The renal dynamic imaging Gates method offers a reliable and noninvasive measurement of GFR [3, 4]. However, numerous elements can influence the determination of GFR by the Gates method . The attenuation coefficient was 0.153 cm–1 in γ-rays in soft tissues, with a 14—16% deviation in GFR for every 1 cm change in kidney depth , making the correction for kidney depth particularly important.
In this study, a new rotation method was selected to use the multi-angle projection data of the anterior probe and calculate the depth of kidneys. It was more accurate than the formula method. It did not add any additional radiation dose. There was no significant difference between the renal depth measured by the rotation method and CT and GFR obtained by renal dynamic imaging.
Renal depth measurement in multiple methods of GFR calculation
Tonnesen’s formula [6, 9] is the most commonly used formula for obtaining renal depth, with some limitations: only 55 white race subjects were included, and the age factor was discounted; ultrasound examinations were performed to measure the depth, and the position of kidney was different between ultrasound and renal dynamic imaging, which changed the position of kidney. And it is not applicable to Asians.
Several studies [5, 6] have shown that Tonnesen’s formula significantly underestimates the depth of kidney, which results in lower GFR. This study also confirmed these findings, with the Tonnesen’s formula significantly underestimating the depth and depth difference between the two kidneys and the total and single renal GFR.
The CT scan is the most accurate procedure for measuring renal depth , and Yang Yi et al.  demonstrated the feasibility of direct measurement by SPECT with CT instead of Tonnesen’s formula. The GFR measured by the 99mTc-DTPA dual plasma method was recommended by the American Society of Nuclear Medicine Committee on Nephrology [14, 15]. Chen Li  considered the dual plasma method as the "gold standard" to evaluate the difference between the kidney depth measured by CT and Tonnesen's formula, respectively, showing a slight difference in the GFR between CT and the dual plasma method. However, CT adds additional ionizing radiation. Additionally, artifacts from respiratory motion can deteriorate the renal contours , so CT is not yet routinely used to measure renal depth.
The CT method is the reference standard used for establishing many formulas. Taylor  derived a new formula using CT measurements as the standard while incorporating age, but the study was based on the white race. Hui et al.  indicated that the Li-Qian’s formula was effective in improving the accuracy, but it failed to incorporate individual differences, and therefore, there were still unavoidable errors in the estimation of the depth difference between two kidneys.
In some studies, lateral plane images of the kidney were taken alone after completion of dynamic kidney acquisition [13, 20] to directly determine kidney depth, but this approach might not be suitable because peak uptake of the kidney usually occurs 2–4 min after injection of the developer, and the lateral images are not completed until after dynamic acquisition when intrarenal radioactivity is already at a low level, and body contours are blurred, compromising their measurement accuracy.
In this study, the rotational method was used, in which the anterior probe was rotated at 3 min after the start of renal dynamic imaging to acquire the renal projection images for a total of 8 min so that the whole acquisition process could be completed in the first 10 min when the renal image was clearly outlined. This allowed the measurement results to be highly accurate while allowing individual differences and without the need for additional acquisition time and additional radiation dose. In this study, the accuracy of the rotational method was also evaluated using the CT values as the standard, and the Tonnesen’s formula and the Li-Qian’s formula were compared. The results of the study showed no significant differences in total and single renal GFR and depth of the two kidneys compared to CT between the rotation method and Li-Qian’s formula.
Renal depth difference of single renal GFR
Renal function was determined jointly by the left and right single kidneys. Single renal function measurement is an important component of the preoperative evaluation in many clinical contexts [21, 22]. The absolute single renal function includes absolute and relative single renal function . The relative single renal function is the relative contribution of the left and right kidneys to total renal function, and the measures include the percentage of the relative function of the left and right kidneys.
From the formula of the Gates method , the single renal GFR can be obtained based on the ratio of the single kidney uptake rate to the dual kidney uptake rate: [(CXK-CXB)/e–0.153YX]/[(CLK-CLB)/e–0.153YL + (CRK-CRB)/e–0.153YR]. The ratio of the single GFR value to the total GFR value is the relative renal function.
The difference in depth between the two kidneys affects the function of the single kidney. Gruenewald et al.  concluded if the two kidneys had the same renal function and the depth difference between the two kidneys was 1 cm, the single renal function ratio would change from 50:50 to 54:46. For a depth difference of 2 cm, it would change to 57:43, and for 3 cm, it would change to 61:39. Any formula would underestimate the depth difference between two kidneys. The depth difference between two kidneys estimated by Tonnesen’s formula was less than 0.1 cm for each subject, and that estimated by Li-Qian’s formula fluctuated within a small range.
In this study, the depth difference calculated by Tonnesen's and Li-Qian's formulas varied within a narrow range of 0.02 to 0.12 cm, whereas the depth difference between the two kidneys measured by CT was 0.39 ± 0.33 cm and by the rotation method was 0.49 ± 0.37 cm. Thus, both Tonnesen's and Li-Qian's formula significantly underestimated the depth difference between the two kidneys. The difference between the depth difference measured by CT and that measured by Li-Qian's formula and the mean value of the two were linearly correlated, which was probably because the depth difference measured by Li-Qian's formula was not accurately obtained and the depth difference measured was nearly constant.
In this study, although the differences between the two groups and the total and single kidney GFR values obtained from the Li-Qian’s formula were not statistically significant after grouping the kidney depths measured by CT and rotation, the depth difference was positively correlated with the resulting changes in single kidney function (|R(CT)-R(Li-Qian)|), (|R(Rotation)-R(Li-Qian)|) (r = 0.881, 0.641, P < 0.01).
Several scholars [18, 24] found the proportion of all subjects with a difference in depth between the two kidneys > 1 cm ranged from 7.5% to 42%. In this study, the proportion of patients with a difference in depth between the two kidneys ≥ 1 cm (measured by CT) was 15.28%. Thus, the changes in single kidney function due to differences in kidney depth also need attention. After grouping the kidney depths measured by CT and rotation method, the differences between the two groups and the total and single GFR obtained from the Li-Qian’s formula were not statistically significant. This might be because only a few cases were included in this study, and few cases had a difference in depth between the two kidneys ≥ 1 cm.
In this study, the exclusion of cases with severe hydronephrosis, and severe renal tumors to the point of renal displacement, might result in no difference in renal depth between CT, rotation method, and Li-Qian’s formula. For patients with severe renal failure or unilateral near-nonfunctioning kidney, the information of renal position cannot be identified due to low uptake of imaging agents, which in turn leads to the inability to accurately calculate the kidney depth. Since the anterior probe of the rotation method serves for positioning, it is not an option for patients with ectopic and transplanted kidneys. It is therefore limited in its scope of application which is a common problem with various methods. Furthermore, the rotation method involved in this study was based on the measurement of kidney depth to estimate GFR, and the correlation between poor kidney depth and the gold standard GFR needs to be confirmed.