Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points.

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.

A procedure for determining subject-specific pulse oxygen saturation response.

The oxyhemoglobin dissociation curve describes the relationship between the partial pressure of oxygen and the percent of hemoglobin saturated with oxygen and varies with chemical and physical factors that differ for every patient. If variability could be determined, patient-specific oxygen therapy could be administered. We have developed a procedure for characterizing variations in the oxygen dissociation curve. The purpose of this study was to validate this procedure in surgical patients. The procedure uses an automated system to alter oxygen therapy during surgery, within safe operational levels, and fit to Hill's equation non-invasive measurements of end-tidal oxygen and peripheral pulse oxygen saturation. The best-fit parameters for the Hill equation, estimated by iterative least squares, provide an apparent dissociation curve, meaningful of the patient-specific pulse oximeter response. Thirty-nine patients participated in this study. Using patient-specific parameter values increases correlation when compared with standard values. The procedure improved the model fit of patient saturation values significantly in 19 patients. This paper has demonstrated a procedure for determining patient-specific pulse oximeter response. This procedure determined best-fit parameters resulting in a significantly improved fit when compared with standard values. These best-fit parameters increased the coefficient of determination R2 in all cases. Graphical Abstract This patient-specific procedure improves fit significantly compared to standard estimates.

Comparing Nasal End-Tidal Carbon Dioxide Measurement Variation and Agreement While Delivering Pulsed and Continuous Flow Oxygen in Volunteers and Patients.

BACKGROUND: Supplemental oxygen is administered during procedural sedation to prevent hypoxemia. Continuous flow oxygen, the most widespread method, is generally adequate but distorts capnography. Pulsed flow oxygen is novel and ideally will not distort capnography. We have developed a prototype oxygen administration system designed to try to facilitate end-tidal carbon dioxide (ETCO2) measurement. We conducted a volunteer study (ClinicalTrials.gov, NCT02886312) to determine how much nasal ETCO2 measurements vary with oxygen flow rate. We also conducted a clinical study (NCT02962570) to determine the median difference and limits of agreement between ETCO2 measurements made with and without administering oxygen. METHODS: Both studies were conducted at the University of Utah and participants acted as their own control. Inclusion criteria were age 18 years and older with an American Society of Anesthesiologists physical status of I-III. Exclusion criteria included acute respiratory distress syndrome, pneumonia, lung or cardiovascular disease, nasal/bronchial congestion, pregnancy, oxygen saturation measured by pulse oximetry <93%, and a procedure scheduled for <20 minutes. For the volunteer study, pulsed and continuous flow was administered at rates from 2 to 10 L/min using a single sequence of technique and flow. The median absolute deviation from the median value was analyzed for the primary outcome of ETCO2. For the clinical study, ETCO2 measurements (the primary outcome) were collected while administering pulsed and continuous flow at rates between 1 and 5 L/min and were compared to measurements without oxygen flow. Due to institutional review board requirements for patient safety, this study was not randomized. After completing the study, measurements with and without administering oxygen were analyzed to determine median differences and 95% limits of agreement for each administration technique. RESULTS: Thirty volunteers and 60 patients participated in these studies which ended after enrolling the predetermined number of participants. In volunteers, the median absolute deviation for ETCO2 measurements made while administering pulsed flow oxygen (0.89; 25%-75% quantiles: 0.3-1.2) was smaller than while administering continuous flow oxygen (3.93; 25%-75% quantiles: 2.2-6.2). In sedated patients, the median difference was larger during continuous flow oxygen (-6.8 mm Hg; 25%-75% quantiles: -12.5 to -2.1) than during pulsed flow oxygen (0.1 mm Hg; 25%-75% quantiles: -0.5 to 1.5). The 95% limits of agreement were also narrower during pulsed flow oxygen (-2.4 to 4.5 vs -30.5 to 2.4 mm Hg). CONCLUSIONS: We have shown that nasal ETCO2 measurements while administering pulsed flow have little deviation and agree well with measurements made without administering oxygen. We have also demonstrated that ETCO2 measurements during continuous flow oxygen have large deviation and wide limits of agreement when compared with measurements made without administering oxygen.

Evaluation and application of a method for estimating nasal end-tidal O2 fraction while administering supplemental O2.

This paper describes a method for estimating the oxygen enhanced end-tidal fraction of oxygen (FetOe), the end-tidal fraction of oxygen (FetO2) that is raised by administering supplemental oxygen. The paper has two purposes: the first is to evaluate the method's accuracy on the bench and in volunteers; the second purpose is to demonstrate how to apply the method to compare two techniques of oxygen administration. The method estimates FetOe by analyzing expired oxygen as oxygen washes out of the lung. The method for estimating FetOe was first validated using a bench simulation in which tracheal oxygen was measured directly. Then it was evaluated in 30 healthy volunteers and compared to the bench simulation. Bland-Altman analysis compared calculated and observed FetOe/FetO2 measurements. After the method was evaluated, it was implemented to compare the FetOe obtained when administering oxygen using two different techniques (pulsed and continuous flow). A total of eighteen breath washout conditions were evaluated on the bench. FetOe estimates and tracheal FetO2 had a mean difference of - 0.016 FO2 with 95% limits of agreement from - 0.048 to 0.016 FO2. Thirteen breath washouts per volunteer were analyzed. Extrapolated and observed FetO2 had a mean difference of - 0.001 FO2 with 95% limits of agreement from - 0.006 to 0.004 FO2. Pulsed flow oxygen (PFO) achieved the same FetOe values as continuous flow oxygen (CFO) using 32.1% ± 2.27% (mean ± SD) of the CFO rate. This paper has demonstrated that the method estimates FetO2 enhanced by administering supplemental oxygen with clinically insignificant differences. This paper has also shown that PFO can obtain FetO2 similar to CFO using approximately one-third of the oxygen volume. After evaluating this method, we conclude that the method provides useful estimates of nasal FetO2 enhanced by supplemental oxygen administration.

Novel mandibular advancement bite block with supplemental oxygen to both nasal and oral cavity improves oxygenation during esophagogastroduodenoscopy: a bench comparison.

Drug-induced respiratory depression is a major cause of serious adverse events. Adequate oxygenation is very important during sedated esophagogastroduodenoscopy (EGD). Nasal breathing often shifts to oral breathing during open mouth EGD. A mandibular advancement bite block was developed for EGD using computer-assisted design and three-dimensional printing techniques. The mandible is advanced when using this bite block to facilitate airway opening. The device is composed of an oxygen inlet with one opening directed towards the nostril and another opening directed towards the oral cavity. The aim of this bench study was to compare the inspired oxygen concentration (FiO2) provided by the different nasal cannulas, masks, and bite blocks commonly used in sedated EGD. A manikin head was connected to one side of a two-compartment lung model by a 7.0 mm endotracheal tube with its opening in the nasopharyngeal position. The other compartment was driven by a ventilator to mimic "patient" inspiratory effort. Using this spontaneously breathing lung model, we evaluated five nasal cannulas, two face masks, and four new oral bite blocks at different oxygen flow rates and different mouth opening sizes. The respiratory rate was set at 12/min with a tidal volume of 500 mL and 8/min with a tidal volume of 300 mL. Several Pneuflo resistors of different sizes were used in the mouth of the manikin head to generate different degrees of mouth opening. FiO2 was evaluated continuously via the endotracheal tube. All parameters were evaluated using a Datex anesthesia monitoring system. The mandibular advancement bite block provided the highest FiO2 under the same supplemental oxygen flow. The FiO2 was higher for devices with oxygen flow provided via an oral bite block than that provided via the nasal route. Under the same supplemental oxygen flow, the tidal volume and respiratory rate also played an important role in the FiO2. A low respiratory rate with a smaller tidal volume has a relative high FiO2. The ratio of nasal to oral breathing played an important role in the FiO2 under hypoventilation but less role under normal ventilation. Bite blocks deliver a higher FiO2 during EGD. The ratio of nasal to oral breathing, supplemental oxygen flow, tidal volume, and respiratory rate influenced the FiO2 in most of the supplemental oxygen devices tested, which are often used for conscious sedation in patients undergoing EGD and colonoscopy.