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Quantifying the performance of MEG source reconstruction using resting 1

state data 2

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Simon Little1ɸ, James Bonaiuto2, Sofie S Meyer3,4, Jose Lopez5, Sven 4

Bestmann1,3* & Gareth Barnes3* 5

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1. Sobell Department of Motor Neuroscience & Movement Disorders, UCL Institute of 8

Neurology, Queen Square, London. UK 9

2. Centre de Neuroscience Cognitive, CNRS UMR 5229-Université Claude Bernard Lyon I, 69675 10

Bron Cedex, France 11

3. Wellcome Centre for Human Neuroimaging, UCL Institute of Neurology, 12 Queen Square, 12

London, UK 13

4. Institute of Cognitive Neuroscience, University College London, London, WC1N 3AR, UK 14

5. Electronic Engineering Department, Universidad de Antioquia, UdeA, Calle 70 No. 52-21, 15

Medellín, Colombia 16

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ɸ Corresponding Author 18

Simon Little - [email protected] 19

* Joint last author 20

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was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (whichthis version posted January 15, 2018. ; https://doi.org/10.1101/248252doi: bioRxiv preprint

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Abstract 23

Resting state networks measured with magnetoencephalography (MEG) form transiently stable 24

spatio-temporal patterns in the subsecond range, and therefore fluctuate more rapidly than 25

previously appreciated. These states populate and interact across the whole brain, are simple to 26

record, and possess the same dynamic structure of task related changes. They therefore provide a 27

generic, heterogeneous, and plentiful functional substrate against which to test different MEG 28

recording and reconstruction approaches. Here we validate a non-invasive method for quantifying the 29

resolution of different inversion assumptions under different recording regimes (with and without 30

head-casts) based on resting state MEG. Spatio-temporally partitioning of data into self-similar periods 31

confirmed a rich and rapidly dynamic temporal structure with a small number of regularly reoccurring 32

states. To test the anatomical precision that could be resolved through these transient states we then 33

inverted these data onto libraries of systematically distorted, subject specific, cortical meshes and 34

compared the quality of the fit using Cross Validation and a Free Energy metric. This revealed which 35

inversion scheme was able to best support the least distorted (most accurate) anatomical models. 36

Both datasets showed an increase in model fit as anatomical models moved towards the true cortical 37

surface. In the head-cast MEG data, the Empirical Bayesian Beamformer (EBB) algorithm showed the 38

best mean anatomical discrimination (3.7 mm) compared with Minimum Norm / LORETA (6.0 mm) 39

and Multiple Sparse priors (9.4 mm). This pattern was replicated in the second (conventional dataset) 40

although with a marginally poorer prediction of the missing (cross-validated) data. Our findings 41

suggest that the abundant resting state data now commonly available could be used to refine and 42

validate MEG source reconstruction methods or recording paradigms. 43

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Introduction 46

Resting state network analyses have emerged as a powerful tool for deconstructing and mapping 47

large scale networks in the human brain. These have been shown to be linked to a strikingly wide 48

range of cognitive functions in health and neurological and psychiatric disorders (Barttfeld et al., 49

2015; Kaiser et al., 2015; Lewis et al., 2009; Li et al., 2012; Peterson et al., 2014; Philippi et al., 2015; 50

Reineberg et al., 2015; Sheline and Raichle, 2013; Tessitore et al., 2012; Venkataraman et al., 2012; 51

Wu et al., 2014; Wurina et al., 2012). Emerging evidence from magnetoencephalography (MEG) 52

suggests that resting state networks may have a significantly finer temporal scale than previously 53

recognised, with network state fluctuations occurring on the scale of 100-200 milliseconds (Baker et 54

al., 2014; Koenig et al., 2002; Wackermann et al., 1993; Woolrich et al., 2013). These states are 55

thought to be relevant because they effectively rehearse the transient dynamic patterns observed 56

during task performance (O’Neill et al., 2017). 57

MEG detects electromagnetic fields at sensors outside the head with the resultant challenge of 58

inferring the neuronal sources responsible for these measured external electromagnetic changes. 59

One solution is to restrict the multiple potential solutions to this challenge through a priori 60

assumptions relating to the model of neural activity, including the anatomical structure of the brain 61

(the cortical mesh) and temporal relationship between sources (i.e. source co-variance matrix). Both 62

these priors have uncertainty attached to them: for the anatomy, the uncertainty regarding head 63

position, due to co-registration error and within-session head movement (Bonaiuto et al., 2018; 64

Hillebrand and Barnes, 2011; Meyer et al., 2017b; Troebinger et al., 2014a, 2014b); whereas 65

assumptions about the temporal relationship between sources are continually being refined and 66

debated (Baillet, 2015; Baillet et al., 2001; Wipf and Nagarajan, 2009). 67

Here we leverage new analytic techniques to quantify the sensitivity of MEG source inversion 68

schemes by progressively deforming the anatomical models (López et al., 2017, 2012; Stevenson et 69

al., 2014). Specifically, here we quantify how distortions in the MRI-extracted cortical manifold affect 70

our ability to predict or model the underlying current distribution (through cross validation error and 71

Free Energy respectively). The rationale is that the best MEG inversion scheme will be the most 72

sensitive to subtle distortions of the anatomy (as we know that MEG data derives from grey matter 73

structure). This spatial distortion metric then provides a principled choice between different a priori 74

inversion assumptions (i.e. different algorithms) and recording techniques. 75

In addition to distinguishing between algorithms, here we also tested whether we could use the 76

same methods to distinguish between datasets collected with a head-cast (Meyer et al., 2017a; 77


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Troebinger et al., 2014a, 2014b), where the forward model is more precisely known, and those 78

collected without. 79

The paper proceeds as follows. We first parcellated our two resting state datasets into brief epochs, 80

based on the dominant spatio-temporal network during short temporal epochs, using a hidden 81

Markov model. The epochs for the four most dominant networks were then amalgamated into four 82

enriched datasets and taken forwards for inversion. These datasets were then inverted onto a library 83

of subject specific distorted meshes, for which we had control over the spatial detail available in the 84

forward model. For each of these meshes, and inversion scheme we quantified model fit using Cross 85

validation and Free Energy metrics. We found an approximately monotonic improvement in model 86

fit with decreasing amounts of distortion towards the real mesh. We then used this spatial 87

quantification to compare different inversion co-variance prior assumptions as implemented in a 88

number of different, commonly utilised schemes. For these data we found that the beamformer 89

based priors (EBB) were the most sensitive to small deviations from the true anatomy. Finally we 90

directly compared data recorded with head-casts to data recorded conventionally and found 91

marginal (but not significant) differences between the two recording techniques. 92

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Methods 94

MRI 95

Subjects underwent two MRI scans using a Siemens Tim Trio 3 T system (Erlangen, Germany). For 96

the head-cast scan, the acquisition time was 3 min 42 s, in addition to 45 s for the localizer 97

sequence. The sequence implemented was a radiofrequency (RF) and gradient spoiled T1 weighted 98

3D fast low angle shot (FLASH) sequence with image resolution 1 mm3 (1 mm slice thickness), field-of 99

view set to 256, 256, and 192 mm along the phase (A–P), read (H–F), and partition (R–L; second 3D 100

phase encoding direction) directions respectively. A single shot, high readout bandwidth (425 101

Hz/pixel) and minimum echo time (2.25ms) was used. This sequence was optimised to preserve head 102

and scalp structure (as opposed to brain structure). Repetition time was set to 7.96 ms and 103

excitation flip angle set to 12° to ensure sufficient SNR. A partial Fourier (factor 6/8) acquisition was 104

used in each phase-encoded direction to accelerate acquisition. For the anatomical scan later used 105

to construct the cortical model, multiple parameter maps (MPM) were acquired to optimise spatial 106

resolution of the brain image (to 0.8 mm). The sequence comprised three multi-echo 3D FLASH (fast 107

low angle shot) scans, one RF transmit field map and one static magnetic (B0) field map scan 108

(Weiskopf et al., 2013). 109


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Head-cast construction 111

Scalp surfaces from the head-cast MRI data were extracted using SPM12 112

(http://www.fil.ion.ucl.ac.uk/spm/) by registering MRI images to a tissue probability map which 113

classified voxels according to tissue makeup (e.g. skull, skin, grey matter etc.). The skin tissue 114

probability map was transformed into a surface using the ‘isosurface’ function in MATLAB® and then 115

into standard template library format with the outlines of three fiducial coils digitally placed at 116

conventional sites (left/right pre-auricular & nasion). Next, a positive head model was printed using 117

a Zcorp 3D printer (600 x 540 dots per inch resolution) and this model placed inside a replica dewar-118

helmet with liquid resin poured between the two, resulting in a flexible, subject specific, foam head-119

cast with fiducial indentations in MRI-defined locations (Meyer et al., 2017a). 120

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MEG recording 122

Resting state data was acquired from 12 healthy subjects using head-casts (age: 26.6 ± 1.0 yrs) and 123

12 other healthy subjects without head-casts (age: 25.2 ± 1.9 yrs). All subjects were right handed, 124

had normal or corrected-to-normal vision, and had no history of neurological or psychiatric disease. 125

Informed written consent was given by all subjects and recordings were carried out after obtaining 126

ethical approval from the University College London ethics committee (ref. number 3090/001). 127

All subjects underwent a 10 minutes resting state scan with eyes open, using a CTF 275 Omega MEG 128

system. The head was localised using the three head-cast-embedded fiducials (head-cast subjects) or 129

fiducials placed on the nasion and left/right pre-auricular points (non-head-cast subjects). Average 130

absolute range of head movement within the 10 minute resting state recording was 0.26 ± 0.06, 0.24 131

± 0.05, 1.1 ± 0.54 mm (X,Y,Z directions; ± SEM) for head-cast and 3.2 ± 0.5, 3.0 ± 0.5, 3.3 ± 0.2 (X,Y,Z 132

directions; ± SEM) for non-head-cast data. The data were sampled at a rate of 1200 Hz, imported 133

into SPM12 and filtered (4th order butterworth bandpass filter: 1-90 Hz, 4th order butterworth 134

bandstop filter 48-52 Hz) and downsampled to 250 Hz. 135

In order to parcellate the data into self-similar periods that capture the resting state network 136

transitions (100-200 ms), a Hidden Markov Model (HMM) was used that could identify the rapid 137

formation and dissolution of recurring resting state networks. With this, a ‘statepath’ was estimated 138

for each 10 minute resting state block, which tracks the fine spatiotemporal dynamics and allocates 139

each point in time to one of eight dominant network states (Baker et al., 2014). For this statepath 140

determination, a copy of each subject data was dimensionally reduced using principle component 141


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analysis (PCA) to derive 40 components of unit variance and mean (Woolrich et al., 2013). With 142

these data, an 8 state Hidden Markov model (HMM; www.fmrib.ox.ac.uk/∼woolrich/HMMtoolbox) 143

was then applied to derive the most probable state at all points in time (the statepath) (Fig. 1A) 144

(Baker et al., 2014). The continuous 600s of data were then epoched into 200ms blocks/epochs (the 145

average scale of individual state transitions (Baker et al., 2014) and each 200ms data epoch allocated 146

to a new dataset according to the state that was most dominant during that time period. This 147

resulted in 8 new datasets each with a collection of epochs that corresponded to a distinct network 148

state as identified by the HMM. The four most dominant states for each individual subject (as 149

measured by most time spent in that state) was taken forward for further analysis and spatial 150

estimates averaged across those four inversions for each subject. As the HMM was performed on 151

individual, rather than group concatenated data, state numbers did not directly correspond across 152

subjects. This however permits superior partitioning within subjects since it allows the model to 153

optimally fit states to the individual subjects, rather than fitting individual data to group states that 154

are common across all subjects. This resulted in 815 ± 56.9 data segments per partitioned dataset - 155

equivalent to 163s of continuous data. Since the HMM selected periods of self-similarity within the 156

resting state, partial correlation maps were examined for all subjects to check that segregation into 157

separate networks had occurred and this segregation did not relate to eye blinks, muscle artefacts or 158

cardiac interference (Figure 1B). 159


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Figure 1. MEG data and Hidden Markov Model network allocation. A. Top panels show a selection of MEG 162 sensor time series for head-cast subject 1 (representative and chosen at random). Middle panel demonstrates 163 the statepath as determined by the HMM, showing rapid transitions between different states. Timecourses 164 recorded from a random subset of sensors is shown. Bottom panel shows a short (2s) period of data, expanded 165 with the corresponding section of the statepath (black line). Overlying the statepath trace (black) is the modal 166 statepath for each 200ms period (dash red line) and this modal statepath trace was used to sort each 200ms 167 data epoch into to 1 of 8 states according to which state was most frequent during that period. These epochs 168 of data for each of these states were aggregated together to form 8 new datasets. B. The statepath traces for 169 the three most dominant states here (1, 7, 5) are shown correlated against the time series amplitudes in all 170 sensors to derive a map of activity (red, greater positive correlation, blue, less positive correlation) associated 171 with each particular state. Data are shown in sensor space in order to check that differential network 172 parcellation had indeed occurred according to the statepath detection method and was not artefactual (e.g. 173


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that the topography resembles that expected for an eye blink). In the example shown here – state 5 is the 174 most common state – corresponding to the posterior alpha rhythm. 175

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Subject specific cortical mesh libraries 177

To extract the cortical pial mesh surface, Freesurfer software was used, optimised for MPM scans 178

(anisotropic Freesurfer filter and a hard white matter threshold with no normalisation) (Lutti et al., 179

2014). Then, for each individual subject, the pial cortical mesh was taken and deformed using a 3D 180

weighted Fourier analysis that effectively decomposes the original 3D mesh structure into spatial 181

harmonic components (Chung et al., 2007). These are then sequentially combined to form a set of 182

meshes of progressively increasing spatial detail (Figure 2B) (Stevenson et al., 2014). These meshes 183

are called the Weighted Fourier Series (WFS) and result in a library of meshes for each subjects with 184

different levels of spatial detail, from a completely smooth pair of ovoid surfaces (mesh 1) up to a 185

mesh similar to that of the real brain (mesh 50) (see Figure 2B). The WFS can be expressed as 186

follows: 187

188

where σ is the bandwidth of the smoothing kernel (set at 0.0001), L is the harmonic order of the 189

surface, Slm is the spherical harmonic of degree l and order m, and the Fourier coefficients are given 190

by flm=〈f, Slm〉, where f is determined by solving a system of linear equations (Chung et al., 2007). All 191

meshes, including the true mesh, were downsampled by a factor of 10 in Freesurfer to ~ 33,000 192

vertices to aid computational efficiency. 193

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Source reconstruction 195

HMM parcellated datasets were projected from 272 spatial (3 channels damaged) and 16 temporal 196

modes and inverted sequentially using our library of individualised and distorted cortical meshes 197

(WFS) for each subject. Notably, using a cortical mesh further constrains solutions to those which are 198

located at the cortical surface. We firstly implemented an Empirical Bayesian Beamformer (EBB) 199

inversion. Beamforming makes a direct estimate of source covariance based on the assumption that 200

there are no zero-lag correlated sources, a form of spatial filtering that ensures that no two parts of 201

the brain has exactly the same neuroelectric activity at any given time. This was compared with 202

alternative inversion schemes that are based on different prior assumptions regarding source co-203


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variance. Here we used standard (and non-optimized) versions of Minimum norm (MMN) (Uutela et 204

al., 1999), LORETA (LOR) (Pascual-Marqui et al., 2002), Empirical Bayes Beamformer (EBB) and 205

Multiple Sparse priors (MSP) (Friston et al., 2008) inversion schemes as implemented in SPM12. Each 206

of these methods can be described by a different selection of source covariance matrices 207

(Belardinelli et al., 2012; Friston et al., 2008; López et al., 2014). 208

In order to quantify the quality of the fit we used two complementary metrics: cross validation and 209

Free energy. For cross validation error, a subset of sensors (10%; 27 sensors) are turned off. An 210

estimate of current flow is made based on the remaining 90% of the MEG channels (and a specific 211

inversion scheme). This current flow is then projected back outside of the head to the 10% of 212

disabled sensors and the error between the predicted and measured data calculated. This was 213

repeated 10 times for each inversion with different randomly selected subsets of removed sensors 214

for each iteration. The cross validation error was then converted to a percentage of source data 215

explained and averaged across all iterations and across the 4 network datasets inverted per subject. 216

The Free Energy metric approximates the log model evidence for the final generative model based 217

on all of the sensor data by rewarding the accuracy of fit whilst also penalizing model complexity 218

(Friston et al., 2007). 219

Both cross validation error explained and Free Energy provide metrics which can be used to directly 220

compare different models of the same data with increasing values of each suggesting an improved 221

model fit (Henson et al., 2009). Whilst the Free Energy provides a useful relative model fit metric for 222

any given dataset the absolute value is data dependent and therefore cannot be used to compare 223

between datasets. In contrast, the cross validation error explained gives a meaningful quantification 224

of the total amount of data explained and can be used to compare across the different groups (head-225

cast versus non head-cast). 226

Here we performed these inversions using our subject specific libraries of anatomically degraded 227

meshes from the WFS with different levels of distortion and compared them to an inversion 228

performed using the real mesh for each subject. In order to facilitate comparisons of how the 229

anatomical distortion affected the inversions for different subjects with different baseline measures 230

of model fit to their real brain meshes, we normalised the cross validation percentage error 231

explained and free energy metrics by subtracting the values for the real mesh to derive a relative 232

measure (ΔCV & ΔF). As such, a worse fit gives a negative value of ΔCV / ΔF and we would predict 233

that as the anatomical complexity of the mesh increases (mesh is less distorted) and approaches that 234

of the real mesh – the quality of the model should improve and the ΔCV / ΔF should approach zero. 235

Across our group of subjects we determined the level of distortion at which this first becomes 236


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statistically distinguishable from the real mesh using a t-test of ΔCV values for each harmonic 237

compared to zero and similarly for ΔF using Bayesian model comparison. This point, labelled the 238

highest distinguishable harmonic (HDH), identifies the minimum amount of mesh distortion that can 239

be reliably distinguished from the real mesh by inversion and can be converted into a conventional 240

spatial metric (mms) by comparing vertex distances. The three dimensional (Euclidean) distance (in 241

mm) between every vertex from the HDH to the corresponding vertex on the true mesh was 242

therefore calculated and the upper, 95th percentile, distance averaged over all vertices in the mesh. 243

This method is more conservative than that previously employed (Stevenson et al., 2014), as this 244

directly matches corresponding vertices and therefore reduces the underestimation that could result 245

if, following harmonic distortion, a vertex now lies closer to a non-corresponding other vertex. This 246

distance therefore represents an upper bound on the spatial discriminability of both head-cast and 247

non-head-cast resting state data. 248

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Control analyses 250

In order to verify our findings, we performed a number of control analyses with distorted 251

data/sensors positions for the head-cast / EBB inversion. Firstly, we used our same data but 252

destroyed its correspondence with the MEG sensor locations by randomly shuffling the MEG 253

channels labels and repeated the analysis above 10 times for each subject and averaged over the 254

ΔCV and ΔF for these different shuffled dataset inversions. Following this, we used the correct 255

sensor labels but next degraded our data by introducing different amounts of scaled white noise to 256

change the signal-to-noise ratio of the sensor level data (5 dB TO - 20 dB) (Troebinger et al., 2014a). 257

In both cases (sensor shuffling and noise addition) one would expect the ability to discriminate the 258

true generative model from distorted ones to decrease. 259

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RESULTS 261

Anatomical cortical model 262

In order to determine the sensitivity of the inversion to the level of detail in the underlying 263

anatomical mesh model we calculated the ΔCV and ΔF for each subject in the head-cast dataset 264

across their subject specific library of distorted meshes (Fig. 2). This showed increasing cross 265

validation sensor data explained (ΔCV; reduced error) and increasing Free energy (ΔF) for all 266

subjects. Statistical group level testing revealed that meshes lower (more deformed) than the 35 267

harmonic could be distinguished from the real mesh by ΔCV (HDH 35; t11= -2.49, p=0.03) and lower 268

than 31 by ΔF (BMC, exceedance p = 0.046; Fig. 2) 269

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Figure 2. Relative Cross Validation and Free Energy results for a library of different meshes for head-cast 272 resting data using an EBB inversion. A. Increasing cross validation data explained (ΔCV) and relative Free 273 Energy ΔF with improving spatial resolution of harmonic meshes (from left right). Top plots show individual 274 subject ΔCV (left) and ΔF (right) values with superimposed mean value (dashed black line). Lower panels show 275 the group level statistical significance using t test (ΔCV) and Bayesian model comparison (ΔF). B. Example 276


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selection of meshes from 1 subject showing different levels of distortion, from smooth ovoid surfaces (WFS 277 mesh 1) up to real mesh (shown inset). 278

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Inversion algorithms / source covariance priors 280

The effect of source co-variance prior assumptions was then assessed by repeating the process for 281

three other commonly implemented inversion algorithms (MNM, LOR, MSP) on our head-cast 282

dataset. These showed lower anatomical mesh discriminability for all alternative algorithms with an 283

HDH for MNM of 25 (t11=-1.80 -, p=0.036 ), an HDH of 25 (t11=-1.79; p=0.039) for LOR and an HDH of 284

17 for MSP (t11=-2.55; p=0.027) (Fig 3A). 285

The mean distance between vertices on these meshes and the real mesh was then calculated for 286

each subject. These were then averaged to give a spatial measure of anatomical discriminability (Fig 287

3A), under the different prior covariance assumptions as implemented in the different inversion 288

algorithms. This ranged from 3.7 mm for EBB to 6.0 mm for MNN/LOR and 9.4 mm for MSP (Fig 3B). 289

Directly comparing the absolute cross validation error explained (CVp) across inversion conditions 290

(using the real mesh) demonstrated a significant difference between EBB and the other 3 algorithms 291

(EBB/MMN; paired t-test – t11=7.6 ,p

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MMN and LOR have very similar values and therefore lines are closely overlapping). B. Mean 300 distance of vertices from highest significant mesh identified in the left hand panel and the real mesh 301 for each subject. Error bars show SEM of this distance across subjects using their individualised 302 meshes and group level HDH. 303

Notably – a 2 factor within subject ANOVA of cross validation with factors – inversion type (EBB, 304

MMN, MSP) and mesh smootheness (harmonic 1 & harmonic 50) showed a strongly significant 305

interaction between inversion type and mesh harmonic level (F2=29.9, p

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Figure 4. Comparison of head-cast versus conventional MEG Cross validation results. A. 321 Comparison of ΔCV for different recording methodologies with head-cast data (blue) showing higher 322 discrimination (35) than non-head-cast data (red; 29). B. Absolute cross validation error explained is 323 also higher in the head-cast versus the conventional MEG. Note that this holds for all inversion types 324 and for all levels of mesh distortion, but was not significantly different on statistical testing. 325

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Control analyses 327

Finally, we checked our analyses by repeating our inversions (Head-cast dataset, EBB algorithm) but 328

only after degrading the consistent relationship between our sensor positions and sources by 329

shuffling the sensor labels. As expected, this resulted in a breakdown of the previously shown 330

relationship between Cross validation and Free Energy with mesh distortion. Notably we found that 331

lower harmonics (smoother) meshes now showed higher ΔCV (Fig 5A) (smoother surfaces superior 332

when sensors shuffled). Thereafter we degraded our data (without sensor shuffling) by the addition 333

of varying levels of Gaussian white noise (5 -50 dB) and again repeated our analysis (Figure 4B). 334

This demonstrated that with increasing levels of noise (decreasing SNR), the curve describing the 335

relationship between Cross validation and harmonic mesh function flattened and the crossing point 336

(HDH) reduced, indicating that the inversion was no longer able to statistically distinguish the more 337

complex meshes from the real mesh, as would be expected if the data are primarily noise. 338

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Figure 5. Effects of shuffling sensors (A) and replacing data with varying levels of Gaussian White noise (B). 344 A. The relationship between the Cross validation % error explained (ΔCV) of inversion and increasing harmonic 345 mesh after random shuffling of sensor labels. Note the decreasing Cross validation fit with increasing mesh 346 harmonic (increasing mesh detail) with the dashed line showing the average across all subjects. B. The 347 relationship between (mean of all 12 subjects) ΔCV of inversion and increasing harmonic mesh after addition 348 of Gaussian white noise across a range of noise additions (from SNR 5 to SNR -20). 349

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Discussion 352

Resting state data is rapidly dynamic, emulates task induced network changes and is simple to 353

acquire (Baker et al., 2014; O’Neill et al., 2017). Here we show that it can provide a ready substrate 354

for principled testing of MEG recording methods and inversion assumptions including anatomical 355

forward modelling and functional (co-variance) priors. 356

We showed that in moving the cortical surface from heavily distorted to the true anatomy, all of the 357

models, based on commonly used imaging assumptions, showed a significant and monotonic 358

improvement. This improvement saturated for some imaging assumptions before others, with the 359

beamformer based algorithms (closely followed by Minimum norm) continuing to improve up until 360

the cortical surface deviated by on average 4mm from the ground-truth. We also found that a 361

marginal, although non-significant, improvement in our models when using MEG data based on 362

head-cast recordings compared to conventional recordings. Critically rather than compare methods 363

through simulation or through a limited task set (with ground truth from another modality) we have 364

presented a method to optimize MEG recording methods, forward and inverse models without 365

introducing selection bias and based on a plentiful supply of non-invasive human data. 366

We compared between algorithms in two ways: by the model fit (or amount of data predicted), and 367

by comparing the sensitivity of each algorithm to the true anatomy. These two tests need not 368

necessarily have been in accord. For example- had we used a bunny-shaped blancmange mould 369

instead of a cortical surface we would still have been able to rank the algorithms based the amount 370

of data predicted; but we would not have expected any monotonic improvement as features were 371

added to the bunny. A related control analysis (figure 5) is that when used the same data but with 372

shuffled lead-fields (destroying the link between the sensors and the anatomy) the amount of data 373

we are able to predict actually decreases as the cortical model approaches the truth. It is therefore 374

striking that the models that benefitted most from the true cortical manifold were also those that 375

predicted the most data. This not only adds anatomical validity (confirming that the data being 376

described is indeed generated by pyramidal cell populations normal to the cortical surface) but also 377

allows us to quantify algorithm performance in millimetres (Stevenson et al., 2014). 378


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Across anatomy (Fig. 2) and inversion assumptions (Fig. 3), the parametric (Free energy from 379

empirical Bayes) and non-parametric (cross-validation) metrics of model fit were in accord. This 380

helps build confidence in the parametric free-energy metric which is considerably faster, makes use 381

of all the available data, and has a direct probabilistic interpretation. The Bayesian formalism is 382

however predicated on comparing how different models explain the same data; the use of cross-383

validation, which provides an absolute quantitative measure of data predicted, also allowed us to 384

compare between different datasets (head-cast and non-head-cast). 385

Resting state MEG analysis has been impeded by the spectral/dimensional complexity of the 386

datasets (Vidaurre et al., 2016) as well as reduced spatial resolution that limits the ability to 387

discriminate different sources (Colclough et al., 2016; Liuzzi et al., 2016). Recent improvements in 388

methods have permitted enhanced temporal discrimination (Baker et al., 2014; Woolrich et al., 389

2013). These and other development have resulted in the emergence of a number of potential 390

clinical applications for resting state MEG, although these have yet to transition to clinical utilisation, 391

in part due to reduced spatial resolution (Bosboom et al., 2006; Bosma et al., 2009; Hinkley et al., 392

2011). It is notable that most of the empirical MEG literature on the resting state is dominated by 393

what we found here to be the most likely functional priors (beamformer and Minimum norm 394

assumptions). 395

We confirm here earlier reports that within-session head movements are greatly reduced for head-396

cast versus non-head-cast MEG (Bonaiuto et al., 2017b; Meyer et al., 2017a, 2017b) however we 397

were surprised that the head-cast did not offer a greater modelling improvement over the non-398

head-cast data. Empirically this could be due to recording problems- for example in some subjects it 399

is possible that their heads were not within the head-casts in their expected position. i.e. although 400

the head-casts remained still the subject’s anatomy was not where we expected it to be. Another 401

limitation could be that the models we are using do not capture the physics or physiology of the 402

generators of the measured magnetic fields; and that the resolution is constrained by the models 403

and not the recording. This could include for example, unmodelled noise sources such as the 404

heartbeat, eye-blinks and other sources of noise. Although the HMM states we used were visually 405

inspected to avoid common artefacts such as eye-blinks, it is possible that some of the modelling 406

deficiencies come from failure to explain data that does not arise from the cortex (eg heart-beats, 407

passing cars etc). Finally, the head-cast and non-head-cast cohorts did not overlap and a more 408

sensitive analysis would have been to perform a within subject comparison. 409

We found the Multiple Sparse Priors algorithm had the least dependence on the true anatomy and 410

also explained the least data. We should note however that the MSP-based analyses implemented 411


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17

here were generic and constructed from a limited set of 512 patches (or priors) placed at evenly 412

spaced vertices. The MSP algorithm, although perhaps the most elegant and comprehensive method 413

we tested, is also computationally disadvantaged by the need to search over a large space of 414

possible patch/prior combinations and the inherent pitfalls of local extrema in this optimization. A 415

more robust way to implement this algorithm would have been to select the best model from many 416

random patch choices (Troebinger et al., 2014b). 417

This study was analysed using broadband (1-90 Hz) resting state data. Therefore, whether a similar 418

level of spatial discriminability at the mm scale can be demonstrated when more selective data is 419

used (e.g. frequency filtered or spatially restricted) remains to be shown. For example, future work 420

might test different frequency bands (eg 30Hz) against different anatomy for example 421

infra/supra granular cortical surfaces (Arnal and Giraud, 2012; Bastos et al., 2012; Bonaiuto et al., 422

2017a, 2017b). 423

Conclusion 424

This study uses resting state data to compare different forward models, inversion assumptions and 425

recording methods to provide a principled (non – biased) method for optimising and quantifying 426

source localisation. All source localisation techniques were able to benefit from increasing 427

anatomical precision in the underlying model but this was most pronounced for EBB in head-cast 428

recorded data. Using this method, we demonstrate a notably high sensitivity (

18

REFERENCES 432

Arnal, L.H., Giraud, A.-L., 2012. Cortical oscillations and sensory predictions. Trends Cogn. Sci. 16, 433

390–8. doi:10.1016/j.tics.2012.05.003 434

Baillet, S., 2015. Forward and Inverse Problems of MEG/EEG, in: Encyclopedia of Computational 435

Neuroscience. Springer, New York. 436

Baillet, S., Mosher, J.C., Leahy, R.M., 2001. Electromagnetic brain mapping. IEEE Signal Process. Mag. 437

18, 14–30. doi:10.1109/79.962275 438

Baker, A.P., Brookes, M.J., Rezek, I. a., Smith, S.M., Behrens, T., Smith, P.J.P., Woolrich, M., 2014. 439

Fast transient networks in spontaneous human brain activity. Elife 2014, 1–18. 440

doi:10.7554/eLife.01867 441

Barttfeld, P., Uhrig, L., Sitt, J.D., Sigman, M., Jarraya, B., Dehaene, S., 2015. Signature of 442

consciousness in the dynamics of resting-state brain activity. Proc. Natl. Acad. Sci. U. S. A. 112, 443

887–92. doi:10.1073/pnas.1418031112 444

Bastos, A.M., Usrey, W.M., Adams, R.A., Mangun, G.R., Fries, P., Friston, K.J., 2012. Canonical 445

Microcircuits for Predictive Coding. Neuron. 446

Belardinelli, P., Ortiz, E., Barnes, G.R., Noppeney, U., Preissl, H., 2012. Source reconstruction 447

accuracy of MEG and EEG Bayesian inversion approaches. PLoS One 7, e51985. 448

doi:10.1371/journal.pone.0051985 449

Bonaiuto, J.J., Meyer, S.S., Little, S., Rossiter, H., Callaghan, M.F., Dick, F., 2017a. Laminar-specific 450

cortical dynamics in human visual and sensorimotor cortices 1–25. doi:10.1101/226274 451

Bonaiuto, J.J., Rossiter, H.E., Meyer, S.S., Adams, N., Little, S., Callaghan, M.F., Dick, F., Bestmann, S., 452

Barnes, G.R., 2018. Non-invasive laminar inference with MEG: Comparison of methods and 453

source inversion algorithms. Neuroimage 167. doi:10.1016/j.neuroimage.2017.11.068 454

Bonaiuto, J.J., Rossiter, H.E., Meyer, S.S., Adams, N., Little, S., Callaghan, M.F., Dick, F., Bestmann, S., 455

Barnes, G.R., 2017b. Non-invasive laminar inference with MEG: Comparison of methods and 456

source inversion algorithms. bioRxiv. 457

Bosboom, J.L.W., Stoffers, D., Stam, C.J., van Dijk, B.W., Verbunt, J., Berendse, H.W., Wolters, E.C., 458

2006. Resting state oscillatory brain dynamics in Parkinson’s disease: an MEG study. Clin. 459

Neurophysiol. 117, 2521–31. doi:10.1016/j.clinph.2006.06.720 460

Bosma, I., Reijneveld, J.C., Klein, M., Douw, L., van Dijk, B.W., Heimans, J.J., Stam, C.J., 2009. 461


https://doi.org/10.1101/248252

19

Disturbed functional brain networks and neurocognitive function in low-grade glioma patients: 462

a graph theoretical analysis of resting-state MEG. Nonlinear Biomed. Phys. 3, 9. 463

doi:10.1186/1753-4631-3-9 464

Chung, M.K., Dalton, K.M., Shen, L., Evans, A.C., Davidson, R.J., 2007. Weighted Fourier series 465

representation and its application to quantifying the amount of gray matter. IEEE Trans. Med. 466

Imaging 26, 566–581. doi:10.1109/TMI.2007.892519 467

Colclough, G.L.L., Woolrich, M., Tewarie, P.K.K., Brookes, M.J.J., Quinn, A.J.J., Smith, S.M.M., 2016. 468

How reliable are MEG resting-state connectivity metrics? Neuroimage 138, 284–293. 469

doi:10.1016/j.neuroimage.2016.05.070 470

Friston, K., Harrison, L., Daunizeau, J., Kiebel, S., Phillips, C., Trujillo-Barreto, N., Henson, R., Flandin, 471

G., Mattout, J., 2008. Multiple sparse priors for the M/EEG inverse problem. Neuroimage 39, 472

1104–1120. doi:10.1016/j.neuroimage.2007.09.048 473

Friston, K., Mattout, J., Trujillo-Barreto, N., Ashburner, J., Penny, W., 2007. Variational free energy 474

and the Laplace approximation. Neuroimage 34, 220–234. 475

doi:10.1016/j.neuroimage.2006.08.035 476

Henson, R.N., Mattout, J., Phillips, C., Friston, K.J., 2009. Selecting forward models for MEG source-477

reconstruction using model-evidence. Neuroimage 46, 168–176. 478

doi:10.1016/j.neuroimage.2009.01.062 479

Hillebrand, A., Barnes, G.R., 2011. Practical constraints on estimation of source extent with MEG 480

beamformers. Neuroimage 54, 2732–2740. doi:10.1016/j.neuroimage.2010.10.036 481

Hinkley, L.B.N., Vinogradov, S., Guggisberg, A.G., Fisher, M., Findlay, A.M., Nagarajan, S.S., 2011. 482

Clinical symptoms and alpha band resting-state functional connectivity imaging in patients with 483

schizophrenia: Implications for novel approaches to treatment. Biol. Psychiatry 70, 1134–1142. 484

doi:10.1016/j.biopsych.2011.06.029 485

Kaiser, R.H., Andrews-Hanna, J.R., Wager, T.D., Pizzagalli, D.A., RJ, D., J, J., 2015. Large-Scale Network 486

Dysfunction in Major Depressive Disorder. JAMA Psychiatry 72, 603. 487

doi:10.1001/jamapsychiatry.2015.0071 488

Koenig, T., Prichep, L., Lehmann, D., Sosa, P.V., Braeker, E., Kleinlogel, H., Isenhart, R., John, E.R., 489

2002. Millisecond by Millisecond, Year by Year: Normative EEG Microstates and Developmental 490

Stages. Neuroimage 16, 41–48. doi:10.1006/nimg.2002.1070 491

Lewis, C.M., Baldassarre, A., Committeri, G., Romani, G.L., Corbetta, M., 2009. Learning sculpts the 492


https://doi.org/10.1101/248252

20

spontaneous activity of the resting human brain. Proc. Natl. Acad. Sci. U. S. A. 106, 17558–63. 493

doi:10.1073/pnas.0902455106 494

Li, P., Li, S., Dong, Z., Luo, J., Han, H., Xiong, H., Guo, Z., Li, Z., 2012. Altered resting state functional 495

connectivity patterns of the anterior prefrontal cortex in obsessive-compulsive disorder. 496

Neuroreport 23, 681–686. doi:10.1097/WNR.0b013e328355a5fe 497

Liuzzi, L., Gascoyne, L.E., Tewarie, P.K., Barratt, E.L., Boto, E., Brookes, M.J., 2016. Optimising 498

experimental design for MEG resting state functional connectivity measurement. Neuroimage 499

In Press. doi:10.1016/j.neuroimage.2016.11.064 500

López, J.D., Litvak, V., Espinosa, J.J., Friston, K., Barnes, G.R., 2014. Algorithmic procedures for 501

Bayesian MEG/EEG source reconstruction in SPM. Neuroimage 84, 476–487. 502

doi:10.1016/j.neuroimage.2013.09.002 503

López, J.D., Penny, W.D., Espinosa, J.J., Barnes, G.R., 2012. A general Bayesian treatment for MEG 504

source reconstruction incorporating lead field uncertainty. Neuroimage 60, 1194–1204. 505

doi:10.1016/j.neuroimage.2012.01.077 506

López, J.D., Valencia, F., Flandin, G., Penny, W., Barnes, G.R., 2017. Reconstructing anatomy from 507

electro-physiological data. Neuroimage 163, 480–486. doi:10.1016/j.neuroimage.2017.06.049 508

Lutti, A., Dick, F., Sereno, M.I., Weiskopf, N., 2014. Using high-resolution quantitative mapping of R1 509

as an index of cortical myelination. Neuroimage 93, 176–188. 510

doi:10.1016/j.neuroimage.2013.06.005 511

Meyer, S.S., Bonaiuto, J.J., Lim, M., Rossiter, H., Waters, S., Bradbury, D., Bestmann, S., Brookes, M., 512

Callaghan, M.F., Weiskopf, N., Barnes, G.R., 2017a. Flexible head-casts for high spatial precision 513

MEG. J. Neurosci. Methods 276, 38–45. doi:10.1016/j.jneumeth.2016.11.009 514

Meyer, S.S., Rossiter, H., Brookes, M., Woolrich, M., Bestmann, S., Barnes, G.R., 2017b. Using 515

generative models to make probabilistic statements about hippocampal engagement in MEG. 516

Neuroimage 149, 468–482. doi:10.1016/j.neuroimage.2017.01.029 517

O’Neill, G.C., Tewarie, P.K., Colclough, G.L., Gascoyne, L.E., Hunt, B.A.E., Morris, P.G., Woolrich, 518

M.W., Brookes, M.J., 2017. Measurement of dynamic task related functional networks using 519

MEG. Neuroimage 146, 667–678. doi:10.1016/j.neuroimage.2016.08.061 520

Pascual-Marqui, R.D., Esslen, M., Kochi, K., Lehmann, D., 2002. Functional imaging with low-521

resolution brain electromagnetic tomography (LORETA): a review. Methods Find. Exp. Clin. 522

Pharmacol. 24 Suppl C, 91–5. 523


https://doi.org/10.1101/248252

21

Peterson, A., Thome, J., Frewen, P., Lanius, R.A., 2014. Resting-State Neuroimaging Studies: A New 524

Way of Identifying Differences and Similarities among the Anxiety Disorders? Can. J. Psychiatry 525

59, 294–300. doi:10.1177/070674371405900602 526

Philippi, C.L., Pujara, M.S., Motzkin, J.C., Newman, J., Kiehl, K.A., Koenigs, M., 2015. Altered Resting-527

State Functional Connectivity in Cortical Networks in Psychopathy. J. Neurosci. 35. 528

Reineberg, A.E., Andrews-Hanna, J.R., Depue, B.E., Friedman, N.P., Banich, M.T., 2015. Resting-state 529

networks predict individual differences in common and specific aspects of executive function. 530


Sheline, Y.I., Raichle, M.E., 2013. Resting State Functional Connectivity in Preclinical Alzheimer’s 532

Disease. Biol. Psychiatry 74, 340–347. doi:10.1016/j.biopsych.2012.11.028 533

Stevenson, C., Brookes, M., López, J.D., Troebinger, L., Mattout, J., Penny, W., Morris, P., Hillebrand, 534

A., Henson, R., Barnes, G.R., 2014. Does function fit structure? A ground truth for non-invasive 535

neuroimaging. Neuroimage 94, 89–95. doi:10.1016/j.neuroimage.2014.02.033 536

Tessitore, A., Amboni, M., Esposito, F., Russo, A., Picillo, M., Marcuccio, L., Pellecchia, M.T., Vitale, C., 537

Cirillo, M., Tedeschi, G., Barone, P., 2012. Resting-state brain connectivity in patients with 538

Parkinson’s disease and freezing of gait. Parkinsonism Relat. Disord. 18, 781–787. 539

doi:10.1016/j.parkreldis.2012.03.018 540

Troebinger, L., Lopez, J., Lutti, A., Bestmann, S., Barnes, G.R., 2014a. Discrimination of cortical 541

laminae using MEG. Neuroimage (in press). 542

Troebinger, L., López, J.D., Lutti, A., Bradbury, D., Bestmann, S., Barnes, G.R., 2014b. High precision 543

anatomy for MEG. Neuroimage 86, 583–91. doi:10.1016/j.neuroimage.2013.07.065 544

Uutela, K., Hämäläinen, M., Somersalo, E., 1999. Visualization of Magnetoencephalographic Data 545

Using Minimum Current Estimates. Neuroimage 10, 173–180. doi:10.1006/nimg.1999.0454 546

Venkataraman, A., Whitford, T.J., Westin, C.-F., Golland, P., Kubicki, M., 2012. Whole brain resting 547

state functional connectivity abnormalities in schizophrenia. Schizophr. Res. 139, 7–12. 548

doi:10.1016/j.schres.2012.04.021 549

Vidaurre, D., Quinn, A.J., Baker, A.P., Dupret, D., Tejero-Cantero, A., Woolrich, M., 2016. Spectrally 550

resolved fast transient brain states in electrophysiological data. Neuroimage 126, 81–95. 551

doi:10.1016/j.neuroimage.2015.11.047 552

Wackermann, J., Lehmann, D., Michel, C.M., Strik, W.K., 1993. Adaptive segmentation of 553


https://doi.org/10.1101/248252

22

spontaneous EEG map series into spatially defined microstates. Int. J. Psychophysiol. 14, 269–554

283. doi:10.1016/0167-8760(93)90041-M 555

Weiskopf, N., Suckling, J., Williams, G., Correia M., M.M., Inkster, B., Tait, R., Ooi, C., Bullmore T., 556

E.T., Lutti, A., 2013. Quantitative multi-parameter mapping of R1, PD*, MT, and R2* at 3T: A 557

multi-center validation. Front. Neurosci. 7, 1–11. doi:10.3389/fnins.2013.00095 558

Wipf, D., Nagarajan, S., 2009. A unified Bayesian framework for MEG/EEG source imaging. 559


Woolrich, M., Baker, A.P., Luckhoo, H., Mohseni, H., Barnes, G.R., Brookes, M., Rezek, L., 2013. 561

Dynamic state allocation for MEG source reconstruction. Neuroimage 77, 77–92. 562

doi:10.1016/j.neuroimage.2013.03.036 563

Wu, J., Srinivasan, R., Kaur, A., Cramer, S.C., 2014. Resting-state cortical connectivity predicts motor 564

skill acquisition. Neuroimage 91, 84–90. doi:10.1016/j.neuroimage.2014.01.026 565

Wurina, Zang, Y.-F., Zhao, S.-G., 2012. Resting-state fMRI studies in epilepsy. Neurosci. Bull. 28, 449–566

455. doi:10.1007/s12264-012-1255-1 567

568

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