2.1.

Instrumentation

For our study we used a Critikon 2020 Cerebral RedOx monitor (Johnson & Johnson, UK), which is based on a two channel sensor and a coupling compensation system. It uses four laser diodes with wavelengths at 776.5, 819.0, 871.4, and 908.7 nm. Silicon photodiode detectors are placed at 10 and 37 mm from the emitter’s window. Placed in the middle between those two is a light emitting diode (LED). The light intensity of the LED should be the same at both detectors. Hence a difference in coupling can be compensated for.

2.2.

Theory

2.2.1.

tHbg Method

The aim of the tHbg method and specially designed sensor is to determine the cerebral hemoglobin concentrations without any influence from the extracerebral layers: skin, skull, and cerebro spinal fluid. The signal from detector 1 (Figure 1) is mainly affected by these layers, while the signal of detector 2 has a predominant component that refers to the brain. A ratio of the signals of detector 2 and detector 1 is calculated, which reduces the influence of the extracerebral layers. In the case of pure scattering without any absorption, the light intensity will decrease with the squared distance to the source. Thus the effect of scattering can be taken into account. The remaining effect is due to absorption. The absolute concentrations of deoxyhemoglobin (HHb in μmol/L) and of oxyhemoglobin (O ₂ Hb in μmol/L) can be calculated using a modified Beer–Lambert law. The complete algorithm is given by

$$\begin{array}{ccc}\left[\begin{array}{c}\text{HHb}\hfill \\ {\text{O}}_2\text{Hb}\hfill \end{array}\right]\hfill & =\hfill & \left[\begin{array}{cccc}{\mathit{k}}_{1{\lambda }_1}\hfill & {\mathit{k}}_{1{\lambda }_2}\hfill & {\mathit{k}}_{1{\lambda }_3}\hfill & {\mathit{k}}_{1{\lambda }_4}\hfill \\ {\mathit{k}}_{2{\lambda }_1}\hfill & {\mathit{k}}_{2{\lambda }_2}\hfill & {\mathit{k}}_{2{\lambda }_3}\hfill & {\mathit{k}}_{2{\lambda }_4}\hfill \end{array}\right]\hfill \\ \hfill & \hfill & \times \left\{\begin{array}{cc}\frac{-1000}{{\mathit{B}}_{{\lambda }_1}*({\mathit{r}}_2-{\mathit{r}}_1)}*{\text{log}}_{10}[{\left(\frac{{\mathit{r}}_2}{{\mathit{r}}_1}\right)}^2*\frac{{\mathit{I}}_{2{\lambda }_1}}{{\mathit{I}}_{1{\lambda }_1}}*\frac{{\text{LED}}_1}{{\text{LED}}_2}]\hfill & \hfill \\ \frac{-1000}{{\mathit{B}}_{{\lambda }_2}*({\mathit{r}}_2-{\mathit{r}}_1)}*{\text{log}}_{10}[{\left(\frac{{\mathit{r}}_2}{{\mathit{r}}_1}\right)}^2*\frac{{\mathit{I}}_{2{\lambda }_2}}{{\mathit{I}}_{1{\lambda }_2}}*\frac{{\text{LED}}_1}{{\text{LED}}_2}]\hfill & \hfill \\ \frac{-1000}{{\mathit{B}}_{{\lambda }_3}*({\mathit{r}}_2-{\mathit{r}}_1)}*{\text{log}}_{10}[{\left(\frac{{\mathit{r}}_2}{{\mathit{r}}_1}\right)}^2*\frac{{\mathit{I}}_{2{\lambda }_3}}{{\mathit{I}}_{1{\lambda }_3}}*\frac{{\text{LED}}_1}{{\text{LED}}_2}]\hfill & \hfill \\ \frac{-1000}{{\mathit{B}}_{{\lambda }_4}*({\mathit{r}}_2-{\mathit{r}}_1)}*{\text{log}}_{10}[{\left(\frac{{\mathit{r}}_2}{{\mathit{r}}_1}\right)}^2*\frac{{\mathit{I}}_{2{\lambda }_4}}{{\mathit{I}}_{1{\lambda }_4}}*\frac{{\text{LED}}_1}{{\text{LED}}_2}]\hfill & \hfill \end{array}\right\}\hfill \\ \hfill & \hfill & -\left[\begin{array}{c}{\text{O}}_1\hfill \\ {\text{O}}_2\hfill \end{array}\right]\text{,}\hfill \end{array}$$

Eq. (1)

$$$$

where k=the coefficient matrix, which depends on the absorption coefficients of HHb and O ₂ Hb, B=the differential pathlength factor for each wavelength, r_x=the distance between the emitter and detector x, I_x=the light intensity of the laser diode’s emitter at detector x for each wavelength, LED _x=the light intensity of the LED at detector x, and O _x=the offset due to water absorption: O ₁=7.5 μmol/L and O ₂=28.8 μmol/L.

Figure 1

Diagram showing the geometrical setup of the sensor.

Since HHb and O ₂ Hb are quantified absolutely, tHbg can be determined as the sum of both (Figure 2). The algorithm is described in detail by in Ref. 4.

Figure 2

Example showing consecutive slow changes in oxygenation analyzed by the tHbg algorithm. The arterial oxygen saturation (SaO ₂) and oxyhemoglobin (O ₂ Hb) decrease and the deoxyhemoglobin (HHb) increases simultaneously during alteration of FiO ₂. The sum of O ₂ Hb and HHb corresponds to tHbg.

2.2.2.

tHbo Method

If only the signal from detector 2 (Figure 1) is analyzed, the Critikon instrument is technically equivalent to other systems such as the Hamamatsu NIRO 500 (Japan), the NIRO 300 (with respect to the O ₂ Hb, HHb, and tHb concentrations), or the Critikon 2001 (UK). Even the wavelengths employed by the Hamamatsu NIRO 500 (775, 810, 870, and 904 nm), the NIRO 300 (775, 810, 850, and 913 nm), and the Critikon 2001 (same as the Critikon 2020) are quite similar to ours. These instruments only quantify changes in the hemoglobin concentration.

At the beginning of each measurement the light attenuation is set to zero and only subsequent changes in light attenuation are taken into consideration. It is assumed that these changes can be attributed to changes in the hemoglobin concentration in the tissue under investigation. To convert the changes in attenuation to concentration changes, the Beer–Lambert law was modified [Eq. (2)]. This modification is in agreement with the diffusion approximation, which is valid if scattering is much higher than absorption.

Eq. (2)

$$\begin{array}{ccc}\left[\begin{array}{c}\Delta \text{HHb}\hfill \\ \Delta {\text{O}}_2\text{Hb}\hfill \end{array}\right]\hfill & =\hfill & \left[\begin{array}{cccc}{\mathit{k}}_{1{\lambda }_1}\hfill & {\mathit{k}}_{1{\lambda }_2}\hfill & {\mathit{k}}_{1{\lambda }_3}\hfill & {\mathit{k}}_{1{\lambda }_4}\hfill \\ {\mathit{k}}_{2{\lambda }_1}\hfill & {\mathit{k}}_{2{\lambda }_2}\hfill & {\mathit{k}}_{2{\lambda }_3}\hfill & {\mathit{k}}_{2{\lambda }_4}\hfill \end{array}\right]\hfill \\ \hfill & \hfill & \times \left[\begin{array}{c}\frac{-1000}{{\mathit{B}}_{{\lambda }_1}*{\mathit{r}}_2}*{\text{log}}_{10}({\mathit{I}}_{2{\lambda }_1})\hfill \\ \frac{-1000}{{\mathit{B}}_{{\lambda }_2}*{\mathit{r}}_2}*{\text{log}}_{10}({\mathit{I}}_{2{\lambda }_2})\hfill \\ \frac{-1000}{{\mathit{B}}_{{\lambda }_3}*{\mathit{r}}_2}*{\text{log}}_{10}({\mathit{I}}_{2{\lambda }_3})\hfill \\ \frac{-1000}{{\mathit{B}}_{{\lambda }_4}*{\mathit{r}}_2}*{\text{log}}_{10}({\mathit{I}}_{2{\lambda }_4})\hfill \end{array}\right]\text{.}\hfill \end{array}$$

Our second algorithm corresponds to the UCL4 algorithm described in Ref. 6 for the Hamamatsu NIRO 500.

To determine the absolute tHb, the tHbo method requires a slow change in oxygenation, which is achieved by altering the oxygen fraction inspired. SaO ₂ is measured by pulse oximetry (a Hellige SMK132 with a 3 s averaging time or a Nellcor N-200 with a 2 s averaging time) and is kept within a normal range (85–99). The relative O ₂ Hb signal, which is measured just like in conventional NIRS, varies parallel to the SaO ₂ (Figure 3). The tHb can be quantified by comparing the change in O ₂ Hb to the change in SaO ₂ [Eq. (3)]. The change in O ₂ Hb is equal but opposite to the change in HHb as long as the tHb remains constant. Under this circumstance it is possible to improve the signal to noise ratio by taking (ΔO ₂ Hb–ΔHHb)/2 instead of ΔO ₂ Hb [Eq. (3)].

Eq. (3)

$$\begin{array}{ccc}\text{tHbo}\hfill & =\hfill & {100}^{*}\Delta {\text{O}}_2\text{Hb}/\Delta {\text{SaO}}_2\hfill \\ \hfill & =\hfill & {100}^{*}(\Delta {\text{O}}_2–\Delta \text{HHb})/(2^{*}\Delta {\text{SaO}}_2)(\mu \text{mol}/\mathit{L})\text{.}\hfill \end{array}$$

This method is described in detail in Ref. 3.

Figure 3

Same slow changes in oxygenation as in Fig. 2 evaluated by the tHbo algorithm. The arterial oxygen saturation (SaO ₂) and the cerebral oxyhemoglobin concentration (O ₂ Hb) increase and decrease simultaneously as the inspired oxygen fraction is altered.

2.3.

Data Analysis

All data used in this study had adequate technical quality, i.e., the instrument did not indicate poor signal quality.

The data with a sample time of 1 s were converted into 10 s values by averaging. Changes in oxygenation were analyzed using a computer program according to the procedure in Ref. 3. The beginning and the end of a decrease or increase in oxygenation was identified by looking at the SaO ₂ trace only. A change in oxygenation was defined to be any change in SaO ₂ of more than 4 over a period of more than 1.2 min.

In each infant at least six changes in oxygenation were carried out consecutively and for each one tHbo and tHbgo were calculated by a computer program. For the tHbo method 36 of the measurements passed the quality criteria established in Ref. 3: the change in SaO ₂ was >4 over >1.2 min, the line of regression had an r²>0.85, and the ΔtHb was smaller than 25 of the (ΔO ₂ Hb–ΔHHb)/2. Only 24 of the tHbgo method measurements fulfilled the quality criteria so all measurements of four infants were rejected.

Several changes in oxygenation yielded a valid tHbo value, while the tHbgo value was rejected due to poor quality or vice versa. In that case the valid value was removed too, because we wanted to compare both methods for exactly the same data. For each remaining tHbgo measurement the mean of the continuously available tHbg was calculated. The test retest variability (TRV) (in ) was determined for each method by analysis of the variance. For each infant the mean of tHbg, tHbo, and tHbgo was determined. The data were checked for normality.

To compare the three methods we proceeded in the following way. Two methods were compared at a time and their correlation coefficient (r) was calculated. Furthermore we calculated the limits of agreement as described in the literature.⁷

Using a regression procedure with variable selection by Mellow’s C(p), ⁸ we determined other parameters which influence the tHbg, tHbo, and tHbgo. The following parameters were available: gestational age (GA) (in weeks), birthweight (BW) (in g), postnatal age (PA) (in days), cHb, pCO ₂, heart rate (HR) (in bpm), and mean arterial blood pressure (MAP) (in mmHg) measured continuously through an umbilical arterial catheter.

4.1.

Comparison of tHbg and tHbgo

For the tHbg and tHbgo algorithm, validation studies of neonatal head phantoms have been carried out.^{5 13} In Ref. 13 a clear layer that mimicked cerebro spinal fluid was inserted into the phantom. According to Ref. 14 this kind of uniformly thick clear layer does not represent the effect of cerebro spinal fluid in vivo. Therefore we consider the model in Ref. 5 to best reflect the situation in the infant. In that study⁵ it was shown, on the one hand, that changes in O ₂ Hb and HHb were quantified correctly, independent of the light scattering and, on the other hand, that the absolute O ₂ Hb and HHb values had substantial offsets, i.e., the values overestimated the actual concentration by a constant amount. These offsets depended on light scattering. Their origin was unclear. From these findings we would expect the tHbgo to be correct, because it only takes changes of O ₂ Hb and HHb into account whereas the tHbg is subject to the offsets.

The slope of the line of regression (Figure 4) of 0.92, which is close to the expected value of 1 and the high offset of 68.0 μmol/L, supports this, that is, that the disagreement between these two methods is caused by this offset. Thus the results are in agreement with the study using the phantom.

r is lower than expected: r=0.736. This means, that there is relatively large intersubject variability between the tHbg and tHbgo. Although it is beyond the scope of this paper to identify the exact reasons for this, we want to point out the likeliest reasons.

4.2.

Comparison of tHbo and tHbgo

The tHbo method has neither been validated in infants nor are phantom data available. It has been tested in infants for internal consistency.² The tHb was changed by altering the pCO ₂. When the relative change in tHb measured directly by this algorithm was compared to the difference in tHbo before and after the change in pCO ₂ a fourfold discrepancy was found. Thus the algorithm, which is used for the tHbo method, failed to demonstrate any internal consistency.

In comparing tHbo and tHbgo (Table 1 and Figure 5) we find high and significant bias, but also a high correlation with r=0.94, which is remarkably close to 1. This shows that the strong disagreement is highly systematic. Again we want to point out the most likely reasons for the strong disagreement, i.e., why the tHbo gives significantly lower values than the tHbgo.

The most likely reason for the high correlation between the two methods is the operating dependence, i.e., the same NIRS and pulse oximeter data are used for the same period of time.

4.3.

Comparison of tHbg and tHbo

The discrepancy between these two methods can be explained by combining the effects mentioned for tHbg versus tHbgo and for tHbo versus tHbgo.

4.4.

Comparison to Physiological Data

All three, tHbg, tHbo, and tHbgo, showed a highly significant correlation to physiological data (p<0.0001).

It is known that the acute changes in pCO ₂ affect the tHb (e.g., in Ref. 2) within patients. This does not necessarily mean that this is the case when making a comparison among infants. Considering the wide range of pCO ₂ among infants (4.7–7.6 kPa), it still is the most likely reason why pCO ₂ is the variable most strongly associated with tHbg, tHbo, and tHbgo.

In healthy infants cerebral autoregulation is assumed to keep cerebral hemodynamics independent of the MAP. However, in critically ill infants autoregulation may be abolished,¹⁷ which could be the reason why the variable MAP is found in all three models.

It is reasonable that we find the variable cHb in the models for tHbgo and tHbo. The higher the concentration of hemoglobin in the blood the more likely it is to find a high cerebral concentration. This variable is also significantly related to tHbgo in a bivariate model. The PA is significantly negatively correlated to the cHb. This could be the reason why PA is associated with tHbg instead of with cHb.

The association of BW with tHbg previously discussed is probably due to the offsets of this method, which depend on scattering.⁵ It has been shown that scattering is dependent on the gestational age, which is closely correlated to the BW.¹⁵

4.5.

Advantages and Disadvantages of Each Method

tHbg is much easier to apply than the other methods, because it does not require a change in oxygenation. Hence tHbg is the only usable method for infants who do not require additional oxygen. The parameters are continuously available. Furthermore, the geometrical method allows one to measure the tissue’s oxygen saturation.⁴ It also shows the highest correlation to the physiological variables. From this point of view one could conclude that the tHbg method is the most trustworthy method. However, according to the phantom study,⁵ tHbg is subject to offsets, which depend on scattering of the tissue. The relationship between the tHbg and the BW confirms this drawback. The tHbo method requires changes in oxygenation and thus is only applicable in infants who require additional oxygen. It was not internally consistent according to previous findings.² The high correlation (r=0.94) between tHbo and tHbgo shows that both methods are systematically highly related, although their absolute values are quite different.

The tHgo method also requires changes in oxygenation. It is probably less trustworthy than tHbo, because it has a lower correlation to physiological variables for the same model. However, tHbgo also shows a significant correlation with cHb in the bivariate model. The difference between the two methods is probably small and in addition in the tHbgo method the rejection rate of measurements is much higher.

Thus it is difficult to recommend one particular method. Whatever method is used, it will be important to consider that the absolute values depend strongly on the method.