PBPK model structure. A PBPK model structure consists of seven compartments including the lung, heart, brain, fat, muscle, kidney, and liver. All of the organ compartments are linked together by the blood circulation system. The lung is the site of an interchange of the arterial and venous blood. The brain is the major site of action of PI. PI is assumed to solely be eliminated from the body through the liver. Adipose tissue is the storage organ for PI in the body. Additional organs including the heart and kidney are included in the model regarding their role in the pharmacokinetics and pharmacodynamics of PI. The structure of our PBPK model of PB and PI is depicted in Figure 1.

Tissue model specification. A perfusion rate-limited and well-stirred tissue model hypothesis was assumed for all organs.

Model parameterization and equations. Physiological parameters including organ blood flow (Q) and organ volume (V) were obtained from published literature ^{13– 15} . Pharmacokinetic parameters including bioavailability and absorption rate constant were acquired from published literature ^{16, 17} and optimized using Berkeley Madonna Software. Physicochemical parameters including partition coefficient of each compartment were calculated using an approach from the literature ¹⁸ . A PBPK model was coded and performed using Berkeley Madonna Software version 8.3.18 (developed by Robert Macey and George Oster of the University of California at Berkeley). Replication of the simulation results from our PBPK model using an alternative and freely available software is possible; recently, Zurlinden T.J. et al. ¹⁹ have developed a physiologically based pharmacokinetic model of a rifapentine model using the Python software (version 2.7.2) as their computational tool along with these numby, scipy and matplotlib packages ^{20– 23} . All of the parameters used in the PBPK model are summarized in Table 1.

Routes of PI administration. In this development of the PBPK model of PB and PI in rats and humans, there were two different routes of administration. Those included 1) intravenous (IV) administration and 2) oral administration. Differential equations ( Equation 1 – Equation 3) describing the respective routes of administration are as follows:

1) Intravenous administration:

I n p u t I V = D o s e ∗ B W ∗ K c / T i m e Eq. 1

where Dose is an administered dose of PI (mg), BW is the body weight (kg), Time is the duration period of the injection (h), and Kc is the conversion rate constant.

2) Oral administration:

I n p u t o r a l = K a ∗ A G U Eq. 2

A G U = D o s e ∗ B W ∗ F ∗ K c Eq. 3

where A _GU is the amount of PI in the gut lumen after an oral administration (μg), k _a is the absorption rate constant (1/h), F is the bioavailability, and Kc is the conversion rate constant.

Organ compartments. In this PBPK model, there were seven organ compartments. Differential equations ( Equation 4 – Equation 20) describing concentration-time profiles of PI in each of seven compartments are as follows:

1) Lung:

d A L u / d t = Q c ∗ ( C V − C A L U ) Eq. 4

C A L U = C L U / P L U = A L U / V L U ∗ P L U Eq. 5

where A _LU is the amount of PI in the lung (µg), QC is the cardiac output (l/h), C _V is the concentration of PI in venous blood (µg/l), C _ALU is the concentration of PI in arterial blood leaving the lung (µg/l), C _LU is the concentration of PI in the lung (µg/l), V _LU is the volume of the lung (l), and PLU is the lung/blood partition coefficient.

2) Heart:

d A H / d t = Q H ∗ ( C A − C V H ) Eq. 6

C V H = C H / P H = A H / V H ∗ P H Eq. 7

where A _H is the amount of PI in the heart (µg), Q _H is the blood flow to the heart (l/h), C _A is the concentration of PI in arterial blood (µg/l), C _VH is the concentration of PI in venous blood leaving from the heart (µg/l), C _H is the concentration of PI in the heart (µg/l), V _H is the volume of the heart (l), and P _H is the heart/blood partition coefficient.

3) Brain:

d A B R / d t = Q B R ∗ ( C A − C V B R ) Eq. 8

C V B R = C B R / P B R = A B R / V B R ∗ P B R Eq. 9

where A _BR is the amount of PI in the brain (µg), Q _BR is the blood flow to the brain (l/h), C _A is the concentration of PI in arterial blood (µg/l), C _VBR is the concentration of PI in venous blood leaving from the brain (µg/l), C _BR is the concentration of PI in the brain (µg/l), V _BR is the volume of the brain (l), and P _BR is the brain/blood partition coefficient.

4) Fat:

d A F / d t = Q F ∗ ( C A − C V F ) Eq. 10

C V F = C F / P F = A F / V F ​ ∗ P F Eq. 11

where A _F is the amount of PI in the fat (µg), Q _F is the blood flow to the fat (l/h), C _A is the concentration of PI in arterial blood (µg/l), C _VF is the concentration of PI in venous blood leaving from the fat (µg/l), C _F is the concentration of PI in the fat (µg/l), V _F is the volume of the fat (l), and P _F is the fat/blood partition coefficient.

5) Muscle:

d A M U / d t = Q M U ∗ ( C A − C V M U ) Eq. 12

C V M U = C M U / P M U = A M U / V M U ∗ P M U Eq. 13

where A _MU is the amount of PI in the muscle (µg), Q _MU is the blood flow to the muscle (l/h), C _A is the concentration of PI in arterial blood (µg/l), C _VMU is the concentration of PI in venous blood leaving from the muscle (µg/l), C _MU is the concentration of PI in the muscle (µg/l), V _MU is the volume of the muscle (l), and P _MU is the muscle/blood partition coefficient.

6) Kidney:

d A K / d t = Q K ∗ ( C A − C V K ) Eq. 14

C V K = C K / P K = A K / V K ∗ P K Eq. 15

where A _K is the amount of PI in the kidney (µg), Q _K is the blood flow to the kidney (l/h), C _A is the concentration of PI in arterial blood (µg/l), C _VK is the concentration of PI in venous blood leaving from the kidney (µg/l), C _K is the concentration of PI in the kidney (µg/l), V _K is the volume of the kidney (l), and P _K is the kidney/blood partition coefficient.

7) Liver:

d A L I / d t = Q L I ∗ ( C A − C V L I ) − L I M e t Eq. 16

C V L I = C L I / P L I = A L I / V L I ∗ P L I Eq. 17

L I M e t = ( V m a x ∗ C V L I ) / ( K m + C V L I ) Eq. 18

where A _LI is the amount of PI in the liver (µg), Q _LI is the blood flow to the liver (l/h), C _A is the concentration of PI in arterial blood (µg/l), C _VLI is the concentration of PI in venous blood leaving from the liver (µg/l), C _LI is the concentration of PI in the liver (µg/l), V _LI is the volume of the liver (L), P _LI is the liver/blood partition coefficient, LI _Met is the amount of PI excreted via liver metabolism, Vmax is the maximum velocity of UGT1A10 (μmol/h), and Km is Michaelis-Menten constant of UGT1A10 (μM).

8) Blood:

d A V / d t = Q H ∗ C V H + Q B R ∗ C V B R + Q F ∗ C V F + Q M U ∗ C V M U + Q K ∗ C V K + Q L I ∗ C V L I − Q C ∗ C V Eq. 19

d A A / d t = Q C ∗ C A L U − C A ∗ ( Q H + Q B R + Q F + Q M U + Q K + Q L I ) Eq. 20

where A _V and A _A are the amount of PI in the venous and arterial blood, Q _H, Q _BR, Q _F, Q _MU, Q _K, Q _LI are the blood flow rate into the heart, brain, fat, muscle, kidney, and liver (l/h), and C _VH, C _VBR, C _VF, C _VMU, C _VK, C _VLI are the concentration of PI in the venous blood leaving from the heart, brain, fat, muscle, kidney, and liver (μg/).

From a search in PubMed from inception to July 2019, the search terms “psilocybin; psilocin; magic mushroom; pharmacokinetic” were used as keywords. Studies were included if they met the selection criteria as follows: pharmacokinetic studies of psilocybin or psilocin that were conducted in animals or humans and different of routes of administration. Studies were excluded if they conducted pharmacokinetic studies in unhealthy or pregnancy animals or humans. From the following information in the literature, three studies were retrieved and were subsequently used for further model development. The PBPK model was evaluated based on visual inspection of goodness of fit. A summary of the selected studies is as follows:

In the study by Chen et al. ²⁶ , Sprague-Dawley rats (n = 10, BW = 220 – 250 g) were orally administered with a single dose of G. spectabilis extract, which is equivalent to 10.1 mg/kg of PI. Then, a serial of blood samples was collected at 5, 10, 20, 30, 45, 60, 90, 120, 180, 240, 360, and 420 minutes after oral administration. Then, the samples were analysed for PI using ultra-performance liquid chromatography coupled to photodiode array detection (UPLC-PDA).

In the study by Hasler et al. ¹⁷ , nine healthy male volunteers (BW = 56 – 72 kg) were intravenously administered with a single dose of 1 mg PB. Subsequently, blood samples were collected at 0.75, 1.5, 2.5, 3.75, 5, 6.75, 10, 15, 20, 30, 60, and 120 minutes. In addition, six healthy male and female volunteers (BW = 53 – 88 kg) were orally administered with a single oral dose of 0.224 mg/kg PB. Blood samples were collected at 15, 30, 4.5, 60, 7.5, 90, 105, 120, 150, 180, 220, 300, 350, and 390 min after the oral PB administration. Then, the samples were analysed using high performance liquid chromatography coupled with electrochemical detection (HPLC-ECD).

In Brown et al. ¹⁶ , 12 healthy volunteers were given a single oral administration of PB 0.3 mg/kg. Blood collections were performed at 0.25, 0.5, 0.75, 1, 2, 3, 4, 6, 8, 12, 18, and 24 hours. Subsequently, the samples were analysed for PI concentration using a HPLC technique.

PI concentration levels shown in figures for the selected studies were extracted using WebPlotDigitizer version 4.4 (Free Software Foundation, Inc., Boston, MA). Assessment of model qualification was based on visual inspection of the agreement between observed and simulated PI concentrations. Regression analysis between the simulated and observed PI levels was also performed in Microsoft Excel version 2019.

Following a single oral administration of PI (10.1 mg/kg) in rats, the simulated results of PI concentration profiles in plasma from the developed model compared to observed data acquired from the study by Chen et al. ²⁶ is demonstrated in Figure 2A with the simulated PI concentration-time profiles in the brain ²⁷ . Subsequently, simulated results of PI concentration-time profiles in the lung, heart, muscle, kidney, and liver are illustrated in Figure 2B.

Following a single IV administration of PB (1 mg) in humans, simulated PI concentration-time profiles in plasma compared to the observed data acquired from Hasler et al. ¹⁷ are demonstrated in Figure 3A. In addition, PI concentration-time profiles in the human brain were simulated and are presented in Figure 3A. Simulated PI concentration-time profiles of other tissues are illustrated in Figure 3B.

In the selected studies, two different doses of PB (0.224 mg/kg and 0.3 mg/kg) were administered to humans via a single oral administration. Simulated results of PI concentration-time profiles in plasma following oral administration of PB (0.224 mg/kg and 0.3 mg/kg) compared to the observed data acquired from Hasler et al. ¹⁷ and Brown et al. ¹⁶ are presented in Figure 4A and Figure 5A, respectively. Simulated brain concentration-time profiles of PI for both doses (0.224 mg/kg and 0.3 mg/kg) are also presented in Figure 4A and Figure 5A, respectively. Then, from the developed model following oral administration of PB (0.224 mg/kg and 0.3 mg/kg), the simulated results of PI in organs of interest including the lungs, fat tissue, muscle, kidney, and liver are depicted in Figure 4B and Figure 5B.

Our model simulations in both species included different routes of administration including an oral dose of PI in rats (10.1 mg/kg), IV dose of PB in humans (1 mg), and different oral doses of PB in humans (0.224 mg/kg and 0.3 mg/kg). Key parameters including maximum concentration (C _max), time to reach maximum concentration (T _max), and area under the curve from time equals zero to the last time point (AUC _0-t) from the developed PBPK model and experimental data in both rats and humans are demonstrated in Table 2.

Zenodo: Heang60/PBPK-of-Magic-Mushroom: Coding for PBPK of Magic Mushroom. https://doi.org/10.5281/zenodo.4536617 ²⁷ .

This project contains the following underlying data:

Zenodo: Heang60/PBPK-of-Magic-Mushroom: Coding for PBPK of Magic Mushroom. https://doi.org/10.5281/zenodo.4536617 ²⁷ .

This project contains the following extended data:

Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0).