Saturable drug absorption

Drug absorption is the process by which a drug molecule moves from the site of administration to the systemic circulation. Following intravenous administration, there is no absorption process since the drug is directly introduced into the blood stream. However, for oral, intramuscular, subcutaneous, sublingual, buccal, transdermal, (and a many other routes), there will be an absorption process that occurs. Since there are so many different variants of extravascular administration, let’s focus on oral administration to explain the concept of saturable drug absorption. Following ingestion of a drug capsule or tablet, the drug enters the gastrointestinal (GI) tract and begins to dissolve in the GI fluids and is absorbed into the body via passive and active transport systems. The drug then passes through the portal vein to the liver and then into the systemic circulation. If any of these processes becomes saturated, then increases in the administered dose will not correspond to increases in amount of drug absorbed into the body. This is called saturable drug absorption.

Dissolution
If the drug is poorly soluble in the GI fluid, then you may encounter saturation of the dissolution process. At some point, no more drug can dissolve into the GI fluid to be available for absorption. This results in a plateau in drug exposure where increasing the dose will not increase the exposure. Sometimes, dissolution can be aided by adding additives that assist in the dissolution process, or change the pH of the GI fluid to aid in dissolution.

Transport-mediated uptake
Some drugs are absorbed through transport-mediated uptake mechanisms. For example, valacyclovir is absorbed by active transport by the peptide transporter PEPT1. Drug transporters can be saturated if the substrate (drug) levels are sufficiently high. Once the transporter is saturated, no additional drug can be absorbed from the GI tract, even if it is available for transport. Similar to the example of dissolution, increases in the dose will not increase the exposure. These transport-mediated limitations are difficult to modulate without re-desigining the drug molecule to take advantage of multiple transport systems.

Passive uptake
Most drugs are absorbed through passive mechanisms that are generally not saturable. These absorption mechanisms depend only on the available surface area of the GI tract and the strength of the concentration difference between the lumen of the GI tract and the portal vein. Thus, saturation of passive uptake mechanisms is very rare. On occassion, with very large doses, absorption can slow due to the large amount of drug present in a confined space. In general, saturable absorption does not occur in situations with passive uptake.

If you encounter saturable drug absorption, there is generally no harm because higher doses will not result in higher drug exposure.  Understanding the type of saturation (transporter or dissolution) will be useful information to make a decision on they approach to address the issue. If the saturation is in the dissolution, it may be possible to address it with reformulation and addition of specific materials to help the drug dissolve in the GI fluid. If the saturation is due to transport-mediated uptake, there is not much you can do to change the outcome.

When you have saturable absorption, drug exposure will plateau at higher doses. When you have saturable elimination (or clearance), the total exposure will increase faster than dose at higher doses. By plotting the exposure (area under the curve or AUC) on the y-axis and dose on the x-axis, you can determine if absorption and/or elimination are being saturated across the dose range studied.

What is hysteresis in PK/PD analysis?

I apologize to all my readers for such a long lapse between posts. After a very busy summer and fall, I am back to posting regularly to my blog about PK/PD topics.

When analyzing PK/PD data, one of the most important plots used to visualize the data is to plot time-matched PK/PD data on a scatter plot. The X-axis has the PK concentration and the Y-axis has the PD data. Two examples of these scatter plots are shown below.

No Hysteresis

Hysteresis

The first plot shows a relationship with no hysteresis, and the second shows hysteresis. The easiest way to identify hysteresis is by drawing a vertical line on the concentration-effect plot. If that line crosses the curve in 2 places, indicating 2 different response levels for a single drug concentration, then you have hysteresis. In the first plot (no hysteresis) a vertical line at 40 ng/mL corresponds to a single effect level (20%). However, in the second plot (hysteresis) a vertical line at 40 ng/mL corresponds to both effect levels of 40% and 100%.

A hysteresis is neither good nor bad when reviewing PK/PD data. A hysteresis loop simply means that there is a time delay between the measured concentration and the effect response. Normally this means that the measured effect is indirectly affected by the measured concentration. To properly model this relationship, you would want to use an effect compartment or an indirect PK/PD model.

So a hysteresis loop simply provides information on how to model your PK/PD data.

How can PK/PD analysis add value to patient care?

In May 2011, T.J. Smith and B.E. Hillner published an opinion piece in the New England Journal of Medicine titled “Bending the Cost Curve in Cancer Care” (link). In this opinion piece, Smith and Hillner suggest that the rapidly increasing cost of treating cancer is not sustainable.

“We must find ways to reduce the costs of everyday care to allow more people and advances to be covered without bankrupting the health care system.”

Suggestions to re-balance the cost-effectiveness included limiting chemotherapy based on performance metrics, switching to palliative therapy when chances of success are small, having appropriate end-of-life discussions, and executing comparative-effectiveness and cost effectiveness analyses. These solutions are not novel or unique, but they challenge the standard method of treating patients.

This article made me think about my contributions and how I might contribute to reducing the cost burden on the healthcare system while continuing to provide the best possible therapies to patients. Pharmacokinetic/Pharmacodynamic analysis should provide significant information to optimize therapy for patients, but I don’t think we have achieved that lofty goal. This discipline which we practice uses pharmacostatistical models to relate drug doses to clinical response information. As these models are developed, we include patient demographic information to refine the predictions and customize our models. We also link PK and PD together to create integrated exposure-response models that link dosing to clinical efficacy. Despite all of this effort, many of these PK/PD models never reach clinicians who prescribe the medications nor do they reach the patients who could benefit from our work.

What can we do to change this sad fact? Here are some of my ideas:

• Integrate more clinically relevant features into our models. Focus on demographic measures commonly made in a physician’s office, not those measured in a clinical study.
• Package our models into tools that physicians can use. Provide PK/PD models as web apps, mobile apps, or in conjunction with other physician software packages. Help physicians simplify the process of prescribing medication.
• Provide our models to patients. Provide simplified models to patients as scientific communications, not promotional tools. Today’s patient is educated, curious, and connected to the internet. Let’s recognize that inquisitive nature and provide tools to help patients discuss their medication with their physician
• Simplify our models and target clinical outcomes. Too many models focus on esoteric measures of pharmacodynamic measures. Let’s spend more time integrating clinical outcomes (even those that are categorical) into our models so that they can be more meaningful to physicians and patients.

What do you think we can do to use PK/PD to add value to patient care? Leave your comments below.

WinNonlin Software Review – Part 1

WinNonlin by Pharsight has been a fixture in pharmacokinetic analysis software for over 20 years. While it has been known as a tool for noncompartmental analysis and model-based analysis of single subject data, the new Phoenix WinNonlin creates an entirely new platform for pharmacokinetic and pharmacodynamic analysis. Similar to my review of NONMEM, I will be evaluating features and usability of the Phoenix WinNonlin software from a user’s perspective.

Part 1 will review the Phoenix platform and integration with other tools. Part 2 will review the noncompartmental and individual pharmacokinetic model fitting tools. Finally Part 3 will review the new nonlinear mixed effects module (NLME).

The installation of Phoenix was simple and easy. A standard Windows installation program was used with the default options on computers with Windows Vista, Windows 7, and a Mac running Windows Vista through a Virtual Machine. WinNonlin is not natively supported on operating systems other than Windows (e.g. Linux, Mac OS X, and UNIX).

The new Phoenix platform is best described with a picture (Click image to enlarge).

Phoenix Workflow

The newly designed interface has a centerpiece called the “workflow”. The left side of the image shows the object browser. This is where you have a list of all the objects in your file, and it is organized much like a set of nested folders. Users who are familiar with the Windows File Explorer or the SPlus statistical package will be immediately comfortable with the object browser. The right side of the image shows the workflow space. Within this white space you can place objects and then cause them to interact with one another. The orange box titled “External Sources” is a collection of data sets from external sources. Those data sets act as the input for 5 different noncompartmental analysis (NCA) objects that each have their own properties and output. The NCA in the lower left of the image is then the source of a summary statistics worksheet titled “Descriptive Stats”.

The types of objects available to use in Phoenix include: worksheets, plots, NCA, nonlinear modeling, nonlinear mixed effects modeling, in vitro-in vivo correlation tools, tables, NONMEM, SAS shell, SigmaPlot shell, SPlus script, R scripts, and other workflow objects. Each object in the workflow (or box on the white space) has its own inputs, results, and outputs. Each of these outputs can then be directed to become the input of another object (e.g. a set of final PK parameters from an NCA object can be sent to a table object). These workflow connections are illustrated by arrows and are saved in the single Phoenix project file. This allows a single workflow to be used as a template. For example, you could set up a template workflow for a drug-drug interaction study that includes the following:

• NCA analysis for Drug 1
• NCA analysis for Drug 2
• Summary statistics worksheet for Drug 1
• Summary statistics worksheet for Drug 2
• Statistical comparison of drug-drug interaction
• Tables for summary statistics of Drug 1, Drug 2, and drug-drug interaction
• Plots with individual and mean concentration-time data

This workflow could be saved as a Phoenix template file and then when a new study is conducted the concentration-time data can be added to the workflow, linked to the NCA analyses and a single button click will perform all analyses, calculate summary statistics, and produce the desired tables and figures. This ability to automate can revolutionize traditional pharmacokinetic analysis to simplify the work, standardize output, and allow for faster data analysis.

A new feature with Phoenix is is the ability to incorporate different analysis types on a single workflow. A single workflow can contain NCA, individual nonlinear models, and nonlinear mixed effects or population models. No need to switch back and forth between multiple model files for different analyses on a single set of data! You can conduct your NCA for initial estimates, along with 1- and 2-compartment model fits on the same workflow.

In addition to the workflow feature, Phoenix integrates well with other software packages such as NONMEM, SAS, R, SPlus, and ODBC-compliant databases like Watson LIMS. This integration is achieved through the Phoenix Connect module that allows seamless transfer of Phoenix output to selected software programs, and then the ability to receive output from those same programs. An example of this is the export of AUC values to SAS for statistical analysis followed by the import of the bioequivalence summary statistics into Phoenix for inclusion in a table object. This allows the Phoenix workflow to control data analysis procedures from beginning to end, while allowing a user to interact with their preferred software solution.

Overall, the new workflow layout and design is a significant advance in pharmacokinetic software. And although the new Phoenix user interface is a departure from the previous one, the flexibility and power of the new workflow will create a great opportunity for users to streamline their work processes and simplify data analysis.

More to come in Part 2 (NCA and individual model fitting) and Part 3 (NLME) of my review of Phoenix WinNonlin.

An evaluation copy of Phoenix was provided by Pharsight with the WinNonlin, Connect & NLME modules. You can learn more about Phoenix WinNonlin by visiting the vendor’s website, by calling your local Pharsight representative, or by requesting information from Pharsight.

Is a Monte Carlo simulation an exotic drink?

The term “Monte Carlo simulation” is often used in the modeling and simulation literature with PK/PD analysis. When I was first exposed to this term, I was thoroughly confused and thought that it was some exotic statistical method that required 3 PhDs and a few days to comprehend. Well, I was very wrong.

A Monte Carlo simulation is a simulation that utilizes the “Monte Carlo Method“. It was named after the famous Monte Carlo Casino in Monaco.

Monte Carlo Casino Monaco

At the Monte Carlo Casino, people take their money and gamble on games of chance. Games of chance are based on probabilities of random events ocurring. For example, roullette is a game where a ball bounces around a spinning platform and eventually comes to rest on one of 36 spots. Players can make various bets on the chance that the ball will stop on a specific spot or spots.

You may ask, “what in the world does that have to do with simulations?!” Well, let me tell you. Prior to the Monte Carlo method, simulations were performed with specific parameter values to generate a single simulation. For example, let’s assume we have the following PK model:

$C(t)=\frac{Dose}{V}*e^{(-\frac{CL}{V}*t)}$

We can predict a concentration-time curve by providing a value for CL and V. We can then do that for various combinations of CL and V. It would look something like this:

Discrete Simulation

This gives us 2 concentration-time curves. While this is useful, we don’t always know the exact values of CL and V for a given individual before they take the drug. What we usually know is that the CL and V have some average value along with a variance. In other words, we have a distribution of values for CL and V, with some being more likely than others. Thus instead of just choosing a few sets of values for CL and V, what if we chose many values. And what if we used the known distribution to select more likely values more often and less likely values less often? Well, we would then have a simulation that looks like this:

Monte Carlo Simulation

As output, we would get a large distribution of plasma concentration-time curves that would represent the range of possibilities, and the more likely possibilities would occur more frequently. This is extremely useful in PK/PD simulations because we can quantify both the mean response and the range of responses.

To do a Monte Carlo simulation, you simply have to have a program (like NONMEM or WinNonlin) that randomly selects a parameter value from a known distribution. Then runs the PK model and saves the output. That process is repeated many times (usually between 1,000 and 10,000 times) to generate the expected outcomes.

Hopefully you understand Monte Carlo simulations better now … and if not, you should go get an exotic drink and try reading this post again tomorrow!

What are direct and indirect pharmacodynamic models?

When constructing pharmacodynamic (PD) models, you will often encounter the adjectives “direct” and “indirect” describing the associated PD model. This terminology was very confusing to me when I was learning about PD modeling. Hopefully a brief explanation will help you.

Let’s start with the direct PD model. In this type of model, the drug is directly responsible for the pharmacodynamic response being measured. One example of a direct PD model is the pharmacodynamic response to moxifloxacin (AVELOX®). As moxifloxacin concentrations increase, the QT interval also increases. Thus, the PD measure (QT interval) is directly related to the drug (moxifloxacin) concentration.

Direct pharmacodynamic model

The indirect PD model is slightly different in that the drug does not directly affect the pharmacodynamic response. Instead, the drug affects a precursor which then influences the pharmacodynamic measure. An example of an indirect PD model is the pharmacodynamic response to warfarin (Coumadin). As warfarin levels increase, the inhibition of prothrombin synthesis is inhibited, which in turn has anti-coagulant effects. In this case, there is a separation (space and time) between the PD measure and the action of the drug (inhibition of synthesis of prothrombin).

Indirect pharmacodynamic model

In a direct model, the drug is directly responsible for the PD response that is measured. In the indirect model, the drug is “indirectly” responsible for the PD response measured. When trying to decide which type of PD model you should use, most people will start with the indirect model because it is more consistent with our understanding of receptor-mediated drug effects and signaling cascades. However, the indirect model is difficult to use if the PD response profile follows the drug concentration profile. Thus, when no temporal delay in response is seen, direct response models should be used. On the other hand, when there are time delays between peak drug levels and peak PD effects, the indirect model should be used. For more information, look up publications by William J Jusko of the University of Buffalo.

I hope you have a better understanding of direct and indirect pharmacodynamic models. Happy modeling!

What is Modeling and Simulation?

I am currently attending a short conference on modeling and simulation in pediatric clinical pharmacology, and I noticed that many people in the conference don’t have a good grasp on what “Modeling and Simulation” means. I think most of them think that it is an extremely complicated mathematical concoction that is intended to keep everyone confused and in awe of the speaker that is presenting. They couldn’t be further from the truth. But, first, let’s talk about saving money.

Imagine you are given \$1,000 from a relative. You would like to use that money to “make some money”, so you put it into an investment that is guaranteed to make 8% growth annually. If you left that money there for 20 years, how much money would you have?

To solve this problem, you need to know what the future value of the principle given the 8% annual growth, compounded monthly for 20 years. There is an equation for that:

$FV=PV*(1+i)^t$      Equation 1

$PV=\char36 1,000\;\;\;i=\frac {0.08}{12} = 0.00667\;\;\;t=20*12=240$

$FV=\char36 1,000*(1+0.00667)^{240} = \char36 4,930.72$      Equation 2

So after 20 years, you have almost 5 times as much money as you were given. The method we just worked through to determine how much we would have in the future can be thought of as modeling and simulation. Equation 1 is the model, and Equation 2 is the simulation.

I think I just heard you say, “What! It can’t be that simple! No way!” Well, it is true, the estimation of future savings is nothing more than a simulation of a known financial model for compounding interest.

Now we can convert this into the pharmaceutical world. A model is a set of mathematical equations that describe observations. In some cases the observations are plasma concentrations, in other cases it is intraocular pressure, or enzyme inhibition. The “parameters” of the model are derived from the observations. (In Equation 1, the parameters are PV, i and t.)

A simulation is when you use a model to predict something. Instead of estimating parameters from observed data, you take the model, and a set of parameters to simulate some data. As we did in Equation 2, we set PV, i and t to specific values for the desired situation, then we calculated FV. Or, in other words, we simulated FV given a set of parameters.

So, when you hear about modeling and simulation, just think about your bank savings account and remember that you and your bank do modeling and simulation every month.

What is Pharmacodynamics?

Starting with definitions is always helpful … so after defining pharmacokinetics, a definition for pharmacodynamics is in order. The definition of pharmacodynamics (PD) is much less controversial than the definition for pharmacokinetics.
The word pharmacodynamics is from two greek words (see wikipedia for more):

pharmakon: Drug
dynamikós : force or power
Thus, pharmacodynamics is the study of the effects of drugs.

Whether we are talking about pharmaceutical therapeutics or recreational drugs, people take drugs to achieve a desired pharmacological effect. And two key questions often asked prior to taking the drug are: “How long before I feel the effect?” and “How long will the effect last?”. Both of these questions can be answered by using pharmacodynamic analyses.

Most drugs are developed based on the theory that the drug interacts with a biological structure (e.g. receptor, enzyme, transporter, etc.), and that interaction leads to a specific effect on the body. The strength and length of this interaction determines how quickly the drug initiates the effect, and how long the effect lasts.

Penicillin
Penicillin is recognized as one of the first drugs to enter mass production, leading to a significant reduction of bacterial infections across the world. Penicillin is an antibiotic, which means it kills bacteria. The penicillin molecule binds to a bacterial enzyme (DD-transpeptidase) that creates “cross-links” in the bacterial cell wall, preventing the cross-linking action. Thus penicillin prevents bacteria from creating strong cell walls, in effect killing the bacteria. The interaction between penicillin and the DD-transpeptidase enzyme depends on the amount of penicillin present. When large amounts of penicillin are available, the enzyme is completely blocked. When small amounts of penicillin are available, the enzyme resumes normal function. Thus the bacterial-killing activity of penicillin changes as drug levels in the body change. This is considered the “pharmacodynamics” of penicillin. Using this information, physicians can properly prescribe the penicillin dosing frequency to ensure high drug levels over the course of treatment.

Why have a blog about PK and PD?

Many blogs you will find on the internet are related to personal ventures, technology, or hobbies … all topics that are suited to the light-hearted fare that is common in the blogosphere. I believe that blogs can communicate knowledge in unique ways to a broad audience. Instead of developing a blog about my personal life, or some hobby, I decided to create a blog about my scientific passion, pharmacokinetics (PK) and pharmacodynamics (PD).

Who am I?
I have been involved in the pharmaceutical industry since 1997 with expertise and training in clinical pharmacology. Over the course of this time, I have seen an evolution of the science of pharmacokinetics from a mathematical necessity of calculating PK parameters to the scientific artistry of simulating clinical responses. During that evolution, the clinical pharmacology field has failed to adequately train new scientists and it has failed to properly educate colleagues about the scientific basis of this work.