In this paper, a mathematical optimization formula for estimating the optimal channel dimensions of active transport molecular communication is presented. More specifically, rectangular channels with constant microtubule (MT) concentration are considered. It is shown, both using our formula and using Monte Carlo simulations, that square-shaped channels are optimal. Furthermore, when the value of time per channel use is on the order of a few minutes, which is the range of interest for a lot of potential applications such as diagnostic chips for healthcare, it is shown that our optimization formula can quickly and accurately estimate the optimal channel dimensions.
I. INTRODUCTIONMolecular communication, which is used in nature for intercellular and intracellular communication, relies on particles such as molecules for transmission of information. These information carrying molecules propagate in fluidic microchannels, either passively or actively. In passive transportation, the information molecules diffuse in the channel via Brownian motion from the transmitter to the receiver, while in active transport, the information molecules are transported as cargoes using a molecular motor system which could consist of static kinesin motors and microtubule (MT) carries. Moreover, molecular communication has attracted attention as a communication method in nanonetworks [1], [2]. Related works in this field include a general formulation of molecular communication as a timing channel under Brownian motion [3], [4], an analysis of information transfer rates using molecular motors [5], [6], mathematical channel models for continuous diffusion [7], binary concentration-encoded molecular communication [8]. Concerning active transport molecular communication, in [9], [10] basic channel design is considered for designing molecular sorters and rectifiers.Our previous work includes a simple mathematical transport model for active transport propagation [11], and optimization of the transmission zone and vesicular encapsulation [12].In this work we extend our earlier work on transmission zone design, and consider the optimization of channel shape in active transport molecular communication. Design and optimization of these channels in wet labs are extremely time consuming and laborious. Therefore, previous works have relied on computer simulations for design and optimization. However, computer simulations can also become computationally intensive and tedious in solving design problems. In this