PLASMA INPUT AND METABOLITE FRACTION

MODELS

http://pet.utu.fi/staff/vesoik/reports/tpcmod0000.html

TPCMOD0009Models for plasma metabolite correction

TPCMOD0010Modelling input function

PLASMA METABOLITES

http://pet.utu.fi/staff/vesoik/analysis/doc/metab_corr.html

MODELLING PLASMA METABOLITES: WHY?

• Removes ”noise” in the measured parent tracer fraction curve

• Interpolation of the fraction curve

• Extrapolation of the fraction curve

• Population based average metabolite correction?

MODELLING PLASMA METABOLITES: HOW?

• Linear interpolation (no modelling)

• Mathematical function fitting

• Kinetic models

http://pet.utu.fi/staff/vesoik/reports/tpcmod0009.pdf

MATHEMATICAL FUNCTIONS

• Exponential functions

• Hill-type function

• Watabe’s empirical equation

Hill-type functions

0 15 30 45 60 75 900.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Fra

ctio

n o

f au

the

ntic

[11C

]FL

B

Time (min)

t

tfMet

http://pet.utu.fi/staff/vesoik/programs/doc/fit_hill.html

KINETIC MODELS FOR PLASMA METABOLITES

• Huang et al. 1991, Reith et al. 1990, Gjedde et al. 1991

• Carson et al. 1997

• Models for [15O]O2: Huang et al. 1991, Iida et al. 1993

http://pet.utu.fi/staff/vesoik/reports/tpcmod0009.pdf

Huang’s plasma metabolite model

http://pet.utu.fi/staff/vesoik/reports/tpcmod0009_app_a.pdf

C0PARENT

C1MET1 C2MET1K01

k21

k12

C3MET2 C4MET2K03

k43

k34

PLASMA

Extended Carson’s plasma metabolite model

http://pet.utu.fi/staff/vesoik/reports/tpcmod0009_app_b.pdf

Cpa Cta

Ctm

K1a

k2a

k3

CpmK1m

k2m

PLASMA

New plasma metabolite model

http://pet.utu.fi/staff/vesoik/reports/tpcmod0009_app_c.pdf

Cpa

Ct1m

Ct2m

km

Cpmk3m

k4m

PLASMA

k1m

k2m

TISSUE

KINETIC PLASMA METABOLITE MODELS MAY

FAIL IF:

• Noise in measured plasma or blood curve

• Missing plasma samples during tracer infusion

MODELLING PLASMA CURVE: WHY?

• Removes noise

• Interpolation

• Extrapolation

• Reduces bias caused by missing samples

• Population based curve applying few late-time venous samples

MODELLING PLASMA CURVE: HOW?

• Linear interpolation (no modelling)

• Spline fitting

• Mathematical function fitting

• Kinetic models

http://pet.utu.fi/staff/vesoik/reports/tpcmod0010.pdf

MATHEMATICAL FUNCTIONS

• Sum of exponential functions

• Thompson and Golish bolus input function

• Gamma variate function

• Feng et al. (based on compartmental models)

http://pet.utu.fi/staff/vesoik/reports/tpcmod0010.pdf

http://pet.utu.fi/staff/vesoik/programs/doc/fit_feng.html

Examples of Thompson’s function with asymptotic recirculation term by Golish et al.

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

/exp1exp)1exp(

)( 000

0max ttCtt

ttCtC p

KINETIC MODELS FOR PLASMA CURVE

• Feng et al. 1993

• Graham 1997

GRAHAM’S MODEL

Vp

Vt

Vi

Bolus or Infusion

Renal loss

PS1

PS2

Vp

Vt

Vi

Bolus or Infusion

Renal loss

PS1

PS2

Vc

PS3

http://pet.utu.fi/staff/vesoik/reports/tpcmod0010_app_a.pdf

GRAHAM’S MODEL FOR PLASMA CURVE AND

A METABOLITE

http://pet.utu.fi/staff/vesoik/reports/tpcmod0010_app_b.pdf

Vpa

Vta

Via

Bolus or Infusion

PS1a

PS2a

GFRa

Vpm

Vtm

VimPS1m

PS2m

GFRm

MR1

MR2

Example fit

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

90

100

Co

nce

ntr

atio

n in

pla

sma

(kB

q/m

L)

Time (min)

Con

cent

ratio

n in

pla

sma

(kB

q/m

L)

Time (min)

[11C]flumazenil Measured Fitted Parent tracer Metabolite

Example fit (cont.)

0 10 20 30 40 50 600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0F

ract

ion

of [11

C]fl

umaz

enil

Time (min)

Measured fractions Fitted with extended Graham model Fitted with Hill-type function

PROBLEMS

• Model contains up to 18 parameters

• Difficult to weight metabolite fractions in relation to plasma

• Peak is not fitted well: may need a constraint

• Fast metabolism: are the first measured fractions correct?