# Robust Porcine GFR Measurement with Radiotracers and Only Late Blood Samples

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## Abstract

**:**

^{99m}Tc]Tc-DTPA. The reference clearance (Cl, GFR; range 41–85 mL/min) was measured from the full curve under the data. For simpler determination, an approximate clearance, Cl

_{1}, was based on the last five blood samples (acquired 120–240 min post injection). (3) The following formula for the GFR was developed: Cl = 1.27 · (Cl

_{1})

^{0.92}. The spread (SD) was within 4% of the reference GFR. A comparison with the literature data showed that our correction formula was robust in pigs of various breeds, sizes up to approximately 200 kg, and GFRs up to approximately 400 mL/min, with a spread of up to 8%. The formula was also applicable for iohexol as the tracer. (4) A formula was developed that allows porcine GFR to be measured using only 4–5 late blood samples. This new formula can be applied across a wide range of swine breeds, animal sizes, and GFR ranges, allowing for robust determination of the GFR in pigs without full-curve blood sampling and without urine collection.

## 1. Introduction

## 2. Material and Methods

#### 2.1. Animals

^{99m}Tc]Tc-DTPA) in 20 female juvenile Danish Landrace pigs. For each animal, the measurement was performed twice, one week before and two weeks after a laparoscopic partial nephrectomy. During the partial nephrectomy, the upper right kidney pole was excised, corresponding to removing approximately one-third of the entire kidney. While this would naturally reduce renal function, the growth of the juvenile pigs during three weeks could, in itself, increase renal function. Overall, the two GFR measurements took place at different times and in different settings, with potentially changed GFR from the first to the second measurement. The pigs weighed 26.0–38.0 kg at the time of the first measurement and 31.4–43.8 kg at the time of the second measurement.

#### 2.2. Reference GFR: Plasma Clearance Based on Full-Curve Data (Cl_{ref})

^{99m}Tc]Tc-DTPA was considered equal to GFR without any conversion [10,11].

^{99m}Tc]Tc-DTPA by intravenous injection. Blood samples were taken 5, 10, 15, 30, 45, 60, 90, 120, 150, 180, 210, and 240 min after the injection. The samples were centrifuged for 15 min at 2200× g, after which 2 mL plasma samples were drawn and measured to 10,000 counts in a Wizard

^{2}2480 gamma counter (PerkinElmer, Waltham, MA, USA). The area under the curve (AUC) was determined by bi-exponential fitting. A sample fit is shown in Figure 1.

_{ref}, was calculated as the injected activity divided by AUC (Formula (A1) in the Appendix A); overall, if clearance (Cl, GFR) is high then the curve decays quickly (small AUC), while a slowly decaying curve (large AUC) reflects a low clearance.

#### 2.3. One-Pool Approximation Cl_{1} Based on Late-Sample Data

_{1}, was calculated based on the final, mono-exponential curve (dashed curve in Figure 1) using Formula (A4). This curve can be calculated based on only the late blood samples. As detailed in Appendix A, the approximation Cl

_{1}, sometimes called one-pool clearance, corresponds to replacing the full-curve AUC with AUC

_{slow}, the area under the dashed curve in Figure 1. As AUC

_{slow}is a smaller area than the full-curve AUC, one-pool clearance Cl

_{1}overestimates the actual clearance Cl. Thus, Cl

_{1}must be corrected to give Cl.

_{1}were determined from the last 5 blood samples, corresponding to the time interval 120–240 min post-injection (p.i.). To determine if a smaller time window could be used, Cl

_{1}values were also calculated based on the last 4 (150–240 min p.i.) and the last 3 (180–240 min p.i.) blood samples.

#### 2.4. Porcine GFR Correction Formula

_{corr}= 0 for Cl

_{1}= 0, and, unlike a quadratic correction, it does not impose a maximal value on Cl

_{corr}.

## 3. Results

_{ref}range was 41–85 mL/min. The individual data points are given in Supplementary Table S1.

_{corr}and Cl

_{1}in mL/min.

## 4. Discussion

^{99m}Tc]Tc-DTPA.

_{0}, of the injected activity, a first (one-pool) approximation, Cl

_{1}, for the clearance was calculated: Formula (A4).

#### 4.1. Choice of Tracer

^{51}Cr]Cr-EDTA, but this has, in recent years, been taken over by [

^{99m}Tc]Tc-DTPA; these two tracers were shown to give GFR measurements that, for clinical purposes, can be considered equal [12,13,14]. Likewise, two pig studies by Frennby et al. [6,15] found that [

^{51}Cr]Cr-EDTA and iohexol were interchangeable.

^{51}Cr]Cr-EDTA is no longer available on the market, the choice between iohexol or [

^{99m}Tc]Tc-DTPA in practice, therefore, depends upon whether nuclear medicine procedures are available or not. Radiotracers can be measured in extremely small concentrations (10 MBq of [

^{99m}Tc]Tc-DTPA corresponds to approximately 5 × 10

^{−13}mol = 0.5 pmol of the radiotracer molecule), and the radiation dose from 10 MBq [

^{99m}Tc]Tc-DTPA is minute (<0.1 mSv in an adult patient, slightly higher in small children). For these reasons, [

^{99m}Tc]Tc-DTPA is widely used for GFR measurements in humans. Iohexol does not involve the handling of radioactivity but requires macroscopic amounts (grams) to be injected for the concentrations to be precisely measurable.

#### 4.2. Previous Studies

_{1}to Cl). A summary of each study is given below.

#### 4.2.1. Frennby Studies

^{51}Cr]Cr-EDTA, with an excellent correlation between the two tracers. For the simplified determinations, four blood samples 180–360 min p.i. were used, and the authors reported the weight-scaled results in mL/min/10 kg. With our notation, their correction formula was

^{51}Cr]Cr-EDTA plasma clearance based on the full curve, the GFR was in the range of 16.5–26.3 mL/min/10 kg in the pigs with normal renal function. For the nephrectomised pigs, the range was 5.3–11.3 mL/min/10 kg.

#### 4.2.2. Palnæs Hansen Study

^{51}Cr]Cr-EDTA. They found that the plasma clearance of [

^{51}Cr]Cr-EDTA was indistinguishable from the renal clearance of the GFR, i.e., Cl

_{plasma,EDTA}was indistinguishable from the classical gold standard of GFR measurement. The authors then measured the clearance of [

^{51}Cr]Cr-EDTA with the single-injection technique (as in the present study) in n = 12 pigs and compared it with the clearance from late samples (“slope clearance”, Cl

_{1}). Blood sampling was up to 240 min p.i. It was found that the approximation Cl

_{1}could be corrected by a factor:

_{corr,Palnæs}= 0.75 · Cl

_{1}

#### 4.2.3. Luis-Lima Study

#### 4.2.4. Van Gelder Study

#### 4.3. Comparison of Corrections

_{1}), allowing for a direct comparison with their data. As shown in Figure 3, our correction (2) can be extrapolated to cover their data from much larger, adult pigs without a new fit. (Note for the curious reader: a fit to the combined data material (ours + Luis-Lima) gave the coefficients a = 0.925 ± 0.010 and b = 1.241 ± 0.058, i.e., essentially the same coefficients as those from our data alone, only with narrower spreads.) As seen in the figure, the Luis-Lima correction (4) fails if it is extrapolated downwards to cover the range of mL/min relevant for our data.

^{99m}Tc]Tc-DTPA, or [

^{51}Cr]Cr-EDTA; the developed correction was common for these tracers.

#### 4.4. Time Range for Late Samples

_{ref}) was very low and had a spread (SD) of less than 4% (Table 1). If fewer data were used (180–240 min, three blood samples), the spread was larger, and a considerable number of outliers was observed (Figure 2).

#### 4.5. Strengths and Limitations

_{1}, to the actual clearance, Cl. For comparison, widely used human corrections [4,5] are independent of sex.

#### 4.6. Perspectives

^{99m}Tc]Tc-DTPA (and, indirectly, [

^{51}Cr]Cr-EDTA) as well as the nonradioactive tracer iohexol.

## 5. Conclusions

^{99m}Tc]Tc-DTPA as measure of the glomerular filtration rate (GFR), we developed a correction Formula (1) that allows for the determination of the GFR in pigs based on only four or five late blood samples taken 150–240 min or 120–240 min after the injection of a radiotracer. Within our own data material of juvenile pigs with a GFR of 41–85 mL/min, the results had a spread (SD) of approximately 4% around the reference value. In comparison to the data from the literature, we extended the validated range to adult pigs with a GFR of up to 400 mL/min, with a spread of approximately 8% around the reference value. Furthermore, we stated reasons why the correction is applicable for a GFR lower than 40 mL/min.

^{99m}Tc]Tc-DTPA and iohexol (and for [

^{51}Cr]Cr-EDTA, if available) as the chosen tracer.

## Supplementary Materials

_{1}) for the pigs in the present study.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Theory of Plasma Clearance Measurements

_{0}= quantity of injected tracer

_{0}may be the Bq of the radioactivity, or it may be the counts per minute (cpm) of a sample in a gamma counter. If the radioactivity concentration is measured in units of Bq/mL, then the unit for the AUC is min·Bq/mL. See, e.g., the classical study by Brøchner-Mortensen [4] for GFR determination in humans or a study by Frennby et al. [15] for a description of this principle for GFR determination in pigs.

_{0}. Therefore, Formula (A1) can be used without urine sampling, while blood sampling is needed to determine the AUC.

_{slow}can be calculated based on only the late, more slowly falling part of the curve. The late, slow part of the plasma concentration curve behaves as a mono-exponential function:

_{1}approximation is sometimes called one-pool clearance: the late, single exponential reflects the situation where the total extracellular volume behaves as a single pool of the tracer, reflected by a single exponential.

_{slow}is smaller than the full area of the AUC (Figure 1), the one-pool approximation, Cl

_{1}, overestimates the actual clearance, Cl.

## References

- Sachs, D.H. The Pig as a Potential Xenograft Donor. Vet. Immunol. Immunopathol.
**1994**, 43, 185–191. [Google Scholar] [CrossRef] [PubMed] - Luis-Lima, S.; García-Contreras, C.; Vázquez-Gómez, M.; Astiz, S.; Carrara, F.; Gaspari, F.; Negrín-Mena, N.; Jiménez-Sosa, A.; Jiménez-Hernández, H.; González-Bulnes, A.; et al. A Simple Method to Measure Renal Function in Swine by the Plasma Clearance of Iohexol. Int. J. Mol. Sci.
**2018**, 19, 232. [Google Scholar] [CrossRef] [PubMed] - Chade, A.R.; Williams, M.L.; Engel, J.; Guise, E.; Harvey, T.W. A Translational Model of Chronic Kidney Disease in Swine. Am. J. Physiol. Ren. Physiol.
**2018**, 315, F364–F373. [Google Scholar] [CrossRef] [PubMed] - Brøchner-Mortensen, J. A Simple Method for the Determination of Glomerular Filtration Rate. Scand. J. Clin. Lab. Investig.
**1972**, 30, 271–274. [Google Scholar] [CrossRef] [PubMed] - Jødal, L.; Brøchner-Mortensen, J. Reassessment of a Classical Single Injection
^{51}Cr-EDTA Clearance Method for Determination of Renal Function in Children and Adults. Part I: Analytically Correct Relationship between Total and One-pool Clearance. Scand. J. Clin. Lab. Investig.**2009**, 69, 305–313. [Google Scholar] [CrossRef] [PubMed] - Frennby, B.; Sterner, G.; Almén, T.; Chai, C.-M.; Jönsson, B.A.; Mansson, S. Clearance of Iohexol,
^{51}Cr-EDTA and Endogenous Creatinine for Determination of Glomerular Filtration Rate in Pigs with Reduced Renal Function: A Comparison between Different Clearance Techniques. Scand. J. Clin. Lab. Investig.**1997**, 57, 241–252. [Google Scholar] [CrossRef] [PubMed] - van Gelder, M.K.; Stevens, J.; Pieters, T.T.; Vaessen, K.R.D.; Joles, J.A.; Verhaar, M.C.; Gerritsen, K.G.F. Simplified Iohexol-Based Method for Measurement of Glomerular Filtration Rate in Goats and Pigs. Biology
**2021**, 10, 461. [Google Scholar] [CrossRef] [PubMed] - Palnæs Hansen, C.; Bie, P.; Stadil, F. Assessment of Renal Function by
^{51}Cr-EDTA and Endogenous Creatinine Clearances in the Pig. Acta Physiol. Scand**1997**, 161, 253–260. [Google Scholar] [CrossRef] [PubMed] - Brignone, J.; Jensen, M.; Jensen, B.L.; Assersen, K.B.; Goetze, J.P.; Jødal, L.; Andersen, T.B.; Magnusdottir, S.O.; Kloster, B.; Jønler, M.; et al. Protective Effect of Sacubitril/Valsartan (Entresto) on Kidney Function and Filtration Barrier Injury in a Porcine Model of Partial Nephrectomy. Nephrol. Dial. Transplant.
**2023**, 38, 80–92. [Google Scholar] [CrossRef] [PubMed] - Fleming, J.S.; Zivanovic, M.A.; Blake, G.M.; Burniston, M.; Cosgriff, P.S. Guidelines for the Measurement of Glomerular Filtration Rate Using Plasma Sampling. Nucl. Med. Commun.
**2004**, 25, 759–769. [Google Scholar] [CrossRef] [PubMed] - Burniston, M. Clinical Guideline for the Measurement of Glomerular Filtration Rate (GFR) Using Plasma Sampling—Report 2018; British Nuclear Medicine Society: London, UK, 2018; p. 23. [Google Scholar]
- Andersen, T.B.; Jødal, L.; Nielsen, N.S.; Petersen, L.J. Comparison of Simultaneous Plasma Clearance of
^{99m}Tc-DTPA and^{51}Cr-EDTA: Can One Tracer Replace the Other? Scand. J. Clin. Lab. Investig.**2019**, 79, 463–467. [Google Scholar] [CrossRef] [PubMed] - Rehling, M.; Møller, M.L.; Thamdrup, B.; Lund, J.O.; Trap-Jensen, J. Simultaneous Measurement of Renal Clearance and Plasma Clearance of
^{99m}Tc-Labelled Diethylenetriaminepenta-Acetate,^{51}Cr-Labelled Ethylenediaminetetra-Acetate and Inulin in Man. Clin. Sci.**1984**, 66, 613–619. [Google Scholar] [CrossRef] [PubMed] - Simonsen, J.A.; Thilsing-Hansen, K.; Høilund-Carlsen, P.F.; Gerke, O.; Andersen, T.L. Glomerular Filtration Rate: Comparison of Simultaneous Plasma Clearance of
^{99m}Tc-DTPA and^{51}Cr-EDTA Revisited. Scand. J. Clin. Lab. Investig.**2020**, 80, 408–411. [Google Scholar] [CrossRef] [PubMed] - Frennby, B.; Sterner, G.; Almén, T.; Chai, C.-M.; Anders Jönsson, B.; Månsson, S. Clearance of Iohexol, Chromium-51-Ethylenediaminetetraacetic Acid, and Creatinine for Determining the Glomerular Filtration Rate in Pigs with Normal Renal Function: Comparison of Different Clearance Techniques. Acad. Radiol.
**1996**, 3, 651–659. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Radiotracer concentration in plasma samples as a function of time. The full curve is a bi-exponential fit to all data, and the dashed curve is the single exponential fitted to the late part of the curve.

**Figure 2.**One-pool approximation, Cl

_{1}, and reference clearance data, Cl

_{ref}. The dotted line, y = x, represents no correction. The full curve, y = 1.27 x

^{0.92}, is a fit to the data points, with Cl

_{1}based on the last 5 samples (black circles). For comparison, data points based on only 4 samples (white triangles) or 3 samples (grey squares) are also plotted.

**Figure 3.**Comparison of the developed correction with data and correction from Luis-Lima et al. [2] and with the correction from van Gelder et al. [7]. Black circles are our data, and open circles are the Luis-Lima data. The grey full curve is the Luis-Lima correction (4) along with downward extrapolation. At low GFR, the grey dashed curve with upward extrapolation is the van Gelder correction (5). The black curve is our correction (1), fitted only to the black circle data points but shown in the full range of available data.

No. of Samples (Time Interval) | Mean Deviation ± SD | |
---|---|---|

Absolute | Relative | |

five (120–240 min) | 0.0 ± 2.3 mL/min | 0.1% ± 3.6% |

four (150–240 min) | −0.2 ± 2.6 mL/min | −0.2% ± 3.9% |

three (180–240 min) | −1.1 ± 5.2 mL/min | −1.5% ± 7.0% |

Luis-Lima data * | −2.2 ± 17.7 mL/min | −0.2% ± 7.2% |

Study | Pigs | No. of GFR Measurements | GFR * | Correction Equation | |
---|---|---|---|---|---|

Weights | Sexes | ||||

Present study | 26–44 kg | ♀ | 40 in 20 pigs | 41–85 mL/min | (1) |

Frennby et al. (normal) [15] | 21–27 kg | (not stated) | 19 | 16.5–26.3 mL/min/10 kg | (2) |

Frennby et al. (reduced) [6] | 21–26 kg | ♀♂ | 21 | 5.3–11.3 mL/min/10 kg | |

Palnæs Hansen et al. [8] | 30–40 kg | ♀ | 12 | ~45–85 mL/min | (3) |

Luis-Lima et al. [2] | 101–212 kg | ♀ | 16 | 112–392 mL/min | (4) |

van Gelder et al. [7] | 34–80 kg | (not stated) | 23 in 5 pigs | ~17–44 mL/min | (5) |

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**MDPI and ACS Style**

Jødal, L.; Brignone, J.I.; Ladefoged, P.-K.C.; Lund, L.; Andersen, T.B.
Robust Porcine GFR Measurement with Radiotracers and Only Late Blood Samples. *Biologics* **2023**, *3*, 296-307.
https://doi.org/10.3390/biologics3040015

**AMA Style**

Jødal L, Brignone JI, Ladefoged P-KC, Lund L, Andersen TB.
Robust Porcine GFR Measurement with Radiotracers and Only Late Blood Samples. *Biologics*. 2023; 3(4):296-307.
https://doi.org/10.3390/biologics3040015

**Chicago/Turabian Style**

Jødal, Lars, Juan Ignacio Brignone, Pui-Ki Chan Ladefoged, Lars Lund, and Trine Borup Andersen.
2023. "Robust Porcine GFR Measurement with Radiotracers and Only Late Blood Samples" *Biologics* 3, no. 4: 296-307.
https://doi.org/10.3390/biologics3040015