Dynamic causal modelling of effective connectivity from fMRI: are results reproducible and sensitive to Parkinson's disease and its treatment?

Abstract

Dynamic causal modelling (DCM) of functional magnetic resonance imaging (fMRI) data offers new insights into the pathophysiology of neurological disease and mechanisms of effective therapies. Current applications can be used both to identify the most likely functional brain network underlying observed data and estimate the networks' connectivity parameters. We examined the reproducibility of DCM in healthy subjects (young 18-48 years, n=27; old 50-80 years, n=15) in the context of action selection. We then examined the effects of Parkinson's disease (50-78 years, Hoehn and Yahr stage 1-2.5, n=16) and dopaminergic therapy. Forty-eight models were compared, for each of 90 sessions from 58 subjects. Model-evidences clustered according to sets of structurally similar models, with high correlations over two sessions in healthy older subjects. The same model was identified as most likely in healthy controls on both sessions and in medicated patients. In this most likely network model, the selection of action was associated with enhanced coupling between prefrontal cortex and the pre-supplementary motor area. However, the parameters for intrinsic connectivity and contextual modulation in this model were poorly correlated across sessions. A different model was identified in patients with Parkinson's disease after medication withdrawal. In "off" patients, action selection was associated with enhanced connectivity from prefrontal to lateral premotor cortex. This accords with independent evidence of a dopamine-dependent functional disconnection of the SMA in Parkinson's disease. Together, these results suggest that DCM model selection is robust and sensitive enough to study clinical populations and their pharmacological treatment. For critical inferences, model selection may be sufficient. However, caution is required when comparing groups or drug effects in terms of the connectivity parameter estimates, if there are significant posterior covariances among parameters.

Fig. 1

Schematic representations of the 48 models compared in this study. Models are illustrated in sets, grouped by intrinsic connectivity structure (letters A–F) and by the modulation of connectivity by the difference between chosen and specified conditions (numbers 1–8). Models E1 and E2 are enlarged. The free energy estimate of the log evidence, F, is greatest for model E2 in young and old healthy subjects, and patients on dopaminergic therapy. Model E1 is more likely in patients in a relative “off” state induced by medication withdrawal. The models differ in the contextual modulation of task related connectivity, which is manifest in changing connectivity of prefrontal to pre-SMA connectivity (E2) or prefrontal to premotor cortex connectivity (E1). PFC = prefrontal cortex, pre-SMA = pre-supplementary motor area, PM = premotor cortex, M1 = primary motor cortex. For clarity, the labels are omitted from the small model illustrations. The contextual modulation is illustrated by a dotted arrow.

Fig. 2

(A) For all healthy subjects the difference in log-evidence, estimated by the free energy F for each model, is plotted against the number of user specified connection parameters in the models. For each set of structural models (labelled A–F, according to Fig. 1) there are further differences in F according to the bilinear effects representing contextual modulation of connectivity. The most likely model of all E2 is referenced at F = 0. (B) The log-evidence estimate F is plotted against the model rank over all healthy subjects, from least likely = 1 to most likely = 48. (C) The 48 model evidences summed over 15 elderly control subjects on each of two sessions A and B, indicating a strong positive correlation. Evidences are plotted relative to the most likely model, E2. (D) The group differences in log-evidence estimates F for models E1 and C2 are plotted relative to the overall preferred model E2. Bars represent the difference between models, for each group by session. For older control subjects (OC) the two sessions were randomly assigned to sessions A and B, matched for first and second sessions. Similarly, for patients with PD, one session was in a relative “off” state induced by medication withdrawal, while the other session was in a relative “on” state with usual medication. Horizontal lines indicate thresholds for positive evidence (dotted) or strong evidence (dashed) in favour of model E2 (if below the line) or against model E2 (if above the line).

Fig. 3

Random effects and fixed effects approaches to group model selection. For a fixed effects analysis of the 48 models (in six sets A to F, see also Fig. 1) the models can be compared using (A) the sum of log-evidences (cf. the Group Bayes Factor for the model) or (B) the equivalent posterior model probability. The leading three models from the groups analysis are E2 > C2 > E1. A random effects analysis using a hierarchical Bayesian model selection procedure (see Methods) over all 48 models compares models in terms of (C) the expected posterior probability that a given subject had generated data according to a given model or (D) the exceedance probability representing the confidence that a given model is more likely than any other model.

Fig. 4

Random effects and Fixed effects Bayesian Model Selection approaches to group model selection for Healthy older controls, PD patients “on” and PD patients “off,” for the leading models E2, E1 and C2. Fixed effects analyses results are presented as log-evidences and Posterior Model Probability (PMP). Random effects analyses are presented as Expected Posterior Probability (EPP) or Exceedance Probabilities (ExPr). It can be seen that by both approaches, model E2 is preferred in Healthy Controls and PD “on” patients, but that model E1 is preferred in PD “off” patients. The difference between fixed and random effects models is seen for PD “on” patients, for whom model E1 is second most likely by the random effects method, but very unlikely by the fixed effects method.

Fig. 5

The estimates of intrinsic connectivity PFC → pre-SMA across two sessions was poorly correlated in healthy older controls (OC, panel A) but positively correlated in patients with Parkinson's disease (PD, panel B). The estimate of the bilinear term in older healthy control subjects (C) and PD patients (D), each group repeating the same paradigm on two occasions. These estimates of the bilinear term express the modulation of PFC → pre-SMA connectivity by trial context (chosen vs. specified response trials). The parametric correlations are not significant, but see also Results for non-parametric statistics.

Fig. 6

The posterior covariances among parameter estimates (output matrix DCM.Cp) have been normalised to correlation matrices, and averaged across healthy older control subjects (A) and patients with PD (B). The matrices show the group averaged posterior correlations among intrinsic connections represented by the DCM.A matrix “A,” the two bilinear effects from DCM.B “B” and the direct driving inputs from DCM.C “C.” At a glance, one can see the prevalence of non-zero correlations between connectivity parameters, and the similarity of these posterior covariances in the two groups. (C) The map of t-statistics from 2-tailed one-sample t-tests at each element of the posterior correlation matrix for healthy subjects. The absolute values of correlations in panels (A) and (B) were small (typically less than ± 0.1 and all less than ± 0.3) but these interdependencies are significantly different from zero across the group (C). The asterisk indicates t-threshold for significance (p < 0.05, Bonferroni corrected for multiple tests). In panel (D) we show that the averaged values in the posterior correlations matrices from a group of older healthy subjects are reproduced on two sessions for the preferred model (E2) (Spearmans' rho = 0.99) and that these values are mostly negative (61/78 = 78%).