## 1. Introduction

This review article is an attempt to discuss a traditional goal of neuroscience, the characterization of the relation between structure and function in the brain, from the perspective of general system theory (von Bertalanffy, 1969). The article starts with an overview of causal and correlative approaches in neuroscience towards the investigation of structure–function relationships (SFRs) in neural systems. Introducing a few simple concepts from general system theory, some formal implications for the investigation of SFRs in neural systems are derived. These implications are then evaluated in the context of functional neuroimaging. I will argue that classic applications of functional neuroimaging are insufficient to provide insights into SFRs and need to be complemented by principled models of neural systems that properly reflect the connectional structure of the system as well as the bridging principles from structure to function. One of the most useful ways of expressing these bridging principles is in terms of effective connectivity. Several models of effective connectivity are introduced and their strengths and limitations are discussed.

Many of the ideas expressed in this article are not novel and have been expressed in similar ways before (e.g. Horwitz et al. 1999; McIntosh, 2000; Friston, 2002). What this article hopes to contribute, however, is a generic perspective on models of SFRs in neural systems that is derived from basic principles of general system theory. A further aim of this article is to lend support to the current transformation of neuroimaging from a field using exploratory analyses and data-driven interpretations of the results to a hypothesis-led, model-based discipline that gradually merges with computational neuroscience in order to provide mathematical descriptions of SFRs in the brain.

Although I believe that neural systems cannot be understood without formal mathematical models, I have tried to keep the mathematical descriptions simple, in the hope that those neuroscientists who have not had much exposure to mathematical models of neural systems will find the material accessible. All models discussed here are essentially linear models at the level of larger brain regions (e.g. cortical areas) and do not require a sophisticated knowledge of mathematics to understand them. Furthermore, to present general concepts in a tutorial style, I have expanded on some issues that may appear unnecessarily detailed for readers with experience in system analysis. The latter readers are referred to mathematically more advanced texts on neural system modelling as found, for example, in Friston (2003), Jirsa (2004) or Dayan & Abott (2001).