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)

Gamma radiation dose rate and absorbed dose

Here, it is possible to calculate the dose rate in a distance of R from the radiation source of activity A in a medium with linear attenuation coefficient (or energy absorption coefficient) of μ_l, and the absorbed dose.

A
R
Γ		• ² •
B		XXXXX
μ_l		^-1
T_(1/2)
t
Calculate

Symbols and operations A: activity,
R: distance,
Γ: γ-ray dose constant,
B: buildup factor (default: 1),
μ_l: linear attenuation coefficient
(or energy absorption coefficient),
T_(1/2): half time,
t: time elapsed;
H^•: dose rate,
H: absorbed dose;
Calculation:
H^•= B • A • Γ / R² • exp(-μ_l•R),
H= B • A • Γ • t / R² • exp(-μ_l•R);
Calculation of absorbed dose is possible only, if the T_(1/2) is specified. If t=0, the t is regarded to tend to infinity (in comparison to T_(1/2)).
Examples of radiation sources:

Radionuclide	Γ [μSv⋅m²⋅h^-1⋅GBq^-1]	T_(1/2) [d]
₅₃I-131	76,4	8,02
₆₂Sm-153	24,4	1,93
₇₁Lu-177	7,64	6,65

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