Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

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Fitting Linear Mixed-Effects Models Using lme4

Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

Thirty years of brain imaging research has converged to define the brain’s default network—a novel and only recently appreciated brain system that participates in internal modes of cognition Here we synthesize past observations to provide strong evidence that the default network is a specific, anatomically defined brain system preferentially active when individuals are not focused on the external environment Analysis of connectional anatomy in the monkey supports the presence of an interconnected brain system Providing insight into function, the default network is active when individuals are engaged in internally focused tasks including autobiographical memory retrieval, envisioning the future, and conceiving the perspectives of others Probing the functional anatomy of the network in detail reveals that it is best understood as multiple interacting subsystems The medial temporal lobe subsystem provides information from prior experiences in the form of memories and associations that are the building blocks of mental simulation The medial prefrontal subsystem facilitates the flexible use of this information during the construction of self-relevant mental simulations These two subsystems converge on important nodes of integration including the posterior cingulate cortex The implications of these functional and anatomical observations are discussed in relation to possible adaptive roles of the default network for using past experiences to plan for the future, navigate social interactions, and maximize the utility of moments when we are not otherwise engaged by the external world We conclude by discussing the relevance of the default network for understanding mental disorders including autism, schizophrenia, and Alzheimer’s disease

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The Brain's Default Network Anatomy, Function, and Relevance to Disease

The majority of functional neuroscience studies have focused on the brain's response to a task or stimulus. However, the brain is very active even in the absence of explicit input or output. In this Article we review recent studies examining spontaneous fluctuations in the blood oxygen level dependent (BOLD) signal of functional magnetic resonance imaging as a potentially important and revealing manifestation of spontaneous neuronal activity. Although several challenges remain, these studies have provided insight into the intrinsic functional architecture of the brain, variability in behaviour and potential physiological correlates of neurological and psychiatric disease.

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Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging.

Functional neuroimaging studies have started unravelling unexpected functional attributes for the posteromedial portion of the parietal lobe, the precuneus. This cortical area has traditionally received little attention, mainly because of its hidden location and the virtual absence of focal lesion studies. However, recent functional imaging findings in healthy subjects suggest a central role for the precuneus in a wide spectrum of highly integrated tasks, including visuo-spatial imagery, episodic memory retrieval and self-processing operations, namely first-person perspective taking and an experience of agency. Furthermore, precuneus and surrounding posteromedial areas are amongst the brain structures displaying the highest resting metabolic rates (hot spots) and are characterized by transient decreases in the tonic activity during engagement in non-self-referential goal-directed actions (default mode of brain function). Therefore, it has recently been proposed that precuneus is involved in the interwoven network of the neural correlates of self-consciousness, engaged in self-related mental representations during rest. This hypothesis is consistent with the selective hypometabolism in the posteromedial cortex reported in a wide range of altered conscious states, such as sleep, drug-induced anaesthesia and vegetative states. This review summarizes the current knowledge about the macroscopic and microscopic anatomy of precuneus, together with its wide-spread connectivity with both cortical and subcortical structures, as shown by connectional and neurophysiological findings in non-human primates, and links these notions with the multifaceted spectrum of its behavioural correlates. By means of a critical analysis of precuneus activation patterns in response to different mental tasks, this paper provides a useful conceptual framework for matching the functional imaging findings with the specific role(s) played by this structure in the higher-order cognitive functions in which it has been implicated. Specifically, activation patterns appear to converge with anatomical and connectivity data in providing preliminary evidence for a functional subdivision within the precuneus into an anterior region, involved in self-centred mental imagery strategies, and a posterior region, subserving successful episodic memory retrieval.

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The precuneus: a review of its functional anatomy and behavioural correlates.

Daytime performance changes were examined during chronic sleep restriction or augmentation and following subsequent recovery sleep. Sixty-six normal volunteers spent either 3 (n = 18), 5 (n= 16), 7 (n = 16), or 9 h (n = 16) daily time in bed (TIB) for 7 days (restriction/augmentation) followed by 3 days with 8 h daily TIB (recovery). In the 3-h group, speed (mean and fastest 10% of responses) on the psychomotor vigilance task (PVT) declined, and PVT lapses (reaction times greater than 500 ms) increased steadily across the 7 days of sleep restriction. In the 7- and 5-h groups speed initially declined, then appeared to stabilize at a reduced level; lapses were increased only in the 5-h group. In the 9-h group, speed and lapses remained at baseline levels. During recovery, PVT speed in the 7- and 5-h groups (and lapses in the 5-h group) remained at the stable, but reduced levels seen during the last days of the experimental phase, with no evidence of recovery. Speed and lapses in the 3-h group recovered rapidly following the first night of recovery sleep; however, recovery was incomplete with speed and lapses stabilizing at a level comparable with the 7- and 5-h groups. Performance in the 9-h group remained at baseline levels during the recovery phase. These results suggest that the brain adapts to chronic sleep restriction. In mild to moderate sleep restriction this adaptation is sufficient to stabilize performance, although at a reduced level. These adaptive changes are hypothesized to restrict brain operational capacity and to persist for several days after normal sleep duration is restored, delaying recovery.

https://onlinelibrary.wiley.com/doi/pdf/10.1046/j.1365-2869.2003.00337.x

Patterns of performance degradation and restoration during sleep restriction and subsequent recovery: a sleep dose-response study

To assess dynamic changes in brain function throughout the sleep-wake cycle, CBF was measured with H2(15)O and PET in 37 normal male volunteers: (i) while awake prior to sleep onset; (ii) during Stage 3-4 sleep, i.e. slow wave sleep (SWS); (iii) during rapid eye movement (REM) sleep; and (iv) upon waking following recovery sleep. Subjects were monitored polysomnographically and PET images were acquired throughout the course of a single night. Stage-specific contrasts were performed using statistical parametric mapping. Data were analysed in repeated measures fashion, examining within-subject differences between stages [pre-sleep wakefulness-SWS (n = 20 subjects); SWS-post-sleep wakefulness (n = 14); SWS-REM sleep (n = 7); pre-sleep wakefulness-REM sleep (n = 8); REM sleep-post-sleep wakefulness (n = 7); pre-sleep wakefulness-post-sleep wakefulness (n = 20)]. State dependent changes in the activity of centrencephalic regions, including the brainstem, thalamus and basal forebrain (profound deactivations during SWS and reactivations during REM sleep) are consistent with the idea that these areas are constituents of brain systems which mediate arousal. Shifts in the level of activity of the striatum suggested that the basal ganglia might be more integrally involved in the orchestration of the sleep-wake cycle than previously thought. State-dependent changes in the activity of limbic and paralimbic areas, including the insula, cingulate and mesial temporal cortices, paralleled those observed in centrencephalic structures during both REM sleep and SWS. A functional dissociation between activity in higher order, heteromodal association cortices in the frontal and parietal lobes and unimodal sensory areas of the occipital and temporal lobes appeared to be characteristic of both SWS and REM sleep. SWS was associated with selective deactivation of the heteromodal association areas, while activity in primary and secondary sensory cortices was preserved. SWS may not, as previously thought, represent a generalized decrease in neuronal activity. On the other hand, REM sleep was characterized by selective activation of certain post-rolandic sensory cortices, while activity in the frontoparietal association cortices remained depressed. REM sleep may be characterized by activation of widespread areas of the brain, including the centrencephalic, paralimbic and unimodal sensory regions, with the specific exclusion of areas which normally participate in the highest order analysis and integration of neural information. Deactivation of the heteromodal association areas (the orbital, dorsolateral prefrontal and inferior parietal cortices) constitutes the single feature common to both non-REM and REM sleep states, and may be a defining characteristic of sleep itself. The stages of sleep could also be distinguished by characteristic differences in the relationships between the basal ganglia, thalamic nuclei and neocortical regions of interest.

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Regional cerebral blood flow throughout the sleep-wake cycle. An H2(15)O PET study

Regional cerebral blood flow throughout the sleep- wake cycle

The recent discovery of a circuit of brain regions that is highly active in the absence of overt behavior has led to a quest for revealing the possible function of this so-called default-mode network (DMN). A very recent study, finding similarities in awake humans and anesthetized primates, has suggested that DMN activity might not simply reflect ongoing conscious mentation but rather a more general form of network dynamics typical of complex systems. Here, by performing functional MRI in humans, it is shown that a natural, sleep-induced reduction of consciousness is reflected in altered correlation between DMN network components, most notably a reduced involvement of frontal cortex. This suggests that DMN may play an important role in the sustenance of conscious awareness.

https://www.pnas.org/content/pnas/106/27/11376.full.pdf

Decoupling of the brain's default mode network during deep sleep

Recent blood oxygenation level dependent functional MRI (BOLD fMRI) studies of the human brain have shown that in the absence of external stimuli, activity persists in the form of distinct patterns of temporally correlated signal fluctuations. In this work, we investigated the spontaneous BOLD signal fluctuations during states of reduced consciousness such as drowsiness and sleep. For this purpose, we performed BOLD fMRI on normal subjects during varying levels of consciousness, from resting wakefulness to light (non-slow wave) sleep. Depth of sleep was determined based on concurrently acquired EEG data. During light sleep, significant increases in the fluctuation level of the BOLD signal were observed in several cortical areas, among which visual cortex was the most significant. Correlations among brain regions involved with the default-mode network persisted during light sleep. These results suggest that activity in areas such as the default-mode network and primary sensory cortex, as measured from BOLD fMRI fluctuations, does not require a level of consciousness typical of wakefulness.

Thomas J. Balkin

Papers

Patterns of performance degradation and restoration during sleep restriction and subsequent recovery: a sleep dose-response study

Regional cerebral blood flow throughout the sleep-wake cycle. An H2(15)O PET study

Regional cerebral blood flow throughout the sleep- wake cycle

Decoupling of the brain's default mode network during deep sleep

Low frequency BOLD fluctuations during resting wakefulness and light sleep: a simultaneous EEG-fMRI study.