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)

Successive radioactive decay

Here, you can calculate the quantity of the radioactive daughter-nuclide, which arises from decay of its mother-nuclide. Physical half-times of the nuclides and the time elapsed, and the nuclides quantities have to be entered in the same units. The calculations are based on Bateman-equations and their limits. A chart will be dynamically generated to the result.

If you need to calculate the time difference between two time points ("time elapsed"), this algorithm can be helpful.

The decay goes according to the following equation:
nuclide 1 → nuclide 2 → nuclide 3.

Abbreviations:
T_(1/2)1 - half-time of the nuclide 1
T_(1/2)2 - half-time of the nuclide 2
f_(1→2) - branching ratio - the fraction of the nuclide 1,
which decays to the nuclide 2; the remainder decays in another way
t - time elapsed (form the beginning)
N₀₍₁₎ - quantity (mass) of the nuclide 1 at the beginning
A₀₍₁₎ - activity of the nuclide 1 at the beginning
N₀₍₂₎ - quantity (mass) of the nuclide 2 at the beginning
A₀₍₂₎ - activity of the nuclide 2 at the beginning
N_t(1) - quantity (mass) of the nuclide 1 after the time t
A_t(1) - activity of the nuclide 1 after the time t
N_t(2) - quantity (mass) of the nuclide 2 after the time t
A_t(2) - activity of the nuclide 2 after the time t
T_{(2_max)} - time, after which the mass/activity of the nuclide 2 will be maximal
N_{(2_max)} - maximal quantity (mass) of the nuclide 2
A_{(2_max)} - maximal activity of the nuclide 2

quantity of the nuclide	number of atoms (moles, mass)
quantity of the nuclide	activity (f.e., Bq)
T_1/2(1)
N₀₍₁₎ (or A₀₍₁₎)
T_1/2(2)
N₀₍₂₎ (or A₀₍₂₎)
f_(1→2) [%]
t
calculate