a respiratory signal, only the signal sections corresponding to the dominant breathing pattern were subsequently used for derivation of morphological CSs.
Figure 2.
The proposed algorithm flow diagram. The figure illustrates all the phases of the algorithm—image acquisition, point cloud processing, depth variation data extraction and analysis, and morphological cross-section (CS) extraction and analysis. To allow the derivation of depth variation data, point cloud processing was applied to an acquired sequence of RGB-D images. Each image underwent a consistent chain of rigid transformations and was searched for the depth values on the previously determined coordinates of the grid of channels. Since depth variation data was perceived as represent of a respiratory signal, only the signal sections corresponding to the dominant breathing pattern were subsequently used for derivation of morphological CSs.
Figure 3.
Cropped point cloud: (a) depicts the selection of marker points that was performed before rigid transformations; (b) depicts an example result of the marker detection. The detected marker is shown on an RGB image, which was obtained after the point cloud projection to the plane; The dark red color represents the marker, while the light red color represents the marker boundary obtained after detection. (c) depicts the point cloud after rigid transformations—the resulting regions of interest (ROIs) are marked in red and blue, where blue represents the channels that were used for further analysis; (c) also illustrates the coordinate system for the enumeration of depth extraction channels—index enumerates rows and index enumerates columns of the grid of channels. Because of the rigid transformations, all the rows are perpendicular to the axes, while all the columns are perpendicular to the axes of the coordinate system. The ROI that is being pointed to in the image is the central channel of the grid, in the following text also referred to as the central location. The channels of interest for subsequent derivation of CSs are colored in blue.
Figure 3.
Cropped point cloud: (a) depicts the selection of marker points that was performed before rigid transformations; (b) depicts an example result of the marker detection. The detected marker is shown on an RGB image, which was obtained after the point cloud projection to the plane; The dark red color represents the marker, while the light red color represents the marker boundary obtained after detection. (c) depicts the point cloud after rigid transformations—the resulting regions of interest (ROIs) are marked in red and blue, where blue represents the channels that were used for further analysis; (c) also illustrates the coordinate system for the enumeration of depth extraction channels—index enumerates rows and index enumerates columns of the grid of channels. Because of the rigid transformations, all the rows are perpendicular to the axes, while all the columns are perpendicular to the axes of the coordinate system. The ROI that is being pointed to in the image is the central channel of the grid, in the following text also referred to as the central location. The channels of interest for subsequent derivation of CSs are colored in blue.
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Figure 4.
Derivation of depth variation signal: (a) illustration of variables used to calculate the depth variation signal, r(t), in a single point of interest. Green point is an observed single point; (b) the zoomed-in low pass filtered depth variation signal originating on one of the channels—(i, j) = (5, 4)—along with the detected extrema that were used for breath separation; (c) example of depth variation signals derived from 9 depth extraction channels that represent a subset of the channels of interest, a single trial.
Figure 4.
Derivation of depth variation signal: (a) illustration of variables used to calculate the depth variation signal, r(t), in a single point of interest. Green point is an observed single point; (b) the zoomed-in low pass filtered depth variation signal originating on one of the channels—(i, j) = (5, 4)—along with the detected extrema that were used for breath separation; (c) example of depth variation signals derived from 9 depth extraction channels that represent a subset of the channels of interest, a single trial.
Figure 5.
Artifact removal phase: (a) shows the magnitude scalogram of the wavelet transform of depth variation signals, and corresponding 1D power profiles (artifact removal criterion function), calculated for a single trial. A colormap is used to represent the magnitude of the wavelet coefficients—blue represents lower magnitude values, indicating weaker signal components at corresponding times and scales, while yellow represents higher magnitude values, and stronger signal components; (b) shows the criteria function more closely for the three channels of the 5th row—it can be observed that larger wavelet coefficients, as well as larger values of criteria function temporally correspond to the onset of artifact in depth variation signals. Threshold is a constant (yellow line); (c) shows artifacts detected on the same channels as in (b). The red full lines represent final artifacts: signal segments that temporally correspond to the onset of artifact on any of the channels. Red circles mark the extrema of breath curves that are contaminated with artifacts, and that will, thus, be omitted from further analysis; in this figure, all the signals are centered around zero for better visualization.
Figure 5.
Artifact removal phase: (a) shows the magnitude scalogram of the wavelet transform of depth variation signals, and corresponding 1D power profiles (artifact removal criterion function), calculated for a single trial. A colormap is used to represent the magnitude of the wavelet coefficients—blue represents lower magnitude values, indicating weaker signal components at corresponding times and scales, while yellow represents higher magnitude values, and stronger signal components; (b) shows the criteria function more closely for the three channels of the 5th row—it can be observed that larger wavelet coefficients, as well as larger values of criteria function temporally correspond to the onset of artifact in depth variation signals. Threshold is a constant (yellow line); (c) shows artifacts detected on the same channels as in (b). The red full lines represent final artifacts: signal segments that temporally correspond to the onset of artifact on any of the channels. Red circles mark the extrema of breath curves that are contaminated with artifacts, and that will, thus, be omitted from further analysis; in this figure, all the signals are centered around zero for better visualization.
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Figure 6.
Breath curve analysis: the intersection of two Gaussian distributions with a probability of membership of at least 5% to each of the distributions gave a group of breaths that was used to generate morphological CSs. Graphs illustrate the projection of distributions to 2D Euclidean space, and the legend shows the number of breaths that belonged to both of the distributions. The results are depicted for three patients. In (a), there were 64 and 78 breaths in Session 1 and Session 2, in that order, retained for the next phase; in (b), there were 49 and 61; and in (c), there were 69 and 43 retained breaths, and 43 was the smallest number of breaths per patient that was retained for the next phase.
Figure 6.
Breath curve analysis: the intersection of two Gaussian distributions with a probability of membership of at least 5% to each of the distributions gave a group of breaths that was used to generate morphological CSs. Graphs illustrate the projection of distributions to 2D Euclidean space, and the legend shows the number of breaths that belonged to both of the distributions. The results are depicted for three patients. In (a), there were 64 and 78 breaths in Session 1 and Session 2, in that order, retained for the next phase; in (b), there were 49 and 61; and in (c), there were 69 and 43 retained breaths, and 43 was the smallest number of breaths per patient that was retained for the next phase.
Figure 7.
Cross-sectional representation of data illustrated for inspiration phase and in the level of CS1. CS was initially defined in 7 adjacent locations (), and other values were linearly interpolated. Each graph represents a phase in CS processing, and all of them show the dispersion in the group of CSs—which decays when outliers are removed—the outliers were not included in the calculation; (a) shows initial outliers: a CS is an outlier if any of its data points is an outlier on an observed location . If CS is an outlier, other CSs that are obtained for the same time sample are also considered outliers and removed, which is why the number of outlying cross-sections increases in (b); (c) depicts CS1 cross-section representative.
Figure 7.
Cross-sectional representation of data illustrated for inspiration phase and in the level of CS1. CS was initially defined in 7 adjacent locations (), and other values were linearly interpolated. Each graph represents a phase in CS processing, and all of them show the dispersion in the group of CSs—which decays when outliers are removed—the outliers were not included in the calculation; (a) shows initial outliers: a CS is an outlier if any of its data points is an outlier on an observed location . If CS is an outlier, other CSs that are obtained for the same time sample are also considered outliers and removed, which is why the number of outlying cross-sections increases in (b); (c) depicts CS1 cross-section representative.
Figure 8.
Boxplot of depth values of CSs acquired in different locations (
). Outliers were calculated for each location individually and are depicted as red plus signs. If an outlier was present in any location, the cross-section containing that point was also considered an outlier and removed. This figure illustrates how outlying CSs from
Figure 7a were detected.
Figure 8.
Boxplot of depth values of CSs acquired in different locations (
). Outliers were calculated for each location individually and are depicted as red plus signs. If an outlier was present in any location, the cross-section containing that point was also considered an outlier and removed. This figure illustrates how outlying CSs from
Figure 7a were detected.
Figure 9.
The coefficient of variation of areas under the CSs that belong to the same CS type. For each type of CS, the dispersion is calculated for maxima CSs (inspiration moments, Max), and minima CSs (expiration moments, Min). The left side of the graphs contains the results for Session 1 (Max1, Min1), while the right side contains the results for Session 2 (Max2, Min2); (a) shows the dispersion for the CS1; (b) shows the dispersion for CS2; (c) shows the dispersion for CS3; no value was greater than 2%, and the maximal value was 1.84% in the level of CS3 in Session 1. At the same time, this value is considered an outlier for the dispersion of maxima CSs in Session 1 in the CS3 level and is depicted as a red plus sign.
Figure 9.
The coefficient of variation of areas under the CSs that belong to the same CS type. For each type of CS, the dispersion is calculated for maxima CSs (inspiration moments, Max), and minima CSs (expiration moments, Min). The left side of the graphs contains the results for Session 1 (Max1, Min1), while the right side contains the results for Session 2 (Max2, Min2); (a) shows the dispersion for the CS1; (b) shows the dispersion for CS2; (c) shows the dispersion for CS3; no value was greater than 2%, and the maximal value was 1.84% in the level of CS3 in Session 1. At the same time, this value is considered an outlier for the dispersion of maxima CSs in Session 1 in the CS3 level and is depicted as a red plus sign.
Figure 10.
Results of statistical tests: (a) depicts the percentage change in the area of the inspiration representative curve relative to the expiration representative curve, a proposed indicator of chest The results showed that there was no statistically significant change in chest movement amount between the two sessions; (b) depicts change in morphology between the sessions; It was expressed as a percentage change in the area of representative inspiration curves (Dmax) and a percentage change in the area of representative expiration curves (Dmin); On the CS1 and C2 level, they were compared by a paired sample t-test, and on the CS3, they were compared by Wilcoxon signed rank test. Neither one of the tests showed a statistically significant difference between the groups. Outliers are represented as red plus signs, and are found in the CS3 level—one outlier for the change in representative inspiration curves, and three for the change in representative expiration curves. These were also included in the statistical test.
Figure 10.
Results of statistical tests: (a) depicts the percentage change in the area of the inspiration representative curve relative to the expiration representative curve, a proposed indicator of chest The results showed that there was no statistically significant change in chest movement amount between the two sessions; (b) depicts change in morphology between the sessions; It was expressed as a percentage change in the area of representative inspiration curves (Dmax) and a percentage change in the area of representative expiration curves (Dmin); On the CS1 and C2 level, they were compared by a paired sample t-test, and on the CS3, they were compared by Wilcoxon signed rank test. Neither one of the tests showed a statistically significant difference between the groups. Outliers are represented as red plus signs, and are found in the CS3 level—one outlier for the change in representative inspiration curves, and three for the change in representative expiration curves. These were also included in the statistical test.
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Figure 11.
Results of statistical tests. Both figures depict the parameter area under the representative CS curve, comparatively depicted for Session 1 and Session 2; (a) shows the comparison of inspiration CSs, while (b) shows the comparison of expiration CSs; neither of the results indicate a statistically significant difference between the sessions; Red plus signs in the CS3 level of Session 2 represent the outliers. They were also included in the statistical tests.
Figure 11.
Results of statistical tests. Both figures depict the parameter area under the representative CS curve, comparatively depicted for Session 1 and Session 2; (a) shows the comparison of inspiration CSs, while (b) shows the comparison of expiration CSs; neither of the results indicate a statistically significant difference between the sessions; Red plus signs in the CS3 level of Session 2 represent the outliers. They were also included in the statistical tests.
Table 1.
Dispersion of features for transverse cross-sections, expressed as coefficient of variation of estimated depth for each of 21 locations, mean and std value for ten patients, Session 1 and Session 2. Shown for expiration phase. Measures are expressed in percentages.
Table 1.
Dispersion of features for transverse cross-sections, expressed as coefficient of variation of estimated depth for each of 21 locations, mean and std value for ten patients, Session 1 and Session 2. Shown for expiration phase. Measures are expressed in percentages.
Exp. Phase (Sess. 1) | j = 1 | j = 2 | j = 3 | j = 4 | j = 5 | j = 6 | j = 7 |
CS1 | 0.99 (0.51) | 0.82 (0.41) | 0.73 (0.33) | 0.74 (0.33) | 0.74 (0.33) | 0.82 (0.34) | 1.1 (0.34) |
CS2 | 0.71 (0.32) | 0.55 (0.24) | 0.56 (0.35) | 0.61 (0.34) | 0.52 (0.23) | 0.63 (0.24) | 0.86 (0.3) |
CS3 | 0.71 (0.34) | 0.7 (0.28) | 0.98 (0.46) | 1.11 (0.64) | 0.99 (0.64) | 0.82 (0.4) | 0.9 (0.27) |
Exp. Phase (Sess. 2) | j = 1 | j = 2 | j = 3 | j = 4 | j = 5 | j = 6 | j = 7 |
CS1 | 0.82 (0.29) | 0.68 (0.17) | 0.61 (0.17) | 0.51 (0.19) | 0.6 (0.28) | 0.7 (0.28) | 0.96 (0.34) |
CS2 | 0.76 (0.13) | 0.46 (0.1) | 0.36 (0.15) | 0.4 (0.2) | 0.4 (0.19) | 0.5 (0.13) | 0.8 (0.23) |
CS3 | 0.72 (0.21) | 0.64 (0.22) | 0.8 (0.35) | 0.9 (0.42) | 0.81 (0.37) | 0.67 (0.21) | 0.85 (0.33) |
Table 2.
Dispersion of features for transverse cross-sections, expressed as coefficient of variation of estimated depth for each of 21 locations, mean and std value for ten patients, Session 1 and Session 2. Shown for inspiration phase. Measures are expressed in percentages.
Table 2.
Dispersion of features for transverse cross-sections, expressed as coefficient of variation of estimated depth for each of 21 locations, mean and std value for ten patients, Session 1 and Session 2. Shown for inspiration phase. Measures are expressed in percentages.
Insp. Phase (Sess. 1) | j = 1 | j = 2 | j = 3 | j = 4 | j = 5 | j = 6 | j = 7 |
CS1 | 1 (0.51) | 0.86 (0.35) | 0.75 (0.3) | 0.68 (0.34) | 0.71 (0.32) | 0.79 (0.31) | 1.08 (0.25) |
CS2 | 0.7 (0.25) | 0.54 (0.24) | 0.56 (0.33) | 0.65 (0.41) | 0.61 (0.32) | 0.63 (0.22) | 0.91 (0.35) |
CS3 | 0.84 (0.35) | 0.77 (0.37) | 0.92 (0.53) | 1.06 (0.55) | 1.04 (0.52) | 0.84 (0.41) | 0.98 (0.31) |
Insp. Phase (Sess. 2) | j = 1 | j = 2 | j = 3 | j = 4 | j = 5 | j = 6 | j = 7 |
CS1 | 0.95 (0.29) | 0.77 (0.2) | 0.67 (0.19) | 0.6 (0.21) | 0.63 (0.23) | 0.73 (0.25) | 0.93 (0.31) |
CS2 | 0.76 (0.17) | 0.44 (0.11) | 0.36 (0.16) | 0.4 (0.1) | 0.45 (0.18) | 0.52 (0.14) | 0.78 (0.19) |
CS3 | 0.73 (0.2) | 0.77 (0.23) | 1.03 (0.26) | 1.17 (0.27) | 1.04 (0.28) | 0.82 (0.2) | 0.85 (0.25) |
Table 3.
Dispersion of features expressed as coefficient of variation of area under each CS type, mean and std for ten patients. Shown for expiration and inspiration phase. Measures are expressed in percentages.
Table 3.
Dispersion of features expressed as coefficient of variation of area under each CS type, mean and std for ten patients. Shown for expiration and inspiration phase. Measures are expressed in percentages.
| Exp. Phase (Session 1) | Exp. Phase (Session 2) | Insp. Phase (Session 1) | Insp. Phase (Session 2) |
---|
CS1 | 0.74 (0.35) | 0.55 (0.19) | 0.73 (0.32) | 0.62 (0.21) |
CS2 | 0.52 (0.25) | 0.34 (0.13) | 0.54 (0.27) | 0.34 (0.11) |
CS3 | 0.77 (0.41) | 0.61 (0.29) | 0.81 (0.44) | 0.83 (0.21) |
Table 4.
Results of the statistical test that compared the chest mobility between the two different sessions. The chest mobility was calculated as a percentage change in the area under the representative CSs for inspiration and expiration phases. Neither of the tests showed a statistically significant change between the groups.
Table 4.
Results of the statistical test that compared the chest mobility between the two different sessions. The chest mobility was calculated as a percentage change in the area under the representative CSs for inspiration and expiration phases. Neither of the tests showed a statistically significant change between the groups.
CS1 | t(9) = 1.66, p = 0.13 |
CS2 | t(9) = −0.46, p = 0.66 |
CS3 | t(9) = 0.10, p = 0.92 |
Table 5.
Results of the statistical test that compared the change in morphology based on the areas of the maximum representative CSs, and minimum representative CSs. Neither of the tests shows a statistically significant change between the groups.
Table 5.
Results of the statistical test that compared the change in morphology based on the areas of the maximum representative CSs, and minimum representative CSs. Neither of the tests shows a statistically significant change between the groups.
CS1 | t(9) = 1.68, p = 0.13 |
CS2 | t(9) = −0.47, p = 0.65 |
CS3 | W = 30, p = 0.85 |
Table 6.
Results of the statistical test that compared the area of the representative CSs between the two different sessions. First column is for the inspiration CSs, second for expiration CSs. Neither of the tests show a statistically significant change between the groups.
Table 6.
Results of the statistical test that compared the area of the representative CSs between the two different sessions. First column is for the inspiration CSs, second for expiration CSs. Neither of the tests show a statistically significant change between the groups.
| Inspiration CSs | Expiration CSs |
---|
CS1 | t(9) = 1.64, p = 0.14 | t(9) = 1.32, p = 0.22 |
CS2 | t(9) = 1.74, p = 0.12 | t(9) = 1.88, p = 0.09 |
CS3 | t(9) = 1.05, p = 0.32 | t(9) = 1.03, p = 0.33 |