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Detecting Drug Effects in the Brain

  1. 1. Detecting Drug Effects in the Brain Heather Turner, Phil Brain and Foteini Strimenopoulou Nonclinical Statistics Pfizer, UK 18 August 2011
  2. 2. 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)
  3. 3. EEG • Electrodes placed on scalp • Monitor difference in voltage between baseline electrode and others • Produces virtually continuous signal
  4. 4. 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 0.00020 q q FFT Power (µV2) −→ − q q q 0.00010 qq q q qqqq qq q q q q q q q q q q q qqq q 0.00000 qqqqqq qqqqqqqqqq qqqqqqqqq qqqq 0 5 10 15 20 25 30 35 Frequency (Hz)
  5. 5. 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)
  6. 6. PK Models 0.4 Double Exponential 0.3 0.2 Critical Exponential Response 0.1 0.0 −0.2 0 10000 20000 30000 40000 Time
  7. 7. GSLCCA (in pictures) Spectrum "Observed" Value 0.00020 Power (µV2) 0.00000 0.2 0 5 15 25 35 Frequency (Hz) 0.1 Response × −→ 0.0 Signature 500 1000 Coefficient −0.1 0 −500 0 10000 20000 30000 40000 0 5 15 25 35 Time Frequency (Hz)
  8. 8. GSLCCA (in pictures) Spectrum Fitted Values 0.00020 Power (µV2) q q q q q 0.00000 q 0.2 q q q q q q 0 5 15 25 35 q q q q Frequency (Hz) 0.1 Response q q q × −→ q q 0.0 q q Signature q q q q q 500 1000 qq q qq q q q q q qq q q q q qq q q q q q q Coefficient q q q −0.1 q q q qq q q q q q q q q qq q q 0 −500 0 10000 20000 30000 40000 0 5 15 25 35 Time Frequency (Hz)
  9. 9. 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
  10. 10. 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
  11. 11. 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
  12. 12. 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
  13. 13. Fitted Model plot(result, "fitted")
  14. 14. Observed + Fitted plot(result, "scores")
  15. 15. 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)
  16. 16. 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 0 5 10 15 20 25 30 35 Frequency (Hz)
  17. 17. 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)
  18. 18. 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
  19. 19. 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
  20. 20. 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
  21. 21. 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
  22. 22. 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

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