Lab-on-chip devices and point-of-care diagnostic chip devices are composed of many different components such as nanosensors that must be able to communicate with other components within the device. Molecular communication is a promising solution for on-chip communication. In particular, kinesin driven microtubule (MT) motility is an effective means of transferring information particles from one component to another. However, finding an optimal shape for these channels can be challenging. In this paper we derive a mathematical optimization model that can be used to find the optimal channel shape and dimensions for any transmission period. We derive three specific models for the rectangular channels, regular polygonal channels, and regular polygonal ring channels. We show that the optimal channel shapes are the square-shaped channel for the rectangular channel, and circular-shaped channel for the other classes of shapes. Finally, we show that among all 2 dimensional shapes the optimal design choice that maximizes information rate is the circular-shaped channel.