Keywords

1 Introduction

Tissue oxygen saturation (StO2) has a great potential to become an important clinical parameter, especially in neonatology [3, 4]. It is related to the oxygen metabolism in the tissue on an absolute scale. Slightly different approaches are used to calculate StO2, depending on the manufacturer. This is reflected in different naming, e.g., tissue oxygenation index for the NIRO (Hamamatsu Photonics, Japan) [5] or regional oxygen saturation for the INVOS (Somanetics Corp., USA) or Critikon (Johnson & Johnson, UK). Studies have been published, which compared the values obtained from the three different devices and found differences between INVOS and Critikon [6] and agreement between the NIRO and INVOS [7, 8]. However, both found unacceptable baseline differences. Several reasons were given as explanation: Differences in the technical setup, the effect of extracranial blood flow and differences in the algorithm.

However, the influence of the algorithm itself has to our knowledge not been evaluated. Our aim was to test the influence of basic assumptions of the multi-­distance approach [1], which is similar to spatially resolved spectroscopy [2]. Using the different approaches on the same data sets excludes the instrumentation or extracranial blood flow as a source of differences.

2 Methods

2.1 Subjects

Data sets from two different studies have been evaluated. First, 30 newborn infants have been studied previously in our group with the aim to identify precision of NIRS [9]. Second, eight adult subjects (all male, age range 26–45, median 29.5) were investigated within a still ongoing study. Both studies were approved by the ethical committee of the Kanton of Zurich and informed consent was obtained prior to the study.

2.2 Protocol

Neonatal group. The frontal and temporal cerebral region was measured four times for approximately 1 min. The sensor was repositioned between the measurements [9].

Adult group. Five repeated measurements per subject were taken from the nondominant forearm, near to musculus brachioradialis. The sensor was fixated with an elastic bandage around the forearm. Each measurement took 1 min, in between measurements the bandage was completely removed and the sensor was repositioned to approximately the same place as before.

2.3 NIRS Measurement

The neonatal group was measured with the MCPII, which is described in detail elsewhere [10]. It uses three wavelengths (750, 800, and 875 nm) at distances of 1.25 and 2.5 cm.

The adult group was assessed by a novel continuous wave NIRS device, the OxyPrem, which is similar to previous wireless sensors [11]. It measures light attenuation at 760 and 870 nm, at distances of 1.5 and 2.5 cm.

2.4 Theory

Tissue oxygen saturation was calculated by a self-calibrating multi-distance approach [1] based on the diffusion approximation of the radiative transport equation and using two sources and two detectors. The light intensity decreases with the distance. This relation is linear (semi-infinite boundary condition).

$$ \mathrm{ln}(dc(r){r}^{2})=r{\text{Sl}}_{dc}({\mu }_{\text{a}},{\mu }_{\text{s}}{}^{\prime })+{\text{In}}_{dc}{}^{\prime }(D,{K}_{dc}),$$
(24.1)

dc(r) is the average light intensity as a function of distance r, Sl dc the slope of the intensity loss and \( {\text{In ′}}_{dc}\)the intercept. μ a and \( {\mu }_{\text{s}}{}^{\prime }\)are the absorption and the reduced scattering coefficient, respectively. K dc is a constant. The diffusion constant D equals

$$ D=\frac{1}{3{\mu }_{\text{a}}+3{\mu }_{\text{s}}{}^{\prime }}\cong \frac{1}{3{\mu }_{\text{s}}{}^{\prime }}.$$
(24.2)

μ a is often neglected because tissue scattering is much larger than absorption (\( {\mu }_{\text{s}}{}^{\prime }\)). However, here we distinguish between simplified and exact diffusion constant (as seen below).

When evaluating (24.1) at two distances r L and r S and subtracting them, the slope can be calculated from the ratio of the measured intensities.

$$ {\text{Sl}}_{dc}=\frac{\frac{1}{2}\mathrm{ln}\left(\frac{d{c}_{1}\left({r}_{\text{L}}\right)d{c}_{2}\left({r}_{\text{L}}\right)}{d{c}_{1}\left({r}_{\text{S}}\right)d{c}_{2}\left({r}_{\text{S}}\right)}\right)+2\mathrm{ln}\left(\frac{{r}_{\text{L}}}{{r}_{\text{S}}}\right)}{{r}_{\text{L}}-{r}_{\text{S}}},$$
(24.3)

where r L is the longer source–detector distance and r S the shorter one, respectively. Equation (24.3) is a special self-calibrating form, whereby the use of two source–detector pairs [giving the four intensity values dc 1,2(r L, r S)] the coupling factors between the tissue and source/detector cancel out [1]. Then μ a can be calculated as

$$ {\mu }_{\text{a}}={\text{Sl}}_{dc}^{2}D.$$
(24.4)

When the absorption is determined at least at two wavelengths, concentrations of oxygenated ([O2Hb]) and deoxygenated hemoglobin ([HHb]) and the tissue oxygen saturation can be calculated. We used the absorption coefficients from Matcher et al. [12], averaged over the measured intensity spectrum of each light source. Coefficients for scattering were taken from Matcher et al. [13] for the adult arm and from ISS OxyPlex measurements on 36 term infants [14] for the neonates, extrapolated to 750, 800, and 875 nm (3.81, 3.49, and 3.01[cm−1]).

$$ \left[\begin{array}{c}\left[\text{HHb}\right]\\ \left[{\text{O}}_{2}\text{Hb}\right]\end{array}\right]={A}^{-1}\left[\begin{array}{c}{\mu }_{\text{a}}\left({\lambda }_{1}\right)\\ {\mu }_{\text{a}}\left({\lambda }_{2}\right)\end{array}\right],\text A=\left[\begin{array}{cc}{a}_{\text{HHb},{\lambda }_{1}}& {a}_{{\text{O}}_{2}\text{Hb,}{\lambda }_{1}}\\ {a}_{\text{HHb},{\lambda }_{2}}& {a}_{{\text{O}}_{2}\text{Hb},{\lambda }_{2}}\end{array}\right]$$
(24.5)

where a i,j is the absorption coefficient for i = ([HHb], [O2Hb]) at the wavelength j. StO2 is calculated as [O2Hb]/([O2Hb] + [HHb]). We examine five different assumptions A1–A5 for the determination of the absorption:

  1. A1.
    $${\mu }_{\text{a}}=-\frac{{{\mu }^{\prime }}_{\text{s}}}{2}+\sqrt{\frac{1}{4}{{\mu }^{\prime }}_{\text{s}}{}^{2}+\frac{1}{3}{\text{Sl}}_{dc}^{2}}-{a}_{{\text{H}}_{2}\text{O},\lambda }55.5\text{M}\frac{{P}_{{\text{H}}_{2}\text{O}}}{100\%}, $$
    (24.6)
  2. A2.
    $${\mu }_{\text{a}}=-\frac{{{\mu }^{\prime }}_{\text{s}}}{2}+\sqrt{\frac{1}{4}{{\mu }^{\prime \prime }}_{\text{s}} 2+\frac{1}{3}{\text{Sl}}_{dc}^{2}}, $$
    (24.7)
  3. A3.
    $$ {\mu }_{\text{a}}=\frac{{\text{Sl}}_{dc}^{2}}{3{\mu }_{\text{s}}{}^{\prime }}-{a}_{{\text{H}}_{2}\text{O},\lambda }55.5\text{M}\frac{{p}_{{\text{H}}_{2}\text{O}}}{100\%},$$
    (24.8)
  4. A4.
    $$ {\mu }_{\text{a}}=\frac{{\text{Sl}}_{dc}{}^{2}}{3{\mu }_{\text{s}}{}^{\prime }},$$
    (24.9)
  5. A5.
    $$ {\text{StO}}_{2}=\frac{{a}_{\text{HHb},{\lambda }_{1}}-{a}_{\text{HHb},\lambda 2}{\left(\frac{{\text{Sl}}_{dc}\left({\lambda }_{1}\right)}{{\text{Sl}}_{dc}\left({\lambda }_{2}\right)}\right)}^{2}}{({a}_{\text{HHb},{\lambda }_{1}}-{a}_{{\text{O}}_{2}\text{Hb},{\lambda }_{1}})-({a}_{\text{HHb},{\lambda }_{2}}-{a}_{{\text{O}}_{2}\text{Hb,}{\lambda }_{2}}){\left(\frac{{\text{Sl}}_{dc}\left({\lambda }_{1}\right)}{{\text{Sl}}_{dc}\left({\lambda }_{2}\right)}\right)}^{2}},$$
    (24.10)

Equations (24.6) and (24.7) use the exact diffusion constant, while (24.8)–(24.10) use the simplified one. In (24.10), \( {\mu }_{\text{s}}{}^{\prime }\)is assumed to be constant over the wavelength. Hence, it cancels out in StO2 calculation as shown. Equations (24.6) and (24.8) are accounting for water in tissue. Here aH2O,λ is the absorption of water at the wavelength λ in 1/(M*cm) and p H2O is the amount of water in the tissue. We used 70% for the adult forearm and 90% for the neonatal head. Water contains approximately 55.5 mol atoms/l.

2.5 Statistics

Between-subject variability and within-subject variability were determined using R (version 2.6.1, R Development Core Team, Austria) with its linear mixed effects function LME. StO2 was the random variable and subject the factor.

3 Results

For the neonatal head measurements the mean StO2 ± standard deviation (SD), the within-subject variability (Varwithin) and the between-subject variability (Varbet) are given in Table 24.1. In Table 24.2 the values for the adult group are shown.

Table 24.1 StO2, within-subject variability and between-subject variability for 30 newborn infants measured on the head for the five different assumptions A1–A5
Full size table
Table 24.2 StO2, within-subject variability and between-subject variability for eight adults measured on the forearm for the five different assumptions A1–A5
Full size table

In both adults and the neonates assumption A5 deviates in value ∼10%. In neonates including a water term (A1 vs. A2, A3 vs. A4) has a minor effect on StO2, but the use of the exact or simplified diffusion constant (A1 vs. A3, A2 vs. A4) induces a change in StO2 by 5%. In contrast, on the adult arm, the water term makes a large difference of ∼15%, while the diffusion constant assumption does induce smaller changes. For both groups, between-subject variability and within-subject variability are smaller when not including the water term (A2 and A4). Both variables are ∼0.3% larger when additionally assuming \( {\mu }_{\text{s}}{}^{\prime }\) to be constant (A5 against A2, A4).

4 Discussion and Conclusion

Our results show, that slight differences in the assumptions have a relevant influence on the final StO2 value. This difference is also dependent on the measured tissue. The water term seems to have a smaller influence in neonates than the tissue homogeneity (\( {\mu }_{\text{a}}\ll {\mu }_{\text{s}}{}^{\prime }\)). This may reflect the influence of the cerebral spinal fluid in the brain [15]. Since the water term only induces a small correction of StO2 we believe that the water correction is more or less correct. However, the variability within and in between subjects is smaller when not including the water term, although only by ∼0.2%.

Regarding the arm tissue of the adults, the concentration of lipid is higher and the water concentration is lower than for the neonatal head. While the diffusion constant assumption does not affect the StO2 value, the water term makes a difference of ∼15%. Since no real reference value exists for StO2, it is not possible to state if one assumption is more valid than another. From a mathematical point of view, the water term has no relevant influence if the slope (24.3) is much larger than the water term. Hence, the ratio between the long and short distances is much smaller than 1. If the ratio is close to 1, the slope will be small and the water term (usually in the order of 10−2) dominates. This means the ratio is closer to 1 when measuring the adult arm. This may be due to the lipid concentration in the arm, which has not been taken into account, or due to the 70% water assumption, which may be too high, or both. We calculated the body mass index (BMI) for the subjects, which correlated with the change in StO2 (data not shown), i.e., the higher the BMI and hence the lipid concentration, the higher the change of StO2 when taking water into account. The latter is supported by the fact that not subtracting the water lowers the variability. The additional assumption A5 lowers the StO2 values, compared to A2 and A4. This suggests that this assumption is not valid, neither in the neonatal head nor in the adult arm.

In conclusion, we investigated the effect of the assumptions \( {\mu }_{\text{s}}{}^{\prime }\), \( {\mu }_{\text{a}}\ll {\mu }_{\text{s}}{}^{\prime }\) = constant over the wavelengths and the water contribution and their combinations when using the multi-distance approach of StO2 calculation. We found significant differences in StO2 and its variability, depending on the assumptions made and the tissue investigated.