Edited by: Pedro Antonio Valdes-Sosa, Centro de Neurociencias de Cuba, Cuba
Reviewed by: Jim Voyvodic, Duke University, USA; Philippe CIUCIU, Commissariat à l'Energie Atomique et aux Energies Alternatives, France
*Correspondence: Kevin J. Black
This article was submitted to Brain Imaging Methods, a section of the journal Frontiers in Neuroscience
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We recently described rapid quantitative pharmacodynamic imaging, a novel method for estimating sensitivity of a biological system to a drug. We tested its accuracy in simulated biological signals with varying receptor sensitivity and varying levels of random noise, and presented initial proof-of-concept data from functional MRI (fMRI) studies in primate brain. However, the initial simulation testing used a simple iterative approach to estimate pharmacokinetic-pharmacodynamic (PKPD) parameters, an approach that was computationally efficient but returned parameters only from a small, discrete set of values chosen
Measuring the sensitivity of an organ to a drug
Here we revisit the simulation testing using a Bayesian method to provide continuous estimates of the PKPD parameters. The Bayesian approach also identifies data too noisy to produce meaningful parameter estimates (using a model selection package described below). Bayesian methods have been used successfully in other PKPD analyses (Lavielle,
We used a standard sigmoid PKPD model (Holford and Sheiner,
As in the previous work, the concentration of drug in plasma over time is modeled as
The full model is then
The test curves were generated using
Finally we added Gaussian noise to each time point. This was done 1000 times for each of the 6 curves above and for each of 8 noise levels from
In the simulated data described above, each of the 48,006 time courses were analyzed using the “Image Model Selection” package from the Bayesian Data-Analysis Toolbox (Bretthorst,
indicated the full model,
To provide more even sampling of parameter space across the conventional logarithmic abscissa for concentration-effect curves,
Since tissues with high values of
We tested the model described above using the same phMRI (pharmacological fMRI) data we analyzed previously with the iterative method, namely, regional BOLD-sensitive fMRI time-signal curves from midbrain and striatum in each of two animals (Black et al.,
The iterative analysis had allowed only values of 5 or 30 min for the half-life of drug disappearance from the blood during the scan session; here we used a uniform prior probability over [2, 60] min for
Figure
The full PKPD model explained the data better than a simpler model, i.e., prob(model) >0.5, except when signal was low (higher
For the data sets containing no intentional signal, i.e., noise added to the
Accuracy of the
The full PKPD model was selected for 6 of the 8 regional time-signal curves (see Table
A | 4 | 1 | Midbrain | 1.00 | 12.59 | 3.44 | 58.33 | 0.98 |
B | 4 | 1 | Striatum | 1.00 | −13.58 | 4.15 | 59.48 | 0.81 |
C | 4 | 2 | Midbrain | 1.00 | 29.27 | 6.32 | 3.93 | 0.23 |
D | 4 | 2 | Striatum | 1.00 | −2.48 | 0.001 | 40.58 | 0.01 |
E | 8 | 1 | Midbrain | 0.00 | – | – | – | – |
F | 8 | 1 | Striatum | 0.02 | – | – | – | – |
G | 8 | 2 | Midbrain | 0.76 | 7.38 | 0.418 | 13.16 | 0.18 |
H | 8 | 2 | Striatum | 1.00 | −13.9 | 1.63 | 2.00 | 0.72 |
Bayesian parameter estimation for the QuanDyn™ quantitative pharmacodynamic imaging method produced excellent results in simulated data: first, the Model Select method very accurately identified time courses with a meaningful drug-related signal, until noise overwhelmed signal, i.e., when SNR < about 3.5. The Bayesian Data-Analysis Toolbox successfully avoided false positives, correctly refraining from identifying a signal in every noise-only time course, even where sensitivity was 100%. In time courses with a signal, mean accuracy was reasonable even in the face of low SNR, as shown in Figures
This simulation used a simple noise model that may be best suited to a temporally stable, quantitative outcome measure, such as positron emission tomography, arterial spin labeling, or quantitative BOLD. However, because the PKPD model
Similar comments hold for the signal as well as for noise: the QuanDyn™ quantitative pharmacodynamic imaging method will perform less well if the PKPD model does not realistically model the data. However, prior to initiating an expensive imaging study, one would determine the appropriate family of PKPD models for the drug to be tested, based on traditional dose-response experiments. We discuss this point further in Black et al. (
Even with the relatively simple signal and noise models adopted for this initial testing, the tested method appeared to handle reasonably the
The QuanDyn™ method described here has several potential advantages compared to the traditional approach to quantifying a drug effect, which is to estimate the population
The following information was supplied regarding the deposition of related data: The simulated data sets (1000 time courses for each set of parameter values and noise level) are available at the journal web site as Supplementary Data.
JK performed the experiments, analyzed the data, contributed analysis tools, reviewed and critiqued the manuscript. MV performed the experiments, analyzed the data, reviewed and critiqued the manuscript. GB contributed analysis tools, reviewed and critiqued the manuscript. KB conceived and designed the experiments, performed the experiments, analyzed the data, wrote the paper.
Supported by the U.S. National Institutes of Health (NIH), grants R01 NS044598, 1 R21 MH081080-01A1, 3 R21 MH081080-01A1S1, K24 MH087913 and R21 MH098670, and by the McDonnell Center for Systems Neuroscience at Washington University in St. Louis. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Authors KB and JK have intellectual property rights in the QuanDyn™ method (U.S. Patent #8,463,552 and patent pending 13/890,198, “Novel methods for medicinal dosage determination and diagnosis.”). KB is an Associate Editor for the Brain Imaging Methods section of Frontiers in Neuroscience. The other authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Some of these results were presented previously (JK, GB, KB: A novel analysis method for pharmacodynamic imaging. Program #504.1, annual meeting, Society for Neuroscience, Chicago, 20 Oct 2009), and a preprint was posted on bioRxiv (DOI: 10.1101/017921).
The Supplementary Material for this article can be found online at: