De opkomst van wiskundige optimalisatie

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Lid geworden op: 11 sep 2013, 22:42

De opkomst van wiskundige optimalisatie

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Hyperthyroidism in the personalized medicine era: the rise of mathematical optimization
Fanwen Meng, Enlin Li, Paul Michael Yen and Melvin Khee Shing Leow
Published:26 June 2019 -


Thyroid over-activity or hyperthyroidism constitutes a significant morbidity afflicting the world. The current medical practice of dose titration of anti-thyroid drug (ATD) treatment for hyperthyroidism is relatively archaic, being based on arbitrary and time-consuming trending of thyroid function that requires multiple clinic monitoring visits before an optimal dose is found. This prompts a re-examination into more deterministic and efficient treatment approaches in the present personalized medicine era.

Our research project seeks to develop a personalized medicine model that facilitates optimal drug dosing via the titration regimen. We analysed 49 patients' data consisting of drug dosage, time period and serum free thyroxine (FT4). Ordinary differential equation modelling was applied to describe the dynamic behaviour of FT4 concentration. With each patient's data, an optimization model was developed to determine parameters of synthesis rate, decay rate and IC50.

We derived the closed-form time- and dose-dependent solution which allowed explicit estimates of personalized predicted FT4. Our equation system involving time, drug dosage and FT4 can be solved for any variable provided the values of the other two are known. Compared against actual FT4 data within a tolerance, we demonstrated the feasibility of predicting the FT4 subsequent to any prescribed dose of ATD with favourable accuracy using the initial three to five patient-visits' data respectively.

This proposed mathematical model may assist clinicians in rapid determination of optimal ATD doses within allowable prescription limits to achieve any desired FT4 within a specified treatment period to accelerate the attainment of euthyroid targets.


The current practice of titration of ATD for treating Graves' disease based on TFT trend is empirical and time-consuming before an optimal dose is found. In this age of artificial intelligence and precision medicine, antiquated medical practices as such should be superseded by modern approaches that promulgates efficiency, accuracy and cost-effectiveness while eradicating guesswork from the clinicians' modus operandi as much as possible.

Our personalized medicine model permits optimal drug dosing of ATD based on parameters such as synthesis rate, decay rate and IC50. We developed an equation system involving three variables, i.e. time, drug dosage and FT4, for solving the value of any variable provided the values of the other two are known. Compared against actual FT4 data within a tolerance of 4.5 pmol l−1, favourable accuracy was attainable.

The proposed mathematical model when integrated into computerized algorithms and even mobile phone apps in the near future may assist clinicians in rapidly determining optimal ATD dosages to achieve any desired serum FT4 value within any specified treatment period to accelerate achievement of euthyroid targets.

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