Reliability of MRI-derived measurements of human cerebral cortical thickness: the effects of field strength, scanner upgrade and manufacturer

In vivo MRI-derived measurements of human cerebral cortex thickness are providing novel insights into normal and abnormal neuroanatomy, but little is known about their reliability. We investigated how the reliability of cortical thickness measurements is affected by MRI instrument-related factors, including scanner field strength, manufacturer, upgrade and pulse sequence. Several data processing factors were also studied. Two test-retest data sets were analyzed: 1) 15 healthy older subjects scanned four times at 2-week intervals on three scanners; 2) 5 subjects scanned before and after a major scanner upgrade. Within-scanner variability of global cortical thickness measurements was <0.03 mm, and the point-wise standard deviation of measurement error was approximately 0.12 mm. Variability was 0.15 mm and 0.17 mm in average, respectively, for cross-scanner (Siemens/GE) and cross-field strength (1.5 T/3 T) comparisons. Scanner upgrade did not increase variability nor introduce bias. Measurements across field strength, however, were slightly biased (thicker at 3 T). The number of (single vs. multiple averaged) acquisitions had a negligible effect on reliability, but the use of a different pulse sequence had a larger impact, as did different parameters employed in data processing. Sample size estimates indicate that regional cortical thickness difference of 0.2 mm between two different groups could be identified with as few as 7 subjects per group, and a difference of 0.1 mm could be detected with 26 subjects per group. These results demonstrate that MRI-derived cortical thickness measures are highly reliable when MRI instrument and data processing factors are controlled but that it is important to consider these factors in the design of multi-site or longitudinal studies, such as clinical drug trials.     

Analysis of between-trial and within-trial neural spiking dynamics

Recording single-neuron activity from a specific brain region across multiple trials in response to the same stimulus or execution of the same behavioral task is a common neurophysiology protocol. The raster plots of the spike trains often show strong between-trial and within-trial dynamics, yet the standard analysis of these data with the peristimulus time histogram (PSTH) and ANOVA do not consider between-trial dynamics. By itself, the PSTH does not provide a framework for statistical inference. We present a state-space generalized linear model (SS-GLM) to formulate a point process representation of between-trial and within-trial neural spiking dynamics. Our model has the PSTH as a special case. We provide a framework for model estimation, model selection, goodness-of-fit analysis, and inference. In an analysis of hippocampal neural activity recorded from a monkey performing a location-scene association task, we demonstrate how the SS-GLM may be used to answer frequently posed neurophysiological questions including, What is the nature of the between-trial and within-trial task-specific modulation of the neural spiking activity? How can we characterize learning-related neural dynamics? What are the timescales and characteristics of the neuron's biophysical properties? Our results demonstrate that the SS-GLM is a more informative tool than the PSTH and ANOVA for analysis of multiple trial neural responses and that it provides a quantitative characterization of the between-trial and within-trial neural dynamics readily visible in raster plots, as well as the less apparent fast (1-10 ms), intermediate (11-20 ms), and longer (>20 ms) timescale features of the neuron's biophysical properties.     

Dynamic classification using credible intervals in longitudinal discriminant analysis

Recently developed methods of longitudinal discriminant analysis allow for classification of subjects into prespecified prognostic groups using longitudinal history of both continuous and discrete biomarkers. The classification uses Bayesian estimates of the group membership probabilities for each prognostic group. These estimates are derived from a multivariate generalised linear mixed model of the biomarker's longitudinal evolution in each of the groups and can be updated each time new data is available for a patient, providing a dynamic (over time) allocation scheme. However, the precision of the estimated group probabilities differs for each patient and also over time. This precision can be assessed by looking at credible intervals for the group membership probabilities. In this paper, we propose a new allocation rule that incorporates credible intervals for use in context of a dynamic longitudinal discriminant analysis and show that this can decrease the number of false positives in a prognostic test, improving the positive predictive value. We also establish that by leaving some patients unclassified for a certain period, the classification accuracy of those patients who are classified can be improved, giving increased confidence to clinicians in their decision making. Finally, we show that determining a stopping rule dynamically can be more accurate than specifying a set time point at which to decide on a patient's status. We illustrate our methodology using data from patients with epilepsy and show how patients who fail to achieve adequate seizure control are more accurately identified using credible intervals compared to existing methods.     

Measuring the signal-to-noise ratio of a neuron

The signal-to-noise ratio (SNR), a commonly used measure of fidelity in physical systems, is defined as the ratio of the squared amplitude or variance of a signal relative to the variance of the noise. This definition is not appropriate for neural systems in which spiking activity is more accurately represented as point processes. We show that the SNR estimates a ratio of expected prediction errors and extend the standard definition to one appropriate for single neurons by representing neural spiking activity using point process generalized linear models (PP-GLM). We estimate the prediction errors using the residual deviances from the PP-GLM fits. Because the deviance is an approximate χ² random variable, we compute a bias-corrected SNR estimate appropriate for single-neuron analysis and use the bootstrap to assess its uncertainty. In the analyses of four systems neuroscience experiments, we show that the SNRs are −10 dB to −3 dB for guinea pig auditory cortex neurons, −18 dB to −7 dB for rat thalamic neurons, −28 dB to −14 dB for monkey hippocampal neurons, and −29 dB to −20 dB for human subthalamic neurons. The new SNR definition makes explicit in the measure commonly used for physical systems the often-quoted observation that single neurons have low SNRs. The neuron’s spiking history is frequently a more informative covariate for predicting spiking propensity than the applied stimulus. Our new SNR definition extends to any GLM system in which the factors modulating the response can be expressed as separate components of a likelihood function.The signal-to-noise ratio (SNR), defined as the amplitude squared of a signal or the signal variance divided by the variance of the system noise, is a widely applied measure for quantifying system fidelity and for comparing performance among different systems (1–4). Commonly expressed in decibels as 10log₁₀(SNR), the higher the SNR, the stronger the signal or information in the signal relative to the noise or distortion. Use of the SNR is most appropriate for systems defined as deterministic or stochastic signals plus Gaussian noise (2, 4). For the latter, the SNR can be computed in the time or frequency domain.Use of the SNR to characterize the fidelity of neural systems is appealing because information transmission by neurons is a noisy stochastic process. However, the standard concept of SNR cannot be applied in neuronal analyses because neurons transmit both signal and noise primarily in their action potentials, which are binary electrical discharges also known as spikes (5–8). Defining what is the signal and what is the noise in neural spiking activity is a challenge because the putative signals or stimuli for neurons differ appreciably among brain regions and experiments. For example, neurons in the visual cortex and in the auditory cortex respond respectively to features of light (9) and sound stimuli (10) while neurons in the somatosensory thalamus respond to tactile stimuli (11). In contrast, neurons in the rodent hippocampus respond robustly to the animal’s position in its environment (11, 12), whereas monkey hippocampal neurons respond to the process of task learning (13). As part of responding to a putative stimulus, a neuron’s spiking activity is also modulated by biophysical factors such as its absolute and relative refractory periods, its bursting propensity, and local network and rhythm dynamics (14, 15). Hence, the definition of SNR must account for the extent to which a neuron’s spiking responses are due to the applied stimulus or signal and to these intrinsic biophysical properties.Formulations of the SNR for neural systems have been studied. Rieke et al. (16) adapted information theory measures to define Gaussian upper bounds on the SNR for individual neurons. Coefficients of variation and Fano factors based on spike counts (17–19) have been used as measures of SNR. Similarly, Gaussian approximations have been used to derive upper bounds on neuronal SNR (16). These approaches do not consider the point process nature of neural spiking activity. Moreover, these measures and the Gaussian approximations are less accurate for neurons with low spike rates or when information is contained in precise spike times.Lyamzin et al. (20) developed an SNR measure for neural systems using time-dependent Bernoulli processes to model the neural spiking activity. Their SNR estimates, based on variance formulae, do not consider the biophysical properties of the neuron and are more appropriate for Gaussian systems (16, 21, 22). The Poisson regression model used widely in statistics to relate count observations to covariates provides a framework for studying the SNR for non-Gaussian systems because it provides an analog of the square of the multiple correlation coefficient (R²) used to measure goodness of fit in linear regression analyses (23). The SNR can be expressed in terms of the R² for linear and Poisson regression models. However, this relationship has not been exploited to construct an SNR estimate for neural systems or point process models. Finally, the SNR is a commonly computed statistic in science and engineering. Extending this concept to non-Gaussian systems would be greatly aided by a precise statement of the theoretical quantity that this statistic estimates (24, 25).We show that the SNR estimates a ratio of expected prediction errors (EPEs). Using point process generalized linear models (PP-GLM), we extend the standard definition to one appropriate for single neurons recorded in stimulus−response experiments. In analyses of four neural systems, we show that single-neuron SNRs range from −29 dB to −3 dB and that spiking history is often a more informative predictor of spiking propensity than the signal being represented. Our new SNR definition generalizes to any problem in which the modulatory components of a system’s output can be expressed as separate components of a GLM.