| 1. |
- Cirillo, Marco Domenico, et al.
(författare)
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Improving burn depth assessment for pediatric scalds by AI based on semantic segmentation of polarized light photography images
- 2021
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Ingår i: Burns. - : Elsevier. - 0305-4179 .- 1879-1409. ; 47:7, s. 1586-1593
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Tidskriftsartikel (refereegranskat)abstract
- This paper illustrates the efficacy of an artificial intelligence (AI) (a convolutional neural network, based on the U-Net), for the burn-depth assessment using semantic segmentation of polarized high-performance light camera images of burn wounds. The proposed method is evaluated for paediatric scald injuries to differentiate four burn wound depths: superficial partial-thickness (healing in 0–7 days), superficial to intermediate partial-thickness (healing in 8–13 days), intermediate to deep partial-thickness (healing in 14–20 days), deep partial-thickness (healing after 21 days) and full-thickness burns, based on observed healing time.In total 100 burn images were acquired. Seventeen images contained all 4 burn depths and were used to train the network. Leave-one-out cross-validation reports were generated and an accuracy and dice coefficient average of almost 97% was then obtained. After that, the remaining 83 burn-wound images were evaluated using the different network during the cross-validation, achieving an accuracy and dice coefficient, both on average 92%.This technique offers an interesting new automated alternative for clinical decision support to assess and localize burn-depths in 2D digital images. Further training and improvement of the underlying algorithm by e.g., more images, seems feasible and thus promising for the future.
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| 2. |
- Cirillo, Marco Domenico, et al.
(författare)
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Tensor Decomposition for Colour Image Segmentation of Burn Wounds
- 2019
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Ingår i: Scientific Reports. - : NATURE PUBLISHING GROUP. - 2045-2322. ; 9
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Tidskriftsartikel (refereegranskat)abstract
- Research in burns has been a continuing demand over the past few decades, and important advancements are still needed to facilitate more effective patient stabilization and reduce mortality rate. Burn wound assessment, which is an important task for surgical management, largely depends on the accuracy of burn area and burn depth estimates. Automated quantification of these burn parameters plays an essential role for reducing these estimate errors conventionally carried out by clinicians. The task for automated burn area calculation is known as image segmentation. In this paper, a new segmentation method for burn wound images is proposed. The proposed methods utilizes a method of tensor decomposition of colour images, based on which effective texture features can be extracted for classification. Experimental results showed that the proposed method outperforms other methods not only in terms of segmentation accuracy but also computational speed.
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| 3. |
- Cirillo, Marco Domenico, et al.
(författare)
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Time-Independent Prediction of Burn Depth using Deep Convolutional Neural Networks
- 2019
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Ingår i: Journal of Burn Care & Research. - : Oxford University Press. - 1559-047X .- 1559-0488. ; 40:6, s. 857-863
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Tidskriftsartikel (refereegranskat)abstract
- We present in this paper the application of deep convolutional neural networks, which are a state-of-the-art artificial intelligence (AI) approach in machine learning, for automated time-independent prediction of burn depth. Colour images of four types of burn depth injured in first few days, including normal skin and background, acquired by a TiVi camera were trained and tested with four pre-trained deep convolutional neural networks: VGG-16, GoogleNet, ResNet-50, and ResNet-101. In the end, the best 10-fold cross-validation results obtained from ResNet- 101 with an average, minimum, and maximum accuracy are 81.66%, 72.06% and 88.06%, respectively; and the average accuracy, sensitivity and specificity for the four different types of burn depth are 90.54%, 74.35% and 94.25%, respectively. The accuracy was compared to the clinical diagnosis obtained after the wound had healed. Hence, application of AI is very promising for prediction of burn depth and therefore can be a useful tool to help in guiding clinical decision and initial treatment of burn wounds.
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| 4. |
- Elawa, Sherif, et al.
(författare)
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Microcirculatory changes in the skin after postmastectomy radiotherapy in women with breast cancer
- 2024
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Ingår i: Scientific Reports. - : Nature Publishing Group. - 2045-2322. ; 14:1
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Tidskriftsartikel (refereegranskat)abstract
- Postmastectomy radiotherapy (PMRT) increases the risk for complications after breast reconstruction. The pathophysiological mechanism underlying this increased risk is not completely understood. The aim of this study was to examine if there is a relationship between PMRT and microvascular perfusion in the skin directly after, and at 2 and 6 months after PMRT and to assess if there is impaired responsiveness to a topically applied vasodilator (Methyl nicotinate-MN) after PMRT. Skin microvascular responses after PMRT were measured on two sites in the irradiated chest wall of 22 women before, immediately after, and at 2 and 6 months after unilateral PMRT with the contralateral breast as a control. A significant increase in basal skin perfusion was observed in the irradiated chest wall immediately after RT (p < 0.0001). At 2 and 6 months after RT, there was no longer a difference in basal skin perfusion compared to the contralateral breast and compared to baseline. Similarly, the blood flow response in the skin after application of MN was stronger immediately after RT compared to before RT (p < 0.0001), but there was no difference at later time points. These results indicate that the increased risk for complications after surgical procedures are not directly related to changes in skin perfusion and microvascular responsiveness observed after postmastectomy RT.
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| 5. |
- Elawa, Sherif, et al.
(författare)
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Skin blood flow response to topically applied methyl nicotinate: Possible mechanisms
- 2020
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Ingår i: Skin research and technology. - : WILEY. - 0909-752X .- 1600-0846. ; 26:3, s. 343-348
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Tidskriftsartikel (refereegranskat)abstract
- Background Methyl nicotinate (MN) induces a local cutaneous erythema in the skin and may be valuable as a local provocation in the assessment of microcirculation and skin viability. The mechanisms through which MN mediates its vascular effect are not fully known. The aim of this study was to characterize the vasodilatory effects of topically applied MN and to study the involvement of nitric oxide (NO), local sensory nerves, and prostaglandin-mediated pathways. Methods MN was applied on the skin of healthy subjects in which NO-mediated (L-NMMA), nerve-mediated (lidocaine/prilocaine), and cyclooxygenase-mediated (NSAID) pathways were selectively inhibited. Microvascular responses in the skin were measured using laser speckle contrast imaging (LSCI). Results NSAID reduced the MN-induced perfusion increase with 82% (P < .01), whereas lidocaine/prilocaine reduced it with 32% (P < .01). L-NMMA did not affect the microvascular response to MN. Conclusion The prostaglandin pathway and local sensory nerves are involved in the vasodilatory actions of MN in the skin.
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| 6. |
- Elawa, Sherif, et al.
(författare)
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The microvascular response in the skin to topical application of methyl nicotinate : Effect of concentration and variation between skin sites
- 2019
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Ingår i: Microvascular Research. - : Academic Press. - 0026-2862 .- 1095-9319. ; 124, s. 54-60
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Tidskriftsartikel (refereegranskat)abstract
- BackgroundMethyl nicotinate (MN) induces a local cutaneous erythema in the skin and may be used as a local provocation in the assessment of microcirculation and skin viability. The aims were to measure the effects of increasing doses of MN, to find the concentration that yields the most reproducible effect from day to day and between sites, and to study the variation between skin sites.MethodsMicrovascular responses to topically applied MN at different concentrations were measured in 12 subjects on separate days and on contralateral sides, using laserspeckle contrast imaging (LSCI). MN effects were measured in four different body sites.ResultsAt 20 mmol/L, the response to MN was most reproducible day-to-day and site-to-site, and resulted in a plateau response between 5 and 20 min after application.The skin region of the lower back had a lower perfusion value compared to the epigastric region (p = 0.007). When responses were compared to nearby, unprovoked areas, a significantly larger increase in perfusion was seen in the forearm, compared to all other anatomical sites (p < 0.03).ConclusionA concentration of 20 mmol/L MN generated the most reproducible microvascular response in the skin. The response varies between different body sites.
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| 7. |
- Elmasry, Moustafa, 1981-, et al.
(författare)
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Laser speckle contrast imaging in children with scalds : Its influence on timing of intervention, duration of healing and care, and costs
- 2019
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Ingår i: Burns. - : Elsevier. - 0305-4179 .- 1879-1409. ; 45:4, s. 798-804
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Tidskriftsartikel (refereegranskat)abstract
- BackgroundScalds are the most common type of burn injury in children, and the initial evaluation of burn depth is a problem. Early identification of deep dermal areas that need excision and grafting would save unnecessary visits and stays in hospital. Laser speckle contrast imaging (LSCI) shows promise for the evaluation of this type of burn. The aim of this study was to find out whether perfusion measured with LSCI has an influence on the decision for operation, duration of healing and care period, and costs, in children with scalds.MethodsWe studied a group of children with scalds whose wounds were evaluated with LSCI on day 3–4 after injury during the period 2012–2015. Regression (adjustment for percentage total body surface area burned (TBSA%), age, and sex) was used to analyse the significance of associations between degree of perfusion and clinical outcome.ResultsWe studied 33 children with a mean TBSA% of 6.0 (95% CI 4.4–7.7)%. Lower perfusion values were associated with operation (area under the receiver-operating characteristic curve 0.86, 95% CI 0.73–1.00). The perfusion cut-off with 100% specificity for not undergoing an operation was ≥191 PU units (66.7% sensitivity and 72.7% accurately classified). Multivariable analyses showed that perfusion was independently associated with duration of healing and care period.ConclusionLower perfusion values, as measured with LSCI, are associated with longer healing time and longer care period. By earlier identification of burns that will be operated, perfusion measurements may further decrease the duration of care of burns in children with scalds.
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| 8. |
- Mirdell, Robin, et al.
(författare)
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Accuracy of laser speckle contrast imaging in the assessment of pediatric scald wounds
- 2018
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Ingår i: Burns. - : ELSEVIER SCI LTD. - 0305-4179 .- 1879-1409. ; 44:1, s. 90-98
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Tidskriftsartikel (refereegranskat)abstract
- Background: Changes in microvascular perfusion in scalds in children during the first four days, measured with laser speckle contrast imaging (LSCI), are related to the time to healing and need for surgical intervention. The aim of this study was to determine the accuracy (sensitivity and specificity) of LSCI on different days after injury in the prediction of healing outcome and if the accuracy can be improved by combining an early and a late measurement. Also, the accuracy of LSCI was compared with that of clinical assessment. Methods: Perfusion was measured between 0-24h and between 72-96h using LSCI in 45 children with scalds. On the same occasions, burn surgeons assessed the burns as healing amp;lt; 14days or healing amp;gt; 14days/surgery. Receiver operating characteristic (ROC) curves were constructed for the early and late measurement and for the double measurement (DM) using two different methods. Results: Sensitivity and specificity were 92.3% (95% CI: 64.0-99.8%) and 78.3% (95% CI: 69.985.3%) between 0-24h, 100% (95% CI: 84.6-100%) and 90.4% (95% CI: 83.8-94.9%) between 72-96h, and was 100% (95% CI: 59.0-100%) and 100% (95% CI: 95.1-100%) when combining the two measurements into a modified perfusion trend. Clinical assessment had an accuracy of 67%, Cohens k=0.23. Conclusion: The perfusion in scalds between 72-96h after injury, as measured using LSCI, is highly predictive of healing outcome in scalds when measured. The predictive value can be further improved by incorporating an early perfusion measurement within 24h after injury. (C) 2017 Elsevier Ltd and ISBI. All rights reserved.
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| 9. |
- Mirdell, Robin, 1989-
(författare)
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Blood Flow Dynamics in Burns
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Objectives:Burns of intermediate thickness are hard to evaluate clinically. This often leads to unnecessary delays of up to 14 days before a surgical decision can be made. To counter this, several objective methods have been developed to determine the healing potential of the wound. Over the years, measurement of perfusion has proven to be the most successful method for evaluation of healing potential. Laser Doppler imaging (LDI) is currently the most used method and can determine surgical need 2 days after injury with an accuracy >90%. There are however emerging techniques like laser speckle contrast imaging (LSCI), which also measure perfusion. LSCI have several advantages over LDI and is easier to use. LSCI can also investigate aspects of the microcirculation, previously not possible with LDI. The aim of this thesis was to investigate LSCI’s ability to evaluate surgical need in burns of indeterminate partial-thickness. The first objective was to investigate the dynamics of perfusion the first 14 days after injury. The purpose was to find the optimal time-window for perfusion measurements. The next goal was to determine the accuracy of different perfusion cut-offs. In this second study, the benefit of a subsequent measurement was also investigated. After this, interobserver variation between different profession groups was studied. Both the agreement of perfusion measurements and observer assessments were evaluated. Finally, cardiac vasomotion in combination with perfusion (pulsatility) was investigated as a method to determine surgical need <48 hours after injury. Methods:Perfusion was measured in a total of 77 patients at the Department of Plastic Surgery, Hand Surgery and Burns at Linköping University Hospital, Sweden. Most of these patients were children and the most common type of burn was scalds. A laser speckle contrast imager (PeriCam PSI System, Perimed AB, Järfälla, Sweden) was used to measure perfusion. Results: In the first paper we showed a clear relation between perfusion dynamics and the healing potential of the wound. The changes in perfusion were largest the first 5 days after injury, why this time interval was selected for subsequent papers. Perfusion measurements done day 3-4 after injury could predict surgical need with a sensitivity of 100% (95% CI: 83.9-100%) and a specificity of 90.4% (95% CI: 83.8-94.9%). If two measurements were used, <24 hours and 3-4 days after injury, the accuracy was 100%. Furthermore, we found that different observers could consistently predict perfusion, while there was a large variation in their clinical assessments. This was not improved by extensive burn experience. Finally, pulsatility could be used to predict surgical need the same day as the injury occurred with a sensitivity of 100% (95% CI: 88.1-100%) and a specificity of 98.8% (95% CI: 95.7- 99.9%). Conclusions: LSCI is a promising method for evaluation of burns and provides several benefits over LDI. The surgical need of burns can be determined mere hours after injury when pulsatility is measured. However, the benefits of early scald diagnostics in children with LSCI need to be evaluated in a prospective study before the method is ready for routine clinical use.
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| 10. |
- Mirdell, Robin, 1989-, et al.
(författare)
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Data on microcirculatory perfusion dips in the resting nail bed
- 2018
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Ingår i: Data in Brief. - : Elsevier. - 2352-3409. ; 21, s. 1232-1235
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Tidskriftsartikel (refereegranskat)abstract
- This article contains the raw data from the article entitled: "The presence of synchronized perfusion dips in the microcirculation of the resting nail bed" Mirdell et al. (in press). A laser speckle contrast imager (LSCI) was used to make a total of 21 recordings of the perfusion in the resting nail bed of 10 healthy test subjects. The first 10 recordings were acquired after 5?min of acclimatization. An additional 10 recordings were acquired in the same test subjects, after 20?min of acclimatization. In the last recording, a digital nerve block was applied to the left dig III. The data show the presence of highly irregular perfusion variations, a phenomenon we like to call perfusion dips. The data also show how the perfusion dips can be abolished through a digital nerve block. An algorithm for the quantification of the perfusion dips is included in the data.
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| 11. |
- Mirdell, Robin, et al.
(författare)
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Interobserver reliability of laser speckle contrast imaging in the assessment of burns
- 2019
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Ingår i: Burns. - : ELSEVIER SCI LTD. - 0305-4179 .- 1879-1409. ; 45:6, s. 1325-1335
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Tidskriftsartikel (refereegranskat)abstract
- Objectives: Laser speckle contrast imaging (LSCI) is an emerging technique for the assessment of burns in humans and interobserver differences have not been studied. The aim of this study was to compare assessments of perfusion images by different professional groups regarding (i) perfusion values and (ii) burn depth assessment. Methods: Twelve observers without LSCI experience were included. The observers were evenly recruited from three professional groups: plastic surgeons with experience in assessing burns, nurses with experience in treating burns, and junior doctors with limited experience of burns. Ten cases were included. Each case consisted of one digital photo of the burn with a pre-marked region of interest (ROI) and two unmarked perfusion images of the same area. The first and the second perfusion image was from 24h and 72-96h after injury, respectively. The perfusion values from both perfusion images were used to generate a LSCI recommendation based on the perfusion trend (the derivative between the two perfusion values). As a last step, each observer was asked to estimate the burn depth using their clinical experience and all available information. Intraclass correlation (ICC) was calculated between the different professional groups and among all observers. Results: Perfusion values and perfusion trends between all observers had an ICC of 0.96 (95% CI 0.91-0.99). Burn depth assessment by all observers yielded an ICC of 0.53 (95% CI: 0.31-0.80) and an accuracy of 0.53 (weighted kappa). LSCI recommendations generated by all observers had an ICC of 0.95 (95% CI: 0.90-0.99). Conclusion: Observers can reliably identify the same ROI, which results in observer-independent perfusion measurements, irrespective of burn experience. Extensive burn experience did not further improve burn depth assessment. The LSCI recommendation was more accurate in all professional groups. Introducing LSCI measurements would be likely improve early assessment of burns. (C) 2019 Elsevier Ltd and ISBI. All rights reserved.
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| 12. |
- Mirdell, Robin, et al.
(författare)
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Microvascular blood flow in scalds in children and its relation to duration of wound healing: A study using laser speckle contrast imaging
- 2016
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Ingår i: Burns. - : ELSEVIER SCI LTD. - 0305-4179 .- 1879-1409. ; 42:3, s. 648-654
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Tidskriftsartikel (refereegranskat)abstract
- Background: Microvascular perfusion changes in scalds in children during the first weeks after injury is related to the outcome of healing, and measurements of perfusion, based on laser Doppler imaging, have been used successfully to predict the need for excision and grafting. However, the day-to-day changes in perfusion during the first weeks after injury have not to our knowledge been studied in detail. The aim of this study, based on a conservative treatment model where excision and grafting decisions were delayed to day 14 after injury, was to measure changes in perfusion in scalds using laser speckle contrast imaging (LSCI) during the first three weeks after injury. Methods: We measured perfusion with LSCI in 34 patients at regular intervals between 6 h after injury until complete reepithelialization or surgery. Duration of healing was defined as the time to complete reepithelialization. Results: Less perfusion, between 6 and 96 h after injury, was associated with longer duration of healing with the strongest association occurring between 72 and 96 h. Burns that healed within 14 days had relatively high initial perfusion, followed by a peak and subsequent slow decrease. Both the maximum perfusion and the time-to-peak were dependent on the severity of the burn. Burns that needed excision and grafting had less initial perfusion and a gradual reduction over time. Conclusion: The perfusion in scalds in children shows characteristic patterns during the first weeks after injury depending on the duration of wound healing, the greatest difference between wounds of different severity being on the 4th day. Perfusion should therefore preferably be measured on the fourth day if it is to be used in the assessment of burn depth. (c) 2015 Elsevier Ltd and ISBI. All rights reserved.
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| 13. |
- Mirdell, Robin, et al.
(författare)
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The presence of synchronized perfusion dips in the microcirculation of the resting nail bed
- 2019
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Ingår i: Microvascular Research. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0026-2862 .- 1095-9319. ; 121, s. 71-81
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Tidskriftsartikel (refereegranskat)abstract
- Objectives: Laser speckle contrast imaging (LSCI) has seen limited use in the study of perfusion dynamics such as vasomotion. The aim of this study was to investigate the effects of a prolonged seated position on perfusion dynamics in the nail bed using LSCI. Methods: Perfusion was recorded in digits II to IV bilaterally for 20 min during two separate sessions in ten healthy volunteers. The acclimatization period was 5 min for the 1st session and 20 min for the 2nd. Perfusion variability and the presence of recurring perfusion dips were analyzed. A digital nerve block was done to verify suspected nervous origin of phenomenon. Results: Synchronized phases of vasoconstriction were observed in all subjects with perfusion dips in all digits bilaterally and simultaneously. Application of a digital nerve block abolished perfusion dips. The frequency of this phenomenon increased by 25.0% (95% CI: 1.6 to 49.2%) in the left-hand digits after a prolonged seated position. Perfusion variability increased by 11.6% (95% CI: 2.6 to 20.3%) in the digits of the left hand. Perfusion changes in right-hand digits did not significantly increase. During the 1st session, temperature increased by 2.7 degrees C (1.1 to 4.2) while it decreased by 1.3 degrees C (0.2 to 2.4) during the 2nd session. Conclusion: The observed perfusion dips are of a centrally mediated nervous origin but are also affected by local factors. They are affected by seating duration and differ between left and right hands, likely because of local micro perfusion dips. This phenomenon seems related to digital thermoregulation.
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| 14. |
- Mirdell, Robin, et al.
(författare)
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Using blood flow pulsatility to improve the accuracy of laser speckle contrast imaging in the assessment of burns
- 2020
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Ingår i: Burns. - : ELSEVIER SCI LTD. - 0305-4179 .- 1879-1409. ; 46:6, s. 1398-1406
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Tidskriftsartikel (refereegranskat)abstract
- Objectives: Measurement of perfusion is an establishedmethod to evaluate the depth of burns. However, high accuracy is only achievable >48 h after injury. The aim of the study was to investigate if measurement of blood flow pulsatility, combined with perfusion measurement, can improve early assessment of burn depth using laser speckle contrast imaging (LSCI). Methods: Perfusion and pulsatility were measured with LSCI in 187 regions of interest in 32 patients, between 0 and 5 days after injury. The reproducibility of pulsatility was tested for recording durations between 1 and 12 s. The most reproducible duration was chosen, and receiver operator characteristics were created to find suitable pulsatility cut-offs to predict surgical need. Results: A measurement duration of 8 s resulted in a good reproducibility of the pulsatility (% CV: 15.9%). Longer measurement durations resulted in a small improvement of the accuracy of the assessment. A pulsatility of <1.45 (Perfusion Units)(2) on day 0-2 after injury predicted surgical need with a sensitivity of 100% (95% CI: 83.2-100%), specificity of 100% (95% CI: 95.2-100%), a positive predictive value of 100%, and a negative predictive value of 100%. Pulsatility was not significantly different when comparing measurements done day 0-2 today 3-5. Perfusion was however significantly higher day 3-5 compared today 0-2 for wound shealing with in 3 weeks. Conclusion: Measurement of pulsatility improves the accuracy of the assessment of burns with LSCI and makes it possible to predict the need for surgery during day 0-2 after injury with a high accuracy. (C) 2020 Elsevier Ltd and ISBI. All rights reserved.
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| 15. |
- Pham, Tuan, et al.
(författare)
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Automated VSS-based Burn Scar Assessment using Combined Texture and Color Features of Digital Images in Error-Correcting Output Coding
- 2017
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Ingår i: Scientific Reports. - : Nature Publishing Group. - 2045-2322. ; 7
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Tidskriftsartikel (refereegranskat)abstract
- Assessment of burn scars is an important study in both medical research and clinical settings because it can help determine response to burn treatment and plan optimal surgical procedures. Scar rating has been performed using both subjective observations and objective measuring devices. However, there is still a lack of consensus with respect to the accuracy, reproducibility, and feasibility of the current methods. Computerized scar assessment appears to have potential for meeting such requirements but has been rarely found in literature. In this paper an image analysis and pattern classifcation approach for automating burn scar rating based on the Vancouver Scar Scale (VSS) was developed. Using the image data of pediatric patients, a rating accuracy of 85% was obtained, while 92% and 98% were achieved for the tolerances of one VSS score and two VSS scores, respectively. The experimental results suggest that the proposed approach is very promising as a tool for clinical burn scar assessment that is reproducible and cost-efective.
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| 16. |
- Zötterman, Johan, et al.
(författare)
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Methodological concerns with laser speckle contrast imaging in clinical evaluation of microcirculation
- 2017
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Ingår i: PLOS ONE. - : PUBLIC LIBRARY SCIENCE. - 1932-6203. ; 12:3
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Tidskriftsartikel (refereegranskat)abstract
- Background Laser Speckle Contrast Imaging (LSCI) is a non-invasive and fast technique for measuring microvascular blood flow that recently has found clinical use for burn assessment and evaluation of flaps. Tissue motion caused by for example breathing or patient movements may however affect the measurements in these clinical applications, as may distance between the camera and the skin and tissue curvature. Therefore, the aims of this study were to investigate the effect of frame rate, number of frames/image, movement of the tissue, measuring distance and tissue curvature on the measured perfusion. Methods Methyl nicotinate-induced vasodilation in the forearm skin was measured using LSCI during controlled motion at different speeds, using different combinations of frame rate and number of frames/image, and at varying camera angles and distances. Experiments were made on healthy volunteers and on a cloth soaked in a colloidal suspension of polystyrene microspheres. Results Measured perfusion increased with tissue motion speed. The relation was independent of the absolute perfusion in the skin and of frame rate and number of frames/image. The measured perfusion decreased with increasing angles (16% at 60, p = 0.01). Measured perfusion did not vary significantly between measurement distances from 15 to 40 cm (p = 0.77, %CV 0.9%). Conclusion Tissue motion increases and measurement angles beyond 45 decrease the measured perfusion in LSCI. These findings have to be taken into account when LSCI is used to assess moving or curved tissue surfaces, which is common in clinical applications.
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