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Determining Optimal Drug Doses
March 27, 2014   
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A method developed at the Polish Academy of Sciences’ Institute of Physical Chemistry in Warsaw will make it possible to determine the diffusion coefficients
of chemical substances in fluids and the equilibrium constants of reactions—quickly, at low cost, and, most importantly, universally.


How strongly do two dissolved chemical substances react with each other? Such information is of paramount importance not only in chemistry and molecular biology, but also in medicine or pharmacy, where it is used, for example, to determine optimal drug doses.

In many types of medical treatment, a prerequisite for efficient treatment is to maintain an appropriate drug concentration in the patient’s blood. Simple measurement devices making use of a method for measuring equilibrium constants of chemical substances in fluids developed at the Institute of Physical Chemistry will soon be available to help medical professionals select the optimal dose for patients. Just a few milliliters of blood will enable doctors to quickly and precisely adapt a drug dose to the patient’s specific needs.

The Institute of Physical Chemistry has been conducting research on diffusion for a long time. The research is based on phenomena occurring during the flow of a liquid, similar to those observed in rivers—in a river bed, water flows faster in the central part than by the banks, and when vortices appear in the current, water masses are mixed more effectively.

The key component of the apparatus used by the institute is a very long (30-meter) and very thin polymer tube called a capillary. Inside the capillary there flows a carrier liquid: water at room temperature and with a pH value corresponding to that of human blood. The capillary is tightly coiled, and the flowing water moves at high velocity. The combination of the two factors makes the flow in the capillary not fully homogeneous and results in the generation of small vortices.

When a small amount of an analyte—a chemical substance subject to analysis—is injected into a stream of carrier liquid flowing in the capillary, it spreads out quickly into a long streak. Researchers from the Institute of Physical Chemistry looked at the analyte concentration in the carrier liquid at the outlet from the capillary. In line with expectations, the highest concentration was in the center of the capillary, while the lowest one was found at the walls. A graph of the distribution of the analyte concentration along the capillary diameter was bell-shaped, producing the famous Gauss curve. Anna Lewandowska, a doctoral student at the Institute of Physical Chemistry, said, “In spite of the high flow rate and the presence of vortices, we were able to find a correlation between the variations in the distribution of the analyte concentration in the cross-section at the end of the capillary, which means, simply speaking, the width of the Gauss bell—and the flow rate, the viscosity of the carrier liquid, the capillary curvature, and the diffusion coefficient of the analyte. The first three factors are known, which means that in practice it’s enough to measure the width of the ‘bell’ in order to determine the diffusion coefficient.”

Prof. Robert Hołyst, director of the Institute of Physical Chemistry, added, “Interestingly, the results of our measurements were inconsistent with current theoretical models, constructed on the basis of approximate solutions of the famous Navier-Stokes equations. These equations describe the movement of fluids, and at present their solutions are known for the simplest flows only. So, we had to determine experimentally our own formula describing our measurement system and the phenomena occurring within it.”

In earlier versions of the apparatus, the measurements were carried out at low flow rates, only 0.05 milliliter per minute. The analysis of a single analyte took 40 minutes, yielding results with errors reaching up to 30 percent for some macromolecules. Now the flow speed is 20 times higher. The time needed to determine the diffusion coefficient was reduced down to three minutes, and the accuracy of the measurements increased more than five times.

The shortening of the analysis time is important from the perspective of medical practice. The determination of a drug dose optimal for a specific patient requires not one, but three measurements.

Aldona Majcher, a doctoral student at the Institute of Physical Chemistry, said, “First, we have to introduce drug molecules into the capillary and to determine the rate of their diffusion. Then we measure the diffusion of the protein with which the drug is expected to bind, for instance, albumin. In the third measurement, we inject both the drug and the protein, with which the drug interacts, into the capillary filled with the same protein. A comparison of the results makes it possible to find out how efficiently the drug will bind to the protein in the patient’s blood.”

The patent-pending method for determining the diffusion coefficient in fluids is fast, versatile, and simple. It does not require any expensive or complicated measurement equipment, and so it has a chance of becoming popular and being used in many hospitals and health centers as well as chemical and biological laboratories. The experiments at the Institute of Physical Chemistry have shown that the method has passed the test in measurements involving salts, amino acids, peptides, proteins and drugs.

The research was supported by grants from the Polish National Science Center and the Foundation for Polish Science.
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