Donders is dead: cortical traveling waves and the limits of mental chronometry in cognitive neuroscience David M. Alexander, Chris Trengove & Cees van Leeuwen Cognitive Processing International Quarterly of Cognitive Science ISSN 1612-4782 Cogn Process DOI 10.1007/s10339-015-0662-4 1 23 Your article is published under the Creative Commons Attribution license which allows users to read, copy, distribute and make derivative works, as long as the author of the original work is cited. You may self- archive this article on your own website, an institutional repository or funder’s repository and make it publicly available immediately. 1 23 Cogn Process DOI 10.1007/s10339-015-0662-4 RESEARCH REPORT Donders is dead: cortical traveling waves and the limits of mental chronometry in cognitive neuroscience 1 1 1,2 David M. Alexander • Chris Trengove • Cees van Leeuwen Received: 8 December 2014 / Accepted: 4 June 2015 Ó The Author(s) 2015. This article is published with open access at Springerlink.com Abstract An assumption nearly all researchers in cog- coordinates of measurements. We illustrate what the failure nitive neuroscience tacitly adhere to is that of space–time of space–time separability implies for cortical activation, separability. Historically, it forms the basis of Donders’ and what consequences this should have for cognitive difference method, and to date, it underwrites all difference neuroscience. imaging and trial-averaging of cortical activity, including the customary techniques for analyzing fMRI and EEG/ Keywords Cortex Á Traveling waves Á Difference method MEG data. We describe the assumption and how it licenses common methods in cognitive neuroscience; in particular, we show how it plays out in signal differencing and Donders’ method averaging, and how it misleads us into seeing the brain as a set of static activity sources. In fact, rather than being Franciscus Cornelis Donders (1818–1889) was the first static, the domains of cortical activity change from moment scientist to apply the subtraction method to cognition. By to moment: Recent research has suggested the importance comparing simple to choice reaction times, he was able to of traveling waves of activation in the cortex. Traveling draw conclusions regarding the time course of choice waves have been described at a range of different spatial processing. scales in the cortex; they explain a large proportion of the The idea occurred to me to interpose into the process variance in phase measurements of EEG, MEG and ECoG, of physiological time some new components of and are important for understanding cortical function. mental action. If I investigated how much this would Critically, traveling waves are not space–time separable. lengthen the physiological time, this would, I judged, Their prominence suggests that the correct frame of ref- reveal the time required for the interposed term erence for analyzing cortical activity is the dynamical (Donders 1969, p. 418) trajectory of the system, rather than the time and space This idea is now a central tenet of cognitive neuro- This article is part of the special issue on ‘Complexity in brain and science. The point is that we can take one cognitive process cognition’ and has been guest-edited by Scott Jordan. (possibly a baseline or resting state) and compare a second process that differs in only one important respect. The Electronic supplementary material The online version of this difference between two cognitive processes is revealed in article (doi:10.1007/s10339-015-0662-4) contains supplementary material, which is available to authorized users. the difference between the two sets of measurements associated with them. Further, the properties of the extra & David M. Alexander cognitive component can be isolated by making this sub- [email protected] traction. These properties involve the time course of the 1 Brain & Cognition Research Unit, University of Leuven, extra component (in Donders’ example) or brain activation Leuven, Belgium patterns in the case of fMRI, EEG and MEG. 2 Kaiserslautern University of Technology, Kaiserslautern, The subtraction method allows cognitive operations to Germany be inferred in a straightforward manner by subtracting 123 Cogn Process measurements from a baseline condition. That the results A ubiquitous methodological practice in cognitive neu- are thereby meaningful derives from what we shall call the roscience is to obtain measure of brain activity by ana- assumption of additivity. The measured signal can be lyzing the time course of activity alone, or the spatial described as a linear combination of different signal sour- topography of activity alone. This usually results in ces. This assumption is of primary importance for the throwing away most of the data as irrelevant: It is con- subtraction method. However, an additional assumption is sidered enough to analyze the time series at a site of often implicit in how differencing is usually undertaken in interest, or to take spatial snapshots at some relevant times. neuroscience. This assumption is called space–time sepa- This practice boils down to treating brain data as if it were rability. We will argue that the failure of space–time sep- space–time separable. arability in neuroscience means that the assumption of The assumption of space–time separability in cognitive additivity is misleadingly applied. neuroscience is usually left implicit, but covers quite a As far back as 1868, Donders understood the potential range of methods. Before continuing on to the evidence as limits and shortcomings of his method: to why this assumption does not hold, we will spell out the implications as follows: It is readily seen that the course taken in the research was not irreproachable… If one enters a room from (1) The additivity assumption states that cortical activity two sides successively to do something there, it is may be considered as a sum of component patterns unlikely that in both cases one will leave the room of activity. through a third door within the same interval of (2) Each component pattern can be represented as (a) a time… Thus it is not surprising that in repetitions of topographic array of activations multiplied by the experiments, mainly keeping to the same method, (b) corresponding task/stimulus-locked activation very divergent results were obtained. (ibidem, time series. pp. 415–416). (3) A consequence of (2) is that (a) and (b) may be considered separately in further analyses as separa- Here we will argue that the problem expressed by the ble functions of space and time, respectively. ‘different doors’ metaphor is much more common than the (4) The separate component functions of the signal, widespread use of the difference method in cognitive defined by (3), can each be mapped into a common neuroscience would suggest. The key empirical evidence temporal or spatial coordinate system. comes from recent insights into traveling waves of activity (5) The mapping in (4) can be achieved by affine linear in the cortex. We suggest (but will not fully demonstrate) transformations of either the time domain or the that the problem is an in-principle one. So the problem spatial domain, e.g., scaling and translation of the arises at the base of theory, not simply as a limitation of data. methods. In this sense, the problem is akin to the errors of (6) The scaling and translation of the spatial or temporal the four humors, the four classical elements, or sponta- domain are constant for a given subject, task neous generation. It is not akin to flat earth as a local condition, or signal type of interest. This enables approximation, Newtonian mechanics at low velocities, or averaging the signals within conditions or the methodological conveniences such as ignoring air resis- function type of interest. tance in the measurement of falling bodies. According to additivity assumption (1), the total activity measured during an experiment is assumed to be the sum of Space–time separability in neuroscience task-related component A1 and other non-task components A2 … An. The first component derives from the cognitive Cortical signals are measured at different brain locations function of interest, the others from the baseline task. The and over a range of times. The activity measurements may difference method states that the baseline condition A2 … be in microvolts (in the case of EEG) or femtoTesla (in the An can be subtracted from A1, A2 … An leaving only the case of MEG) or rise and fall of Blood-oxygen-level-de- activity of interest, A1. pendent (BOLD) response (in the case of fMRI) (Boynton According to (2), the activity of interest, A1, is under- et al. 1996). The different spatial locations are determined stood as signal measurements in space, x, and time, t, such by the position of an EEG or MEG sensor or the coordi- that: nates of an imaged voxel of fMRI. Each measurement type A1ðÞt; x ¼ ftðÞÂ gxðÞ; has a characteristic time course, whether it involves oscillations in the alpha-band at the 100-ms timescale, or where f and g are independent. What this means is that the rise and fall of brain metabolic measures over a few one component of A1 is a function of time, and only time, seconds, in the case of fMRI. and one component is a function of space, and only space. 123 Cogn Process Examples of such functions are given in Fig. 1. Panel A of the signal that are purely a function of space, i.e., g(x). (upper) shows a topographical map of cortical activation, This is what we do when we compare two snapshots of typical in fMRI. This map corresponds to g(x) after behavior, discounting their temporal courses, or two fMRI thresholding. Two conditions (usually one of them a images. The converse case is where the spatial function baseline) are compared by taking a difference map.