The Uses and Advantages of Kirchhoff's Laws vs. Differential Equations in Pharmacology, Pharmacokinetics, and (Even) Chemistry

In chemistry, rate processes are defined in terms of rate constants, with units of time-1, and are derived by differential equations from amounts. In contrast, when considering drug concentrations in biological systems, particularly in humans, rate processes must be defined in terms of clearance, with units of volume/time, since biological volumes, which are highly dependent on drug partition into biological tissues, cannot be easily determined. In pharmacology, pharmacokinetics, and in making drug dosing decisions, drug clearance and changes in drug clearance are paramount. Clearance is defined as the amount of drug eliminated or moved divided by the exposure driving that elimination or movement. Historically, all clearance derivations in pharmacology and pharmacokinetics have been based on the use of differential equations in terms of rate constants and amounts, which are then converted into clearance equations when multiplied/divided by a hypothesized volume of distribution. Here, we show that except for iv bolus dosing, multiple volumes may be relevant. We have recently shown that clearance relationships, as well as rate constant relationships, may be derived independent of differential equations using Kirchhoff's Laws from physics. Kirchhoff's Laws may be simply translated to recognize that when two or more rate-defining processes operate in parallel, the total value of the overall reaction parameter is equal to the sum of those rate-defining processes. In contrast, when two or more rate-defining processes operate in series, the inverse of the total reaction parameter is equal to the sum of the inverse of those rate-defining steps.

Synthesis and use of radio cobaltic EDTA as an extracellular marker in rabbit heart

A new gamma-labeled marker for extracellular space is the cobaltic form of 58Co-ethylenediaminetetraacetic acid (58Co-EDTA). The cobaltic ion has a much higher affinity for EDTA than the cobaltous ion; it is prepared as a potassium salt, K+(58Co3+-EDTA4-), and is apparently biologically inert. Testing by equilibration in intact rabbits and comparing the myocardial content with that of [14C]sucrose give values of the volume of distribution in the myocardium of 0.294 +/- 0.052 ml/g for 58Co-EDTA and 0.303 +/- 0.051 ml/g for [14C]sucrose (SD, n = 130, for two hearts), with the ratios of 58Co-EDTA/sucrose averaging 0.973 +/- 0.043 (n = 130). The average value of the extracellular fluid measured in isolated rabbit interventricular septum using Co-EDTA was 0.51 +/- 0.05 ml/g (SD, n = 16) and 0.46 +/- 0.04 ml/g using [14C]sucrose as an extracellular fluid space (ECF) marker. Flushing with a high concentration of nontracer Co-EDTA does not reveal any release from binding sites. The gamma-energy (811 KeV), long half-life (71.4 days), stability, and lack of binding to tissue components make 58Co-EDTA a useful marker for ECF.

Influence of parathyroid state on calcium uptake in bone

The exchange of calcium and strontium ions in bone was studied in control dogs, dogs made hypocalcemic by parathyroidectomy, and dogs rendered hypercalcemic by injection of parathyroid hormone. After injections of tracer into the tibial nutrient artery, extraction of tracer during transcapillary passage was measured and expressed as a fraction of 1. Extraction over the first 3 min in normal dogs was 0.46 +/- 0.09 (n = 6), in hypocalcemic dogs it was increased to 0.53 +/- 0.07 (n = 6), and in hypercalcemic dogs it was decreased to 0.39 +/- 0.07 (n = 5). Subsequent washout was less rapid than normal in hypoparathyroid dogs and more rapid than normal in hyperparathyroid dogs. We conclude from this that the immediate volume of distribution in bone (or the number of available binding sites) for strontium diminishes as the parathyroid hormone level increases.