## Publications (2)2.29 Total impact

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**ABSTRACT:**More than 70 years after the discovery of the pituitary thyroid feedback control mechanism, a classical endocrine regulation system, most of its parameters have been identified. However, the regulation of its central component in the pituitary gland, probably responsible for pulsatile release of thyrotropin (TSH), remains obscure. In order to infer its structure from the system ’s behavior, four different pituitary models were created and compared regarding their fractal properties. Based on the simplest model showing noncompetitive inhibition of TSH release by thyroid hormones — a physiologically plausible correlation — one alternative model added stochastic stimulation by central signals and one added an additional intrapituitary feedback loop, whereas a fourth model combined both effects. This latter model combining noncompetitive inhibition with the two additional effects showed the same fractal dimensions as a real time series, whereas the simpler models yielded significantly lower time-series complexity. These results suggest that both stochastic stimulation and ultrashort loop feedback are involved in the generation of TSH pulses in the human pituitary. -
##### Article: The pituitary-thyroid feedback control: stability and oscillations in a new nonlinear model

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**ABSTRACT:**The central role thyroid hormones play for the control of growth, differentiation and metabolic activity requires precise regulation mechanisms as they are materialized by a multiloop feedback system with nonlinear integrating characteristics. In order to study the effects that the individual signal transfer mechanisms exert on the entire control system we developed a modular extendable cybernetic model. Making use of our simplest model we can describe the changes in TSH level as d[TSH]/dt=VH*[TRH]/((DH+[TRH])*LS*[FT3])-bS*[TSH], where VH is an amplification factor of the pituitary, determining the maximum secretion rate of TSH, DH an attenuating constant, which is responsible for the curve form of the relationship, LS a feedback coefficient and bS a clearance constant for the degradation of TSH. The TSH concentration in the steady state is then [TSH]=aS*VH*[TRH]/(bS*(DH+[TRH])*LS*[FT3]) with aS as saturation constant. In a similar way it follows that [T4]=aT*VT*[TSH]/(bT*(DT+[TSH])). T4 is bound to plasma proteins, especially TBG and TBPA, so that the equifinal level of free T4 is [FT4]=[T4]/(1+K41*[TBG]+K42*[TBPA]) where K41 and K42 are dissociation constants. The deiodation to T3 is a linear process with the amplification factor VD: [T3]=a3*VD*[FT4]/b3. The resulting concentration of free T3 ist then [FT3]=[T3]/(1+K30*[TBG]) with the dissociation constant K30. Simplifying VH*aS/(LS*bS) to K1, VT*aT/(bT*(1+K41*[TBG]+k42*[TBPA])) to K22 and VD*a3/(b3*(1+K30*[TBG]) to K32 we can summarize the equations to a second degree quadratic equation with the two solutions [TSH]1,2=K1*[TRH]/(2*(DH+[TRH])*K32*K22)+,-sqrt((-K1*[TRH]/(DH+[TRH])*K32*K22))^2+4*DT*K1*[TRH]/((DH+[TRH])*K32*K22))/2. Due to mathematical reasons there is one positive and one negative solution, while the positive one is identical with the level of TSH the feedback system is aiming at in steady state. In similar ways the equifinal levels for FT4 and FT3 can be calculated. By the integration of further relations, e. g., time constants, this simple model can be stepwise refined to the desired level of complexity. Using a such improved model within a computer simulation shows fading oscillations and a remarkably high grade of stability against external disturbances.

#### Publication Stats

18 | Citations | |

2.29 | Total Impact Points | |