# Science presentation

Posted on Sun Feb 12th, 2017 @ 10:16am by Lieutenant Commander Alekelia illm A'olha

**Mission:**
Winter Shoreleave
**Location:** Conference
**Timeline:** After arrival

Alekelia had been surprised to be asked to give a small presentation on some of her work. It seemed that there was a small science section as well in attendance. Sharing of new ideas that way was a good way to smooth diplomatic relationships as well. Scientists tended to be less bound to lines on a map and more willing to listen and share. Their voices were not always heard, but they had a way of making them.

She had put together a quick presentation and now was being introduced to the small section of attendees. She thanked the moderator as she went to the podium and smiled. Faces looked up and one could see even in the glare that most were interested. She would not belabor the point any further and got into her presentation noting the time on the wall. She was supposed to report to her new ship in an hour and this would consume most of the time.

"Today I wanted to talk about the use of fractal geometry in the use of describing pharmacokinetic interactions. As a way of introduction let me remind that pharmacokinetics is the study of the absorption, distribution, metabolism, and eventual elimination of a drug from the body, or what used be called ADME, absorption, distribution, metabolism and elimination. It is a quantitative tool used in drug development and subsequent therapy. Pharmacokinetic models are mathematical constructs whose parameters can be estimated from experimental data, which typically consist of discrete values of the drug concentration as a function of time.

Pharmacokinetic models can be divided broadly into two classes, compartmental models and non-compartmental models. The latter include moment curve and residence time analysis. In compartmental modeling, the body is divided into compartments, with a compartment being defined as the number of drug molecules having the same probability of undergoing a set of chemical kinetic processes. The exchange of drug molecules between compartments is described by kinetic rate coefficients, which may be related to physiological parameters such as molecular binding rates and organ volumes."

Alekelia put a slide up.

"Because the rate of change of the concentration is as important as its magnitude, most pharmacokinetic models are expressed as a set of differential equations. Modeling is most efficient when these equations can be solved analytically to produce algebraic equations that can be fit to experimental data using linear and nonlinear regression techniques.

However, some models, especially those with nonlinear or time-dependent terms, lead to equations that can only be solved numerically. In such cases, including the growing set of fractal models, alternate methods must be developed to estimate the model parameters.

The concept of the use of fractals in pharmacokinetics to describe the influence of heterogeneous structures and physiology on drug processes occurring within the body. Fractals can describe complex objects that cannot be characterized by one spatial scale. Fractal structures in the body include the bifurcating patterns of the bronchial tree, vascular system, bile-duct system, renal urine collection tubules, and the neuronal network. In addition, the architecture, growth, and blood supply of tumors for example can be shown to exhibit growth that can be modeled using fractal processes.

However, the concept of fractals can also extend to processes that do not have a characteristic time scale. Drug processes that have been found to exhibit fractal behaviour include drug release, aerosol transport in the lungs, transport across membranes, diffusion, binding and dissociation kinetics, washout from the heart, and tissue trapping of drugs. Transport and chemical reactions that occur on or within a fractal medium obey anomalous, fractal behaviour. Specifically, the kinetic rate coefficient follows a decreasing power of time such that can be expressed thusly."

Alekelia put up a slide with an equation. k = k0t- α

"Thus alpha is the fractal exponent and is equal to or greater than zero and less than one like so:"

0 ≤ α <1.

"The quantity t- α is considered dimensionless, and both k and k0 are in units of inverse time (h-1). Since the equation has a singularity at t=0 for h>0, we can consider a modified form of the equation based off Zipf-Mandelbrot dirstribution yielding:"

k=k0 ( τ+t) - α

"Where the constant tau is the critical time from which the rate constant is driven by fractal effects. However, if tau is very small, equation our original equation represents is a good approximation.

My own work suggests that such application of fractal kinetics to the study of drugs, to make better predictions of the volume of distribution, the clearance and half-life of administered compounds.

For example here we can see a fractal compartmental model that fits quite well the actual data for the cardiac drug myofradil. Since myofradil is dispersed quickly into the plasma but the model shows correctly that the fractal geometry of the liver slows down the rate of elimination. In contrast by using classical compartment kinetics the drug remained constant in time and thus the model does not approximate the actual elimination rate very well."

She went through several slides comparing real data with experimental data with a summary.

"Simulations involving other drugs shown here, show that the proposed new model with a fractal exponent describes drug absorption, distribution and elimination fit the actual data and have a near correspondence to the actual concentration-time curves."

She then showed and went through a few more examples.

Thus the advantage of the fractal compartmental model in addressing clinical questions include both traditional compartmental framework and the relatively simple adjustments that can take into account the effects of heterogeneity."

That was the final bit and she prepared herself as she asked, "Questions, observations, thoughts?"

By Commander Berdas on Sun Feb 12th, 2017 @ 11:00amHoly cow! Way to go with the technical talk! Most of it went over my head, but I still enjoyed reading it. Well done!!!