MIRD Pamphlet No. 19: Absorbed Fractions and Radionuclide S Values for Six Age-Dependent Multiregion Models of the Kidney

KIDNEY ANATOMY AND PHYSIOLOGY

The kidneys lie between the dorsal body wall and the parietal peritoneum within the superior lumbar region. The lateral surface of each kidney is convex. Its medial surface is concave encompassing a vertical cleft, the renal hilus, which leads to a space interior to the kidney called the renal sinus. Structures such as the ureters, renal blood vessels, lymphatics, and nerves enter and exit the kidney at the hilus and occupy the sinus.

Internally, the kidneys may be divided into 3 distinct anatomic regions as shown in Figure 1 (9). The most superficial region is the renal cortex, which is light in color and has a granular appearance. Deep with respect to the cortex is the darker renal medulla composed of cone-shaped tissue masses called medullary pyramids. The base of each pyramid faces toward the cortex and the apex, or papilla, points internally to the kidney hilus. The pyramids appear striped as they are formed almost entirely by roughly parallel bundles of microscopic urine-collecting ducts. Separating the pyramids are deeper penetrations of the cortex (renal columns). Each medullary pyramid and its adjacent cap of cortical tissue constitute 1 of ∼6–18 lobes of the kidney. Lateral to the hilus within the renal sinus is the renal pelvis: a flat, funnel-shaped tube that is continuous with the ureter as it leaves the hilus. Branching extensions of the pelvis form 2 or 3 major calyces, each of which subdivides to form several minor calyces, cup-shaped areas that enclose the papillae of the pyramids. The calyces collect urine that drains continuously from the papillae and is emptied to the renal pelvis. Urine then flows through the renal pelvis and into the ureter, where it is transported to the urinary bladder.

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FIGURE 1.

Anatomic diagram of kidney. (Adapted from Figure 26.3 with permission of (9).)

The microanatomy of the kidneys is dominated by 2 structures: (1) nephrons, which are the functional units that perform blood filtration and urine formation, and (2) the collecting ducts, each of which collects urine from several nephrons and conveys it to the renal pelvis. Each nephron is composed of a glomerulus (cluster of capillaries) encased within a capsule structure and connected to a renal tubule. The glomerular capsules are located within the renal cortex, whereas the renal tubules (carrying the filtrate) begin as the proximal convoluted tubules and then form hairpin loops (Loop of Henle) that penetrate into the adjacent medullary pyramid. These penetrations into the medulla are small for cortical nephrons (constituting ∼85% of all nephrons) but are substantial for juxtamedullary nephrons, whose glomeruli lie just lateral to the cortical-medullary junction. The ascending limbs of the tubules return the filtrate (which now becomes newly formed urine) to within the renal cortex, where they form the distal convoluted tubules. Urine is then sent by the collecting ducts back through the medullary pyramids and into the renal pelvis.

REVIEW OF PUBLISHED DOSIMETRIC MODELS OF KIDNEYS

In 1969, Snyder et al. published MIRD Pamphlet No. 5, the first standardized anthropomorphic computational model of the adult (10). In this model, the kidneys were represented as 2 symmetric ellipsoids cut by a plane with no differentiation of their internal structure. The mass and volume of both kidneys were taken to be 288 g and 288 cm³, respectively, for unit density tissue. This mass is relatively consistent with the 310-g kidney mass of the Reference Man as given in ICRP Publication 23 (11). In MIRD Pamphlet No. 5, absorbed fractions of energy were tabulated for various target organs and a uniformly distributed source of photons in both kidneys.

In the subsequent revision to the MIRD Pamphlet No. 5 adult model (12), the geometry of the kidneys remained the same. A change in the tissue density to 0.98 g cm⁻³ resulted in a corresponding change of total kidney mass to 284.2 g. In MIRD Pamphlet No. 5 Revised, the kidneys were also considered as a uniform photon source for the tabulation of specific absorbed fractions of energy. These values were also used in tabulating radionuclide S values for the adult anthropomorphic model in MIRD Pamphlet No. 11 (13).

In 1980, Cristy published a series of anthropomorphic computational models representing a newborn, 1 y old, 5 y old, 10 y old, 15 y old (also representing a female), and an adult (14). The geometric representation of the kidneys was taken to be the same as that in the adult MIRD Pamphlet No. 5 Revised model. For the adult, the only change made was an increase in the density of soft tissue to 1.04 g cm⁻³, giving a revised total kidney mass of 299 g. Kidney volumes for the younger ages were derived on the basis of reference kidney masses published in ICRP Publication 23 (11). In 1987, Cristy and Eckerman published absorbed fractions of energy for monoenergetic photon sources originating from various source organs within these 6 anthropomorphic models (7). In their calculations, the kidneys were considered as both a uniform source and a target region.

The only nonuniform computational model of the kidney was published in 1969 by McAfee (1). To calculate the radiation dose for radionuclides excreted by the kidneys, McAfee represented each kidney as 3 regions: the renal cortex and medulla, represented as 2 concentric elliptic shells, and the renal pelvis, represented as a wedge-shaped hollow structure at the center of each kidney. Individual medullary pyramids were not considered. The volume of each kidney was taken as 151 cm³ for a mass of 151 g. The corresponding dimensions of the cortex, medulla, and pelvis were derived from percentage volume measurements on 1 human kidney, later published in ICRP Publication 23 (11). The volume of the cortex was measured as 70% of the total kidney volume, the medulla as 25%, and the collecting system (pelvis) as 5%. Although the McAfee model was thus available for making nonuniform kidney dose estimates, the model has not been widely adopted in nuclear medicine dose estimates, primarily due to lack of imaging techniques needed to quantify differential kidney uptake in vivo.

DESCRIPTIONS OF REVISED DOSIMETRIC MODELS

The new series of dosimetric kidney models provides suborgan definitions not previously considered in the MIRD Pamphlet No. 5 Revised adult kidney model (12) or in the Oak Ridge National Laboratory (ORNL) kidney series (7,14). In the following section, equations describing each region within the kidney model series are given using the Cartesian coordinate system defined for the full anthropomorphic mathematic models. In this system, the models are assumed to be erect, with the origin taken as the center of the base of the trunk, the positive x-axis directed to the model’s left, the positive y-axis toward the model’s back, and the positive z-axis upward toward the model’s head. Within this coordinate system, the equations for each kidney region are given in their most general form. Definitions for the variables used in these equations are given in Table 1. Furthermore, values of these variables for the different age-specific models are listed within Table 2.

The new model is formed of 12 regions for each kidney: 5 medullary pyramids, 5 papillae, the renal pelvis, and the renal cortex. The number of medullary pyramids in the model is less than that seen in the real anatomy (6–18 pyramids) and represents a compromise between mathematic simplicity needed for Monte Carlo transport calculations and the need for an improved anatomic representation over the concentric ellipsoid-shell model of McAfee (1). Each region is derived from dimensions and volumes given in ICRP Publication 23 (11) for both the newborn and the adult. For the other ages, the volume ratios between the different kidney subregions are assumed to remain constant: ∼70% of the total kidney volume is assumed to be cortex, ∼25% medulla, ∼4% pelvis, and ∼1% papillae. Table 3 gives the volume of each kidney subregion for the 6 different ages considered. The elemental composition of the kidney tissues, given in Table 4, is assumed to be uniform and is taken as soft tissue (as defined in (7)).

Outside Shape of Kidney Models

The uniform kidney model included within the ORNL phantom series (7) is used to define the outer shape of the new kidney model series. Each kidney is modeled as an ellipsoid cut by a plane perpendicular to the x-axis. Both kidneys are symmetrically positioned relative to the (y, z) plane. A 3D representation of the kidneys can be seen in Figure 2A. Equation 1 defines the outer dimensions of each kidney. The ± sign is used to indicate either the right (+) or left (−) kidney, respectively: Eq. 1

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FIGURE 2.

Three-dimensional representation of computational kidney model. (A) Exterior portion of ellipsoid representing kidney is seen with, at cutting plane, renal pelvis. (B) Cut through kidney reveals 5 medullary pyramids, renal pelvis at organ’s center, and surrounding renal cortex. (C) Cut through pelvis shows medullary pyramids within pelvis. One medullary pyramid is removed to reveal papillae at apex of each pyramid.

ABSORBED FRACTIONS OF ENERGY

To simulate the transport of photon and electron particles within the present series of kidney models, the Monte Carlo electron-photon transport code EGS4 (15,16) is used. Additionally, the trunk region as defined in the ORNL phantom series is added to the simulation geometry to keep track of the energy escaping the kidneys. The methodology to calculate absorbed fractions of energy with a corresponding SD as described in MIRD Pamphlet No. 15 is used (17).

Absorbed fractions of energy, listed within Appendix A, are calculated for both monoenergetic photon and electron sources by considering 12 energies ranging from 10 keV to 4 MeV. A total of 1,000,000 source particles are simulated for each energy and source combination (10 runs of 100,000 particles). Source regions include uniform distributions within the renal cortex, the renal medulla, the renal pelvis, and the renal papillae. Target regions include these same 4 regions as well as the tissue regions outside the kidneys (trunk region). Footnotes at the bottom of the tables in Appendix A indicate when the coefficients of variation (CVs) on the absorbed fraction exceed 30%.

RADIONUCLIDE S VALUES

The mean absorbed dose to the target region per unit cumulated activity in the source region (S value) is calculated for a variety of radionuclides of interest in nuclear medicine. These results are listed in Appendix B. The list of radionuclides and source regions considered is shown in Table 5. In these calculations, the radionuclide decay data files of Eckerman et al. (18,19) have been used, in which the β-particle and positron energy spectra are finely divided into logarithmic intervals. The absorbed fractions for photon sources are used for all photon radiation components of the decay scheme. The absorbed fractions for electron sources are used for all β-particle and positron radiation components.

DISCUSSION

Values of radionuclide S values given in Appendix B may be used to compare regional kidney doses to values obtained by the standard single-region model. Under the present multiregion model, the mean dose per unit administered activity, A₀, to tissues of the renal cortex is given as: Eq. 13 where τ_cort, τ_med, and τ_pel represent the residence times in the renal cortex, medulla, and pelvis, respectively. For the present example, residence times in the small volumes of the medullary papillae are not considered. In addition, values of τ_cort and τ_med correspond to uptake in both the organ’s blood pool as well as the parenchyma. In the single-region kidney model, the mean dose across the whole organ is determined as: Eq. 14 where τ_kidney represents the total resident time in the kidney (τ_cort + τ_med + τ_pel). Dividing Equation 13 by Equation 14 yields the ratio of renal cortex dose to average kidney dose for a fixed administered activity and total kidney residence time: Eq. 15 where f_cort, f_med, and f_pel represent the fractional residence times within the renal cortex, medulla, and pelvis, respectively. A similar expression can be derived for the renal medulla as a target region.

Table 6 presents values of dose ratios given by Equation 15 for compounds labeled with ⁹⁰Y as a function of the percentage total residence time assigned to the renal medulla and renal pelvis. The difference in any combination of fractional residence times is assigned to the renal cortex. Consequently, for compounds that are filtered by the glomerular capsules and then concentrated in the tubules of the renal cortex, the cortex dose is shown to be 1.29 times that predicted by the single-region model (f_med and f_pel are 0%). Likewise, the dose to the medullary tissues is only 26% of that predicted by D̄_{kidney-single region}. For compounds that are rapidly filtered in the kidneys and then rapidly transported without tubular accumulation, Table 6 shows that the dose to the renal cortex decreases to only 48% of that predicted by the single-region model, whereas the tissues of the medulla may approach a factor of 1.88 times as great.

Corresponding dose ratios are shown in Table 7 for compounds labeled with ¹³¹I. For compounds exhibiting specific renal uptake in proximal or distal tubules, the dose enhancement to the cortex is similar to that for ⁹⁰Y (dose ratio of 1.27), whereas the dose to the renal medulla is only 10% of the mean kidney dose. For compounds filtered by the glomeruli, the mean dose to the kidneys is representative of the cortex dose only when ∼80% of the kidney residence time is assigned to the renal cortex (f_med + f_pel = 20%). The mean kidney dose is representative of the medullary dose only when ∼30% of the total residence time is within the renal medulla.

Radionuclide S values for the single-region model are 4.87 × 10⁻⁴ and 1.64 × 10⁻⁴ mGy MBq⁻¹ s⁻¹ for ⁹⁰Y and ¹³¹I, respectively. Consequently, for the total kidney residence times of 0.5, 1.0, 2.0, and 3.0 h, the mean kidney dose per unit administered activity is 0.877, 1.75, 3.51, and 5.26 mGy MBq⁻¹, respectively, for ⁹⁰Y and 0.294, 0.589, 1.18, and 1.77 mGy MBq⁻¹, respectively, for ¹³¹I. These values may then be used to assign absorbed doses to the renal cortex and medulla given the relative dose ratios shown in Tables 6 and 7.

Full utilization of the new model requires serial imaging of the kidneys with regions of interest assigned to the renal cortex and medulla. Whereas the inherent radiosensitivity of the kidneys is defined at the cellular level, the multiregion model can also be used to aid in predicting potential biologic response. If the dose-limiting cells of the kidneys are those of the glomeruli, proximal convoluted tubules, or distal convoluted tubules, then the appropriate radiation target in the new model is the renal cortex. If, however, the dose-limiting cells are those of the collecting ducts, the appropriate target region in the revised model is the renal medulla. A more extensive treatment of kidney dose nonuniformity can also be pursued using emission tomography to assess renal activity uptake and retention coupled with tissue volume measurements via CT. Full 3D assessments of kidney tissue dose can then be made through a convolution of voxel-based radionuclide S values with voxel-based measurements of the cumulated activity (8).

CONCLUSION

Six new stylized mathematic models of the kidney are presented for use in internal dose assessment for both diagnostic and therapeutic nuclear medicine procedures. These models permit the consideration of both nonuniform distributions of renal uptake and suborgan dose assessment to the renal cortex, medullary pyramids, and renal papillae. In the new model, the renal cortex dose is considered representative of the mean dose to the glomeruli and the proximal or distal collecting tubules. The renal medulla dose is considered representative of the mean dose to the ascending or descending tubules and collecting ducts.

For the adult, the absorbed dose to the renal cortex for ⁹⁰Y-labeled compounds retained within that subregion is ∼1.29 times that predicted by the single-region kidney model, whereas the medullary dose is only 26% of that same single-region value. For compounds that are rapidly filtered in the kidneys, the renal cortex dose is approximately one-half of that predicted under the single-region model, whereas the tissues of the medullary pyramids receive an absorbed dose 1.5–1.8 times larger.