Q: What is this dog thinking about?

He’s thinking about two things: 1. Saturable processes. 2. Solving the FDG model.

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.)

Glucose and Deoxy-Glucose Uptake and Metabolism

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 *

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.

where do these terms come from?

‘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).

What’s the solution to the FDG model (aka the ‘Sokoloff’ model)? Just another modified Blood Flow model.

Solving the Sokoloff model Analytical expression for the extracellular compartment also called the “precursor pool” NOTE: for FDG, all these quantities are * ’ d

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.

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

…lets think about the FDG model again for a moment…

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

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

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 cell’s capacity to metabolize, then we use the same reasoning as in previous slide to assign a 1st order rate constant, k 3

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

Non-Fasted Care of Jeniece Nott, Ph.D., Ned Rouze, Ph.D. FDG images of Mouse Brain Fasted for 14 Hours

Care of Jeniece Nott, Ph.D. Uptake into brain varies with fasting state

The FDG model What do the (grey) boxes mean? State equations --- I.e., unknowns We need to write a balance eqn on each compartment.

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

How to relate LCMRglc = f(K 1, k 2, k 3 ) to LCMRglc = f(measured, estimated quantities)? Glucose parameters

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

…so the question for interpretation of the London et al. paper is: Are cocaine addicts more like normals or like PD or Alzheimer’s patients?

What if we don’t want to solve it? There are ways to linearize it (called the ‘Patlak’ plot).

Interpretation: What does the parameter K 1 k 3 represent? (k 2 +k 3 ) ? Blood Door #2 Metabolism Door #3 k2k2 k3k3 Think Baye’s theorem…

? 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

Why does the data keep going up? Because there’s no k ? Is this realistic? Over the time frame of the scan, perhaps.

irreversibility… like ‘early’ and ‘late’ depends on context. FDG may be effectively irreversible during a 2 hr scan… but not over 24 hrs.

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.

We could include heterogeneity into the model. (Just as we included radioactive decay.) But this might mean too many parameters.

time Input Function What’s needed to Solve the Model? Input Function, P, Drives the Model. P

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.

…well, as long as they were right handed!

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 , 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?