Q: What is this dog thinking about?. He’s thinking about two things: 1. Saturable processes. 2....
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- Slide 1
- Q: What is this dog thinking about?
- Slide 2
- Hes thinking about two things: 1. Saturable processes. 2.
Solving the FDG model.
- Slide 3
- Why use FDG in particular? Product of phosphorylation by
hexokinase reaction gets trapped in cell. Accumulation of metabolic
product is a measure of glucose usage. 1. Assumption: FDG acts just
like glucose - this is not exactly true. (The lumped constant
arises to correct for differences.)
- Slide 4
- Glucose and Deoxy-Glucose Uptake and Metabolism
http://www.nuc.ucla.edu/html_docs/frame_pet.html
- Slide 5
- Keep in mind What we want is a measure of GLUCOSE metabolism.
Not a measure of FDG phosphorylation. How do we get from a model of
FDG uptake to a value of GLUCOSE metabolism? 1.Use a single
measurement technique which descends from the autoradiographic
method in animals. 2.Or Solve model of FDG uptake in terms of K 1
*, k 2 *, k 3 * 2. Fit PET data to FDG model. 3. Relate LCMRglc to
K 1 *, k 2 *, k 3 *
- Slide 6
- from Herscovitch chapter in Valk et al, Springer, 2003 Cp =
measured concentration of glucose (assumed constant) Cp*(t)
=measured, time-varying concentration of FDG in plasma C(T) =
tissue concentration of FDG, measured at time T (only) LC = lumped
constant measured in other animals/people; reconciles glucose with
FDG other terms: can be calculated from integral of the FDG curve
in plasma and parameters for FDG measured in other
animals/people.
- Slide 7
- where do these terms come from?
- Slide 8
- Sokoloff model 1. X * --- designates FDG. 2. Assumes that there
is NO dephosphorylation of FDG-6-P over course of scan (i.e., k4 =
0).
- Slide 9
- Whats the solution to the FDG model (aka the Sokoloff model)?
Just another modified Blood Flow model.
- Slide 10
- Solving the Sokoloff model Analytical expression for the
extracellular compartment also called the precursor pool NOTE: for
FDG, all these quantities are * d
- Slide 11
- from Herscovitch chapter in Valk et al, Springer, 2003 Cp =
measured concentration of glucose (assumed constant) Cp*(t)
=measured, time-varying concentration of FDG in plasma C(T) =
tissue concentration of FDG, measured at time T (only) LC = lumped
constant measured in other animals/people; reconciles glucose with
FDG other terms: can be calculated from integral of the FDG curve
in plasma and parameters for FDG measured in other
animals/people.
- Slide 12
- so, in at least 4 of the subjects in the London et al paper,
the authors are measuring a single time-point C(45-55) and
converting that map of measured concentrations of FDG to CMRglc via
the preceeding operational equation which requires the blood curve
and population- average parameters for FDG
- Slide 13
- lets think about the FDG model again for a moment
- Slide 14
- Tracer Kinetics Puzzle How can a tracer be described by a first
order kinetic process when we know that the tracee molecule follows
Michaelis-Menten kinetics? A process may be saturable in terms of
enzymes and the concentration of the tracee, but, for a given
system, if the tracee is not perturbed, it remains at a single
set-point on this curve. V tracee Operating point for system
- Slide 15
- Consider the K 1 C p term in FDG model A transporter molecule
helps FDG across the blood-brain-barrier. Therefore, the uptake
process from blood to tissue might be saturable and NOT first order
in FDG concenctration. V tracee velocity of FDG transport (via the
glucose transporter) from plasma, across BBB in presence of the
competitor, glucose
- Slide 16
- Glucose-6-P inside the cell is also mediated by a specific
enzyme, hexokinase. As long as glucose is at steady state, and we
are not near maxing out the cells capacity to metabolize, then we
use the same reasoning as in previous slide to assign a 1st order
rate constant, k 3
- Slide 17
- What would max out cells ability to transport FDG in from
blood? What happens? Lots of glucose in the blood! Transporter
operates at different set-point. V tracee
- Slide 18
- Non-Fasted Care of Jeniece Nott, Ph.D., Ned Rouze, Ph.D. FDG
images of Mouse Brain Fasted for 14 Hours
- Slide 19
- Care of Jeniece Nott, Ph.D. Uptake into brain varies with
fasting state
- Slide 20
- The FDG model What do the (grey) boxes mean? State equations
--- I.e., unknowns We need to write a balance eqn on each
compartment.
- Slide 21
- Keep our goal in mind Solving for GLUCOSE metabolic rate
Solving the Sokoloff model - 3 But we assume that glucose is in
steady state. but these k i are glucose parameters, not FDG
parameters
- Slide 22
- How to relate LCMRglc = f(K 1, k 2, k 3 ) to LCMRglc =
f(measured, estimated quantities)? Glucose parameters
- Slide 23
- Slide 24
- Dynamic FDG scanning here the LC is the lumped constant that
corrects K1, k2, k3 for K1*, k2*, k3* but in any case, this
approach requires fitting all the data to a model
- Slide 25
- so the question for interpretation of the London et al. paper
is: Are cocaine addicts more like normals or like PD or Alzheimers
patients?
- Slide 26
- What if we dont want to solve it? There are ways to linearize
it (called the Patlak plot).
- Slide 27
- Interpretation: What does the parameter K 1 k 3 represent? (k 2
+k 3 ) ? Blood Door #2 Metabolism Door #3 k2k2 k3k3 Think Bayes
theorem
- Slide 28
- ? LCMRglc ~ p(metabolism | transport from blood) = choose
metabolism out of Sum of [return to blood+metabolism], given
already transported =(k 3 /[k 2 +k 3 ])K 1
- Slide 29
- Why does the data keep going up? Because theres no k ? Is this
realistic? Over the time frame of the scan, perhaps.
- Slide 30
- irreversibility like early and late depends on context. FDG may
be effectively irreversible during a 2 hr scan but not over 24
hrs.
- Slide 31
- Heterogeneity: what if our pixels are too large to measure a
truly homogenous region? Say, we get white and gray matter in a
single pixel.
- Slide 32
- We could include heterogeneity into the model. (Just as we
included radioactive decay.) But this might mean too many
parameters.
- Slide 33
- time Input Function Whats needed to Solve the Model? Input
Function, P, Drives the Model. P
- Slide 34
- Questions 1.subjects (polydrug users!) in withdrawal from other
drugs? 2.static analysis assumes that population parameters apply?
and that lumped constant is valid across all subjects. 3.no data or
details given for fitting of data and estimating paramters in 4
subjects 4.training sessions are these good or bad? 5.how can it be
double-blind? 6.preselected the cohort for big responders is this
fair? 7.how many slices on the NeuroEcat? 8.why all the detail
about positioning by the orbitomeatal line? 9.no corrections for
multiple comparisons 10.why do we need plasma glucose levels?...
aha! 11.did they give enough cocaine no one felt good, energetic,
or anxious compared to saline 12.no statistically signif effect of
drug (coc v sal) on high - should we worry about this? figure
mis-labeled.
- Slide 35
- well, as long as they were right handed!
- Slide 36
- The effects of cocaine: A shifting target over the course of
addiction Linda J. Porrino, Hilary R. Smith, Michael A. Nader,
Thomas J.R. Beveridge Center for the Neurobiological Investigation
of Drug Abuse, Department of Physiology and Pharmacology, Wake
Forest University School of Medicine, Medical Center Boulevard,
Winston-Salem, NC 27157-1083, USA Available online 4 September 2007
Can we do this with FDG in living monkeys? Why? Why not? is 5 days
really initial is 100 days really chronic? What does Porrino think
about the London paper does it relate?
- Slide 37
- Slide 38