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Nuclear Medicine

Calculator

(formerly accessible on: www.nuk.bieganski.org)

General math & medicine options

Arithmetic mean and standard deviation
Regression of points to straight line, correlation coefficient
Finding of natural divisors
The highest common divisor
Polynomials
Time difference
Estimation of some human biometric parameters
Concentration conversion
Pharmacokinetic compartment models

Calculations related to nuclear physics

Examples of application of the programs below are accessible here.
Simple radioactive decay (1 radioactive nuclide: A → B)
Successive radioactive decay (2 radioactive nuclides: A → B → C)
Successive radioactive decay (3 radioactive nuclides: A → B → C → D)
Conversion of activity units (traditional into SI-derived and vice versa)
Conversion of mass into activity and vice versa (mass-units into activity-units and vice versa)

Calculations related to nuclear medicine

Instruction for the programs below is accessible here.
(1.) Calculation of thyroid volumen on the basis of the lobes diameters
(2.) Calculation of (radio)nuclide uptake (f.e. uptake of radioiodine in the thyroid)
 (2a.) Calculation of uptake of I-131 in the thyroid (This program can be saved as a file and launched in another PC, a browser with HTML and JavaScript is necessary; in Polish).
(3.) Calculation of radioiodine dose (simplified)
(4.) Kinetic modeling I. (effective half-time, maximal uptake and others, based on a series of measures) - for radionuclide therapy
(5.) Kinetic modeling II. (effective half-time, maximal uptake and others, based on three measures) - for radionuclide therapy
(6.) Calculation of dose of radioiodine or another radionuclide for treatment (modified Marinelli-formula)
(7.) Dosimetry of α- and β-radiation
(8.) Dose rate and absorbed dose of γ radiation (in a distance from a point source)

Pharmacokinetic compartment models

Here, calculation of macro-constants (or hybrid-constants) for compartment models with number of compartments ranging from one to five. The quantities and concentrations of the substance (e.g., drug) in each compartment after time t can be calculated as well. For passive transport, if only intercompartmental clearances are known, the first option allows calculating of the elimination rate constants which are needed in next steps. Algorithms published in own articles were used here. Basic assumption: the transport obeys the rules of first-order kinetics. Symbols used:
Vi: volume of compartment i,
Cti, Qti: concentration / quantity of the substance in compartment i after time t,
C0i, Q0i: initial (t= 0) concentration / quantity in compartment i,
R1: infusion rate into compartment 1,
Micro-constants (input data):
kij: elimination rate constant from i to j,
kji: elimination rate constant from j to i,
ki0: elimination rate constant from i to the environment.
Macro-constants (hybrid-constants, output data):
bi: exponent rates,
ci, di, etc.: multiplying factors;
When entering the data, one must take care on the conservation of the units.

Accessible options

Calculation of elimination rate constants from clearances (passive transport)
Single-compartment model
Two-compartment model
Three-compartment model
Four-compartment model
Five-compartment model

Choose above the option desired.

©Author: Cyprian Świętaszczyk, 2013; last update: 07.2020