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Model of Neurotransmitter PET (ntPET)

Overview

The changes of endogenous neurotransmitter by PET scanning after a stimulus have been proved with different approaches. In stead of detecting the increase or decrease of a neurotransmitter, it is important to characterize the temporal change of a neurotransmitter after a stimulus. Morris proposed the new technique (called ntPET) for capturing the dynamic changes of a neurotransmitter after a stimulus and demonstrated the ability of this method to reconstruct the temporal characteristics of an enhance in neurotransmitter concentration.

Generally, there are two separate injections of tracer for ntPET: one for the rest condition (without any stimuli) and the other for the activation condition (after a stimulus). Therefore, the model can be described as:

This model can be described by the differential equations:

dF/dt = K₁C_p - K₂F - K_on[B_max - B - B2 - B^en]F + k_offB

dB/dt = K_on[B_max - B - B2 - B^en]F - k_offB

dF2/dt = K₁C_p2 - K₂F2 - K_on[B_max - B - B2 - B^en]F2 + k_offB2

dB2/dt = K_on[B_max - B - B2 - B^en]F2 - k_offB2

dB^en/dt = K^en_on[B_max - B - B2 - B^en]F^en -k^en_offB^en

C_p is the plasma concentration of tracer at the first injection (the "rest" condition).

F and B are free (unbound) and bound molar concentrations of tracer after the first injection

C_p2 is the plasma concentration of tracer at the second injection (the "activation" condition).

F2 and B2 are free (unbound) and bound molar concentrations of tracer after the second injection.

F^en and B^en are free and bound molar concentrations of a neurotransmitter released by endogenous ligand after a stimulus.

B_max is the maximum number of receptors that can be bound by neurotransmitter or tracer.

B_max - B - B2 - B^en is the concentration of available receptors. This also indicates that binding is saturable.

K₁, K₂,K_on,K_off, K^en_on and K^en_off are rate constants.