Simulate intravenous radiotracer kinetics across the blood-brain barrier: model plasma delivery (K1), venous clearance (k2), metabolic trapping or receptor binding (k3, k4), and perform real-time Patlak and Logan graphical linearization.
Core Concepts of PET Pharmacokinetic Modeling:
1. The Two-Tissue Compartment Model: Radiotracers delivered via an arterial plasma input Cp(t) cross the capillary endothelial blood-brain barrier with rate constant K1 (mL/g/min) into the free tissue compartment C1(t). From there, tracer either washes back out into venous blood (k2) or binds specifically to receptors / is phosphorylated by enzymes into the bound/trapped compartment C2(t) via k3.
2. Irreversible Tracers & The Patlak Graphical Plot: For metabolic tracers like 18F-fluorodeoxyglucose (FDG), hexokinase phosphorylates FDG into FDG-6-phosphate, which cannot be metabolized further and cannot cross cell membranes (k4 ≈ 0). The Patlak plot linearizes late-time data (t > 15 min):
CPET(t) / Cp(t) = Ki · [∫ Cp(τ)dτ / Cp(t)] + V0
The slope yields the net metabolic influx rate Ki = K1k3 / (k2 + k3). Multiplying Ki by plasma glucose and dividing by the Lumped Constant yields the Cerebral Metabolic Rate of Glucose (CMRglu).
3. Reversible Ligands & The Logan Graphical Plot: For neuroreceptor ligands (e.g. dopamine D2/D3 ligands), the radiotracer reversibly dissociates from the receptor (k4 > 0). The Logan plot linearizes the time course:
[∫ CPET(τ)dτ / CPET(t)] = VT · [∫ Cp(τ)dτ / CPET(t)] + int
The slope yields the Total Distribution Volume VT = (K1/k2)(1 + k3/k4). The ratio k3/k4 directly reflects the non-displaceable Binding Potential (BPND), proportional to available receptor density (Bavail).
4. Vascular Blood Spillover: Total PET activity recorded by the scanner detector ring always includes a small vascular blood contribution: CPET(t) = (1 − Vb)(C1(t) + C2(t)) + VbCp(t).