SHAM(e) math [NCA / SHAM]

posted by Helmut Homepage – Vienna, Austria, 2020-06-23 17:55 (1394 d 00:06 ago) – Posting: # 21566
Views: 5,429

Hi Nastia,

Uno puede estar mirando las estrellas y al mismo tiempo verse la punta de las pestañas (Julio Cortázar)

Though I never just couldn’t get into Cortázar’s books, that’s a nice quote (though having both estrellas and pestañas in focus would be a difficult feat).

❝ […] I have strong doubts that our local library has books on pharmacokinetics on german printed in 50th :-)

I believe it. I had only the “expanded edition”:

Dost FH. Grundlagen der Pharmakokinetik. Stuttgart: Verlag G. Thieme; 1968.

Forget to steal it when I left my CRO. ;-)
See also there.

❝ ❝ As a rule of thumb at \(\small{MRT}\) ~⅔ of the drug is eliminated. […]

❝ I was wondering from where such a rule of thumb was going and integrated the area for simple exponential elimination. It turns out that at MRT (1-exp(-1))~0,632 of the drug is eliminated for IV and slightly lower for EV (so the rule of pinky is 0,632 versus the rule of thumb (2/3=0,(6))

Absolutely correct! This was a presentation for physicians (‼); I wanted to keep it simple. A relative error of 5.2% doesn’t hurt to make a point. Of course, much worse than Archi­medes’ phantastic \(\small{3+\frac{10}{71}}<\pi<3+\frac{1}{7}\).

❝ As for physics there exists inaccuracy in the considerations on the slide "Excursion to Hydrodynamics". "Same proportions is emptied in the same time interval" is true only when you are solving school problems with a pool. Exactly the unexpired volume leaked depends on the form of the vessel. For the cylindric vessel for example water height and thus the volume is proportional to t2. If you want to have a constant proportion you need a vessel with a form of parabola x4 that is clepsydraor consider Mariotte’s bottle.

Correct again! I brainlessly used examples of old textbooks (as usual). Homework: what happens if we drill a hole in a Klein bottle?

❝ I've calculated Cc for several real studies according to simple linear trapezoidal rule:

❝ $$C_c=\frac{1}{3}\frac{\sum\limits_{i}(t_{i+1}-t_i)(C^{2}_{i}+C^{2}_{i+1}+C_{i}\cdot C_{i+1})}{\sum\limits_{i}(t_{i+1}-t_{i})(C_{i+1}+C_i)}$$ Although it has C2 in it, it's variability was always lower than that of Cmax, but I should've check it more carefully.

Surprises me. Given, I didn’t assess it for ages. Maybe I’m wrong again.

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