Quantification of blood flow index in diffuse correlation spectroscopy using a robust deep learning method

Diffuse correlation spectroscopy (DCS) is a powerful, noninvasive optical technique for measuring blood flow. Traditionally the blood flow index (BFi) is derived through nonlinear least-square fitting the measured intensity autocorrelation function (ACF). However, the fitting process is computationally intensive, susceptible to measurement noise, and easily influenced by optical properties (absorption coefficient $$ and reduced scattering coefficient $$) and scalp and skull thicknesses.

We aim to develop a data-driven method that enables rapid and robust analysis of multiple-scattered light's temporal ACFs. Moreover, the proposed method can be applied to a range of source-detector distances instead of being limited to a specific source-detector distance.

We present a deep learning architecture with one-dimensional convolution neural networks, called DCS neural network (DCS-NET), for BFi and coherent factor ($$) estimation. This DCS-NET was performed using simulated DCS data based on a three-layer brain model. We quantified the impact from physiologically relevant optical property variations, layer thicknesses, realistic noise levels, and multiple source-detector distances (5, 10, 15, 20, 25, and 30 mm) on BFi and $$ estimations among DCS-NET, semi-infinite, and three-layer fitting models.

DCS-NET shows a much faster analysis speed, around 17,000-fold and 32-fold faster than the traditional three-layer and semi-infinite models, respectively. It offers higher intrinsic sensitivity to deep tissues compared with fitting methods. DCS-NET shows excellent anti-noise features and is less sensitive to variations of $$ and $$ at a source-detector separation of 30 mm. Also, we have demonstrated that relative BFi (rBFi) can be extracted by DCS-NET with a much lower error of 8.35%. By contrast, the semi-infinite and three-layer fitting models result in significant errors in rBFi of 43.76% and 19.66%, respectively.

DCS-NET can robustly quantify blood flow measurements at considerable source-detector distances, corresponding to much deeper biological tissues. It has excellent potential for hardware implementation, promising continuous real-time blood flow measurements.