## 1 Introduction
To satisfy these constraints, experimental measurements of DCS typically use long SDS (\(>\)1 cm) and near-infrared laser sources. However, there could be clinical opportunities for using endoscopically compatible DCS probes to assess tissue perfusion in vivo, which will need to use short SDS for signal acquisition. Further, recent reports have employed DCS measurements at short SDS (\(<\)1 cm) for quantifying tissue perfusion in small animal models [27; 28; 29; 30; 31]. Surprisingly, these studies all reported that the classical diffusion-theory based theoretical expression in Equation (2) still provided good parametrization of relative changes in tissue perfusion even at short SDS used. Here, we further investigate the utility of Equation (2) to parametrize absolute and relative changes in flow in turbid media measured experimentally data in controlled flow-phantoms at short SDS. Additionally, we also investigate the use of Equation (2) to parametrize numerically simulated data at short SDS. Monte Carlo (MC) based modeling of photon migration provide direct, numerical solutions to the radiative transport equation and have been extensively used in the field of tissue spectroscopy [32]. They are well developed and have been used to quantify experimental measurements of diffuse reflectance obtained in phantoms, animal models and human studies [33; 34; 35; 36; 37]. MC simulations can be programmed to incorporate heterogeneous tissue architectures and can be used to accurately model diffuse reflectance and correlation even at short SDS [32; 38]. Thus, MC based photon transport methods have been used to compute normalized field correlation in semi-infinite media, simulate intensity correlation decays in complex layered scattering media and to validate improved theoretical models [31; 39; 40; 41; 42]. Here, we first examine the impact of using Equation (2) to quantitatively retrieve \(\langle\Delta r^{2}(\tau)\rangle\) from \(g_{1}(\tau)\) that were simulated using MC models of semi-infinite media spanning a range of absorption, scattering and Brownian flow diffusion coefficient \(D_{B}\) at varying SDS. Next, we acquired DCS measurements at a fixed short SDS of 0.15 cm, experimentally, in a set of flow-phantoms that included an embedded flow-channel (containing the same liquid as the phantom). The phantoms were designed to investigate how two physical parameters--the depth of the flow-channel from the optical probe and the flow type and rate of fluid in the channel--influenced DCS measurements obtained on the surface. In Section 2, we describe the experimental methods used including the instrumentation, the design of liquid phantoms and the construction of the flow-channel. We then outline the MC modeling approach to simulate photon correlation transport and the tissue models simulated for analysis, discuss the use of Equation (2) to parametrize simulated and experimental data and provide a description of the goodness-of-fit metrics used. Section 3 presents the results of the analysis of the MC simulations of semi-infinite models, followed by results from theoretical analysis of the experimental phantom, and then show the comparison between MC models developed to simulate experimental measurements on flow phantoms.