Extraction of diffuse correlation spectroscopy flow index by integration of Nth-order linear model with Monte Carlo simulation

Abstract

Conventional semi-infinite solution for extracting blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements may cause errors in estimation of BFI (aD B ) in tissues with small volume and large curvature. We proposed an algorithm integrating Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in tissue for the extraction of aD B . The volume and geometry of the measured tissue were incorporated in the Monte Carlo simulation, which overcome the semi-infinite restrictions. The algorithm was tested using computer simulations on four tissue models with varied volumes/geometries and applied on an in vivo stroke model of mouse. Computer simulations shows that the high-order (N ! 5) linear algorithm was more accurate in extracting aD B (errors < 62%) from the noise-free DCS data than the semi-infinite solution (errors: À5.3% to À18.0%) for different tissue models. Although adding random noises to DCS data resulted in aD B variations, the mean values of errors in extracting aD B were similar to those reconstructed from the noise-free DCS data. In addition, the errors in extracting the relative changes of aD B using both linear algorithm and semi-infinite solution were fairly small (errors < 62.0%) and did not rely on the tissue volume/geometry. The experimental results from the in vivo stroke mice agreed with those in simulations, demonstrating the robustness of the linear algorithm. DCS with the high-order linear algorithm shows the potential for the inter-subject comparison and longitudinal monitoring of absolute BFI in a variety of tissues/organs with different volumes/geometries. is an emerging technology for probing microvascular blood flow in deep tissues. DCS for the measurement of blood flow variations has been broadly validated against other standards, including power spectral Doppler ultrasound, Doppler ultrasound, laser Doppler flowmetry, Xenon computed tomography, fluorescent microsphere flow measurement, and arterial-spin-labeled magnetic resonance imaging. 2,5 DCS has also been used for blood flow monitoring in a variety of tissues/organs including brain, tumor, and skeletal muscle. 2,5Conventionally, blood flow index (BFI) was extracted by fitting the autocorrelation function measured by DCS to analytical solutions of correlation diffusion equation under regular tissue boundaries (e.g., semi-infinite homogenous media, [6][7][8][9] multi-layer slabs, 10,11 a sphere inside a slab 12 ). Some of those analytical solutions were proposed to account for the influence of non-scattering layer tissues 11 or to improve the signal-to-noise ratio in deep tissues.9 However, the commonly used semi-infinite approximation may lead to BFI estimation errors in small volume tissues with large curvature. 13 Seeking analytical solutions is mathematically complicated 10,12 and likely impossible for irregular geometries.With more and more clinical and pre-clinical applications of DCS, there is an urgent need to develop an algorithm that can accurately extr...

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