Flexible multi-step hypothesis testing of human ECoG data using cluster-based permutation tests with GLMEs.

BACKGROUND: Time series analysis is critical for understanding brain signals and their relationship to behavior and cognition. Cluster-based permutation tests (CBPT) are commonly used to analyze a variety of electrophysiological signals including EEG, MEG, ECoG, and sEEG data without a priori assumptions about specific temporal effects. However, two major limitations of CBPT include the inability to directly analyze experiments with multiple fixed effects and the inability to account for random effects (e.g. variability across subjects). Here, we propose a flexible multi-step hypothesis testing strategy using CBPT with Linear Mixed Effects Models (LMEs) and Generalized Linear Mixed Effects Models (GLMEs) that can be applied to a wide range of experimental designs and data types. METHODS: We first evaluate the statistical robustness of LMEs and GLMEs using simulated data distributions. Second, we apply a multi-step hypothesis testing strategy to analyze ERPs and broadband power signals extracted from human ECoG recordings collected during a simple image viewing experiment with image category and novelty as fixed effects. Third, we assess the statistical power differences between analyzing signals with CBPT using LMEs compared to CBPT using separate t-tests run on each fixed effect through simulations that emulate broadband power signals. Finally, we apply CBPT using GLMEs to high-gamma burst data to demonstrate the extension of the proposed method to the analysis of nonlinear data. RESULTS: First, we found that LMEs and GLMEs are robust statistical models. In simple simulations LMEs produced highly congruent results with other appropriately applied linear statistical models, but LMEs outperformed many linear statistical models in the analysis of "suboptimal" data and maintained power better than analyzing individual fixed effects with separate t-tests. GLMEs also performed similarly to other nonlinear statistical models. Second, in real world human ECoG data, LMEs performed at least as well as separate t-tests when applied to predefined time windows or when used in conjunction with CBPT. Additionally, fixed effects time courses extracted with CBPT using LMEs from group-level models of pseudo-populations replicated latency effects found in individual category-selective channels. Third, analysis of simulated broadband power signals demonstrated that CBPT using LMEs was superior to CBPT using separate t-tests in identifying time windows with significant fixed effects especially for small effect sizes. Lastly, the analysis of high-gamma burst data using CBPT with GLMEs produced results consistent with CBPT using LMEs applied to broadband power data. CONCLUSIONS: We propose a general approach for statistical analysis of electrophysiological data using CBPT in conjunction with LMEs and GLMEs. We demonstrate that this method is robust for experiments with multiple fixed effects and applicable to the analysis of linear and nonlinear data. Our methodology maximizes the statistical power available in a dataset across multiple experimental variables while accounting for hierarchical random effects and controlling FWER across fixed effects. This approach substantially improves power leading to better reproducibility. Additionally, CBPT using LMEs and GLMEs can be used to analyze individual channels or pseudo-population data for the comparison of functional or anatomical groups of data.

Reliability of visual review of intracranial electroencephalogram in identifying the seizure onset zone: A systematic review and implications for the accuracy of automated methods.

Visual review of intracranial electroencephalography (iEEG) is often an essential component for defining the zone of resection for epilepsy surgery. Unsupervised approaches using machine and deep learning are being employed to identify seizure onset zones (SOZs). This prompts a more comprehensive understanding of the reliability of visual review as a reference standard. We sought to summarize existing evidence on the reliability of visual review of iEEG in defining the SOZ for patients undergoing surgical workup and understand its implications for algorithm accuracy for SOZ prediction. We performed a systematic literature review on the reliability of determining the SOZ by visual inspection of iEEG in accordance with best practices. Searches included MEDLINE, Embase, Cochrane Library, and Web of Science on May 8, 2022. We included studies with a quantitative reliability assessment within or between observers. Risk of bias assessment was performed with QUADAS-2. A model was developed to estimate the effect of Cohen kappa on the maximum possible accuracy for any algorithm detecting the SOZ. Two thousand three hundred thirty-eight articles were identified and evaluated, of which one met inclusion criteria. This study assessed reliability between two reviewers for 10 patients with temporal lobe epilepsy and found a kappa of .80. These limited data were used to model the maximum accuracy of automated methods. For a hypothetical algorithm that is 100% accurate to the ground truth, the maximum accuracy modeled with a Cohen kappa of .8 ranged from .60 to .85 (F-2). The reliability of reviewing iEEG to localize the SOZ has been evaluated only in a small sample of patients with methodologic limitations. The ability of any algorithm to estimate the SOZ is notably limited by the reliability of iEEG interpretation. We acknowledge practical limitations of rigorous reliability analysis, and we propose design characteristics and study questions to further investigate reliability.

Taking an engineer's view: Implications of network analysis for computational psychiatry.

An engineer's viewpoint on psychiatry asks: What are the failure modes that underlie psychiatric dysfunction? And: How can we modify the system? Psychiatry has made great strides in understanding and treating disorders using biology; however, failure modes and modification access points can also exist extrinsically in environmental interactions. The network analysis suggested by Borsboom et al. in the target article provides a new viewpoint that should be incorporated into current theoretical constructs, not placed in opposition to them.

Parsing the phonological loop: activation timing in the dorsal speech stream determines accuracy in speech reproduction.

Despite significant research and important clinical correlates, direct neural evidence for a phonological loop linking speech perception, short-term memory and production remains elusive. To investigate these processes, we acquired whole-head magnetoencephalographic (MEG) recordings from human subjects performing a variable-length syllable sequence reproduction task. The MEG sensor data were source localized using a time-frequency optimized spatially adaptive filter, and we examined the time courses of cortical oscillatory power and the correlations of oscillatory power with behavior between onset of the audio stimulus and the overt speech response. We found dissociations between time courses of behaviorally relevant activations in a network of regions falling primarily within the dorsal speech stream. In particular, verbal working memory load modulated high gamma power in both Sylvian-parietal-temporal and Broca's areas. The time courses of the correlations between high gamma power and subject performance clearly alternated between these two regions throughout the task. Our results provide the first evidence of a reverberating input-output buffer system in the dorsal stream underlying speech sensorimotor integration, consistent with recent phonological loop, competitive queuing, and speech-motor control models. These findings also shed new light on potential sources of speech dysfunction in aphasia and neuropsychiatric disorders, identifying anatomically and behaviorally dissociable activation time windows critical for successful speech reproduction.

Individual differences in uncertainty evaluation explain opposing exploratory behaviors in anxiety and apathy.

Navigating uncertain environments is a fundamental challenge for adaptive behavior, and affective states such as anxiety and apathy can profoundly influence an individual's response to uncertainty. Uncertainty encompasses both volatility and stochasticity, where volatility refers to how rapidly the environment changes and stochasticity describes outcomes resulting from random chance. This study investigates how anxiety and apathy modulate perceptions of environmental volatility and stochasticity and how these perceptions impact exploratory behavior. In a large online sample (N = 1001), participants completed a restless three-armed bandit task, and their choices were analyzed using latent state models to quantify the computational processes. We found that anxious individuals attributed uncertainty more to environmental volatility than stochasticity, leading to increased exploration, particularly after reward omission. Conversely, apathetic individuals perceived uncertainty as more stochastic than volatile, resulting in decreased exploration. The ratio of perceived volatility to stochasticity mediated the relationship between anxiety and exploratory behavior following adverse outcomes. These findings reveal distinct computational mechanisms underlying anxiety and apathy in uncertain environments. Our results provide a novel framework for understanding the cognitive and affective processes driving adaptive and potentially maladaptive behaviors under uncertainty, with implications for the characterization and treatment of neuropsychiatric disorders.

Assessing expert reliability in determining intracranial EEG channel quality and introducing the Automated Bad Channel Detection algorithm.

OBJECTIVES: To evaluate the inter- and intra-rater reliability for the identification of bad channels among neurologists, EEG Technologists, and naïve research personnel, and to compare their performance with the automated bad channel detection (ABCD) algorithm for detecting bad channels. Methods: Six Neurologists, ten EEG Technologists, and six naïve research personnel (22 raters in total) were asked to rate 1440 real intracranial EEG channels as good or bad. Intra- and interrater kappa statistics were calculated for each group. We then compared each group to the ABCD algorithm which uses spectral and temporal domain features to classify channels as good or bad. Results: Analysis of channel ratings from our participants revealed variable intra-rater reliability within each group, with no significant differences across groups. Inter-rater reliability was moderate among neurologists and EEG Technologists but minimal among naïve participants. Neurologists demonstrated a slightly higher consistency in ratings than EEG Technologists. Both groups occasionally misclassified flat channels, and participants generally focused on low-frequency content for their assessments. The ABCD algorithm, in contrast, relied more on high-frequency content. A logistic regression model showed a linear relationship between the algorithm's ratings and user responses for predominantly good channels, but less so for channels rated as bad. Sensitivity and specificity analyses further highlighted differences in rating patterns among the groups, with neurologists showing higher sensitivity and naïve personnel higher specificity. Significance: Our study reveals the bias in human assessments of iEEG data quality and the tendency of even experienced professionals to overlook certain bad channels, highlighting the need for standardized, unbiased methods. The ABCD algorithm, outperforming human raters, suggests the potential of automated solutions for more reliable iEEG interpretation and seizure characterization, offering a reliable approach free from human biases. .

Using Fractal Geometry and Universal Growth Curves as Diagnostics for Comparing Tumor Vasculature and Metabolic Rate With Healthy Tissue and for Predicting Responses to Drug Therapies.

Healthy vasculature exhibits a hierarchical branching structure in which, on average, vessel radius and length change systematically with branching order. In contrast, tumor vasculature exhibits less hierarchy and more variability in its branching patterns. Although differences in vasculature have been highlighted in the literature, there has been very little quantification of these differences. Fractal analysis is a natural tool for comparing tumor and healthy vasculature, especially because it has already been used extensively to model healthy tissue. In this paper, we provide a fractal analysis of existing vascular data, and we present a new mathematical framework for predicting tumor growth trajectories by coupling: (1) the fractal geometric properties of tumor vascular networks, (2) metabolic properties of tumor cells and host vascular systems, and (3) spatial gradients in resources and metabolic states within the tumor. First, we provide a new analysis for how the mean and variation of scaling exponents for ratios of vessel radii and lengths in tumors differ from healthy tissue. Next, we use these characteristic exponents to predict metabolic rates for tumors. Finally, by combining this analysis with general growth equations based on energetics, we derive universal growth curves that enable us to compare tumor and ontogenetic growth. We also extend these growth equations to include necrotic, quiescent, and proliferative cell states and to predict novel growth dynamics that arise when tumors are treated with drugs. Taken together, this mathematical framework will help to anticipate and understand growth trajectories across tumor types and drug treatments.

A low dimensional manifold of human exploratory behavior reveals opposing roles for apathy and anxiety.

Exploration-exploitation decision-making is a feature of daily life that is altered in a number of neuropsychiatric conditions. Humans display a range of exploration and exploitation behaviors, which can be affected by apathy and anxiety. It remains unknown how factors underlying decision-making generate the spectrum of observed exploration-exploitation behavior and how they relate to states of anxiety and apathy. Here, we report a latent structure underlying sequential exploration and exploitation decisions that explains variation in anxiety and apathy. 1001 participants in a gender-balanced sample completed a three-armed restless bandit task along with psychiatric symptom surveys. Using dimensionality reduction methods, we found that decision sequences reduced to a low-dimensional manifold. The axes of this manifold explained individual differences in the balance between states of exploration and exploitation and the stability of those states, as determined by a statistical mechanics model of decision-making. Position along the balance axis was correlated with opposing symptoms of behavioral apathy and anxiety, while position along the stability axis correlated with the level of emotional apathy. This result resolves a paradox over how these symptoms can be correlated in samples but have opposite effects on behavior. Furthermore, this work provides a basis for using behavioral manifolds to reveal relationships between behavioral dynamics and affective states, with important implications for behavioral measurement approaches to neuropsychiatric conditions.

Flexible Multi-Step Hypothesis Testing of Human ECoG Data using Cluster-based Permutation Tests with GLMEs.

Background: Time series analysis is critical for understanding brain signals and their relationship to behavior and cognition. Cluster-based permutation tests (CBPT) are commonly used to analyze a variety of electrophysiological signals including EEG, MEG, ECoG, and sEEG data without a priori assumptions about specific temporal effects. However, two major limitations of CBPT include the inability to directly analyze experiments with multiple fixed effects and the inability to account for random effects (e.g. variability across subjects). Here, we propose a flexible multi-step hypothesis testing strategy using CBPT with Linear Mixed Effects Models (LMEs) and Generalized Linear Mixed Effects Models (GLMEs) that can be applied to a wide range of experimental designs and data types. Methods: We first evaluate the statistical robustness of LMEs and GLMEs using simulated data distributions. Second, we apply a multi-step hypothesis testing strategy to analyze ERPs and broadband power signals extracted from human ECoG recordings collected during a simple image viewing experiment with image category and novelty as fixed effects. Third, we assess the statistical power differences between analyzing signals with CBPT using LMEs compared to CBPT using separate t-tests run on each fixed effect through simulations that emulate broadband power signals. Finally, we apply CBPT using GLMEs to high-gamma burst data to demonstrate the extension of the proposed method to the analysis of nonlinear data. Results: First, we found that LMEs and GLMEs are robust statistical models. In simple simulations LMEs produced highly congruent results with other appropriately applied linear statistical models, but LMEs outperformed many linear statistical models in the analysis of "suboptimal" data and maintained power better than analyzing individual fixed effects with separate t-tests. GLMEs also performed similarly to other nonlinear statistical models. Second, in real world human ECoG data, LMEs performed at least as well as separate t-tests when applied to predefined time windows or when used in conjunction with CBPT. Additionally, fixed effects time courses extracted with CBPT using LMEs from group-level models of pseudo-populations replicated latency effects found in individual category-selective channels. Third, analysis of simulated broadband power signals demonstrated that CBPT using LMEs was superior to CBPT using separate t-tests in identifying time windows with significant fixed effects especially for small effect sizes. Lastly, the analysis of high-gamma burst data using CBPT with GLMEs produced results consistent with CBPT using LMEs applied to broadband power data. Conclusions: We propose a general approach for statistical analysis of electrophysiological data using CBPT in conjunction with LMEs and GLMEs. We demonstrate that this method is robust for experiments with multiple fixed effects and applicable to the analysis of linear and nonlinear data. Our methodology maximizes the statistical power available in a dataset across multiple experimental variables while accounting for hierarchical random effects and controlling FWER across fixed effects. This approach substantially improves power and accuracy leading to better reproducibility. Additionally, CBPT using LMEs and GLMEs can be used to analyze individual channels or pseudo-population data for the comparison of functional or anatomical groups of data.

Prolonged Physiological Stress Is Associated With a Lower Rate of Exploratory Learning That Is Compounded by Depression.

BACKGROUND: Stress is a major risk factor for depression, and both are associated with important changes in decision-making patterns. However, decades of research have only weakly connected physiological measurements of stress to the subjective experience of depression. Here, we examined the relationship between prolonged physiological stress, mood, and explore-exploit decision making in a population navigating a dynamic environment under stress: health care workers during the COVID-19 pandemic. METHODS: We measured hair cortisol levels in health care workers who completed symptom surveys and performed an explore-exploit restless-bandit decision-making task; 32 participants were included in the final analysis. Hidden Markov and reinforcement learning models assessed task behavior. RESULTS: Participants with higher hair cortisol exhibited less exploration (r = -0.36, p = .046). Higher cortisol levels predicted less learning during exploration (ß = -0.42, false discovery rate [FDR]-corrected p [pFDR] = .022). Importantly, mood did not independently correlate with cortisol concentration, but rather explained additional variance (ß = 0.46, pFDR = .022) and strengthened the relationship between higher cortisol and lower levels of exploratory learning (ß = -0.47, pFDR = .022) in a joint model. These results were corroborated by a reinforcement learning model, which revealed less learning with higher hair cortisol and low mood (ß = -0.67, pFDR = .002). CONCLUSIONS: These results imply that prolonged physiological stress may limit learning from new information and lead to cognitive rigidity, potentially contributing to burnout. Decision-making measures link subjective mood states to measured physiological stress, suggesting that they should be incorporated into future biomarker studies of mood and stress conditions.

Pretrial predictors of conflict response efficacy in the human prefrontal cortex.

The ability to perform motor actions depends, in part, on the brain's initial state. We hypothesized that initial state dependence is a more general principle and applies to cognitive control. To test this idea, we examined human single units recorded from the dorsolateral prefrontal (dlPFC) cortex and dorsal anterior cingulate cortex (dACC) during a task that interleaves motor and perceptual conflict trials, the multisource interference task (MSIT). In both brain regions, variability in pre-trial firing rates predicted subsequent reaction time (RT) on conflict trials. In dlPFC, ensemble firing rate patterns suggested the existence of domain-specific initial states, while in dACC, firing patterns were more consistent with a domain-general initial state. The deployment of shared and independent factors that we observe for conflict resolution may allow for flexible and fast responses mediated by cognitive initial states. These results also support hypotheses that place dACC hierarchically earlier than dlPFC in proactive control.

Computational validity: using computation to translate behaviours across species.

We propose a new conceptual framework (computational validity) for translation across species and populations based on the computational similarity between the information processing underlying parallel tasks. Translating between species depends not on the superficial similarity of the tasks presented, but rather on the computational similarity of the strategies and mechanisms that underlie those behaviours. Computational validity goes beyond construct validity by directly addressing questions of information processing. Computational validity interacts with circuit validity as computation depends on circuits, but similar computations could be accomplished by different circuits. Because different individuals may use different computations to accomplish a given task, computational validity suggests that behaviour should be understood through the subject's point of view; thus, behaviour should be characterized on an individual level rather than a task level. Tasks can constrain the computational algorithms available to a subject and the observed subtleties of that behaviour can provide information about the computations used by each individual. Computational validity has especially high relevance for the study of psychiatric disorders, given the new views of psychiatry as identifying and mediating information processing dysfunctions that may show high inter-individual variability, as well as for animal models investigating aspects of human psychiatric disorders. This article is part of the theme issue 'Systems neuroscience through the lens of evolutionary theory'.

Personalizing Dual-Target Cortical Stimulation with Bayesian Parameter Optimization Successfully Treats Central Post-Stroke Pain: A Case Report.

Central pain disorders, such as central post-stroke pain, remain clinically challenging to treat, despite many decades of pharmacological advances and the evolution of neuromodulation. For treatment refractory cases, previous studies have highlighted some benefits of cortical stimulation. Recent advances in new targets for pain and the optimization of neuromodulation encouraged our group to develop a dual cortical target approach paired with Bayesian optimization to provide a personalized treatment. Here, we present a case report of a woman who developed left-sided facial pain after multiple thalamic strokes. All previous pharmacologic and interventional treatments failed to mitigate the pain, leaving her incapacitated due to pain and medication side effects. She subsequently underwent a single burr hole for placement of motor cortex (M1) and dorsolateral prefrontal cortex (dlPFC) paddles for stimulation with externalization. By using Bayesian optimization to find optimal stimulation parameters and stimulation sites, we were able to reduce pain from an 8.5/10 to a 0/10 during a 5-day inpatient stay, with pain staying at or below a 2/10 one-month post-procedure. We found optimal treatment to be simultaneous stimulation of M1 and dlPFC without any evidence of seizure induction. In addition, we found no worsening in cognitive performance during a working memory task with dlPFC stimulation. This personalized approach using Bayesian optimization may provide a new foundation for treating central pain and other functional disorders through systematic evaluation of stimulation parameters.

Unraveling why we sleep: Quantitative analysis reveals abrupt transition from neural reorganization to repair in early development.

Sleep serves disparate functions, most notably neural repair, metabolite clearance and circuit reorganization. Yet the relative importance remains hotly debated. Here, we create a novel mechanistic framework for understanding and predicting how sleep changes during ontogeny and across phylogeny. We use this theory to quantitatively distinguish between sleep used for neural reorganization versus repair. Our findings reveal an abrupt transition, between 2 and 3 years of age in humans. Specifically, our results show that differences in sleep across phylogeny and during late ontogeny (after 2 or 3 years in humans) are primarily due to sleep functioning for repair or clearance, while changes in sleep during early ontogeny (before 2 or 3 years) primarily support neural reorganization and learning. Moreover, our analysis shows that neuroplastic reorganization occurs primarily in REM sleep but not in NREM. This developmental transition suggests a complex interplay between developmental and evolutionary constraints on sleep.

The Visual Word Form Area compensates for auditory working memory dysfunction in schizophrenia.

Auditory working memory impairments feature prominently in schizophrenia. However, the existence of altered and perhaps compensatory neural dynamics, sub-serving auditory working memory, remains largely unexplored. We compared the dynamics of induced high gamma power (iHGP) across cortex in humans during speech-sound working memory in individuals with schizophrenia (SZ) and healthy comparison subjects (HC) using magnetoencephalography (MEG). SZ showed similar task performance to HC while utilizing different brain regions. During encoding of speech sounds, SZ lacked the correlation of iHGP with task performance in posterior superior temporal gyrus (STGp) that was observed in healthy subjects. Instead, SZ recruited the visual word form area (VWFA) during both stimulus encoding and response preparation. Importantly, VWFA activity during encoding correlated with the magnitude of SZ hallucinations, task performance and an independent measure of verbal working memory. These findings suggest that VWFA plasticity is harnessed to compensate for STGp dysfunction in schizophrenia patients with hallucinations.

Intervention-specific patterns of cortical function plasticity during auditory encoding in people with schizophrenia.

Schizophrenia is a neurocognitive illness characterized by behavioral and neural impairments in both early auditory processing and higher order verbal working memory. Previously we have shown intervention-specific cognitive performance improvements with computerized, targeted training of auditory processing (AT) when compared to a computer games (CG) control intervention that emphasized visual processing. To investigate spatiotemporal changes in patterns of neural activity specific to the AT intervention, the current study used magnetoencephalography (MEG) imaging to derive induced high gamma band oscillations (HGO) during auditory encoding, before and after 50 h (∼10 weeks) of exposure to either the AT or CG intervention. During stimulus encoding, AT intervention-specific changes in high gamma activity occurred in left middle frontal and left middle-superior temporal cortices. In contrast, CG intervention-specific changes were observed in right medial frontal and supramarginal gyri during stimulus encoding, and in bilateral temporal cortices during response preparation. These data reveal that, in schizophrenia, intensive exposure to either training of auditory processing or exposure to visuospatial activities produces significant but complementary patterns of cortical function plasticity within a distributed fronto-temporal network. These results underscore the importance of delineating the specific neuroplastic effects of targeted behavioral interventions to ensure desired neurophysiological changes and avoid unintended consequences on neural system functioning.

Auditory Cortical Plasticity Drives Training-Induced Cognitive Changes in Schizophrenia.

Schizophrenia is characterized by dysfunction in basic auditory processing, as well as higher-order operations of verbal learning and executive functions. We investigated whether targeted cognitive training of auditory processing improves neural responses to speech stimuli, and how these changes relate to higher-order cognitive functions. Patients with schizophrenia performed an auditory syllable identification task during magnetoencephalography before and after 50 hours of either targeted cognitive training or a computer games control. Healthy comparison subjects were assessed at baseline and after a 10 week no-contact interval. Prior to training, patients (N = 34) showed reduced M100 response in primary auditory cortex relative to healthy participants (N = 13). At reassessment, only the targeted cognitive training patient group (N = 18) exhibited increased M100 responses. Additionally, this group showed increased induced high gamma band activity within left dorsolateral prefrontal cortex immediately after stimulus presentation, and later in bilateral temporal cortices. Training-related changes in neural activity correlated with changes in executive function scores but not verbal learning and memory. These data suggest that computerized cognitive training that targets auditory and verbal learning operations enhances both sensory responses in auditory cortex as well as engagement of prefrontal regions, as indexed during an auditory processing task with low demands on working memory. This neural circuit enhancement is in turn associated with better executive function but not verbal memory.

A quantitative theory of solid tumor growth, metabolic rate and vascularization.

The relationships between cellular, structural and dynamical properties of tumors have traditionally been studied separately. Here, we construct a quantitative, predictive theory of solid tumor growth, metabolic rate, vascularization and necrosis that integrates the relationships between these properties. To accomplish this, we develop a comprehensive theory that describes the interface and integration of the tumor vascular network and resource supply with the cardiovascular system of the host. Our theory enables a quantitative understanding of how cells, tissues, and vascular networks act together across multiple scales by building on recent theoretical advances in modeling both healthy vasculature and the detailed processes of angiogenesis and tumor growth. The theory explicitly relates tumor vascularization and growth to metabolic rate, and yields extensive predictions for tumor properties, including growth rates, metabolic rates, degree of necrosis, blood flow rates and vessel sizes. Besides these quantitative predictions, we explain how growth rates depend on capillary density and metabolic rate, and why similar tumors grow slower and occur less frequently in larger animals, shedding light on Peto's paradox. Various implications for potential therapeutic strategies and further research are discussed.

Scaling of number, size, and metabolic rate of cells with body size in mammals.

The size and metabolic rate of cells affect processes from the molecular to the organismal level. We present a quantitative, theoretical framework for studying relationships among cell volume, cellular metabolic rate, body size, and whole-organism metabolic rate that helps reveal the feedback between these levels of organization. We use this framework to show that average cell volume and average cellular metabolic rate cannot both remain constant with changes in body size because of the well known body-size dependence of whole-organism metabolic rate. Based on empirical data compiled for 18 cell types in mammals, we find that many cell types, including erythrocytes, hepatocytes, fibroblasts, and epithelial cells, follow a strategy in which cellular metabolic rate is body size dependent and cell volume is body size invariant. We suggest that this scaling holds for all quickly dividing cells, and conversely, that slowly dividing cells are expected to follow a strategy in which cell volume is body size dependent and cellular metabolic rate is roughly invariant with body size. Data for slowly dividing neurons and adipocytes show that cell volume does indeed scale with body size. From these results, we argue that the particular strategy followed depends on the structural and functional properties of the cell type. We also discuss consequences of these two strategies for cell number and capillary densities. Our results and conceptual framework emphasize fundamental constraints that link the structure and function of cells to that of whole organisms.