BASIC MODELS IN DIAGNOSTICS

Turku PET Centre2008-03-04

vesa.oikonen@utu.fi

PET basics I

Simple methods favoured

• to reduce scan time– to increase service produced or– to allow more scans per patient (whole body imaging)– to make it easier for seriously ill patients

• to produce diagnostic images with better visual quality• to produce numerical results with smaller variance• to be able to use built-in software• Feasible with all scanners and institutions

Qualitative analysis: procedure

• inject the radiotracer (FDG)• wait for the radiotracer (re)distribute and

accumulate• scan (whole body, if possible)• visual evaluation of the image:

– preoperative detection– determination of biopsy site– differentiating between recurrence and scarring

Quantitative analysis

• Needed in:– intermediate cases (with defined cut-off values)– staging of disease– detection of residual masses or relapses after radical

treatment– early monitoring of response to treatment

• Increases the effect size (but also variation)

Qualitative

Semi-quantitative

Quantitative

Visual assessment

SUV, T/N ratio

FURMTGACompartment

model fit

What happens to the radiotracer in a PET study?

• Radiotracer is administrated as a short bolus into large vein (in forearm)

• Blood that is coming from all veins is well mixed in the heart

• Arterial blood carries into all body tissues the same concentration of radiotracer per blood volume

• Biochemical properties of the tracer and biology of the target tissue determine at which rates the radioactivity accumulates and is washed away

time

Arterial blood

time

Myocardium

time

Brain

time

Liver

What can be measured?

• the properties of the tracer determine what properties of the tissue you can measure– perfusion and first-pass extraction– activity and saturation of membrane transporter– activity of enzymatic pathway in tissue– concentration and affinity of receptor

• Select a suitable tracer !

Properties of FDG

• FDG is glucose analogue• Glucose and FDG share (compete for) the same

membrane transporters and hexokinase; but with different affinities

• phosphorylated glucose is further metabolized, but FDG-6-PO4 is not

• FDG-6-PO4 is trapped inside cells where it is formed (except in liver and kidneys which contain glucose-6-phosphatase)

[11C]-Methyl-D-glucose

• Transported into cells like glucose and FDG, but can not be phosphorylated

• Could be used to measure glucose transport and glucose concentration in the tissue

• Not used in diagnostics, but demonstrates the importance of tracer selection!

Tracer and isotope label

• We are interested in the concentration of tracer in tissues (pmol/mL)

• PET can be used to measure concentration of isotope label (Bq/mL); isotope label is decaying

• Physical decay of the label, physiological clearance of the tracer, and sensitivity of PET scanner set the limits on how long the tracer concentration can be followed

Tracer and isotope label

0 15 30 45 600

5

10

15

20

25

30

[F-18]FDG corrected for decay [F-18] not corrected for decay [F-18]FDG molar concentration

Time from injection (min)

kBq/

mL

0

200

400

600

800

1000

pM

• PET and blood data is corrected for decay to the common time (usually the time of injection, t=0)

• Decay-corrected radioactivity concentrations are directly relational to molar concentrations

Physical decay

21

2ln,)()0(

TwhereetCC t

Semiquantitative methods

• Standardized uptake value (SUV)– sometimes named differential uptake ratio (DUR) or

differential absorption ratio (DAR)• Tissue-to-reference tissue ratio

– or tissue-to-normal tissue (T/N) ratio

Standardized uptake value 1/3

• Enables to compare patients and healthy subjects semi-quantitatively by taking into account– different radiotracer doses and– different body weight (total distribution space of

injected tracer)• Total or lean body mass, or body surface area

Standardized uptake value 2/3

• Tissue radioactivity and dose must be decay corrected to the same time point

• Instead of weight, body surface area (BSA) is recently recommended: SUVBSA

• In FDG PET, correcting for plasma glucose should be considered

weightsPatientdoseInjected

TCSUV PET

BW '

)(

SUV is time-dependent 3/3

NCI PET Guidelines, 2006

Tissue-to-reference tissue ratio 1/3

• Inter-individual variation in doses, body weight, and plasma clearance is taken into account by normalizing tissue radioactivity concentration with normal (reference) tissue that is with certainty not affected by the disease

• Commonly used in the brain studies; cerebellum is often used as reference tissue; or the other hemisphere

Asymmetry index (AI)

2sin

sin

CC

CCAI

dx

dx

Tissue-to-reference tissue ratio 2/3

• Even simpler method than SUV, because reference tissue is in the same image:– no need to calibrate PET scanner– no need to worry about physical decay corrections

• Problems:– normal tissue not always available– not easy to define the same normal tissue in

repeated scans– image data in low-uptake tissue may be noisy– ratio is a complex function of time

Tissue-to-reference tissue ratio 3/3

• Muscle is frequently used as reference for tumor• FDG uptake in muscle may increase if patient is

nervous or position is hard to keep

SUV vs T/N ratio

Scores

SUV T/N ratio

“Normal” tissue not required ++ --

Dynamic scanning not required + +

Blood sampling not required +++++ +++++

Time-independent ---- ----

Cross-calibration not required - +

Independent of plasma clearance -- ++

What is the optimal scan time?

• Initially, do long dynamic PET scans• Take blood samples: blood sampling allows to

use of quantitative analysis methods that are not time-dependent

• Calculate results from different time ranges:– Select the scan time that best predicts clinical

outcome– Select the scan time that best correlates with

quantitative method

If semiquantitative method does not work

• develop a new better radiotracer, or• collect more information in the PET studies

– blood sampling– dynamic scanning– extended scanning times

• and use kinetic analysis methods to separate the important tissue property from the less important but more prominent ones

Tracer concentration in blood

• Arterial concentration from injection time to the end of PET scan

• When used in the kinetic model:– accounts for plasma clearance– reference tissue is not needed

(but may be useful, if it exists)

Arterial blood curve

• Arterial catheterization:– Burdensome– Applied in diagnostic studies only if absolutely

necessary• Non-invasively from dynamic PET image

– if heart is visible, or– if abdominal aorta is visible, or– if other main arteries are visible with high-resolution

scanners

Arterialized venous blood curve

• Venous blood curve can not be used, because it has very different shape (lower peak)

• Solution: hand is warmed to increase blood flow and shunting

• Resulting venous blood curve is acceptable for diagnostic studies

Quantitative methods

• Multiple-time graphical analysis (MTGA):– Gjedde-Patlak plot (“Patlak”)

• Fractional uptake rate (FUR)– Logan plot

• Compartment model fit• Distributed model• Spectral analysis

Gjedde-Patlak plot• There can be any number of

reversible compartments, where the tracer can come and go.

• After some time, tracer concentrations in these compartments start to follow the tracer concentration changes in plasma (ratio does not change).

• Then, any change in the total tissue concentration (measured by PET) per plasma concentration, represents the change in irreversible compartments.

Gjedde-Patlak plot

Ki and metabolic rate

• If PET tracer is an analogue of glucose (e.g. [F-18]FDG) or fatty acids (e.g. [F-18]FTHA) or other native substrate, then

• Ki can be used to calculate the metabolic rate of the native substrate

• For example; [F-18]FDG PET study:

LC

CKMR

PlasmaGluc

iGluc

Fractional uptake rate (FUR)

FUR

• FUR is an approximation to the Gjedde-Patlak plot slope Ki:– at large T (late time after injection) the effective

distribution volume term in Gjedde-Patlak analysis is not important, and y axis intercept can be assumed to be 0

• Fractional uptake rate was previously sometimes called retention index (Ri)

Logan plot

0 5 10 15 20 25 300

20

40

60

80

100

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140

160

CR

OI i

nte

gra

l / C

RO

I

CPLASMA

integral / CROI

• Y-axis: Integral of tissue curve divided by tissue concentration

• X-axis: Integral of plasma curve divided by plasma concentration

• Slope equals volume of distribution, VT

Irreversible or reversible uptake?

• Make Gjedde-Patlak plot (MTGA for irreversible tracers

• If plot becomes linear, then uptake is irreversible (during PET scanning)

• If plot turns down, try Logan plot (MTGA for reversible tracers)

• If plot becomes linear, then uptake is reversible

Summary of MTGA• Gjedde-Patlak plot for irreversible uptake, Logan plot for

reversible• Linearity of plots must be checked; otherwise time-independent• Plasma or reference region input can be used, depending on the

tracer• Outcome from Gjedde-Patlak plot is net influx constant Ki which

may be used further to calculate metabolic rate, or Kiref with

reference region input• Outcome from Logan plot is distribution volume VT, or distribution

volume ratio DVR = VT/VTREF with reference region input

• Easy and fast to calculate pixel-by-pixel from dynamic PET images to produce Ki or VT images

Perfusion with [15O]H2O

• Based on the principle of exchange of inert gas between blood and tissues (Kety-Schmidt, 1945)

• Perfect first-pass extraction

Perfusion with [15O]H2O: ARG

• Autoradiographic (ARG) method:– 1.5 - 5 min scan time– Arterial blood curve from PET image or from arterial

line using on-line sampler– Partition coefficient of water (p) is assumed to be

known; when true value is different, bias is introduced

– Produces high-quality images of perfusion

Computation using ARG 1/3

• Take measured PET image• Calculate the AUC (integral from

scan start to end) of each voxel curve

• create a (look-up) table with two columns

• in the first column, write perfusion values from the whole physiological range with reasonable distance

PerfusionmL*(100g*min)-1

Tissue AUC(Bq/mL)*min

0

1

2

3

4

...

• take the measured blood curve• for each row, calculate the predicted tissue curve with

that perfusion (f) and assumed p

• calculate AUC of predicted tissue curve and write it in the second column

Computation using ARG 2/3

Computation using ARG 3/3• Go through the AUC image one voxel

at a time– get the AUC image voxel value– look for the closest AUC value from the

second column of the table– replace the voxel value with the

corresponding perfusion value from the first column

• Now you have a “parametric” image, where each voxel value represents quantitative perfusion in units mL blood / 100 g tissue / min

PerfusionmL*(100g*min)-1

Tissue AUC(Bq/mL)*min

0 0

1 2389

2 5378

3 7822

4 10231

... 13106

Region of interest and target size

• If target is large,small ROI will givecorrect result

• If target is small,result is alwaysunderestimated

Region of interest and target size

Region of interest andtissue heterogeneity

• Tissue heterogeneitywill lead tomixture of tissuesinside any ROI

• At its best, regionalresult represents theaverage

Models for heterogeneous data

• Results from multiple-time graphical analysis (MTGA) represent (weighed) average of tissues inside the ROI

• Optimal scan time for SUV may change• Methods based on assumption of homogenous

tissue may lead to over- or underestimation

Clinical model validation

• Repeatability coefficient (RC) and intra-class correlation coefficient (ICC) must be high (test-retest setting)

• Effect size and discriminating power must high (patient-control or treatment-placebo study)

• Any new simplification needs to be fully evaluated before it is used in large-scale studies

Selecting the method

• Follow international guidelines in clinical use• The best method in science lab may not be

feasible in clinical lab:– Higher dose and longer scan would provide better

image quality– Blood sampling would increase effect size– FDG usually is the only available tracer, although

another tracer would provide better results

References1. In Vivo Imaging of Cancer Therapy. Series: Cancer Drug Discovery and

Development. Shields AF, Price P (Eds.); 2007, XII, 326 p., Humana Press. ISBN: 978-1-58829-633-7.

2. Positron Emission Tomography. Basic Sciences. Bailey DL, Townsend DW, Valk PE, Maisey MN (Eds.); 2005, 382 p., Springer. ISBN: 978-1852337988.

3. Hoekstra CJ, Paglianiti I, Hoekstra OS, Smit EF, Postmus PE, Teule GJJ, Lammertsma AA. Monitoring response to therapy in cancer using [18F]-2-fluoro-2-deoxy-D-glucose and positron emission tomography: an overview of different analytical methods. Eur J Nucl Med. 2000; 27(6): 731-743.

4. Logan J, Alexoff D, Kriplani A. Simplifications in analyzing positron emission tomography data: effects on outcome measures. Nucl Med Biol. 2007; 743-756.

5. Shankar LK, et al. Consensus recommendations for the use of [18F]-FDG PET as an indicator of therapeutic response in patients in National Cancer Institute trials. J Nucl Med. 2006; 47(6): 1059-1066.

6. van den Hoff J. Principles of quantitative positron emission tomography. Amino Acids 2005; 29: 341-353.