## 3 Results
### Simulating Experimental Data Using MC
#### 3.3.2 Modeling Phantoms with Actively Pumped Flow  
As described above, measurements from phantoms were obtaining by changing both the depth of the flow channel and the fluid flow rate in the channel. There were thus 12 phantoms with actively pumped fluid flow--they are identified individually by a combining a flow rate (\(F_{1}\)-\(F_{3}\)), with the channel depth (\(D_{0}\)-\(D_{3}\)). In order to simulate measurements using MC models in these phantoms, inputs for the thickness of Layer 1 (height of the liquid layer \(h\), above the flow channel) and flow \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Phantom** & **Layer1 Thickness \(z_{1}\) [cm]** & \(D_{B}\) [cm\({}^{2}\)/s] (Layers 1\&3) & \(D_{B}\) [cm\({}^{2}\)/s] (Layer 2) & \(V\) [cm\({}^{2}\)/s] (Layer 2) \\ \hline \hline DOF0 & & & \(3.6\times 10^{-9}\) & - \\ \hline DOF1 & \multirow{2}{*}{\(h_{0}=0.02\)} & \multirow{2}{*}{\(3.6\times 10^{-9}\)} & - & \(5.7\times 10^{-3}\) \\ \cline{3-5} DOF2 & & & - & \(1.42\times 10^{-2}\) \\ \cline{3-5} DOF3 & & & - & \(2.28\times 10^{-2}\) \\ \hline DIF0 & & & \(7.9\times 10^{-9}\) & - \\ \hline DIF1 & \multirow{2}{*}{\(h_{1}=h_{0}+\Delta h=0.05\)} & \multirow{2}{*}{\(7.9\times 10^{-9}\)} & - & \(5.7\times 10^{-3}\) \\ \cline{3-5} DIF2 & & & - & \(1.42\times 10^{-2}\) \\ \cline{3-5} DIF3 & & & - & \(2.28\times 10^{-2}\) \\ \hline D2F0 & & & \(8.9\times 10^{-9}\) & - \\ \cline{3-5} D2F1 & \multirow{2}{*}{\(h_{2}=h_{1}+\Delta h=0.08\)} & \multirow{2}{*}{\(8.9\times 10^{-9}\)} & - & \(5.7\times 10^{-3}\) \\ \cline{3-5} D2F2 & & & - & \(1.42\times 10^{-2}\) \\ \cline{3-5} D2F3 & & & - & \(2.28\times 10^{-2}\) \\ \hline D3F0 & & & \(9.3\times 10^{-9}\) & - \\ \cline{3-5} D3F1 & \multirow{2}{*}{\(h_{3}=h_{2}+\Delta h=0.11\)} & \multirow{2}{*}{\(9.3\times 10^{-9}\)} & - & \(5.7\times 10^{-3}\) \\ \cline{3-5} D3F2 & & & - & \(1.42\times 10^{-2}\) \\ \cline{3-5} D3F3 & & & - & \(2.28\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input coefficients for MC flow phantom models. \(\Delta h\) was constrained to be \(0.03\) cm experimentally while the relative change in fluid flow speed from flow rate of \(F_{1}\) to \(F_{2}\) was \(2.5\) (change from \(F_{1}\) to \(F_{3}\) was \(4\)). Figure 11: DCS measurements (symbols) for phantoms \(D_{0}F_{0}-D_{3}F_{0}\), (**a–d**, respectively) with theoretical fits using a Brownian-flow model (dashed line) and MC predictions (solid line). Each MC model used input \(D_{B}\) values obtained from scaling the theoretically fitted values (see text). coefficients for the three layers were needed. For active pumping, correlation transport in Layer 2 (the flow channel) was modeled as random flow, while in Layers 1 and 3 (the liquid media above and below the flow channel, respectively) it was modeled as Brownian, with both layers having the same \(D_{B}\). These \(D_{B}\) input values were obtained, for each depth, from corresponding MC models shown in Figure 11 (i.e., from phantoms with no active flow). Input values for two remaining parameters--the depth of the flow channel from surface and the flow speed of the medium in the flow channel--had to be determined. Across 12 phantoms with active flow, relative changes (in both these parameters) were experimentally well controlled. Increases in channel depth (from one depth to the next) was experimentally estimated to approximately be \(\Delta h=0.03\) cm. Therefore, if the phantoms at depth \(D_{0}\) had Layer 1 thickness of \(h_{0}\), then Layer 1 thickness for phantoms with flow channel at depth \(D_{1}\) would be \(h_{1}=h_{0}+\Delta h\) (and further as \(h_{2}=h_{1}+\Delta h\) and \(h_{3}=h_{2}+\Delta h\)). Similarly, changes in flow speeds could be calculated from experimentally used flow rates--i.e., if the input flow speed \(V_{1}\) was known for phantoms with flow \(F_{1}\), the flow speeds for flow \(F_{2}\) and \(F_{3}\) would scale as \(V_{2}=V_{1}F_{2}/F_{1}\) and \(V_{3}=V_{1}F_{3}/F_{1}\).