In the measurement of particle size distribution, light scattering methods have the advantages of a wide measurement range, high speed, and non-contact measurement. Among them, the dynamic light scattering technique is an important method to measure the size distribution of nanometer to micron particles.

In medical testing, the analysis of red blood cells is a common method for disease diagnosis. The variation coefficient of the red cell volume distribution width (RDW) is generally used to characterize the uniformity in size and shape of red blood cells in blood samples, whose increment often indicates diseases. The variation coefficient of RDW can be calculated by inversion of the particle size distribution of blood cells, which can provide reliable support in the early detection and diagnosis of some major diseases.

Current particle size inversion algorithms are mostly based on the regularization method, but the traditional regularization algorithm lacks the inversion model and algorithm for the particle size distribution of non-spherical particle systems. Moreover, its performance on narrowly distributed particle systems and the multi-angle scattered light analysis are not satisfying, which limits its application in biomedical fields.

Therefore, the corresponding model and algorithm for particle size distribution analysis based on machine learning are developed in this study, and the simulation results are provided.

It has been shown that neural networks have advantages in expressing complex objective functions such as particle size distribution, which can hierarchically describe effective data characteristics from a large amount of input data. Of the neural networks, generalized regression neural networks have been proven to be effective for function approximation. Thus, it can be widely used in various research fields requiring parameter inversion of nonlinear pathological equations without a priori knowledge of the complex arithmetic relations involved in the problem model.

In this paper, the idea of introducing generalized regression neural networks into the inversion of particle size distribution is adopted. A generalized regression neural network based on the inversion model and algorithm for the particle size distribution of particle systems is designed, which can be applied to the particle size analysis by the multi-angle dynamic light scattering method. The proposed algorithm is tested by simulations using biconcave-disk and ellipsoidal red blood cells as typical non-spherical particle models in the biomedical field.

The evaluation indexes selected in the training process of the inversion model are clarified, and the particle size distributions of non-spherical particle systems such as biconcave-disk red blood cells (Fig. 4) and ellipsoidal red blood cells (Fig. 7) are retrieved by the neural network. The optimization method for the training matrix expansion is proposed in the training process of the network (Table 1 and Table 3). During the inversion of the particle size distribution curves of biconcave-disk and ellipsoidal models, the use of 20 sets of training matrices to jointly train the neural network can result in evaluation indexes with mean values as small as 1.0027 and 0.6568, respectively.

The network (Table 2 and Table 4) is tested, and the result reveals that it has a significant advantage over the conventional regularized Tikhonov algorithm (Fig. 5 and Fig. 8) using at least two scattering angles. The use of only two scattering angles means that it is easier to build and debug a multi-angle dynamic light scattering measurement system for practical applications, which can reduce the systematic errors introduced by the consistency of concerned devices.

The experimental results show that compared with the conventional regularized Tikhonov algorithm, the inversion algorithm designed in this paper is more accurate and less time-consuming, and the neural network model can be well adapted to biconcave-disk and ellipsoidal models. The number of scattering angles in the multi-angle dynamic light scattering method is also considered, and the results show that the accurate inversion of the particle size distribution of non-spherical particle systems can still be achieved with data obtained at only two scattering angles. As long as the shape of the particles in the particle system to be measured can be clearly expressed, such as a mathematical expression for the particle shape, the network model can be extended to many other cases of non-spherical particle systems.

As an example of analyzing a non-spherical particle system, if the RDW-CV is to be further calculated after the inversion of the particle size distribution of the red blood cells, it is required that the particle size distribution curve obtained from the inversion is as close as possible to the actual particle size distribution curve at each particle size. The evaluation indexes used in this study can precisely characterize the difference between the two particle size distribution curves. Hence, it is expected that if the accuracy step of particle size inversion is appropriately reduced, it can be applied to rapid clinical detection of the particle size distribution of red blood cells for early detection and diagnosis of some major diseases.