## 2 Materials and Methods
### Monte Carlo Simulations of Correlation Transport  
Light propagation in tissue-like media can be numerically simulated by construction of stochastic trajectories of individual photon packets, where the variables governing the evolution of these trajectories are determined by an input tissue model's optical properties and sampled using MC techniques [32; 50]. In these simulations, several (\(10^{6}\)-\(10^{8}\)) individual photon packets are launched and aggregate quantities of interest (such as the photon flux, fluence, absorbance and fluorescence) are tracked spatio-temporally, for a given tissue model. For the studies here, we modified a time-resolved MC photon transport model (previously described in detail [49; 51]) to include simulate of photon field correlations in reflection geometry. We note that MC modelling of photon transport in scattering media are well discussed elsewhere [50; 51], and we therefore confine description of aspects pertinent only to tracking of field correlations in the MC model. Correlation transport was integrated into the MC model by adding a new variable (programmed into the simulation) to track the field correlation carried by each photon packet, as it was transported from the source to the detector, following the methodology described before [15; 39; 40]. To track the decay of the normalized photon-field correlation \(g_{1}(\tau)\), it was assumed that moving particles were uniformly distributed in each tissue layer modeled, moved uncorrelated to each other and that all photon scattering events were from dynamically moving particles. Under those conditions, \(g_{1}(\tau)\) was expressed as  
\[g_{1}(\tau)=\exp\left[-\frac{1}{6}q^{2}\langle\Delta r^{2}(\tau)\rangle\right] \tag{3}\]  
In Equation (3), \(\langle\Delta r^{2}(\tau)\rangle\) represents the mean-squared displacement term of particles contributing to dynamic scattering in time \(\tau\), while \(q\) is the magnitude of momentum transfer due to a scattering event. Each scattering event undergone by a photon packet tracked in the MC simulation provides specific \(q\) associated with it. Thus, in the geometry of the MC model, if \(\overset{\rightarrow}{k}_{1}\) and \(\overset{\rightarrow}{k}_{2}\) represented directions associated the incoming and scattered photon packets, then \(q^{2}=2k^{2}(1-\cos\theta)\), where \(\theta\) is the single-scattering angle (i.e., the angle between \(\overset{\rightarrow}{k}_{1}\) and \(\overset{\rightarrow}{k}_{2}\)) sampled by the MC model, for the photon packet being tracked [15; 40]. Since \(|\overset{\rightarrow}{k}_{1}|=|\overset{\rightarrow}{k}_{2}|=k=2\pi/\lambda\), and \(\lambda\) (the wavelength of the laser) is known, Equation (3) was used to update this variable, through the flight of the photon packet simulated using  
\[g_{1}^{N+1}(\tau)\to g_{1}^{N}(\tau)\cdot\exp\left[-\frac{1}{6}q^{2} \cdot\Delta r_{i}^{2}(\tau)\right] \tag{4}\]  
In Equation (4) the superscripts \(N\) and \(N+1\) refer to the field correlation variable (for a given photon packet within the MC simulation) before the \(N^{th}\) and \((N+1)^{th}\) scattering event, respectively with \(q^{2}\) being computed at the \(N^{th}\) scattering event. \(\Delta r_{i}^{2}(\tau)\) was the mean-squared displacement of the scattering particles in layer \(i\) (where the scattering event occurred) and was set either to \(6D_{B}\tau\) for Brownian flow, or to \(V^{2}\tau^{2}\) for random flow [15]. Thus, inputs to the MC simulations (for each layer) required flow coefficients \(D_{B}\) (or \(V^{2}\)) together with the layer optical properties. \(\Delta r_{i}^{2}(\tau)\) in Equation (4)was computed (depending on inputs either as Brownian or as Random flow) dynamically, through the path of each photon packet tracked. Each photon packet launched had initial value of \(g_{1}^{1}(\tau)=1\).