The document summarizes a two-compartment pharmacokinetic model for analyzing contrast agent behavior. The model includes compartments for plasma, extracellular space (EES), and tumors. It defines variables like contrast agent concentrations and transfer rates between compartments. The summary also outlines how signal intensity data from MRI scans can be converted to contrast agent concentrations using calibration curves.

1. Two Compartment Model

3. Pharmacokineticc Behavior of Contrast Agents Review S : capillary surface area P : capillary permeability F : capillary blood flow

4. Summary of variables Materials and Methods m/min Permeability constant P m 2 /kg Surface area per unit mass S L/kg ·min Isodirectional transfer rate per unit volume between the plasma and the tumor compartments K p↔t L/kg ·min Transfer rate per unit volume from the tumor to the plasma compartment K t  p L/kg ·min Transfer rate per unit volume from the plasma to the tumor compartment K p  t L/kg ·min Transfer rate per unit volume from the plasma compartment to the kidneys K p  k L/kg ·min Isodirectional transfer rate per unit volume between the plasma and the EES compartment K p↔e L/kg ·min Transfer rate per unit volume from the EES to the plasma compartment K e  p L/kg ·min Transfer rate per unit volume from the plasma to the EES compartment K p  e mM Concentration in the tumor compartment Ct [CA t (t)] mM Concentration in the extravascular extracellular space(EES) compartment Ce [CA e (t)] mM Concentration in the plasma compartment Cp [CA p (t)] Units Meaning Standardized quantities Variable

5. Summary of variables Materials and Methods Units Meaning Standardized quantities Variable mM Contrast agent concentration [CA] Normalized signal intensity S/S 0 l/min Excretion rate constant β l/min Distribution rate constant α kg/L Normalized concentration amplitudes for unit dose a 1,2 mmole/kg Dose D Plasma volume fraction of the tumor volume v p EES volume fraction of the tumor volume v e L/kg Tumor volume (per unit mass of tumor) or inverse tumor density V T L/kg Tumor EES volume (per unit mass of tumor) V t L/kg Plasma volume (per unit mass of body) V p L/kg EES volume (per unit mass of body) V e m 3 /kg ·min Permeability-surface area product per unit mass, isodirectional transfer between the plasma and the tumor compartments P p↔t S pt m 3 /kg ·min Permeability-surface area product per unit mass, transfer from the tumor to the plasma compartment P t  p S pt m 3 /kg ·min Permeability-surface area product per unit mass, transfer from the plasma to the tumor compartment P p  t S pt

6. Tofts model Review Kidneys Tumor Compartment Extravascular Extracellular Space Compartment (Whole body) Plasma Compartment (Whole body) Excretion Tow-compartment model with parameters defined in the text Distribution

7. Pharmacokinetic behavior of contrast agents Materials and Methods [CA p (t)] (mM) : The constast agent concentration in the plasma compartment [CA e (t)] (mM) : The contrast agent concentration in the EES compartment V p (L/kg) : The plasma volume of the whole animal (per unit mass) K e  p (L/kg·min) : The trasnfer rate per unit volume from the volume of distribution (EES) to the plasma compartment K p  e ( L/kg·min) : The transfer rate per unit volume from the plasma to the EES compartment K p  k ( L/kg·min) : The excretion transfer rate per unit volume caused by the unidirectional transit of the contrast agent from the plasma compartment to the kidneys K i  j = P i  j S ij K j  i = P j  i S ji = P i  j S ij K i↔j = P i ↔j S ij P i  j (m/minute) : The permeability constant between compartments i and j S ij (m 2 /kg) : The surface area per unit mass of the capillaries (S ij = S ji ) (1) (2)

8. Pharmacokinetic behavior of contrast agents Materials and Methods V e (L/kg) : The volume of distribution or EES volume per unit mass Important to note : V p and V e are more accurately described as the volume of the compartment permeated by the contrast agent per unit mass  Contrast agents of differing size will express different compartment volumes in the same animal Assume : Simple diffusive trasport : (3)

9. Pharmacokinetic behavior of contrast agents Materials and Methods D (mmole/kg) : The dose K p↔e (L/kg·min) : Represents the iso-directional transfer rate per unit volume between the plasma and EES compartments Distribution rate constant (1/minute) : Excretion rate constant (1/minute) : (4) (5) (6)

10. Pharmacokinetic behavior of contrast agents Materials and Methods The normalized concentration amplitudes for unit dose, a 1,2 (kg/liter), are given by : Essentially, the tumor compartment is composed of fractions of the plasma and EES compartments [CA t (t)] (mM) : The constrast agent concentration in the tumor compartment v p : The tumor’s plasma volume fraction v e : The tumor’s EES volume fraction permeated by the agent (7) (8) (9)

15. Mathematics of the Two-Compartment Model

22. Relating Signal Intensities to Contrast Agent Concentrations