A learning algorithm for computational connected cellular network

The objective of computational connected cellular network (CCCN) is to model a network of bone cells and study the mechanical loading induced signal communication pattern among them. Our previous study (2000, 2001) has shown that a backpropagation (BP) neural network model can be used to capture the functional relation between the mechanical loading and the amount of bone formation. To emulate the cell-to-cell communication pattern in bone matrix, a new computational connected cellular network (CCCN) learning system has been developed with a structure that closely mimics the actual biological structure of cell-connections in a bone. An error-correcting learning algorithm is proposed for CCCN based on a two-dimensional extension of the backpropagation algorithm. The CCCN is divided into numerous BP networks, whose architecture changes with weights and cell-state updating cycles. The conventional BP learning algorithm can be applied to each BP network. It is convergent because of the constraints enforced by the characteristics of a real bone cell. Application of the CCCN to an animal bone adaptation experiment produces interesting cell communication patterns.

1. Introduction

It is believed that bone cells can sense and transmit signals produced by external mechanical loading. The signals are processed and integrated through cell-to-cell communications-in a connected cellular network (CCN) before reaching bone forming cells on bone surface [4]. However, the mechanism of bone intercellular communication is still unknown. A new computational con- nected cellular network (CCCN) learning system has been developed with a structure that closely mimics the actual biological structure of a CCN in a bone. The network is represented as a two-dimensional grid with rows and columns (for a detail description of this architecture refer to [3]). The cells within the bone cell network respond to mechanical loading by generating biological signals. These signals must propagate through the network of bone cells until they reach, the last layer of the network where the bone forming cells are located. We use the data from a bone adaptation experiment on roosters [1]. The input-output function is learned by the network with the help of the proposed weight and the state adaptation rules. The final values of the weights provide the connections pattern established between cells. This in turn shows the travel paths of the signals through the network. There are three major steps in the learning algorithm: (1) initialization, (2) update of states of bone cells, computation of actual cell output and calculation of error at each bone forming cell in the last layer and (3) weight update.