Tracer Methods in Hormone Research

1. Rates in Open System in the Steady State: Definitions and Relations.- A. One Pool Embedded in a Multicompartmental System.- Rates of Entry.- Production Rate.- Rates of Removal.- B. Two Related Pools Embedded in a Multicompartmental System.- Rates of Entry, Exit, and Transfer.- The Transfer Factor.- Calculations of Rates from Values of Production Rates (PR's) and Transfer Factors (?'s).- Further Description of the Rate of Transfer of Material from One Pool to Another.- The Contribution Factor.- Application of the Two-Pool Analysis to a Hormonal System.- C. Three Related Pools Embedded in a Multicompartmental System.- Rates of Entry, Exit, and Transfer.- Production Rates.- Contribution Factor.- Calculation of Rates from Values of PR's and ?'s.- Application of the Three-Pool Analysis to a Hormonal System.- D. General Systems of m Related Pools.- Expanded Subsystems of Pools.- 2. Infusion of Tracers at a Constant Rate.- A. Multicompartmental System in Which Only One Pool is Studied.- B. Multicompartmental System in Which Two Pools are Studied.- Rates.- Transfer Factors (?).- Contribution Factors (?).- Rates of Transfer Which Exclude Recycle.- C. Multicompartmental System in Which Three Pools are Studied.- Rates.- Contribution Factors.- "Non-Recycling" Transfer Rates.- Transfer Factors in a Subsystem of Three Primary Pools Connected in Series.- D. General m-Primary-Pool Subsystem.- Rates.- Rates in Terms of PR's and ?'s.- Contribution Factors.- Proof of the Relationship PR1 = v01 + ?21 v02 +...+ ?m1 v0m.- Relationships Between Rates in a System of m-Primary Pools and a Subsystem of Some of these Pools.- 3. Rapid Injection of Tracers.- A. Calculations Based on Areas under Specific Activity Curves.- Production Rates (PR) and Transfer Factors (?).- Rates.- B. Relationships Between Data Obtained by Rapid Injection and by Constant Infusion of a Tracer.- C. Calculations Based on the Shape of Specific Activity Curves.- Total Number of Pools in the System Undetermined.- Pool Size.- Rates of Exit.- Rates of Reentry, Fractional Loss.- "Turnover Times".- Mean Residence Time (T?).- Mean Transit Time (t?).- Mean Number of Cycles (v).- Mean Recycling Time (t?ii).- Mean Transfer Time (t?ij).- Two-Primary-Pool Subsystem.- D. Determination of Areas and Shapes of Specific Activity Curves.- Graphic Methods to Measure Areas.- Procedures to Determine Specific Activity Functions.- "Peel-off" Graphic Method.- Numerical (Computer) Methods.- 4. Tracer Kinetics in Compartmental Models.- Rate Constants (k's).- Fractional Rates (h's).- A. One-Pool System.- Rapid Injection of the Tracer.- Infusion of the Tracer at a Constant Rate.- B. Two-Pool Systems.- Rapid Injection of the Tracer.- Analysis of Two-Pool Systems with Equal Exponential Constants.- Analysis of a Two-Pool Closed System.- Calculation of Parameters of the Two-Pool System from Values of ?'s and D's.- Infusion of Tracers into the Pools at a Constant Rate.- C. Multiple-Pool Systems.- h's in Terms of ?'s and D's.- Unrestricted Three-Pool Systems.- Irreducible System: Number of Pools Versus Number of Exponential Terms in Specific Activity Functions.- Linearly Dependent Specific Activities.- Repeated ?'s.- Complex ?'s.- 5. Interpretation of Isotopic Data from Blood-Borne Compounds.- I. Data: Isotopic Steady-State Values or Areas under Concentration Curves.- A. One Tracer Administered.- Production Rates.- Metabolic Clearance Rates.- Sources of a Circulating Hormone.- Measurement of Blood Flow.- B. Two Tracers Administered.- Conversion Factors (?'s).- Rates of Secretion and Metabolism.- Pathways of Conversion of a Circulating Hormone to Another.- Fetomaternal Transfer and Production of Hormones.- Rates of Metabolism in Specific Organs.- C. Three Tracers Administered.- II. Data: Specific Activity Functions.- Size of the Pool of Fast Initial Distribution of the Intravenously Injected Tracer.- "Volume" of the Space of Fast Initial Distribution.- Rates of Exit of a Compound from Circulation.- Reentry into Circulation.- Average Times of Transit, Residence, and Recycling of Hormones in Circulation.- III. Calculations Based on Models Involving a Limited Number of Compartments.- IV. Analysis of Systems that are Not at the Steady State.- Note 5.- "Peel-off" Method.- Computer Method (R. J. Bogumil).- Discussion of Results.- 6. Rates of Secretion and Metabolism of Hormones Estimated from Specific Activities of Urinary Metabolites.- A. Estimation of Hormone Secretion Rates.- Case 1. Metabolites Derived from one Secreted Precursor (e.g., Aldosterone).- Case 2. Metabolites Derived from Two Secreted Precursors (e.g., Dehydroisoandrosterone).- Case 3. Metabolites Derived from Several Secreted Precursors (e.g., Testosterone).- B. Interpretation of Specific Activity Data Obtained from Labeled Urinary Metabolites.- C. Parameters of Metabolism Estimated from Labeled Urinary Metabolites.- Conversion of a Precursor to Urinary Metabolites.- Relative Conversion of Two Precursors to a Metabolite.- Metabolites "Uniquely Derived5' Transfer Rates.- Transfer Factors in a Subsystem of Three Primary Pools Connected in Series.- D. General m-Primary-Pool Subsystem.- Rates.- Rates in Terms of PR's and ?'s.- Contribution Factors.- Proof of the Relationship PR1 = v01 + ?21 v02 +...+ ?m1 v0m.- Relationships Between Rates in a System of m-Primary Pools and a Subsystem of Some of these Pools.- 3. Rapid Injection of Tracers.- A. Calculations Based on Areas under Specific Activity Curves.- Production Rates (PR) and Transfer Factors (?).- Rates.- B. Relationships Between Data Obtained by Rapid Injection and by Constant Infusion of a Tracer.- C. Calculations Based on the Shape of Specific Activity Curves.- Total Number of Pools in the System Undetermined.- Pool Size.- Rates of Exit.- Rates of Reentry, Fractional Loss.- "Turnover Times".- Mean Residence Time (T?).- Mean Transit Time (t?).- Mean Number of Cycles (v).- Mean Recycling Time (t?ii).- Mean Transfer Time (t?ij).- Two-Primary-Pool Subsystem.- D. Determination of Areas and Shapes of Specific Activity Curves.- Graphic Methods to Measure Areas.- Procedures to Determine Specific Activity Functions.- "Peel-off" Graphic Method.- Numerical (Computer) Methods.- 4. Tracer Kinetics in Compartmental Models.- Rate Constants (k's).- Fractional Rates (h's).- A. One-Pool System.- Rapid Injection of the Tracer.- Infusion of the Tracer at a Constant Rate.- B. Two-Pool Systems.- Rapid Injection of the Tracer.- Analysis of Two-Pool Systems with Equal Exponential Constants.- Analysis of a Two-Pool Closed System.- Calculation of Parameters of the Two-Pool System from Values of ?'s and D's.- Infusion of Tracers into the Pools at a Constant Rate.- C. Multiple-Pool Systems.- h's in Terms of ?'s and D's.- Unrestricted Three-Pool Systems.- Irreducible System: Number of Pools Versus Number of Exponential Terms in Specific Activity Functions.- Linearly Dependent Specific Activities.- Repeated ?'s.- Complex ?'s.- 5. Interpretation of Isotopic Data from Blood-Borne Compounds.- I. Data: Isotopic Steady-State Values or Areas under Concentration Curves.- A. One Tracer Administered.- Production Rates.- Metabolic Clearance Rates.- Sources of a Circulating Hormone.- Measurement of Blood Flow.- B. Two Tracers Administered.- Conversion Factors (?'s).- Rates of Secretion and Metabolism.- Pathways of Conversion of a Circulating Hormone to Another.- Fetomaternal Transfer and Production of Hormones.- Rates of Metabolism in Specific Organs.- C. Three Tracers Administered.- II. Data: Specific Activity Functions.- Size of the Pool of Fast Initial Distribution of the Intravenously Injected Tracer.- "Volume" of the Space of Fast Initial Distribution.- Rates of Exit of a Compound from Circulation.- Reentry into Circulation.- Average Times of Transit, Residence, and Recycling of Hormones in Circulation.- III. Calculations Based on Models Involving a Limited Number of Compartments.- IV. Analysis of Systems that are Not at the Steady State.- Note 5.- "Peel-off" Method.- Computer Method (R. J. Bogumil).- Discussion of Results.- 6. Rates of Secretion and Metabolism of Hormones Estimated from Specific Activities of Urinary Metabolites.- A. Estimation of Hormone Secretion Rates.- Case 1. Metabolites Derived from one Secreted Precursor (e.g., Aldosterone).- Case 2. Metabolites Derived from Two Secreted Precursors (e.g., Dehydroisoandrosterone).- Case 3. Metabolites Derived from Several Secreted Precursors (e.g., Testosterone).- B. Interpretation of Specific Activity Data Obtained from Labeled Urinary Metabolites.- C. Parameters of Metabolism Estimated from Labeled Urinary Metabolites.- Conversion of a Precursor to Urinary Metabolites.- Relative Conversion of Two Precursors to a Metabolite.- Metabolites "Uniquely Derived5' from a Circulating Compound.- Relation Between the Specific Activities of a Circulating Compound and of a Urinary Metabolite Uniquely Derived from It.- Measurement of Production Rates and Rates of Interconversion of Circulating Compounds.- Production Rates.- Rates of Interconversion.- D. Labeled Urinary Metabolites in Pregnancy.- Secretion Rates.- Fetomaternal Transfers.- E. Comments.- 7. In vitro Tracer Superfusion Experiments.- Superfusion Versus Batch Incubations.- Use of Two Metabolically Related Tracers in Superfusion Experiments.- Model.- Calculation of Rates of Entry of Superfused Tracer into Cells.- Fraction of a Superfused Tracer Returning from the Cells to the Medium.- Fraction of Superfused Tracer Appearing in the Perfusate as a Metabolite.- Conversion Factors.- Rates in the Superfusion Model.- Intracellular Clearance.- A Special Case: Nonsteroidogenic Tissue.- Validation of the Model.- Applications.- References.