Modeling Duct Flow for Molecular Communication

TL;DR

As advection-only transport is typically overlooked and hence not analyzed in the molecular communication literature, the symbol error rate for exemplary on-off keying as performance metric is evaluated.

Abstract

Active transport such as fluid flow is sought in molecular communication to extend coverage, improve reliability, and mitigate interference. Flow models are often over-simplified, assuming one-dimensional diffusion with constant drift. However, diffusion and flow are usually encountered in three-dimensional bounded environments where the flow is highly non-uniform such as in blood vessels or microfluidic channels. For a qualitative understanding of the relevant physical effects inherent to these channels, based on the Peclet number and the transmitter-receiver distance, we study when simplified models of uniform flow and advection-only transport are applicable. For these two regimes, analytical expressions for the channel impulse response are derived and validated by particle-based simulation. Furthermore, as advection-only transport is typically overlooked and hence not analyzed in the molecular communication literature, we evaluate the symbol error rate for exemplary on-off keying as performance metric.

Figures (5)

• Figure 1: System model geometry (a) in the cross-section, and (b) along the axis. The red shading in (a) reflects the flow velocity which is maximum in the center and vanishes at the boundary. The corresponding parabolic shape, $x=v(r)\cdot t$, on which released particles reside when not diffusing after a uniform release, is sketched in (b) for three different time instances. Point and uniform transmitter release are shown as black dot and as a blue line, respectively. The receiver region is shaded in blue.
• Figure 2: Sketch of regions of different transport regimes. Adapted from probstein_physicochemical_2005. All four simulation scenarios are shown as black dots. For $a=10µm$, we have $\mathop{\mathrm{Pe}}\nolimits=100$ and $d/a=20,80$. For $a=200µm$, we have $\mathop{\mathrm{Pe}}\nolimits=2000$ and $d/a=1,4$.
• Figure 3: Snapshot of particle positions for $a=10µm$ and at $t=0.02,0.2,0.8s$ after uniform release at $x=0$ and $t=0$ shown in different colors and starting from left to right, respectively. In total, $N_\textsc{tx}=e3$ are released.
• Figure 4: Impulse responses for (a) $a=10µm$, and (b) $a=200µm$. Simulation results are shown for both uniform and point release. For (b), additionally the simulated and analytical impulse responses due to a point release are scaled by the constant factor 0.1 for a better visualization. Simulation results are averaged using $N_\textsc{tx}=e6$.
• Figure 5: Symbol error rate in \ref{['eq:ser']} as a function of the symbol interval length for $d=200,400,600,800µm$. Parameters are chosen as $N_\textsc{tx}=e3$, $N_\mathrm{n}=4$, $D=e-12m^2\per s$, and $K=8$. Results are averaged over e4 independent realizations.