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Quantifying the performance of MEG source reconstruction using resting 1
state data 2
3
Simon Little1ɸ, James Bonaiuto2, Sofie S Meyer3,4, Jose Lopez5, Sven 4
Bestmann1,3* & Gareth Barnes3* 5
6
7
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
17
ɸ Corresponding Author 18
Simon Little - [email protected] 19
* Joint last author 20
21
22
was not certified by peer review) is the author/funder.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
https://doi.org/10.1101/248252
2
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
44
45
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
https://doi.org/10.1101/248252
3
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
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
https://doi.org/10.1101/248252
4
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
93
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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https://doi.org/10.1101/248252
5
110
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
121
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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6
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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160
161
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
176
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
194
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
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
https://doi.org/10.1101/248252
9
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
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
https://doi.org/10.1101/248252
10
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
249
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
260
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11
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
270
271
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
279
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
13
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
14
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
326
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
339
340
341
342
343
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15
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
350
351
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
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
https://doi.org/10.1101/248252
16
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
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
https://doi.org/10.1101/248252
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
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