Principles of fMRI PDF

Principles of fMRI Tor D. Wager and Martin A. Lindquist This book is for sale at http://leanpub.com/principlesoffmri This version was published on 2015-10-12 This is a Leanpub book. Leanpub empowers authors and publishers with the Lean Publishing process. Lean Publishing is the act of publishing...

Principles of fMRI Tor D. Wager and Martin A. Lindquist This book is for sale at http://leanpub.com/principlesoffmri This version was published on 2015-10-12 This is a Leanpub book. Leanpub empowers authors and publishers with the Lean Publishing process. Lean Publishing is the act of publishing an in-progress ebook using lightweight tools and many iterations to get reader feedback, pivot until you have the right book and build traction once you do. ©2015 Tor D. Wager and Martin A. Lindquist Contents What’s in this book?....................................... 1 About the Authors......................................... 3 Martin Lindquist........................................ 3 Tor Wager........................................... 3 Part 1: Motivation................................. 5 Chapter 1 - Introduction..................................... 6 MRI, PET, and beyond: A quick tour............................. 6 Principles............................................ 8 Chapter 2 - Why fMRI? Neuroimaging and the movement toward multidisciplinary science 9 Neuroimaging and the ‘common language’ of the brain................... 9 Multiple roles, multiple fields: An example.......................... 12 Challenges and motivation for multidisciplinary science.................. 13 Chapter 3 - Types of imaging: What PET and fMRI can measure.............. 15 MRI: Multiple measures, multiple modalities......................... 15 Structural MRI imaging.................................... 16 Functional imaging with fMRI and PET........................... 18 Chapter 4 - Brain mapping: A conceptual overview...................... 22 What is a brain map?..................................... 22 Fundamental assumptions and principles........................... 25 Types of inference: What brain maps can and cannot tell us................ 30 Chapter 5 - Limitations in inferences from brain maps.................... 35 Seven caveats in brain map inferences............................ 35 A non-imaging example.................................... 38 Chapter 6 - How to lie with brain imaging........................... 39 How to tell a story about the “one brain region’’....................... 39 How to make your results look really strong......................... 40 Overlapping processes: How to make two maps look the same............... 41 CONTENTS How to make two maps look really different......................... 42 Conclusions.......................................... 43 Part 2: Fundamentals: The origins of PET and fMRI signals in the brain................................ 44 Chapter 7 - fMRI basics: Processing stages, terminology, and data structure........ 45 fMRI basics........................................... 45 Data structure in fMRI experiments............................. 54 Conclusions.......................................... 57 Chapter 8 - The MRI environment and human factors.................... 58 MR basics and safety..................................... 58 Physical limitations on data collection............................ 59 Chapter 9 - A head-to-head comparison of PET and MRI................... 63 Acquisition options and fidelity................................ 63 Available signal types and their interpretability....................... 63 Spatial and temporal resolution................................ 64 Accessibility to a broad community............................. 65 Conclusions.......................................... 65 Chapter 10 - Fundamentals of MRI Physics........................... 66 Chapter 11 - Physiological basis of fMRI signals........................ 68 Chapter 12 - Constraints on fMRI spatial and temporal resolution............. 70 Spatial Limitations....................................... 70 Temporal Limitations..................................... 71 Part 3: Basics of fMRI signal processing and analy- sis................................................. 73 Chapter 14 - Experimental Design................................ 74 Block designs.......................................... 74 Event-related fMRI...................................... 75 Optimized experimental designs............................... 76 Chapter 15 - Resting state, natural viewing, and non-experimental designs........ 77 Resting state.......................................... 77 Natural viewing and non-experimental designs....................... 79 Chapter 16 - Essentials of fMRI signal processing....................... 80 CONTENTS BOLD signal.......................................... 80 Noise and nuisance signal................................... 82 Chapter 17 - Preprocessing.................................... 85 Reconstruction......................................... 85 Slice-timing correction.................................... 86 Motion correction....................................... 86 Co-registration......................................... 87 Normalization......................................... 88 Spatial smoothing....................................... 89 Chapter 18 - The General Linear Model and Foundations of Analysis........... 90 Setting up the GLM...................................... 91 GLM Estimation........................................ 91 Chapter 19 - Conditions and Contrasts............................. 93 Chapter 20 - Design Specification: Flexible Hemodynamics and Mis-modeling...... 94 Chapter 21 - Design Specification: Dealing with Artifacts and Noise............ 97 Chapter 22 - Group Analysis................................... 100 Chapter 23 - Multiple Comparisons............................... 103 FWE correction........................................ 104 FDR control.......................................... 105 Chapter 24 - Assessing Brain Connectivity........................... 106 Functional connectivity.................................... 106 Effective connectivity..................................... 107 Network analysis....................................... 109 Part 4: Predictive Mapping......................... 110 Chapter 25 - Multivariate brain analysis: From maps to models............... 111 From univariate mapping to multivariate brain models................... 112 Basic criteria for a good model................................ 120 Chapter 26 - Advantages of MVPA from a neuroscientific perspective........... 121 MPVA analysis choices: Spatial scope and flexibility.................... 121 Sensitivity to neural topography............................... 125 Sensitivity to distributed representations........................... 128 Benefits in testing generalizability across individuals and studies.............. 130 Resources and further reading.................................. 133 CONTENTS Other books about fMRI.................................... 133 What’s in this book? The field of neuroimaging is spreading its tendrils far and wide, and is reaching into various fallow fields and corners of the public consciousness. Neuroimaging results are bread and butter for psychologists and neuroscientists, and are becoming more and more relevant for physicians, economists, lawyers, engineers and physicists curious about biology, biologists curious about computation and the human mind, and anyone who wants to understand science news at a deeper level and is curious about what we’re discovering, or not, about the human mind and brain. The increasing popularity of neuroimaging, particularly Functional Magnetic Resonance Imaging (fMRI), poses a particular challenge. It is inherently a technical enterprise, requiring a mish-mash of biological, computational, statistical, and psychological expertise that spans fields and is contained in no single training program. That is why we created this book. We have been teaching fMRI experimental design and analysis for 15 years, to various groups of people–from doctors to engineers to statisticians to businesspeople– and we have gained an appreciation for how challenging it can be to put all the pieces together and be a smart consumer, and a smart creator, of neuroimaging research. This book is designed to convey essential knowledge about how fMRI works, and the principles that underlie it, for both practitioners and readers who may not sit down at a computer and analyze fMRI data themselves, but want to take their understanding of how it works to the next level. What’s in this book? 2 The book is divided into five sections. In the first section, we provide some basic context on fMRI in relation to other brain-focused techniques, and discuss why fMRI is being intensively developed and what some of those developments are. In the second section, we cover the origins of PET and fMRI signals in the brain, their spatial and temporal resolution, and what we can and cannot measure with MRI and PET. In the third section, we review key concepts underlying the process of fMRI data analysis, from signal processing fundamentals to statistical inference. In the fourth section, we focus on inference, and particularly on the kinds of claims that are currently being made based on brain imaging data. The data analysis strategy is often not matched to the types of inferences that researchers want to make, and the result is a number of ’crises’ in neuroscience that are largely avoidable. A community of researchers and public consumers of research that is better educated on how valid inferences can be made, and the limitations involved, will be better positioned to make discoveries that will shape our world for the better. Finally, in the fifth section, we discuss some emerging approaches that are changing the way we analyze fMRI data and the kinds of valid claims that we can make about the human brain and mind. About the Authors Martin Lindquist Professor, Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Dr. Lindquist is a Professor of Biostatistics at Johns Hopkins University. He received his Ph.D. in Statistics from Rutgers University in 2001, and served as an Assistant and Associate Professor at Columbia University from 2003-2012. His research focuses on mathematical and statistical problems relating to functional Magnetic Resonance Imaging (fMRI). Dr. Lindquist is actively involved in developing new analysis methods to enhance our ability to understand brain function using human neuroimaging. Twitter: @fMRIstats Martin’s web page at JHU¹ Tor Wager Professor, Department of Psychology and Neuroscience and the Institute of Cognitive Science University of Colorado, Boulder ¹http://www.biostat.jhsph.edu/~mlindqui/ About the Authors 4 Dr. Wager is a Professor of Psychology and Neuroscience and a faculty member in the Institute for Cognitive Science at the University of Colorado, Boulder. He received his Ph.D. from the University of Michigan in cognitive psychology in 2003, and served as an Assistant and Associate Professor at Columbia University from 2004-2009. Since 2010, he has directed Boulder’s Cognitive and Affective Neuroscience laboratory. He has a deep interest in how thinking influences affective experiences, affective learning, and brain-body communication. His laboratory also focuses on the development and deployment of analytic methods, and has developed several publicaly available software toolboxes for fMRI analysis. He has been teaching fMRI analysis methods since 2003. Twitter: @torwager, @canlab Cognitive and Affective Neuroscience Lab web page² ²http://wagerlab.colorado.edu Part 1: Motivation Chapter 1 - Introduction Welcome to Principles of fMRI. This book, its companion volume, and their accompanying courses on Coursera are part of a series on Functional Magnetic Resonance Imaging designed to benefit both those who are practitioners of fMRI and those not actually engaged in fMRI research but who want to be “smart consumers’’ of contemporary brain science. Neuroimaging refers to any technique used to obtain and integrate multiple measures of brain structure or function into a picture - or a series of pictures - of the brain. One of the most exciting advances in the psychological, behavioral, and brain sciences over recent decades is the ability to non-invasively image the living human brain. This human imaging reveals both brain structure (i.e., anatomy) and function: it demonstrates images of brain electrical, neurochemical, and metabolic processes which occur as living humans engage in any number of various mental states including solving problems, experiencing emotion, feeling one’s bodily state, thinking about other people, or dreaming. Many types of human neuroimaging are available today. Some are invasive and require opening the skull to make brain measurements. These include optical imaging and intracranial recording or electrocorticography (known as ECoG), which are electrophysiology techniques that can be used to create maps or, in some cases, images. The most widely used methods, however, are minimally or non-invasive and can support large-scale studies of healthy humans. These methods include electroencephalography (EEG), magnetoencephalography (MEG), single-photon emission tomography (SPECT), near-infrared spectroscopy (NIRS), positron emission tomography (PET), and magnetic resonance imaging (MRI). MRI, in turn, encompasses multiple techniques employed to image brain structure and function. Each of these methods has strengths and weaknesses, and provides a complementary window into the function of the brain and mind. Among the diverse neuroimaging methods, MRI is now the most widely used. The family of techniques used to assess brain function is called “functional magnetic resonance imaging’’, or fMRI, and is the primary focus of this book. Though we concentrate on fMRI, many of the principles and techniques we cover apply broadly to other types of imaging and beyond to further scientific fields. Many of the principles underlying experimental design and statistical modeling and inference are not unique to neuroimaging at all and accordingly pertain across various areas of scientific inquiry. MRI, PET, and beyond: A quick tour In later chapters, we discuss more fundamentals of how the techniques above relate to one another and what their relative strengths and weaknesses are. To orient you, however, here are a few key ideas that also provide a rationale for limiting the scope of this book to MRI. Chapter 1 - Introduction 7 Among the various human neuroimaging techniques, MRI and PET are unique in their capacity to create images of the entire living human brain with fairly veridical localization of where in the brain the signals originate. EEG and MEG record, respectively, electrical and magnetic information from the brain surface. These measurements directly reflect neuronal electrical activity at high temporal resolution (e.g., every millisecond), which is an enormous advantage. NIRS also makes measurements at the skull, but does so using light. However, EEG and (to a lesser degree) MEG rely on complex mathematical models to make inferences about where the signals in the brain originate, which require one to make strong statistical assumptions. These postulations are difficult to validate and are often violated, thus leaving quite a bit of uncertainty about the origination of the signals within the brain. In addition, these three techniques - EEG, MEG, and NIRS - are all quite limited in their sensitivity to brain areas. Each is largely restricted to detecting signals from the cortical surface, though one can find a number of MEG papers that also make claims about signal sources in deeper brain structures. By contrast, both MRI and PET provide the capacity to reconstruct three-dimensional brain volumes with fairly high spatial resolution (in some cases less than 1 mm) across the entire brain. For this reason, the term “neuroimaging’’ is often used to describe primarily MRI and PET. MRI can provide measures related to many physiological features of interest, including: * Gray- matter density and cortical thickness * White-matter tract density and location * Brain elasticity and shearing forces * The sizes, location, and course of blood vessels * The flow of cerebrospinal fluid * Measures of a few selected neurotransmitter levels, like GABA, and specific proteins related to metabolism * Moment-by-moment measures of cerebral blood flow * Moment-by-moment measures related to blood oxygenation, flow, and oxygen metabolism. This last measure refers to Blood Oxygen Level-Dependent (BOLD) signal, which is the most widely used measure of functional activity in fMRI. With modern BOLD imaging, we can sample signals throughout the whole brain with spatial resolution around 3 mm and temporal resolution of one brain volume per second. This entails sampling about 100,000 brain locations, or Òvoxels,Ó every second, which provides a rich picture of activity in the cortex and dynamics across brain networks. PET provides unique measures which complement the strengths of fMRI. PET can image cerebral blood flow and glucose metabolism, which, along with fMRI measures, are often referred to as activity'' oractivation’’. PET is an invasive technique that involves injecting radioactively labeled compounds into the bloodstream. It can therefore be used to image a wide variety of molecular and cellular processes, and is limited mainly by the types of compounds which can be radiolabeled and their actions on the brain’s receptors. There are now hundreds of radiolabeled compounds which have been used to examine brain function, including those processes related to dopamine, serotonin, acetylcholine, opioids, microglial function, and neuroinflammation. Though in theory many compounds are available, their radioactive labeling means each compound must be developed and manufactured on-site next to the scanner with precise control over the time from manufacture to injection into the research participant. These constraints place practical limitations on the scope of molecular imaging research. Chapter 1 - Introduction 8 Principles Using each of these techniques effectively requires a great deal of specialized knowledge. However, it also requires understanding the basic principles of experimental design, statistical analysis, inference, and brain localization and function that cut across all of these techniques. We focus on MRI and fMRI in part because of their advantages and widespread availability, and in part becauseÑhey, it’s what we do. However, many of the principles contained in this book apply to other types of neuroimaging and beyond. Chapter 2 - Why fMRI? Neuroimaging and the movement toward multidisciplinary science Neuroimaging and the ‘common language’ of the brain Human neuroimaging, especially fMRI and PET, is a growing new field now with thousands of publications per year. Why all the excitement? One of the goals of neuroimaging is a movement towards multidisciplinary science. This is one thing we’re particularly excited about. For many years, people in different fields have been studying diverse aspects of the mind, the brain, and the body. Psychologists study the mind and behavior while neuroscientists study the brain. Medical and clinical researchers study the treatment and prevention of illness including those of the mind and the brain, which we increasingly understand to be interconnected with other body systems. Clinical trials study health related interventions and biologists study living systems. The fields of statistics, engineering, and computer science have each emerged as leading disciplines in the study of complex computational and biological processes with different traditions of techniques and approaches. Figure 2.1. A plot of the number of publications per year in PubMed with the term fMRI in either its title or abstract. Chapter 2 - Why fMRI? Neuroimaging and the movement toward multidisciplinary science 10 These fields form rich but largely separate traditions. This is in some sense inevitable as a field grows and matures with a strongly shared history of knowledge and increasingly specialized techniques among its practitioners. This canalization and deepening of roots is complemented by new growth of fields that evolve at the intersections among established fields before developing their own research traditions. Psychophysiologists study the mind as related to peripheral physiology. Neuroimmunologists study the brain as related to the immune system. Psychoneuroimmunologists study intersections of the mind, brain, and immune functions. Each of these disciplines provides a crucial but incomplete window into the most exciting frontier in contemporary science: the study of the mind and the brain - the study of us. There is an old story about a group of blind people who each feel an elephant and try to understand together what they are observing. One person feels something long, rubbery, and flexible. Another perceives a smooth, firm surface and a third identifies a flat, delicate membrane. The study of the mind and the brain is a really, really big elephant. Its study spans several dimensions of analysis. One is a dimension of scale ranging from molecules to cells to systems. Another is a dimension of time from the opening and closing of ion channels in nanoseconds to the long-term relationships between brain and mind over a human lifetime or perhaps over the lifespan of a culture or a species. A third is a dimension of abstractness from concrete physiology to our capacities for abstract thought and emotion: for love, hope, cruelty, and empathy. Each discipline brings something unique to the table, but each specializes in a different “piece of the elephantее. To understand the whole image, we need to study these pieces deeply and rigorously, and then put them together into a picture of the integrated function of the human brain, mind, body, and environment. Chapter 2 - Why fMRI? Neuroimaging and the movement toward multidisciplinary science 11 Figure 2.2. An illustration of the diverse disciplines working in neuroimaging. The potential for such integration is one of the most exciting things about fMRI as a technique. Not only does the technology for collecting fMRI data draw on knowledge and techniques from at least a half dozen disciplines but fMRI can also be used to study just about anything related to the brain and the mind. This includes everything from abstract thought to cognitive performance, to mental illness and psychopathology, to brain regulation of inflammation in the body. For a practitioner to integrate the information and techniques required to do these studies well draws on knowledge from dozens of other disciplines. fMRI and other types of neuroimaging also provide a way for practitioners of different disciplines to come together and speak in the “common language’’ of the brain. For example, consider a neuroscientist studying the molecular basis of learning, a pharmacologist interested in antipsychotic drugs, a psychiatrist examining depression, and a social psychologist investigating the nature of altruistic behavior. What do all these researchers have in common and what could they possibly converse about relating to each of their core scientific interests? Why, the dopamine system, of course! It is very likely each of these researchers has been studying brain processes related to the mesolimbic dopamine system, which connects the midbrain, ventral striatum, and prefrontal cortex. The researchers each might have results related to brain activity in the ventral striatum that could help inform the others’ ideas about what the system is doing in relation to their outcomes of interest. Neuroimaging research can even help establish bridges between researchers in the same field who didn’t realize their ideas were grounded in similar neurophysiological processes. For example, some Chapter 2 - Why fMRI? Neuroimaging and the movement toward multidisciplinary science 12 social psychologists study motivation and appetite, others the effects of psychological distance, still others emotion regulation, and another group stereotyping and prejudice. All these areas contain a proliferation of theories, many of which include specific names and concepts (e.g., “construal level theory’’). How do the mechanisms underlying these theories relate? Do some rely on the same core processes and systems and, if so, what are they and how are they related? Once again, the ventral striatum and medial prefrontal cortex likely play prominent roles in all these areas of social psychological inquiry. Grounding theories in models of brain function can help establish premises in measurable processes. These theories can then be shared across researchers and fields to facilitate building a cumulative science of social cognition and behavior. Multiple roles, multiple fields: An example Letеs look at some of the unique roles different disciplines play in an fMRI study by using an example of a basic fMRI study on how antidepressants work. Yes, we still don’t really know much about how antidepressants, opioids, or any of the other systemic drugs (which we have been administering for decades or longer) work. This is in large part because these drugs affect neurons and glia all over the brain and we don’t know much about the effects on the various systems that support thought, emotion, and decision-making. We don’t even have a good consensus on which brain systems sustain those processes and which implement basic functions like attention, learning, and emotion. We do know a lot, but - to continue with our example - if we find that an antidepressant affects the prefrontal cortex, it is difficult to say what that means regarding the course of a personеs mental health or their life. So, back to our study - we won’t try to solve the whole mystery at once. Rather, this study will simply seek to establish which brain regions change with antidepressant treatment in order to test whether the drugs do indeed alter the function of the prefrontal cortex and other brain regions. The psychologist uses expertise in experimental design to construct a task which can isolate particular mental processes related to depression. The psychologist and statistician both have expertise in ascertaining that the design is efficient and well powered, and that it will produce valid causal inferences about the effects of the drug on the brain. A pharmacologist has information about the cellular and molecular mechanisms of the drug’s action and the kinetics of its absorption into brain tissue; the pharmacologist possibly also has data about its effects on brain vasculature and blood gas levels that may produce artifacts. A psychiatrist knows how drug dose and time course relate to expected clinical efficacy. A neuroscientist may have unique knowledge about how the drug penetrates into the brain and about the effects on neurons, glia, and/or various neural systems. The right training uniquely positions an MR physicist or biomedical engineer to ensure that we can obtain high-quality functional and structural images, and ideally minimize artifacts in the brain areas about which we care the most. The physicist or biomedical engineer may also have crucial information about how vascular and physiological drug effects might impact the fMRI signal independent of neural function. A computer scientist can manage and process the potentially huge volume of data acquired during the experiment, likely by borrowing signal processing techniques from mathematics and electrical engineering. During data analysis, the statistician again plays a Chapter 2 - Why fMRI? Neuroimaging and the movement toward multidisciplinary science 13 critical role in examining the data and the assumptions underlying the statistical tests, ultimately giving us a (hopefully valid!) picture of which brain areas the drug affects. A neuroanatomist can help localize the effects that emerge. The neuroscientist’s purview, together with the psychologist and psychiatrist, is interpreting the results and their meaning. That provides an overview of the different roles and contributions of various fields in an fMRI study. This description does not imply we need a team of 12 experts to do the study б in fact, that would be highly impractical. For the best science, we need collaboration of experts in multiple disciplines and individuals with proficiency in diverse aspects of design, analysis, and interpretation. A scientist using fMRI might come from any one of these disciplines, but likely has some capability in nearly all of them. While it’s probably impossible to truly be an expert in each of these areas, a good scientist will know something about all of them, have some idea about what she or he doesnеt know, and recognize when and how to ask for advice from colleagues. A confluence is the running together of rivers into a greater river. This is what the collaboration of disciplines is like: many great rivers running together with their ideas and techniques intermingling and combining. This process is very good for both science and society far beyond the immediate applications of fMRI. This confluence can help those who learn and practice collaboration become educated in a rich set of scientifically grounded ideas. It can lead to new ways of thinking about the mind, health, and disease. Challenges and motivation for multidisciplinary science All this sounds great, right? The catch is that it’s actually not easy for people from different disciplines to work together because they must learn and talk about unfamiliar concepts and be willing to not be the expert. Collaboration requires scientists from different disciplines to care about ideas and problems outside the scope of their defined interests and perhaps to publish in journals unfamiliar to or not prestigious in their particular field (very few journals are prestigious across all fields). It also requires time spent educating other team members about basic concepts which are not groundbreaking within one’s own discipline but which may be crucial and perhaps innovative in the context of interdisciplinary science. For example, many MRI physicists are rewarded for innovating new methods to acquire data, not for explaining the basics of tried-and-true clinical study methods like our example above or for spending time tweaking those methods to minimize the artifacts in the brain structures which impact neuroscientists. Those who are willing to talk to the rest of us should be treated like gold, as should statisticians and others with specialized knowledge to contribute. So how do we get people to talk to one another and work together? One answer lies in individual scientists developing multiple types of expertise, so that the gulf between the psychologist and the physicist, or the pharmacologist and the statistician, is not so great that they have nothing to say to one another. “Bridge’’ scientists are the glue that holds the team together. A little knowledge goes a long way in that respect, just like knowing a few words of someone else’s language can produce a Chapter 2 - Why fMRI? Neuroimaging and the movement toward multidisciplinary science 14 dramatically different social interaction than sharing no words. Offering a route to develop expertise is one of the reasons we wanted to write this book. Another answer is the movement towards multidisciplinary science, which is a challenging but laudable goal. Multidisciplinary refers to the idea that the study makes novel contributions to multiple disciplines. Take our example of the antidepressant fMRI study. If it is the study of a relatively novel drug with still unexplored mechanisms of action in the brain, it will be of interest to pharmacology. If it links two strong changes in thought and emotion, it may be of interest to psychologists and clinicians. If it involves novel innovations in data acquisition, it may be of interest in the field of MR physics. And if it involves novel computational methods to analyze brain networks, it might be of interest to the fields of computer science, informatics, and related disciplines. Not only is this difficult to pull off but also most studies should probably not try to be novel in so many different ways. However, the potential for innovation in multiple disciplines is one of the things that draw scientists from different areas together to contribute their expertise, creativity, and ideas. Chapter 3 - Types of imaging: What PET and fMRI can measure MRI: Multiple measures, multiple modalities MRI is one of the primary tools in the modern neuroscientist’s toolbox. Along with other, complementary techniques, it helps us develop integrated models of the human brain and discover how the brain relates to performance and health. In addition to being the seat of cognition, emotion, personality, motor control, perception, and social behavior, the brain is a central node in many body systems. It communicates with - among others - the muscular, circulatory, digestive, neuroendocrine, and immune systems. Understanding these relationships offers great prospects for improving our lives and helping us achieve our fullest potential. One of the great things about fMRI and MRI is that we can use them to look at the complicated brain system in multiple ways. In a single MRI session lasting approximately two hours, we can obtain multiple types of images related to diverse aspects of brain physiology. Some of these are shown in Figure 3.1 and are described in more detail below. We can associate these measures with many aspects of cognitive function, emotional function, and peripheral physiology (e.g. the skeletomotor, digestive, autonomic, endocrine, circulatory, and immune systems) to provide a comprehensive set of relationships between the brain, the mind, and our health. The two main types of brain measures that MRI and PET can collect are structural and functional images; see Figure 3.2. Structural brain imaging deals with the study of the brain’s gray and white matter through static pictures of the distribution of neurochemical receptors. A close link exists between structural images and the diagnosis of disease and injury. For example, if your physician checks you for brain trauma after an accident, suspects that you had a stroke, or believes that you have Alzheimer’s or Parkinson’s disease, s/he might obtain structural images to help diagnose the problem. Functional brain imaging, on the other hand, includes measures of “activation’’ related to oxygen use, glucose use, and/or blood flow. It also incorporates molecular imaging techniques, which study the dynamics of neurotransmitters and other brain chemicals. Chapter 3 - Types of imaging: What PET and fMRI can measure 16 Figure 3.1. The multiple measures of MRI. In a single MRI session, we generally obtain multiple types of images related to diverse aspects of brain physiology. These measures can be associated with many aspects of cognitive function, emotional function, and peripheral physiology to provide a comprehensive set of relationships between the brain, the mind, and our health. Structural MRI imaging The most commonly collected structural images are so-called T1-weighted and T2-weighted images, which provide basic anatomical pictures of the brain. Researchers most frequently collect T1 images, which they use to register functional images as well as for multiple types of anatomical analyses related to outcomes. This type of image is sensitive to the water content of tissue, so it produces different image intensities in the major in-brain tissue classes of gray matter, white matter, and cerebro-spinal fluid (CSF). T2 images provide a different type of contrast between tissue types; they are particularly useful for identifying the boundaries of certain iron-rich nuclei, such as the subthalamic nucleus and the substantia nigra. Chapter 3 - Types of imaging: What PET and fMRI can measure 17 Figure 3.2. An illustration of various structural and functional images. In addition to demonstrating basic anatomy based on tissue types, MRI can identify the major fiber tracts (fiber tracts are white-matter pathways composed of axon bundles connecting the disparate brain regions). The family of techniques researchers use for this identification is called diffusion weighted imaging (DWI) because of its sensitivity to directional water molecule diffusion in three-dimensional space. The first type of DWI was diffusion tensor imaging (DTI), which uses information about anisotropic (directional) water diffusion to estimate tensors (mathematical constructs that, for our purposes, we can think of as three-dimensional ellipsoids oriented along the direction of fiber bundles). There are now many varieties of DWI, which differ in both signal acquisition and in analysis techniques used to reconstruct the locations and the directions of white- matter tracts. A third type of structural imaging is vascular imaging, which includes MR angiography and veinography³. These types of images are sensitive to flow in the large blood vessels, and thus produce an image of the vessels’ locations. These various image types demonstrate the versatility of MRI. The pulse sequences that control the parameters of the magnetic fields and radiofrequency applied to the brain can be configured to be sensitive to multiple properties of tissue. Creative uses continue to emerge. For example, MR ³http://www.ajnr.org/content/21/1/74.full Chapter 3 - Types of imaging: What PET and fMRI can measure 18 elastography⁴ measures the mechanical properties of brain tissue by ‘palpating’ the brain with sound waves. This technique may be useful for detecting subtle types of damage due to shearing forces of closed-head injuries and perhaps also for identifying normal variants. Functional imaging with fMRI and PET Functional images measure parameters related to variations in metabolic activity, oxygen use, and release and reception of neurotransmitters in local brain regions. Both PET and fMRI can provide useful, complementary windows onto brain function, as shown in Figure 3.2. Meaningful effects can occur on time scales from seconds to years (or longer) and on spatial scales from neural column-level resolution to large-scale brain systems. As we discuss later on, different MRI and PET techniques are sensitive to different subsets of these effects depending on the imaging type and the analysis. Both PET and fMRI can provide useful, complementary windows onto brain function ⁴http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3066083/ Chapter 3 - Types of imaging: What PET and fMRI can measure 19 Imaging brain “activity’’: blood flow and metabolism Most functional imaging papers describe their results in terms of brain “activity” or “activation”. This is admittedly a vague term that can mean different things depending on which imaging modality the researchers used. PET can measure several types of activation related to (among other possibilities) local cerebral blood flow (CBF), oxygen metabolism (CMRO2, or the “cerebral metabolic rate of oxygen”), and glucose utilization. PET involves synthesizing a radioactive isotope or “label” on-site and attaching it biochemically to a molecule of interest. Researchers then inject the radiolabeled compound into the blood. When the radioactive isotope decays, it emits two positrons - subatomic particles with the same mass but the opposite charge as an electron -that travel in opposite directions through the brain; an array of detectors positioned around the head then detects the positrons. Researchers mathematically reconstruct the frequencies of these emissions at different positions into three-dimensional volumes. The most common radioactive tracers for assessing “activation” are 15 O (“oxygen-15”), which assesses CBF, and 18 F (fluorine), which aids in deoxyglucose mapping. Researchers attach other radiolabels - for example, 11 C (carbon) or 123 I (iodine) - to other molecules and use them in a wide variety of molecular imaging applications. In fMRI, “activation” typically refers to Blood Oxygen Level Dependent (BOLD) signal, which is a complex set of changes usually coupled to the oxygen demand and the blood flow in local blood vessels. For details of the relationships between these parameters and how they relate to BOLD signal, we refer the reader to a number of more detailed⁵ descriptions⁶ published elsewhere. The physiology of BOLD is also complex in its relationships to neural and glial processes, a subject we return to later in the book. Relative to other “activation” measures obtained with fMRI, BOLD signal is large in magnitude, robust, and obtainable via standard commercial pulse sequences (programs that run the scanner hardware). It is also safe to repeat, according to current wisdom, and does not require radioactive compound injection. For these reasons, about 95-99% of current fMRI studies use BOLD signal. An increasingly popular alternative to BOLD is perfusion imaging. Perfusion imaging is a family of techniques that can obtain more direct measurements of local cerebral blood flow (CBF). Most notable among this family is arterial spin labeling (ASL)⁷, a method that allows for quantitative measurement of regional CBF, in many cases, across long time scales (e.g. before and after cognitive training, mood induction, or clinical intervention). ASL uses radiofrequency pulses to magnetically label water molecules entering the brain through the carotid arteries, and then researchers compare the labeled MR images to the unlabeled MR images. With appropriate models⁸, one can estimate local blood flow throughout the brain. There are many variants of ASL, but in recent years a technique called pseudo-continuous ASL (“PCASL”) has emerged as a stable and advantageous technique; it is now commercially available from scanner vendors. ASL can test the same types of functional ⁵http://www.ncbi.nlm.nih.gov/pubmed/9621908 ⁶http://www.ncbi.nlm.nih.gov/pubmed/11449264 ⁷http://www.ncbi.nlm.nih.gov/pubmed/8068529 ⁸http://www.ncbi.nlm.nih.gov/pubmed/9621908 Chapter 3 - Types of imaging: What PET and fMRI can measure 20 effects as BOLD, which include task-induced activation and connectivity, resting-state connectivity, and relationships between brain activity and performance (or other outcomes). Beyond activation: Molecular imaging Both MRI and PET have other ways of acquiring signal that go beyond “activation” and blood flow. These allow researchers to investigate regional functional brain changes in specific neurochemical systems. These include MR spectroscopy and PET molecular imaging. We turn to these next. Another branch of MR techniques is spectroscopy. MR spectroscopy provides a way of testing a brain volume of interest for the presence of biochemicals and some kinds of gene expression. Nuclear magnetic resonance (NMR) spectroscopy takes advantage of the fact that molecules’ resonant frequency depends on their atomic characteristics, including the electron quantity and the proximity and composition of the tissue’s atomic nuclei. The resonant frequency determines the frequencies of the radiofrequency energy absorbed by local tissue. Thus certain molecules produce a relatively unique molecular “signature” in the power spectrum, with peaks at specific frequencies. NMR spectroscopy is a field in its own right, which has a growing number of detectable biochemical properties including GABA - a major, generally inhibitory neurotransmitter - and proteins related to specific aspects of the Krebs cycle - a fundamental series of molecular interactions that governs energy production within cells. Though promising, spectroscopy has shortcomings in limits in the detectable number of molecules and the relatively long time it takes to image each local brain region. Researchers do not yet widely apply spectroscopy in the cognitive neurosciences, although this may change as the field of neuroimaging matures. PET provides the most comprehensive and versatile way of assessing specific neurotransmitters, neuropeptides, and glial cell function markers related to cognitive and health outcomes. Radioactive labels can attach to hundreds of different compounds - though for each compound, a great deal of work to understand the pharmacology and develop each research site’s procedures must be done before it can be used. Researchers have developed imaging techniques for many of the major neuro- transmitters and neuropeptides, which include (among others) dopamine, serotonin, acetylcholine, norepinephrine, and opioids. The compounds are usually sub-pharmacological doses of receptor agonists or antagonists, which, like all drugs, bind to particular classes of receptors. In dopamine imaging, for example, a common technique is [11 C]raclopride, which has high affinity for D2 receptors concentrated mainly in the striatum. An increasingly popular alternative is [18 F]fallypride, which binds more powerfully to other dopamine receptor classes that are strongly cortically con- centrated. Some other examples include muscarinic cholinergic receptors using [11 C]scopolamine, mu-opioids using [11 C]carfentanil, and benzodiazepines using [11 C]flumazenil. Recent years have seen development of ligands for many other substances and cell markers as well, like those related to [neuroinflammation](http://www.ncbi.nlm.nih.gov/pubmed/18006619 and glial-cell activity⁹. These types of molecular imaging may be very useful for both basic research and to understand and diagnose clinical disorders. For example, PET imaging with a compound called “Pittsburgh ⁹http://www.ncbi.nlm.nih.gov/pubmed/25582579 Chapter 3 - Types of imaging: What PET and fMRI can measure 21 Compound B” or “PIB”¹⁰ is sensitive to molecules found in neurofibrillary tangles characteristic of Alzheimer’s disease, so it is now used clinically as a marker for early-onset Alzheimer’s. ¹⁰http://www.ncbi.nlm.nih.gov/pubmed/14991808 Chapter 4 - Brain mapping: A conceptual overview What is a brain map? Understanding the basics of brain mapping is increasingly important for a broad segment of society as brain images make their way into media, medical practices, courtrooms, advertisements, and other sectors of public life. However, without an explanation of the process and some of the ground rules, our understanding of how we construct brain images and what they can and cannot tell us about the brain and the mind is not obvious. Both functional and structural imaging rely on construction of brain maps, which are maps of localized signals. There are many types of brain signals that we can map which relate to many external (outside the brain) conditions and outcomes. However, different types of brain maps rely on many of the same principles and underlying assumptions. We will devote this chapter to a conceptual overview of how researchers construct brain maps, what we can learn from them, and what some of those assumptions and limitations are. The brain maps like those shown in Figure 4.1, generally speaking, are statistical constructions. In some cases, brain images display actual data values; this is typical in neuroradiology, in which experts ‘read’ an image and come up with an opinion or diagnosis. However, in most scientific areas, researchers want to make quantitative inferences, which means statistically comparing image data across conditions or individuals and then showing maps of the statistical results. We often call this practice statistical parametric mapping. Such maps show brain areas where researchers have deemed some effect of interest statistically significant. Chapter 4 - Brain mapping: A conceptual overview 23 Figure 4.1. An example of a statistical map. These types of maps show brain areas where researchers have deemed some effect of interest statistically significant. Types of maps The types of processes that researchers map to local brain regions or networks are numerous. They include: Effects of experimental manipulations Correlations with behavior, clinical status, or other person-level outcomes Correlations with performance or other within-person variables Brain areas’ correlation with other specific areas Brain areas’ that are part of a group of areas (e.g. a cluster or network) Accordingly, a first question to ask about any brain map is what effect it actually maps. Types of inference A second question to ask is to whom does the map apply - which individual or population of individuals? Data from only a single individual, scanned repeatedly, can be used to construct some maps as shown in Figure 4.2’s top panel. We refer to these as single-subject maps. These maps are common in some sub-fields, such as vision science or primate neuroimaging, and are increasingly present in clinical and legal applications. Researchers can construct single-subject maps by comparing data from one condition (e.g. one experimental task) with another across repeated measurements, which thus test statistical significance in each brain region or ‘voxel’ (a three- dimensional cube of brain). Another method to construct these maps is by comparing an individual with a population of other individuals. If the statistics are valid (a big if!), such maps can say something useful about how an individual’s brain differs from others’ brains. Chapter 4 - Brain mapping: A conceptual overview 24 Figure 4.2. Examples of single-subject maps (top row) and group-level maps (bottom row). However, single-subject maps cannot tell us much about the brain’s general organization: researchers cannot use them to make population inferences, which are claims about how the brain functions in general. To make such claims, it is necessary to scan a group of participants and conduct statistical tests which explicitly evaluate how well the findings likely will generalize to new individuals. We refer to these as group-level maps; they identify brain areas that show consistent effects across individuals. The bottom panel of Figure 4.2 shows a schematic view of a group-level map’s construction. Technically speaking, such maps require a statistical procedure which we often call random effects analysis because the statistical model treats each participant as a random effect. We will return to this in more detail in later chapters. The map shown in Figure 1 is a group-level brain activity map. Maps can widely vary in what they reflect, but they all share the same underlying basic distinction between single-subject and population inference. For example, Figure 4.3 shows maps of three different kinds of brain connectivity. In this case, the colored regions do not show the significant effects of interest; here the lines connecting regions show the effects: they indicate significant functional associations across regions. The left map comes from a dynamic causal model (DCM), which analyzes dynamic regional changes from one second to the next, while controlling for other regions and experimental task variables, to examine relationships among regions. Lines show significant associations at a population level. The center map comes from a method which identifies Chapter 4 - Brain mapping: A conceptual overview 25 the most likely connections among regions and their variations across time. The connections the lines identify are not necessarily individually significant. This is common practice with many multivariate map types: one must be careful to make the correct inference because regions associated with a ‘network’ are not necessarily all significantly associated. Finally, the map at the right shows a large scale network in which each colored circle represents a brain region or system and each line shows significant associations across studies. Clearly, knowledge of a map’s construction process and its level of analysis are crucial for understanding what it means. Figure 4.3. Maps illustrating three different kinds of brain connectivity. Fundamental assumptions and principles In order to make statistical maps of all kinds, we rely on the assumption that the brain signals we measure reflect both effects of interest and noise. Researchers further assume that the noise is independent from the effects of interest (e.g. “random’’). Repeated measurements in which the noise varies independently and stochastically allow us to obtain an average map that contains the true effect and reduces noise to a minimum. As the noise randomly varies around the true effect, it ‘averages out’, so the more data we collect, the closer the average noise will get to zero - as long as the noise is independent of the interest effect. Consider the example in Figure 4.4. The brain - we show one representative horizontal slice here - contains some areas with a true effect, shown in blue. Perhaps this is a working memory task that requires people to maintain more versus less information in their minds; the map reflects concentration of the blue areas in frontal and parietal cortico-striatal networks. We observe a mixture of the true effects (signal) plus random noise, in red here. Chapter 4 - Brain mapping: A conceptual overview 26 Figure 4.4. (Top) A single slice of the brain contains some areas with a true effect, shown in blue. We observe a mixture of the true effects (signal) plus random noise, in red here. Statistical test are used to infer which voxels show true effects. (Bottom) Three common data types that go into such maps: task-related group analyses that compare a task of interest to a control task; brain-behavior correlations; and the average accuracy in predicting a stimulus category or behavior from each voxel’s local multivariate patterns of brain activity. Importantly, this noise is non-zero even averaged across the observed data, so we need to first separate it from the signal and then decide which areas really show the effect. We do this with a statistical test which compares each voxel’s observed effect with its noise level (i.e. signal/noise). Common statistics, which include T-scores, F-values, and Z-scores, are all examples of such signal- to-noise ratios. We then compare the resulting statistic value with an assumed distribution to obtain each voxel’s p-value. The p-value reflects the probability of observing a statistic value (e.g. a T- score) as or more extreme then that actually observed under the null hypothesis - that is, if there is no true effect. The lower the P-value is, the less likely that we believe the null hypothesis is true. We compare p-values with a fixed value to threshold the map and to infer which voxels show true effects. Because of the many possible tests, researchers often set a very high bar for significance (i.e. low p-values) by correcting for multiple comparisons. When we use standard statistic values like T-scores and compare them with their canonical, assumed distributions, we are using parametric statistics. When we use the data itself to estimate the null Chapter 4 - Brain mapping: A conceptual overview 27 hypothesis’ Ñ which often involves fewer assumptions Ñ we are using nonparametric statistics. In most cases, we test each voxel in the brain separately, ignoring other voxels’ potential influence, to construct brain maps. This is the case whether one maps activations which respond to a task, structural differences between groups, or functional correlation of areas with a ‘seed’ region of interest. It is a big assumption that the rest of the brain doesn’t matter, so many multivariate analyses relax this assumption in certain ways (depending on the specifics of the multivariate model). However, the assumption is in some ways quite useful as we can interpret one brain area’s effects independently of other area’s responses. For example, a brain map which correlates activity levels in an anger-induction task with self-reported anger levels can provide a simple picture of which areas are associated with anger and so can be a starting point for more sophisticated models. This basic brain mapping procedure applies to the vast majority of published neuroimaging findings, including both structural and functional imaging using MRI and PET. Figure 4.4’s bottom panels show three common data types that go into such maps. On the left, the statistical brain map’s voxels reflect a task-related group analysis that compares a task of interest to a control task. Each data point that goes into the test at that voxel (the circles) is the [task - control] contrast magnitude from one participant; the null hypothesis here is that the population’s [task - control] differences are zero. The center map shows a brain-behavior correlation in which the test statistic is the correlation between the activity levels (often in a [task - control] contrast) and an external outcome, as in the anger example above. The right map shows an “information-based mapping’’ test in which the test statistic is the average accuracy in predicting a stimulus category or behavior from each voxel’s local multivariate patterns of brain activity. In all of these cases, the above principles and assumptions apply. Bringing prior information to bear: Anatomical hypotheses Regardless of the type of map constructed and the variables involved, researchersÕ basic question is, “is there some effect at this location?’’ As Figure 4.5 shows, researchers can apply hypothesis tests to each brain voxel or to a set of voxels in pre-defined regions of interest (ROIs). They can also apply hypothesis tests to voxels in a single ROI or to signals averaged over voxels in one or more ROIs. These examples illustrate a progression from conducting many tests across the brain to performing few tests, a movement that depends on the prior information brought to bear to constrain hypotheses. Chapter 4 - Brain mapping: A conceptual overview 28 Figure 4.5. Researchers can apply hypothesis tests to each brain voxel, to a set of voxels in pre-defined regions of interest (ROIs), to voxels in a single ROI, or to signals averaged over voxels in one or more ROIs, depending on the prior information brought to bear to constrain hypotheses. The more tests researchers perform then the more stringent the correction for multiple comparisons must be if they are to interpret all significant results as ‘real’ findings. As the threshold becomes more stringent, statistical power - the chance of finding a true effect if it exists - drops, often dramatically, which entails increasingly missed activations. In the extreme case in which there is only one ROI and the signal in its voxels is averaged, researchers perform only one test and do not need multiple comparisons correction. Researchers need not limit a priori hypotheses to single regions; it is also possible to specify a pattern of interest, in which an average or a weighted average is taken across a set of brain region, and a single test is performed. Figure 4.6 shows an example from a working memory study¹¹. We first defined a pattern of interest based on previous working memory studies from neurosynth.org¹², which is an online repository of over 10,000 studies’ activation results. Then we applied the pattern to working memory-related maps from two participant groups - a group exposed to a social evaluative ¹¹http://cercor.oxfordjournals.org/content/early/2014/09/22/cercor.bhu206.full ¹²http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3146590 Chapter 4 - Brain mapping: A conceptual overview 29 threat (SET) stressor and a control group - by calculating a weighted voxel activity average in the pattern of interest. Applying the pattern allowed us to (a) establish that, in our study, working memory produced robust activation in the pattern expected from previous studies and (b) test for SET effects on working memory-related activation without needing multiple comparison correction. Figure 4.6. An example from a working memory study. A pattern of interest based on previous working memory studies was created. The pattern was applied to data from two groups (one exposed to a stressor and a control group)by calculating a weighted voxel activity average in the pattern of interest. This allowed for a test of stressor effects on working memory-related activation without requiring multiple comparison correction. There are thus many benefits to specifying anatomical hypotheses a priori. However, when we specify a priori hypotheses, we must truly specify the region or pattern in advance based on data whose errors are independent from the dataset testing the effect, otherwise the p-values and the inferences will not be valid. We suspect there are many unreported cases of post-hoc “a priori’’ selection of ROIs. Chapter 4 - Brain mapping: A conceptual overview 30 Types of inference: What brain maps can and cannot tell us What can we infer from thresholded brain maps of all types, regardless whether they concern anatomy, neurochemistry, or functional activation? What we can make inferences about is rather specific and may not be exactly what you expect. Below, we discuss inferences about brain effects, a term which applies to many types of images that span beyond task-based activation, anatomical relationships with behavior, or maps of molecular imaging. First we discuss inferences about brain effects’ presence, size, and location. Then we discuss forward and reverse inference, which, respectively, relate to making inferences about the brain and our psychological states (or other outcomes). Inferences about the presence, size, and location of effects The basic brain mapping procedure involves a test of significance at each voxel; this is a hypothesis test. This allows us to reject the null hypothesis that a subset of voxels has no effect in favor of an alternative hypothesis. That alternative hypothesis, however, is not very precise: it is merely that there is some non-zero effect. As we will see in the next chapter, this does not let us conclude anything about how big or how meaningful the effects are; attempts to do so using standard hypothesis testing procedures can be highly misleading. At best, then, brain maps can allow inference that a set of significant voxels has some effect, but not how much effect. Standard brain maps are also not very good for determining which voxels do versus do not show effects. Thus they are not useful to show us the complete pattern of activity (or structural effects, etc.) across the brain. This is primarily because of the stringent thresholds that usually limit the false positive findings. Current thresholding procedures do not optimally balance the number of false positives and false negatives (missed findings). Another thing in which standard brain maps are not particularly good for is precise determination where the effects are in the brain. This may seem very surprising as researchers nearly always interpret thresholded brain maps in terms of where the most statistically significant results lie in the brain. However, the trouble lies in brain maps providing confidence intervals (which researchers use as a guide for how strongly to believe in the effect) on whether each voxel is significant but not on the significant voxels’ locations. They provide a ‘yes/no’ value for whether a significant effect appears at each voxel. Inferences about result locations, then, are heuristic rather than quantitative. This limitation becomes intuitive if we consider the brain map in Figure 4.1. The map contains significant activation (yellow) in the ventrolateral prefrontal cortex (vlPFC), marked with a red arrow. Imagine repeating this experiment again. What are the chances that the exact same voxels in vlPFC would be active? Or that the most active voxel would fall in the exact same location? We do not know. Standard mapping procedures do not provide p-values or confidence intervals on the activationÕs location or shape. However, we know from meta-analyses like the one in Figure 4.7 Chapter 4 - Brain mapping: A conceptual overview 31 that the location of the peak voxel will likely be quite variable, possibly around plus or minus 1 Ð 1.5 cm. Incidentally, Figure 4.7 does show spatial 95% confidence intervals for the across study mean location for positive (green) and negative (red) emotions, drawn as 3-D ellipsoids. In addition to noise related uncertainty about local effects’ locations and shapes, we also must keep in mind that artifacts and imprecision in anatomical alignment can also cause mis-localized effects. All brain images have an intrinsic point-spread function, or a blurring of localized true effects at one local brain point into a broader ‘blob’ of observable signal. BOLD images in particular are susceptible to arterial inflow and draining vein artifacts; they are also typically overlaid on an anatomical reference image which may not perfectly align with the functional map. Figure 4.7. An illustration of the variability in the location and shape of activation. The upshot of all this is that though we can make inferences about certain areas’ activity, we must be cautious about over-interpreting size and location of significant findings and about the completeness of the picture thresholded maps provide. If these types of inferences sound limited, we agree! Standard brain maps are very limited - we devote much of the next chapter to further unpacking their limitations. Fortunately emerging alternative methods avoid some of standard brain maps’ problems. These include (a) specific multivariate Chapter 4 - Brain mapping: A conceptual overview 32 pattern analyses types that build predictive models and (b) spatial models that we can use to make inferences about the location of effects. Forward and reverse inference Inferences drawn from brain maps have another limit. Typically, researchers either (a) induce a psychological state by manipulating experimental variables or (b) observe a behavior of interest or other outcome. Then researchers assume that the state or behavior is known and make inferences about the statistical reliability of brain activity given (or conditional on) the state or behavior. In Bayesian terms, we infer the probability of brain activity given a psychological state or behavior, or P(Brain | Psy). This is forward inference, which can tell us about how the brain functions under different psychological or behavioral conditions but not much about the psychological state or behavior itself (see Figure 4.8). Standard brain maps provide information on forward inferences. Though above we expressed them in terms of probability, the same concept applies to effect size measurements. The stronger a brain map’s statistical effects then the more likely we are to observe a significant result in probabilistic terms. Figure 4.8. An illustration of forward and reverse inference. Why can’t standard brain maps teach us much about psychological states? Forward inferences take psychological states as given. They do not tell us how brain measures constrain our theories of which psychological processes are engaged. For that, the inference we want concerns P(Psy | Brain), the probability (or, heuristically, the strength) of a psychological process’ engagement given activity in a particular brain region or pattern. Neuroimaging literature has termed this reverse inference. Though related through Bayes’ Rule, forward and reverse inference are not the same thing qualitatively or quantitatively. Chapter 4 - Brain mapping: A conceptual overview 33 The field of logic calls fallacious reverse inference ‘affirming the consequent’. For example, assume this statement is true: ‘If one is a dog, then one loves ice cream’, or P(Ice Cream | Dog) = 1 for short. Then given that Mary loves ice cream, i.e. P(Ice cream) = 1, one might erroneously infer that Mary is a dog. The problem is that all dogs love ice cream, but not all ice-cream lovers are dogs. P(Ice Cream | Dog) = 1 does not imply that P(Dog | Ice cream) = 1. Standard brain maps’ limitations in constraining psychological theory have led many researchers to be critical of neuroimaging, often¹³ rightly so¹⁴. Examples of papers that make fallacious reverse inferences - like, for example, inferences that long-term memory processes were engaged (Psy) because the hippocampus was activated (Brain) - litter neuroimaging literature. In fact, some psychologists have argued that neuroimaging has not taught us anything¹⁵ about the mindÑyet. Reverse inference is actually possible; it is a major piece of the puzzle in constraining psychological (and behavioral and clinical) theory with brain measures. To understand how, let’s revisit forward and reverse inference from a diagnostic testing perspective. P(Brain | Psy) is the ‘hit rate’ of significant activity given a psychological state; testing theory calls it sensitivity. In a standard test, e.g. a diagnostic test for a disease, Brain is analogous to having a positive diagnostic test, and Psy to having the disease. P(Psy | Brain) is the test’s positive predictive value - how likely one is to have the disease given a positive test. High positive predictive value requires both high sensitivity and high specificity, which entails a low probability of a positive test if one does not have the disease - or, in brain imaging terms, low P(Brain | ∼Psy), where ∼ means ‘not’. To use a brain example, before we can infer that hippocampal activity implies memory involvement, we must first show that hippocampal activity is specific to memory and that other processes do not activate it. Thus to make reverse inferences about psychological states we must estimate the relative probabil- ities of a defined psychological hypotheses set given the data, typically by using Bayes Rule. This requires analysts to construct brain maps of multiple - ideally many - psychological conditions and assess the brain findings’ positive predictive value formally. In addition to assessing positive predictive value, analysts can optimize maps and models of brain function to maximize function - that is, to strongly and specifically respond to particular classes of psychological events, behaviors, or other prompts. This is the goal of an increasing number of studies which use multivariate pattern analysis with machine learning or statistical learning algorithms. This is a promising direction; we devote a great deal of space to these techniques later in the book. Ability to infer a psychological process’ presence or strength is important in its own right. It opens up various possibilities for testing and constraining psychological theories - or at least, their biological bases. Valid reverse inferences could allow, in some cases, researchers to infer a number of processes otherwise problematic or impossible to confidently measure. Among others, these states include being in pain, experiencing an emotion, lying or hiding information, and engaging in cognitive work. Researchers can use reverse inferences to probe the unconscious and to help study mental processes in cognitively impaired, very young, or otherwise unresponsive individuals. And, finally, comparing brain markers for different psychological processes could allow us to develop new mental ¹³http://www.ncbi.nlm.nih.gov/pubmed/8585670 ¹⁴http://www.ncbi.nlm.nih.gov/pubmed/16406760 ¹⁵http://www.ncbi.nlm.nih.gov/pubmed/16771037 Chapter 4 - Brain mapping: A conceptual overview 34 process typologies - including emotion, memory, and other processes - which, regardless whether they match our heuristic psychological categories, may have their own diagnostic value. In conclusion, standard brain maps provide specific types of inference about brain activity. Though there are a number of fundamental limits to these inferences, new techniques are circumventing many of those limitations and providing a more complete range of inferences about the brain and mind. In the next chapter, we further explore those limitations, some ways that researchers exploit brain maps to support erroneous conclusions, and how you can become a savvy consumer of neuroimaging results. Chapter 5 - Limitations in inferences from brain maps In these next chapters, we explore the dark side of neuroimaging results. In this chapter, we elaborate on seven limitations in what one can infer from significant results in standard neuroimaging maps. In the next chapter, we discuss several fallacious arguments for which to watch as inspired by the classic book, ‘How to lie with statistics’. We discuss statistical inference and multiple comparisons extensively in later chapters, but for now it is worth remembering a few relevant points which fundamentally constrain what we can say about the brain based on maps like those discussed above. First we start with seven caveats in what brain maps allow us to infer about local regional activation. Then we provide a non-imaging example to drive home some of the statistical points. Seven caveats in brain map inferences Not significant does not mean not important Statistical significance in only some brain areas does not mean that effects in other brain areas are negligible. Most studies have extremely low statistical power, which is the chance of finding a true effect if it exists. Additionally, most tasks and outcomes of interest likely involve many more brain areas than are visible on thresholded maps. Multiple comparison correction reduces the false positive rate but also reduces power, often dramatically. Maps are noisy Not only is every statistical map noisy but also the smaller a sample size is, the greater noise- related variability becomes. This fact means one should not over-interpret voxel significance without evidence that the significant voxels’ pattern is reproducible. In addition, maps across multiple tasks and outcomes, even if they reflect the same underlying processes, are likely to yield different activation patterns directly proportionate to the maps’ noisiness. In addition, more stringent multiple comparisons correction increases the dependence of the choice which voxels are or are not significant on the tails of the applied statistical distribution, which means increased influence of noise. More studies are starting to examine the reproducibility of the maps themselves. Chapter 5 - Limitations in inferences from brain maps 36 We cannot infer the size of the effects in significant regions Thresholded maps cannot effectively tell us how large (i.e. how important and meaningful) effects in ‘significant’ regions really are for two reasons. First, the statistical tests we described above are hypothesis-testing procedures which test whether an effect is zero or not, but don’t tell us how large it is. Second, thresholding the maps creates a voxel selection bias which inflates apparent effect sizes in significant regions and makes it impossible to determine how large they are. Every significant region contains some true signal (if they are true positive findings), but also contains noise that may favor the hypothesis by chance. This makes effects appear very large in some studies, particularly those with small sample sizes, with higher variability. Multiple comparison correction does not help; it actually makes this problem worse by increasing ‘selection pressure’. This may sound surprising, but it’s true; below, we illustrate why this problem occurs through a non-imaging example. Maps are relative comparisons Brain maps nearly always compare one condition with another: [Task - Control], individuals high in a trait versus those who are low, patients versus controls, etc. That means that the baseline condition against which researchers compare an active condition matters too. Though many maps do not seem to have a comparison condition, they have an implicit baseline, which is often resting activity levels. This is true for all image types, even ‘quantitative’ cerebral blood flow (CBF) measures made with PET or ASL imaging. For example, we might measure motor cortex blood flow as 50ml/min during motor task performance, but this value is only meaningful when compared to a no-movement or related baseline, or to another group of individuals. The same is also true for molecular imaging, anatomical imaging, and spectroscopy. With BOLD fMRI, the comparisons we can make are even more limited. Because BOLD’s absolute units are not very stable from person to person and scanner to scanner, BOLD maps nearly universally involve comparisons between conditions rapidly fluctuating over time (i.e. every few seconds to every few minutes). Functional connectivity measures, including correlations in BOLD time series among brain areas, can potentially reveal changes happening across longer time scales. However, like other brain mea- sures, their usefulness in this respect depends on how reproducible the levels of those connectivity measures are across time, participants, and, ultimately, scanners. Random variations in the absolute levels of the response or in the signal scaling and noise levels can affect the utility of brain measure. Significant does not mean causal All brain imaging is essentially correlational, so it is difficult to confidently conclude that brain effects cause behavioral effects and other outcomes. For example, researchers robustly associate Alzheimer’s disease with reduced medial prefrontal cortex gray matter density. But those asso- ciations alone do not warrant inferences that those changes cause memory impairment or other symptoms. Researchers often base such inferences on converging evidence from other neuroimaging studies and methods, particularly on animal studies which can manipulate the brain and provide for invasive measurements. Showing that such structural changes correlate with memory symptoms Chapter 5 - Limitations in inferences from brain maps 37 is helpful, but such effects are subject to indirect effects of other brain regions’ changes and other unmeasured common causes of brain changes and memory impairment. Experimental manipula- tions, which can be exogenously randomized, provide the strongest evidence for causality. But these also do not strongly imply that an experimentally manipulated task independently activates each significant brain area shown in the thresholded brain map. Connections with areas that are more central for task processing may indirectly activate some areas. Others may be driven by alternative extraneous processes or even by artifacts like head movement. With any brain map, it is useful to consider all the processes that might drive brain activation. For example, seeing faces evokes some relatively face-specific perceptual processes. But a map comparing face viewing versus rest does not necessarily isolate those processes. Activity could reflect any process which differs between face viewing and rest, including attention direction, associative memory retrieval, eye movements, emotional and motivational responses, arousal, or autonomic physiological responses. Just because a brain map is nominally ‘about’ some process doesn’t mean all observed activity reflects that process. Statistically stronger does not mean more important We often use an effect’s statistical strength as a guide to its importance, but one should make such inferences with caution. Significance in a group-level map implies an effect which is consistent across individual participants. However, both large effects and low inter-individual variability can drive strong effects. Thus the most statistically reliable effects may be the least important for determining individual differences in performance or other outcomes. In addition, noise and artifact levels vary widely across the brain. The most important regions for a task or an outcome may often be those with high noise or poor signal quality which result in weak effects. Lastly, large effects do not guarantee importance. Many of the players critical in virtually every system are often not the most numerous. This applies to the brain even at neural or neurochemical levels: take, for example, motivating events which induce dopamine, opioid, serotonin, and other neurochemical release. Finding that more dopamine D1 than D2 receptors are bound during reward states does not imply that D2 receptors are more important for any particular behavior. Anatomical localization is imprecise The functional images used to create statistical brain maps are usually inherently blurry and are often subject to artifacts including spatial distortions. In addition, these maps usually overlay an anatomical image that, while higher resolution, does not perfectly align with the functional images and is not subject to the same distortions. Often researchers register and overlay group results on a standard brain atlas constructed from averaged brains, which necessarily reduces spatial precision. All this means that we should interpret locations of functional results cautiously. Higher- resolution imaging at higher field strengths and individualized single-person analysis have potential to circumvent, to some degree, many such problems. However, these techniques have their own costs and so researchers do not yet widely use them. Chapter 5 - Limitations in inferences from brain maps 38 A non-imaging example Let’s consider a non-imaging example to illustrate some issues with inference in the brain mapping framework. Imagine observing a casino’s roulette games over a year’s time: maybe 100,000 such games would occur, each which involves a gambler’s attempt to win money by spinning the roulette wheel exactly 8 times. Each game is like one voxel’s test of significance with the null hypothesis that the table’s odds are ‘fair’, or as stated. The set of 100,000 games together is like a brain map composed of 100,000 voxels, which is a typical number. In roulette, a player can bet on black or on red with just under a 50% chance of each occurring - 47.37%, to be precise, because the house constructs the odds in its favor. What are the chances the roulette ball will land on black all 8 times? The answer is 0.47378 , or p = 0.0025. If we just observed one game which came up black 8 times in a row, we might provisionally reject the null hypothesis and conclude the table may be biased. However, now imagine a fair table (there are no true biases) on which we observe 100,000 games, just like we might observe 100,000 voxels. What is the chance we will observe 8 consecutive black outcomes (at p = 0.0025 per outcome) in at least one game? It is essentially 100%. In fact, there is a 92% chance that we’ll get at least one ‘significant’ test - a game with 8 black outcomes, or equivalently a result somewhere in the brain - with only 1,000 tests. Brain image noise is not independent across space, so though it’s tricky to determine the effective number of tests in our 100,000 voxel map, it is safe to say that we’ll find a significant result at p < 0.0025 in a brain map every time. This is why we need to correct for multiple comparisons. Now comes the rub in terms of estimating how large effects are. Let’s say we threshold our 100,000 test results at p = 0.0025 uncorrected, then consider only games (voxels) with significant results. WeÕd expect 250 of 100,000 games to be significant on average even if the table is fair. The true value for the average number of blacks is just under 4 per game. However, if we examine only the winners - that is, we condition on a significant result - the average number of blacks is 8, double the true effect size. Similarly, picking out brain voxels with significant effects always inflates the apparent effect size, often dramatically. Chapter 6 - How to lie with brain imaging In this chapter, we explore the dark side of neuroimaging results. We discuss several fallacious arguments for which to watch out. In writing this, we are inspired by two classic books. One is called ‘How to lie with statistics’, which, of course, really tells you how you should not lie with statistics or at least how to avoid being fooled by those who do. The other book is Bob Cialdini’s terrific ‘Influence’, in which he claims that his own gullibility inspired him to study persuasive power and resistance. Accordingly, this is not really a chapter about how you can lie with brain imaging, in case you were wondering. It’s really a chapter about what not to believe. Below, we describe five tricks to make your results look specific, strong, and compelling, and also to make them come out like your theory predicted. For example, if you have a theory that requires two psychological tasks to produce highly overlapping brain activity, we can help you make that happen. Or if your theory specifies that patients and controls engage very different brain systems, we can help with that too. Of course, these are not the only ways to lie with brain images. There are the obvious ways - plain old making stuff up or engaging in a little self-deception like defining ‘a priori’ ROIs after peeking at the statistical maps (because you would have expected activation in the precuneus, right?). There are also techniques like ‘P-Hacking’, which include sleights of hand such as continuing data collection, adding and removing covariates, or transforming outcome measures until you have a significant result. We’ll discuss those more later. Here, we’re interested in techniques that are, at least in some cases, a little bit more subtle and that apply even to brain maps generated through otherwise valid means. How to tell a story about the “one brain region’’ The high-threshold Most clinical disorders and many processes which psychology studies are likely distributed across multiple brain systems. How can we make such a bold claim? To be encapsulated in one brain region, a process must be relatively pure, which implies that localized lesions produce complete and specific deficits. This is true in a few cases: V1 lesions produce cortical blindness and specific inferior temporal lesions produce prosopagnosia, a face recognition deficit. But most processes, even evolutionarily conserved and sensory-driven ones like pain, are highly distributed. The trouble with this is that a neuropsychological tradition which focused on selected cases of specific deficits after focal lesions created a past ‘culture of modularity’. Prestigious journals like Nature and Science have Chapter 6 - How to lie with brain imaging 40 historically vastly preferred simple results with one-point headliner messages like ‘this brain region implements this complex psychological process’ (we won’t pick on any specifics). So how do you get your results to tell that simple story? The answer is very simple: the high-threshold. Simply raise the bar for statistical significance until you have one region (or very few) left in your map. Not only is this useful for writing a paper around a single brain region which enables emotion, goal setting, attention shifting, hypothesis testing, or whatever you’re studying but it is also really useful if you see significant activation in the white matter or the ventricles - places you shouldn’t see activation in artifact-free statistical maps. The antidote is to (a) choose the threshold a priori and (b) require researchers to show the entire map, including the ventricles (or at least to check it). How to make your results look really strong Strong results mean large effect sizes which include high correlations between healthy-sized, meaty- looking blobs with bright colors and brain measures and outcomes. There are two techniques to ensure your brain map looks as it should no matter how weak the effects actually are. Circular selection (this technique is also known as the voodoo correlation) Let’s face it: most complex personality traits and clinical symptoms are unlikely to strongly correlate with any one brain voxel. The reliability of both brain and outcome measures limit such correlations’ true values. The heterogeneity of outcome measures also limits them: there is no single reason why people feel depressed, experience neuropathic pain, or are schizophrenic, courageous, or optimistic. Additional limits include person-level factors which affect brain response magnitude unconnected to outcomes of interest: among these factors are individual differences in hemodynamic responses and vascular compliance, blood iron levels, alertness, and caffeine intake. However, isn’t it more convincing if your brain findings correlate with optimism or anxiety above r = 0.8? Yes, virtually any study can achieve this. The procedure is simple: first run a correlation map across the whole brain, then select the peak region and test that region’s correlation. If your sample contains 16 participants, then any voxel with a p-value less than 0.005 will show a correlation of at least r = 0.8 or so. Now, maybe you’re worried about not finding any voxels with such a low P-value…. but don’t be. If you test only 1,000 independent comparisons, you have a 99% chance to get at least one significant result, even with no true signal anywhere in the brain. Add to this that brain maps can easily contain 100,000 voxels, though they are not independent. And, of course, if you have some voxels with more modest true correlations - say, in the r = 0.1 range - then the chances are even greater that you will select a voxel with an apparent r = 0.8 correlation, or higher. Small sample sizes will increase your success, too, because they are more variable across the brain. With only 8 participants, the average significant voxel at p < 0.005 will correlate above r = 0.93. Chapter 6 - How to lie with brain imaging 41 There is more good news as well: this technique will work for any effect size measure whether it is a correlation, a difference between experimental conditions, or a multivariate pattern analysis classification accuracy. If you do not want others’ circular selection to fool you, you will need to know that (a) there was a priori selection of all tested regions and (b) the report includes all tested effects. And keep in mind that (c) if there are many tests, some will show large effects by chance. The low-threshold extent correction Circular selection will make your effects look really strong, but won’t create those large, fruit-colored blobs on your brain map. Such blobs are important because human minds naturally confuse ‘lots of reported areas’ with ‘strong effects’, even if the two are unrelated. The solution is to lower the statistical threshold until you get large blobs - and possibly to mask out the pesky white matter and ventricle activations that tend to appear at low thresholds. The problem is that reviewers are savvy and will ask you to report results with multiple comparisons correction. There is a method to lower your statistical threshold and still claim rigorous multiple comparisons correction. How is this possible? Fortunately the technique called cluster extent-based correction lets you set as liberal a ‘primary threshold’ as you want (say, p < 0.05 uncorrected) and then correct for multiple comparisons based on the extent of the blob. Among other problems, correction methods are too liberal with such low thresholds (http://www.ncbi.nlm.nih.gov/pubmed/24412399). The bonus is that your figures’ maps will show all the voxels significant at the liberal, uncorrected threshold even though you can at best actually only claim that the activated area has some true signal somewhere in the activated area. This antidote to this trick is to use more stringent primary thresholds, to clearly indicate each significant region’s identity in figures, and to make it evident that most voxels which appear in the figure may not actually be activated. Or, of course, to avoid extent-based thresholds altogether. Overlapping processes: How to make two maps look the same The overlap zoom-in Let’s say that your theory focuses on overlap across two or more processes such as two types of emotion, pain, or cognitive control. You scan two tasks and compare each one’s activation maps with its respective control condition. To support your theory, simply focus on the overlapping voxels and assume non-overlapping ones are due to noise. Now even if the maps are 95% different across the brain, you can still claim support for your theory. You might also do a multivariate ‘searchlight’ analysis that looks explicitly for similar brain regions across the two processes. Anything significant in the map is positive evidence and the remaining brain areas in which the tasks are dissimilar are just inconclusive null results attributable to low power. Chapter 6 - How to lie with brain imaging 42 If you are not getting enough overlap, the low-threshold extent correction can greatly amplify the extent of your activation patterns and thus increase the apparent overlap. Hopefully most reviewers will not realize that this is not a valid test as your comparison is between two maps with ‘some true signal somewhere’ at each individual voxel, as though each voxel were significant. And, finally, to enhance any of these techniques, you can make a figure that focuses selectively on the overlap locations. The antidote of this technique is to provide unbiased similarity measures across the whole brain including regions that might be shared or unique. Such approaches are not common in neuroimaging literature yet, which makes this technique particularly hard to counteract. The low-level control If the overlap zoom-in does not provide enough ‘evidence’ for overlapping activation, try this additional technique. Similarity is relative: an apple and a banana are dissimilar when compared to an orange but are quite similar when compared to roast beef. Likewise the technique for making the activity maps of two tasks very similar is to compare them to a very dissimilar control condition. Of course, reviewers might object if you compare your two tasks to a third which is very dissimilar. Fortunately, however, there is a perfect comparison condition that will not raise eyebrows, namely rest. Imagine you have a theory that altruism is an automatic human response (which it actually may be). You posit that punishing others produces internal decision conflict even if they deserve it. Thus you would like to demonstrate that brain responses are similar when unfairly punishing others and within a cognitive ‘conflict’ task. No problem. Simply compare each to rest then look at the overlap of the resulting activation maps. Many low-level processes will activate in each map: processes involved in most cognitive tasks such as orienting attention, making basic motor decisions, and executing them. If your study is sufficiently powered, you will observe beautiful overlapping activation in areas including the anterior cingulate, the anterior insula, and the supplementary motor cortices. The antidote to this technique is to require tight control of the tasks or, even better, to track parametric strength increases of each process in which you are trying to assess the overlap. Then the maps you compare will be more tightly constrained to reflect the cognitive processes o