1. Introduction

2. Materials and Methods

2.3. Design and Realisation of an Automated Processing System for Blood Oxygen Measurement Data

2.3.1. Removal of Mutant Noise

In the process of analysing and processing the blood oxygen measurement data, we found that, under the influence of the photoelectric sensor, there is often a sudden change in the data (as shown in Fig. 5), which appears randomly and has no fixed frequency, and when it appears, it completely masks the original signal value, which belongs to the other noises in the fourth type mentioned above, and it is impossible to remove them by using the traditional filtering methods. At the same time, this type of noise can cause serious interference to the signal calculation results, such as causing the peaks and valleys detection algorithm to fail, which in turn leads to measurement failure. Define (Pa, Pb, Pc, Pd) to denote the four stages of the mutation noise, the beginning of the mutation, the mutation recovery, and the end of the mutation, respectively, and the corresponding instantaneous slopes of the four points (as Ka, Kb, Kc, Kd), respectively. Among them, if downward mutation noise occurs, the corresponding instantaneous slopes of the signals will, in general, reflect the characteristic of ‘down (Ka-Kb)-up (Kb-Kc)-down (Kc-Kd)’ in the lower right of Fig. 6(A); if upward mutation noise occurs, the corresponding instantaneous slopes will reflect the characteristic of ‘up-down-up (Kc-Kd)’ in the lower left of Fig. 6(A); and if upward mutation noise occurs, the corresponding instantaneous slopes will reflect the characteristic of ‘up-down-down-up (Kc-Kd)’ in the lower left of Fig. 6(A). ‘up-down-up’ feature in the lower left of Fig. 6(A). When continuous mutation in time and long duration mutation occurs, there will be more than one mutation point appearing, at which time the mutation point Pb becomes a collection including (Pb1, Pb2, Pb3) and so on appearing in it.

Figure 5. Schematic diagram of mutation noise.

Figure 5. Schematic diagram of mutation noise.

Figure 6. Classification of mutation noise. The upper vertical coordinate is the oximetry data (PPG), and the lower graph shows the corresponding instantaneous slope of the signal. Figure 6(A) shows a schematic diagram of “upward” and “downward” mutation noise, and Figure 6(B) shows a schematic diagram of continuous and sustained mutation noise, where a denotes continuous mutation noise and b denotes sustained mutation noise.

Figure 6. Classification of mutation noise. The upper vertical coordinate is the oximetry data (PPG), and the lower graph shows the corresponding instantaneous slope of the signal. Figure 6(A) shows a schematic diagram of “upward” and “downward” mutation noise, and Figure 6(B) shows a schematic diagram of continuous and sustained mutation noise, where a denotes continuous mutation noise and b denotes sustained mutation noise.

According to the different directions in the amplitude when it occurs, the noise can be classified into upward mutation and downward mutation, and this kind of noise can be further classified into three kinds according to the continuity in time: a single occurrence, a number of consecutive occurrences, and a long period of time continually occurring (shown in Fig. 5). After a mutation noise, followed by a mutation noise, if the first-order difference between Kb2 and Kb3 set a point equivalent to the level of Ka, i.e., the first and last of the two single mutation first-order difference features ‘down-up-down’. The situation where the mutation noise occurs and is not recovered for a continuous period of time is called long lasting mutation noise, as shown on the right side of Fig. 6. According to the statistical analysis, when this situation occurs, the signal value will remain unchanged at the mutation position, i.e., Pb1=Pb2=Pb3, etc., and therefore, the corresponding first-order difference value also remains unchanged and equals to zero, i.e., Kb2=Kb3=0.

Taking full consideration of the characteristics of the noise itself, we propose the idea of utilizing four-point slope features to locate the noise and remove it. The whole noise process is divided into four processes: start, mutation, mutation recovery, and end, and the key points of these four processes are identified in the signal by first-order difference. The instantaneous slope values were approximated by calculating the first-order difference of the oximetry data using the formula as shown in equation (2) below.

$${\mathrm{x}}^{\mathrm{\text{'}}}\left({\mathrm{t}}_{\mathrm{i}}\right)={\displaystyle \frac{\mathrm{x}\left({\mathrm{t}}_{\mathrm{i}}\right)-\mathrm{x}\left({\mathrm{t}}_{\mathrm{i}-1}\right)}{{\mathrm{t}}_{\mathrm{i}}-{\mathrm{t}}_{\mathrm{i}-1}}},\mathrm{i}=\mathrm{2,3},...,\mathrm{N}$$

(2)

According to the described time domain morphological features, the algorithm is designed to determine whether a noise point is suspicious by using the magnitude and direction of the change of the instantaneous slope. If the instantaneous slopes ${\mathrm{x}}^{\mathrm{\text{'}}}\left({\mathrm{t}}_{\mathrm{i}}\right)$ and ${\mathrm{x}}^{\mathrm{\text{'}}}\left({\mathrm{t}}_{\mathrm{i}-1}\right)$ corresponding to a point t_i and its previous point t_i-1 satisfy the relationship described in equation (3), the current signal point is considered suspicious.$△\mathrm{x}\mathrm{\text{'}}$ as a slope threshold, which can be set as an observation or as a variance of the instantaneous slope close to $\mathrm{P}\mathrm{b}$ for a period of time, the threshold can be used to regulate the sensitivity of the algorithm, and the larger the threshold, the less sensitive the algorithm is to small magnitude mutant noise. Further the found suspicious noise point is noted as $\mathrm{P}\mathrm{b}$. Subsequently further search for related points $\mathrm{P}\mathrm{a},\mathrm{P}\mathrm{c},\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{P}\mathrm{d}$ is required, and if all are matched successfully, then $\mathrm{P}\mathrm{b}$ is recognized as mutant noise. The matching process needs to take into account both continuous and persistent situations to finalize the removal of the noise.

$$\left|\mathrm{x}\mathrm{\text{'}}\left({\mathrm{t}}_{\mathrm{i}}\right)-\mathrm{x}\mathrm{\text{'}}\left({\mathrm{t}}_{\mathrm{i}-1}\right)\right|>△\mathrm{x}\mathrm{\text{'}}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{x}\mathrm{\text{'}}\left({\mathrm{t}}_{\mathrm{i}}\right)\times \mathrm{x}\mathrm{\text{'}}\left({\mathrm{t}}_{\mathrm{i}-1}\right)<0$$

(3)

2.3.2. Calculation of Pressure Release Recognition Points

The pressure release point is the point in time when the pressure is maintained for a period of time and then suddenly released. Prior to this point, the hemoglobin level in the blood remains stable at a low level due to the continuous maintenance of pressure, and after the pressure release point, the oxygen level in the blood rises rapidly due to the refilling of the capillaries and then returns to the baseline level, with the overall characteristic of “level-rapidly rising”. The overall characteristic of “level-rapid rise”, so as long as the blood oxygen measurement data to locate such a section of the characteristics, you can find the pressure release point. In practice, however, the fluctuation of the sensitivity of the device and the presence of mutation noise make the implementation of the feature recognition algorithm based on the raw data more complicated. The identification of the press-release point seems to be more concerned with the overall trend of the signal, so we propose the quadratic Exponentially Weighted Averages-K (EWAK) algorithm. Exponentially Weighted Averages (EWA) were firstly applied to the PPG data to remove some of the high frequency and mutation noise effects while flattening the signal, based on which the corresponding instantaneous slopes of the signals were calculated using Eq. (4), and finally the exponentially weighted averages were used again to finally get the smoother EWAK curve as the approximate first-order derivative curve of the PPG. Among them, the calculation of exponentially weighted average can effectively reduce the influence of high-frequency information in the signal and facilitate the observation of the overall trend, and the EWA calculation formula is as follows:

$$\mathrm{E}\mathrm{W}\mathrm{A}\left({\mathrm{t}}_{\mathrm{i}}\right)=\mathsf{\beta }\times \mathrm{E}\mathrm{W}\mathrm{A}\left({\mathrm{t}}_{\mathrm{i}-1}\right)+\left(1-\mathsf{\beta }\right)\times \mathrm{x}\left({\mathrm{t}}_{\mathrm{i}}\right),\mathsf{\beta }\in \left[0,\left.1\right)\right.$$

(4)

$\mathrm{E}\mathrm{W}\mathrm{A}\left({\mathrm{t}}_{\mathrm{i}}\right)$ as an estimate of moment ${\mathrm{t}}_{\mathrm{i}}$, which can be substituted for the actual observation at this moment and is approximately equal to the average of the actual observations in the past 1/$\left(1-\mathsf{\beta }\right)$ moments, where indicates the weight of the data in the past period, which is an adjustable parameter, where larger values indicate that more past data are used, and smaller values indicate that the data at the current moment have a greater weight. When $\mathsf{\beta }=0.9$, $\mathrm{E}\mathrm{W}\mathrm{A}\left({\mathrm{t}}_{\mathrm{i}}\right)$ is approximately the average of the last 10 values. However, setting $\mathsf{\beta }$ too large means that more past data are used, which will cause a significant signal hysteresis that may result in points being recognized later than when they really occurred.

The instantaneous slopes are computed to approximate the first-order derivatives, and their peak points serve as the basis for critical point identification. A segment of the PPG signal is represented using a straight line, and the computed EWAK curve is represented using a dashed line. An example of the comparison of the PPG signal with the corresponding quadratic sliding average-derivative values is shown in Figure 7. The EWAK curve corresponding to the oximetry data near the point of pressure release shows a steady characteristic, i.e., it rises rapidly after a nearly horizontal curve and reaches the maximum point of the whole curve, as shown in the figure using the red highlights. The EWAK curve approximates a first-order derivative, and the maximum point means the point of maximum velocity in the oximetry data, which corresponds to the fastest point in capillary filling in the real sense. phase. Therefore, the algorithm starts from the maximum point and looks for such a smooth curve to the left, and at the transition between the smooth curve and the rising curve, the corresponding point in the oximetry data is the point to be searched for the pressure release point, as shown by the intersection of the vertical dashed line and the PPG signal in the figure.

3. Results and Discussion

4. Conclusions

5. Patents

References

1. Bakker J, Ince C. Monitoring coherence between the macro and microcirculation in septic shock. Curr Opin Crit Care 2020, 26, 267–272. [Google Scholar] [CrossRef] [PubMed]
2. Ince, C. Hemodynamic coherence and the rationale for monitoring the microcirculation. Crit Care 2015, 19 (Suppl 3), S8. [Google Scholar] [CrossRef] [PubMed]
3. Merdji H, Curtiaud A, Aheto A, et al. Performance of Early Capillary Refill Time Measurement on Outcomes in Cardiogenic Shock: An Observational, Prospective Multicentric Study. Am J Respir Crit Care Med. 2022, 206, 1230–1238. [Google Scholar] [CrossRef] [PubMed]
4. Bodolea, C. The Role of Microcirculation in Haemodynamics: A Journey from Atlas to Sisyphus. J Crit Care Med (Targu Mures). 2024, 10, 115-118. Published 2024 Apr 30. [CrossRef]
5. Kattan E, Ibarra-Estrada M, Ospina-Tascón G, Hernández G Perspectives on peripheral perfusion assessment. Curr Opin Crit Care 2023, 29, 208–214. [CrossRef] [PubMed]
6. Hariri G, Joffre J, Leblanc G et al Narrative review: clinical assessment of peripheral tissue perfusion in septic shock. Ann Intensive Care 2019, 9, 37. [CrossRef] [PubMed]
7. Contreras R, Hernández G, Valenzuela ED et al Exploring the relationship between capillary refill time, skin blood flow and microcirculatory reactivity during early resuscitation of patients with septic shock: a pilot study. J Clin Monit Comput. 2022.
8. Brunauer A, Koköfer A, Bataar O et al Changes in peripheral perfusion relate to visceral organ perfusion in early septic shock: A pilot study. J Crit Care 2016, 35, 105–109. [CrossRef] [PubMed]
9. Lara B, Enberg L, Ortega M et al Capillary refill time during fluid resuscitation in patients with sepsis-related hyperlactatemia at the emergency department is related to mortality. PLoS ONE 2017, 12, e0188548.
10. Zampieri FG, Damiani LP, Bakker J et al Effects of a resuscitation strategy targeting peripheral perfusion status versus serum lactate levels among patients with septic shock. A Bayesian reanalysis of the ANDROMEDA-SHOCK trial. Am J Respir Crit Care Med 2020, 201, 423–429. [Google Scholar]
11. Hernandez G, Ospina-Tascon G, Damiani LP et al Effect of a resuscitation strategy targeting peripheral perfusion status vs serum lactate levels on 28-day mortality among patients with septic shock. Andromeda-Shock Randomiz Clin Trial JAMA 2019, 321, 654–664.
12. Kattan E, Hernández G, Tascón GO et al A lactate - targeted resuscitation strategy may be associated with higher mortality in patients with septic shock and normal capillary refill time : a post hoc analysis of the ANDROMEDA - SHOCK study. Ann Intensive Care 2020, 10, 114. [CrossRef] [PubMed]
13. Hernandez G, Carmona P, Ait-Oufella H. Monitoring capillary refill time in septic shock. Intensive Care Med. 2024, 50, 580–582. [Google Scholar] [CrossRef] [PubMed]
14. Kleinman ME, Chameides L, Schexnayder SM, et al. Pediatric advanced life support: 2010 American Heart Association Guidelines for Cardiopulmonary Resuscitation and Emergency Cardiovascular Care. Pediatrics. 2010, 126, e1361–e1399. [Google Scholar] [CrossRef] [PubMed]
15. Reinhart, K.; Daniels, R.; Kissoon, N.; Machado, F.R.; Schachter, R.D.; Finfer, S. Recognizing Sepsis as a Global Health Priority - A WHO Resolution[J]. N Engl J Med. 2017, 377, 414–417. [Google Scholar] [CrossRef] [PubMed]
16. Fernández-Sarmiento J, De Souza D, Jabornisky R,et al. Paediatric inflammatory multisystem syndrome temporally associated with COVID-19 (PIMS-TS): a narrative review and the viewpoint of the Latin American Society of Pediatric Intensive Care (SLACIP) Sepsis Committee[J]. BMJ Paediatr Open. 2021, 5, e000894. [Google Scholar] [CrossRef] [PubMed]
17. Huber W, Zanner R, Schneider G, et al. . Assessment of Regional Perfusion and Organ Function: Less and Non-invasive Techniques[J]. Front Med (Lausanne). 2019, 6, 50. [Google Scholar]
18. Mosorov, V. The Lambert-Beer law in time domain form and its application[J]. Appl Radiat Isot 2017, 10, 1–5. [Google Scholar] [CrossRef] [PubMed]