TLDR: I built a dutasteride simulator based on mathematical models from two research papers. The researchers fit their models to real data from study participants. In my implementation, serum dutasteride and serum/scalp DHT can be predicted, and various dosing schedules may be simulated to predict steady state dutasteride concentrations. Irregular dosing schedules like twice per week dosing and large loading doses can be simulated as well. The application and its source code can be found on the GitHub page.
Why predict serum (blood) dutasteride? It helps to find out when a certain dosing schedule reaches steady state (maximum efficacy). Why predict serum DHT? It helps to gauge the systemic effects of dutasteride. Why predict scalp DHT? Researchers discovered a correlation between scalp DHT and hair count increases after 6 months, implying that more scalp DHT suppression grows more hair [3].
Medical disclaimer: This model is based on population averages. It will not exactly predict values for individuals because every person’s body is different. The predictions provided by this application should not be used as a basis for making medical decisions. Do not modify your dosage or alter your dosing schedule based on the information from this application. Always consult your doctor before making any changes to your medication regimen.
I recently finished implementing this dutasteride simulator in Python based on two research papers which outline models for the pharmacokinetics and pharmacodynamics of dutasteride. References to the papers I used will be at the bottom of the post. The papers provide systems of differential equations which may be integrated numerically to predict serum dutasteride and serum DHT in real time. The scalp DHT prediction is my own addition; it is not necessarily in real time, and should only be assessed at steady state (3-6 months of consistent dosing). The dotted blue line represents the scalp DHT reduction whose efficacy is about equal to finasteride 5 mg/day.
Screenshots:
Dosing spikes look irregular due to down-sampling when plotting data points; this is just a visual artifact.
0.5 mg/day for 6 months:
Loading dose of 2 mg/day for a week, then 0.5 mg/day for 3 months:
(4 months of each) 1 capsule per week, 2 per week, 3 per week, then daily dosing:
2.5 mg/day for 6 months, then 0.5 mg/day for 6 months:
0.5 mg absorption curve (24 hours):
Serum DHT prediction at steady state:
Scalp DHT prediction at steady state:
Scalp DHT relative efficacy by daily dose:
Note: C(D) and P(D) represent steady state dutasteride levels of the central and peripheral compartments based on daily dose. These can be found by setting the compartment derivatives equal to zero (compartments are described in the next paragraph).
Technical details:
For predicting serum dutasteride concentrations, the authors provide three differential equations. One for the absorption compartment (represents how the drug is absorbed into the blood), one for the central compartment (represents dutasteride levels in the blood + central organs), and one for the peripheral compartment (represents dutasteride levels in the muscle, fat, and skin tissues). These can be integrated over time while adding a fixed amount of the drug into the absorption compartment periodically to represent a dosing schedule.
- A1 is the amount in the absorption compartment (μg).
- A2 is the amount in the central compartment (μg).
- A3 is the amount in the peripheral compartment (μg).
- dAi/dt is the rate of change (μg/h).
- Other variables are intercompartmental rate constants and volume constants.
Read reference [1] for more information.
For predicting serum DHT suppression, the authors provide differential equations for 5 alpha reductase activity (type 1 and 2), and a differential equation for DHT suppression. These can be integrated over time based on the serum dutasteride concentrations from the previous paragraph. They also provide equations for computing DHT suppression at steady state based on steady state drug concentrations.
- 5ARi is the activity of 5AR type i (as a ratio between 0 and 1).
- d5ARi/dt is the rate of change of the activity of 5AR type i.
- ki is the turnover rate for 5AR type i.
- koij is the rate of elimination of 5AR type i from dutasteride binding to it. The j can be ignored, it is replaced with F for finasteride or G for dutasteride, so it’s G here.
- Cj is the plasma concentration of the drug.
Read reference [2] for more information.
- DHT is the current DHT concentration.
- dDHT/dt is the rate of change of the DHT concentration.
- kout is the elimination rate of DHT.
- DHTSS is the baseline DHT concentration.
- FAR2 is the proportion of DHT formed by 5AR2 (as a ratio between 0 and 1).
- 5ARi is the activity of 5AR type i (as a ratio between 0 and 1).
Read reference [2] for more information.
Equation for percent DHT remaining from baseline (DHT/DHTSS). This equation is not for real time prediction, but is for predicting steady state DHT suppression.
Read reference [2] for more information.
For the scalp DHT suppression (which was not included in the papers), I took three of the known values for scalp DHT suppression from the Olsen et al. study [3] and substituted them into the steady state DHT equation along with steady state dutasteride concentrations to create a system with three equations and three unknowns. I then solved for the appropriate variables (FAR2, k1/ko1, k2/ko2). I was able to use overall tissue concentrations of dutasteride without knowing skin concentrations specifically, because this DHT suppression model only cares about ratios between concentrations, not the absolute concentrations themselves. Based on the concept of intercompartmental rates leading to consistent ratios between compartments, these ratios will be the same no matter what the absolute drug concentration is. For example, if the ratio between drug concentrations in the central and peripheral compartments is 1:2 at steady state, then that ratio should always be 1:2 no matter the absolute drug concentration.
To try this application yourself, visit the GitHub page (application and source code).
References:
- Gisleskog, P. O., Hermann, D., Hammarlund-Udenaes, M., Karlsson., M. O. (2001). The pharmacokinetic modelling of GI198745 (dutasteride), a compound with parallel linear and nonlinear elimination. British Journal of Clinical Pharmacology. https://doi.org/10.1046/j.1365-2125.1999.00843.x
- Gisleskog, P. O., Hermann, D., Hammarlund-Udenaes, M., Karlsson., M. O. (1998). A model for the turnover of dihydrotestosterone in the presence of the irreversible 5a-reductase inhibitors G1198745 and finasteride. Clinical Pharmacology and Therapeutics. https://doi.org/10.1016/S0009-9236(98)90054-6
- Olsen, E. A., Hordinsky, M., Whiting, D., Stough, D., Hobbs, S., Ellis, M. L., Wilson, T., Rittmaster, R. S. (2006). The importance of dual 5alpha-reductase inhibition in the treatment of male pattern hair loss: results of a randomized placebo-controlled study of dutasteride versus finasteride. Journal of the American Academy of Dermatology. Redirecting