(Updated: 2025-01-11)

Here is fitted some unkown parameters of compartmental model. The "compartmental matrix" shall be written: {{1,2,k12},...{i,j,kij},...,{n,n,k_nn}},where kij is the transfer rate -clearance- from compartment i to compartment j, k_ij can be constant or function of t. The radioactive decay constant, if available, will be expressed in the same units as the rate transfer constants. All units must be consistent; therefore, if k_ij is given in days^-1, the time t used for evaluating retention must also be in days. The unknown parameters will be fitted by taking measurements from one compartment i. Numeric methods are applied, starting points values for the unkown parameters are requiered.

Enter the rate transfer values (if some values are unkwoun write a symbol (e.g., {1,4, k14): {{1,2,k12},{1,0,1.9404},{2,3,k23 },{3,0,0.01155},{3,1,0.0462}} Number of compartments:    Decay constant:   Initial conditions at time t = 0: Input function in each compartment : All values of this field must be {0,.., 0} if it is an impulsive single-input, because the inputs are the initial conditions.

Parameters fo be fitted (i.e.:{k1, k2}) : Starting points:

Range of t applied to solve the diferential equation system:  From t-min  to t-max

Compartment number where the samples are taken: Enter the experimental data{{t1,m1, u1}, ...,{ti, mi, u1}: {{2, 0.12, 0.02}, {3, 0.161, 0.02}, {4, 0.2, 0.02}, {5, 0.208, 0.02}, {6, 0.212, 0.02}, {7, 0.217, 0.02}, {8, 0.217, 0.02}, {9, 0.227, 0.02}, {10, 0.223, 0.02}, {11, 0.207, 0.02},{12, 0.205, 0.02}, {13, 0.186, 0.02}, {14, 0.182, 0.02}, {15, 0.163, 0.02}, {16, 0.147, 0.015}, {17, 0.15, 0.015}, {18, 0.142, 0.015}, {19, 0.118, 0.01}, {20, 0.11, 0.01}, {21, 0.1, 0.01}, {22, 0.091, 0.01}, {24, 0.092, 0.01}, {25, 0.081, 0.01}, {27, 0.067, 0.01}}

Differential equations


Solution



Plot

The default values represents the ICRP 78 iodine model -see the figure - where compartment 1 is the blood, compartment 2 is the thyroid , compartment 3 is the rest of the body (compartment 4 is considered out for the system)" . The example represents the iodine model: the rate transfer values (clearance), in days^-1, k10= 1.9404 , k30 =0.01155 and k31= 0.046; k12 and k23 are assumed unkown. It is suppossed an input of I-125 (decay constant Log[2]/59.4 in days^-1) in compartment 1 given by the input function 0.3 Exp[-0.2 t] + 0.1 Exp[-4.2 t]. Also it is supossed as initial contition {0, 0, 0}. There are taken measurements of I125 in compartment 2. Using this measurements k12 and k23 are fitted (starting values k12 and k23 are requiered).

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