Validation of the Linearity in Image Reconstruction Methods for Speckle Contrast Optical Tomography

Speckle contrast optical spectroscopy (SCOS) is an optical technique capable of measuring human cerebral blood flow and brain function non-invasively. Its tomographic extension, speckle contrast optical tomography (SCOT), can provide blood flow variation maps with measurements using overlapping source-detector channel pairs. Linearity is often assumed in most image reconstruction methods, but non-linearity could exist in the relations between measured signals and blood flow variations. We have constructed a forward model for SCOT using the Rytov approximation to solve the correlation diffusion equation and compared it with the first Born approximation as well as the more accurate, but computationally expensive Monte Carlo simulation approach. We have shown that the results obtained using the Rytov approximation are in good agreement with the Monte Carlo simulations, while the first Born approximation deviates from the other two methods for large blood flow variations. For instance, the first Born approximation breaks down at around 30% cerebral blood flow (CBF) changes within a volume of size $60\times 50 \times 40$ $\text{mm}^{3}$, therefore we recommend using the Rytov approximation above this threshold. We have shown that our defined blood flow index (BFi) measured in SCOT is linearly related to local CBF variations, thus the forward and inverse problems can be solved linearly using the sensitivity matrix approach. We have then demonstrated image reconstruction experimentally showing human brain activations using our recently developed high-density SCOS system. Our method guides experimental system design and data analysis for SCOT.