Photoacoustic molecular imaging has been extensively applied to biomedical research. The accurate quantification of molecular probe concentrations has paramount importance in relevant disease investigation. Nevertheless, during in-vivo detection, the signals emitted by exogenous probes are often mixed with those originating from endogenous biological tissues, thereby diminishing the quantification accuracy of probe concentrations. Traditional photoacoustic molecular imaging relies on the linear photoacoustic effect, and some methods have been proposed to enhance the concentration quantification accuracy under complex environments. One approach is based on multi-wavelength detection, but multi-wavelength switching complicates the signal acquisition process and reduces the quantification speed. Another approach is proposed according to single-wavelength background subtraction, while it lacks universality due to reliance on employing molecular probes with switchable responses. Consequently, it becomes an urgent need to develop a concentration quantification method predicated on single-wavelength excitation that does not depend on specific probe responses to advance photoacoustic molecular imaging. The Grüneisen-relaxation nonlinear photoacoustic effect exhibits promising potential to meet this need. Unlike the linear relationship between signal amplitude and absorption coefficient in the linear photoacoustic effect, the Grüneisen-relaxation (GR) photoacoustic effect shows a quadratic nonlinearity between the two physical parameters. Based on this, we propose a method for quantifying concentrations using the Grüneisen-relaxation nonlinear photoacoustic effect by single-wavelength excitation. This approach adopts the nonlinear relationship between the two physical parameters to improve the ratio between the target and background signals, effectively diminishing the background interference. Consequently, we present a novel and promising solution for improving the concentration quantification accuracy.

To demonstrate the advantages of our method, we conduct theoretical numerical simulations followed by experimental validations to assess its feasibility. For the first experiment, we first construct a Grüneisen-relaxation nonlinear system. Subsequently, we perform an experiment using phantom samples comprising red dye (representing the target component) and blue dye (representing the background component). This initial experiment serves as a preliminary validation of the principle feasibility of our method. Then, we validate the feasibility of the method in a simulated scenario that is close to in-vivo photoacoustic molecular imaging. In the second experiment, we utilize a sample consisting of the molecular probe Rhodamine 6G (representing the target component) and hemoglobin (representing the background component) to simulate the scenario in which the probe encounters interference from endogenous components.

The numerical simulation results from concentration quantification in different signal-to-background ratios (R_SB) are shown in (Table 1). The error coefficients of the linear and GR nonlinear methods can be visually represented as different sides of a triangle in Fig. 1(a). The sum of two perpendicular sides of the triangle corresponds to the error coefficient of the linear method, while the hypotenuse length represents the error coefficient of the nonlinear method. According to the triangle inequality, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Therefore, the error coefficient of the linear method consistently exceeds that of the nonlinear method. Consequently, the quantification results obtained from the nonlinear method exhibit a closer approximation to the actual value of the target component compared to those obtained from the linear method. Fig. 1(b) illustrates the relative error of the concentration quantification results. Compared with the linear method, the nonlinear method not only performs well at high R_SB values but also significantly reduces the concentration quantization error at low R_SB (R_SB=1). Therefore, the method has good applicability over a wide range of R_SB values. For the experimental results, Figs. 4(a) and 6(a) show the concentration quantification outcomes for both pigment and molecular probes respectively. The relative errors of the quantification results for both methods are depicted in Figs. 4(b) and 6(b). The experimental results show a decrease in concentration quantification errors for both methods with the increasing R_SB. Additionally, the quantification results obtained from the nonlinear method are always closer to the actual concentration of the target component. The consistency between the experimental and theoretical results not only confirms the reliability of the proposed method but also validates its error suppression capability, affirming its robust applicability in diverse scenarios.

We present a novel method to suppress background interference and improve the concentration quantification accuracy. Compared to conventional linear single-wavelength methods, the proposed method yields concentration quantification results closer to the target component concentration. Meanwhile, the relaxed generation conditions associated with the Grüneisen-relaxation nonlinear effect render this method highly versatile and applicable in various situations. We provide a novel approach to the concentration quantification of photoacoustic molecular imaging and lay a foundation for future applications.