# Medical convention: Anlya's address to the gathering

Posted on Mon Nov 27th, 2017 @ 6:18pm by Captain Raymond Wulfe & Lieutenant Commander Anlya D'Tries

**Mission:**
24. Shore leave: another wildwest wilderness vacation!
**Location:** Medical convention auditorium
**Timeline:** 28 November 2391

ON:

The first three speeches were all chief medical officers. The second round of speeches after a lunch break would be lead off by another doctor from the Asgard. The Celebrity announcer had looked up information on each speaker and the two on the first day from the Asgard were well documented and esteemed in any crowd of professionals.

The man took the podium looking over the well fed crowd of Doctors "Leading off the afternoon's event is a well known Scientist who just happens to be a Doctor as well. When she is not making historic discoveries in Science she is helping the medical team aboard the USS Asgard. Please a warm welcome for Commander Anlya D'Treis." The applause was welcoming even if some were unsure? Everyone knew of her scientific and historical discoveries but many had no idea she was a medical doctor!

Anlya thanked the moderator for the introduction and went to the podium and put the title slide of the talk.

"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.

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."

Anlya put up 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.

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.

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."

"Questions?" Anlya asked.

There were a few and some discussion between a few members but overall nothing that seemed too hard to handle. A couple of questions and observations would be good for future research and she made note of them.

The Moderator lead the applause as he retook the podium. The crowd of Doctors had received her dissertation warmly and she had gotten the attention focused on the entire crowd. The next two speakers had an enthusiastic audience as the people listening found the information gained was well worth thinking on. Some even were already making plans for inclusion of these practices in their own treatment schedules.

OFF: