Dopaminergic effects on electrophysiological and functional MRI measures of human cortical stimulus–response power laws O.J. Arthurs, a,1 C.M.E. Stephenson, b,1 K. Rice, c V.C. Lupson, a D.J. Spiegelhalter, c S.J. Boniface, a and E.T. Bullmore a,b, * a Wolfson Brain Imaging Centre, Addenbrooke’s Hospital, University of Cambridge, Cambridge, CB2 2QQ, UK b Brain Mapping Unit, Department of Psychiatry, Addenbrooke’s Hospital, University of Cambridge, Cambridge, CB2 2QQ, UK c MRC Biostatistics Unit, Institute of Public Health, University Forvie Site, Cambridge, CB2 2SR, UK Received 8 May 2003; revised 5 September 2003; accepted 26 September 2003 Power laws have been widely used to formulate relationships between objective intensity of stimulation and subjective intensity of sensation. We investigated the effects of dopaminergic drug treatment (sulpiride) on the relationship between somatosensory stimulus intensity and cortical response measured electrophysiologically by somatosensory- evoked potentials (SEP) and functional magnetic resonance imaging (fMRI). The intensity of stimulation was related by a simple power law to both electrophysiological and fMRI measures of cortical response, with overlapping confidence intervals for both power law exponents. Sulpiride did not modulate the power law exponent, but significantly attenuated the ‘‘gain’’ of both stimulus–response functions. Using path analysis we decomposed dopaminergic effects on fMRI data into an indirect component (16%), predictable by drug effects on SEP, and a direct component (84%), not explained electrophysiologically. Results indicate that sulpiride has comparable effects on power law parameters estimated from SEP and fMRI, but fMRI has superior sensitivity to detect drug effects on somatosensory cortical recruitment by graded stimulation. D 2003 Elsevier Inc. All rights reserved. Keywords: Dopamine; Psychophysics; Scaling; Path analysis; Somatosen- sory; Multimodal Introduction Stevens (1957) first clearly formulated a quantitative relation- ship between sensation or perception ( P) and physical intensity of stimulation (I), which has since became known as the ‘‘fundamen- tal law of psychophysics’’ (Laming, 1997): P ¼ CI h ð1Þ or logP ¼ logC þ hlogI ð2Þ where C represents the ‘gain’ and h the power law exponent. Stevens further supposed that the form of this magnitude estima- tion function reflected isomorphic power law relationships between intensity of stimulation and physiological measures of neuronal response subserving subjective sensation or perception (Laming, 1997). Such power laws have since been demonstrated for the coupling between stimulus intensity and firing rate of single units in visual cortex and, at a larger scale of neural organization, for the stimulus–response relationship between luminance and human visual-evoked potential (VEP) latency (Osaka and Yamamoto, 1978). There is recent evidence for analogous relationships be- tween cognitive complexity (numerosity) and neural activity in the prefrontal cortex of monkeys (Nieder and Miller, 2003); see also Gisiger (2001) and Goldberger et al. (2002) for general reviews of power law scaling in biological systems. Various explanations have been proposed to account for the success of power laws in succinctly describing (psycho)physiolog- ical stimulus – response relationships. At the level of single units, power laws relating input voltage to firing rate can be accounted for by a noisy linear-threshold function (Miller and Troyer, 2002). At the level of subjective experience and behaviors, power laws might arise by averaging multiple independent exponential decay processes (Anderson, 2001). More generally, power laws or scaling relationships are very common in biological systems (Gisiger, 2001; Goldberger et al., 2002) and might represent the ensemble behavior of self-organized critical systems dynamically far from equilibrium (Linkenkaer-Hansen et al., 2001). An alternative general view is that scaling behavior may be typical of systems that have evolved or been designed to support maximum dynamic diversity at minimum cost or to cope with a physical environment that is constituted predominantly by scale-invariant or fractal forms (Chater and Brown, 1999). There have been no previous investigations of possible power law relationships between intensity of somatosensory stimulation and electrophysiological or functional neuroimaging measures of human cortical response. Moreover, there has been no previous 1053-8119/$ - see front matter D 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2003.09.067 * Corresponding author. Brain Mapping Unit, Department of Psychia- try, Addenbrooke’s Hospital, University of Cambridge, Hills Road, Cambridge CB2 2QQ, UK. Fax: +44-1223-336581. E-mail address: etb23@cam.ac.uk (E.T. Bullmore). URL: http://www-bmu.psychiatry.cam.ac.uk. 1 These authors contributed equally to this work. Available online on ScienceDirect (www.sciencedirect.com.) www.elsevier.com/locate/ynimg NeuroImage 21 (2004) 540 – 546