New physiological framework for dynamic causal modeling of fMRI data Martin Havlicek1, Alard Roebroeck1, Karl Friston2, Dimo Ivanov1, Anna Gardumi1 and Kamil Uludag1

1 Dept. of Cognitive Neuroscience, Faculty of Psychology and Neuroscience, Maastricht University, Netherlands; 2 The Wellcome Trust Center for Neuroimaging, UCL, WC1N 3BG, UK.

E-mail: havlicekmartin@gmail.com

Objectives

CONCLUSION

References

Dynamic causal modeling (DCM) [2] is widely used approach for assessing e�ective connectivity (EC) from fMRI data. DCM uses a forward model of biophysical processes, linking neuronal activity to the observed hemodynamic response. For a decade, DCM has been used for the analysis of fMRI data albeit with simpli�cations on the physi-ological level.

We propose and test a new physiologically motivated forward model for DCM, which extends the standard DCM (S-DCM) [2] and the two-state DCM (2S-DCM) [3]:

At the neuronal level, we model local (regional) activity as exhibiting excitatory and inhibitory (E-I) balance [3]. We introduce a new model of neurovascular coupling (NVC) to link the output of the neuronal model with blood

�ow. We treat blood volume as potentially uncoupled from blood �ow, as in the original balloon model [5]. We test the new physiologically motivated DCM model (P-DCM) on arterial spin labeled (ASL) fMRI data measur-

ing both the BOLD signal and blood �ow, and compare its performance using Bayesian model selection (BMS) [7].

ASL-fMRI data acquisition and analysis

[1] Havlicek, M. (2013), OHBM, Seattle. [2] Friston, K. (2003), NeuroImage. [3] Marreiros, A.C. (2008), Neuroimage.[4] Buxton, R. (2004), NeuroImage.

We have introduced a new physiologically realistic DCM and applied it to ASL-fMRI data that models E-I neuronal balance, proper neurovascular coupling, and the actual balloon e�ect. New P-DCM is clearly more accurate com-pared to S-DCM and 2S-DCM as indicated by various metrics, including precisely modeling of neuronal and vascu-lar origins of the hemodynamic response undershoot. Therefore, we suggest that P-DCM will play an important role in assessing e�ective connectivity from fMRI data.

ASL-fMRI data (N=6) were acquired on 3T Siemens Prisma scanner (Scannexus, Maastricht, NL) using a PICORE-Q2TIPS sequence with the following parameters: TR/TE 2200/17 ms, �ip angle=80°, voxel size=3×3×3 mm3, TI1/TI2 = 900/1600 ms, 10 oblique slices. Six subjects performed a block-design visual-motor task in 4 runs, each 840 s long. Data were realigned, smoothed (4 mm FWHM) and analyzed using modi�ed SPM12 functions. From GLM results (p<0.05; FWE), 5 ROIs (r=10 mm) were selected (V1 and M1 from left and right hemispheres and SMA) and average (detrended) ASL time-courses were used for DCM. S-DCM, 2S-DCM and P-DCM were used for �tting ASL data [1] and they were compared using Bayesian model selection (BMS).

S-DCM 2S-DCM P-DCM

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DCM generative model propertiesS-DCM

Neuronal model: Only excitatory neuronal dynamics. Does not model dynamics as observed using elecotrophysiological recordings.NVC: Based on feedforward-backward mecha-nism [6] - physiologically unlikely! Generates undershoot in blood �ow and BOLD signal - not correct!Hemodynanic model (HDM): Does not include balloon e�ect; i.e. slow recovery of blood volume to produce BOLD post-stimulus undershoot. Very rigid - does not allow to model vari-aty of responses commonly observed in fMRI.

2S-DCMNeuronal model: Models both excitatory and inhibitory neuronal populations. But produces very limited range of neuro-nal dynamics - not very useful!NVC and HDM: Same limitations as S-DCM.

Bayesian model selection

P-DCM in equations - compared to old models

P-DCMNeuronal model: Properly models E-I balance. Can model all neuronal dynamics com-monly observed using elecotrophysiological recordings (in LFPs and MUA responses). Can model post-stimulus deactivation.NVC: Based on strictly feedforward mechanism - physiologically plausible!

HDM: Includes balloon e�ect to generate BOLD post-stimuls undershoot. Post-stimulus BOLD undershoot can have both pasive (balloon e�ect) and active (neuronal deactivation) origin.Overall, it can produce very rich dynamics of neuronal, blood, and oxygen changes with minimal increase of model complexity.

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DCM connectivity properties

Examples of BOLD responses fitted by DCMs

S-DCM Can model both positive and negative re-sponses within the same network. Limited in modeling hemodynamic tran-sients (i.e. undershoots and overshoots).

2S-DCM Unable to model transformation from posi-tive to negative (neuronal) BOLD response. P-DCM Overcomes limitations of S-DCM and 2S-DCM. E-I balance is propageted through connec-tions between di�erent regions. Neuronal and vascular contribution to BOLD response transients.

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Fig 1. Comparison of responses to sustained stimulus generated by S-DCM, 2S-DCM, and P-DCM, respectively, with di�erent parameterization. From neuronal (left)to BOLD (right) response.

Carries neuronal post-stimulus deactiavtion to blood �ow response.

Fig 2.A Three region connectivity pattern. Activity in region A is driven by exogenous input and propagated to region B and C. Connection A-B is modulated and connection A-C is negative.

Fig 2.B Connection strengths are kept �xed, but di�erent values of neuronal model and hemodynamic model are considered to generate di�eret neuronal and BOLD responses.

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S-DCM Does not explain post-stimulus BOLD un-dershoot (see left V1 and right M1). Improper delay of �tted BOLD response (see right M1). Explaines negative BOLD response, but not post-stimulus overshoot (see left M1).

2S-DCM Similar limitations as S-DCM plus: Unable to �t negative BOLD response. Large errors in modeled response delay and amplitude (see right M1).

P-DCM Fixes inaccuracies of S-DCM and 2S-DCM. Completely explains BOLD post-stimulus undershoots (neuronal + vascular origin). Can model negative BOLD response as a result of decrease in neuronal activity, in-cluding post-stimulus overshoot (neuronal + vascular origin). Has proper timing of �tted responses.

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Fig 4. 3D bar-plots show between subject variability in connectity parameters estimates for P-DCM and S-DCM measured by symetrized KL-distance (left) and the same measure summed up over all six subjects (right).

Fig 3. Summary results of BMS in terms of relative log-evidence (left) and posterior probability (right) based on 6 subject data-sets.

[5] Buxton, R. (1998), Magnetic Resonance in Medicine.[6] Friston, K. (2000), NeuroImage.[7] Penny, W. (2012), NeuroImage.

Conclusion

Fig 6. Comparison of �tted BOLD responses to measured BOLD responses provided by S-DCM, 2S-DCM and P-DCM. Averaged condition-subject-speci�c responses across all 4 runs are displayed.

Using BMS, P-DCM was selected as the most likely model compared to S-DCM and 2S-DCM, scoring the highest relative model log-evidence (note that only results of main models are shown in Fig. 3). These results are consistent across all six subjects. All new model components, i.e. neuronal model, NVC and balloon e�ect were found statistically better than older versions (results not shown). Compared to S-DCM, P-DCM exhibits about 27 % less between subject variability in estimated connec-tivity parameters (see Fig. 4)

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Fig 5. Connectivity results based on S-DCM, 2S-DCM, and P-DCM obtained by Bayesian averaging over posterior estimates of six subjects (each 4 runs). The right panel shows connectivity during ipsilateral motor responses and the left panel connectivity modulated by contralateral motor responses on visual stimuli.

We can see strong di�erences in estimated connectiv-ity patterns between S-DCM, 2S-DCM and P-DCM. One might wonder why : Implausible connectivity patterns provided by S-DCM and 2S-DCM result from large �tting errors to the data (see below). Unlike S-DCM and 2S-DCM, P-DCM is consistent with physiological observations; provides good model �ts; and is statistically superior to S-DCM and 2S-DCM.

\( (. . (( ?

S-DCM 2S-DCM

P-DCM