ANALYSIS OF PET STUDIESTurku PET Centre 2001-05-07 V Oikonen

PE

T R

aw D

ata

(sin

ogra

m)

Res

ults

Par

amet

ric

Sin

ogra

mP

ET

Im

age

Par

amet

ric

Imag

eR

egio

nal

TA

Cs

+ Blood Data

+ Blood Data

+ Blood Data

Reconstruction

Model Calculations Reconstruction

Model Calculations

Model CalculationsDrawingRegions

DrawingRegions

SPM

BLOOD DATA

VenousBolus Infusion

Arterial Time-ActivityCurve (TAC)

t t

Mixing in Plasma VolumeExchange with Interstitial Volume

Exchange with intracellular VolumeTime Delay

BLOOD vs PLASMATracer Persists in Red Blood Cells (RBC)

[15O]O2

[15O]CO

Blood

Plasma

c

t

Note that the metabolite of [15O]O2

is [15O]H2O, which is in equilibriumbetween plasma and RBC

CBlood = HCR*CRBC

BLOOD vs PLASMATracer Persists in Plasma

[11C]Palmitate[18F]FTHA

[Carbonyl-11C]WAY-100635

Blood

Plasma

c

t

CBlood = (1-HCR)*CPlasma

Note that one of the labeledmetabolites of palmitate is [11C]CO2,

which penetrates RBC membrane

BLOOD vs PLASMATracer Penetrates RBC Membrane Instantly

[15O]H2O [11C]FETNIM[18F]CFT [11C]HED

[11C]FLB-457 [11C]MP4A

Blood

Plasma

c

t

CBlood = HCR*CRBC + (1-HCR)*CPlasma

Note that the concentration may be differentin RBC and in plasma.

Note that a labeled metabolite may notpenetrate RBC membrane.

BLOOD vs PLASMATracer Penetrates RBC Membrane Slowly

[18F]FDOPA[11C]Methionine

[18F]FDG

Blood

Plasma

c

t

Note that the concentration may be differentin RBC and in plasma.

Note that a labeled metabolite may notpenetrate RBC membrane.

CBlood = HCR*CRBC + (1-HCR)*CPlasma

METABOLITES IN PLASMA

0 15 30 450.0

0.2

0.4

0.6

0.8

1.0

Fra

ctio

n o

f au

then

tic

trac

er

Time (min)

0 15 30 45 600

10

20

30

40

50

60

70

80

90

100

Rad

ioac

tivi

ty c

on

c. (

kBq

/mL

)

Time (min)

Plasma TAC Authentic tracer Metabolized tracer

PET DATA

0 15 30 45 60 75 900

10

20

30

40

50

60

70

80

90

Co

nce

ntr

atio

n o

f au

then

tic

trac

er (

kBq

/mL

)

Time (min)

0 15 30 45 60 75 900

10

20

30

40

50

60

70

80

90

Co

nce

ntr

atio

n in

tis

sue

(kB

q/m

L)

Time (min)

”input” ”output”Authentic tracer

concentrationavailable in

arterial blood

Concentrationin tissue

measured byPET scannerPerfusion

Endothelial permeabilityVascular volume fraction

Transport across cell membranes

Specific binding to receptorsNon-specific binding

Enzyme activity

MODEL CALCULATIONS”black box”

BLOODor

PLASMATAC

TISSUE TAC-sinogram or-image or-regional

RESULTS(model parameters)

MODEL

MODEL CALCULATIONS”Garbage In-garbage Out” Paradigm

PERFECT MODEL

GARBAGE MODEL

GARBAGEDATA

PERFECT DATA

GARBAGERESULTS

GARBAGERESULTS

COMPARTMENTAL MODEL

k6k

5

k4

k3

k2

K1

CBC

F

CNS

CP

CP = concentration of tracer in plasma

CF = free tracer in brain

CB = receptor bound tracer

CNS= non-specifically bound tracer

K1-k6 = rate constants; the fraction of tracer that is leaving compartment in time unit

DISTRIBUTION VOLUME

PlasmainTracerofionConcentrat

TissueinTracerofionConcentratDV

0

0

PlasmainTracerofionConcentrat

TissueinTracerofionConcentrat

DV

Constant Infusion of Tracerafter equilibrium is achieved

Bolus Infusion of Tracer

DISTRIBUTION VOLUMEReceptor Model

k6k5

k4

k3

k2

K1

CBC

F

CNS

CP

4

3

2

1 1k

k

k

KDV

Binding Potential:

4

3max'

k

k

K

BBP

d

B’max = density (concentration) of free receptorsKd = dissociation rate constant

RECEPTOR DENSITYand affinity to the ligand

0 10 20 30 40 500

1

2

3

4

5

Kd=2 nM

Bmax/2

Bmax=5 nM

Bo

un

d r

ec

ep

tor

(nM

)

Ligand (nM)

DISTRIBUTION VOLUMEDistribution Volume Ratio

k6k5

k4

k3

k2

K1

CBC

F

CNS

CP

DV in reference region:

Reference region = (brain) region which has no receptors,i.e. region with no specific binding,i.e. region where k3=0 and Bmax=0, and thus BP=0

BPk

KDV 1

2

1

2

1

2

1

k

K

k

KDV

reference

referencereference

BPDV

DVDVR

reference 1

Distribution Volume Ratio:

LOGAN ANALYSISPlasma Input

0 5 10 15 20 25 300

20

40

60

80

100

120

140

160

CR

OI i

nte

gra

l / C

RO

I

CPLASMA

integral / CROI

Distribution volume=

Slope of the Logan plot

Distribution volumeRatio

=Ratio of slopes of the ROI

and reference regionLogan J. Graphical analysis of PET data applied to reversibleand irreversible tracers. Nucl Med Biol 2000;27:661-670

LOGAN ANALYSISReference Region Input

Distribution volumeRatio

=Slope of the Logan plot

calculated usingreference region input

Logan J. Graphical analysis of PET data applied to reversibleand irreversible tracers. Nucl Med Biol 2000;27:661-670

0 10 20 30 40 500

20

40

60

80

100

120

140

160

CR

OI i

nte

gra

l / C

RO

I

CREFERENCE

integral / CROI

BP = DVR - 1

LOGAN ANALYSISSummary

• For reversible binding

• Linearity of the plot must be checked

• Plasma/Reference region input

• Result: DV or DVR

• Easily applied to image or sinogram data

SIMPLIFIED REFERENCE TISSUE MODEL

• Only for tracers with simple kinetics

• No plasma samples nor metabolite analysis

• Result: BP and R1

• Easily applied to image data with RPM

• Could be applied to sinogram data

Lammertsma AA, Hume SP. Simplified reference tissue modelfor PET receptor studies. NeuroImage 1996;4:153-158

RATIO METHOD

0 15 30 45 60 75 900

10

20

30

40

50 ROI REF ROI-REF

Time (min)

Rad

ioac

tivi

ty c

on

cen

trat

ion

(kB

q/m

l)

BP = (ROI - REF) / REF

Region-of-interest (ROI)to reference regionratio correlates withdensity of availablereceptors

GJEDDE-PATLAK ANALYSIS”Irreversible” uptake

A

RT

ER

IAL

PL

AS

MA

IRREVERSIBLE COMPARTMENT(S)

GJEDDE-PATLAK ANALYSISGraphical Analysis

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Vo

lum

e o

f d

istr

ibu

tio

n (

mL

/mL

)

Normalized Plasma Integral (min)

Plot is linear after the tracer concentrationin plasma and in reversible compartmentsare in equilibrium

Slope of the linear phase of plot is the uptake(influx) rate constant Ki

Unit of Ki is min-1, or (mL tissue/mL plasma)min-1

Patlak CS, Blasberg RG. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data.Generalizations. J Cereb Blood Flow Metab 1985;5:584-590.

Logan J. Graphical analysis of PET data applied to reversibleand irreversible tracers. Nucl Med Biol 2000;27:661-670

GJEDDE-PATLAK ANALYSISMetabolic Rate of Glucose

GlucoseGlucose-

6-Phosphate

Glucose

K1 k3

k2

k4

[18F]FDG[18F]FDG -

6-Phosphate

[18F]FDG

K*1 k*3

k*2

k*4

*3

*2

*3

*1*

kk

kKK i

Lumped constant (LC) correctsfor the different affinities oftransporters and hexokinaseto glucose and FDG

*][iglu K

LC

GluMR

Influx rate constant:

Unit of MRglu:

minmin

tissuemL

Glumol

tissuemL

plasmamL

plasmaL

GlummolMRglu

GJEDDE-PATLAK ANALYSISSummary

• For irreversible uptake

• Linearity of the plot must be checked

• Plasma/Reference region input

• Result: Ki (influx rate constant)

• Easily applied to image or sinogram data

RETENTION INDEX”one-sample Patlak plot”

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Vo

lum

e o

f d

istr

ibu

tio

n (

mL

/mL

)

Normalized Plasma Integral (min)

T

P

Tt

dttC

tCR

0

)(

)(

Requirements for data:-one late-time PET frame (static image), CT

-TAC of authentic tracer from beginning, CP

PERFUSION

0 60 120 180 240 3000

5

10

15

20

f = 0 ml min-1dL-1

f = 1 ml min-1dL-1

f = 2 ml min-1dL-1

f = 3 ml min-1dL-1

f = 4 ml min-1dL-1

f = 5 ml min-1dL-1

Ra

dio

act

ivit

y in

mu

scle

(kB

q/m

L)

Time from injection (s)

0 60 120 180 240 3000

20

40

60

80

100

120

140

f = 0 ml min-1dL-1

f = 20 ml min-1dL-1

f = 60 ml min-1dL-1

f = 100 ml min-1dL-1

f = 140 ml min-1dL-1

f = 180 ml min-1dL-1

Rad

ioac

tiv

ity

in b

rain

(k

Bq

/mL

)

Time from injection (s)

Kety-Schmidt:change in tissue concentration is equalto the difference between arterial and

venous concentrations (CA and CV)multiplied by blood flow, f

For [15O]H2O:

)()()(

tCtCfdt

tdCVA

T

)()()(

tCp

ftCf

dt

tdCTA

T

PERFUSIONAutoradiography

Procedure:1. Bolus [15O]H2O infusion2. Arterial blood sampling3. Static Imaging (90 or 250 s)4. Blood and PET TACs corrected for

radioactive decay5. Correction for time delay6. Blood TAC corrected for dispersion7. Calculation of look-up table using

measured and corrected blood TAC8. Image pixel values are replaced by

flow values from the look-up table

Look-up Table

0 50 100 150 2000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Inte

gra

l of

pix

el T

AC

(kB

q/m

L *

s)

Blood flow (ml min-1dL-1)