On Piterbarg's max-discretisation theorem for homogeneous Gaussian random fields

On Piterbarg's max-discretisation theorem for homogeneous Gaussian random fields

JOURNAL OF VASCULAR SURGERY Volume 61, Number 6 4. Mills JL Sr, Conte MS, Armstrong DG, Pomposelli FB, Schanzer A, Sidawy AN, et al. The Society for ...

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4. Mills JL Sr, Conte MS, Armstrong DG, Pomposelli FB, Schanzer A, Sidawy AN, et al. The Society for Vascular Surgery Lower Extremity Threatened Limb Classification System: risk stratification based on wound, ischemia, and foot infection (WIfI). J Vasc Surg 2014;59:220-2. 5. Montero-Baker M, Schmidt A, Bräunlich S, Ulrich M, Thieme M, Biamino G, et al. Retrograde approach for complex popliteal and tibioperoneal occlusions. J Endovasc Ther 2008;15:594-604. 6. Bosanquet DC, Glasbey JC, Williams IM, Twine CP. Systematic review and meta-analysis of direct versus indirect angiosomal revascularisation of infrapopliteal arteries. Eur J Vasc Endovasc Surg 2014;48:88-97. 7. Rumsey WL, Vanderkooi JM, Wilson DF. Imaging of phosphorescence: a novel method for measuring oxygen distribution in perfused tissue. Science 1988;241:1649-51. 8. Lo LW, Koch CJ, Wilson DF. Calibration of oxygen-dependent quenching of the phosphorescence of pd-meso-tetra (4-carboxyphenyl) porphine: a phosphor with general application for measuring oxygen concentration in biological systems. Anal Biochem 1996;236:153-60. 9. Vinogradov SA, Grosul P, Rozhkov V, Dunphy I, Shuman L, Dugan BW, et al. Oxygen distributions in tissue measured by phosphorescence quenching. Adv Exp Med Biol 2003;510:181-5. 10. Wilson DF, Vinogradov SA, Grosul P, Sund N, Vacarezza MN, Bennett J. Imaging oxygen pressure in the rodent retina by phosphorescence lifetime. Adv Exp Med Biol 2006;578:119-24. 11. Montheard JP, Chatzopoulos M, Chappard D. 2-hydroxyethyl methacrylate (HEMA): chemical properties and applications in biomedical fields. J Macromol Sci Rev 1992;32:1-34. 12. Helton KL, Ratner BD, Wisniewski NA. Biomechanics of the sensortissue interface-effects of motion, pressure, and design on sensor performance and the foreign body response-part I: theoretical framework. J Diabetes Sci Technol 2011;5:632-46. 13. Klueh U, Liu Z, Feldman B, Henning TP, Cho B, Ouyang T, et al. Metabolic biofouling of glucose sensors in vivo: role of tissue microhemorrhages. J Diabetes Sci Technol 2011;5:583-95. 14. Lakowicz JR. Introduction to fluorescence. Principles of fluorescence spectroscopy. Berlin: Springer; 1999. p. 1-23. 15. Wood SN. Low-rank scale-invariant tensor product smooths for generalized additive mixed models. Biometrics 2006;62:1025-36. 16. Sinaasappel M, Ince C. Calibration of Pd-porphyrin phosphorescence for oxygen concentration measurements in vivo. J Appl Physiol (1985) 1996;81:2297-303.

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17. Box GE, Jenkins GM, Reinsel GC. “Model identification”. Time series analysis: forecasting and control. 4th edition. Hoboken, NJ: John Wiley and Sons, Inc; 2008. p. 195-230. 18. Ljung GM, Box GE. On a measure of lack of fit in time series models. Biometrika 1978;65:297-303. 19. Said SE, Dickey DA. Testing for unit roots in autoregressivemoving average models of unknown order. Biometrika 1984;71: 599-607. 20. Kariya T, Kurata H. “Generalized least squares estimators”. Generalized least squares. Chichester, UK: John Wiley & Sons; 2004. p. 25-66. 21. Breton M, Kovatchev B. Analysis, modeling, and simulation of the accuracy of continuous glucose sensors. J Diabetes Sci Technol 2008;4: 4-14. 22. Mills J. Intraoperative fluorescence vascular angiography: a case report. J Diabetes Sci Technol 2012;6:204-8. 23. Comerota AJ, Throm RC, Kelly P, Jaff M. Tissue (muscle) oxygen saturation (StO2): a new measure of symptomatic lower-extremity arterial disease. J Vasc Surg 2003;38:724-9. 24. Cheatle TR, Potter LA, Cope M, Delpy DT. Near-infrared spectroscopy in peripheral vascular disease. Br J Surg 1991;78:405-8. 25. Keller A. Noninvasive tissue oximetry for flap monitoring: an initial study. J Reconstr Microsurg 2007;23:189-97. 26. Caselli A, Latini V, Lapenna A, Di Carlo S. Transcutaneous oxygen tension monitoring after successful revascularization in diabetic patients with ischaemic foot ulcers. Diabet Med 2005;22:460-5. 27. Braun JD, Rajguru P, Armstrong DG, Mills JL. Indocyanine green angiographic criteria using ingress and ingress rate to detect SVS lower extremity threatened limb classification (WIfI) grade 3 ischemia. J Vasc Surg 2014;60:538. 28. Arsenault KA, Al-Otaibi A, Devereaux PJ, Thorlund K, Tittley JG, Whitlock RP. The use of transcutaneous oximetry to predict healing complications of lower limb amputations: a systematic review and metaanalysis. Eur J Vasc Endovasc Surg 2012;43:329-36.

Submitted Sep 29, 2014; accepted Dec 20, 2014.

Additional material for this article may be found online at www.jvascsurg.org.

DISCUSSION Dr Dennis F. Bandyk (San Diego, Calif). Does knowledge of tissue oxygenation enhance clinical decision-making in caring for the patient with critical limb ischemia (CLI)? This clinical question was the basis for the presented pilot study that utilized an implantable oxygen sensor to measure tissue oxygen concentration in the foot during and following an endovascular procedure. The authors implanted a non-FDA approved device in 10 patients with CLI to evaluate the safety and feasibility of implantable oxygen sensors to monitor tissue oxygenation changes prior to, during, and following an endovascular revascularization procedure. Measurements were continued for 28 days, although this sensor can be used for more than a year to monitor tissue oxygen levels. Implantation of the sensor was well tolerated by the subjects, no major adverse events occurred at the implant sites, and surgical site infections developed. The sensors functioned appropriately in 7 of the 10 patients during the 28-day study period, and changes in tissue oxygen concentration were observed. In the index limb studied, increases in oxygen concentration occurred with revascularization which continued to rise during the subsequent week. I have three questions to the authors: 1. Seven of 10 patients studied had ischemic ulcers and the sensor was place in the angiosome appropriate to the ulcer location. Did that sensor demonstrate an increase in tissue

oxygenation, when was increased was measured, and did values correlate with ulcer healing? 2. The authors performed other physiologic testing, including ankle-brachial index (ABI) and pulse oximetry. Was an increase in tissue oxygenation demonstrated in all limbs having an endovascular intervention and did the increase correlate with other physiologic testing parameters? 3. Do the authors believe the clinical role for the implantable oxygen sensor is to monitor the procedure or demonstrate adequacy of tissue perfusion for healing when this technology is submitted as a pivotal study to the FDA for use in human approval? Dr Miguel F. Montero-Baker. We appreciate Dr Bandyk’s comments and questions regarding our initial study of implantable oxygen sensors in patients with limb-threatening ischemia. As to the responses to each question, here are our answers: 1. As explained in the manuscript, there was a trend to more responsiveness in more distal interventions than proximal interventions. It’s true that all three angiosomes were attempted to be evaluated, but the final amount of data was small to create differences among angiosomes treated. An in-depth analysis of the presence or absence of the pedal arch was not performed in this initial study. A smaller percent

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of the patients had more proximal (iliofemoral) disease and the rest had popliteal and tibial disease. Our intention with a larger cohort would be to look at the mentioned angle: complete or incomplete arch, direct vs indirect angiosome revascularization, presence of choke-vessel disease, effect of chronic kidney disease, etc. 2. In Table I of our manuscript, you will find the mean ABI of the group preoperatively. In response to your comment, we have decided to add the postoperative mean ABI for the group. We don’t find of great value to have an additional table with all specific details on each patient’s ABI since we only have available noninvasive data for four of the 10 patients.


This was not a required data point in our study proposal, since this is a first-in-man study to determine safety and feasibility. 3. The ‘Si Se Puede’ first-in-man study has shown that the MOXY sensor appears to be a safe and effective tool to measure tissue oxygen concentrations in real-time in patients with limb-threatening ischemia during the perioperative period of planned revascularization procedures. The study results show that use of these sensors merits further testing to determine its potential impact during on-table clinical decision making and moreover long-term follow up with the ultimate goal of improved wound healing and limb salvage rates.