A simple method for determining split renal function from dynamic ^99mTc-MAG3 scintigraphic data

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. The 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 study was to evaluate a new method for determining SRF 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 one blood-pool and two renal ROIs. Data from 107 patients who underwent ^99mTc-MAG3 scintigraphy were used to determine SRF values. Values calculated using the BPC method were compared to those obtained with 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 obtained with the BPC method did not differ significantly from those obtained with the PR method and showed no consistent bias, while SRF values obtained with the IN method showed significant differences with some bias in comparison to those obtained with either the PR or BPC method. No significant interobserver variability was found between two observers calculating SRF using the BPC method.

Conclusion

The BPC method requires only three ROIs to produce reliable estimates of SRF, 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.

Appendix: model of renal activity during the early extraction phase, to illustrate the linear parametric relationship between renal and hepatic activity

In addition to the kidneys, which excrete MAG3, radionuclide images show nonexcretory 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 MAG3 accumulation in the kidneys from the total count rate in the kidney ROI. Assuming that the time-course of the summed intravascular and interstitial signal (loosely termed ‘blood-pool’ in this paper) is similar in the kidney and in other blood-rich nonexcretory organs such as the heart, liver and spleen, the latter organs can be used as models of the kidneys without excretory function. For example, following injection, the liver count rate peaks (typically during the first minute) and subsequently decreases with time, while the renal counts increase before the peak of the renal curve, which normally occurs at 2.5 – 3.0 min, although this timing can vary between patients. The count rate from the liver ROI acts as a model of the contribution to total kidney count rate from mostly blood pooling, where the blood pool is defined here as intrarenal vascular plus interstitial organ activity during the ascending portion of the renal TAC. 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 in the blood pool within the kidney and that the kidney accumulates extracted activity in proportion to that in the blood pool. That is, we are assuming that the renal blood pool is a scaled renal feed function, f (t), thus

$$ f(t)=c{e}^{-\lambda t}\kern1em c>0\kern0.5em \mathrm{and}\kern0.5em \lambda >0 $$

(A1)

and

$$ K(t)=f(t)+\alpha {\displaystyle {\int}_0^{t<T}f\left(\tau \right)}d\tau, $$

(A2)

where α > 0 is proportional to the extraction fraction and τ is a dummy variable. Substituting Eq. A1 into Eq. A2 yields:

$$ K(t)=c{e}^{-\lambda t}+\alpha {\int}_0^{t<T}c{e}^{-\lambda \tau }d\tau =\left(1-\frac{\alpha }{\lambda}\right)c{e}^{-\lambda t}+\frac{\alpha c}{\lambda }. $$

(A3)

Now, let us assume (ignoring trace hepatocyte extraction of MAG3), that H(t) is some constant, h, multiplied by f (t) over the time interval of interest, then

$$ H(t)=hf(t)=hc{e}^{-\lambda t}\kern2em h>0 $$

(A4)

and

$$ K(t)=\left(1-\frac{\alpha }{\lambda}\right)\frac{1}{h}H(t)+\frac{\alpha c}{\lambda }. $$

(A5)

Note that this has the same form as

$$ K(t)=sH(t)+b, $$

(A6)

where $s=\left(1-\frac{\alpha }{\lambda}\right)\frac{1}{h}$ and $b=\frac{\alpha c}{\lambda }$. Note that the slope, s, is positive when $\left(1-\frac{\alpha }{\lambda}\right)>0$ or negative when $\left(1-\frac{\alpha }{\lambda}\right)<0$, while b is strictly positive. Since we can obtain s and b directly from ordinary least squares linear regression of a parametric function of the data, it is not necessary to inspect the plot or know the values of c, α and λ 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 the parametric liver count rate is zero.

Equation A6 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 = {t ₁,t ₂,t ₃,…t _n }. However, the linearity of the result in Eq. A6 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 collinear and/or almost linear relationships between K(t) and H(t) in 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 be as simple as possible while still explaining the data. Finally, as the parametric relationship between K(t) and H(t) is collinear during the desired period of observation, quality assurance is possible by testing the linear goodness of fit for the least squares analysis of K(t) and H(t).