Multiresponse Fitting

(Updated: 2020-06-06. Beta version to test. Comments to: guillermo2046(at)

Here the intake can be estimated using measurements from two different bioassay types: Whole body, Urine excretion, Faecal excretion, Thyroid (only for Iodine) and Lungs (only for uranium by Inhalation). For instance, whole body measurements and urine measurements can be used to estimate the intake that best fits both set of data.
The ICRP 130, ICRP 134 and ICRP 137 biokinetic models are used.
Different intake pathways can be selected and different kind of intake (acute or chronic). If chronic intake is chosen then the last day of exposure should be indicated, after this date it is assumed that the intake ceases.
The decay constant is charged choosing the isotope, if not available it can be entered, expresed in days^-1, writing its value (e.g 0.011674 for I 125, or as an expression e.g: Log[2]/(5.13*10^6/(24*60*60)), if one knows the half-life in seconds).

The absortion factors (fA- ingestion or inhalation-, fr, sr, ss) and the the Dose coefficient e(50) can be obtained using the OIR (ICRP134/137) data viewer

The data by default represent the whole body and 24-Urine excretion data from a person that he has been exposed to acute unkown intake by inhalation of Co-60. It should be selected: Element: Cobalt, Intake pathway: Inhalation, Intake type: Acute, Decay constant: Co-60 (or write 000360010) (d^1), AMAD: 5, Class CobaltS, Bioassay type 1: Wholebody Bioassay type 2: Urine SFB: 1.70 Dose coefficient e(50): 3.1*10^-5 then run the example, the solution should be around 29 kBq.

Select Element: Select pathway: Intake type: Time of exposure for chronic intake (in days): (if constant intake is selected)
Decay constant (in days^-1): Or
In case of ingestion: fA (for Ingestion):

In case of inhalation select:

Bioassay 1:
Bioassay data {{t1, m1, s1}, {t2, m2, s2}, ...} , being ti=time, mi=measurement(Bq), si=uncertainty.

Scattering factor B:

Bioassay 2:
Bioassay data {{t1, m1, s1}, {t2, m2, s2}, ...} , being ti=time, mi=measurement(Bq), si=uncertainty.

Scattering factor B:

Dose coefficient e(50)(mSv/Bq):
LimitPlot: {min, max}:

Push EVALUATE, wait a few seconds.

IRF and excretion factors

Click Crt + Evaluate to open the ouput in a new window. The solution are given as an formated table, you can save it as usual (ej.: pick in the table with your mouse and paste it into a file -ej.: MS EXCEL- for later uses).
Rodríguez-Díaz Juan M. ; Sánchez-León Guillermo; “Efficient parameter estimation in multiresponse models measuring radioactivity retention” Radiation and Environmental Biophysics 2019. (