How of get Initial values of a pharmacokinetic and pharmacodynamic model.

I am getting contraddicting values from my calculations opposed to that of research papers and I can't figure why this is so.

The following model allows us to determine the level of hypnosis (in our case Bis index) given an anesthesic drug infusion U.

I am making use of a pharmacokinetic model to describe the distribution of the anesthetic drug in the body. I use a three compartmental model illustrated as follows, where the constants represent the frequency at which the drug is redistributed from compartment i to compartment j.

The input of this model is U which is the drug's infusion rate while its output is the drug concetration of the primary compartment C1.

I then use a pharmacodynamic model to model the drugs effect, mapping the primary compartment concentration C1 to a level of hypnosis through 2 steps.

Step 1 : Map to

represents the drug concentration of the site where the drug actually causes its effect on the body.

Step 2 : Map to Bis index

The last step is to then map to an actual level of hypnosis to measure the patients consciousness. I used a hill sigmoid function for this.

where a andγrepresents given parameters of the patient.

Research papers state that the Bis index at time t=0, corresponding to the absence of the anesthetic drug should be 100 or 1 if normalized.

But this result of Bis(0) = 1 doesn't align with the results that I get from the differential equations.

at time t=0

, which means there can't be any drug flow to the effect site so

if then

So how come do research papers model Bis(0) equal to 1 ?

Answer 1

[Star Strider]

First, supply some of the relevant research papers (as PDFs, since I have personal access only to some medical journals and Science) and I’ll look through them to see if I can discover the problem. This seems an interesting inquiry.

Second, if the intent is to model the differential equations from data, and the data are available, estimating the initial conditions (as parameters to be estimated in addition to the kinetic parameters) is relatively straightforward using the techinques in thie search.

[Mohammed Azeez]

Hi, Thanks for taking your time in responding, this is a link to my github repository containing the pdf papers and the matlab code of the project.

The pdf papers of interest are called Main paper 1, Main paper 2, Main paper 3.

This is the link: https://github.com/Med-is-great/CSB

[Star Strider]

My pleasure!

Noted!

Main paper 1, Main paper 2, Main paper 3

I’ll check these and reply when I’ve read them and can comment on them.

EDIT — (6 Jan 2022 at 19:56)

‘So how come do research papers model Bis(0) equal to 1 ?’

Because they define it that way. A value of 1 or 100 is the maximum alert state in the absence of any propofoll having been infused. The input to the pharmacokinetic models is the propofol infusion rate, not BIS, so the pharmacokinetic models act as a sort of state estimator (without the rigor usually associated with that). The papers view this problem from a pharmacokinetic perspective, not a control perspective, so it’s a bit difficult to interpret them in that respect, at least as I read them.

I read the articles over the seekend, and dit a short PubMEd search as well. I’m not certain the approach in those papers is the most efficient, however using the ‘NeuroSense’ wavelet based, linear, sensor is likely better and more robust than BIS. (The 2016 Khaqan paper is the most rigorous.) The more I think about it, the more convinced I am that a Kalman filter approach is likely most appropriate. I have an excellent reference on them that I’m currently reading to bring me back up to speed, and also studying the Control System Toolbox documentation section on Kalman Filtering. There’s not much on Kalman filters and propofol infusion in the literature, and this PubMed search brought up only two. (They’re both behind a paywall, so unavailable to me.)

I am not certain that the pharmacokinetic model is actually necessary. What do you want to do with it?

(For what it’s worth, I did a one-month anaesthesiology elective in med school, and liked it, and was good at it. I decided that internal medicine was more interesting, so didn’t pursue my interest in anaesthesiology, although I gave some thought later to doing a fellowship in pulmonary and critical care medicine, and now regret that I didn’t follow through on it.)

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