Tracer kinetics and basic compartmental analysis

Question 1

What are the main requirements of a tracer?

Answer 1

Must be both radio-logically distinguishable but biologically indistinguishable from the molecule it traces.

Question 2

Tracer requirements

Answer 2

• Follow a physiological / biochemical process
• Naturally occurring / analogues of natural substances
• Behave same as natural substance / in known, predictable way
• Mass of tracer must not alter process being studied, isotope is a different weight, i.e. 14C is heavier than 12C
  usually < 1% of natural compound
• High specific activity for imaging or assay
  without change in behaviour or process

Question 3

Describe Compartmental Analysis

Answer 3

A simplified model of how a tracer behaves in the human body

Question 4

What is a compartment? open? closed?

Answer 4

Compartment: A vol/space where the tracer rapidly become uniformly distributed

Open: tracer can escape to other compartments

Closed: tracer cannot escape

Question 5

What is the single compartment model? define concentration?

Answer 5

A closed system

Concentration, 𝐶= 𝑀/𝑉1 MBq / ml

Question 6

How can concentration be used to ind the volume of a 2nd compartment?

Answer 6

C1 . V1 = C2 (V1 + V2)

C1 . V1 = C2 .V1 + C2 .V2

𝑉2=𝑉1 (𝐶1/𝐶2 - 1)

Assuming V2&raquo_space; V1

𝑉2= (𝑉1 . 𝐶1)/𝐶2

Question 7

What percentage of blood volume is haematocrit (RBC) ?

Answer 7

50%

Question 8

What is the volume of distribution ?

Answer 8

Vd = (𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (𝐵𝑞))/(𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (𝐵𝑞/𝑚𝑙))

Question 9

How is loss from an open system determined?

Answer 9

Using the exponential rate factor k

dM = -κ.M
dt

𝑀=𝑀0 . 𝑒^(−κ𝑡)

Question 10

What is mean transit time?

Answer 10

τ = 1/ κ also called turnover time

Question 11

What is half time?

Answer 11

Time for half of the activity of an open system to depart

t½ = ln 2 / κ analog of half life

Question 12

Define total clearance

Answer 12

Biological clearance + Radiological clearance

𝑀=𝑀0 . 𝑒^(−(κ+λ)𝑡)

Effective half life:

1/𝑇𝑒 = 1/𝑇𝑏+ 1/𝑇𝑟

Question 13

Describe the flow of a two compartment model

Answer 13

(𝑑𝑀1 )/𝑑𝑡 = κ2 . M2 – κ1 . M1

i.e Flux out of 1st compartment plus flux back from 2nd compartment

Question 14

What are catenary and mamilliary systems?

Answer 14

Catenary: two compartment system - compartments are connected in series

Mamilliary: two compartment system - compartments are supplied by a central compartment (multi-expo)

Question 15

What a fundamental physiological variables?

Answer 15

• Distribution volume : ml : volume = Activity / conc
• Mean transit time : min
• Extraction :

= Blood flow : ml /min or Perfusion: ml /min per mg

= Clearance : ml / min

Question 16

What is transit time? and mean transit time ?

Answer 16

Time for a particle to travel between point A and B

Multiple particles following different pathways through the system

-> frequency distribution of transit times, h(t)

Mean Transit Time: Mean of all times taken over outflow curve,h(t)

𝞃= (∫ 𝑡 . ℎ(𝑡). 𝑑t)/(∫ℎ(𝑡). 𝑑t)

Question 17

What is the central volume principle? flow rate?

Answer 17

Single input of tracer distributed along different paths in proportion to blood flow rate.

Flow rate, F (mL/min)

F = 𝑉/𝜏

Volume of distribution, V (mL)
Mean transit time of tracer molecules, 𝜏 (min)

Question 18

How can mean transit be calculated from retention ?

Answer 18

𝞃= (𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛)/(𝐼𝑛𝑖𝑡𝑖𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛)

Question 19

What is an extraction fraction ?

Answer 19

Fraction of incoming tracer that is removed by an organ in one pass through the organ.

𝐸= (Ca −Cv) / Ca if E=1, extraction = blood flow

Ca=arterial conc Cv=vessel conc

High blood flow -> low extraction fraction

Question 20

How is organ uptake determined?

Answer 20

Organ uptake is a function of i) blood flow, ii) extraction fraction.

Question 21

How is blood flow determined?

Answer 21

Transit time equation: F = V / τ

Blood flow per mass of tissue, ml/min/g

Question 22

What is the ficke principle?

Answer 22

A tracer is subject to the conservation of matter within the system.

The rate of change of tracer in an organ is proportional to diff between the amount of tracer in the input compared to the output

= Blood flow x Tracer concentration difference between artery and vein

Question 23

What is the net uptake rate of an organ?

Answer 23

𝑄=𝐹 . (𝐶𝑎 −𝐶𝑣) where Flow F (ml/min)

Input – arterial concentration, Ca

Output – venous concentration, Cv

Net uptake rate of organ Q (mg/min)

Question 24

how is cardiac output calculated?

Answer 24

Volume of O2 consumed/min = Cardiac Output x (O2 artery – O2 vein)

(HR x SV) heart x systolic volume

Question 25

Describe clearance

Answer 25

Volume of plasma completely cleared per minute, CL (ml/min)

Rate of change of Activity = Rate constant x concentration = CL . P(t)

Total Activity =𝐶l∫𝑃(𝑡)𝑑t over the time

Activity up to time t = Clearance x Area under the Plasma curve (t)

𝐶l=(𝐷𝑜𝑠𝑒.𝑘)/𝑃0 ml / min Area under curve = P0 / k

Question 26

Describe multi-exponential curve

Answer 26

If k1 and k2 are sufficiently different, curve will approach a straight line of rate constant = k2 (slowest)