UNCORRECTED PROOF 1 Connective field modeling 2 Koen V. Q1 Haak a, b, c, ⁎, Jonathan Winawer d , Ben M. Harvey e , Remco Renken b , Serge O. Dumoulin e , 3 Brian A. Wandell d , Frans W. Cornelissen a, b 4 a Laboratory for Experimental Ophthalmology, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands 5 b BCN Neuroimaging Center, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands 6 c York Neuroimaging Centre, Department of Psychology, University of York, York, United Kingdom 7 d Department of Psychology, Stanford University, Stanford, CA, United States 8 e Helmholtz Institute, Experimental Psychology, Utrecht University, Utrecht, The Netherlands 9 10 abstract article info 11 Article history: 12 Accepted 6 October 2012 13 Available online xxxx 14 15 16 17 Keywords: 18 Visual cortex 19 fMRI 20 Functional connectivity 21 Connective field 22 Population receptive field 23 The traditional way to study the properties of visual neurons is to measure their responses to visually 24 presented stimuli. A second way to understand visual neurons is to characterize their responses in terms of 25 activity elsewhere in the brain. Understanding the relationships between responses in distinct locations in 26 the visual system is essential to clarify this network of cortical signaling pathways. Here, we describe and val- 27 idate connective field modeling, a model-based analysis for estimating the dependence between signals in 28 distinct cortical regions using functional magnetic resonance imaging (fMRI). Just as the receptive field of a 29 visual neuron predicts its response as a function of stimulus position, the connective field of a neuron predicts 30 its response as a function of activity in another part of the brain. Connective field modeling opens up a wide 31 range of research opportunities to study information processing in the visual system and other topographi- 32 cally organized cortices. 33 © 2012 Elsevier Inc. All rights reserved. 34 35 36 37 38 Introduction 39 The interpretation of visual neuroscience measurements made in 40 different parts of the brain is unified by the receptive field concept. 41 A measurement at any point in the visual pathway is usually summa- 42 rized by referring to the stimulus properties (location, contrast, color, 43 motion) that are most effective at driving a neural response. 44 Stimulus-referred receptive fields provide a common framework for 45 understanding the sequence of visual signal processing. The classic 46 receptive field construct summarizes the entire set of signal process- 47 ing steps from the stimulus to the point of measurement. This 48 sequence of signal processing can be made explicit by modeling 49 how the activity of one set of neurons predicts the responses in a dis- 50 tinct set of neurons. Characterizing the responses of a cortical neuron 51 in terms of the activity of neurons in other parts of cortex can provide 52 insights into the computational architecture of visual cortex. Such 53 measurements are exceptionally difficult to achieve with single-unit 54 recordings. The relatively large field of view in functional magnetic 55 resonance imaging (fMRI) offers an opportunity to measure re- 56 sponses in multiple brain regions simultaneously, and thus to derive 57 neural-referred properties of the cortical responses. These cortical 58 response properties provide important information about how 59 neuronal signals are transformed along the visual processing path- 60 ways. For example, stimulus-referred measurements in cortex show 61 that visual space is sampled according to a compressive function 62 (i.e., the V1 cortical magnification factor corresponds to a logarithmic 63 compression of cortical space with eccentricity). Neural-referred 64 measurements show that this compression is established at the earli- 65 est stages of vision; later visual field maps sample early maps uni- 66 formly and inherit the early compressive representation (Harvey 67 and Dumoulin, 2011; Kumano and Uka, 2010; Motter, 2009). 68 A limitation in developing models of how fMRI responses in two parts 69 of cortex relate to each other is that the problem is under-constrained. 70 For example, there are many voxels in visual area V1, and there are 71 many ways in which these responses could be combined to predict the 72 response in a voxel in V2. Hence, any estimate requires imposing some 73 kind of prior constraint on the set of possible solutions. Heinzle and 74 colleagues (Heinzle et al., 2011), for example, used a support vector 75 machine approach to reduce the dimensionality of the solution of V1 sig- 76 nals and predict responses in extrastriate cortex. Here, we take a differ- 77 ent approach based on the idea that in retinotopic cortex connections 78 are generally spatially localized. We build on a model-based population 79 receptive field (pRF) analysis that was developed to estimate the 80 stimulus-referred visual receptive field of a voxel (Dumoulin and 81 Wandell, 2008). In the pRF analysis, the receptive field is modeled and 82 fit to the fMRI signals elicited by visual field mapping stimuli. This is 83 done by generating fMRI signal predictions from a combination of the 84 receptive field model and the experimental stimuli. In the present NeuroImage xxx (2012) xxx–xxx ⁎ Corresponding author at: York Neuroimaging Centre, Department of Psychology, University of York, York, United Kingdom. E-mail address: koenhaak@gmail.com (K.V. Haak). YNIMG-09880; No. of pages: 9; 4C: 1053-8119/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.neuroimage.2012.10.037 Contents lists available at SciVerse ScienceDirect NeuroImage journal homepage: www.elsevier.com/locate/ynimg Please cite this article as: Haak, K.V., et al., Connective field modeling, NeuroImage (2012), http://dx.doi.org/10.1016/j.neuroimage.2012.10.037