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1 Department of Diagnostic Radiology, Justus-Liebig Universität Giessen,
Klinikstr. 36, Giessen 35385, Germany.
2 Department of Urology, Justus-Liebig Universität Giessen, Giessen 35385,
Germany.
3 Department of Clinical Pharmacology, Justus-Liebig Universität Giessen,
Giessen 35385, Germany.
Received May 28, 2002;
accepted after revision December 31, 2002.
Address correspondence to N. Hackstein.
Abstract
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SUBJECTS AND METHODS. Twenty adult patients treated with percutaneous nephrostomy were studied. The CT protocol consisted of an unenhanced scan and three subsequent scans obtained 38, 71, and 102 sec after the initiation of the contrast medium injection. Plasma clearance of the contrast medium was determined and used as the reference. Additionally, single-kidney excretory clearance was determined by separate urine collections from the left and right kidneys. A three-compartment model calculation was made using all data available to estimate volume and transfer rate constant of the interstitial space.
RESULTS. The GFR determined using plasma clearance correlated well with the GFR determined using excretory clearance, with a correlation coefficient of r = 0.94 and a regression line of y = -6 + 0.97 x x. GFR of both kidneys as measured using CT was overestimated according to the GFR determined using plasma clearance, with a correlation coefficient of r = 0.80, and a regression line of y = 35 + 0.79 x x. Single-kidney excretory clearance GFR was similarly overestimated using single-kidney CT GFR, with a correlation coefficient of r = 0.81 and a regression line of y = 20 + 0.84 x x. Single-kidney parenchymal volume was used as an indicator of interstitial space enlargement. The overestimation of excretory clearance GFR using CT correlated significantly with the parenchymal volume of the individual kidneys. A high correlation was also found between overestimation of total GFR determined with CT and interstitial space estimated using a three-compartment model calculation. Relative interstitial space was estimated to be 25% (range, 9-46%) of total kidney volume.
CONCLUSION. Using the interstitial space as a third compartment may introduce an error into the measurement of GFR with the Patlak plot technique. We found that the CT protocol in our study resulted in considerable overestimation of GFR as determined with the Patlak plot in patients with increased interstitial space.
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In the past, glomerular filtration rate (GFR) was measured with the Patlak plot based on single-location dynamic CT, which resulted in GFR per milliliter of renal parenchyma [4-6]. In two preceding studies [7, 8], we introduced a two-point Patlak plot technique based on one unenhanced and two enhanced single-detector helical CT scans of the entire kidneys, hereinafter referred to as CT GFR. CT GFR gives GFR values for the left kidney and the right kidney in milliliters per minute. The measurement of GFR with the Patlak plot technique introduces an error by neglecting the renal interstitial space, which is not represented by this model as a third compartment [9, 10]. Our study addressed the question of whether accuracy is diminished if single-kidney GFR is measured using CT GFR in patients with enlarged interstitial space. To this end, we studied patients with acute pyelonephritis or hydronephrosis or both.
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All patients had pyeloureteral obstructions of at least one kidney that were caused by stones in seven patients and by various tumors in the other 13 patients (prostatic carcinoma, two; carcinoma of the bladder, five; cervical carcinoma, three; rectal carcinoma, one; malignant histiocytoma localized in the pelvis, one; and carcinoma of the ureter, one). All patients underwent contrast-enhanced CT for clinical indications.
Of the 40 kidneys examined, 28 had been treated with percutaneous nephrostomy (right and left kidney in eight patients, right kidney only in eight, and left kidney only in four). Percutaneous nephrostomy catheters had been placed 5 or fewer days before CT in 10 patients and 6 or more days before CT in 18 patients. Of the 40 kidneys, three were diagnosed as having pyelonephritis (leukocyturia or bacteriuria) without undergoing percutaneous nephrostomy, and 13 kidneys were diagnosed as having pyelonephritis and underwent percutaneous nephrostomy. Five kidneys were diagnosed with obstructions on the basis of sonographic or CT findings showing ectasia of the renal pelvis; these findings obviated percutaneous nephrostomy. Two of these five kidneys also had pyelonephritis. The remaining 19 kidneys were healthy.
Contrast Medium and Injection Technique
Each patient received one injection of contrast medium for
contrast-enhanced CT and determination of plasma clearance. All patients
received iopromide (300 mg I/mL, Ultravist 300, Schering, Berlin, Germany).
The injection was administered with an EnVision CT power injector (Medrad,
Indianola, PA) through a peripheral venous cannula placed in the forearm.
Patients routinely received an injection of 120 mL of contrast medium at an injection rate of 3 mL/sec (n = 13). In patients with an elevated serum creatinine level, the amount of contrast medium was reduced in relation to their weight. The amounts given to these patients were 60 mL (one patient), 90 mL (one patient), and 100 mL (five patients) of iopromide. The injection rate was reduced to 2 mL/sec in two of these patients.
Iodine-Plasma Concentration Curve Determination
The iodine-plasma concentration curve, C(t) (resulting from the
iopromide injection for CT) was used to calculate plasma clearance and
excretory clearance of iopromide. After the single-shot injection of the
nonionic contrast medium, the plasma-concentration curve follows the sum of
two exponential functions in equation 1:
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A baseline blood sample was obtained as a reference. Then eight 5-mL heparinized blood samples were drawn 10, 20, and 40 min and 1, 2, 3, 4, and 8 hr after the injection of the contrast medium. For blood sampling, a cannula (not the one used for the injection) was inserted to prevent contamination with iodine. The blood was centrifuged, and the iodine concentration in the plasma was measured using an X-ray fluorescence analyzer (L. Kaufman, San Francisco, CA; EG&G Ortec, Munich, Germany). A two-exponential function was fitted on the iodine measurements.
GFR Measured by Plasma Clearance
Plasma clearance of iopromide (plasma GFR measured in milliliters per
minute) served as the reference for the global GFR of a patient. Plasma
clearance of iopromide was calculated using equation 2, where Q
equals the amount of iodine injected (measured in milligrams):
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GFR Measured by Excretory Clearance
Excretory clearance served as the reference for single-kidney GFR. Because
every patient had at least one percutaneous nephrostomy, separate urine
collections for the left and the right kidneys were possible. Excretory
clearance of iopromide (excretory GFR) of the right and left kidneys was
calculated using equation 3, which represents the clearance definition:
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The single-kidney excretion GFR is the GFR of a single kidney measured in milliliters per minute. Esingle kidney (t1) (mg I) is the amount of iodine that is excreted by a single kidney after a contrast medium injection during the period t = 0 to t = t1. Esingle kidney (t1) was calculated by measuring the amount of urine excreted by the kidney up to t = t1 multiplied by the iodine concentration in the collected urine. Iodine concentration in the well-mixed urine was measured using X-ray fluorescence analysis. Urine collection was ended when the last blood sample was taken 8 hr after injection of contrast medium (t1 = 8 hr).
GFR Measured on CT
The GFR of a single kidney measured on CT (single-kidney CT GFR) was
calculated using the Patlak plot. An unenhanced CT scan of both kidneys and
three contrast-enhanced CT scans of both kidneys provided data for calculation
of left-kidney CT GFR and right-kidney CT GFR (measured in milliliters per
minute). The formulas for GFR calculation using the Patlak plot model have
been described in detail in a previous article
[8]. For calculation of CT GFR,
a hematocrit correction was performed, using the hematocrit value measured
just before the CT examination.
CT Examination
CT was performed on a Somatom Plus 4 (Siemens, Erlangen, Germany), which is
a single-detector CT scanner. Patients were encouraged to drink water
liberally before the CT examination and for as long as plasma samples were
being taken. Oral contrast material (barium sulfate for CT) was given if
necessary, depending on the clinical indication. Both kidneys were scanned
before and after administration of IV contrast material, in the latter case
during the arterial and parenchymal phases. A third enhanced scan (the early
parenchymal scan) was obtained between the arterial and parenchymal
(diagnostic) scans to gain sufficient data on the aortic density curve
The mean delay was 38 sec (range, 24-53 sec) after injection for the arterial phase, 71 sec (range, 54-87 sec) after injection for the early parenchymal phase, and 102 sec (range, 84-151 sec) after injection for the late parenchymal phase. All times refer to the midpoint of the kidney scanning phase.
All study scans were used as diagnostic images. Bolus triggering was performed with a 3-sec interscan delay and a tube current of 25 mAs. The threshold for bolus triggering was 100-200 H. The bolus-triggering CT scans were all obtained with the table position at the level of the upper renal pole to minimize table movement between the end of bolus triggering and the start of the first enhanced CT scan.
Scanning the whole kidney volume took between 10 and 15 sec, depending on the slice thickness and anatomic variations. Pitch was 1.5, and rotation time was 0.75 sec. The usual abdominal CT protocol was used: 120 kV and 98 mAs for unenhanced and 150 mAs for enhanced CT scans. Slice thickness was either 5 or 8 mm. For most patients, we used an 8-mm slice thickness for the unenhanced scan and a 5-mm slice thickness for at least one of the enhanced scans. However, slice thickness was always adapted to the diagnostic needs of the patients. We encountered no pelvic kidneys in our study.
Kidney Attenuation
Regions of interest were manually drawn around the left and right kidneys
and around the aortic lumen (Fig.
1) using MagicView software (Siemens). The borders of the regions
of interest were drawn as close to the periphery of the renal parenchyma as
possible. The renal pelvis and clearly discernible abnormalities inside the
kidney, such as cysts or stones, were excluded. Whole-kidney attenuation,
KCT(t) was calculated by multiplying the mean attenuation,
area of the region of interest, and slice distance for each slice of kidney
parenchyma and then adding these numbers for the whole kidney.
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Aortic Density
For calculation of the Patlak plot, the aortic density curve, represented
as b(t) was used as the input function. A circular region of interest
was placed inside the aortic lumen in slices at the level of the kidneys. The
unenhanced density of the aorta was calculated as the mean of five consecutive
aortic density measurements and was subtracted from the enhanced scans.
Missing parts of the curve were extrapolated linearly.
Three-Compartment Model Calculation
A simple mathematic three-compartment model based on the Patlak plot was
implemented, with the interstitial space added as a third compartment
(Fig. 2). In every patient,
data on both kidneys were analyzed together. Thus, parameters for left and
right kidneys, such as renal parenchyma volume, were added together. The
parameters used for this model are defined in Appendix 1. The aim of each
model calculation was to find adequate parameters for the interstitial
space—interstitial space volume (Iv) and
interstitial space transfer rate constant (kbi)—to
approximate kidney contrast medium amounts, represented by K(t), to
those measured on CT, represented by KCT(t).
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The model was implemented using Excel (Microsoft, Redmond, WA) and a 1-sec time grid. Two parameters were taken from CT measurements: aortic density b(t) and volume of the vascular compartment Bv. Bv was calculated with the Patlak plot analysis of the CT data as described in our previous study [8]. In accordance with Peters' [9] theoretic considerations, Bv was calculated from the first two CT scans (arterial and early parenchymal scans) [10]. The actual GFR was taken from the reference measurement, which was plasma clearance. By manually choosing the two parameters Iv and kbi, we calculated concentration curves of the interstitial space and contrast medium amount curves for all three compartments—including the amount of contrast medium in the whole kidney, K(t). The parameters Iv and kbi were chosen arbitrarily so as to approximate K(t) to the three KCT(t) measurements from CT.
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In 18 patients, total GFR as measured by excretory clearance correlated well with plasma clearance (Fig. 3), thus indicating proper urine collection. Two patients had to be excluded from our study because of collecting errors. In another patient, only total excretory clearance (the sum for the left and right kidneys) could be determined because of a residual flow of urine into the bladder from the kidney with the percutaneous nephrostomy that was revealed on antegrade urography via percutaneous nephrostomy after CT.
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When total GFR as measured by CT was compared with plasma clearance, considerable overestimation of GFR by CT GFR was found, as shown in Figure 4. Mean total CT GFR was 22 mL/min higher than mean plasma GFR.
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Single-kidney GFR as measured by excretory clearance and by CT GFR is shown in Figure 5, whereas Figure 6 presents a Bland-Altmann plot of that data [11]. As in the comparison of total GFR as measured by CT GFR and plasma GFR, CT GFR considerably overestimated GFR in kidneys with percutaneous nephrostomy as well as in kidneys with hydro-nephrosis or pyelonephritis or a combination of both diseases. The highest overestimation occurred in two kidneys of different patients, both with pyelonephritis and untreated hydronephrosis.
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Enlargement of an interstitial space of an organ appears both clinically and radiologically as organ swelling. For our purposes, the best indicator of the degree of interstitial space enlargement using direct measurements is gross parenchymal volume determined with CT planimetry. The normal parenchymal volume of the kidney in an adult is 150 mL [12]. We correlated the discrepancy in single-kidney GFR as measured with CT GFR and excretory clearance with the individual single-kidney parenchymal volume. Overestimation of GFR as measured with CT GFR as compared with GFR as measured with excretory clearance was calculated by subtracting single-kidney excretory GFR from single-kidney CT GFR. Figure 7 shows that a statistically significant correlation exists between enlargement of the kidneys and overestimation of GFR. Overestimation of GFR by CT GFR was not dependent on the magnitude of the GFR itself, as is illustrated in the Bland-Altmann plot (Fig. 6). Figures 8A, 8B shows an example of kidneys swollen as a result of pyelonephritis and hydronephrosis; CT GFR considerably overestimated GFR in this patient.
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Results of the Three-Compartment Model Calculation
In 17 patients, model computations were performed to determine Iv
and kbi. We decided to exclude patients from this analysis if we
could not satisfactorily approximate KCT with the parameters
Iv and kbi. Three patients were excluded for this
reason.
None of the KCT values of the patients measured with CT could be explained by only the sum of the contrast medium in the vascular space and contrast medium excreted in the nephron. We found that we could close this gap by introducing the measurement of interstitial space.
Interstitial space parameters were chosen such that the amount of contrast medium in the kidney that was calculated with the model approached the amount measured with CT, with a mean discrepancy of K(t) compared with KCT(t) of 3% (range, 0.7-7.1%). The mean relative Bv was 32% (range, 19-46%). The mean Iv was calculated to be 25% (range, 9-46%). The mean kbi was 0.015 mL (range, 0.008-0.035 mL). The equilibrium point—the intercept of the concentration of contrast medium in the interstitium and that in the vascular space—determines whether the contrast medium flows from the vascular space into the interstitial space or whether the flow is retrograde; this point was estimated to be reached at 97 sec (range, 57-≥120 sec) after the contrast injection. By way of example, Figures 9A, 9B, 9C shows the results of the computations for a patient with a small interstitial space, and Figures 10A, 10B, 10C shows the results for a patient with a large interstitial space. Figure 11 shows the high correlation between overestimation of GFR as measured with the Patlak plot compared with the size of the interstitial space as calculated by the three-compartment model (r = 0.93).
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The kidney volume we found in the patients in our study was much larger than one would expect in individuals with healthy kidneys, indicating swelling of the kidneys or, speaking pathophysiologically, an increased interstitial space. In healthy kidneys, the interstitial space in the renal cortex as measured by histopathologic techniques is 8.4% and that of the outer stripe of the outer medulla is 17.6% [13]. In the same study, interstitial space increased in patients with acute renal failure by approximately 10% in the renal cortex and by a similar amount in the outer stripe of the outer medulla. According to the results of our study using a three-compartment model, a relative interstitial space of approximately 10% seems to be a normal value, because 10% was the lowest relative interstitial space found in some patients.
In our patients with increased interstitial space, CT GFR considerably overestimated GFR as measured by plasma clearance. A significant correlation was found between overestimation of GFR in single kidneys as measured with CT (Fig. 7) and the amount of swelling in the single kidneys. This correlation was not influnced by the GFR at all (Fig. 6). An even closer correlation was found between overestimation of GFR measured with CT and interstitial volume calculated with a three-compartment model (Fig. 11).
In contrast to that result, total GFR determined by CT GFR and plasma clearance of iopromide were virtually identical in a previous study involving only patients without acute renal disorder [8]. Table 2 summarizes the results of previous studies [6, 8, 14] that measured GFR with the CT-Patlak plot technique. Tsushima et al. [6, 14] conducted two studies that included patients with different renal pathologies and found a good correlation between total GFR determined with the Patlak plot and 24-hr creatinine clearance; however, GFR determined with the Patlak plot was higher than GFR determined with the creatinine clearance. It is unclear whether kidneys with increased interstitial space were included in these two studies. Because the first study involved patients with diabetes mellitus, there should not have been any cases of increased renal interstitial space: diabetic nephropathy is a chronic renal disorder. In their second study, Tsushima et al. included some patients with hydronephrosis and renal tumors and therefore with potentially increased interstitial space. Whether the hydronephrosis was acute or chronic in these patients is unclear. Other patients in this study had chronic diseases such as atrophy and renovascular hypertension.
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What might be the reason for our finding of overestimation of GFR using the Patlak plot technique in patients with increased interstitial space? The Patlak plot technique is based on a two-compartment model [2]. One compartment represents the plasma or vascular space. From this compartment, contrast medium flows unilaterally into the second compartment, the nephron space. The interstitial space, which is a third compartment with bilateral contrast medium exchange with the vascular space, is neglected. Some assumptions in the model calculations do not fit reality. Most important, the model calculations assume the immediate and complete mixing of the contrast medium within the compartments.
Peters [9] described the characteristics of the Patlak plot technique when used to measure GFR. During and shortly after contrast medium injection, the concentration of contrast medium is high in the vascular compartment. In this early phase, contrast medium flows from the vascular space into the interstitial space. Any contrast medium flow from the vascular space into the interstitial space is seen on the Patlak plot as a GFR value; consequently, the Patlak plot furnishes misleadingly high GFR values during the early phase. The experimental findings of our study correspond with this theoretic consideration.
Later, when the plasma concentration of the contrast medium decreases and its concentration in the interstitial space is higher than its concentration in the plasma, contrast medium backflow occurs (contrast medium disappears from the kidney), leading to a flattened slope of the Patlak plots. This phase is the equilibrium phase [15], and it results in underestimation of GFR. The backflow is small, and therefore, underestimation of GFR in the later part of the curve is also likely to be small, if it exists at all.
There is a point between the early and the late phases, the so-called equilibrium point, during which no contrast medium flows between interstitial space and vascular space. At this equilibrium point, the slope of the Patlak plot exactly equals GFR. Theoretically, the equilibrium point occurs after the zenith of the plasma concentration curve. Using calculations from the three-compartment model, we found a value of later than 97 sec after the contrast injection. These results exactly reflected the characteristics of the Patlak plot described earlier by Peters [9]. Furthermore, these results are in keeping with the findings from our previous study in which an early CT GFR (45-75 sec after contrast injection) and a late CT GFR (75-105 sec after contrast injection) were measured in patients without acute renal disorder. Late CT GFR was significantly lower than early CT GFR [8].
The effect of the interstitial space should, therefore, be taken into account when using the Patlak plot for measuring GFR. Ideally, the interstitial space should be included in the model for measuring GFR, thus correcting for the effect of the space. However, the three-compartment model used in our study requires a "true" GFR as a parameter for calculating the interstitial space and interstitial space transfer rate constant.
The Patlak plot produces the most accurate GFR values in patients in whom the interstitial space is small, as in kidneys with no acute disease, but accurate values are also produced during the period in which there is only little or no contrast medium flow between vascular space and interstitial space, a phenomenon that occurs in the equilibrium phase. Therefore, CT measurements could be made during this equilibrium phase. However, Patlak plot measurements in the kidneys are limited by the point at which contrast medium excretion into the renal pelvis begins, approximately 2 min after contrast injection. This time coincides with the renal equilibrium point, and taking measurements much later than 2 min after contrast injection is problematic.
In conclusion, we believe that using the interstitial space as a third space might introduce an error when measuring GFR with the Patlak plot technique. The error is dependent on the timing of the data measurement with respect to the contrast medium injection protocol. Overestimation occurs if measurements are taken too early after contrast medium injection, before the equilibrium phase is reached. The error increases if the interstitial space is enlarged. Use of standard protocols for contrast medium injection and CT scanning and the Patlak plot technique results in considerable overestimation of GFR in patients with increased interstitial space.
Acknowledgments
We thank Schering, Berlin, Germany, for performing the iodine concentration
measurements.
APPENDIX 1. Parameters Used in the Three-Compartment Model Calculations to Measure Single-Kidney Glomerular Filtration Rate
b(t) is the concentration (H) of contrast medium (t) in the vascular space (b) of the kidneys as determined by CT measurement.
Bv is the volume (v) (mL) of vascular space (B) of the kidneys calculated using CT measurements and the Patlak [3] plot.
B(t) is the amount (H x mL) of contrast medium (t) in the vascular space (B) of the kidneys as calculated by the formula B(t) = b(t) x Bv.
kbi is the estimated transfer rate constant (k) (mL/sec) of contrast medium from the vascular space (b) of the kidneys to the interstitium (i).
i(t) is the concentration (H) of contrast medium (t) in the interstitium (i) of the kidneys as calculated by the formula i(t) = i(t - 1) + kbi x (i [t - 1] - b[t - 1]).
Iv is the estimated volume (v) (mL) of the interstitium (I) of the kidneys.
I(t) is the amount (H x mL) of contrast medium
(t) in the interstitium (I) of the kidneys as calculated by
the formula
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kGFR is the transfer rate constant (k) (mL/sec) of contrast medium from the vascular space (B) of the kidneys to the nephron (N), which equals the glomerular filtration rate (GFR). As measured by the plasma clearance of the contrast medium, kGFR equals total GFR.
N(t) is the amount (H x mL) of contrast medium
(t) in the nephron (N) as calculated by the formula
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K(t) is the amount (H x mL) of contrast medium (t) in the kidney (K) as calculated by the formula K(t) = I(t) + B(t) + N(t).
KCT(t) is the amount (H x mL) of contrast medium (t) in the kidney (K) as measured with CT.
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= no disease, • = untreated
hydronephrosis, 
= hydronephrosis and percutaneous nephrostomy (PCN),
= pyelonephritis, 
= pyelonephritis and PCN, + = pyelonephritis
and hydronephrosis.
). As long as contrast medium
concentration in interstitial space, I(t) (
= CT
measurement.
