An activity-driven growth model to simulate cortical morphology 1
1
1
Andrew T. Reid* , John Lewis , Alan C. Evans ; 1. McConnell Centre for Brain Imaging, Montreal Neurological Institute, McGill University, Montreal, QC Canada
* corresponding author:
[email protected]
Methods Dynamics (Wilson-Cowan)
Growth Model
Wavelet Coherence
Ÿ Correlations in cortical morphology (structural
morphology activity (BP)
covariance; SCov) have been used to infer connectivity, under the assumption that they are caused by mutual trophic influences.
mA shrinkage
P
E
ck~
Ÿ Both variables are assumed to have Gaussian
distributions; activity departing from mA drives morphology up or down.
pIE
local connection weights
(EC), along with the activity-dependent morphology assumed in this model, may help validate these inferences.
distribution functions (F) of A and M.
pEI
Ÿ FA is determined from the activity, while FM is
firing thresholds
fixed.
I
interregional connection strength
Ÿ Outputs were obtained across values of the free
weight parameter (c); representing EC.
Gaussian white noise
Ÿ Analyze
simple connectivity patterns, to establish basic relationships between effective and functional connectivity (FC), and SCov.
regions, at 100 time points.
Simulations cab=0.8
Ÿ Environmental variance was simulated with
Ÿ Interregional connections were assigned fixed
(blue; cab) or variable (black; cac) weights
Three regions (3): Common efferent Input signal
V2
Input signal
V3 c1,3=[0.0,1.5]
c1,2=[0.0,1.5]
Simulated activity
V1
c1,2=0.0
V2
Simulated activity c1,3=0.0
c1,2=0.5
SCov c1,2=0.8
Wavelet transformed
c1,2=0.0
c1,3=0.0
c1,2=0.8
c1,3=0.8
FC
FC Simulated morphology
Simulated morphology
c1,2=0.0
c1,3=0.0
c1,2=0.8
c1,3=0.8
c1,2
c1,3
Three regions (1): Serial connectivity Input signal
c2,3=[0.0,1.5] Simulated activity c2,3=0.0
c2,3=0.8
V2 V1
c2,3=0.5 c3,4=0.5
V4
V3
c3,5=0.5
c1,3=[0.0,1.5]
V5
Simulated activity c1,3=0.0
Wavelet transformed
c2,3=0.0
c1,3=0.0
c2,3=0.8
c1,3=0.8
Simulated morphology
c2,3=0.8
Simulated activity
c2,3=0.5 c3,4=0.5
V2
c3,4=[0.0,1.5]
c3,5=0.5 c1,2=0.5
V1
Input signals
V4 V5
SCov
c3,2=0.8
Simulated activity c3,4=0.0
Wavelet transformed
Wavelet transformed c3,4=0.0
c3,2=0.8
c3,4=0.8
FC Simulated morphology c3,2=0.0
change - how does activity relate to neuronal/gross morphology in early-life development, or late-life neurodegeneration? Ÿ Added
c3,4=0.8
c3,2=0.0
FC
the more complex 5-unit models, the relationships between EC, SCov, and FC are less clear. Regions with no EC can have stronger (V4/V5) or weaker (V1/V4) SCov and FC than those with direct EC (V1/V3, V2/V3).
Ÿ More biologically valid model of morphological
Five regions (2) V3
c3,2=0.0
Ÿ For converging input (3-unit common afferent), EC
(BOLD, EEG, MEG), in more realistic, empirical models informed by measured structural connectivity (DWI or tract tracing).
c1,3
c2,3
V2
both direct and indirect (relayed) EC; both are stronger for direct EC.
Ÿ Compare simulated and measured SCov and FC
c1,3=0.8
c3,2=[0.0,1.5]
trivial unidirectional 2-unit model.
Future Directions
c1,3=0.0
Input signals
Ÿ Both SCov and FC are proportional to EC, in a
Simulated morphology
c2,3=0.0
Three regions (2): Common afferent
Conclusions
Ÿ In
FC
Simulated morphology
complexity: bi-directional connectivity (feedback), conduction delays, specific frequency bands, neuromodulation...
Acknowledgements
c3,4=0.0
ATR is supported by a CIHR c3,2=0.8
c1,3
}
Input signal
c1,3=0.8
SCov
FC
SCov
Structural covariance (SCov)
m m34 mfc m m1 2 sfc
SCov and FC can be as strong, or less strong, for unconnected regions than for direct EC.
Five regions (1)
Wavelet transformed
c1,2=0.5
Functional connectivity (FC)
Ÿ For diverging output (3-unit common efferent),
SCov
V1
sscov
relates to SCov and FC in a competitive manner; that is, they are decreased by EC from other inputs.
time (ms)
V3
r3 ...mscov
Ÿ For the 3-unit serial model, SCov and FC reflect
c1,3=0.8
SCov Wavelet transformed
V3
r1 r2
Discussion
Two regions
V1
cac=[0.0,1.5]
C
random external pulse sequences across ntrials runs (left) to input region(s) (red arrow to region A) where scales z=[1:50] correspond to frequencies 16-800 Hz.
compared qualitatively for each simulation.
ls
ntrials
Results
c1,2=0.5
B
Ÿ Relationships between EC, FC, and SCov were
A
time (ms)
Simulated activity (blue) was wavelet transformed ( ), and the total broadband power BPk(t) (red) was obtained as:
time points, and then across subjects.
ria
Broadband Power
Ÿ FC was obtained by first averaging WCo across all
M
dependent growth/shrinkage of cortical GM morphology
pII
activity (a.u.)
Ÿ Develop a preliminary model of activity-
Ÿ SCov was computed across runs for each pair of
BP (a.u.)
effective connectivity and Wilson-Cowan dynamics
, in decibels
nt
power of
Ÿ Develop a set of simple models with defined
V2
Analysis
external input signal
Objectives
V1
Two regional signals (blue and green) and the corresponding WCo (red).
Ÿ The rate of change depends on the cumulative
sigmoid fcn:
Ÿ Modelling the underlying effective connectivity
time (ms)
ls
c~k c~k
mean firing rate of excitatory and inhibitory pools
ria
time constants
over a broad band of frequencies (20-200 Hz).
nt
connectivity, they may also be due to indirect effects (common sources or relayed activity), as well as genetic influences.
Ÿ As a measure of FC, we computed mean WCo
shrinkage
growth
time Ÿ The relationship of activity (A; blue) to morphology (M; red) is shown above.
pEE
Where:
varying measure of signal coherence at specific frequencies, between the activity of two regions.
Mean WCo
Ÿ While such correlations might arise from direct
Ÿ Wavelet coherence [WCo(t,f)] provides a time-
WCo
Motivation
activity (a.u.)
Introduction
c3,4=0.8
Postdoctoral Fellowship
