Medical - Pharmacokinetics and pharmacodynamics

[Kexanone]

Background

In the basic medical system, morphine and epinephrine just heal the pain respective resilience hit zones with a constant rate over a fixed time. During their effect duration, you cannot administer another dose.

Proposal

The idea is to make a new option to replace the behavior described above by a more realistic model, where the drug concentration and effect change over time. Moreover, drugs should no longer heal the hit zones. We introduce instead a drug-adjusted health getter that returns the sum of the hit zone's health and all drug effects. This will turn morphine into a pain suppressor and epinephrine into a resilience enhancer, rather than healer.

Pharmacokinetics

Proposed Model

Two consecutive first-order reactions:

$$\begin{flalign} &\ce{P ->[k_a] A ->[k_d] \otimes}& \end{flalign}$$

• $\ce{P}$: Precursor state
• $\ce{A}$: Active state
• $k_a$: Activation rate constant
• $k_d$: Deactivation rate constant (metabolism)

Corresponding Rate Law

$$\begin{flalign} & \begin{pmatrix}\frac{d\ce{[P]}}{dt} \\ \frac{d\ce{[A]}}{dt}\end{pmatrix} = \begin{pmatrix}-k_a & 0 \\ k_a & - k_d\end{pmatrix}\begin{pmatrix}\ce{[P]} \\ \ce{[A]}\end{pmatrix} & \end{flalign}$$

Solution

$$\begin{flalign} & \begin{pmatrix}\ce{[P]} \\ \ce{[A]}\end{pmatrix}(t) = \begin{pmatrix}e^{-k_a t} \\ \frac{k_a}{k_a-k_d}\Big(e^{-k_d t}-e^{-k_a t}\Big)\end{pmatrix}\ce{[P]}_0 & \end{flalign}$$

Pharmacodynamics

Hill equation:

$$\begin{flalign} & E(t) = \frac{E{max}\cdot\ce{[A]}(t)}{\ce{[A]{EC50}} + \ce{[A]}(t)} & \end{flalign}$$

• $E$: Effect
• $E_{max}$: Maximum effect
• $\ce{[A]}_{EC50}$: Half-maximum effect concentration

Config Parameters

• Administered substance concentration ($\ce{[P]}_0$)
• Activation rate constant ($k_a$)
• Deactivation rate constant ($k_d$)
• Maximum effect ($E_{max}$)
• Half-maximum effect concentration ($\ce{[A]_{EC50}}$)

Additional Notes

• In principle the same model could be used with separate parameters for the Hill equation for simulating OD.
• Guidelines for the medical system should contain recommended dosing intervals to keep a reasonable steady state.
• Drug administration times will have to be logged to be able to dose them properly.

References

1. Meibohm et al. Int. J. Impotence Res. 2007, 19, 253–264.

[bluefieldcreator]

Pharmacokinetics seems like it would be a first in the industry in general, I dont think any other mod or game has or has aimed to simulate pharmaceutical substances before.

Looking torwards more updates on this!

[Kexanone]

Technically, ACE3 already does simulate drug effects as a function of time, but rather than a linear combination of exponentials it uses a parabola for the increase and then switches to a line for the decay and the drug effects have a linear response.