Determinants of renal volume in autosomal-dominant polycystic kidney disease

Abstract

The Consortium of Radiologic Imaging Studies of Polycystic Kidney Disease (CRISP) recently showed that renal enlargement in autosomal-dominant polycystic kidney disease mimicked exponential growth. We determined the effects of cyst initiation rate, total number, and growth rate on the time-dependent change of total cyst volume (TCV). Mathematical models with equations integrating cyst surface area, volume, and an invariant growth rate constant were used to compute the time-dependent change in volume of solitary and multiple cysts. Multiple expanding cysts increased TCV in an exponential-like pattern even when individual cysts formed at different rates or exhibited different but constant growth rates. TCV depended on the rate of cyst initiation and on the total number of cysts; however, the compounding effect of exponential-like growth was the most powerful determinant of long-term cyst expansion. Extrapolation of TCV data plots for individual subjects back to an age of 18 predicted TCV values within an established range. We conclude that cysts started early in life were the main contributor to eventual TCV while their growth rate primarily determined renal size; although the rate of formation and the ultimate number of cysts also contributed. The good fit between the exponential models and the extrapolated CRISP data indicates that the TCV growth rate is a defining trait for individual patients and may be used as a prognostic marker.

Figure 1

Schematic diagram illustrating the evolution of a spherical cyst from a renal tubule.

Figure 2. Dependence of solitary cyst and multiple cyst enlargement on proliferation (growth) rate with k varying 5–25% per year

(a) Solitary cyst. (b) 500 cysts initiated at a common time and growing at a constant rate. In this and subsequent figures, the initial cysts have a diameter of 2 mm (0.0042 cm³).

Figure 3. Dependence of combined cyst enlargement on time of initiation and variable growth rates of individual cysts

(a) Appearance of kidney enlarged by cysts initiated on different dates and growing at the same rate. TCV time course patterns when 40, 80, or 160 cysts are initiated each year and grow at 10% per year. (b) Effect of different cyst growth rates (k = 2.5, 5, 7.5% per year) on configuration of TCV growth curves. All cysts initiated on uniform date, t = 0; 5000 cysts divided equally among three growth rates. Composite curves include all three growth rates. (c) Cysts added at a constant rate for 50 years up to a total of 5000 cysts, growing at three different growth rates (k = 2.5, 5, 7.5% per year). Ordinate values for C are the same as for B. Composite curves include all three growth rates.

Figure 4. Punctuated cyst formation

(a) Solid line, 2000 cysts initiated at t = 0. Dotted line, 1800 cysts initiated at t = 0 and 200 at age 30. (b) Solid line, 2000 cysts initiated at t = 0; Dashed line, 200 cysts initiated at t = 0 and 1800 more added at 30 years of age. Dotted line extends 200 cyst plot. All cysts grew at 10% per year.

Figure 5. Time-course plots of TCV growth curves

(a) Original TCV data from CRISP cohort. (b) Curves extrapolated from 3 to 4 measurements over 3 years in 203 CRISP patients. The intercept window of TCV determined in 21 subjects at 18 years of age (2.8–692 cm³) is shown by horizontal lines.

Figure 6. Time-course plots of TKV growth curves

(a) Original TKV data from CRISP cohort. (b) Curves extrapolated from 3 to 4 measurements over 3 years in 203 CRISP patients. The intercept window of TCV determined in 21 subjects at 18 years of age (276–1341 cm³) is shown by horizontal lines.