A mathematical model was developed for the quantitative analysis of the results of TRH stimulation tests. The derived equation indicating plasma TSH concentration (C) at arbitrary time (t) after TRH was as follows :
C0=α/β-α·Q0 /V (e-αt-e-βt) +C0e-βt
where
α = rate constant for TSH release,
β = rate constant for TSH elimination,
Q0= total amount of TSH released after TRH,
V = distribution volume of released TSH,
C0 = plasma TSH concentration at time of zero.
Based on the results of TRH stimulation tests, the values of parameters α, β and Q0/V were estimated by non-linear least-square methods and the regression curves indicating the time course of Plasma TSH were obtained. The apparent fit of data to the regression curves was reasonable and the multiple correlation coefficients were satisfactory.
The normal ranges for the parameters α, β and Q0/V were 4.46 to 13.07 hr-1, 0.63 to 1.30 hr-1, and 6.7 to 19.7 μU/ml plasma respectively. A slight increase of Q0 /V was observed in patients with simple goiter and euthyroid chronic thyroiditis. Markedly increased Q0/V and decreased a were characteristic of patients with typical hypothyroidism, and decreased β was also observed in some patients. On the other hand, a marked increase of Q0/V was the only finding in patients in transient hypothyroid state. Moderate increases of Q0/V and definite decreases of α were observed in more than half of the patients with pituitary drawfism and seemed to be the cause of the delayed response.
The above results indicate that the mathematical model applied here is useful enough for quantitative analysis of the plasma TSH dynamics after TRH stimulation.
