Objective For fluorescence endoscopic imaging system, the depth of tumor detection determined by the signal-to-noise ratio of the fluorescence image is the core index of its detection ability, which directly affects the effect of tumor resection. During the design process of rigid endoscopic systems, under the condition of working distance determination, the signal-to-noise ratio is determined by the entrance pupil diameter, excitation light irradiance, fluorescent probe concentration, integration time, noise and so on together. Traditional design methods do not consider either the propagation process of illumination light in biological tissues nor the response of the detector, so that the optical design and biological tissues are isolated from each other. The overall performance of endoscope system cannot be optimized theoretically. The overall design index lacks the theoretical guidance of the signal-to-noise ratio model. At present, most of the tumor depth is estimated by CT, ultrasound and other diagnostic means, and there is a lack of assessment methods using fluorescence endoscopy. So, it’s necessary to apply auxiliary diagnosis by other methods while using fluorescence endoscopy, which does not meet the practical application requirements. Therefore, it is necessary to establish an whole-link signal-to-noise model, which not only provides theoretical guidance and basis for the design of fluorescent rigid endoscopes, but also aids in intraoperative tumor localization by combining the advantages of fluorescent endoscopes in terms of high image contrast, fast imaging speed, low adverse reaction and non-contact measurement.

Methods Firstly, starting from the illumination of the end face of the optical fiber, photometric theory is used to calculate the luminescence intensity and the surface irradiance of biological tissues at the working distance of the endoscope. And then the propagation of photons in the tissue body is simulated through the Monte Carlo method, some of the fluorescence generated by it will be transmitted outside the tissues at the same time. The internal distribution of light in biological tissues and its external radiation intensity are calculated based on theory, which can help to obtain the irradiance at the pupil entrance of the fluorescent endoscope. Secondly, the fluorescence is gain-focused on a CMOS detector image through the fluorescent endoscope optics. The noise of the background, detector, and readout circuit is taken into account subsequently. So, the relationship between the signal-to-noise ratio of fluorescence endoscopic imaging and the depth of tumor detection is finally derived (Fig.2).

Results and Discussions When a Gaussian beam with a total power of 2 W, divergence half angle of 45°, and wavelength of 808 nm is incident vertically (Tab.1) and transmitted to a depth of greater than 46 mm from the light source, the irradiance of the excited fluorescence reaching the surface of tissue is much less than 10-30 W/m², which can hardly be received by the detector (Fig.6). When the tumor radius increases from 0.5 mm to 5 mm,the maximum depth of the tumor that fluorescence can reach the surface of tissue increases from 36 mm to 44 mm from the light source (Tab.4). Moreover, when the tumor center is 35 mm from the light source, the fluorescence center irradiance on tissue surface of the tumor with a radius of 5 mm and that of the tumor with a radius of 2.5 mm increases by a factor of 63. The mean irradiance values of fluorescence excited at a depth of 6 mm within the tissue body and at the surface of the tissue body for tumors of radius 2 mm, 3 mm, 4 mm, and 5 mm centered at z=35 mm from the light source are roughly 100-fold, 50-fold, 10-fold, and 5-fold different, respectively, for tumors of the same radius (Fig.7). The fluorescence center irradiance of a tumor with a radius of 5 mm and a center distance of 35 mm from the light source on the surface of the tissue is 35.28 W/m². And the signal-to-noise ratio of the whole-link system is 34.64 dB under the circumstances, which is of good imaging quality (Fig.8). As the radius of the tumor decreases and the center of the tumor deepens, the number and energy of fluorescent photon packets reaching the surface of the tissue are reduced, which results in non-statistical simulation results, so that the signal-to-noise ratio of the whole-link system fluctuates and attenuates. In addition, when the radius of the tumor is less than 2 mm, it is beyond the endoscopic detection ability to measure small volume tumors in deeper locations.

Conclusions The process of establishing the whole-link signal-to-noise ratio model of the fluorescence endoscope system and using it to simulate the depth of tumor detection is proposed. Not only a two-layer tissue-tumor model is established, but also the interaction of photons with the tissue body and the process of fluorescent molecular probes being excited to fluorescence are taken into account. According to the above, the in vivo light distribution law of the biological tissues is obtained and the relationship between the fluorescence endoscopic whole-link signal-to-noise ratio and the depth of tumor detection has been analyzed. This fluorescence endoscopic tumor detection depth analysis method provides theoretical guidance to reduce the detection error. Therefore, it can improve the detection depth and sensitivity of small tumors and metastatic lesion, providing a guarantee for accurate tumor resection.