Maths -- model for drug absorption. Simple, but gives rather realistic graphs.

[VelocideX]

Re: Small world

The graphs are remarkably similar to the charging and discharging of a capacitor, though a resistor (const voltage source). It's also governed by exponential equations

Not surprising, the whole world is governed by exponential equations

and sine + cosine functions, but they're really exponentials too

hell every function can be represented by fourier series anyway

 

[fcuking_in_heaven]

Nice work indeed, but didnt your grade 8 maths teacher ever tell you to label the axis clearly. For example yours seemed to be labelled 't' and 'stuff in blood'. I think its quite easy to assume t=time (hours), but stuff in blood? Are you referring to MDMA or just the contents of the pill itself. Sorry to be picky but i just want to be clear on what you mean.

Fuck in heaven

 

[VelocideX]

I'm doing a physics major, I aways label my axes I couldn't be arsed doing it in MAPLE though, its a pain in the arse

t is in some sort of time unit but ive never actually included a definition of hours minutes or seconds, have I? It depends on what the units of each of the constants are. Here they're all in the same units, or else it wouldn't quite work right. If k1,k2,k3 are in inverse seconds then t is in seconds. if k1,k2,k3 are in inverse days then t is in days. all the k would be experimentally determined constants. I've just made a guess at them that gives a decent graph.

Stuff in blood could be anything you wanted. The units are pretty ambiguous, because you haven't even defined a mass unit at any point -- you'd need another constant out the front to take care of that, but that's alright multiplicative constants are easily dealt with -- just stick an A,B, or C out the front of the equations. Hell it could be a concentration, a number of atoms, mass of particles, etc. Each would be proportional to the other. It could be in atoms per cubic metre, kg, kg/m^3... it could be in dozens per cubic furlong, or protons per cublic lightyear. *shrug*

So yeah I haven't cared particularly about dimensionality, but if you want dimensional consistency then you'll need other constants floating around.

Should it matter if stuff refers to MDMA or the contents of the pill? At no point have I ever taken into account differential rates of absorption between different substances (presumably via diffusive/transporter methods); the implicit assumption is that everything absorbs equally well.

 

[VelocideX]

I just made a compartment model. Check out the graphs when the compartment is very good at absorbing:

and relatively poor at absorbing

hectic

I know that this makes no assumptions about the volume of the compartments; that's something you'd have to try and factor into the appropriate constants...

(The compartment is always the second graph to the right... obviously there's a delay from the blood)

 

[thomo1981m]

so are you guys making good pills or wat surley yas must have some thing better to do then talk about mc = 2

 

[VelocideX]

It's hardly general relativity (which I'm sitting an exam on tomorrow )... What's to stop people having an interest in pharmacology? Some people make their lives out of it. It's rather interesting.

I'm not going to do that, but I'm a physicist. Huge amounts of physics deals with the solutions of differential equations e.g. Maxwell's equations for electromagnetism; Schrodinger's equation for quantum mechanics.

Applied physics involves setting up your own problem and solving it. I've had rather little experience at that, and wondered if I could construct a simple differential model of human absorption. A little hard at first, but not so bad once I started drawing the right diagrams.

 

[phase_dancer]

so are you guys making good pills or wat surley yas must have some thing better to do then talk about mc = 2

This sort of statement really gets up my nose. What the fuck has any of this got to do with manufacturing?

If you can't see the relevance of including science in drug education, and the need for science to be among topics frequently discussed on drugs, then perhaps you need to learn a bit more.

I've been waiting years for some of the recent HQ postings on Bluelight. It's great to have such a diverse range of talents giving their time to the board. We have been in dire need of a drug distribution model, which can be referenced or added to as questions arise. I struggle with complex kinetics equations, so anyone who finds this stuff easy is my friend, and I'll listen to/ read from them all day



Stay along for the ride or go somewhere else, but please don't draw stupid conclusions because you can't determine the difference between a drug absorbance graph and a drug synthesis. If it were meant to be in jest then it should have been indicated e.g.

Well done on the compartmental model VelocideX, and we'll have your calculations if it's not too much trouble.

 

[VelocideX]

The calculation as it stands is wrong because it assumes that the blood and the compartment are of equal volume (the compartment and blood try and equalise the amount of material present). I've got exams for the next three days and so probably won't have much time to spend on it, but the modification shouldn't be that hard (I think)

if F is the amount in the compartment, you need to replace dF/dt = k(B-F) with dF/dT = k(B/Vb-F/Vf) where Vi is the volume of compartment i... (blood being treated as a compartment). that way material will only transfer if concentrations are different...

It's surprising how much you can get out of life by assuming that things equalise exponentially. Even if that's not the case, it's true to a first approximation.

There is another problem with saturation in this model, especially of the transport mechanisms. The equation becomes discontinuous and therefore a fucking bitch to solve. YOou might be able to solve it analytically if you assume the appropriate transfer function but really I think it starts becoming a numerical problem. You'd need a different differential model for non-saturation and saturation, and its not exactly clear how you'd go between the two...