On the Target Detection Performance of a Molecular Communication Network with Multiple Mobile Nanomachines

TL;DR

This work develops a comprehensive analytical framework for target detection in three-dimensional molecular communication networks comprising multiple mobile nanomachines (NMs). By modeling NM placements with Poisson point processes and NM motion as Brownian diffusion, the authors derive closed-form detection probabilities for stationary and mobile targets under direct contact and for indirect sensing via emitted markers, incorporating target degradation with rate $\mu$ and effective diffusion for moving targets. Key contributions include exact results for single and multi-NM configurations, degradable and non-degradable targets, mean detection times, and cumulant-expansion approximations for degradable cases, plus a detailed indirect-sensing analysis with marker concentrations. The framework enables fast, accurate performance assessment and design insights, offering substantial speedups over particle-based simulations and applicability to healthcare, environmental monitoring, and security scenarios where rapid target detection is critical.

Abstract

A network of nanomachines (NMs) can be used to build a target detection system for a variety of promising applications. They have the potential to detect toxic chemicals, infectious bacteria, and biomarkers of dangerous diseases such as cancer within the human body. Many diseases and health disorders can be detected early and efficiently treated in the future by utilizing these systems. To fully grasp the potential of these systems, mathematical analysis is required. This paper describes an analytical framework for modeling and analyzing the performance of target detection systems composed of multiple mobile nanomachines of varying sizes with passive/absorbing boundaries. We consider both direct contact detection, in which NMs must physically contact the target to detect it, and indirect sensing, in which NMs must detect the marker molecules emitted by the target. The detection performance of such systems is calculated for degradable and non-degradable targets, as well as mobile and stationary targets. The derived expressions provide various insights, such as the effect of NM density and target degradation on detection probability.

Figures (9)

• Figure 1: Target detection systems with (a) stationary target and PPP distributed NMs based on direct contact based detection, (a) mobile target and PPP distributed NMs based on direct contact based detection, and (c) PPP distributed NMs based on indirect sensing.
• Figure 2: Probability of detecting the non-degradable target versus time for different values of NM density. The value for a single NM case is also shown. Parameters for single NMs case: $a_1=4\mu m,\ D_1=100\mu m^2/s ,\ d=50\mu m$. Parameters for multiple NM case: $a_1=3\mu m,\ a_2=4\mu m,\ D_1=100\mu m^2/s,\ D_2=75\mu m^2/s,\ r=30\mu m,\ \text{ and \ } \lambda_1=1\times 10^{-6} \text{NMs}/\mu m^3$.
• Figure 3: Probability of detecting a stationary target within time $t$ versus time for a degradable target for various values of NM radius and degradation rate. Parameters : $D_1=100\mu m^2/s,\ D_2=75\mu m^2/s,\ \text{ and \ } \ \lambda_1=\lambda_2=1\times 10^{-6} \text{NMs}/\mu m^3,\ r=30\mu m$.
• Figure 4: Analytical results showing the variation of the mean number of NMs detecting a stationary target and a mobile target within time $t$. Parameters : $a_1=3\mu m,\ a_2=4\mu m, D_t=100\mu m^2/s, D_1=100\mu m^2/s,\ D_2=75\mu m^2/s, \ \lambda_1=\lambda_2=1\times 10^{-5} \text{NMs}/\mu m^3,\ \text{ and \ } r=30\mu m$.
• Figure 5: Probability of detecting a mobile target within time $t$ versus time. Parameters : $a_1=3\mu m,\ a_2=4\mu m, D_t=100\mu m^2/s, D_1=100\mu m^2/s,\ D_2=75\mu m^2/s, \ \lambda_1=\lambda_2=1\times 10^{-5} \text{NMs}/\mu m^3,\ \text{ and \ } r=30\mu m$.

Theorems & Definitions (15)

• Lemma 1
• Lemma 2
• Theorem 1
• Corollary 1
• Lemma 3
• Theorem 2
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5