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Addison PS, Cohen C, Borg UR, Antunes A, Montgomery D, Batchelder P. Accurate and continuous respiratory rate using touchless monitoring technology. Respir Med 2023; 220:107463. [PMID: 37993024 DOI: 10.1016/j.rmed.2023.107463] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Revised: 10/03/2023] [Accepted: 11/05/2023] [Indexed: 11/24/2023]
Abstract
PURPOSE Respiratory rate is a commonly used vital sign with various clinical applications. It serves as a crucial marker of acute health issues and any significant alteration in respiratory rate may be an early warning sign of major issues such as infections in the respiratory tract, respiratory failure, or cardiac arrest. Timely recognition of changes in respiratory rate enables prompt medical action, while neglecting to detect a change may lead to adverse patient outcomes. Here, we report on the performance of respiratory rate determined using a depth sensing camera system (RRdepth) which allows for continuous, non-contact 'touchless' monitoring of this important vital sign. METHODS Thirty adult volunteers undertook a range of set breathing rates to cover a target breathing range of 4-40 breaths/min. Depth information was acquired from the torso region of the subjects using an Intel D415 RealSense camera positioned above the bed. The depth information was processed to generate a respiratory signal from which RRdepth was calculated. This was compared to a manually scored capnograph reference (RRcap). RESULTS An overall RMSD accuracy of 0.77 breaths/min was achieved across the target respiratory rate range with a corresponding bias of 0.05 breaths/min. This corresponded to a line of best fit given by RRdepth = 1.01 x RRcap - 0.22 breaths/min with an associated high degree of correlation (R = 0.997). A breakdown of the performance with respect to sub-ranges corresponding to respiratory rates or ≤7, >7-10, >10-20, >20-30, >30 breaths/min all exhibited RMSD accuracies of less than 1.00 breaths/min. We also had the opportunity to test the performance of spontaneous breathing of the subjects which occurred during the study and found an overall RMSD accuracy of 1.20 breaths/min with corresponding accuracies ≤1.30 breaths/min across each of the individual sub-ranges. CONCLUSIONS We have conducted an investigative study of a prototype depth sensing camera system for the non-contact monitoring of respiratory rate. The system achieved good performance with high accuracy across a wide range of rates including both clinically important high and low rates.
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Affiliation(s)
| | | | - Ulf R Borg
- Medtronic Patient Monitoring, Boulder, CO, USA
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Borg U, Katilius JZ, Addison PS. Near-Infrared Spectroscopy Monitoring to Detect Changes in Cerebral and Renal Perfusion During Hypovolemic Shock, Volume Resuscitation, and Vasoconstriction. Mil Med 2023; 188:369-376. [PMID: 37948242 DOI: 10.1093/milmed/usad158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2023] [Revised: 02/10/2023] [Accepted: 08/16/2023] [Indexed: 11/12/2023] Open
Abstract
INTRODUCTION Rapidly changing hemodynamic conditions, such as uncontrolled hemorrhage and the resulting hypovolemic shock, are a common contributor to active duty military deaths. These conditions can cause cerebral desaturation, and outcomes may improve when regional cerebral oxygen saturation (CrSO2) is monitored using near-infrared spectroscopy (NIRS) and desaturation episodes are recognized and reversed. The purpose of this porcine study was to investigate the ability of NIRS monitoring to detect changes in regional cerebral and regional renal perfusion during hypovolemia, resuscitation by volume infusion, and vasoconstriction. MATERIALS AND METHODS Hemorrhagic shock was induced by removing blood through a central venous catheter until mean arterial pressure (MAP) was <40 mmHg. Each blood removal step was followed by a 10-minute stabilization period, during which cardiac output, blood pressure, central venous pressure, blood oxygen saturation, and CrSO2 and regional renal oxygen saturation (RrSO2) were measured. Shock was reversed using blood infusion and vasoconstriction separately until MAP returned to normal. Statistical comparisons between groups were performed using the paired t-test or the Wilcoxon signed-rank test. RESULTS Using volume resuscitation, both CrSO2 and RrSO2 returned to normal levels after hypovolemia. Blood pressure management with phenylephrine returned CrSO2 levels to normal, but RrSO2 levels remained significantly lower compared to the pre-hemorrhage values (P < .0001). Comparison of the percent CrSO2 as a function of MAP showed that CrSO2 levels approach baseline when a normal MAP is reached during volume resuscitation. In contrast, a significantly higher MAP was required to return to baseline CrSO2 during blood pressure management with phenylephrine (P < .0001). Evaluation of carotid blood flow and CrSO2 indicated that during induction of hypovolemia, the two measures are strongly correlated. In contrast, there was limited correlation between carotid blood flow and CrSO2 during blood infusion. CONCLUSIONS This study demonstrated that it is possible to restore CrSO2 by manipulating MAP with vasoconstriction, even in profound hypotension. However, MAP manipulation may result in unintended consequences for other organs, such as the kidney, if the tissue is not reoxygenated sufficiently. The clinical implications of these results and how best to respond to hypovolemia in the pre-hospital and hospital settings should be elucidated by additional studies.
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Affiliation(s)
- Ulf Borg
- Department of Medical Science, Patient Monitoring, Medtronic, Boulder, CO 80301, USA
| | - Julia Z Katilius
- Department of Medical Science, Patient Monitoring, Medtronic, Boulder, CO 80301, USA
| | - Paul S Addison
- Department of Research and Development, Patient Monitoring, Medtronic, Technopole Centre, Edinburgh EH26 0PJ, UK
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Addison PS, Antunes A, Montgomery D, Smit P, Borg UR. Robust Non-Contact Monitoring of Respiratory Rate using a Depth Camera. J Clin Monit Comput 2023:10.1007/s10877-023-01003-7. [PMID: 37010708 PMCID: PMC10068187 DOI: 10.1007/s10877-023-01003-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Accepted: 03/23/2023] [Indexed: 04/04/2023]
Abstract
PURPOSE Respiratory rate (RR) is one of the most common vital signs with numerous clinical uses. It is an important indicator of acute illness and a significant change in RR is often an early indication of a potentially serious complication or clinical event such as respiratory tract infection, respiratory failure and cardiac arrest. Early identification of changes in RR allows for prompt intervention, whereas failing to detect a change may result in poor patient outcomes. Here, we report on the performance of a depth-sensing camera system for the continuous non-contact 'touchless' monitoring of Respiratory Rate. METHODS Seven healthy subjects undertook a range of breathing rates from 4 to 40 breaths-per-minute (breaths/min). These were set rates of 4, 5, 6, 8, 10, 15, 20, 25, 30, 35 and 40 breaths/min. In total, 553 separate respiratory rate recordings were captured across a range of conditions including body posture, position within the bed, lighting levels and bed coverings. Depth information was acquired from the scene using an Intel D415 RealSenseTM camera. This data was processed in real-time to extract depth changes within the subject's torso region corresponding to respiratory activity. A respiratory rate RRdepth was calculated using our latest algorithm and output once-per-second from the device and compared to a reference. RESULTS An overall RMSD accuracy of 0.69 breaths/min with a corresponding bias of -0.034 was achieved across the target RR range of 4-40 breaths/min. Bland-Altman analysis revealed limits of agreement of -1.42 to 1.36 breaths/min. Three separate sub-ranges of low, normal and high rates, corresponding to < 12, 12-20, > 20 breaths/min, were also examined separately and each found to demonstrate RMSD accuracies of less than one breath-per-minute. CONCLUSIONS We have demonstrated high accuracy in performance for respiratory rate based on a depth camera system. We have shown the ability to perform well at both high and low rates which are clinically important.
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Affiliation(s)
- Paul S Addison
- Medtronic Patient Monitoring, Technopole Centre, Edinburgh, UK.
| | - André Antunes
- Medtronic Patient Monitoring, Technopole Centre, Edinburgh, UK
| | - Dean Montgomery
- Medtronic Patient Monitoring, Technopole Centre, Edinburgh, UK
| | - Philip Smit
- Medtronic Patient Monitoring, Technopole Centre, Edinburgh, UK
| | - Ulf R Borg
- Medtronic Patient Monitoring, Boulder, CO, USA
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Addison PS, Smit P, Jacquel D, Addison AP, Miller C, Kimm G. Continuous non-contact respiratory rate and tidal volume monitoring using a Depth Sensing Camera. J Clin Monit Comput 2021; 36:657-665. [PMID: 33743106 PMCID: PMC7980749 DOI: 10.1007/s10877-021-00691-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2020] [Accepted: 03/04/2021] [Indexed: 11/26/2022]
Abstract
The monitoring of respiratory parameters is important across many areas of care within the hospital. Here we report on the performance of a depth-sensing camera system for the continuous non-contact monitoring of Respiratory Rate (RR) and Tidal Volume (TV), where these parameters were compared to a ventilator reference. Depth sensing data streams were acquired and processed over a series of runs on a single volunteer comprising a range of respiratory rates and tidal volumes to generate depth-based respiratory rate (RRdepth) and tidal volume (TVdepth) estimates. The bias and root mean squared difference (RMSD) accuracy between RRdepth and the ventilator reference, RRvent, across the whole data set was found to be -0.02 breaths/min and 0.51 breaths/min respectively. The least squares fit regression equation was determined to be: RRdepth = 0.96 × RRvent + 0.57 breaths/min and the resulting Pearson correlation coefficient, R, was 0.98 (p < 0.001). Correspondingly, the bias and root mean squared difference (RMSD) accuracy between TVdepth and the reference TVvent across the whole data set was found to be - 0.21 L and 0.23 L respectively. The least squares fit regression equation was determined to be: TVdepth = 0.79 × TVvent-0.01 L and the resulting Pearson correlation coefficient, R, was 0.92 (p < 0.001). In conclusion, a high degree of agreement was found between the depth-based respiration rate and its ventilator reference, indicating that RRdepth is a promising modality for the accurate non-contact respiratory rate monitoring in the clinical setting. In addition, a high degree of correlation between depth-based tidal volume and its ventilator reference was found, indicating that TVdepth may provide a useful monitor of tidal volume trending in practice. Future work should aim to further test these parameters in the clinical setting.
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Affiliation(s)
- Paul S Addison
- Video Biosignals Group, Patient Monitoring, Medtronic, Technopole Centre, Edinburgh, EH26 0PJ, UK.
| | - Philip Smit
- Video Biosignals Group, Patient Monitoring, Medtronic, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - Dominique Jacquel
- Video Biosignals Group, Patient Monitoring, Medtronic, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - Anthony P Addison
- Video Biosignals Group, Patient Monitoring, Medtronic, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - Cyndy Miller
- Respiratory Interventions, Medtronic, Ventilation, Carlsbad, CA, USA
| | - Gardner Kimm
- Respiratory Interventions, Medtronic, Ventilation, Carlsbad, CA, USA
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Addison AP, Addison PS, Smit P, Jacquel D, Borg UR. Noncontact Respiratory Monitoring Using Depth Sensing Cameras: A Review of Current Literature. Sensors (Basel) 2021; 21:1135. [PMID: 33561970 PMCID: PMC7915793 DOI: 10.3390/s21041135] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Revised: 02/01/2021] [Accepted: 02/03/2021] [Indexed: 12/17/2022]
Abstract
There is considerable interest in the noncontact monitoring of patients as it allows for reduced restriction of patients, the avoidance of single-use consumables and less patient-clinician contact and hence the reduction of the spread of disease. A technology that has come to the fore for noncontact respiratory monitoring is that based on depth sensing camera systems. This has great potential for the monitoring of a range of respiratory information including the provision of a respiratory waveform, the calculation of respiratory rate and tidal volume (and hence minute volume). Respiratory patterns and apneas can also be observed in the signal. Here we review the ability of this method to provide accurate and clinically useful respiratory information.
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Affiliation(s)
- Anthony P. Addison
- Medtronic, Video Biosignals Group, Patient Monitoring, Edinburgh EH26 0PJ, UK; (A.P.A.); (P.S.); (D.J.)
| | - Paul S. Addison
- Medtronic, Video Biosignals Group, Patient Monitoring, Edinburgh EH26 0PJ, UK; (A.P.A.); (P.S.); (D.J.)
| | - Philip Smit
- Medtronic, Video Biosignals Group, Patient Monitoring, Edinburgh EH26 0PJ, UK; (A.P.A.); (P.S.); (D.J.)
| | - Dominique Jacquel
- Medtronic, Video Biosignals Group, Patient Monitoring, Edinburgh EH26 0PJ, UK; (A.P.A.); (P.S.); (D.J.)
| | - Ulf R. Borg
- Medtronic, Medical Affairs, Patient Monitoring, Boulder, CO 80301, USA;
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Montgomery D, Brown C, Hogue CW, Brady K, Nakano M, Nomura Y, Antunes A, Addison PS. Real-Time Intraoperative Determination and Reporting of Cerebral Autoregulation State Using Near-Infrared Spectroscopy. Anesth Analg 2020; 131:1520-1528. [PMID: 33079875 PMCID: PMC7319873 DOI: 10.1213/ane.0000000000004614] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/26/2019] [Indexed: 01/17/2023]
Abstract
BACKGROUND Cerebral blood flow (CBF) is maintained over a range of blood pressures through cerebral autoregulation (CA). Blood pressure outside the range of CA, or impaired autoregulation, is associated with adverse patient outcomes. Regional oxygen saturation (rSO2) derived from near-infrared spectroscopy (NIRS) can be used as a surrogate CBF for determining CA, but existing methods require a long period of time to calculate CA metrics. We have developed a novel method to determine CA using cotrending of mean arterial pressure (MAP) with rSO2that aims to provide an indication of CA state within 1 minute. We sought to determine the performance of the cotrending method by comparing its CA metrics to data derived from transcranial Doppler (TCD) methods. METHODS Retrospective data collected from 69 patients undergoing cardiac surgery with cardiopulmonary bypass were used to develop a reference lower limit of CA. TCD-MAP data were plotted to determine the reference lower limit of CA. The investigated method to evaluate CA state is based on the assessment of the instantaneous cotrending relationship between MAP and rSO2 signals. The lower limit of autoregulation (LLA) from the cotrending method was compared to the manual reference derived from TCD. Reliability of the cotrending method was assessed as uptime (defined as the percentage of time that the state of autoregulation could be measured) and time to first post. RESULTS The proposed method demonstrated minimal mean bias (0.22 mmHg) when compared to the TCD reference. The corresponding limits of agreement were found to be 10.79 mmHg (95% confidence interval [CI], 10.09-11.49) and -10.35 mmHg (95% CI, -9.65 to -11.05). Mean uptime was 99.40% (95% CI, 99.34-99.46) and the mean time to first post was 63 seconds (95% CI, 58-71). CONCLUSIONS The reported cotrending method rapidly provides metrics associated with CA state for patients undergoing cardiac surgery. A major strength of the proposed method is its near real-time feedback on patient CA state, thus allowing for prompt corrective action to be taken by the clinician.
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Affiliation(s)
- Dean Montgomery
- From the Medtronic Respiratory & Monitoring Solutions, Edinburgh, United Kingdom
| | - Charles Brown
- Department of Anesthesiology and Critical Care Medicine, Johns Hopkins University School of Medicine, Baltimore, Maryland
| | - Charles W. Hogue
- Department of Anesthesiology, Northwestern University Feinberg, School of Medicine, Chicago, Illinois
| | - Ken Brady
- Department of Anesthesiology, Northwestern University Feinberg, School of Medicine, Chicago, Illinois
- Cardiac Anesthesia, Ann & Robert Lurie Children’s Hospital, Chicago, Illinois
| | - Mitsunori Nakano
- Department of Anesthesiology and Critical Care Medicine, Johns Hopkins University School of Medicine, Baltimore, Maryland
| | - Yohei Nomura
- Department of Cardiovascular Surgery, Saitama Medical Center, Jichi Medical University, Saitama, Japan
| | - Andre Antunes
- From the Medtronic Respiratory & Monitoring Solutions, Edinburgh, United Kingdom
| | - Paul S. Addison
- From the Medtronic Respiratory & Monitoring Solutions, Edinburgh, United Kingdom
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Addison PS, Smit P, Jacquel D, Borg UR. Continuous respiratory rate monitoring during an acute hypoxic challenge using a depth sensing camera. J Clin Monit Comput 2019; 34:1025-1033. [PMID: 31701371 PMCID: PMC7447672 DOI: 10.1007/s10877-019-00417-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Accepted: 10/31/2019] [Indexed: 11/28/2022]
Abstract
Respiratory rate is a well-known to be a clinically important parameter with numerous clinical uses including the assessment of disease state and the prediction of deterioration. It is frequently monitored using simple spot checks where reporting is intermittent and often prone to error. We report here on an algorithm to determine respiratory rate continuously and robustly using a non-contact method based on depth sensing camera technology. The respiratory rate of 14 healthy volunteers was studied during an acute hypoxic challenge where blood oxygen saturation was reduced in steps to a target 70% oxygen saturation and which elicited a wide range of respiratory rates. Depth sensing data streams were acquired and processed to generate a respiratory rate (RRdepth). This was compared to a reference respiratory rate determined from a capnograph (RRcap). The bias and root mean squared difference (RMSD) accuracy between RRdepth and the reference RRcap was found to be 0.04 bpm and 0.66 bpm respectively. The least squares fit regression equation was determined to be: RRdepth = 0.99 × RRcap + 0.13 and the resulting Pearson correlation coefficient, R, was 0.99 (p < 0.001). These results were achieved with a 100% reporting uptime. In conclusion, excellent agreement was found between RRdepth and RRcap. Further work should include a larger cohort combined with a protocol to further test algorithmic performance in the face of motion and interference typical of that experienced in the clinical setting.
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Affiliation(s)
- Paul S Addison
- Medtronic, Video Biosignals Group, Patient Monitoring, Technopole Centre, Edinburgh, EH26 0PJ, UK.
| | - Philip Smit
- Medtronic, Video Biosignals Group, Patient Monitoring, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - Dominique Jacquel
- Medtronic, Video Biosignals Group, Patient Monitoring, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - Ulf R Borg
- Medtronic, Medical Affairs, Patient Monitoring, Boulder, CO, USA
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Addison PS, Jacquel D, Foo DMH, Borg UR. Video-based heart rate monitoring across a range of skin pigmentations during an acute hypoxic challenge. J Clin Monit Comput 2018; 32:871-880. [PMID: 29124562 PMCID: PMC6132623 DOI: 10.1007/s10877-017-0076-1] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2017] [Accepted: 10/28/2017] [Indexed: 11/25/2022]
Abstract
The robust monitoring of heart rate from the video-photoplethysmogram (video-PPG) during challenging conditions requires new analysis techniques. The work reported here extends current research in this area by applying a motion tolerant algorithm to extract high quality video-PPGs from a cohort of subjects undergoing marked heart rate changes during a hypoxic challenge, and exhibiting a full range of skin pigmentation types. High uptimes in reported video-based heart rate (HRvid) were targeted, while retaining high accuracy in the results. Ten healthy volunteers were studied during a double desaturation hypoxic challenge. Video-PPGs were generated from the acquired video image stream and processed to generate heart rate. HRvid was compared to the pulse rate posted by a reference pulse oximeter device (HRp). Agreement between video-based heart rate and that provided by the pulse oximeter was as follows: Bias = - 0.21 bpm, RMSD = 2.15 bpm, least squares fit gradient = 1.00 (Pearson R = 0.99, p < 0.0001), with a 98.78% reporting uptime. The difference between the HRvid and HRp exceeded 5 and 10 bpm, for 3.59 and 0.35% of the reporting time respectively, and at no point did these differences exceed 25 bpm. Excellent agreement was found between the HRvid and HRp in a study covering the whole range of skin pigmentation types (Fitzpatrick scales I-VI), using standard room lighting and with moderate subject motion. Although promising, further work should include a larger cohort with multiple subjects per Fitzpatrick class combined with a more rigorous motion and lighting protocol.
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Affiliation(s)
- Paul S Addison
- Medtronic, Video Biosignals Group, Patient Monitoring, Technopole Centre, Edinburgh, EH26 0PJ, UK.
| | - Dominique Jacquel
- Medtronic, Video Biosignals Group, Patient Monitoring, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - David M H Foo
- Medtronic, Video Biosignals Group, Patient Monitoring, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - Ulf R Borg
- Medtronic, Medical Affairs, Patient Monitoring, Boulder, CO, USA
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Addison PS. Introduction to redundancy rules: the continuous wavelet transform comes of age. Philos Trans A Math Phys Eng Sci 2018; 376:rsta.2017.0258. [PMID: 29986912 PMCID: PMC6048575 DOI: 10.1098/rsta.2017.0258] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/29/2018] [Indexed: 05/27/2023]
Abstract
Redundancy: it is a word heavy with connotations of lacking usefulness. I often hear that the rationale for not using the continuous wavelet transform (CWT)-even when it appears most appropriate for the problem at hand-is that it is 'redundant'. Sometimes the conversation ends there, as if self-explanatory. However, in the context of the CWT, 'redundant' is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form-the CWT-is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy. Once the signal information is in CWT form, a range of powerful analysis methods can then be employed for its extraction, interpretation and/or manipulation. This theme issue is intended to provide the reader with an overview of the current state of the art of CWT analysis methods from across a wide range of numerate disciplines, including fluid dynamics, structural mechanics, geophysics, medicine, astronomy and finance.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.
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Addison PS, Jacquel D, Foo DMH, Antunes A, Borg UR. Video-Based Physiologic Monitoring During an Acute Hypoxic Challenge: Heart Rate, Respiratory Rate, and Oxygen Saturation. Anesth Analg 2017; 125:860-873. [PMID: 28333706 DOI: 10.1213/ane.0000000000001989] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
BACKGROUND The physiologic information contained in the video photoplethysmogram is well documented. However, extracting this information during challenging conditions requires new analysis techniques to capture and process the video image streams to extract clinically useful physiologic parameters. We hypothesized that heart rate, respiratory rate, and oxygen saturation trending can be evaluated accurately from video information during acute hypoxia. METHODS Video footage was acquired from multiple desaturation episodes during a porcine model of acute hypoxia using a standard visible light camera. A novel in-house algorithm was used to extract photoplethysmographic cardiac pulse and respiratory information from the video image streams and process it to extract a continuously reported video-based heart rate (HRvid), respiratory rate (RRvid), and oxygen saturation (SvidO2). This information was then compared with HR and oxygen saturation references from commercial pulse oximetry and the known rate of respiration from the ventilator. RESULTS Eighty-eight minutes of data were acquired during 16 hypoxic episodes in 8 animals. A linear mixed-effects regression showed excellent responses relative to a nonhypoxic reference signal with slopes of 0.976 (95% confidence interval [CI], 0.973-0.979) for HRvid; 1.135 (95% CI, 1.101-1.168) for RRvid, and 0.913 (95% CI, 0.905-0.920) for video-based oxygen saturation. These results were obtained while maintaining continuous uninterrupted vital sign monitoring for the entire study period. CONCLUSIONS Video-based monitoring of HR, RR, and oxygen saturation may be performed with reasonable accuracy during acute hypoxic conditions in an anesthetized porcine hypoxia model using standard visible light camera equipment. However, the study was conducted during relatively low motion. A better understanding of the effect of motion and the effect of ambient light on the video photoplethysmogram may help refine this monitoring technology for use in the clinical environment.
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Affiliation(s)
- Paul S Addison
- From the *Video Biosignals Group, Medtronic Respiratory & Monitoring Solutions, Technopole Centre, Edinburgh, United Kingdom; and †Medical Affairs, Medtronic Respiratory & Monitoring Solutions, Boulder, Colorado
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Bergese SD, Mestek ML, Kelley SD, McIntyre R, Uribe AA, Sethi R, Watson JN, Addison PS. In Response. Anesth Analg 2017; 125:1075-1076. [PMID: 28742782 DOI: 10.1213/ane.0000000000002294] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Sergio D Bergese
- Department of Anesthesiology, The Ohio State University Wexner Medical Center, Columbus, Ohio, Respiratory and Monitoring Solutions, Medtronic, Boulder, Colorado Department of Surgery, University of Colorado Hospital, Aurora, Colorado Department of Anesthesiology, The Ohio State University Wexner Medical Center, Columbus, Ohio Respiratory and Monitoring Solutions, Medtronic, Boulder, Colorado Respiratory and Monitoring Solutions, Medtronic, Edinburgh, United Kingdom
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Bergese SD, Mestek ML, Kelley SD, McIntyre R, Uribe AA, Sethi R, Watson JN, Addison PS. In Response. Anesth Analg 2017; 125:1077-1078. [PMID: 28708663 DOI: 10.1213/ane.0000000000002292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Sergio D Bergese
- Department of Anesthesiology, The Ohio State University Wexner Medical Center, Columbus, Ohio, Respiratory and Monitoring Solutions, Medtronic, Boulder, Colorado Department of Surgery, University of Colorado Hospital, Aurora, Colorado Department of Anesthesiology, The Ohio State University Wexner Medical Center, Columbus, Ohio Respiratory and Monitoring Solutions, Medtronic, Boulder, Colorado Respiratory and Monitoring Solutions, Medtronic, Edinburgh, United Kingdom
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Bergese SD, Mestek ML, Kelley SD, McIntyre R, Uribe AA, Sethi R, Watson JN, Addison PS. Multicenter Study Validating Accuracy of a Continuous Respiratory Rate Measurement Derived From Pulse Oximetry: A Comparison With Capnography. Anesth Analg 2017; 124:1153-1159. [PMID: 28099286 PMCID: PMC5367492 DOI: 10.1213/ane.0000000000001852] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
Published ahead of print January 17, 2017. BACKGROUND: Intermittent measurement of respiratory rate via observation is routine in many patient care settings. This approach has several inherent limitations that diminish the clinical utility of these measurements because it is intermittent, susceptible to human error, and requires clinical resources. As an alternative, a software application that derives continuous respiratory rate measurement from a standard pulse oximeter has been developed. We sought to determine the performance characteristics of this new technology by comparison with clinician-reviewed capnography waveforms in both healthy subjects and hospitalized patients in a low-acuity care setting. METHODS: Two independent observational studies were conducted to validate the performance of the Medtronic NellcorTM Respiration Rate Software application. One study enrolled 26 healthy volunteer subjects in a clinical laboratory, and a second multicenter study enrolled 53 hospitalized patients. During a 30-minute study period taking place while participants were breathing spontaneously, pulse oximeter and nasal/oral capnography waveforms were collected. Pulse oximeter waveforms were processed to determine respiratory rate via the Medtronic Nellcor Respiration Rate Software. Capnography waveforms reviewed by a clinician were used to determine the reference respiratory rate. RESULTS: A total of 23,243 paired observations between the pulse oximeter-derived respiratory rate and the capnography reference method were collected and examined. The mean reference-based respiratory rate was 15.3 ± 4.3 breaths per minute with a range of 4 to 34 breaths per minute. The Pearson correlation coefficient between the Medtronic Nellcor Respiration Rate Software values and the capnography reference respiratory rate is reported as a linear correlation, R, as 0.92 ± 0.02 (P < .001), whereas Lin’s concordance correlation coefficient indicates an overall agreement of 0.85 ± 0.04 (95% confidence interval [CI] +0.76; +0.93) (healthy volunteers: 0.94 ± 0.02 [95% CI +0.91; +0.97]; hospitalized patients: 0.80 ± 0.06 [95% CI +0.68; +0.92]). The mean bias of the Medtronic Nellcor Respiration Rate Software was 0.18 breaths per minute with a precision (SD) of 1.65 breaths per minute (healthy volunteers: 0.37 ± 0.78 [95% limits of agreement: –1.16; +1.90] breaths per minute; hospitalized patients: 0.07 ± 1.99 [95% limits of agreement: –3.84; +3.97] breaths per minute). The root mean square deviation was 1.35 breaths per minute (healthy volunteers: 0.81; hospitalized patients: 1.60). CONCLUSIONS: These data demonstrate the performance of the Medtronic Nellcor Respiration Rate Software in healthy subjects and patients hospitalized in a low-acuity care setting when compared with clinician-reviewed capnography. The observed performance of this technology suggests that it may be a useful adjunct to continuous pulse oximetry monitoring by providing continuous respiratory rate measurements. The potential patient safety benefit of using combined continuous pulse oximetry and respiratory rate monitoring warrants assessment.
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Affiliation(s)
- Sergio D Bergese
- From the Departments of *Anesthesiology and †Neurological Surgery, The Ohio State University Wexner Medical Center, Columbus, Ohio; ‡Respiratory & Monitoring Solutions, Medtronic, Boulder, Colorado; §Department of Surgery, University of Colorado Hospital, Aurora, Colorado; and ‖Respiratory & Monitoring Solutions, Medtronic, Edinburgh, United Kingdom
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Addison PS, Foo DMH, Jacquel D. Running wavelet archetype aids the determination of heart rate from the video photoplethysmogram during motion. Annu Int Conf IEEE Eng Med Biol Soc 2017; 2017:734-737. [PMID: 29059977 DOI: 10.1109/embc.2017.8036929] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The extraction of heart rate from a video-based biosignal during motion using a novel wavelet-based ensemble averaging method is described. Running Wavelet Archetyping (RWA) allows for the enhanced extraction of pulse information from the time-frequency representation, from which a video-based heart rate (HRvid) can be derived. This compares favorably to a reference heart rate derived from a pulse oximeter.
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Abstract
The potential for a simple, non-invasive measure of respiratory effort based on the pulse oximeter signal - the photoplethysmogram or 'pleth' - was investigated in a pilot study. Several parameters were developed based on a variety of manifestations of respiratory effort in the signal, including modulation changes in amplitude, baseline, frequency and pulse transit times, as well as distinct baseline signal shifts. Thirteen candidate parameters were investigated using data from healthy volunteers. Each volunteer underwent a series of controlled respiratory effort maneuvers at various set flow resistances and respiratory rates. Six oximeter probes were tested at various body sites. In all, over three thousand pleth-based effort-airway pressure (EP) curves were generated across the various airway constrictions, respiratory efforts, respiratory rates, subjects, probe sites, and the candidate parameters considered. Regression analysis was performed to determine the existence of positive monotonic relationships between the respiratory effort parameters and resulting airway pressures. Six of the candidate parameters investigated exhibited a distinct positive relationship (p<0.001 across all probes tested) with increasing upper airway pressure repeatable across the range of respiratory rates and flow constrictions studied. These were: the three fundamental modulations in amplitude (AM-Effort), baseline (BM-Effort) and respiratory sinus arrhythmia (RSA-Effort); two pulse transit time modulations - one using a pulse oximeter probe and an ECG (P2E-Effort) and the other using two pulse oximeter probes placed at different peripheral body sites (P2-Effort); and baseline shifts in heart rate, (BL-HR-Effort). In conclusion, a clear monotonic relationship was found between several pleth-based parameters and imposed respiratory loadings at the mouth across a range of respiratory rates and flow constrictions. The results suggest that the pleth may provide a measure of changing upper airway dynamics indicative of the effort to breathe.
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Affiliation(s)
- Paul S Addison
- Minimally Invasive Therapies Group, Medtronic, The Technopole Centre, Edinburgh EH26 0PJ, Scotland, United Kingdom .
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Addison PS. Slope Transit Time (STT): A Pulse Transit Time Proxy requiring Only a Single Signal Fiducial Point. IEEE Trans Biomed Eng 2016; 63:2441-2444. [DOI: 10.1109/tbme.2016.2528507] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Addison PS. Identifying stable phase coupling associated with cerebral autoregulation using the synchrosqueezed cross-wavelet transform and low oscillation morlet wavelets. Annu Int Conf IEEE Eng Med Biol Soc 2016; 2015:5960-3. [PMID: 26737649 DOI: 10.1109/embc.2015.7319749] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A novel method of identifying stable phase coupling behavior of two signals within the wavelet transform time-frequency plane is presented. The technique employs the cross-wavelet transform to provide a map of phase coupling followed by synchrosqueezing to collect the stable phase regime information. The resulting synchrosqueezed cross-wavelet transform method (Synchro-CrWT) is illustrated using a synthetic signal and then applied to the analysis of the relationship between biosignals used in the analysis of cerebral autoregulation function.
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Addison PS, Antunes A, Montgomery D, Borg UR. Gradient adjustment method for better discriminating correlating and non-correlating regions of physiological signals: application to the partitioning of impaired and intact zones of cerebral autoregulation. J Clin Monit Comput 2016; 31:727-737. [PMID: 27496051 PMCID: PMC5500687 DOI: 10.1007/s10877-016-9913-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Accepted: 07/25/2016] [Indexed: 11/10/2022]
Abstract
Cerebral blood flow (CBF) is regulated over a range of systemic blood pressures by the cerebral autoregulation (CA) control mechanism. This range lies within the lower and upper limits of autoregulation (LLA, ULA), beyond which blood pressure drives CBF, and CA function is considered impaired. A standard method to determine autoregulation limits noninvasively using NIRS technology is via the COx measure: a moving correlation index between mean arterial pressure and regional oxygen saturation. In the intact region, there should be no correlation between these variables whereas in the impaired region, the correlation index should approximate unity. In practice, however, the data may be noisy and/or the intact region may often exhibit a slightly positive relationship. This positive relationship may render traditional autoregulation limit calculations difficult to perform, resulting in the need for manual interpretation of the data using arbitrary thresholds. Further, the underlying mathematics of the technique are asymmetric in terms of the results produced for impaired and intact regions and are, in fact, not computable for the ideal case within the intact region. In this work, we propose a novel gradient adjustment method (GACOx) to enhance the differences in COx values observed in the intact and impaired regions. Results from a porcine model (N = 8) are used to demonstrate that GACOx is successful in determining LLA values where traditional methods fail. It is shown that the derived GACOx indices exhibit a mean difference between the intact/impaired regions of 1.54 ± 0.26 (mean ± SD), compared to 0.14 ± 0.10 for the traditional COx method. The GACOx effectively polarizes the COx data in order to better differentiate the intact and impaired zones and, in doing so, makes the determination of the LLA and ULA points a simpler and more consistent task. The method lends itself to the automation of the robust determination of autoregulation zone limits.
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Affiliation(s)
- Paul S Addison
- Medtronic Respiratory and Monitoring Solutions, Edinburgh, Scotland, UK.
| | - André Antunes
- Medtronic Respiratory and Monitoring Solutions, Edinburgh, Scotland, UK
| | - Dean Montgomery
- Medtronic Respiratory and Monitoring Solutions, Edinburgh, Scotland, UK
| | - Ulf R Borg
- Medtronic Respiratory and Monitoring Solutions, Boulder, CO, USA
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Addison PS, Foo DMH, Jacquel D, Borg U. Video monitoring of oxygen saturation during controlled episodes of acute hypoxia. Annu Int Conf IEEE Eng Med Biol Soc 2016; 2016:4747-4750. [PMID: 28269331 DOI: 10.1109/embc.2016.7591788] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
A method for extracting video photoplethysmographic information from an RGB video stream is tested on data acquired during a porcine model of acute hypoxia. Cardiac pulsatile information was extracted from the acquired signals and processed to determine a continuously reported oxygen saturation (SvidO2). A high degree of correlation was found to exist between the video and a reference from a pulse oximeter. The calculated mean bias and accuracy across all eight desaturation episodes were -0.03% (range: -0.21% to 0.24%) and accuracy 4.90% (range: 3.80% to 6.19%) respectively. The results support the hypothesis that oxygen saturation trending can be evaluated accurately from a video system during acute hypoxia.
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Addison PS. Modular continuous wavelet processing of biosignals: extracting heart rate and oxygen saturation from a video signal. Healthc Technol Lett 2016; 3:111-5. [PMID: 27382479 PMCID: PMC4916481 DOI: 10.1049/htl.2015.0052] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Revised: 02/26/2016] [Accepted: 02/29/2016] [Indexed: 11/20/2022] Open
Abstract
A novel method of extracting heart rate and oxygen saturation from a video-based biosignal is described. The method comprises a novel modular continuous wavelet transform approach which includes: performing the transform, undertaking running wavelet archetyping to enhance the pulse information, extraction of the pulse ridge time-frequency information [and thus a heart rate (HRvid) signal], creation of a wavelet ratio surface, projection of the pulse ridge onto the ratio surface to determine the ratio of ratios from which a saturation trending signal is derived, and calibrating this signal to provide an absolute saturation signal (SvidO2). The method is illustrated through its application to a video photoplethysmogram acquired during a porcine model of acute desaturation. The modular continuous wavelet transform-based approach is advocated by the author as a powerful methodology to deal with noisy, non-stationary biosignals in general.
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Affiliation(s)
- Paul S. Addison
- Medtronic Respiratory & Monitoring Solutions, Technopole Centre, Edinburgh EH26 0PJ, UK
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Montgomery D, Addison PS, Borg U. Data clustering methods for the determination of cerebral autoregulation functionality. J Clin Monit Comput 2015; 30:661-8. [PMID: 26377023 PMCID: PMC5023736 DOI: 10.1007/s10877-015-9774-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Accepted: 09/10/2015] [Indexed: 11/29/2022]
Abstract
Cerebral blood flow is regulated over a range of systemic blood pressures through the cerebral autoregulation (CA) control mechanism. The COx measure based on near infrared spectroscopy (NIRS) has been proposed as a suitable technique for the analysis of CA as it is non-invasive and provides a simpler acquisition methodology than other methods. The COx method relies on data binning and thresholding to determine the change between intact and impaired autoregulation zones. In the work reported here we have developed a novel method of differentiating the intact and impaired CA blood pressure regimes using clustering methods on unbinned data. K-means and Gaussian mixture model algorithms were used to analyse a porcine data set. The determination of the lower limit of autoregulation (LLA) was compared to a traditional binned data approach. Good agreement was found between the methods. The work highlights the potential application of using data clustering tools in the monitoring of CA function.
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Affiliation(s)
- Dean Montgomery
- Respiratory and Monitoring Solutions, Medtronic, Technopole Centre, Edinburgh, EH26 0PJ, UK.
| | - Paul S Addison
- Respiratory and Monitoring Solutions, Medtronic, Technopole Centre, Edinburgh, EH26 0PJ, UK
| | - Ulf Borg
- Respiratory and Monitoring Solutions, Medtronic, 6135 Gunbarrel Avenue, Boulder, CO, 80301, USA
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Abstract
Near-infrared spectroscopy (NIRS) has been proposed as a suitable technique for the analysis of cerebral autoregulation as it provides a simpler acquisition methodology and more artifact-free signal. A number of sophisticated wavelet transform methods have recently emerged to quantify the cerebral autoregulation mechanism using NIRS and blood pressure signals. These provide an enhanced partitioning of signal information via the time-frequency plane, which facilitates improved extraction of the components of interest. This area is reviewed, and enhancements to this form of analysis are suggested.
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Addison PS, Watson JN, Mestek ML, Ochs JP, Uribe AA, Bergese SD. Pulse oximetry-derived respiratory rate in general care floor patients. J Clin Monit Comput 2015; 29:113-20. [PMID: 24796734 PMCID: PMC4309914 DOI: 10.1007/s10877-014-9575-5] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2013] [Accepted: 04/02/2014] [Indexed: 11/02/2022]
Abstract
Respiratory rate is recognized as a clinically important parameter for monitoring respiratory status on the general care floor (GCF). Currently, intermittent manual assessment of respiratory rate is the standard of care on the GCF. This technique has several clinically-relevant shortcomings, including the following: (1) it is not a continuous measurement, (2) it is prone to observer error, and (3) it is inefficient for the clinical staff. We report here on an algorithm designed to meet clinical needs by providing respiratory rate through a standard pulse oximeter. Finger photoplethysmograms were collected from a cohort of 63 GCF patients monitored during free breathing over a 25-min period. These were processed using a novel in-house algorithm based on continuous wavelet-transform technology within an infrastructure incorporating confidence-based averaging and logical decision-making processes. The computed oximeter respiratory rates (RRoxi) were compared to an end-tidal CO2 reference rate (RRETCO2). RRETCO2 ranged from a lowest recorded value of 4.7 breaths per minute (brpm) to a highest value of 32.0 brpm. The mean respiratory rate was 16.3 brpm with standard deviation of 4.7 brpm. Excellent agreement was found between RRoxi and RRETCO2, with a mean difference of -0.48 brpm and standard deviation of 1.77 brpm. These data demonstrate that our novel respiratory rate algorithm is a potentially viable method of monitoring respiratory rate in GCF patients. This technology provides the means to facilitate continuous monitoring of respiratory rate, coupled with arterial oxygen saturation and pulse rate, using a single non-invasive sensor in low acuity settings.
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Affiliation(s)
- Paul S Addison
- Covidien Respiratory and Monitoring Solutions, Edinburgh, Scotland, UK,
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Addison PS, Wang R, Uribe AA, Bergese SD. Increasing signal processing sophistication in the calculation of the respiratory modulation of the photoplethysmogram (DPOP). J Clin Monit Comput 2014; 29:363-72. [PMID: 25209132 PMCID: PMC4420848 DOI: 10.1007/s10877-014-9613-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2014] [Accepted: 08/27/2014] [Indexed: 11/07/2022]
Abstract
DPOP (∆POP or Delta-POP) is a non-invasive parameter which measures the strength of respiratory modulations present in the pulse oximetry photoplethysmogram (pleth) waveform. It has been proposed as a non-invasive surrogate parameter for pulse pressure variation (PPV) used in the prediction of the response to volume expansion in hypovolemic patients. Many groups have reported on the DPOP parameter and its correlation with PPV using various semi-automated algorithmic implementations. The study reported here demonstrates the performance gains made by adding increasingly sophisticated signal processing components to a fully automated DPOP algorithm. A DPOP algorithm was coded and its performance systematically enhanced through a series of code module alterations and additions. Each algorithm iteration was tested on data from 20 mechanically ventilated OR patients. Correlation coefficients and ROC curve statistics were computed at each stage. For the purposes of the analysis we split the data into a manually selected ‘stable’ region subset of the data containing relatively noise free segments and a ‘global’ set incorporating the whole data record. Performance gains were measured in terms of correlation against PPV measurements in OR patients undergoing controlled mechanical ventilation. Through increasingly advanced pre-processing and post-processing enhancements to the algorithm, the correlation coefficient between DPOP and PPV improved from a baseline value of R = 0.347 to R = 0.852 for the stable data set, and, correspondingly, R = 0.225 to R = 0.728 for the more challenging global data set. Marked gains in algorithm performance are achievable for manually selected stable regions of the signals using relatively simple algorithm enhancements. Significant additional algorithm enhancements, including a correction for low perfusion values, were required before similar gains were realised for the more challenging global data set.
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Affiliation(s)
- Paul S Addison
- Advanced Research Group, Covidien Respiratory and Monitoring Solutions, The Technopole Centre, Edinburgh, EH26 0PJ, Scotland, UK,
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Addison PS, Watson JN, Mestek ML, Mecca RS. Developing an algorithm for pulse oximetry derived respiratory rate (RR(oxi)): a healthy volunteer study. J Clin Monit Comput 2012; 26:45-51. [PMID: 22231359 PMCID: PMC3268017 DOI: 10.1007/s10877-011-9332-y] [Citation(s) in RCA: 64] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2011] [Accepted: 12/21/2011] [Indexed: 11/29/2022]
Abstract
Objective The presence of respiratory information within the pulse oximeter signal (PPG) is a well-documented phenomenon. However, extracting this information for the purpose of continuously monitoring respiratory rate requires: (1) the recognition of the multi-faceted manifestations of respiratory modulation components within the PPG and the complex interactions among them; (2) the implementation of appropriate advanced signal processing techniques to take full advantage of this information; and (3) the post-processing infrastructure to deliver a clinically useful reported respiratory rate to the end user. A holistic algorithmic approach to the problem is therefore required. We have developed the RROXI algorithm based on this principle and its performance on healthy subject trial data is described herein. Methods Finger PPGs were collected from a cohort of 139 healthy adult volunteers monitored during free breathing over an 8-min period. These were subsequently processed using a novel in-house algorithm based on continuous wavelet transform technology within an infrastructure incorporating weighted averaging and logical decision making processes. The computed oximeter respiratory rates (RRoxi) were then compared to an end-tidal CO2 reference rate (\documentclass[12pt]{minimal}
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\begin{document}$$ {\text{RR}}_{{{\text{ETCO}}_{ 2} }} $$\end{document} ranged from a lowest recorded value of 2.97 breaths per min (br/min) to a highest value of 28.02 br/min. The mean rate was 14.49 br/min with standard deviation of 4.36 br/min. Excellent agreement was found between RRoxi and \documentclass[12pt]{minimal}
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\begin{document}$$ {\text{RR}}_{{{\text{ETCO}}_{ 2} }} $$\end{document}, with a mean difference of −0.23 br/min and standard deviation of 1.14 br/min. The two measures are tightly spread around the line of agreement with a strong correlation observable between them (R2 = 0.93). Conclusions These data indicate that RRoxi represents a viable technology for the measurement of respiratory rate of healthy individuals.
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Affiliation(s)
- Paul S Addison
- Advanced Research Group, Covidien Respiratory and Monitoring Solutions, Technopole Centre, Edinburgh, EH26 0PJ, UK.
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Romero I, Grubb NR, Clegg GR, Robertson CE, Addison PS, Watson JN. T-wave alternans found in preventricular tachyarrhythmias in CCU patients using a wavelet transform-based methodology. IEEE Trans Biomed Eng 2009; 55:2658-65. [PMID: 18990637 DOI: 10.1109/tbme.2008.923912] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Ventricular tachyarrhythmias are potentially lethal cardiac pathologies and the commonest cause of sudden cardiac death. Efforts to predict the onset of such events are based on feature extraction from the surface ECG. T-wave alternans (TWAs) are considered a marker of abnormal ventricular function that may be associated with ventricular tachycardia (VT) and ventricular fibrillation. A novel TWA detection algorithm utilizing the continuous wavelet transform is described in this paper. Simulated ECGs containing artificial TWA were used to test the algorithm that achieved a sensitivity of 91.40% and a specificity of 94.00%. The algorithm was subsequently used to analyze the ECGs of eight patients prior to the onset of VT. Of these, the algorithm indicated that five patients exhibited TWA prior to the onset of the tachyarrhythmic events, while the remaining three patients did not exhibit identifiable TWA. Healthy individuals were also studied in which one short TWA episode was detected by the algorithm. However, closer visual inspection of the data revealed this to be a likely false positive result.
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Affiliation(s)
- Iñaki Romero
- Department of Medical Physics, German National Institute of Metrology, Berlin D-10587, Germany.
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Watson JN, Addison PS, Uchaipichat N, Shah AS, Grubb NR. Wavelet transform analysis predicts outcome of DC cardioversion for atrial fibrillation patients. Comput Biol Med 2007; 37:517-23. [PMID: 17011542 DOI: 10.1016/j.compbiomed.2006.08.003] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
The aim of this study was to examine whether wavelet transform analysis of the electrocardiogram (ECG) can improve the prediction of the maintenance of sinus rhythm in patients with atrial fibrillation (AF) after external DC cardioversion. We examined a variety of wavelet transform-based statistical markers as potential candidates for the prediction of patient status post-cardioversion. Considering a 'success' as a patient who remains in normal sinus rhythm for one month post cardioversion and 'failure' as a patient who does not, it was shown the proposed non-parametric classification system can achieve 89% specificity at 100% sensitivity using a non-parametric classification method.
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Affiliation(s)
- J N Watson
- CardioDigital Ltd., Elvingston Science Centre, Gladsmuir, East Lothian, EH33 1EH, Edinburgh, Scotland, UK
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Clifton D, Douglas JG, Addison PS, Watson JN. Measurement of respiratory rate from the photoplethysmogram in chest clinic patients. J Clin Monit Comput 2006; 21:55-61. [PMID: 17131084 DOI: 10.1007/s10877-006-9059-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2006] [Accepted: 10/30/2006] [Indexed: 10/23/2022]
Abstract
OBJECTIVE We studied the application of our algorithm for the robust extraction of respiratory information from the pulse oximeter signal acquired from a selection of patients attending the chest clinic. METHODS Photoplethysmograms were obtained from 16 individuals: 13 patients with various conditions in the respiratory ward and three healthy subjects. Wavelet transforms were generated from which respiratory information was extracted to obtain a measure of respiratory rate. This measured rate was compared with the respiratory rate determined by one of a variety of other means (a digital end tidal CO(2) signal, the output from a non-invasive ventilation device, or a switch actuated by the patient or observer.) RESULTS Respiratory rates varied from 6.2 to 35.8 breaths per minute (bpm). The oximeter rate determined through our method matched the marker rate obtained for all patients to within 1 bpm. CONCLUSION The technique allows the measurement of respiratory rate directly from the photoplethysmogram of a pulse oximeter, and leads the way for development of a simple non-invasive combined respiration and saturation monitor useful for patients with all forms of breathlessness.
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Affiliation(s)
- David Clifton
- CardioDigital Ltd, Elvingston Science Centre, Glasdmuir, East Lothian, EH33 1EH, Scotland, UK
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Abstract
BACKGROUND We have developed an automated algorithm to allow the measurement of respiratory rate directly from the photoplethysmogram (pulse oximeter waveform). AIM To test the algorithm's ability to determine respiratory rate in children. METHODS A convenience sample of patients attending a paediatric Accident and Emergency Department was monitored using a purpose-built pulse oximeter and the photoplethysmogram (PPG) recorded. Respiration was also recorded by an observer activating a push-button switch in synchronization with the child's breathing. The switch marker signals were processed to derive a manual respiratory rate that was compared with the wavelet-based oximeter respiratory rate derived from the PPG signal. RESULTS Photoplethysmograms were obtained from 18 children aged 18 mo to 12 y, breathing spontaneously at rates of 17 to 27 breaths per minute. There was close correspondence between the wavelet-based oximeter respiration rate and the manual respiratory rate, with the difference between them being less than one breath per minute in all children. CONCLUSION Our automated algorithm allows the accurate determination of respiratory rate from photoplethysmograms of a heterogeneous group of children. We believe that our automated wavelet-based signal-processing techniques could soon be easily incorporated into current pulse oximetry technology.
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Affiliation(s)
- Paul A Leonard
- Department of Accident and Emergency Medicine, Royal Hospital for Sick Children, Edinburgh, Scotland, UK.
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Shah AS, Addison PS, Watson JN, Uchaipichat N, Grubb NR. P6-49. Heart Rhythm 2006. [DOI: 10.1016/j.hrthm.2006.02.950] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Leonard PA, Douglas JG, Grubb NR, Clifton D, Addison PS, Watson JN. A fully automated algorithm for the determination of respiratory rate from the photoplethysmogram. J Clin Monit Comput 2006; 20:33-6. [PMID: 16532280 DOI: 10.1007/s10877-005-9007-7] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2005] [Accepted: 11/28/2005] [Indexed: 10/24/2022]
Abstract
OBJECTIVE To determine if an automatic algorithm using wavelet analysis techniques can be used to reliably determine respiratory rate from the photoplethysmogram (PPG). METHODS Photoplethysmograms were obtained from 12 spontaneously breathing healthy adult volunteers. Three related wavelet transforms were automatically polled to obtain a measure of respiratory rate. This was compared with a secondary timing signal obtained by asking the volunteers to actuate a small push button switch, held in their right hand, in synchronisation with their respiration. In addition, individual breaths were resolved using the wavelet-method to identify the source of any discrepancies. RESULTS Volunteer respiratory rates varied from 6.56 to 18.89 breaths per minute. Through training of the algorithm it was possible to determine a respiratory rate for all 12 traces acquired during the study. The maximum error between the PPG derived rates and the manually determined rate was found to be 7.9%. CONCLUSION Our technique allows the accurate measurement of respiratory rate from the photoplethysmogram, and leads the way for developing a simple non-invasive combined respiration and saturation monitor.
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Affiliation(s)
- Paul A Leonard
- Department of Accident and Emergency Medicine, The Royal Hospital for Sick Children, Sciennes Rd, Edinburgh EH9 1LF, UK.
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Watson JN, Addison PS, Clegg GR, Steen PA, Robertson CE. Practical issues in the evaluation of methods for the prediction of shock outcome success in out-of-hospital cardiac arrest patients. Resuscitation 2006; 68:51-9. [PMID: 16325328 DOI: 10.1016/j.resuscitation.2005.06.013] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2005] [Accepted: 06/16/2005] [Indexed: 11/28/2022]
Abstract
There is a need for robust, effective predictors of the outcome from shock for out-of-hospital cardiac arrest patients. Such technology would enable the emergency responder to provide a therapy tailored to the patient's needs. Here we report our most recent findings while dwelling intentionally on the rationale behind the decisions taken during system development. Specifically, we illustrate the need for sensible data selection, fully cross-validated results and the care necessary when evaluating system performance. We analyze 878 pre-shock ECG traces, all of at least 10 s duration from 110 patients with cardiac arrest of cardiac aetiology. The continuous wavelet transform was applied to preshock segments of ECG trace. Time-frequency markers are extracted from the transform and a linear threshold derived from a training set to provide high sensitivity prediction of successful defibrillation. These systems are then evaluated on a withheld test set. All experiments are cross-validated. When compared to popular Fourier-based techniques our wavelet transform method, COP (Cardioversion Outcome Predictor), provides a 10-20% improvement in performance with values of 66 +/- 4 specificity at 95 +/- 4 sensitivity, 61 +/- 4 specificity at 97 +/- 2 sensitivity and 56 +/- 1 specificity at 98 +/- 2 sensitivity achieved for datasets limited to 3, 6, and 9 shocks per patient, respectively. Thus, the assessment of the wavelet marker was associated with a high specificity value at or above 95% sensitivity in comparison to previously reported methods. Therefore, COP could provide an optimal index for the identification of patients for whom shocking would be futile, and for whom an alternative therapy could be considered.
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Affiliation(s)
- J N Watson
- CardioDigital Ltd., Elvingston Science Centre, Edinburgh, Scotland, UK.
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Abstract
The wavelet transform has emerged over recent years as a powerful time-frequency analysis and signal coding tool favoured for the interrogation of complex nonstationary signals. Its application to biosignal processing has been at the forefront of these developments where it has been found particularly useful in the study of these, often problematic, signals: none more so than the ECG. In this review, the emerging role of the wavelet transform in the interrogation of the ECG is discussed in detail, where both the continuous and the discrete transform are considered in turn.
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Affiliation(s)
- Paul S Addison
- CardioDigital Ltd, Elvingston Science Centre, East Lothian, UK.
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Abstract
BACKGROUND Children who are unwell often display signs of circulatory compromise. It has been observed that pronounced changes occur in the appearance of the photoplethysmogram (pulse oximeter tracing) in these children. The aim of the study was to discover if wavelet transforms can identify more subtle changes in the photoplethysmogram of children who are unwell. METHODS Photoplethysmograms were obtained from children attending a paediatric accident and emergency department with clinical features suggestive of significant bacterial illness or circulatory compromise. Photoplethysmograms were also obtained from a control group of well children. Wavelet transforms were applied to the traces in an attempt to separate the two groups. RESULTS 20 traces were obtained from unwell children and 12 from controls. Analysis of the entropy of the wavelet transform of the photoplethysmogram allows the differentiation of unwell children from controls (p = 0.00002). CONCLUSIONS Wavelet transform of the photoplethysmogram offers the possibility of a rapid non-invasive method of screening children for significant illness.
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Affiliation(s)
- P Leonard
- Department of Accident and Emergency Medicine, The Royal Hospital for Sick Children, Edinburgh, Scotland.
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Abstract
BACKGROUND Wavelet-based methods of analyzing ECG signals have been used to identify specific features in cardiac arrhythmias. Since some of these features are rate dependent, it is a requirement that they are examined across a range of physiological heart rates. The wavelet transform is a signal analysis tool that can elucidate spectral and temporal information simultaneously from complex signals, including the ECG. The aim of this study was to identify the local frequency characteristics of the ECG using a real-time wavelet scalogram and to study the rate dependence of these features. METHODS We examined the spectral temporal behavior of the local characteristics of the electrocardiogram (ECG) of 10 patients, in whom precise control of heart rate was achieved using right atrial pacing. Temporary reprogramming was used to adjust the paced atrial rate to predetermined values so that a rate-controlled rhythm was produced that closely resembled sinus rhythm. RESULTS Rate-dependent features are seen on time-frequency scalograms. As the rate increases, the temporal spacing of features decrease and the frequency bands shift upward on the plot. Two patients with abnormal atrioventricular conduction demonstrate features of Wenckebach conduction and fusion. CONCLUSIONS Characterization of the rate-dependent features of the ECG in a paced atrial rhythm by wavelet transform techniques has revealed some additional information not readily seen on single lead ECG analysis. This model provides a surrogate for changes that might be expected during rate changes in physiological sinus rhythm. It is envisaged that this method will offer advantages in detecting features of clinical significance that may not be readily seen by existing methods.
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Affiliation(s)
- Martin K Stiles
- Department of Cardiology, Royal Infirmary of Edinburgh, Edinburgh, Scotland, UK.
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Abstract
A wavelet-based method is presented for oxygen saturation measurement using photoplethysmogram signals from a standard pulse oximeter device. The transform moduli of both red and infrared signals are used to derive a novel wavelet ratio surface. Projection of the pulse component onto this surface allows optimal derivation of oxygen saturation.
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Affiliation(s)
- Paul S Addison
- CardioDigital Ltd., Elvingston Science Centre, Glasdmuir, EH33 1EH East Lothian, Scotland, UK.
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Affiliation(s)
- M J Reed
- Emergency Department, Royal Infirmary of Edinburgh, 51 Little France Crescent, Edinburgh EH16 4SA, UK.
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Abstract
BACKGROUND One of the most important limitations of standard pulse oximeters is the inability to detect changes in respiratory rate until oxygenation is affected. This study sought to determine if analysis of the plethysmogram by wavelet transforms would enable the determination of changes in respiratory rate at an earlier stage. METHODS Ten healthy adult volunteers were monitored, breathing at baseline and predetermined respiratory rates, using a standard pulse oximeter. Photo-plethysmograms captured in an attached lap top computer were then analysed using wavelet transforms. RESULTS Determination of baseline respiratory rate and subsequent changes including apnoea were easily identified. COMMENT Wavelet transforms permit the accurate determination of respiratory rate by a standard pulse oximeter.
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Affiliation(s)
- P Leonard
- Department of Accident and Emergency Medicine, The Royal Hospital for Sick Children, Edinburgh, Scotland.
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Abstract
OBJECTIVES To determine if wavelet analysis techniques can be used to reliably identify individual breaths from the photoplethysmogram (PPG). METHODS Photoplethysmograms were obtained from 22 healthy adult volunteers timing their respiration rate in synchronisation with a metronome. A secondary timing signal was obtained by asking the volunteers to actuate a small push button switch, held in their right hand, in synchronisation with their respiration. Each PPG was analyzed using primary wavelet decomposition and two new, related, secondary decompositions to determine the accuracy of individual breath detection. RESULTS The optimal breath capture was obtained by manually polling the three techniques, allowing detection of 466 out of the 472 breaths studied; a detection rate of 98.7% with no false positive breaths detected. CONCLUSION Our technique allows the accurate capture of individual breaths from the photoplethysmogram, and leads the way for developing a simple non-invasive combined respiration and saturation monitor.
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Affiliation(s)
- Paul Leonard
- Department of Accident and Emergency Medicine, The Royal Hospital for Sick Children, Sciennes Rd, Edinburgh, EH9 1LF, Scotland, UK.
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Watson JN, Uchaipichat N, Addison PS, Clegg GR, Robertson CE, Eftestol T, Steen PA. Improved prediction of defibrillation success for out-of-hospital VF cardiac arrest using wavelet transform methods. Resuscitation 2004; 63:269-75. [PMID: 15582761 DOI: 10.1016/j.resuscitation.2004.06.012] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2004] [Accepted: 06/17/2004] [Indexed: 11/22/2022]
Abstract
We report an improved method for the estimation of shock outcome prediction based on novel wavelet transform-based time-frequency methods. Wavelet-based peak frequency, energy, mean frequency, spectral flatness and a new entropy measure were studied to predict shock outcome. Of these, the entropy measure provided optimal results with 60 +/- 6% specificity at 91 +/- 2% sensitivity achieved for the prediction of return of spontaneous circulation (ROSC). These results represent a major improvement in shock prediction in human ventricular fibrillation.
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Affiliation(s)
- James N Watson
- CardioDigital Ltd., Elvingston Science Centre, Edinburgh, Scotland, UK.
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Watson JN, Addison PS, Steen PA, Robertson CE, Clegg GR. Angular velocity: a new method to improve prediction of ventricular fibrillation duration. Resuscitation 2004; 62:122-3. [PMID: 15246595 DOI: 10.1016/j.resuscitation.2004.03.014] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2004] [Accepted: 03/30/2004] [Indexed: 10/26/2022]
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Addison PS, Watson JN, Clegg GR, Steen PA, Robertson CE. Finding coordinated atrial activity during ventricular fibrillation using wavelet decomposition. IEEE Eng Med Biol Mag 2002; 21:58-61, 65. [PMID: 11935988 DOI: 10.1109/51.993194] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
MESH Headings
- Animals
- Atrial Function, Right/physiology
- Death, Sudden, Cardiac/prevention & control
- Diagnosis, Differential
- Electric Stimulation/methods
- Electrocardiography/methods
- Electrocardiography/statistics & numerical data
- Electrophysiologic Techniques, Cardiac/methods
- Heart Arrest, Induced/methods
- Heart Atria/physiopathology
- Humans
- Models, Animal
- Models, Cardiovascular
- Models, Statistical
- Pressure
- Swine
- Tachycardia, Ventricular/diagnosis
- Tachycardia, Ventricular/physiopathology
- Ventricular Fibrillation/diagnosis
- Ventricular Fibrillation/physiopathology
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Affiliation(s)
- Paul S Addison
- Faculty of Engineering and Computing, Nopier University, Edinburgh.
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Addison PS, Watson JN, Clegg GR, Holzer M, Sterz F, Robertson CE. Evaluating arrhythmias in ECG signals using wavelet transforms. IEEE Eng Med Biol Mag 2000; 19:104-9. [PMID: 11016036 DOI: 10.1109/51.870237] [Citation(s) in RCA: 72] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- P S Addison
- Faculty of Engineering and Computing, Napier University, Edinburgh.
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Watson JN, Addison PS, Clegg GR, Holzer M, Sterz F, Robertson CE. A novel wavelet transform based analysis reveals hidden structure in ventricular fibrillation. Resuscitation 2000; 43:121-7. [PMID: 10694172 DOI: 10.1016/s0300-9572(99)00127-6] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
We report a new method of interrogating the surface ECG signal using techniques developed in the field of wavelet transform analysis. Previously unreported structure within the ECG during ventricular fibrillation (VF) is found using a high-resolution decomposition of the signal employing the continuous wavelet transform. We believe that wavelet transform methods could lead to the development of powerful tools for use in the resuscitation of patients with cardiac arrest.
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Affiliation(s)
- J N Watson
- Faculty of Engineering, Napier University, Edinburgh, UK
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Abstract
The mathematical models used to describe the dynamical behavior of a group of road vehicles traveling in a single lane without overtaking are known as car-following models. These models are widely used in many commercially available microscopic traffic simulation software packages. They attempt to mimic the interactions between individual vehicles that are traveling sufficiently close together for the behavior of each vehicle to be dependent upon the motion of the vehicle immediately in front. In this paper we modify the traditional car-following model by adding a new nonlinear term to take account of the driver attempting to achieve a certain desired intervehicle separation distance as well as the traditional aim of matching the velocity of the vehicle ahead. Numerical solution of the resulting coupled system of nonlinear differential equations is used to analyze the stability of the equilibrium solution to a periodic perturbation. For certain parameter values chaotic oscillations are generated, consisting of a broad spectrum of frequency components. Such chaotic motion produces extremely complicated dynamical behavior that has an inherent lack of predictability associated with it. The results of simulating over a range of parameter values are presented and, where it is present, the degree of chaos is estimated. (c) 1998 American Institute of Physics.
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Affiliation(s)
- Paul S. Addison
- Department of Civil and Transportation Engineering, Napier University Edinburgh, Merchiston Campus, 10 Colinton Road, Edinburgh EH10 5DT, Scotland, United Kingdom
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