2.1.

Main Detecting Channel Design

Gas molecules absorbing infrared light of specific wavelengths is reflected by the Lambert- Beer law.^{9, 10} If the CO₂ is lit by IR light from one side of the gas room where the CO₂ is stored, sensors at the opposite side of the room can detect the magnitude of attenuation of the IR light. By doing so, we can find the change of the CO₂ concentration. According to the Lambert-Beer law, we can obtain:

Normal human respiratory gas is a mixture of various gases. The value varies according to the specific type of gas. The absorption relationship for gas I can be defined by:

Figure 1 indicates the related absorption ratio for different gases. The peek value for CO₂ absorption is approximately 4.26 μm.^{11, 12, 13} If there is only light with a wavelength of 4.26 μm in the testing channel, the absorption relationship is approximately:

Fig. 1

Wavelengths of light absorbed by various gases.

A narrow bandpass filter with a 4.1- to 4.3-μm bandpass has been installed at the front end of the IR sensor to enhance the precision of the measurement.

To obtain the value of I, a set of reference light sources and sensors are needed in the detecting channel. The constitution of gas that has an absorption peak value of 4.0 μm is very stable, and thus a narrow bandpass filter with a 3.8- to ∼4.1-μm bandpass could be installed at the front end of the IR sensor.

Figure 2 shows in detail the layout of the testing channel. In this testing channel, we use double light sources and double light sensors, which enable complete separation of the light path for measurement and for reference. Both the light sources and the sensors work at different wavelengths, and thus reduce their interference within the system.

Fig. 2

(a) Detecting channel layout. (b) Framework for the detecting system.

The entry is not in line with the exit openings for the gas. Besides, the size of the entry is 1.5 times as large as that of the exit. Both of these features prevent the gas from passing, the channel too quickly to make complete contact with the sensors. This is beneficial for a thorough measurement of the gas changes.

Figure 2(b) is the block diagram for the monitoring system. The respiratory gas is detected by the sensor, the output of which is later fed into the signal amplification circuit. After that, the signal passes a filter and an AD convertor, and finally the digital processing unit, which is a DSP, processes the quantized values with advanced algorithms. The value of CO₂ concentration and other relevant information will be displayed on the LCD display.

2.2.

Sampling and Controll in the Detecting Channel

2.2.1.

Compensation for respiratory attenuation

In the detecting system, photons are produced by the light sources. When they flow to the sensors at the opposite side, an electrical signal is produced. In a real-world situation, due to the affect that low air exerts on the photons, the signal will be affected as a result. In particular, the signal will be attenuated. Figure 3 shows how air flow can affect the receipt of photons by sensors.

Fig. 3

(a) Photon behavior without respiration affect. (b) Photon behavior with respiration affect.

When the air is still, the voltage of both the main detecting end and the reference end are stable. By contrast, when there is air flow in the gas room, because of the impact exerted by respiration on the photons, the signal generated by both the main detecting end and the reference end will become attenuated.

Consequently, the values acquired at both the main detecting end and the reference end cannot be deployed when CO₂ concentration is to be calculated. We now define the intensity of the incident light as [TeX:] $I_0$ $I_0$ , the voltage at the main detecting end is [TeX:] $v_m$ $v_m$ when respiration is dismissed, and the reference end has a voltage of [TeX:] $v_m$ $v_m$ when respiration is dismissed. Since gas with a peak of 4.0 μm does not participate in respiration, it is stable during the process of human respiration. If the reference end has an output of [TeX:] $v_f$ $v_f$ , the main detecting end has an output of [TeX:] $v_m$ $v_m$ , and the air flow in the channel has a speed of v, we can obtain the attenuation rate:

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation*} \eta = \frac{{v_f - v'_f }}{{v'_f }}. \end{equation*}\end{document} $$\eta =\frac{v_f-v_f^{\prime }}{v_f^{\prime }}.$$

Hence, when there is no respiration, the stable output of the main detecting end is:

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation*} v''_m = \frac{{v_m }}{{1 - \eta }} = \frac{{v_m v'_f }}{{2v'_f - v_f }}. \end{equation*}\end{document} $$v_m^{\prime \prime }=\frac{v_m}{1-\eta }=\frac{v_m{v}_f^{\prime }}{2v_f^{\prime }-v_f}.$$

Currently, the CO₂ concentration value is:

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation*} C_{{\rm co}_2 } = k\, {\rm Ln}\bigg(\frac{{v_m }}{{2v'_f - v_f }}\bigg), \end{equation*}\end{document} $$C_{{\mathrm{co}}_2}=k\mathrm{Ln}\left(\frac{v_m}{2v_f^{\prime }-v_f}\right),$$

where k is a constant for concentration calculation.

2.2.2.

Light source control

In an effort to limit detecting distortion and to acquire data that reflects gases with wavelengths of 4.26 and 4.0 μm, respectively, it is desirable that the light source generate IR light with the different wavelengths.

To meet these ends, the system uses the Parabola series provided by ICX Photonics(Cambridge, Massachusetts).¹⁴ IR light with wavelengths of 4.26 and 4.0 μm can be obtained respectively by using a couple of Parabola light sources.

Because the Parabola series focuses energy within a specific range of angles, it is critical that the light sources and the sensors be installed in the appropriate locations. The axis of the light beam should be adjusted to aim at the center of the sensor so that the energy of a specific range of light spectrum can be focused to the sensor (see Fig. 4). Therefore, when the concentration of the gases changes in the testing channel, such changes can be reflected clearly by the sensors. The system can achieve very high detecting performance, and meanwhile the distortion is reduced.

Fig. 4

IR light emitting and receiving.

2.2.3.

Temperature compensation

The double-end sensor used by the system is the IR sensor. The sensor, which captures radiation energy, is a technologically mature thermopile sensor. The thermopile is manufactured by IC and MEMS technologies. It can be liken to a series of thermocouples. The temperature detecting point of the thermopile will rise as a result of its capturing IR radiation. The Thomson voltage will also be generated, because there is a temperature gradient in the same conductor of the thermocouple. At the joint of the two kinds of metals, voltage is generated, as there is a difference between the electric concentration on one conductor and that on the other. Therefore, there is a thermoelectric voltage between one terminal of the thermocouple and the other.^{15, 16}

The CO₂ concentration detecting sensor captures the IR energy of the wave with a wavelength of 4.23 μm. The temperature gradient is formed at the thermocouple circuit inside the sensor, and therefore the value of the voltage change is obtained. When the concentration is being detected, because of the rise of temperature at the thermocouple as a result of the light coming from the opposite side, the affects that respiratory air flow exerts on the temperature of the sensor, the emiting of energy by the detecting circuit, and other external factors, the subsequent subtle change of the temperature will lead to errors in measurements by the sensor. Accordingly, it is imperative that we compensate for the temperature change caused by the factors mentioned before to more accurately detect CO₂ concentration.

Given the state where the concentration remains stable, if the device is heated, by observing the main detecting end of the sensor, we will find that there are subtle temperature drifts [TeX:] $\Delta V_m$ $\Delta V_m$ and [TeX:] $\Delta V_r$ $\Delta V_r$ at the main detection end and reference end, respectively.

Based on the temperature compensation property the sensor itself possesses, drift values of signals under different temperatures can be normalized under a reference temperature and processed by parameter fitting in the system, as shown in Fig. 5. We fit the temperature to 45- deg centigrade, and the corresponding resistance of the sensors is 15 K.

Fig. 5

Temperature drifts at both detecting ends.

According to the drift values, when the temperature sampled by sensors changes, the system can correct subtle signal drift caused by temperature changes in real time.

3.1.

Signal Analysis

Because of myriad interferences when the signal is being sampled, detecting precision is negatively affected as follows.

For the detecting devices to obtain a precise signal, the data must be processed with respect to the hardware and algorithms.

3.2.

Signal Processing

The signal reflecting CO₂ concentration is obviously unstable. It can be categorized by a short process, which happens abruptly. By frequency analysis, we know that the energy distributes in a range with an upper limit of 10 Hz, as shown in Fig. 6.

Fig. 6

Human respiration frequency-domain plot.

To acquire a more precise signal, we need to use advanced filtering algorithms for signal processing shortly after the signal is processed by the circuits.

The denoising method based on Fourier transformation entails that the signal and noise share as narrow an overlap bandwidth as possible. In this way, denoising can be realized by time-invariant filters. However, when the overlap exists to a great extent, this approach is inappropriate. Wavelet analysis, a novel time-domain analysis method, provides effective tools because of its time-frequency localization property. Since signals can be depicted by wavelet coefficients, those with greater wavelet coefficients carry more energy, and vice versa. Therefore, the weight the wavelet coefficient carries can be measured by the energy the signal carries. In comparison with the wavelet transform, the wavelet packet transform provides an even more complicated and flexible approach, because it decomposes the high-frequency and low-frequency parts of the previous level simultaneously. In this sense, it possesses the ability to do precisely local analysis.

In this work, the signal reflecting CO₂ concentration is processed by filtering process algorithms based on the wavelet packet.^{17, 18, 19} We follow these procedures.

4.1.

Experiment 1

Experiment 1 focuses on a standard CO₂ experiment. At an ambient temperature of 25°C, atmospheric pressure of 101.325 kPa (760 mmHg) and standard CO₂ gas concentration of 5%, respectively, the gas flow is 1.5, 2.0, and 2.5 L/min for the experiment.

The standard gas experiment data are shown in Table 1. Data for the table were collected from three velocity cases—maximum, minimum, and average. Deviation range is less than 3.5%.

Table 1

Standard gas experiment values.

4.2.

Experiment 2

Experiment 2 focuses on the effect of the temperature compensation. After settling the temperature of the novel capnograph to a certain value, the CO₂ signal is measured and processed. The temperature can be reflected by the value of thermal resistance. When the value of resistance presented as 15 K(45°C) and 20 K (60°C), we tested the respiration of a 30-year-old man, and got the result shown in Fig. 7. After the process of temperature compensation algorithm, the maximum derivation in 15 K is 3.1%, and average derivation is 1.2%; and the maximum derivation in 20 K is 3.2%, and average derivation is 1.3%. The experiment also tested the signal with other resistance values, and received similar derivations, which indicates that the novel method proposed in this work can reduces the temperature drift and controls the average derivation under 1.4%.

Fig. 7

Temperature influence of the output signal from the capnograph.

4.3.

Experiment 3

Experiment 3 focues on the filtering performance and the signal detail preservation performance of the novel capnograph. Because we have adopted advanced signal processing algorithms in this work, the details of the signal of the respiratory gases are better retained than the side-stream capnograph does.

The experiment uses Oxycon Pro(Care Fusion, San Diego, California) to generate a relatively complex breath waveform—hackle graph, which is detected simultaneously by a common side-stream capnograph and a new capnograph with a mainstream structure. With respect to the general waveform, as shown in Fig. 8, the new capnograph approximates much better the Oxycon Pro than the common side-stream capnograph does. A closer look at the details of the signals (as circled in Fig. 8) reveals that the new capnograph can quickly track the signal with high accuracy when it changes violently. By contrast, the common side-stream capnogragh introduces distortions to a great extent when the signal changes violently with great detail.

Fig. 8

Hackle graphs compared in detail.

4.4.

Experiment 4

Experiment 4 focuses on the novel capnograph detecting effect on special cases. This work has done some further clinical experiments on a platform groove cracking patient (restoration of spontaneous breathing) and an iceberg graph patient (disappearance of muscle-relaxant side effect), as shown in Fig. 9. From the figure, it can be concluded that the device can detect the key point in special cases (as pointed in the figure).

Fig. 9

Respiration signal of special cases. (a) Platform groove cracking-restoration of spontaneous breathing. (b) Iceberg graph-disappearance–muscle-relaxant side-effect.

4.5.

Experiment 5

Experiment 5 focuses on the clinical research of a novel capnograph. This work selected 100 patients with different ages (from 3 to 80) to perform the clinical experiment. The result shows that the novel device can achieve a similar accuracy compared with the standard Oxycon Pro, with maximum derivation of 3.43% and average derivation of 3%. Accordingly, the design method and compensation filtering algorithm proposed have played a key role in increasing the accuracy of the measurement. From the measuring results it can be concluded that the novel capnograph reaches the same accuracy with the side-stream device.