System Modeling of Microfluidic Molecular Communication: A Markov Approach

TL;DR

The paper addresses the challenge of modeling molecular communication in microfluidic channels by developing a Markov-based, discrete-time state-space model that discretizes both transport and surface chemistry. By constructing a transition matrix that encompasses diffusion, advection, reversible binding, and flow-out, the authors derive a linear channel representation with a channel impulse response (CIR) and an equilibrium gain, enabling analytic characterization of transient and steady-state behavior under pulse and continuous release. Key contributions include the physically consistent Markov framework, closed-form expressions for the CIR and equilibrium gain, and validation against particle-based simulations across flow regimes via the Péclet number. This framework provides a tractable foundation for system-level design, estimation, and control of microfluidic molecular communication links, with potential extensions to noise modeling and MIMO configurations for larger-scale nanonetworks.

Abstract

This paper presents a Markov-based system model for microfluidic molecular communication (MC) channels. By discretizing the advection-diffusion dynamics, the proposed model establishes a physically consistent state-space formulation. The transition matrix explicitly captures diffusion, advective flow, reversible binding, and flow-out effects. The resulting discrete-time formulation enables analytical characterization of both transient and equilibrium responses through a linear system representation. Numerical results verify that the proposed framework accurately reproduces channel behaviors across a wide range of flow conditions, providing a tractable basis for the design and analysis of MC systems in microfluidic environments.

Figures (4)

• Figure 1: Schematic of the microfluidic channel with a receiving boundary.
• Figure 2: Markov chain of the microfluidic MC channel.
• Figure 3: State–space model of the microfluidic MC channel. The hidden Markov state $\bm{x}_k$ evolves according to the transient-state transition matrix $\mathbf{Q}$, driven by the input $\mathbf{b}u_{k-1}$ and the process noise $\mathbf{w}_k$. The observation $z_k^{\mathrm{obs}}$ is obtained from the state $\bm{x}_k$ through the observation vector $\mathbf{h}$, with the observation noise $v_k$ accounting for measurement uncertainty.
• Figure 4: Observed signal $z_k^{\mathrm{obs}}$ under (a) pulse release and (b) continuous release of IMs for different transmitter–receiver distances $d$ and flow velocities $v$. Solid lines show the analytical model from \ref{['eq:pulse_output', 'eq:continuous_output']}, while markers denote particle-based simulation (PBS) results. Simulation parameters: (a) $10^5$ IMs are instantaneously emitted at $t=0$ ($u_0 = 10^5$) according to \ref{['eq:pulse_input']}; (b) $5\times10^3$ IMs are continuously injected per $\Delta t$ ($u_0 = 10^3$) following \ref{['eq:continuous_input']}.