Doctors frequently prescribe long-term drug treatments for patients suffering from chronic illness. For example, those with sustained bipolar disorder often take lithium, while buprenorphine is used to combat opioid dependence — particularly heroin addiction. Some of these drugs, including lithium, can be highly toxic if they accumulate heavily in the bloodstream; yet too low a dosage has no effect at all. Keeping drug concentrations within a healthy yet effective therapeutic window demands accurate, manageable monitoring techniques. One such technique is noninvasive monitoring through patients’ skin.
Noninvasive techniques have the potential to transform and improve how doctors treat chronic patients. During a minisymposium about mathematical pharmacology at the 2017 SIAM Conference on Applications of Dynamical Systems, currently being held in Snowbird, Utah, Jane White of the University of Bath discussed her work with long-term drug distribution in the human body. “It’s really important to understand exactly what the drugs are doing on an individual basis,” she said. Most patients use certain drugs regularly and for extended periods of time, meaning that they accumulate in drug reservoirs—residual buildups or archives—in the outer skin layers. White acknowledges these buildups, which complicate the monitoring process, in the development of her model.
There is a global problem of noncompliance within the pharmaceutical industry. 50 to 80 percent of people don't follow the instructions of their prescriptions, which in turn can impact drug reservoirs on the skin. Image courtesy of Jane White.
She began by highlighting patient habits that might influence drug distribution. “We’re mindful of the fact the that pharmaceutical industry costs public health quite a lot of money,” White said. “But globally there’s a large problem of noncompliance.” She added that despite the cost, between 50 and 80 percent of patients do not take their medications as prescribed. The impact of this disobedience varies on a case-by-case basis, depending on the stability or severity of the illness (i.e., high blood pressure versus bipolar disorder) and thus the corresponding treatment.
White then described the process of drug distribution. When a patient takes a dose (most often orally), blood flow distributes the medication throughout the body. “Some molecules end up in target sites, where they’re meant to go, or they’ll end up in other parts of the body and tissues where there’s no therapeutic effect,” she said. The latter increases the drug reservoir. White mentioned two different experiments that helped her form a theory about distribution. Lithium iontophoresis in vitro, performed on dermatomed pig skin, monitored how lithium on the underside of the skin flowed to the top side. This is in contrast to lithium iontophoresis in vivo, performed on chronically-dosed patients. Together these studies led White to a hypothesis. “For drugs that are taken over a very long period of time, the majority of them do what they should do,” White said. “But some end up in the drug reservoir on the outer layers of the skin.” This is especially true of lithium. Because it doesn’t bind and is a small molecule, the drug seems to penetrate tissue, then migrate into the skin’s outer layers.
After establishing the necessary background, White presented her model, which explores the initial buildup of drug reservoirs over time and their ensuing effect on drug extraction from the skin. “We wanted to create a very simplistic model to understand buildup in this outer layer,” she said. Drug molecules enter the skin through two processes: diffusion and/or desquamation (natural skin regeneration). Every two weeks, the outer layer of skin naturally replaces itself. “Only an unbound drug can make it through the skin after desquamation,” White said.
White’s model is simple, as it only has one spatial dimension. It involves systems of partial differential equations, whose parameters depend on the drugs’ individual physicochemical properties, and includes partition coefficients and concentrations on both the bound and unbound drug molecules. She justified the parameter ranges in terms of various properties, including lipophilicity (dissolvability), molecular weight, and binding. For example, buprenorphine is highly bound, which limits its ability to move freely into the skin. However, it’s lipophilic properties mean that when unbound, it exhibits a preference for the skin’s outer layers.
White examined multiple influential factors, including the impact of diffusion rapidity on drug reservoir size, to observe overall reservoir growth. She also circled back to noncompliance, offering first an example of what happens when a patient misses one dose but otherwise proceeds as normal, and then an example of a patient who misses doses 50 percent of the time (every other day).
The question then becomes as follows: how do you go about measuring the reservoir size in patients? White proposed two noninvasive methods of drug extraction from the skin. One method is reverse iontophoresis, which passes an electric current through patients’ skin and removes molecules for detection. Another is tape stripping, a method of drug quantification that does exactly as it sounds — collects skin cells with adhesive tape. “It gives you a measurement of the total amount of drug in your outer layer of skin,” White said. “If we can collect this type of data, if could be used to interpret what the drug is doing in the body.”
In conclusion, White demonstrates the important link between drug reservoir size and physiochemical drug properties. “The comparison of data extracted with different techniques could improve our understanding of the impact of physiochemical drug properties on distribution in the body,” she said. A better understanding of reservoir buildup could yield useful information about patient treatment history, inspire the development of enhanced drug modeling techniques, and improve chronic patient response to various drug regimes.
|| Lina Sorg is the associate editor of SIAM News.