The brain is critically dependent on adequate oxygenation for function and viability. Routine clinical assessment of cerebral oxygen delivery has been limited to measurement of blood pressure and analysis of arterial oxygenation by pulse oximetry or arterial blood gases. Recent interest has focused on the use of jugular venous bulb blood oxygen tension and content , which reflect the overall adequacy of cerebral oxygen delivery but do not provide an accurate indication of local cerebral perfusion. Moreover, jugular venous bulb catheterization is an invasive technique.
Noninvasive in vivo spectroscopy provides an assessment of regional brain hemoglobin oxygen saturation by measuring the differential absorption of near-infrared light. It has been studied extensively in animals [2-6] and is widely used as a technique for continuously monitoring brain oxygenation in neonates [7-9]. Cerebral oximetry has also been evaluated in adults under anesthesia  and has been used to assess the adequacy of collateral circulation in patients undergoing carotid endarterectomy . The spectroscopic signal changes as quickly in response to progressive cerebral hypoxia as the electroencephalogram [12,13].
Validation of in vivo spectroscopy has been limited by the lack of a "gold standard" against which to compare the generated signal. The saturation measured by the oximeter originates in a local field containing arteries, veins, and capillaries, with a predominantly venous contribution (70%-80%) [2,12,14,15].
The cerebral oximeter produces multiple signals that are then processed (the "algorithm") to determine the average oxygen saturation of hemoglobin in the field CSf O2, where CS stands for cerebral saturation and f stands for field. Using graded hypoxia in volunteers, we adjusted the coefficients of the algorithm to maximize the correlation of its result with the estimated combined cerebral saturation (CScomb O2 = 0.25 Sa O2 + 0.75 Sj O2), where comb stands for combined, Sa O2 is the measured arterial saturation, and Sj O (2) is the measured jugular venous bulb saturation. We then validated this coefficient set in a second group of volunteers.
Description of the Cerebral Oximeter
Cerebral spectroscopy uses near-infrared light of wavelengths ranging from 700 to 1000 nm. The Invos 3100 Registered Trademark (Somanetics, Troy, MI) cerebral oximeter consists of an electronic computer display box, a connecting cable, and a flexible probe containing miniature light-emitting diodes (LED) and light detectors. The LEDs use two wavelengths of near-infrared light, centered at 730 and 810 nm, to measure the ratio of oxyhemoglobin to deoxyhemoglobin in the field beneath the oximeter probe (CSf O2), thus providing an index of changes in brain hemoglobin oxygen saturation. The scattering nature of the sampled tissues causes the photons to travel in random paths through the brain via an average path consisting of an ellipse between emitter and detector . Two siliconecoated photodiodes, which serve as the detectors, are arranged on the sensor at two distances (30 and 40 mm) from the light source. Since the depth of penetration of the average light beam is proportional to the distance of the detector from the light source , the measurement can be depth-resolved, allowing simultaneous monitoring of differing tissue strata. The more distant detector measures the saturation of all of the tissues penetrated by the light beam, including skin, muscle tissue, skull, and brain. The closer detector contains less of a contribution from deeper brain tissue. The signals captured from the detectors may be processed together to produce CSf O2, an approximate hemoglobin oxygen saturation in the underlying brain. Although all photons must pass through scalp and skull, the concentration of blood is greater in brain cortex and may contribute relatively more to the absorption . A modification of the Beer-Lambert law is used to calculate CSf O2 based on the difference in incident and received light at the chosen wavelengths (see Appendix). The validity of this law in estimating optical path length in an inhomogeneous medium has been demonstrated previously both by analytical proof and by Monte Carlo simulation .
In a study approved by the institutional review board, the algorithm for the double-path in vivo cerebral oximeter was optimized for 12 healthy volunteers (aged 23-33 yr). Once determined, it was then validated in an additional 10 volunteers (aged 22-35 yr).
After informed consent was obtained, the volunteers underwent radial arterial and jugular venous bulb catheterization. A Doppler ultrasonic probe (SiteRite II Registered Trademark; Dymax, Pittsburgh, PA) was used to localize the internal jugular vein. Ear discomfort was experienced by volunteers when the catheter was advanced, indicating the jugular bulb had been located. Isotonic saline injection through the catheter produced a characteristic auditory sensation, thus verifying placement of the catheter [19,20]. Volunteers were monitored continuously using a pulse oximeter (Model N 100C; Nellcor, Hayward, CA), an end-tidal carbon dioxide (ETCO2) monitor (Datex Normocap 200; Datex, Helsinki, Finland), an electrocardiogram (Life-scope 6; Nihon Kohden, Tokyo, Japan), and an automated blood pressure monitor (Critikon Vital Signs Monitor 1846-X; Critikon, Tampa, FL) and were studied in the supine position.
A double-path, self-adhesive probe containing a near-infrared light source and detectors was also placed on each subject's right frontal forehead to continuously monitor the four optical density signals (one at each wavelength from each detector) and calculate CSf O2. Subjects breathed randomly ordered hypoxic gas mixtures (FIO2 = 0.13, 0.125, 0.12, 0.11, 0.1, 0.07, and 0.06) through a tight-fitting mask and a closed circuit using a nitrogen and oxygen gas mixture. Room air mixtures were breathed through the mask. Numbered tables were used to randomize the sequence of gas inhalation. Each mixture was breathed until a stable pulse oximeter reading was obtained, at which time simultaneous arterial and jugular venous blood gases were slowly drawn, and heart rate, blood pressure, ETCO2, and pulse oximeter readings were documented. Neurologic function was assessed by verbal communication. ETCO2 was permitted to vary with changes in minute ventilation. Subjects breathed the mixtures for at least 5 min before blood sampling, and were allowed a 5-min interval between readings, during which time 100% oxygen was administered temporarily until baseline oxygen saturation was restored.
The two data sets, i.e., training (12 subjects) and validation (10 subjects), were analyzed separately, but in the same manner. Cerebral oxygen saturation (CS (comb) O2) was computed as CScomb O2 = 0.25 Sa O2 + 0.75 Sj O2. The association between brain oxygen saturation and the in vivo spectroscope (CSf O2) was investigated, assuming a straight-line relationship: Equation 1 where beta0 is the intercept and beta1 is the slope.
Pearson product-moment correlation coefficients between CScomb O (2) and CSf O2 were computed for each subject to measure the intensity of the association. The slope and the intercept were estimated for each subject using ordinary least-squares estimation. The linear relationship of CSf O2 with Sa O2 and Sj O2 was assessed for each subject using multiple linear regression analysis. Equation 2 where beta2 = the slope for Sj O2. Homogeneity of the slopes among subjects was assessed in a manner analogous to the analysis of covariance technique.
Test characteristics (sensitivity and specificity) of the cerebral oximeter were also assessed. Sensitivity was determined as the ability of the oximeter to detect cerebral desaturation as defined by a CScomb O2 < 60%, 55%, and 50%.
Finally, the data sets were also analyzed and plotted using the method of difference testing described by Bland and Altman  for situations in which a new test is compared to a conventional test that does not represent an absolute gold standard.
CScomb O2 and CSf O2 were highly associated for each subject in both the training (r2 = 0.798-0.987) and validation (r2 = 0.794-0.992) sets Figure 1. The slopes for CScomb O2 ranged from 0.72 to 1.31 for the training data and 0.49 to 1.11 for the validation data Table 1. The slopes were not homogeneous for either data set (p = 0.0001) Table 2.
Estimated slopes for Sa O2 and Sj O2 are summarized in Table 3 with the results from the multiple linear regression analysis. For the training data (n = 12), eight slopes for Sa O2 (beta1 in Equation 2) were statistically significantly different from zero, while only three slopes for Sj O2 (beta2 in Equation 2) were statistically significantly different from zero. Similarly, for the validation data (n = 10), seven slopes for Sa O2 (beta1 in Equation 2) were statistically significantly different from zero, while only three slopes for Sj O2 (beta2 in Equation 2) were statistically significantly different from zero. Thus, at the same Sa O (2) level, there was no apparent relation between CSf O2 and Sj O2. The slopes for Sa O2 were homogeneous for the training set (P = 0.1898), but not the validation set (P = 0.0258). The slopes for Sj O2 were inhomogeneous in both training (P = 0.0446) and validation (P = 0.0326) sets.
Test characteristics are summarized in Table 4. Sensitivity ranged from 78.6% to 85.1% for the training data, and from 47.8% to 91.7% for the validation data. Specificity ranged from 78.6% to 95.5% for the training data, and from 88% to 94.7% for the validation data, indicating a decreased sensitivity and enhanced specificity with progressive hypoxia.
Individual Bland-Altman plots are shown in Figure 2, and the descriptive statistics for the differences between CSf O2 and CScomb O2 are summarized in Table 5 and Table 6. These demonstrated a close association between CScomb O2 and CSf O2.
Heart rate increased significantly from baseline values but blood pressure was unchanged when a FIO2 of 0.06 or 0.07 was administered. With a FIO2 of 0.06 the lowest arterial and brain oxygen saturations recorded were 41.5 and 33.1, respectively. All volunteers tolerated the procedure well.
Jobsis et al.  first demonstrated that it was possible to assess brain oxygenation by measuring the attenuation of near-infrared light of specific wavelengths passing through the skull and underlying brain. Infrared light readily penetrates skin and bone [5,16,17,22], so that measuring the attenuation of light of a particular wavelength passed through the skull permits assessment of cerebral hemoglobin oxygen saturation. Contamination of the signal by skin and bone contributions, thought to be minimal, is due mainly to bone contamination, which contributes 5%-9% to the signal [2,13]. Because direct measurement of optical path length is not possible in the brain, an estimation must be made . The estimated path length, and the resulting estimated hemoglobin saturation must then be validated against an established standard. However, there is no directly measured "gold standard" against which to validate the spectroscopic estimate of saturation in the field beneath the probe (CSf O2). In the present study, we have attempted to validate the cerebral oximeter by comparing it with a calculated brain hemoglobin oxygen saturation (CScomb O2), based upon assumed weightings of jugular venous bulb and arterial oxygen saturation. While CScomb O2 may not reflect true brain oxygen saturation, measurement of jugular venous bulb oxygen saturation is well established as an index of global brain oxygenation in the critical care of head-injured patients , and by allowing for the arterial contribution [14,15], should closely reflect cerebral oxygen saturation.
We used a two-wavelength, two-detector sensor first described by McCormick et al. . It differs from technically related devices by using the ratio of the concentrations of oxy- and deoxyhemoglobin to report changes as percent saturation (rather than the more abstract optical density or absorption) and by suppressing the extracerebral contributions to brain saturation by measuring the ratios of two detectors located at different distances from the light source . The spacing between emitter and detector is a critical variable; if too short, the signal may be dominated by extracerebral contamination . In the present prototype, in comparison to previous studies using earlier prototypes [2,12,14,23-25], the detector-emitter spacings were increased to 30 mm and 40 mm from the LED (vs 10 mm and 27 mm in the previous prototype). This longer distance weights brain hemoglobin oxygen saturation more than other tissues because of the high cerebral concentration (nearly 1%) of hemoglobin . Our results suggest that the longer spacings may better remove interfering effects of intersubject differences in the absorption by extracranial constituents.
To further reduce the extracerebral contribution to CSf O2 would require studies using volunteers in whom cerebral venous saturation is varied independently. As such studies are not practical in volunteers, an allowance for extracerebral contamination, based on the conclusions of animal experiments, has instead been incorporated into the algorithm [2,5]. In separate experiments, we have attempted to vary the proportions of the arterial and venous contributions to CScomb O2 by measuring CSf O2 in the Trendelenburg and reverse Trendelenburg positions and to alter cerebral venous saturation by changing PaCO (2) while holding Sa O2 constant [26,27].
We developed the algorithm for converting the transmitted signal to hemoglobin oxygen saturation using the training group and tested it using the second group of volunteers. With the exception of a previous pilot study using closer emitter-detector spacings , this is the first group of volunteers to be studied in this fashion. We found that a close association in individual subjects existed between CSf O2 and CScomb O2 (r2 = 0.79-0.99). The slopes, however, were inhomogeneous, which may reflect variably changing proportions of cerebral arterial and venous blood during severe hypoxia. Because the responses were heterogeneous, absolute calibration of the oximeter using hypoxic challenges was not feasible, as confounding variables still limit the quantitative accuracy of results in any individual patient. Thus, it may be more appropriate to base treatment on trends in CSf O2, rather than to rely on absolute CSf O2 values. The cerebral oximeter may therefore be an adjunct rather than an alternative to established measurements of cerebral oxygenation.
The physiologic implications of CSf O2 also must be further defined. By multivariate linear regression analysis, CSf O2 proved to be more closely associated with Sa O2 than Sj O2. Further research to separate and quantify the contributions of Sa O2 and Sj O2 to CScomb O2 may define a more appropriate gold standard against which to compare CSf O2.
Although these results show good correlations, the agreement is less precise than expected. Correlation coefficients assess the strength of a relationship between two variables, but not the agreement between them. Bland-Altman plots  measure the agreement between two variables, neither of which is an established gold standard, by plotting the differences between the two methods against their mean. Analyzed in this way, our data confirm that an association exists between CS (f) O2 and CScomb O2, as over 95% of the differences are within 2 SD of the mean . However, the collective group limits of agreement for all volunteers are wide, and range from -11.06 to 9.75, suggesting again that CSf O2 trends, rather than absolute values, may provide a better assessment of cerebral oxygenation.
Finally, analysis of the test characteristics suggest that the cerebral oximeter is less accurate with more profound hypoxia. However, as few values <50% were available for comparison, the assumption that accuracy deteriorates with progressive hypoxia may be inaccurate.
Early recognition of changes in neurologic status may be useful to prevent secondary insults after head injury. Permanent damage, however, may have occurred before changes in neurologic status become apparent. Double-path in vivo oximetry is potentially useful as a simple, noninvasive technique for continuously monitoring brain oxygenation in the high-risk patient. By providing an early indication of cerebral hypoxia, it may allow appropriate therapy to be given earlier. It may also prove useful in patients at risk for inadequate cerebral oxygenation under anesthesia . However, additional development and validation are necessary.
Optical density (OD) is frequently used in optics as a convenient way of expressing attenuation of light, and is defined as: Equation 3 where I is the ratio of detected light photons in nonabsorbing tissue, I0 is the ratio of emitted light photons in nonabsorbing tissue, and G is the geometric optical density.
As light is absorbed by oxy- and deoxyhemoglobin present in erythrocytes, an exponential attenuation of the signal occurs, because each successive increment of path removes a constant fraction of photons. Thus: Equation 4 where -di/I is the fractional decrease in photons, sigma is the absorption cross-section of an erythrocyte, rho is the density of erythrocytes, and dz the (infinitesimal) path length.
Solving Equation 4 for I results in the Beer-Lambert law for attenuation as a function of cross-section, density, and path length: Equation 5 or: Equation 6 since ln(n) = 2.3 log(n) Equation 7 where H is the added optical density due to hemoglobin.
Other absorbers (chromophores such as skin pigments or the harmonics of O-H and C-H bonds) may be added to the OD in a similar way: Equation 8 where X is the added optical density due to other absorbers. Thus, the total OD measured between the emitter and detector will be: Equation 9 This can be solved for the red cell cross-section, sigma: Equation 10Equation 11 Knowing the average erythrocyte cross-section, the average oxygen saturation (SAT) is simply: Equation 12 where sigma0 and sigma100 are the known (wavelength-dependent) erythrocyte cross-sections for deoxy- and oxyhemoglobin, respectively.
Solving for SAT as a function of measured OD results in the following equation: Equation 13
By definition, optical spectrophotometry uses two or more wavelengths of light, and the additional wavelength measurement may be used to eliminate a common (background) absorption, or eliminate the sensitivity of subject variation in pigment concentration or optical path length. The detectors are spaced at 30 and 40 mm from the sensor, thus defining two volumes that are separately sampled by photons. The depth of penetration of the average photon is proportional to the emitter-detector spacing ; thus, conceptual subtraction of the ODs of the closer and more distant detector will emphasize the hemoglobin saturation in deeper brain tissue.
The final Equation setis based on an expansion of the single measurement method described in Equation 9: Equation 14, Equation 15, Equation 16, Equation 17 where subscripts 1 and 2 refer to the two wavelengths, subscripts 3 and 4 refer to the 3- and 4-cm emitter-detector spacings, S is the superficial skin, scalp, skull, and some brain contribution, and C is the cerebral parenchymal contribution.
Although in principle the above Equation setmay be solved for SAT using the second wavelength to suppress unknown variables, in practice, an exact solution for SAT is impossible because of the many unknown subject-dependent scattering and absorption cross-sections, densities, and path lengths embedded in these equations. Thus, SAT is solved using a power series with arbitrary coefficients. The terms selected for the algorithm are combinations of the measured optical densities that are more efficient in reducing path length dependence while emphasizing brain parenchymal contribution.
The generation and optimization of the algorithm, performed using four measured variables (two wavelengths and two detectors), attempts to reduce the effect of subject-dependent terms that affect the slopes and offsets of the individual regression lines. Raw optical data points, collected at the time of blood sampling, and estimates of CScomb O2, were combined from all 12 subjects and analyzed as a group in the retrospective study. The coefficients of the Beer-Lambert law were adjusted to reduce the overall errors caused by subject-dependent variables. Traditional optimization techniques and neural network analysis were used to improve the resultant algorithm and provide the best level of agreement for CSf O2. The resulting algorithm was then applied prospectively to 10 validation volunteers to ensure accuracy and applicability in the general population.
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