Low frequency oscillations assessed by diffuse speckle contrast analysis for foot angiosome concept

Low frequency oscillations assessed by diffuse speckle contrast analysis for foot angiosome concept

Cross-correlation based on foot angiosome conceptDSCA representative results from one subjectIn order to analyze the cross correlations among the four different LFOs obtained from the four channels of the DSCA system, we first examined the time-series data of the blood flow index (BFI) in all the optical channel probes. Figure 1 shows the representative results measured by DSCA from a single subject’s foot. Figure 1(a) shows the four channels (from Ch.1 to Ch.4) of the DSCA that were used to obtain data from the sole, based on the foot angiosome concept introduced by Attinger et al.5. As shown in Fig. 1(b), we were able to observe tissue perfusion changes in all the optical channels by changing the body posture (from 90° head-up tilt to supine) and by controlling the blood pressure at the subject’s thigh. Although all the BFIs for both postures seemed to have similar tissue perfusion trends during the baseline period, these BFIs showed dramatic decreases and increases according to cuff-occlusion and release of occlusion, corresponding to autoregulation of blood flow, from which we determined that the DSCA measurement was sensitive to hemodynamic changes in the human foot. Figure 1(c) shows the sectioned timeline BFI data for the baseline (supine), occlusion, and release periods after detrending, normalization, and band pass filter (BPF; pass band frequencies: 0.01–0.15 Hz). Since all BFIs on the four channels fluctuated in a similar manner (i.e., showed LFOs), it was hard to recognize the highly correlated pair intuitively. Figure 1(d) shows the six cross correlations from the four channels for the baseline, occlusion, and release periods, respectively. With the exception of the cross-correlation analysis for the occlusion period, the peaks from all six pairs were distributed around zero lag. In the occlusion period, since the amplitudes of the BFI and LFO decreased owing to the decrease of blood flow supply and autonomic nervous activity, the meaningful relationships disappeared, and we were unable to perform quantitative analyses of the cross correlations. Figure 1(e) illustrates how to obtain the maximum value and its lag time from the cross-correlation graph.Figure 1DSCA representative results of cross-correlation analysis in one subject according to baseline, occlusion, and release periods at supine posture. (a) Measurement positions of blood flow index (BFI) based on foot angiosome with four-channel DSCA probes on subject’s sole. (b) Raw BFI data. (1) Baseline period in tilt posture. (2) Posture change period. (3) Baseline period in supine posture. (4) Cuff-occlusion period in supine posture. (5) Release period in supine posture. (c) Detrended, normalized (processed), and filtered BFI with band pass filter (BPF) based on sectioned BFIs (Left: Baseline period in supine posture; Center: Cuff-occlusion period in supine posture; Right: Release period in supine posture). (d) Cross correlation analyses among four channels based on (c). (e) Maximum value and its lag time analysis in Ch.1 (otimes) Ch.2 relationship.
Table 1 Maximum values, its rank, and lag times from six cross-correlation analysis according to baseline and release periods at supine posture in one subject’s foot.
As shown in Table 1, we analyzed the maximum values for each of the six cross correlations for the baseline and release periods. Then, the ranks and lag times for the maximum values were estimated; from the high ranks among the six relationship pairs, we noted that three pairs (Ch.2 (otimes) Ch.3, Ch.2 (otimes) Ch.4, and Ch.3 (otimes) Ch.4) were highly correlated regardless of the impact of the reactive hyperemia protocol. Compared to the previous hypothesis that Ch.1 (otimes) Ch.3 and Ch.2 (otimes) Ch.4 relationships will show relatively high cross correlations; the obtained result was not fully compatible with the foot angiosome concept.From the cross-correlation analysis in this study, it is possible to estimate the similarities between the tissue perfusion data acquired from the optical channels by measuring how large their values are. Moreover, the time latencies (i.e., lag times) for hemodynamic responses can be estimated via the lead–lag time analysis. Briefly, from the locations of the maximum values with respect to zero lag, the leading or lagging of a specific channel pair can be determined. The negative sign in the lag time indicates that the second channel of the pair is faster, and vice versa. The meaning of zero in lag time analysis is that there is no lag latency between the two channels in the pair within our system resolution. Since the data sampling speed of the DSCA is 3 Hz, each data point of the lag number indicates a time duration of 0.33 (= 1/3) s, as shown in Fig. 1(e).DSCA results of statistical analysis in all subjectsFor the cross-correlation data from all the subjects (N = 10), we performed statistical analyses with the averages and standard deviations of the ranks for the maximum values from among the six cross correlations at two different periods and postures, as summarized in Table 2. From the rank analysis, we found that there were no significant differences compared to the previous representative results (Table 1), thereby showing high ranks for the average maximum values for three relationships (Ch.2 (otimes) Ch.3, Ch.2 (otimes) Ch.4, and Ch.3 (otimes) Ch.4). Furthermore, depending on baseline/release periods and supine/tilt postures, the ranks of the cross correlations were not significantly different from each other.Table 2 Average and standard deviation of the rank for the maximum value from six cross-correlation analyses at baseline and release periods in all subjects, according to supine and 90° head-up tilt posture.Once the statistical analysis for the lag time was performed with the average and standard deviation calculations for all subjects, the deviations were observed to be too high to obtain meaningful results because the lag time for each subject was different. Instead, as shown in Table 3, we counted the number of occurrences of each sign (+ : positive, − : negative, 0: zero, as shown in the top part of Fig. 1(e)) in the sixty outcomes for the baseline and release periods in all subjects (i.e., 60 = 2 (two different periods) × 10 (ten subjects) × 3 (repeat measurement 3 times). Then, we calculated the percentages for each sign depending on the supine and 90° head-up tilt postures. From this analysis, we derived two reproducible results related to hemodynamic responses among all the channel pairs, based on the angiosome concept. The first result was that Ch.1 and Ch.3 in the MPB angiosome space are faster than Ch.2 and Ch.4 in the LPB angiosome, regardless of supine/tilt posture. In the relationships linked with channel 3, except for the Ch.1 (otimes) Ch.3 pair, the highest percentages for the lag time signs in the Ch.2 (otimes) Ch.3 pair were all negative at both supine and tilt postures, whilst they were all positive for the Ch.3 (otimes) Ch.4 pair, showing the highest percentages were above 58.33%. In other words, the blood supply recorded at channel 3 is faster than those at channels 2 and 4. For the relationships linked with channel 1, except for Ch.1 (otimes) Ch.3, the highest percentages for both Ch.1 (otimes) Ch.2 and Ch.1 (otimes) Ch.4 relationships were positive at both supine and tilt postures, suggesting that the blood in channel 1 flowed earlier than those in channels 2 and 4. For the second result, in the relationships between two channels in the same angiosome (i.e., Ch.1 (otimes) Ch.3 and Ch.2 (otimes) Ch.4), the sign dominance for positive/zero/negative was unclear depending on the supine and tilt postures, and the highest percentages showed below 51.67%. The time latency analysis of the cross correlations seems to be somewhat correlated with the foot angiosome concept.Table 3 Percentages for the number of signs of lag time at both baseline and release periods in all subjects for repeat measurement 3 times, according to supine and 90° head-up tilt postures. Bold numbers stand for the highest value among three different situations for the lag time expression.Power spectral density (PSD) Changes depending on reactive hyperemiaRepresentative results in one subjectIn order to analyze the PSD distribution changes for the VLF, LF, and HF ranges with respect to reactive hyperemia, we simultaneously measured the tissue perfusion and heart rate signals using DSCA and ECG, respectively. Figure 2 shows the representative results measured by DSCA (left side in Fig. 2) on the foot and by ECG (right side in Fig. 2) on the whole body from a single subject. In the DSCA measurements, we investigated the frequency oscillation changes of the VLFs (0.001–0.04 Hz), LFs (0.04–0.15 Hz), and HFs (0.15–0.4 Hz) rather than focusing on the change of the LFOs (0.01–0.15 Hz), in order to obtain the spectrum of VLF and to compare the PSD changes of LFs and HFs obtained by ECG. Firstly, we performed timeline selection and detrending/normalization without BPF to acquire entire oscillations during the periods of baseline (90° head-up tilt), occlusion, and release in raw BFI data from the channel 4. Then, we achieved the power spectral analysis with Welch’s method as a non-parametric approach in the frequency range from 0 to 0.5 Hz, as shown in Fig. 2(c). To estimate the changes in PSD distributions for the VLFs, LFs, and HFs with respect to reactive hyperemia, we analyzed the absolute PSD distribution. In the baseline period (90° head-up tilt), the absolute PSDs for the VLFs, LFs, and HFs were (2.20 times 10^{6}), (1.10 times 10^{6}), and (0.61 times 10^{6}) [a.u.], respectively. For the absolute PSDs of the VLFs, LFs, and HFs in the occlusion period, the values were (0.13 times 10^{6}), (0.16 times 10^{6}), and (0.14 times 10^{6}) [a.u.], respectively. In the occlusion period, the absolute PSD of VLFs dramatically decreased by about 17 times, and the absolute powers of LFs and HFs decreased by 7 and 4 times, respectively. In the release period, the absolute PSDs for the VLFs, LFs, and HFs were (2.36 times 10^{6}), (1.66 times 10^{6}), and (1.05 times 10^{6}) [a.u.], respectively, showing recovery to the baseline state via autoregulation. For the analysis of relative PSD distribution changes from DSCA, we examined a proportion of the absolute PSD for each frequency band within total frequency range (0–1.5 Hz) at the sampling rate of 3 Hz. At the baseline period, the relative PSD of VLFs, LFs, and HFs were 38.97, 19.56, and 10.88 [%], respectively. The relative PSD distributions at the occlusion period were 12.83 (VLF), 16.13 (LF), and 13.53 (HF) [%], respectively. In the relative PSD analysis, the proportion of VLFs and LFs decreased by about 26% and 3%, respectively, whereas that of HFs increased by 3%. At the release period, the relative PSD of VLFs, LFs, and HFs were 27.05, 18.97, and 12.06 [%], respectively. In order to examine the relative PSD distribution changes among three frequency bands for reactive hyperemia, based on the proportion of the absolute PSD, we performed pie chart analysis of the PSD distributions, as shown in Fig. 2(d). The relative PSD distribution of VLFs decreased by 26% in the occlusion period and recovered to the baseline values in the release period. In contrast to VLFs, the relative PSD distributions of the LFs and HFs increased by 10% (LFs) and 16% (HFs), respectively.Figure 2Representative results for PSD by DSCA (a–d) and ECG (e–h) in one subject, according to baseline, occlusion, and release periods during 90° head up tilt posture. (a) Raw BFIs in channel 4. (1) Baseline period in supine posture. (2) Posture change period. (3) Baseline period in 90° head-up tilt posture. (4) Cuff-occlusion period in 90° head-up tilt posture. (5) Release period in 90° head-up tilt posture. (b) Detrended and normalized processed BFI from sectioned BFI in channel 4. (c) PSD analysis in channel 4. (d) Relative PSD pie analysis among three frequency bands in channel 4. (e) Detrended and normalized ECG from sectioned ECG data. (f) HRV (R–R interval) from ECG signal. (g) PSD analysis from HRV. (h) Relative PSD pie analysis from HRV.For the ECG results, we first performed timeline selection and detrending/normalization with the raw ECG data according to reactive hyperemia, as shown in Fig. 2(e). Next, we analyzed the HRV signals by estimating the variations in the heart rates and R–R intervals from peak detection in the raw ECG, as displayed in Fig. 2(f). Figure 2(g) shows the results of the power spectral analysis using an autoregressive model as a parametric approach from the HRV in the frequency domain. In contrast to the PSD distribution of the DSCA, two distinct peaks were seen in the LFs and HFs. In the baseline period, the absolute PSDs of the LFs and HFs were 738.28 and 235.64 [ms2], respectively. The absolute PSDs of the LFs and HFs were respectively 596.13 and 385.34 [ms2] in the occlusion period and 521.41 and 197.45 [ms2] in the release period. As shown in Fig. 2(h), we analyzed the relative PSD pie charts with LFs and HFs, except for the VLFs, because the absolute PSD distribution of the VLFs is relatively dominant among three frequency bands, and its origin has not been fully discovered in the ECG study. The changes in PSD distributions for the LFs showed 15% decrease between baseline and occlusion, and 12% increase between occlusion and recovery. For the PSD distribution of the HFs, this increased by 15% for the occlusion period.Results of statistical analysis in all subjectsAs shown in Table 4, we performed statistical analyses with the PSD distributions for the three different frequency ranges, and the data were acquired by both DSCA from channel 4 and ECG with respect to reactive hyperemia. Table 4 shows average and standard deviation of relative PSD distributions from DSCA and ECG measurements. In the DSCA results, because of high standard deviations of the absolute PSD distributions between inter- and intra-subjects, we analyzed relative PSD distributions as the proportion of absolute power within total frequency range. The relative PSD of VLFs among three frequency bands showed the highest changes from baseline to release. The changes in the PSD distributions for the VLFs and LFs were related to magnitude changes in the raw BFIs owing to the effects of autoregulation of blood flow. In the ECG results of Table 4, the absolute PSD distribution of the LFs changed following cuff-occlusion and release, while the absolute power of the HFs did not show any significant differences. Comparing the two results by DSCA and ECG for the reactive hyperemia protocol, both slight decreases in LF band were correlated between the relative (DSCA)- and absolute (ECG) PSD distributions, while the distributions in HF band were not correlated. Figure 3 shows the relative PSD distribution changes among three frequency bands by DSCA and two frequency bands by ECG according to reactive hyperemia. These results were similar to the previous representative results (Fig. 2(d) and (h)) obtained from one subject. The relative PSD for VLFs and LFs decreased and increased from baseline to release in both modalities. The relative PSD distribution changes have similar tendencies between the VLFs and LFs obtained by DSCA and the LFs obtained by ECG. From the PSD distribution change analysis from DSCA measurements, it is worth noting that the PSD distribution for VLFs is remarkably reduced and increased following reactive hyperemia. Therefore, we can state that the frequency oscillation measurements by the DSCA system are especially sensitive to PSD distribution changes of the VLFs in specific tissues, which cannot be estimated from the ECG methodology.Table 4 Average and standard deviation of relative (DSCA)- and absolute (ECG) PSD distributions for VLF, LF, and HF, according to baseline, occlusion, and release periods in all subjects during 90° head up tilt posture. Note that DSCA data was obtained from channel 4. *P < 0.05 compared to baseline period.Figure 3The pie charts of relative PSD distributions among frequency bands according to baseline, occlusion, and release periods in all subjects during 90° head up tilt posture. (a) DSCA measurement in channel 4. (b) ECG measurement.PSD changes depending on 90° head-up tilt protocolRepresentative results in one subjectSeveral years ago, Malik et al.13 reported that the relative PSD distribution of LFs measured by ECG exceeded that of HFs at the 90° head-up tilt, compared to the supine posture. In order to estimate the PSD distribution change of entire frequency oscillations (VLF, LF and HF) achieved by DSCA according to the head-up tilt protocol, we simultaneously performed the PSD analysis with the HRV signal, as shown in Fig. 4. In the DSCA results of Fig. 4(a–b), the peaks in the VLFs (0.001–0.04 Hz), LFs (0.04–0.15 Hz), and HFs (0.15–0.4 Hz) ranges were changed between the two postures. In the supine state, the absolute PSD distributions for the VLFs, LFs, and HFs in channel 4 were (0.61 times 10^{6}), (1.54 times 10^{6}), and (1.20 times 10^{6}) [a.u.], respectively. In the tilt posture, the absolute PSD distributions of the three spectra were (2.20 times 10^{6}) (VLF), (1.10 times 10^{6}) (LF), and (0.61 times 10^{6}) (HF) [a.u.]. The relative PSD distributions of VLFs, LFs, and HFs at the supine posture, for the proportion of the absolute PSD within total frequency range (0–1.5 Hz), were 8.51, 21.41, and 16.61 [%], respectively. At the tilt posture, the relative PSD distributions for VLFs, LFs, and HFs were 38.97, 19.56, and 10.88 [%], respectively. As shown in Fig. 4(c), for the pie chart analysis of the relative PSD distributions among three frequency bands, the VLF distribution were changed in the tilt posture (VLF: 38% increase; LF: 18% decrease; HF: 20% decrease) compared to that of the supine state.Figure 4Representative results for PSD by DSCA (a–c) and ECG (d–f) in one subject, according to supine and head up tilt postures. (a) Detrended and normalized BFI from sectioned BFI in channel 4. (b) PSD analysis in channel 4. (c) PSD pie analysis among three frequency bands in channel 4. (d) HRV (R–R interval) from ECG signal. (e) Relative PSD analysis from HRV. (f) PSD pie analysis from HRV.In the ECG results (Fig. 4(d–f)), we observed similar tendencies for the PSD distribution changes of LFs and HFs as those in Malik et al.13. For the absolute PSD distributions, the LFs and HFs were respectively 430.83 and 365.63 [ms2] at the supine posture and 422.79 and 156.45 [ms2] at the tilt posture. In the PSD pie analysis from HRV (Fig. 4(f)), the relative distribution of the LFs increased by 19% according to the posture change.Results of statistical analysis in all subjectsTable 5 shows the statistical analyses of the relative (DSCA)- and absolute (ECG) PSD distributions for the three different frequency ranges, with respect to the supine and head-up tilt postures. In DSCA, we analyzed the proportions of the absolute PSD within total frequency range, which is the same procedure in Table 4. The relative PSDs for both of VLFs and LFs at the tilt posture were higher than that of the supine posture, and the relative proportion of VLFs showed the highest change among the three frequency bands. However, the relative PSDs for the HFs were nearly unchanged. In the ECG results, the highest change in absolute power was noted for the PSD distribution of HFs. Figure 5 shows the pie charts for the relative PSD distributions among three frequency bands (DSCA) and two frequency bands (ECG). From the DSCA result of Fig. 5(a), we noted that the relative PSD distribution of HFs decreased by 2%. From the ECG result of Fig. 5(b), the PSD distribution of the HFs decreased significantly. Although the change of the PSD distribution of the HFs in DSCA measurement was little, a decreasing tendency was found from the both results.Table 5 Average and standard deviation of relative (DSCA)- and absolute PSD distributions for VLF, LF, and HF, according to supine and head up tilt postures in all subjects. Note that DSCA data were obtained from channel 4. * P < 0.05 compared to supine posture.Figure 5The pie charts of relative PSD distributions among frequency bands according to baseline, occlusion, and release periods in all subjects during 90° head up tilt protocol. (a) DSCA measurement in channel 4. (b) ECG measurement.

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