Nuclear Medicine


(formerly accessible on:

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
Quadratic equation
Time difference
Estimation of some human biometric parameters
Concentration conversion

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)

Calculation of the dosis of radioiodine (or another radionuclide) with the Marinelli-formula

This option has been developed mainly for the nuclear medicine doctors. Calculations play a very important role in the nuclear medicine therapy, however, the decision about the radiopharmaceutical apllied and its dose must be made by the Doctor taking care of the Patient. The Doctor makes the decision not only based on mathematical calculations, but also on his own knowledge and experience, and takes also the full responsibility.

The algorithm calculates the dosis of (mainly) iodine-131 for therapy of benign thyroid disorders. A modified variant of the Marinelli-formula is used. With its use, it is possible to calculate the doses of other nuclides for other therapies - in such a case, another decay energy will be taken into account in the form (kinetic energy of corpuscular radiation with short range in tissue, as α, β, conversion electrons, fission fragments and so on, but not γ- or X-radiation).
The modified formula of Marinelli:

A = 23.28 • m • D (193)(1)

U • T(1/2)ef ECf
A - radionuclide activity [MBq]
m - target mass [g]
D - focal radiation dose [Gy], which should be reached in the above mass
U - radionuclide uptake [%]
T(1/2)ef - effective half time [d]
Cf - correction factor for the number of radioactive disintegrations ("cumulated activity"), default: 1.00
E - mean energy of the corpuscular radiation (i.e. α, β, conversion electrons) per one decay [keV] - specify only when the nuclide different from 131I

Values typical for benign thyroid disorders:
Recommended radiation doses:
- Graves-Basedow disease (attempt of optimization): 100-150 Gy
- Graves-Basedow disease (ablation): 200-300 Gy
- UFA: 350-400 Gy
- MFA: 150-200 Gy
- disseminated autonomy (ablation): 200 Gy
- non-toxic goiter: 100-150 Gy

Effective (mean) half-time:
UFA and Gr.-Bas. disease (hyperthyreose): 4.2 days
UFA (euthyreose), MFA / diss. aut. (hyperthyreose): 4.8 days
MFA / diss. aut. (euthyreose): 5.5 days
Patient ID
Target mass [g]
Radionuclide uptake [%]
Focal radiation dose [Gy]
T(1/2)ef. [d]
Therapy nuclide
Mean particle energy[keV]
Correction factor
Calculate the nuclide dose

©Author: Cyprian Świętaszczyk, 2013;