1. OK. What if we don’t care about the kinetics of a particular tracee molecule (e.g., glucose). Rather, we care about counting up the number of one type of helper molecules. Recall the tragic heroin addict, David, in 1977, cited in a previous reading…

2. How might we image the loss of David’s nigro-striatal neurons?
David had attempted to make a heroin-like substance, MPPP, in his bathtub and instead had made MPTP.
MPTP is a poison that destroys neurons via entry through the Dopamine transporter molecules on those neurons.
How might we image the loss of David’s nigro-striatal neurons?
from the substantia nigra
to the striatum

3. from the substantia nigra to the striatum
Recall that DAT molecules soak up excess Dopamine after it is fired into the synapse by the pre-synaptic neuron. In particular the neurons that run from the substantia nigra to the striatum.
Loss of nigral-striatal neurons is also the primary pathology in Parkinson’s disease.
If we could detect early loss of nigro-striatal projections by detecting loss of DAT on the ends of these neurons, we might have an early diagnosis method for Parkinson’s.
from the substantia nigra
to the striatum
Hint: make this thing radioactive

4. From 1-compartment to 2- or 3-compartment models.
Common application: receptor-ligand modeling
What does this model ‘say’?
Why is the PET pixel drawn as shown?
K1 & k2 are still the blood flow parameters.

5. General PET kinetic model
PET = weighted sum of activity from ligand in various compartments. But, there are multiple comparments. (Ci = [ F B NS ]). Hence multiple….ODEs!!!
Please write them now.

6. But what’s really Special about PET?
Molecular Specificity!
Introduction to PET Modeling

7. What’s in a (Brain) Pixel?
receptor blood vessel
radio-ligand nerve terminal

8. What’s in an Abstract (Brain) Pixel?
Plasma
Free
Bound
Non-specifc
Possible
ligand ‘states’:
Intravascular Free
Bound specifically Non-displaceable

9. What do the Boxes Signify?P F B N
Mass
Balances:

10. What do the Boxes Signify?P F B N
Mass
Balances:
(more precise)
…whereas with FDG we had to be concerned with the effects of glucose, (recall fast vs fed mice) now we need to keep track of cold (not labeled tracer).

11. = P(t) is a measured quantity
Why no Mass Balance on P? P F B N
= P(t) is a measured quantity P
Mass
Balances:

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

13. What are we injecting? Lets look closely…
Tracer (pmol)
labeled tracer (mCi)
Specific Activity = Radioactivity/ mole of tracer
We can also think of specific activity (SA) as the ratio of ‘hot’ tracer molecules to total tracer molecules.

14. What do the Boxes Signify?P F B N
Mass
Balances:
(more precise)
Recall what we are injecting. A mixture of hot and cold ligand.

15. It is time-varying! SA = SA(t). Why?
Specific Activity
What’s SA?
Specific Activity is the ratio of activity to total mass of tracer (e.g., in mCi/pmol). SA allows us to convert between molar concentrations (the units of the mass balance) and radioactivity (the units of the measured PET signal).
It is time-varying! SA = SA(t). Why?
Test your tracer IQ!

16. How to model binding of a tracer via a ‘saturable’ process.

17. Consider the balance on the bound compartment…F B N
Consider the balance on the bound compartment…

18. Bimolecular and Saturable!
How to Model Receptor-Ligand Interactions for Non-equilibrium Kinetics?
rate constant * [available receptors] * [radioligand]
rate constant * [available receptors] * [radioligand]
rate constant * [available receptors] * [radioligand]
Bimolecular and Saturable!

19. Available sites in terms of bound hot tracer and Specific Activity
[hot / (hot / total)]
(Think back to pink quarters.)

20. How to Model Receptor-Ligand Interactions - true ‘tracer’quantities.
rate constant * [available receptors] * [radioligand]
rate constant * [available receptors] * [radioligand]
rate constant * [available receptors] * [radioligand]
Click Here

21. How to Model Receptor-Ligand Interactions? High SA case.
Once again, a nonlinear process appears to be 1st order linear in free (hot) ligand concentration - provided injected dose is given in a ‘tracer’ quantity.

22. It’s all your point-of-view: Sometimes a ‘saturable’ process to an endogenous tracee looks like a first order, nonsaturable process to a tracer.

23. What does it mean if we model
rate constant * receptor number
[min-1] * [pmol/ml]
We cannot distinguish kinetic effects from receptor-density effects.
Consider: y=MNx + B
Test your tracer IQ!

24. Practically speaking…
Even when we know that the data adhere to a 2 or 3-compartment model, we settle for estimation of a subset of (compound) parameters.
Popular linearization
With a single bolus injection, the data just don’t have that much information to identify more than a few parameters.