A Power Law for Determining Renal Sufficiency Using Volume of Distribution and Weight from Bolus 99mTc-DTPA, Two Blood Sample, Pediatric Data

Objectives: (1) Explore power laws for estimating the one-compartment glomerular filtration rate (G₁), i.e., E(G₁), as functions of compartment volume (V), patient mass (W), age (A), height (H) and sex (S). (2) Propose a renal sufficiency index, RSI=G₁/E(G₁). (3) Present the best estimator, E(G₁) = f(V,W) = 10.988 V^0.64717W^0.20185. (4) Present the first clinical application of RSI, prediction of relative bone age (RBA = E(A)/A). Methods: 130 ^99mTc-DTPA imaging and G₁ studies were screened to find 44 normal studies in children 1.46 to 18.5 years old. Results: E(G₁) formulae of the body surface area type, i.e., f(W,H,S) and F(W,H), were found to be statistically unwarranted. Statistically acceptable formulae, in descending adjusted R², were f(V,W), f(V,A), f(V,H), f(V), f(W,A,H), f(W), f(H) and f(A). Kleiber´s law, E(G₁) prop W^frac34, seems to confirm the previously reported relationship GFR_inulin ap 0.87G₁. Our best G₁ estimator, f(V,W), may be related to a physiological volume. RSI as predicted by f(V,W) had the smallest relative standard deviation, 11.3%, no regression bias and good agreement with clinical classification at 95% specificity. RBA was found to be correlated with RSI, with a peak at 88% E(RSI), with RSI accounting for 25% of its variance. Conclusions: Our best RSI predictor, RSI = 90.927gammaV^0.35283W^-0.20185, should be capable of detecting mildly reduced (14.1%) renal sufficiency.