Detecting Drug Effects in the Brain
Heather Turner, Phil Brain and Foteini Strimenopoulou
Nonclinical Statistics
Pfizer, UK
18 August 2011

Background
Aim: identify and characterise effect of drug on the brain
• Drug effect over time
PK/PD model
• EEG experiments
electrical activity in the brain
• Generalised Semi-linear Canonical Correlation Analysis
(GSLCCA)

EEG
• Electrodes placed on scalp
• Monitor difference in voltage between baseline electrode
and others
• Produces virtually continuous signal

EEG Data
• EEG signal converted via FFT to power spectra
”amount” of each frequency for each time slice
multivariate response over time
Examples of frequency periodograms
0.00030
q
0−5 minutes
120−125 minutes
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q q
FFT Power (µV2)
−→
− q
q q
0.00010
qq
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qqq q
0.00000
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0 5 10 15 20 25 30 35
Frequency (Hz)

PK/PD
• Assumptions
drug level in brain follows pharmacokinetics model (PK)
brain response proportional to dose level (PD)
• Expected response over time follows PK model, e.g.
Double Exponential
β(exp(−k1 t) − exp(−k2 t))
Critical Exponential
βtexp(−k1 t)

PK Models
0.4
Double Exponential
0.3
0.2 Critical Exponential
Response
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0.0
−0.2
0 10000 20000 30000 40000
Time

GSLCCA (in pictures)
Spectrum
"Observed" Value
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Power (µV2)
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0.2
0 5 15 25 35
Frequency (Hz)
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Response
× −→
0.0
Signature
500 1000
Coefficient
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−500
0 10000 20000 30000 40000
0 5 15 25 35
Time
Frequency (Hz)

GSLCCA (in pictures)
Spectrum
Fitted Values
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Power (µV2)
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q
q
q q
0.00000
q
0.2
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0 5 15 25 35 q
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Frequency (Hz)
0.1
Response
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× −→ q
q
0.0
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q
Signature q q q
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q
500 1000
qq q
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q q q q qq
q q
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Coefficient
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Time
Frequency (Hz)

GSLCCA Method
• Canonical Correlation Analysis (CCA)
For matrices Y and X, finds loadings a and b to
maximise
cor(Y a, Xb)
• Semi-linear
Y is the matrix of power spectra
X = X(t, θ) defined by PK model
• Generalised
linear coefficients b or nonlinear parameters θ may
depend on treatment factor

gslcca Package
• gslcca function
specify PK model by name/formula
specify which parameters vary by treatment
control over data smoothing
partial CCA option
• plot, print, summary

Clonidine Experiment
• 4 treatments
Control
Low dose
Medium dose
High dose
• 8 rats in 4-period cross-over design
• EEG data recorded for 12 hours post-dose

GSLCCA Analysis
Call:
gslcca(Y = spectra, formula = "Critical Exponential", time = Time,
subject = Rat, treatment = Treatment, separate = TRUE, ref = 1,
data = design, subject.smooth = 4)
GSLCCA based on 8 subjects
Data smoothed at subject level using 4 roots
Nonlinear parameters:
subject 35 subject 36 subject 37 subject 38
K1 Low Dose 7.5576 8.4252 7.8778 9.9125
K1 Middle Dose 7.8786 8.5137 8.0901 8.8885
K1 High Dose 8.9017 9.3213 9.0159 9.1980
subject 39 subject 40 subject 41 subject 42
K1 Low Dose 8.7217 8.0102 8.7103 8.1199
K1 Middle Dose 8.8546 8.5952 9.1854 8.3800
K1 High Dose 9.0439 9.1611 9.3047 8.9933

Fitted Model
plot(result, "fitted")

Observed + Fitted
plot(result, "scores")

Signatures
plot(result, "signatures")
Signatures Corresponding to Different Subjects
Subject 35
Subject 36
Subject 37
500
Subject 38
Subject 39
Subject 40
Subject 41
Subject 42
Coefficient
0
−500
0 5 10 15 20 25 30 35
Frequency (Hz)

Normalised Signatures
Signatures Corresponding to Different Subjects
Subject 35
Subject 36
0.6 Subject 37
Subject 38
Subject 39
0.4
Subject 40
Subject 41
Subject 42
0.2
Coefficient
0.0
−0.2
−0.4
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Frequency (Hz)

Mean Signature
Mean Signature
0.6
• contribution of power
0.4
at each frequency to
PK curve over time
Coefficient
0.2
• assumed to be specific
0.0
to the target drug is
aimed at
−0.2
0 5 10 15 20 25 30 35
Frequency (Hz)

0.6
0.4 Control/Inactive Signature
• if drug inactive, any
dose ≡ control
Coefficient
0.2
• inactive drug has same
0.0
signature as control
−0.2
0 5 10 15 20 25 30 35
Frequency

0.6 Control/Inactive Signature
clonidine
vehicle
0.4
• In this case drug clearly
different from control
Coefficient
0.2
• Drug is active - as
0.0
expected!
−0.2
0 5 10 15 20 25 30 35
Frequency

200 Comparing Active Drugs
Drug A
Drug B
• Two drugs targeting
150
same ion channel,
100
different receptors
Coefficient
50
• Run t-tests to compare
0
loadings at each
−50
frequency
−100
0 20 40 60 80
Frequency

3.0 Snapshot Analysis
delta
theta
alpha
2.5
beta
gamma • P-values adjusted using
2.0
− log10(p)
FDR
1.5
• Frequencies split into
1.0
conventional bands
0.5
0.0
0 20 40 60 80
Frequency

Summary
gslcca package is in development on R-Forge
https://r-forge.r-project.org/projects/gslcca/
Further work needed before release to CRAN, e.g.
• fitting PK/PD model to all rats simultaneously
• adjusting for control response