Quantitative Methods in Renography - Pages - Homenucleus.iaea.org/.../Quantitative_Methods_in_Renography.pdfQuantitative Methods in Renography Radionuclides in Nephrourology, Mikulov

Richard LawsonCentral Manchester Nuclear Medicine Centre

[email protected]

Quantitative Methods in Renography

Radionuclides in Nephrourology, Mikulov 2010

Richard Lawson Central Manchester Nuclear Medicine Centre

Overview• Problems of quantifying the renogram• Complex shape of the curve• Unwanted background

• Background subtraction• Recognising correct subtraction

Tissue and vascular background components• Compare two solutions• Rutland plot• Deconvolution• Quantitative parameters• Relative function• Absolute function• Elimination

ISCORN Consensus Report: Sem.Nucl.Med. 1999, 29:146-159


Renography• Renography is a dynamic study of kidney function• Time is the important dimension• It is the renogram curves that show transit of tracer through the kidneys• So curves are more important than the images• Upslope of curves demonstrate kidney uptake• Relative functionone kidney compared with the other• Absolute functioneach kidney compared with normal

• Downslope of curves demonstrate elimination

It is important to produce the correct curves


The Problems• The kidney activity-time curve is a combination of three factors:• Uptake into the kidney• Transit through the kidney• Elimination from the kidney

• Uptake depends on blood activity, which varies with• Speed of injection• Kidney function• Function of the other kidney • Recirculation of tracer

• Renogram curve is a superimposition of the desired kidney activity and unwanted background activity Renogram quantification must overcome these problems

Background Subtraction


Renogram Model

Time

Conc

entra

tion

KidneyTubules + pelvis

Bladder

ExtravascularTissue

Blood

Conc

entra

tion

Conc

entra

tion

Conc

entra

tion

Time

Time


Renogram Model

Time

Conc

entra

tion

Blood

Bladder

KidneyTubules + pelvis

ExtravascularTissue

Conc

entra

tion

Conc

entra

tion

Conc

entra

tion

Time

Time

This is the curve that we want


Each kidney ROI includes• Renal blood vessels • Renal tubules• Renal pelvis• Overlying tissues

Regions of Interest

Background ROI includes• Some blood vessels • Some tissues

The optimum background ROI must include the correct mixture of both blood and tissue background

Blood background

Tissue backgroundRenogram}

Kidney minus background• Should leave desired renogram

Blood backgroundTissue background


Background Subtraction

If background subtraction is correct, renogram curve should rise smoothly from zero

Kidney ROI curve+ Renal tubules& Renal pelvis

+ BloodTissue

cps

TimeBackground ROI curve

Tissue+ Blood

cps

Time

Background subtracted

Renal tubules& Renal pelvis

cps

Time


Mixing• During the first few seconds after injection• Tracer has not had enough time to mix uniformly throughout all of the bloodTherefore blood activity in the background region may differ from blood activity in the kidney region

So background subtraction may be wrong• Therefore ignore first few seconds of the curve• Until mixing is complete

Varies between patientsOften about 30 secondsPossibly up to 1 minute


Recognising Correct Subtraction

5 min0 1 2 3 4

Curve is not smooth during first minute

Question 1: Is this renogram curve correctly subtracted ?1 = Correct subtraction, 2 = Under-subtracted, 3 = Over-subtracted

Answer: Under-subtracted

Extrapolate to overcome mixing phase



5 min0 1 2 3 4Question 2: Is this renogram curve correctly subtracted ?

1 = Correct subtraction, 2 = Under-subtracted, 3 = Over-subtractedAnswer: Over-subtracted



5 min0 1 2 3 4Question 3: Is this renogram curve correctly subtracted ?

1 = Correct subtraction, 2 = Under-subtracted, 3 = Over-subtractedAnswer: Correct subtraction – after extrapolation



Over-subtracted

5 min0 1 2 3 4

Under-subtracted

Correctly subtractedIf curve has a kink during first minute then extrapolate to overcome mixing phase


Three Phases of the Renogram

• Originally renograms were acquired using probes• Without any means of background subtraction• The vascular phase was always present

• The vascular phase is not part of the true renogram• With modern gamma camera techniques it should be removed by proper computer processing

Phase 1 (Vascular)

Phase 2 (Uptake)

Phase 3 (Elimination)

Textbooks3 phases

Renogram modelNo vascular phase


Teaching Point• Background subtraction is correct when the renogram curve rises smoothly from zeroAfter extrapolating to overcome incomplete mixing during the first minuteAssuming that the bolus appears in kidneys during the first frame of the study – time zero

0 1 min

Background Subtraction Examples


Example 1

• 50 MBq 99mTc MAG3• Good uptake in both kidneys• Both kidneys equal function


Example 1 – Background below kidney

Relative functionLeft kidney: 50%Right kidney: 50%

Answer: Slight under-subtraction

Left Kidney

Right Kidney

Question 4: Are these curves correctly subtracted ?1 = Correct subtraction, 2 = Under-subtracted, 3 = Over-subtracted


Example 1 – Peri-renal background


Answer: Very slight under-subtraction

Left Kidney

Right Kidney



Example 1 – Rutland method


L R

Answer: Correct subtraction

Left Kidney

Right Kidney



Teaching Point

• If using MAG3 and kidney function is goodUsing different background regions only makes a small difference to background subtraction

• If both kidneys have equal functionThen under-subtracting doesn’t alter relative function significantly


Example 2

• 50MBq 99mTc MAG3• Both kidneys poor function• Right worse than left


Example 2 – Background below kidney


Answer: Significantly under-subtracted – after extrapolation

L R

Left KidneyRight Kidney





Answer: Over-subtracted

L R

Left Kidney

Right Kidney





Answer: Correct subtraction – after extrapolation

L R

Left Kidney

Right Kidney



Teaching Point• If using MAG3 and function is poor• Then different background regions can have a big effect

• If using DTPA this happens even with good function• Because of lower extraction efficiency

• If function is asymmetricThen incorrect background subtraction can affect relative function measurement


Example 3

• 50 MBq 99mTc MAG3• Left kidney good function• Right kidney hydronephrotic


Example 3 - Background below kidney


Answer: Under-subtracted

L R

Left Kidney

Right Kidney

Question 10: Is the right kidney curve correctly subtracted ?1 = Correct subtraction, 2 = Under-subtracted, 3 = Over-subtracted

Left kidney little under-subtracted




Answer: Over-subtracted

L R

Left Kidney

Right Kidney


But left kidney is OK




Answer: Correct subtraction

L R

Left Kidney

Right Kidney


For both kidneys


Teaching Point

• If the vascularity of each kidney is differentThen it is difficult to find a single background region that works for both kidneys

• The Rutland method overcomes this by automatically adjusting the amount of vascular background to suit each kidney

The Rutland Method


The Rutland Method *• The real renogram is the response of the kidney to a single injection• Resulting in a blood activity that is continually falling

• Imagine what the renogram would look like if we gave a constant infusion• The blood activity could be kept constant

• The Rutland method predicts what the constant infusion renogram would look like• Based on the real renogram• And the real blood curve

* Rutland MD Nuc.Med.Comm 6: p11-20 (1985)


Constant Infusion Model

Time

Conc

entra

tion

Kidney

Bladder

ExtravascularTissue

Blood

Conc

entra

tion

Conc

entra

tion

Conc

entra

tion

Time

Time


Rutland Theory

Assumptions:

Define:

K = True kidney counts Vascular background+∫ ×+×= BaBdtUCK

aBBdt

UCBK +

×=

∫

Now:

This is the equation of a straight line with slope ‘UC’ and intercept ‘a’

1) Input rate to kidney is proportional to B2) Nothing leaves during first few minutes3) Vascular background = a x B (where a is a background subtraction factor)

‘Rutland time’

True kidney counts = UC x ∫Bdt(where UC is an uptake constant)

B = Vascular ROI counts Tissue ROI counts(scaled for ROI size)-Blood activity

K = Kidney ROI counts Tissue ROI counts(scaled for ROI size)-Kidney activity

Rutland Plot (Patlak plot)


Rutland Practice• Draw regions of interest• Kidneys• Vascular background

heart or spleen• Tissue backgroundbelow kidney• Bladder

• Generate activity-time curves• Subtract tissue background• from kidneys, bladder and vascular

(scaling only for region size) • Construct Rutland plot for each kidney• Select range of points to fit straight line

L R

Post


Choosing the fit range

*** * *

*

Early points may be below the line (incomplete mixing)

Late points will be below the line (kidney is emptying)

Fit should include just points in

straight section

Typical Rutland Plot


Rutland Practice (continued)• Calculate relative function• Using ratio of slopes from Rutland fit

• Subtract vascular background• Using factor from Rutland fit intercept

• Display background subtracted curves as usual• Guarantees that curves start at zero



Summary - RutlandThe Rutland plot is a mathematical manipulation of the renogram that simulates what would happen if blood activity was constant

Rutland PlotRutland TimeKid

ney C

ounts

/ Bloo

d Cou

nts

U ptake

Blood background Intercept tells us how much blood background to

subtract

Slope is a measure of the kidney function

Deconvolution


Simple Kidney Model

Bolus Input

Uptak

e

Transit Elimination

Impulse Retention Function

Blood Activity

time

time

Kidney Activity

Renal Artery

Renal Vein

Ureter

GlomerulusRenal

Tubules

Renal Pelvis


Mean Transit TimeImpulse Retention Function

MTTIni

tial H

eight

Mean transit time is the average time for a molecule to pass through the system

MTT =Area

Initial height

time

Two areas are equal

H(t)


‘Idealised’ Renogram• Perfect bolus Input• But not practicable• Perfect injection• Direct into renal artery• No recirculation

Blood Activity

time

Uptak

e

Transit Elimination

time

Kidney Activity• Impulse Response• But easy to interpret• Uptake, transit and elimination are separated


But what about the real renogram ?• IV injection• Slow recirculation• Blood activity persists

Blood Activity

time

time

Kidney Activity• Real Renogram• What shape is the kidney curve ? ?


100

50

Must be linearMust be stationary

70 3550%

Convolution

Input time

Response time

50%

50

25

Represent blood curve as series of bolus inputs

50%


Deconvolution

Input time

Response time

50100

50

50%

100

70

50

3624

35

2518

12

50

50100

35

2518

12

50

35 25

181240

40%

28 2014

40100

50100


Convolution

Input time

Response time

I(t) R(t)

H(t)

Bolus

I1I2 I3 I4

R1

R2

R3R4

H1 H2 H4H3


Deconvolution

Input time

Response time

I(t) R(t)

H(t)

Bolus

I1I2 I3 I4

R1

R2

R3R4

H1 H2 H4H3


Teaching Point• Given the input to a system I(t) and the response to that input R(t), you can use deconvolution to calculate the expected response to an ideal impulse input• This is the impulse retention function , H(t)• The impulse retention function is easy to interpret because• The initial height represents uptake• The duration represents transit• The downslope represents elimination


How to do it

• Matrix method• As previous illustration

⋅−∆= ∑−

=+−

1

11

1

1 i

jjji

ii HI

tR

IH

1. ISCORN Consensus report. Durand E, et al Semin.Nucl.Med. 2008, 38:82-1022. “Application of mathematical methods in dynamic nuclear medicine studies”

Lawson RS. Phys. Med. Biol. 1999, 44: R57-98

{ } { }

= )()(1)(

tItR-tH F

FF• Constrained optimisation

• Find smooth solution consistent with noise

• Fourier transform• FT of a convolution is

product of FTs

∑=

+− ∆⋅=i

jjiji tHIR

11)(*)()( tHtItR =


Renogram Deconvolution

Blood Activity Renogram

Bolus Input Impulse Response Function

Deconvolution


Effect of Vascular Background

Blood Activity

Vascular Background

Kidney Activity

+ Renogram

=

Not easy to remove

background

Before Deconvolution


Effect of Vascular Background

Blood Activity

Vascular Background

Kidney Activity

+ Renogram

=

Easy to remove

background

After Deconvolution


Renogram Example - Raw CurvesActivity-time curves

After smoothing


After DeconvolutionImpulse Response Functions

Relative MTTFunction

LEFT 41% 10.5 minRIGHT 59% 4.9 min

After trimming

LEFT KIDNEYRIGHT KIDNEY


Practical Considerations• System must be linear

• OK• System must be stationary

• No furosemide• No large pelvic contractions

• Suitable ROI for blood input• Aorta or heart

With tissue background subtracted• Suitable ROI for kidney contents

• Whole kidney• Renal parenchyma (whole kidney - pelvis)

With tissue background subtracted


More Practical Considerations• Correct start time• Problems if kidney activity appears later than heart• Need good statistics• Use higher administered activity• Must smooth curves

But not too much• Identify plateau of retention function• Difficult if curves are too noisy• Height is used to measure relative function• Extrapolate to remove vascular background• Produce background subtracted renogram • By reconvolving subtracted retention function with blood input curve


Summary - DeconvolutionDeconvolution gives the renogram that would be

obtained if an idealised bolus injectioncould be given straight into the renal artery

with no recirculation

Time

ImpulseRetentionFunction

transit

Uptak

e

Eliminat ion

Mean Transit Time

Vascular Background

Quantitative Parameters


Renogram ComponentsUptakeElimination

Transit

Renogram

Time

Activ

ity Difference = kidney contents

Renogram peaks whenrate of uptake = rate of elimination

Uptake only

Elimination starts

Downslope whenrate of elimination is

greater than rate of uptake


Quantifying Relative FunctionDuring first 2 or 3 minutes there is no elimination• So we can calculate relative uptake from:• Relative counts in summed image• eg 1 to 3 min

Difficult to get correct background subtraction• Relative area under uptake phase of curves• eg from 1 to 3 min

Provided background subtraction is correct• Relative height of impulse retention function• After deconvolution

Provided plateau can be identified• Relative slope of Rutland plot• Using linear fit

Guarantees correct background subtraction


Quantifying Absolute Function• Absolute function is much harder than relative function• Compare kidney activity with administered activity• Using known camera sensitivity

eg Manchester method• By imaging dose syringe firsteg Gates method(Gates GF. Am.J.Roentgenol,1982, 138: 565-70)

• Compare kidney activity with blood curve• Calibrate by taking one blood sample(eg Piepsz A et.al. Eur.J.Nucl.Med. 1977, 2:173-77)

• Proper measurement requires formal blood clearance• Multiple blood samples(ISCORN Report. Blaufox et.al. J.Nucl.Med 1997, 37: 1883-1890)


Quantifying Elimination

Time

Activ

ityIntegrate blood input and fit to uptake phase (Rutland plot)

Difference between zero output and Renogram

= Urine output

RenogramBlood (input)

Uptak

e pha

se

Urine Output / Zero Output= Renal Output Efficiency *

* Chaiwatanarat et. al. J.Nucl.Med. 1993, 34: 845-848

Extrapolate to later times = Zero output curve


We have looked at two Methods• The problem

• Variable input functionComplex curve shape & superimposed background

• The solution• Standardise input function

Simpler curve shape with separable background• Delta function input

• Perfect bolus injectionImpossible in practice

Bolus spreading and recirculation• Constant input

• Continuous infusionPossible but complicated

Rutland plot

DeconvolutionCalculate using:


Comparison of Methods

• Quantifies uptake• Quantifies MTT• Facilitates vascular

background removal• Very sensitive to noise• Sensitive to timing

errors• Spoiled by furosemide

• Quantifies uptake• ?• Facilitates vascular

background removal• Insensitive to noise• Robust against timing

errors• Still OK with furosemide

Renogram Deconvolution Rutland Plot


Summary

Integ

rate

Blood ActivityReal renogram

RenogramKidney

Background

Bolus inputDecon-volution

Impulse Retention Function

Kidney

Background

Constant infusionRutlandRutland plot

Kidney

Background

MTT

MTT


ISCORN ReportsQuantification of the renogram

Prigent A, Cosgriff PS, Gates GF, et al.Consensus report on quality control of quantitative measurements of renal function obtained from the renogram.Semin.Nucl.Med. 1999 29:146-159.

Renal transit timesDurand E, Blaufox MD, Britton KE, et alISCORN Consensus on renal transit time measurements.Semin.Nucl.Med. 2008, 38:82-102

Renal clearanceBlaufox MD, Aurell M, Bubeck B et al. Report of the Radionuclides in Nephrourology Committee on renal clearance. J Nucl Med 1997; 37:1883-1890.

Documents

Quantitative Methods in Renography - Pages - Homenucleus.iaea.org/.../Quantitative_Methods_in_Renography.pdfQuantitative Methods in Renography Radionuclides in Nephrourology, Mikulov