1 Introduction

Near-infrared spectroscopy (NIRS) is a non-invasive detection method commonly used today. It uses materials different absorptions for near-infrared light of different wavelengths. The absorbance of the emitted light can be analyzed for different concentrations of substances in the testing sample. Especially in the near-infrared light of 700 nm–1000 nm, have low absorption of biological tissue, which is called the “tissue window”. Light can travel through the skin and fat to deep tissues, and is absorbed by the oxymyoglobin and deoxymyoglobin in the muscle tissue.

Recently, there are many studies using NIRS to measure tissue oxygen concentration in human tissues for different diseases, such as calf tissue and brain. However, many literatures compare different NIRS in the market. It is found that due to the lack of standardization of algorithms, wavelengths and photodiode configurations, it is difficult to compare them under different machines [1].

NIRS continuously measures the oxygen concentration of muscle tissue in peripheral arterial disease (PAD) patients and normal people under exercise conditions. The PAD patients have different characteristics in after exercise [2]. But there is no way to quantify the severity of the blockage. This study is to make a phantom that conforms to the optical characteristics of the human calf muscle tissue, regulate the oxygen concentration change of the prosthesis, simulate the oxygenation and hypoxia of the calf muscle tissue, and use the self-made NIRS to measure and correct the tissue oxygen concentration.

2 Methods and Materials

Human muscle tissue is mainly composed of myoglobin. Oxygen diffuses from capillary’s oxyhemoglobin of red blood cells into the muscle tissue and combines with myoglobin to form oxymyoglobin. In order to let light to penetrates deep under skin to measure change of muscle tissue oxygen saturation.

We choose myoglobin and hemoglobin isosbestic point (808 nm) spectral for measurement, near isosbestic point wavelength light-emitting diode as light source (740 nm and 850 nm), in order to reduce difference of light scatter that influence measurement accuracy. And then, we use two long led-photodiode distance (40 mm, 32 mm) to insure light to penetrate deep into muscle tissue and two light sources can eliminate skin scattering effects [3]. In this research, the homemade NIRS optical probe configuration shows in Fig. 1.

Fig. 1.
figure 1

Photodiode and LED configuration

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The liquid phantom consisted of phosphate-buffered saline (PBS, pH = 7.4, volume in phantom = 750 ml), red blood cells purified from pig blood (volume in phantom = 11 ml), intralipid 20% (volume in phantom = 30 ml) and glucose 50% (volume in phantom = 2.7 ml). Purificatory red blood cells solution is formulated to adjust the absorbance ingredient with oxygen saturation. Optical properties of the liquid phantom are as same as lower limbs muscles optical properties [4].

In order to insure the liquid phantom blood oxygen capacity, using dissolved oxygen meter (D.O. meter, Kai-Yuan, ODO-BTA) to monitor the oxygen dissolved concentration in the liquid phantom. In a container that is closed at room temperature and is sealed, the molar of a gas dissolved in a solvent is proportional to the partial pressure of the gas that is balanced with the solution; this is called Henry’s law:

$$ {\text{p}} = {\text{kc}} $$
(1)

where p is the gas of partial pressure, c is the molar of dissolved in the solvent, k is henry’s constant. Henry’s constant will have different values because of temperature and gas, so use dissolved oxygen concentration to calculate the partial pressure in the solution. When phantom partial pressure increases, oxyhemoglobin proportion and tissue oxygen saturation is also increase. Conversely, phantom partial pressure decrease, oxyhemoglobin proportion and tissue oxygen saturation will decrease. So, k value can be derived from the known oxygen partial pressure.

However, there is no linear relationship between the ratio of hemoglobin to oxygen bonding and the partial pressure of oxygen dissolved in the solution. The corresponding relationship between two ratios is called Hill’s equation:

$$ \delta = \frac{{\left( {\frac{P}{{P_{50} }}} \right)^{n} }}{{1 + \left( {\frac{P}{{P_{50} }}} \right)^{n} }} \times 100\% $$
(2)

where δ is red blood cell solution oxygen saturation (%), P is partial oxygen pressure in phantom, P50 and n is constant.

The calibration experiment is designed a can change oxygen saturation and consist the solution simulated lower limbs muscle optical properties. Using a plastic thin-shell container to hold this solution and can attached optical probe to the outer wall for measurement. Figure 3 shows calibration experiment frame diagram (Fig. 2).

Fig. 2.
figure 2

Calibration experiment frame diagram

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In order to maintain the phantom’s temperature at 37 °C, uniform oxygen saturation and tunable dissolved oxygen concentration. Use hot plate and magnetic stirrer to maintain temperature and slowly stirring the phantom. The oxygen supply system uses mass flow controller (Protec, PC-540). Table 1 shows whole experimental steps.

Table 1. NIRS calibration experiment step
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Data processing was performed using Matlab for signal analysis. The self-made NIR spectrometer used a low-pass digital filter to calculate the ratio of the three wavelengths of near and far light. The dissolved oxygen meter is recorded at a sampling rate of 10 Hz, and is resampled to 6 Hz. The dissolved oxygen amount is converted into the oxygen content of the prosthesis tissue by the above-mentioned conversion method. Finally, the logarithmic regression of the prosthetic tissue oxygen content and the near-far light ratio was carried out to obtain the calibration curve of this study.

In order to prove that the calibration curve can be applied to measure the tissue oxygen concentration in human body, this study recruited a 23-year-old male with a BMI of 25.7. The muscle tissue oxygen concentration of the gastrocnemius muscle was measured under static standing, and a 10-min data was continuously measured for calculation. And observe whether the value is within the normal range. The experimental probe configuration is shown in Fig. 3.

Fig. 3.
figure 3

Schematic diagram of optical probe wearing on the gastrocnemius muscle

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3 Result and Discussion

Figure 4 shows optical probe measure absorbance in the process of experiment. It seems absorbance stable before adding yeast. When oxygen saturation start decreasing, the measurement absorbance start changing and between two light-detector distances have consistent change response in different wavelength.

Fig. 4.
figure 4

Photometric changes of different wavelengths measured by optical probes when changing the oxygen concentration of the phantom

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The ratio of the near 740 to the near 850 in the measured luminosity is compared with the tissue oxygen concentration measured by the D.O meter, and the result is as shown in Fig. 5. The red line represents the oxygen concentration measured by the dissolved oxygen meter. The change, the green line represents the calibration curve after regression analysis. The curve formula is as shown in Eq. 4, where StO2 represents the converted tissue oxygen concentration, R740850 represents the ratio of the wavelength 740 and 850, abcd is the calculation constant, and the determination coefficient of the calibration curve (R2) Is 0.9956.

Fig. 5.
figure 5

Second order exponential calibration curve and D.O meter experiment data

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$$ StO2\left( \% \right) = a\exp \left( {bR_{740850} } \right) + c \exp \left( {dR_{740850} } \right) $$
(4)

Finally, the calibration curve is brought into the static standing experiment. The result is shown in Fig. 6. The average of 10 min is 78.96%, the standard deviation is 0.3485, and the difference is quite small. The calculated StO2 (%) is within the normal range. The study indicated that in 42 normal subjects, the pre-exercise leg StO2 (%) ranged from 47% to 85% [5].

Fig. 6.
figure 6

In vivo measurement in ten minutes standing experiment(%)

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4 Conclusions

In the calibration experiment, using purificatory red blood cell from pig blood and intralipid to simulate the phantom that optical properties similar with lower limbs muscles. By changing the oxygen saturation of the phantom, this research make calibration curve with D.O. meter measure dissolved oxygen saturation to calculate phantom tissue oxygen saturation (Hill’s equation) as a standard reference and homemade optical probe measure tissue absorbance. In the future, use this calibration curve to homemade NIRS perform actual measurement of tissue oxygen saturation. It made our homemade NIRS measurement of tissue oxygen saturation more physiologically significant in clinical.