--Manuscript Draft-- University of Saskatchewan Royal University Hospital Saskatoon, Saskatchewan CANADA. Gary R Conrad, M.D.

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1 European Journal of Nuclear Medicine and Molecular Imaging A simple method for determining split renal function from dynamic mtc-mag scintigraphic data --Manuscript Draft-- Manuscript Number: Full Title: Article Type: Corresponding Author: EJNM-D--00R A simple method for determining split renal function from dynamic mtc-mag scintigraphic data Original Article Carl A. Wesolowski, M.D. University of Saskatchewan Royal University Hospital Saskatoon, Saskatchewan CANADA Corresponding Author Secondary Information: Corresponding Author's Institution: University of Saskatchewan Royal University Hospital Corresponding Author's Secondary Institution: First Author: Michal J Wesolowski, Ph.D. First Author Secondary Information: Order of Authors: Michal J Wesolowski, Ph.D. Gary R Conrad, M.D. Martin Šámal, M.D., Ph.D. Gage Watson, M.D. Surajith N. Wanasundara, Ph.D. Paul Babyn, M.D. Carl A. Wesolowski, M.D. Order of Authors Secondary Information: Funding Information: Sylvia Fedoruk Canadian Centre for Nuclear Innovation (J01-1) Czech Science Foundation (0/0/00) Carl A. Wesolowski Martin Šámal Abstract: Purpose: Commonly used methods for determining split renal function (SRF) from dynamic scintigraphic data require extrarenal background subtraction and additional correction for intrarenal vascular activity. Use of these additional regions of interest (ROIs) can produce inaccurate results and be challenging, e.g. if the heart is out of the camera field of view. The purpose of this article is to evaluate a new SRF method, called the Blood Pool Compensation (BPC) technique, which is simple to implement, does not require extrarenal background correction and intrinsically corrects for intrarenal vascular activity. Methods: In the BPC method SRF is derived from a parametric plot of the curves generated by 1 blood-pool and renal ROIs. Data from patients who underwent mtc-mag scintigraphy were used to determine SRF values. Values calculated using the BPC method were compared to those obtained from the Integral (IN) and Patlak-Rutland (PR) techniques using Bland-Altman plotting and Passing-Bablok regression. The interobserver variability of the BPC technique was also assessed for two observers. Results: The SRF values from the BPC method did not differ significantly from those obtained by PR and showed no consistent bias, while SRF values obtained with the IN Powered by Editorial Manager and ProduXion Manager from Aries Systems Corporation

2 technique showed significant difference with some bias in comparison to those obtained using either the PR or BPC methods. No significant interobserver variability was found between two observers calculating SRF using the BPC method. Conclusion: The BPC method requires only regions of interest to produce reliable estimates of split renal function, was simple to implement, and in this study yielded statistically equivalent results to the PR method with appreciable interobserver agreement. As such, it adds a new reliable method for quality control of monitoring relative kidney function. Response to Reviewers: Powered by Editorial Manager and ProduXion Manager from Aries Systems Corporation

3 Manuscript Click here to download Manuscript Split Renal Function Corrected Submission Sept 0.docx Click here to view linked References 1 A simple method for determining split renal function from dynamic Tc-MAG scintigraphic data Michal J. Wesolowski 1, Gary R. Conrad, Martin Šámal, Gage Watson 1, Surajith N. Wanasundara 1, Paul Babyn 1, Carl A. Wesolowski 1, 1 1. Department of Medical Imaging, University of Saskatchewan, Saskatoon, SK, Canada, SN 0W.. Department of Radiology, University of Kentucky College of Medicine, Lexington, KY, U.S.A. 0.. Department of Nuclear Medicine, First Faculty of Medicine, Charles University Prague & the General 1 University Hospital in Prague, CZ- 00 Praha, Czech Republic Department of Radiology, Memorial University of Newfoundland, St. John s NL, Canada A1B V 0 1 Abstract Purpose Commonly used methods for determining split renal function (SRF) from dynamic scintigraphic data require extrarenal background subtraction and additional correction for intrarenal vascular activity. Use of these additional regions of interest (ROIs) can produce inaccurate results and be challenging, e.g. if the heart is out of the camera field 0 of view. The purpose of this article is to evaluate a new SRF method, called the Blood Pool Compensation (BPC) 1 technique, which is simple to implement, does not require extrarenal background correction and intrinsically corrects for intrarenal vascular activity. Methods In the BPC method SRF is derived from a parametric plot of the curves generated by 1 blood-pool and renal ROIs. Data from patients who underwent m Tc-MAG scintigraphy were used to determine SRF values. Values calculated using the BPC method were compared to those obtained from the Integral (IN) and Patlak-Rutland (PR) 0 1 techniques using Bland-Altman plotting and Passing-Bablok regression. The interobserver variability of the BPC technique was also assessed for two observers. Results The SRF values from the BPC method did not differ significantly from those obtained by PR and showed no consistent bias, while SRF values obtained with the IN technique showed significant difference with some bias in comparison to those obtained using either the PR or BPC methods. No significant interobserver variability was found between two 0 observers calculating SRF using the BPC method. 1 Conclusion The BPC method requires only regions of interest to produce reliable estimates of split renal function, was simple to implement, and in this study yielded statistically equivalent results to the PR method with appreciable interobserver agreement. As such, it adds a new reliable method for quality control of monitoring relative kidney function

4 Introduction Split renal function (SRF) is defined as the relative contribution of each kidney to total renal function. The SRF is useful to distinguish between symmetric and asymmetric renal conditions, to diagnose renovascular hypertension, and to evaluate renal function in obstructive uropathy or urolithiasis within the perioperative setting. While computed tomography [1] and three dimensional magnetic resonance imaging [] have been developed for measuring SRF, dynamic radionuclide renography with intravenous bolus injection of m Tc-DTPA ( m Tc-diethylenetriamine-pentaacetic acid), or m Tc-MAG ( m Tc-mercapto-acetyl triglycine) remains the mainstay for SRF quantification. The resulting renal time-activity curves (TACs) are typically analyzed during the phase of increasing activity, following the bolus first pass, during a time when excreted tracer is held in the kidney, prior to its first appearance outside of the kidney region of interest (ROI). This typically occurs between 1 -. min.values of SRF are then calculated from these curves. Several competing mathematical methods are currently used to extract quantitative data from renograms, these include; the integral, mean slope, normalized slope, and double background correction techniques like Patlak-Rutland plotting. To process renography data for the purpose of determining SRF, both the integral (IN) and Patlak-Rutland (PR) methods have been recommended by published international consensus []. The IN method requires generation of an area normalized extrarenal background ROI for each kidney, for a total of four ROIs. After background subtraction, the method compares the total activity under the uptake portion of the time-activity curve of each kidney [, ]. The accuracy of the integral technique has been shown to be dependent on background subtraction, with a perirenal ROI contouring the entire kidney being acknowledged as representative of a good compromise between extrarenal and the intrarenal background correction []. Under-subtraction of renal blood pool from the renal ROI counts can lead to an overestimation of corrected renal activity []. This overestimation can be increasingly problematic for greater severities of asymmetric renal disease. PR plotting is used in an attempt to avoid this overestimation by removing the remaining vascular activity in the renal ROI following perirenal background subtraction. Similar to IN, PR requires area-normalized background-correction for the kidneys, the corrected kidney TACs then being scaled and fitted to a scaled integral of the cardiac TAC, requiring a total of five ROIs. While the PR method has been shown to be generally robust, with good precision and accuracy, it requires

5 that the gamma camera be positioned to include the heart, which can result in the exclusion of the distal ureters and bladder from the field-of-view in many adult examinations. The PR method is also mathematically complex, requiring several steps, which can lead to systematic errors [-]. The need for five carefully positioned ROIs and a dedicated numerical analysis application increase time and expense when using this technique. Developpment of a simplier SRF technique, which has less dependence on the operator is therefore desireable. This paper presents a simplified method for determining SRF from scintigraphic data, referred to as the blood pool compensation (BPC) technique, which only requires generation of a single hepatic ROI in addition to the two standard renal ROIs. To explore the quality of this method the SRF is calculated for a large patient series (n = ) with wide range of renal function. The resulting BPC SRF values are then compared to those from the IN and PR techniques. The interobserver variability between two observers using the BPC method is also assessed. Methods Patient Data Patient data were obtained from the Database of Dynamic Renal Scintigraphy []. These data were recorded in 00 as part of nuclear medicine services at the General University Hospital in Prague and were collected in compliance with local ethical committee requirements. The study population included men (%) and women (%) ranging from - (mean.1) years of age and suffering from a broad spectrum of kidney or urinary tract diseases, including; chronic renal disease, diabetic and ischaemic nephropathy, recurrent infection, chronic pyelonephritis, nephrosclerosis, polycystic kidneys, and carcinoma of urinary bladder, and nonspecific chronic renal disease among other conditions. In the examined patient population, single blood sample m Tc-MAG plasma clearance [1], had an overall range of - 1 ml/min/1.m with an average value of 10 ± 1 ml/min/1.m with Data Collection After establishing hydration, renal scintigraphy was acquired for n = patients in the posterior projection using a gamma camera positioned to include both kidneys and heart in the field-ofview. Beginning just prior to age-adjusted bolus injection ranging from - 01 MBq of m Tc- MAG, a dynamic acquisition was performed. Standard posterior projection imagess used in this study were collected in 1x1 pixel image matrices. Images (s per frame) were collected for

6 min for a total of 10 frames. The beginning of the study (t = 0) was set to the peak cardiac bolus activity. Additional details of the data base and its collection can be found on the website []. Data Processing The ROIs were drawn manually for the liver, heart, tissue background, and kidneys in compliance with recommendations from the International Scientific Committee of Radionuclides in Nephrourology (ISCORN) []. For absent kidneys, renal ROIs were drawn over soft tissues at the expected site of the absent kidney, with curve generation and processing proceeding as if a kidney were present. These ROIs were used to construct TACs and these curves were then processed using IN, PR and BPC methods to determine the SRF for each patient using custom software code developed in MATLAB []. Integral Method (IN) The activity in each perirenal background ROI was area-normalized to its respective kidney ROI, and the scaled perirenal TAC was subtracted from corresponding renal TAC. The relative function of each kidney was then determined from the total counts (area under the time activity curve) during the cumulative uptake portion of the curve. Patlak Rutland Method (PR) The extrarenal, mainly interstitial background activity in the kidney ROI was first corrected using a perirenal background ROI. The background corrected kidney counts were then normalized by the counts from a cardiac ROI, resulting in the use of ROIs ( kidneys, perirenal backgrounds, 1 heart). These values were then plotted as a function of the integral of the cardiac counts which were also normalized by the cardiac activity. The mean slope of the ascending portion of this graph, which for MAG is commonly between 1-. min, but may vary from patient to patient, was then determined for each kidney and used to measure the relative function []. The Blood Pool Compensation Method (BPC) To determine the SRF using the BPC method, ROIs (Fig. 1a) were used to generate TACs (Fig. 1b) and a parametric plot of kidney counts versus liver counts during the uptake interval was made for each kidney (Fig.1c). A linear fit in this parametric graph is then back extrapolated to the zero liver count rate axis giving the count rate that the kidney has for zero count per min from blood pooling (Fig. 1c). In other words, the y-axis intercept of the regression line represents the activity

7 in the kidney when the kidney region of interest would contain no blood pooling. Here, blood pool is defined as the vascular plus interstitial organ activity during the ascending portion of the TAC. Compensation for the vascular background is therefore intrinsic in this method as the parametric plot is used to isolate the renal extraction. As such, no area weighted subtraction for extravascular or extrarenal background is required. A physiological explanation and mathematical illustration of the BPC model is presented in the Appendix. relationship; The percent of total function for the left kidney (SRFLK) is determined by the simple SRF LK = LK Int LK Int + RK Int 0 where LK Int and RK Int represent the activities from the left kidney and right kidney intercepts respectively (Fig.1b). Statistical Analysis Comparison of three methods Bland-Altman plotting and Passing-Bablok regression analysis were used to compare the left kidney SRF percentage calculated using the IN, PR, and BPC methods. In a conventional Bland- Altman plot, the relationship between the difference and magnitude of two methods of measurement is expressed graphically, as are the mean of the differences and the % limits of agreement [, ]. This method allows for quick visualization of proportional and systematic bias as well as the identification of outliers. The Passing-Bablok linear regression procedure makes no special assumptions regarding the sample distribution or measurement errors and is used to quantify bias when comparing methods [, 1]. When the intercept of the Passing-Bablok regression line has a % confidence interval that contains the value zero, there is less than a % likelihood of a systematic difference between two methods. Similarly, if the slope of the regression line has a value of one within the % confidence interval there is not likely to be a proportional difference between the methods. Interobserver variability of BPC method To test the variability of the BPC method, SRF values for each of the patients within this series were calculated using ROI time activity data gathered from two different observers, one an

8 undergraduate medical student without any prior expertise (GW) and the other a practicing nuclear medicine physician (MS). The disparity in the experience of the observers should provide a measure of the maximum possible variability in the BPC method. Results Comparison of three methods Bland-Altman plots, comparing each of the three methods are shown in Fig. and a summary of the plot parameters is provided in Table 1. Fig. a illustrates the relationship between the Integral and Patlak-Rutland (IN-PR) methods and suggest that the left kidney SRF calculated using the IN method systematically underestimates the left kidney SRF calculated by the PR method. The clear negative slope of the data also suggests a proportional bias in which the IN method overestimates lower SRF values and underestimates higher SRF values, when compared to the values obtained by the PR method. The differences between these methods have a mean value of 1.% and a limits of agreement range of 1.0%. A similar relationship is observed in Fig. b which compares the Integral and Blood Pool Compensation (IN-BPC) methods. As was the case when comparing the IN-PR methods, the IN method systematically produced lower left kidney SRF values than those calculated using the BCP method and shows proportional bias, overestimating low SRF values and underestimating high SRF values. The differences between SRF percentages calculated using these methods have a mean value of 1.% and a limits of agreement range of 1.1%. Finally, Fig. c shows the differences between the Patlak-Rutland and Blood Pool Compensation methods (PR-BPC). In this case, the differences between values of SRF calculated using the PR and BPC methods showed the smallest systematic variation with a mean difference of 0.%, no significant proportional bias and limits of agreement range of.%. Passing-Bablok regression analysis comparing the IN, PR and BPC methods is shown in Figure and summarized in Table 1. Fig. a shows statistically significant differences between IN and PR, with a systematic bias (intercept) of.0% (% CI.0% to.%) and a proportional bias (slope) of 0. (% CI of 0. to 0.). Fig b, shows that similar biases occur between the IN and BPC methods, with a systematic bias of.% (% CI.% to.%) and a proportional bias of 0. (% CI of 0.0 to 0.). Excellent statistical agreement was found between the PR and BPC methods, as shown in Fig. c, with an insignificant systematic bias of 0.% (% CI 1.% to 0.1%), as zero bias is within the confidence limits, and an insignificant proportional

9 bias of 1.01 (% CI of 0. to 1.0), with a slope of one within the confidence interval. In summary, the PR and BPC methods agreed with each other to within a two percent error, and the slope and intercept interrelating the PR and BPC methods were not significantly different from the identity line. Interobserver variability of BPC method Fig. a shows Bland-Altman difference plot and Fig. b presents the Passing-Bablok regression of the left kidney SRF obtained by two different observers. The differences between SRF values from each observer, shown in Fig. a, have a mean value of 0.%, limits of agreement of.0% to.% and no proportional bias is evident in the data plot. Fig b illustrates the results from Passing-Bablok regression and shows good agreement between SRF values calculated by the two observers with a constant bias of 0.% (% CI 0.% to 1.%) which is insignificant as zero is within the confidence limits and a proportional bias of 0. (% CI of 0. to 1.01) not significantly different from one within the confidence interval. Thus, the calculated SRF values did not significantly differ between two observers using the BPC method. Discussion Both IN and PR techniques have been used extensively to calculate relative kidney function from dynamic renal scintigraphic data [-]. Values of SRF calculated using the IN method were found to be statistically different from those of the PR and BPC methods and this behaviour was shown to vary with the degree of asymmetry of relative function. This result is similar to that shown perviously for m Tc-DTPA renography in which SRF values calculated using IN and PR methods showed limited correlation in a group of patients with unilateral kidney tumours []. In that work, the IN method was also found to systematically estimate a higher fraction of renal function on the tumour side compared to that found by the PR method, while little difference was found between the SRF values in a control group of patients. In the current study of patients with a variety of renal diseases who underwent m Tc-MAG renography, the IN method was shown to overestimate the SRF in kidneys with low relative function and underestimate the SRF in kidneys with high relative function when compared to the values from PR and BPC methods, as shown in Fig. a. This finding corroborates with prior work in patients with asymmetric renal disease in

10 which the IN method was shown to undereste the contribution of blood pool activity to total kidney activity [, ]. Both the PR and BPC methods effectively counterbalanced the intrarenal vascular contribution to total renal activity in this study, and the two methods were shown to be statistically indistinguishable. PR plotting has been shown to be an accurate, precise and robust method for determining split renal function, but involves multiple steps and in certain pediatric cases has been shown to be difficult to implement severe outliers from the slope fit [1]. The BPC technique is simple to implement and provides values of split function that are statistically identical to those of the PR method. In this respect, BPC can provide an additional measure of quality control for the calculation of SRF. Besides the simplicity of the BPC technique when compared to PR plotting, the BPC method offers the flexibility of lowering the position of the gamma camera to include the urinanry bladder, thereby eliminating the PR requirement of sampling the heart. Many contemporary renal scan referrals are for investigation of hydronephrosis, and identification of the time of first visualization of the urinary bladder is desirable and sometimes diagnostic. The BPC method, was also shown herein to be robust, with no significant differences between SRF values obtained from two different observers having disparate levels of training and no prior communication. The BPC interobserver variability was found to be comparable to interobserver variability reported for the Patlak-Rutland method [1]. It should be noted that the patient population studied here consisted mainly of adults and as such the BPC technique has not been applied to a fully pediatric patient pool. This is an important next step in validating the method and a retrospective study of a large cohort of pediatric patients is currently under investigation. Conclusion Values of split renal function determined using our newly developed Blood Pool Compensation (BPC) technique did not significantly differ from those calculated through Patlak-Rutland (PR) plotting. The Integral (IN) method was found to produce split renal function values that differed from both the BPC and PR methods. The BPC technique was also found to have excellent agreement between two observers. The new BPC technique produces similar values of relative kidney function with fewer operator steps than the PR method. The data in this study show the

11 BPC method compensates for intrenal vacular activity with only ROIs. As such, it represents a new reliable method for quality control in the calculation of split renal function. Compliance with Ethical Standards Funding: This work was partially supported by funding from the Sylvia Fedoruk Canadian Centre for Nuclear Innovation (grant no. J01-1) and data collection for the database of dynamic renal study was supported by the Czech Science Foundation (grant no. 0/0/00). Conflict of Interest: The authors declare that they have no conflict of interest. Ethical approval: All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1 Helsinki declaration and its later amendments or comparable ethical standards. Informed consent: Informed consent was obtained from all individual participants included in the study. Prior Presentation: A subset of this material was presented in a preliminary form as a poster at the XV ISCORN meeting in Varese, Italy 0//-1. References 1. Summerlin AL, Lockhart ME, Strang AM, Kolettis PN, Fineberg NS, Smith JK. Determination of split renal function by D reconstruction of CT angiograms: a comparison with gamma camera renography. Am J Roentgenol. 00;:-.. Lee VS, Rusinek H, Noz ME, Lee P, M. R, Kramer EL. Dynamic three-dimentional MR renography for the measurement of single kidney function: Initial experience. Radiology. 00;:-.. Prigent A, Cosgriff P, Gates GF, Granerus G, Fine EJ, Itoh K, et al. Consensus report on quality control of quantitative measurements of renal function obtained from the renogram: International Consensus Committee from the Scientific Committee of Radionuclides in Nephrourology. Semin Nucl Med. 1;:-.. Piepsz A, Tondeur M, Ham H. Relative mtc-mag renal uptake: Reproducibility and accuracy. J Nuc Med. 1;0:-.. Moonen M, Jacobsson L, Granerus G, Friberg P, Volkmann R. Determination of split renal function from gamma camera renography: a study of three methods. Nuc Med Comm. 1;:0-.. Piepsz A, Dobbeleir A, Ham H. Effect of background correction on seperate technetium- m-dtpa renal clearance. J of Nuc Med. 10;1:0-.. Rutland MD. A comprehensive analysis of renal DTPA studies. I. theory and normal values. Nuc Med Commu. 1;:-0.. Piepsz A, Kinthaert J, Tondeur M, Ham HR. The robustness of the Patlack-Rutland slope for determination of split renal function. Nuc Med Comm. 1;1:1-1.

12 Patlak CS, Blasberg RG, Fenstermacher JD. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. J Cereb Blood Flow Metab. 1;:1-.. Fleming JS, Kemp PM. A comparison of deconvolution and the Patlak-Rutland plot in renography analysis. J Nuc Med. 1;0:0-.. Šámal M, Piepsz A, Brolin G, Heikkinen JO, Valoušek J. Database of dynamic renal scintigraphy Russell CD, Taylor A, Eshima D. Estimation of technetium-m-mag plasma clearance in adults from one or two blood samples. J Nuc Med. 1;0:1-.. MATLAB and Statistics Toolbox Release 0a ed. Natick, Massachusetts, United States.: The MathWorks, Inc.; 0.. Bland JM, Altman DG. Applying the right statistics: analyses of measurement studies. Ultrasound Obst Gyn. 00;:-.. Bland JM, Altman DG. Statistical methods for assesing agreement betyween two methods of clinical measurement. Lancet. 1;:0-.. Passing H, Bablok W. A new biometrical procedure for testing the equality of measurements from two different analytical methods. J Clin Chem Clin Bioc. 1;1: Bablok W, Passing H. Application of statistical procedures in analytical instrument testing. J Autom Chem. 1;():-. 1. Tondeur M, Nogarede C, Donoso G, Piepsz A. Inter- and intra-observer reproducibility of quantitative renographic parameters of differential function and renal drainage in children. Scand J Clin Lab Invest. 0;:-1.

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14 Figure 1 shows in sample case illustrating the BPC method. Panel a) presents a summed image over 1-. minutes from m Tc-MAG scintigraphy showing liver, right and left kidney region-ofinterest selections. Panel b) illustrates activity versus time curves generated from the ROIs in a) over 0 minutes, while c) shows parametric plot of kidney verus liver counts during the uptake portion (~1-. min) of these curves, with their corresponding fit lines extrapolated forward in time, to intercept with the zero liver count axis. Split renal function is obtained from the ratio of the intercepts. 1

15 Figure Bland-Altman difference plots are shown for, a) the Integral and Patlak-Rutland methods, b) the Integral and Blood Pool Compensation methods and, c) the Patlak-Rutland and Blood Pool Compensation methods. The solid (blue) line represents the mean of the differences between techniques, while the dashed (red) lines represent the limits of agreements to within 1. standard deviations.

16 Figure Passing-Bablok regressions are shown for a) the Integral and Patlak-Rutland methods (intercept.0%, % CI.0% to.%; slope 0., % CI 0. to 0.), b) the Integral and Blood Pool Compensation methods (intercept.%, % CI.% to.%; slope 0., % CI 0.0 to 0.) and c) the Patlak-Rutland and Blood Pool Compensation methods (intercept 0.%, % CI 1.% to 0.1%; slope 1.01, % CI of 0. to 1.0). The solid (red) line represents the linear Passing- Bablok regression line, while the dashed (black) line represent the identity line.

17 Figure illustrates the interobserver variability of the Blood Pool Compensation method, with a) showing a Bland-Altman plot of the differences between left kidney SRF % calculated from data collected by two different observers and b) showing a Passing-Bablok regression (intercept +0.%, % CI 0.% to 1.%; slope 0., % CI of 0. to 1.01). In a) the solid (blue) line represents the mean of the differences, while the dashed (red) lines represent the limits of agreement. In b) the solid (red) line represents the Passing-Bablok regression line and the dashed (black) line is the identity line.

18 Table 1 Parameters for Bland-Altman plots and Passing-Bablok regression derived from comparison of three methods of split renal function measurement; Integral, Patlak-Rutland and the newly developed Blood Pool Compensation. Parameters used in the assessment of the interobserver variability of the Blood Pool Compensation method are also presented. Comparison of methods IN-PR IN-BPC PR-BPC BPC1-BPC Bland-Altman Parameters MD ± SE (LK SRF %) -1. ± ± ± ± 0.0 SD MD + 1. SD ± SE (LK SRF %). ± 0.. ± 0.. ± 0.. ± 0. MD - 1. SD ± SE (LK SRF %) -. ± ± ± ± 0. Passing-Bablok Parameters Slope 0. S 0. S 1.01 NS 0. NS Slope % CI 0. to to to to 1.01 Intercept.0 S. S 0. NS 0. NS Intercept % CI.0 to.. to. 1. to to 1. MD: Mean of Difference, SE: Standard Error, LK: Left Kidney, SRF: Split Renal Function, SD: Standard Deviation, CI: Confidence Interval IN-PR: Integral compared to Patlak-Rutland IN-BPC: Integral compared to Blood Pool Compensation PR-BPC: Patlak-Rutland compared to Blood Pool Compensation BPC1-PBPC: Blood Pool Compensation Observer One compared to Observer Two S Significant to the p = 0.0 level NS Not significant

19 Appendix: Model of renal activity during early extraction phase, to illustrate linear parametric relationship between renal and hepatic activity In addition to the kidneys, which excrete MAG, radionuclide images show non-excretory blood pooling in blood rich organs such as the heart, liver and spleen. The aim of background correction is to isolate the count rate that represents MAG accumulation in the kidneys from the total count rate in the kidney ROI. Assuming that the time course of the summed intravascular and interstitial signals (loosely termed as 'blood-pool' in this paper) is similar in the kidney and in other blood rich non-excretory organs such as the heart, liver and spleen, the latter organs can be used as models of kidneys without excretory function. For example, following injection, the liver count rate peaks (typically during the first minute) and subsequently decreases with time, while renal counts increase before the peak of the renal curve, which normally occurs at.-.0 min, although this timing can vary between patients. The count rates from the liver ROI acts as a model of the contribution to total kidney count rate from mostly blood pooling, where blood pool is defined here as intrarenal vascular plus interstitial organ activity during the ascending portion of the renal time activity curve. The Blood Pool Compensation (BPC) model is then based on similar assumptions to those of the Patlak-Rutland (PR) model, as follows: Let K(t) represent a renal activity versus time function and H(t) represent a hepatic region activity versus time function. Let us assume, as is assumed for the PR technique, that after the bolus arrives in the kidney, and before urine has emptied from the intrarenal collecting structures at time T, that there is a monoexponential decay of the blood pool within the kidney and that the kidney is accumulating extracted activity in proportion to that blood pool. That is, we are assuming that the renal blood pool is a scaled renal feed function, f (t), thus f(t) = ce λt c > 0 and λ > 0 ( 1) and, K(t) = f(t) + α t<t 0 f(τ)dτ ( ) where α > 0 is proportional to the extraction fraction and τ is a dummy variable. Substituting Eq. ( 1) into Eq. ( ) yields K(t) = ce λt = α t<t 0 ce λτ dτ = (1 α λ ) ce λt + αc λ ( )

20 Now, let us assume (ignoring trace hepatocyte extraction of MAG), that H(t) is some constant, h, multiplied by f (t) over the time interval of concern, then H(t) = hf(t) = hce λt h > 0 ( ) and, Note that this has the same form as K(t) = (1 α ) 1 αc H(t) +. ( ) λ h λ K(t) = sh(t) + b, ( ) where s = (1 α ) 1 αc and b =. Note that the slope, s, is positive when (1 α ) > 0, or negative λ h λ λ when (1 α ) < 0, while b is strictly positive. Since we can obtain s and b directly from λ ordinary least square linear regression of a parametric function of the data, it is not necessary to inspect the plot or know the values of c,, and, to determine b. The parameter b relates to the extracted count rate in a kidney with the decaying blood pooling removed, which occurs at a time when parametric liver count rate is zero. Equation ( ) shows that if the blood pool is monoexponentially decreasing during the time interval of fitting, the parametric plot of K(t) and H(t) is linear for t t1, t, t,,, t n. However, the linearity of the result in Eq. ( ) is more general than our selection for an input function. The renal modelling outlined here is appropriate but of necessity somewhat simplistic. It can be shown that other forms of the renal input functions can yield co-linear and/or almost linear relationships between K(t) and H(t) under more complex renal models or states. However, the good agreement of the BPC technique with the best of other methods (PR), while being simpler and making fewer assumptions, provides the best justification for the BPC technique. That is, the BPC model is appropriate in the sense that good models are generally thought to as simple as possible while still explaining the data. Finally, as the parametric relationship of K(t) versus H(t) is collinear during the desired period of observation, quality assurance is possible by testing linear goodness of fit for the least squares analysis of K(t) and H(t).