2.1.

SRS Algorithm in Semi-Infinite Homogeneous Tissue

If Hb and $\mathrm{Hb}{\mathrm{O}}_2$ are the only absorbers in regional tissue, the following formula can be derived according to the definition of the absorption coefficient $\left({\mu }_a\right)$ :

Thus, $\mathrm{rS}{\mathrm{O}}_2$ can be calculated if ${\mu }_a^{{\lambda }_1}∕{\mu }_a^{{\lambda }_2}$ is obtained. Because human tissue is strongly scattering, if a narrow beam of near-IR light with constant intensity $\left(I_0\right)$ is vertically illuminated onto the surface of a semi-infinite homogeneous tissue, its average propagation trace in the tissue is curved so that the emitted light $\left(I\right)$ can be detected on the tissue surface at a certain distance to the incident light (Fig. 1 ). The interaction between the near-IR photons and human tissue is described by the diffusion equation,¹³ and Eq. 4 can be obtained by a series of deductions:

Fig. 1

Incident and emitted light on the tissue surface.

Because tissue ${\mu }_s^{\prime }$ changes little with wavelength in the near-IR band,¹⁴ it can be considered that it is a constant, and Eq. 6 can be derived:

Because Hb and $\mathrm{Hb}{\mathrm{O}}_2$ are the main absorbers in the near-IR band,³ $\mathrm{rS}{\mathrm{O}}_2$ can be calculated when $\partial \mathrm{OD}∕\partial r$ is obtained according to Eqs. 3, 6.

2.2.

Sensor of Our NIRS Oximeter

The SRS algorithm can be used to calculate cerebral $\mathrm{rSc}{\mathrm{O}}_2$ , and a reflective sensor like that shown by Fig. 1 is often used. We calculated the OD of the following two strongly scattering semi-infinite homogeneous tissues by Eq. 4: (1) ${\mu }_a=0.36{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=22{\mathrm{cm}}^{-1}$ and (2) ${\mu }_a=0.48{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=5{\mathrm{cm}}^{-1}$ , corresponding to the optical characteristics of adult and infant cerebral gray matter at $800\mathrm{nm}$ , respectively.^{15, 16} The refraction indices of these two tissues were both 1.4, and $r$ was continuously changed from $2\text{to}5\mathrm{cm}$ . The curves of OD versus $r$ corresponding to the two tissues were calculated (Fig. 2 ). The linearity between OD and $r$ were both excellent and the correlation coefficients were $R=0.9999$ and $R=0.9997$ , respectively. If ${\mu }_s^{\prime }⪢{\mu }_a$ , even though their values were different from those just considered, the preceding linearity could be as excellent as Fig. 2 (here we do not individualize them). Thus, only two detectors are enough to calculate $\partial \mathrm{OD}∕\partial r$ and then $\mathrm{rSc}{\mathrm{O}}_2$ .

Fig. 2

Relationship between OD and $r$ calculated from Eq. 4.

Our oximeter sensor consists of a two-wavelength near-IR light source whose emitting wavelengths are 760 and $850\mathrm{nm}$ , and three near-IR $p\text{-}i\text{-}n$ detectors. The distances between the light source and the three detectors are 20, 30, and $40\mathrm{mm}$ , respectively. Figure 3 is a picture of the sensor. In our experiments, two of the three detectors were used when detecting cerebral $\mathrm{rSc}{\mathrm{O}}_2$ .

Fig. 3

Our oximeter sensor.

The cerebral cortex being detected is under the overlying tissues such as the scalp and the skull, whose optical characteristics are different from those of the cerebral cortex. So the distances between the light source and the two detectors being used should be properly chosen according to the thickness of the overlying tissues, which is often less than $5\mathrm{mm}$ for young children and generally $7\text{to}10\mathrm{mm}$ for adults. The propagation of a large number of photons in the human brain was simulated by a Monte Carlo algorithm¹⁷ in our previous research.¹⁸ The results indicated that for adults, the photons could penetrate through the overlying tissues into the cerebral cortex when $r⩾30\mathrm{mm}$ , and the penetration depth could reach its maximum value when $r=40\mathrm{mm}$ . For children, these were $r⩾20\mathrm{mm}$ and $r=30\mathrm{mm}$ , correspondingly. According to the preceding, the distances between the light source and the two detectors being used were chosen as 30 and $40\mathrm{mm}$ for adults but 20 and $30\mathrm{mm}$ for children.

In addition to $\mathrm{rSc}{\mathrm{O}}_2$ , the concentration changes of Hb and $\mathrm{Hb}{\mathrm{O}}_2$ compared with their original values were also noninvasively monitored by our oximeter simultaneously using modified Lambert-Beer law, noted as $\Delta C_{\mathrm{Hb}}$ and $\Delta C_{\mathrm{Hb}{\mathrm{O}}_2}$ . Here we note $C_{t\mathrm{Hb}}$ as the concentration of total hemoglobin, which is $C_{t\mathrm{Hb}}=C_{\mathrm{Hb}}+C_{\mathrm{Hb}{\mathrm{O}}_2}$ . Thus $\Delta C_{t\mathrm{Hb}}=\Delta C_{\mathrm{Hb}}+\Delta C_{\mathrm{Hb}{\mathrm{O}}_2}$ can also be obtained by our NIRS oximeter.

The sampling rate of our NIRS oximeter was $2\mathrm{s}$ /point.

2.3.

Calibration of Our Oximeter

2.3.1.

Calibration protocol

To assess the accuracy of the oximeter, we made up a liquid tissue model and measured its oxygen saturation by the NIRS oximeter and a blood gas analyzer (Nova m7, Nova Co. US) simultaneously, and the results are noted as $\mathrm{rS}{\mathrm{O}}_2$ and $\mathrm{St}{\mathrm{O}}_2$ , respectively. The tissue model consisted of $40\mathrm{ml}$ of human whole blood as the absorber; $25\mathrm{ml}$ intralipid 20% as the scatter; and $935\mathrm{ml}$ buffer solution, which could keep the pH value of the model at about 7.35 to 7.45 and make it isotonic with blood. According to some previous reports, the absorption and scattering characteristics were near to those of human brain cortex in the near-IR band.^{19, 20} A brief diagram of the calibration is shown in Fig. 4 .

Fig. 4

Brief diagram of calibration.

The $\mathrm{rS}{\mathrm{O}}_2$ of the model could be increased by inflating pure oxygen, and was decreased by adding into it the solution of an inorganic reducer. When we added a certain amount of the reducer solution, the oxygen saturation decreased suddenly to a certain value and could be steady there for a maximum of about $30\min$ . Thus, the oxygen saturation could decrease in a stairlike fashion (Fig. 5 ). The steady time of each “platform” of the “stair” was enough for blood gas analysis. Otherwise, the reducer was completely soluble in the tissue model.

Fig. 5

Stairlike decrease of $\mathrm{rS}{\mathrm{O}}_2$ produced by adding the reducer.

2.3.2.

Assessing the influences of background substances

Note that Eq. 1 is strictly correct only when there is no absorber except $\mathrm{Hb}{\mathrm{O}}_2$ and Hb. But there are absorptions by the background substances, such as water, in human tissue. The sum of the background absorptions is noted as ${\mu }_w$ and often unknown. Thus, the real ${\mu }_a$ should be as follows:

Eq. 7

$${\mu }_a={\epsilon }_{\mathrm{Hb}{\mathrm{O}}_2}{C}_{\mathrm{Hb}{\mathrm{O}}_2}+{\epsilon }_{\mathrm{Hb}}{C}_{\mathrm{Hb}}+{\mu }_w.$$

To assess the influence by the background on the oximeter algorithm, we placed the sensor on the surface of the model. At each “platform” of the “stair”, $\mathrm{rS}{\mathrm{O}}_2$ was measured by our oximeter, and $\mathrm{St}{\mathrm{O}}_2$ was obtained by blood gas analysis. The relationship between $\mathrm{rS}{\mathrm{O}}_2$ and $\mathrm{St}{\mathrm{O}}_2$ is shown as a continuous line in Fig. 6a . Thus, there is excellent linearity between $\mathrm{rS}{\mathrm{O}}_2$ and $\mathrm{St}{\mathrm{O}}_2$ $(R=0.9910)$ . Ideally the result should be $\mathrm{rS}{\mathrm{O}}_2=\mathrm{St}{\mathrm{O}}_2$ , as shown by the dashed line in Fig. 6a. Because the two lines are very close, the $\mathrm{rS}{\mathrm{O}}_2$ is very close to the corresponding $\mathrm{St}{\mathrm{O}}_2$ . Thus, the algorithm is little influenced by the background absorptions.

Fig. 6

Calibration results by liquid tissue model for influences of (a) the background absorption and (b) the overlying tissue.

3.1.

Subjects

All the clinical experiments were completed in the operating room of Anzhen Hospital, Beijing, China. The subjects were 15 patients (six male and nine female, from $1\text{to}66\mathrm{yr}$ old) who underwent cardiac surgeries, all with CPB. Their basic conditions are given in Table 1 . All the experiments were consented by the surgeons and the patients.

Table 1

Basic conditions of all patients ( M=male , F=female ).

3.2.

Main CPB Procedures

In our research, CPB can be divided into the following three procedures:

3.3.

Physiological Parameters Being Monitored

Pulse oxygen saturation $\left(\mathrm{Sp}{\mathrm{O}}_2\right)$ , body temperature, and heart rate of all the patients were detected in real time by a monitor (MP70, Philips Co.). Because the nasal cavity is near to the cerebral tissue, nasal temperature was considered as the body temperature. During CPB, the body temperature was regulated by the temperature of the arterial blood transported from the artificial pump into the aorta.

Perfusion rate (in liters per minute) can be displayed on and regulated by the artificial pump; thus, the amount of the arterial blood transported into the aorta can be regulated. All the results of blood gas analyses during CPB indicated that the oxygen saturation of the arterial blood transported into the aorta was almost 100%.

The absolute value of cerebral $\mathrm{rSc}{\mathrm{O}}_2$ , as well as the values of $\Delta C_{\mathrm{Hb}}$ , $\Delta C_{\mathrm{Hb}{\mathrm{O}}_2}$ , and $\Delta C_{t\mathrm{Hb}}$ of all the patients was monitored by our NIRS oximeter during the whole surgery. The sensor was pasted on the forehead, lateral to the cerebral midline to avoid the sagittal sinus, and above the eyebrow at least $2\mathrm{cm}$ to avoid the frontal sinus. The distances between the light source and two detectors were 30 and $40\mathrm{mm}$ for patients older than $12\mathrm{yr}$ (eight subjects), while they were 20 and $30\mathrm{mm}$ for patients younger than $12\mathrm{yr}$ (seven subjects).

All the preceding parameters were generally recorded every $5\min$ . But during cooling, rewarming, or low-perfusion-rate stages when $\mathrm{rSc}{\mathrm{O}}_2$ might obviously change, the parameters were recorded more frequently, for example, every $2\min$ .

3.4.

Statistical Methods

The difference of the mean values between two $\mathrm{rSc}{\mathrm{O}}_2$ statuses was analyzed by a modified Student- $t$ test.²³ Here $p$ is the significance level, which is generally chosen as $p=0.05$ . All the statistics for the experimental data were calculated by Matlab 6.5 (Mathworks Co.).

4.1.

$\mathrm{rSc}{\mathrm{O}}_2$ and $C_{t\mathrm{Hb}}$ Versus Body Temperature During the First CPB Procedure

During this procedure, the body temperature was decreased significantly and the perfusion rate was kept constant. The body temperature of 14 patients (except patient 5 because of the lack of data) were $36.0\pm 1.1$ and $28.9\pm 4.4°\mathrm{C}$ [ $n=14$ , $p<0.01$ , in Fig. 7a ] at the beginning and end of this procedure, respectively, and the $\mathrm{rSc}{\mathrm{O}}_2$ values were $51.4\pm 5.9$ and $58.9\pm 5.3\%$ [ $n=14$ , $p<0.01$ , in Fig. 7b] correspondingly. Thus, $\mathrm{rSc}{\mathrm{O}}_2$ increased significantly when the body temperature was decreased.

Fig. 7

Statistical results before and after cooling of the 14 patients for (a) body temperature and (b) $\mathrm{rSc}{\mathrm{O}}_2$ .

In addition to $\mathrm{rSc}{\mathrm{O}}_2$ , the changes of cerebral $C_{t\mathrm{Hb}}$ of eight patients (patients 1, 2, 3, 4, 9, 10, 11, and 15) were also measured and analyzed during this procedure. Here cerebral $C_{t\mathrm{Hb}}$ at the beginning of this procedure was selected as its original value, so the $\Delta C_{t\mathrm{Hb}}$ monitored by the NIRS oximeter during cooling showed the change of $C_{t\mathrm{Hb}}$ during this procedure. Because both the cooling duration and extent for the patients were varied, here we only showed the changes of $\Delta C_{t\mathrm{Hb}}$ for one patient (patient 3) during cooling as an example (Fig. 8 ).

Fig. 8

Cerebral $\Delta C_{t\mathrm{Hb}}$ of patient 3 during cooling.

Our statistical results indicated that compared with the beginning of cooling, cerebral $C_{t\mathrm{Hb}}$ of the eight patients at the end of cooling decreased for $2.5\pm 1.5\mu \mathrm{mol}∕\mathrm{L}$ , and their body temperature was decreased by $6.1\pm 2.7°\mathrm{C}$ (Fig. 9 ). Thus, we can see that cerebral $C_{t\mathrm{Hb}}$ decreased along with cooling.

Fig. 9

Decrease of cerebral $C_{t\mathrm{Hb}}$ and body temperature at the end of cooling compared with the beginning-of-cooling values.

4.2.

$\mathrm{rSc}{\mathrm{O}}_2$ Versus Perfusion Rate During the Second CPB Procedure

For the convenience of surgery, the perfusion rate of some patients may be decreased by the surgeons for a short period, the body temperature kept about constant at that time. Here patients 6 to 10 each underwent one of the low-perfusion-rate stages during this procedure. The $\mathrm{rSc}{\mathrm{O}}_2$ and related physiological parameters are shown in Figs. 10a, 10b, 10c, 10d, 10e . Thus, $\mathrm{rSc}{\mathrm{O}}_2$ decreased significantly when the perfusion rate was decreased.

Fig. 10

Graphs of $\mathrm{rSc}{\mathrm{O}}_2$ of five patients during the low perfusion rate stages with constant body temperature for patients (a) 6, (b) 7, (c) 8, (d) 9, and (e) 10.

4.3.

Changes of $\mathrm{rSc}{\mathrm{O}}_2$ During the Third CPB Procedure

This was the rewarming procedure. During the early rewarming stage, $\mathrm{rSc}{\mathrm{O}}_2$ decreased significantly in all the patients. During the late rewarming stage, the decrease trends of $\mathrm{rSc}{\mathrm{O}}_2$ all stopped. Here, we specify 9 of the 15 patients (patients 4 to 6, 8 to 12, and 15). The body temperatures were $26.9\pm 2.9°\mathrm{C}$ at the beginning of rewarming; $30.9\pm 3.0°\mathrm{C}$ at the end of the early rewarming stage, which was also the beginning of the perfusion rate being increased; and $36.8\pm 0.3°\mathrm{C}$ at the end of rewarming [Fig. 11a ]. The $\mathrm{rSc}{\mathrm{O}}_2$ values were $49.9\pm 7.7$ , $41.2\pm 5.1$ , and $50.9\pm 6.2\%$ , correspondingly [Fig. 11b]. Thus the $\mathrm{rSc}{\mathrm{O}}_2$ decreased significantly during the early rewarming stage ( $n=9$ , $t=2.826$ , $p<0.02$ ) along with the body temperature being increased, and increased significantly during the late rewarming stage ( $n=9$ , $t=3.625$ , $p<0.01$ ) along with the perfusion rate being increased, even though the body temperatures were increased simultaneously.

Fig. 11

Statistical results of the nine patients during the whole rewarming process for (a) body temperature and (b) $\mathrm{rSc}{\mathrm{O}}_2$ .

5.1.

Necessity to Monitor Cerebral Oxygenation During CPB

To avoid functional and structural sequelae induced by cerebral hypoxia, cerebral oxygenation must be monitored during CPB, which can be properly reflected² by $\mathrm{rSc}{\mathrm{O}}_2$ and $\mathrm{Sj}{\mathrm{O}}_2$ . But detecting $\mathrm{Sj}{\mathrm{O}}_2$ by blood gas analysis is invasive and painful to patients, and unavailable to continuous measurement.

Pulse oxygen saturation $\left(\mathrm{Sp}{\mathrm{O}}_2\right)$ can be noninvasively monitored during cardiac surgery. But it can be detected only when the arteriole at the finger tip pulses. During CPB, the heart beat stops and the arterial pulsation is very weak, so $\mathrm{Sp}{\mathrm{O}}_2$ cannot be obtained generally.¹⁸

Venous blood oxygen saturation $\left(\mathrm{Sv}{\mathrm{O}}_2\right)$ at the entrance of the artificial pump can be monitored during CPB. But the correlation between it and $\mathrm{rSc}{\mathrm{O}}_2$ is not good in many cases because the oxygen saturation of venous blood differs for different tissues, which will be specified in our future papers.

Cerebral oxygenation, especially $\mathrm{rSc}{\mathrm{O}}_2$ , can be monitored by NIRS, which does not rely on the arterial pulsation, during the whole CPB surgery. Thus, when the arterial pulsation is weak, especially during CPB, NIRS is almost the only available method to monitor cerebral oxygenation continuously and noninvasively.

5.2.

Relationship Between $\mathrm{rSc}{\mathrm{O}}_2$ and the Physiological Parameters Such as Body Temperature and Perfusion Rate During CPB

To avoid cerebral hypoxia during CPB, some physiological parameters such as body temperature and perfusion rate should be regulated according to the physiological status of patients. However, surgeons currently regulate these physiological parameters mainly according to their experience and by observing the physical phenomena of patients by eye. If $\mathrm{rSc}{\mathrm{O}}_2$ can be a quantitative index to assess cerebral oxygenation, surgeons can use it as a guide to regulate the physiological parameters. Thus, the relationship between $\mathrm{rSc}{\mathrm{O}}_2$ and body temperature as well as perfusion rate must be discussed.

In fact, $\mathrm{rSc}{\mathrm{O}}_2$ reflects the dynamic balance between cerebral oxygen supply and consumption. When the body temperature is decreased and the perfusion rate is kept constant, the cerebral oxygen metabolic rate and then the oxygen consumption obviously decreases, but the cerebral oxygen supply does not change obviously because the amount of the arterial blood transported from the artificial pump into the aorta is steady. Thus, the $\mathrm{rSc}{\mathrm{O}}_2$ increases during the first CPB procedure (Fig. 7). On the contrary, $\mathrm{rSc}{\mathrm{O}}_2$ decreases, as observed during the early rewarming stage (Fig. 11).

When the perfusion rate is increased and the body temperature is kept constant, the amount of arterial blood transported into the aorta and thus the cerebral oxygen supply increases but the cerebral oxygen consumption does not change, so $\mathrm{rSc}{\mathrm{O}}_2$ increases. On the contrary, $\mathrm{rSc}{\mathrm{O}}_2$ decreases, as proved by Fig. 10.

During the late rewarming stage of the third CPB procedure, the body temperature and the perfusion rate are increased simultaneously. Because of the increase trend of $\mathrm{rSc}{\mathrm{O}}_2$ induced by the increase of perfusion rate, the decrease trend of $\mathrm{rSc}{\mathrm{O}}_2$ by the increase of body temperature levels off. If the perfusion rate is increased greatly enough, $\mathrm{rSc}{\mathrm{O}}_2$ may even increase, as proved by the nine patients in Fig. 11.

According to the above, $\mathrm{rSc}{\mathrm{O}}_2$ is negatively correlated with body temperature and positively with perfusion rate. And $\mathrm{rSc}{\mathrm{O}}_2$ may be relatively low during the low perfusion rate stage and the early rewarming stage of CPB (see Fig. 10 and Fig. 11). Therefore these two stages are relatively critical. To avoid cerebral hypoxia, $\mathrm{rSc}{\mathrm{O}}_2$ during these two stages should be greatly taken into account, and emergent treatments should be used such as decreasing the duration of the low perfusion rate stage, decreasing the body temperature to some extent when the perfusion rate is decreased, and increasing the perfusion rate as early as possible during rewarming.

5.3.

Changes of Cerebral Total Hemoglobin Concentration $\left(C_{t\mathrm{Hb}}\right)$ During Cooling

Besides $\mathrm{rSc}{\mathrm{O}}_2$ , the changes of cerebral $C_{t\mathrm{Hb}}$ during cooling were also detected, which can be analyzed physiologically as follows. Here $C_{t\mathrm{Hb}}$ is the concentration of total hemoglobin in a unit volume of human brain. It is determined by the following two factors: the ratio of the whole blood volume in the cerebral tissue to the total volume of cerebral tissue [Fig. 12a ] and the ratio of the volume of the red blood cells to that of the preceding whole blood, termed hematocrit [HCT, Fig. 12b].

Fig. 12

Physiological meaning of cerebral $C_{t\mathrm{Hb}}$ for (a) whole blood in cerebral tissue and (b) HCT of the whole blood.

There are currently few reports of the absolute value of cerebral $C_{t\mathrm{Hb}}$ , especially no such report for an adult. Even though the absolute value of $C_{t\mathrm{Hb}}$ cannot be measured by our NIRS oximeter, our group measured the absolute value of $C_{t\mathrm{Hb}}$ of healthy full-term infants using frequency-domain NIRS, and the result was²⁴ about $39.7\mu \mathrm{mol}∕\mathrm{L}$ . In this paper, our results indicate that during the cooling procedure of CPB, cerebral $C_{t\mathrm{Hb}}$ decreased for $2.5\pm 1.5\mu \mathrm{mol}∕\mathrm{L}$ ( $n=8$ , in Fig. 9). Thus, we can see that the decrease of $C_{t\mathrm{Hb}}$ during cooling is small.

During CPB, the HCT of cerebral whole blood was measured using invasive jugular venous blood gas analysis. The results indicated that it was 35 to 40% before CPB. For all the patients at the beginning moment of CPB, to avoid the infarction of cerebral blood vessels, their blood was suddenly diluted and HCT suddenly decreased to 20 to 30%, mostly to about 25%. Then it was steadied at the preceding value during the whole CPB, including cooling. According to large numbers of clinical surgeries, an HCT of 20 to 30% is absolutely safe for patients during CPB.

Because the HCT is steady during cooling, the preceding decrease of $C_{t\mathrm{Hb}}$ possibly reflects cerebral vasoconstriction. A few previous researchers indicated that cerebral blood vessels may shrink to a certain extent induced by cooling, so that the ratio of the whole blood volume in the cerebral tissue to the total volume of cerebral tissue [Fig. 12a] may decrease,²⁵ but there is still no quantitative report that corresponds. From Fig. 9, we can see that the decrease of $C_{t\mathrm{Hb}}$ and then the preceding cerebral vasoconstriction induced by cooling are both small. This may be because the resistance of the cerebral blood vessels may be decreased by the blood dilution at the beginning moment of CPB, which may favor cerebral vasodilatation and then compensate the preceding cerebral vasoconstriction induced by cooling.

During CPB besides $\mathrm{rSc}{\mathrm{O}}_2$ , cerebral $C_{t\mathrm{Hb}}$ is also a relatively important physiological parameter. In this paper, we discuss only the changes of $C_{t\mathrm{Hb}}$ during cooling, and the corresponding results are also preliminary and many special topics require further researches.