Quantitative Methods in Renography - Nucleus

Radionuclides in Nephrourology, Mikulov 2010 

Quantitative Methods in 

Renography 

Richard Lawson 

Central Manchester Nuclear Medicine Centre 

Richard.Lawson@manchester.ac.uk


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 

Central Manchester Nuclear Medicine Centre

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 function 

one kidney compared with the other 

• Absolute function 

each 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 

Extravascular 

Tissue 

Blood 

Kidney 

Tubules + pelvis 

Bladder 

Concentration Concentration Concentration Concentration 

Time 

Time 

Time 



Renogram Model 

Extravascular 

Tissue 

Concentration 

Time 

This is the 

curve that 

we want 

Blood 

Kidney 

Tubules + pelvis 

Bladder 

Concentration Concentration Concentration 

Time 

Time 



Regions of Interest 

Each kidney ROI includes 

• Renal blood vessels 

• Renal tubules 

• Renal pelvis 

• Overlying tissues 

Background ROI includes 

• Some blood vessels 

• Some tissues 

Renogram 

Kidney minus background 

• Should leave desired renogram 

} 

Blood background 

Tissue background 


Tissue background 

The optimum background ROI must include the 

correct mixture of both blood and tissue background 



Background Subtraction 

Kidney ROI curve 

cps 


Tissue 

+ Renal tubules 

& Renal pelvis 

+ Blood 

Time 

Background ROI curve 

cps 

Tissue 

+ Blood 

Time 

cps 

Background subtracted 

Renal tubules 

& Renal pelvis 

Time 

If background 

subtraction is correct, 

renogram curve should 

rise smoothly from zero 


Mixing 

• During the first few seconds after injection 

• Tracer has not had enough time to mix uniformly 

throughout all of the blood 

Therefore 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 patients 

Often about 30 seconds 

Possibly up to 1 minute 



Recognising Correct Subtraction 

Curve is not 

smooth during 

first minute 

Extrapolate to 

overcome 

mixing phase 

0 1 2 3 4 

5 min 

Question 1: Is this renogram curve correctly subtracted ? 

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

Answer: Under-subtracted 




0 1 2 3 4 




Answer: Over-subtracted 




0 1 2 3 4 




Answer: Correct subtraction – after extrapolation 




If curve has a 

kink during first 

minute then 

extrapolate to 

overcome 

mixing phase 

Under-subtracted 

Correctly subtracted 

Over-subtracted 

0 1 2 3 4 




Three Phases of the Renogram 

Phase 1 

(Vascular) 

Phase 2 

(Uptake) 

Phase 3 

(Elimination) 

Textbooks 

3 phases 

Renogram model 

No vascular phase 

• 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 



Teaching Point 

• Background subtraction is correct when the 

renogram curve rises smoothly from zero 

After extrapolating to overcome incomplete mixing 

during the first minute 

Assuming 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 99m Tc MAG3 

• Good uptake in both kidneys 

• Both kidneys equal function 



Example 1 – Background below kidney 

Relative function 

Left kidney: 50% 

Right kidney: 50% 

Right Kidney 

Left Kidney 

Question 4: Are these curves correctly subtracted ? 


Answer: Slight under-subtraction 



Example 1 – Peri-renal background 




Left Kidney 

Right Kidney 



Answer: Very slight under-subtraction 



Example 1 – Rutland method 

L 

R 





Answer: Correct subtraction 

Right Kidney 

Left Kidney 





• If using MAG3 and kidney function is good 

Using different background regions only makes a 

small difference to background subtraction 

• If both kidneys have equal function 

Then under-subtracting doesn’t alter relative 

function significantly 



Example 2 

• 50MBq 99m Tc MAG3 

• Both kidneys poor function 

• Right worse than left 



Example 2 – Background below kidney 

L 

R 




Right Kidney 

Left Kidney 



Answer: Significantly under-subtracted – after extrapolation 




L 

R 





Answer: Over-subtracted 

Right Kidney 

Left Kidney 





L 

R 




Right Kidney 

Left Kidney 



Answer: Correct subtraction – after extrapolation 




• 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 asymmetric 

Then incorrect background subtraction can 

affect relative function measurement 



Example 3 

• 50 MBq 99m Tc MAG3 

• Left kidney good function 

• Right kidney hydronephrotic 



Example 3 - Background below kidney 

L 

R 

Right Kidney 




Left Kidney 

Question 10: Is the right kidney curve correctly subtracted ? 


Answer: Under-subtracted 


Left kidney little under-subtracted 



L 

R 

Right Kidney 




Left Kidney 



Answer: Over-subtracted But left kidney is OK 




L 

R 

Right Kidney 




Left Kidney 



Answer: Correct subtraction 


For both kidneys 



• If the vascularity of each kidney is different 

Then 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 

Extravascular 

Tissue 

Blood 

Kidney 

Bladder 

Concentration Concentration Concentration Concentration 

Time 

Time 

Time 



Define: 

Blood activity 

Kidney activity 

Assumptions: 

Now: 


Rutland Theory 

B = Vascular ROI counts 

K = True kidney counts + Vascular background 

⎛ 

⎜ 

⎝ 

K = Kidney ROI counts 

1) Input rate to kidney is proportional to B 

2) Nothing leaves during first few minutes 

3) Vascular background = a x B (where a is a background subtraction factor) 

K 

K 

B 

⎞ 

⎟ 

⎠ 

= UC × ∫ Bdt + a× 

B 

⎛ Bdt ⎞ 

UC ⎜∫ 

= × ⎟ + a 

⎜ B ⎟ 

⎝ ⎠ 

Tissue ROI counts 

(scaled for ROI size) 

True kidney counts = UC x ∫Bdt 

(where UC is an uptake constant) 

‘Rutland time’ 

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

- 

- 

Tissue ROI counts 

(scaled for ROI size) 

Rutland Plot 

(Patlak plot) 


Rutland Practice 

• Draw regions of interest 

L 

• Kidneys 

• Vascular background 

heart or spleen 

• Tissue background 

below 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 

R 

Post 



Choosing the fit range 

* 

Fit should include 

just points in 

straight section 

* 

* * * * 

Typical Rutland Plot 

Late points will be below the line 

(kidney is emptying) 

Early points may be below the line 

(incomplete mixing) 



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 - Rutland 

The Rutland plot is a mathematical manipulation 

of the renogram that simulates what would 

happen if blood activity was constant 

Kidney Counts / Blood Counts 

U ptake 


Rutland Plot 

Slope is a 

measure of the 

kidney function 

Rutland Time 

Intercept tells us 

how much blood 

background to 

subtract 



Deconvolution

Simple Kidney Model 

Renal 

Artery 

Renal 

Vein 

Blood Activity 

Bolus Input 

Renal 

Tubules 

Glomerulus 

Kidney Activity 

Transit 

time 

Elimination 

Renal 

Pelvis 

Uptake 

Impulse 

Retention 

Function 


Ureter 

time 


Mean Transit Time 

Impulse Retention Function 

MTT 

Mean transit time is 

the average time for 

a molecule to pass 

through the system 

Initial Height 

H(t) 

Two areas are equal 

Area 

MTT = 

Initial height 


time 


‘Idealised’ Renogram 


• Perfect bolus Input 

• But not practicable 

• Perfect injection 

• Direct into renal artery 

• No recirculation 

time 

• Impulse Response 

• But easy to interpret 

• Uptake, transit and 

elimination are separated 

Uptake 


Transit 



time 


But what about the real renogram ? 


• IV injection 

• Slow recirculation 

• Blood activity persists 

time 


• Real Renogram 

• What shape is the 

kidney curve ? ? 


time 


Convolution 

100 

Must be linear 

Must be stationary 

50% 

50% 

70 35 

25 

50 

50% 

50 


Input 

time 

Represent blood curve as 

series of bolus inputs 

Response 

time 


Deconvolution 

100 

70 

50 

100 

50 

100 

50 

100 

50% 

40 

100 

25 

18 

50 

36 

24 

40% 

35 

35 

25 

35 

12 

18 

25 

12 

18 

Input 

time 

50 

50 

50 

40 

28 

20 

12 

14 


Response 

time 


Convolution 

Bolus 

R 4 

R 3 

I(t) 

R 2 

I 1 

I 2 R 1 

I 3 

I 4 

R(t) 

Input 

time 

H(t) 

H 1 H 2 H 3 H 4 


Response 

time 


Deconvolution 

Bolus 

R 4 

R 3 

I(t) 

R 2 

I 1 

I 2 R 1 

I 3 

I 4 

R(t) 

Input 

time 

H(t) 

H 1 H 2 H 3 H 4 


Response 

time 



• 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 

R ( t) 

= I( 

t) * H ( t) 

R 

i 

= 

i 

∑ 

j= 

1 

I 

j 

⋅ 

H 

i−j+ 

1∆ 

t 

• Matrix method 

• As previous illustration 

• Fourier transform 

• FT of a convolution is 

product of FTs 

H 

i 

⎡ 

i 

1 R 

− i 

= ⎢ −∑ I1 

⎣∆t 

j= 

⎛ 

H ( t) 

= F 

-1 

⎜ 

⎝ 

• Constrained optimisation 

• Find smooth solution consistent with noise 

F 

1 

1 

I 

i−j+ 

1 

{ R( 

t) 

} 

F 

⋅ H 

j 

⎥ 

⎦ 

⎤ 

⎞ 

{ I( 

t) 

} ⎟ ⎠ 

1. ISCORN Consensus report. Durand E, et al Semin.Nucl.Med. 2008, 38:82-102 

2. “Application of mathematical methods in dynamic nuclear medicine studies” 

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



Renogram Deconvolution 


Deconvolution 

Renogram 


Bolus Input 

Impulse Response Function 


Effect of Vascular Background 

Before Deconvolution 


= 


+ 

Renogram 


Vascular Background 

Not easy to 

remove 

background 


Effect of Vascular Background 

After Deconvolution 


= 


+ 

Renogram 

Vascular Background 

Easy to 

remove 

background 



Renogram Example - Raw Curves 

Activity-time curves 

After smoothing 



After Deconvolution 

Impulse Response Functions 

Relative 

Function 

MTT 

LEFT 41% 10.5 min 

RIGHT 59% 4.9 min 

After trimming 

RIGHT KIDNEY 

LEFT 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 - Deconvolution 

Deconvolution gives the renogram that would be 

obtained if an idealised bolus injection 

could be given straight into the renal artery 

with no recirculation 

Impulse 

Retention 

Function 

Uptake 

transit 

Vascular 

Background 

Mean Transit Time 

Eliminat ion 


Time 


Quantitative Parameters

Renogram Components 

Uptake 


Activity 


starts 

Uptake 

only 

Transit 

Renogram peaks when 

rate of uptake = rate of elimination 

Difference 

= kidney 

contents 

Downslope when 

rate of elimination is 

greater than rate of uptake 

Renogram 


Time 



Quantifying Relative Function 

During 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 first 

eg 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 

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

Extrapolate to later times = Zero output curve 

Activity 

Uptake phase 

Difference between 

zero output and 

Renogram 

= Urine output 

Urine Output / Zero Output 

= Renal Output Efficiency * 

Renogram 

Blood (input) 

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

Time 



We have looked at two Methods 

• The problem 

• Variable input function 

Complex curve shape & superimposed background 

• The solution 

• Standardise input function 

Simpler curve shape with separable background 

• Delta function input 

• Perfect bolus injection 

Impossible in practice 

Bolus spreading and recirculation 

Calculate using: 

Deconvolution 

• Constant input 

• Continuous infusion 

Possible but complicated 

Rutland plot 



Comparison of Methods 

Renogram 

Deconvolution 

• Quantifies uptake 

• Quantifies MTT 

• Facilitates vascular 

background removal 

• Very sensitive to noise 

• Sensitive to timing 

errors 

• Spoiled by furosemide 

Rutland Plot 

• Quantifies uptake 

• ? 

• Facilitates vascular 

background removal 

• Insensitive to noise 

• Robust against timing 

errors 

• Still OK with furosemide 



Summary 

Real 

renogram 


Kidney 

Background 

Renogram 

Deconvolution 

Bolus input 

Background 

Kidney 

MTT 

Impulse 

Retention 

Function 

Rutland plot 

Integrate 

Rutland 

Constant infusion 

Kidney 

MTT 

Background 




ISCORN Reports 

Quantification 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 times 

Durand E, Blaufox MD, Britton KE, et al 

ISCORN Consensus on renal transit time measurements. 

Semin.Nucl.Med. 2008, 38:82-102 

Renal clearance 

Blaufox MD, Aurell M, Bubeck B et al. 

Report of the Radionuclides in Nephrourology Committee on renal 

clearance. 

J Nucl Med 1997; 37:1883-1890.

Quantitative Methods in Renography - Nucleus

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