What is the “Fish Tank Model” ?

This is an interesting course. You’ll be taking six lessons within this course now I know that many pharmacy students and medical students have found clinical pharmacokinetics to be somewhat challenging. Perhaps confusing, it’s not one of their favorite courses historically. But I think when we go through this course you’ll realize that if we zero in on some very basic concepts and principles. It’s not too challenging and I think you’ll find it to be somewhat easy to master. We’re going to focus on how we can determine the best drug, the best dose of a drug for any patient, using very basic principles and applications of those principles. Assumptions and ground rules for this course are very simple.

First we will use abbreviations and symbols from the Rowland and Tozier textbook that the TMU pharmacy students use the G for pharmacokinetics course here We also utilize exponential functions using natural logs not logs and the reason for this is again to keep things as simple as possible by using natural log with the base e rather than base ten. We don’t have to use the 2.303 factor in all of our calculations. We’re going to approach perspectives from a patient care setting not a laboratory So we’re not going to be functioning in clinical pharmacokinetics from a research perspective. It would be practical patient care applications which actually makes clinical pharmacokinetics much simpler to apply.

Our doses and intervals will be changed in quantum leaps and that’s one of the things that simplifies the process. We’re not going to worry about whether a dosing interval should be seven point four hours or seven point seven hours. In either case we would round it off to every eight hours. The same thing applies to doses. We’re not going to worry about whether dose is a hundred milligrams or 103 milligrams and would round off to a hundred. So by rounding off in quantum leaps it makes it a lot easier to determine the best dose and the best dosing interval for a patient. Unless otherwise indicated we will always assume that by over ability is a hundred percent.

Now we work, we will explore bioavailability and where it applies but for our routine coverage of calculations, we’re going to assume that it’s 100 percent just to simplify the concepts that we’re going to be covering. Unless otherwise indicated, we’ll we will also assume that absorption and distribution occur instantaneously. and I’ll explain more about that when we get into that section of the lesson. We will be focusing on mathematical relationships more so than the manipulation of equations. I’m not as concerned that you know how to plug numbers into an equation to derive a correct answer. What’s much more important is that you understand the relationships between the variables in the various equations.

And lastly our primary frame of reference , for all drugs in the body will be blood. Let me explain that in a little more detail. Clinical pharmacokinetics focuses on serum concentrations. We’re going to focus on what a serum level is in the patient’s blood, or their serum or plasma. We will use these terms interchangeably. Drug is absorbed into the serum or plasma. It distributes away from the serum or plasma. It’s eliminated from the serum or plasma. The efficacy and toxicity as we evaluate it will be based on the concentration in the serum or plasma. So even though a drug probably acts elsewhere from the serum or plasma it’s the serum or plasma that will be our primary frame of reference.

For all the pharmacokinetic monitoring that we’ll be doing. So let’s begin session 1, the fishtank a simplified model of first order elimination. the question that we’re going to try to answer in this video is how can we describe what happens to drugs in the body, in the simplest most straightforward way. When you finish this first lesson, you’ll be able to explain how the fishtank relates to drug elimination. You’ll be able to define volume clearance elimination rate constant and half-life and identify their practical applications. You’ll be able to describe the applications of e to the minus KT and how its applied in various ways. You’ll be able to define area under the curve and describe factors that affect it.

You’ll also be able to define mean residence time. You’ll be able to identify how protein binding affects drug action drug distribution and drug elimination. and you’ll be able to explain how protein binding affects clearance. Now one of the things that I’d like you to keep in mind as we go through this, this early exploration and the clinical pharmacokinetics is that we get we can actually approach clinical pharmacokinetics in one of three levels the most basic fundamental level is population pharmacokinetics. This is the dosing that we find in manufacturers literature that applies to all patients across the board. We can take that to a higher level what I would call second level.

Pharmacokinetics by zeroing in on subpopulations perhaps populations of patients that have varying levels of renal function, or hepatic function, or patients in different age groups, but the highest level of clinical pharmacokinetics is patients specific where we actually measure serum concentrations of a drug in an individual patient and then apply those kinds of concentrations to optimize the drug dosing regimen. My hope is that you will become proficient in all three levels of clinical pharmacokinetics. And you’ll be able to mix and match those levels based on the information that you have available to you on a given patient. So let’s begin, first over elimination using the fishtank.

Now as you know first over elimination is a very simple process that involves the rate of elimination of the drug being proportionate to the drug concentration. Now that seems a little unusual at first and it’s not a it’s not a concept that’s easy to visualize. You can see in the graph at the top of this slide that early on when the serum concentration is highest the rate of elimination or the slope of the line is steepest and then it gradually declines in rate as the serum concentration declines . This relationship is shown in the graph where we see that the rate of elimination is directly proportional to the serum concentration.

For many pharmacy students, this is a difficult concept to grasp why does the concentration affect the rate of elimination? And why is it that if we give a dose of drugs such as the concentration subtly increases that the rate of elimination would increase simply because we gave more drug? I have found that the best way to understand and apply. First order pharmacokinetics is a simple model called the fishtank. I discovered this model back in the late 70s in an old pharmacokinetics textbook. I photocopied a graphic from that textbook what you can see of a man fishing scooping fish out of a tank with a net. Now, the concept of this is really very brilliant.

When you consider what’s involved is first order elimination, if we have a net and we’re going to scoop fish out of a tank, that’s it’s full of fish, as we bring the net through the tank. That net is going to scoop up all the fish in the path of the net. Now as we begin to remove fish from the net and we eliminate the fish from the tank, the concentration of fish in that tank is going to gradually decline. Such that every time, we pull the net through the tank, we’re going to catch fewer and fewer and fewer fish. That’s the beauty of first order elimination is illustrated by the fish tank.

So let’s take a look at this in greater detail. If we consider the volume serum concentration the clearance and the rate of elimination, using our fish tank model. Let’s assume that a human being is a big tank just like a fish tank except it’s shaped like a human. It’s filled with nothing but blood. Now for granted we know that’s not the case, but it will apply to our model and we can explain where it deviates from the actual drug distribution within a human being. So a patient is a tank shaped like a human filled with nothing but blood. Now let’s shift gears and think of the tank as a fish tank filled with fish rather than blood.

We can illustrate what happens when we add drug to the tank with a schematic that I’ve shown on this slide. Now each dot represents a fish. So you can see that we’ve added we have a tank that consists of 20 liters each square of this tank is one liter. We’ve added 200 fish to the tank so within each liter we have 10 fish represented by 10 dots. The concentration therefore is 10 fish per liter. Now the net that we pull through is going to clear fish out of the tank and I’ve indicated that the yellow squares are the ones that our net passes through.

So all the fish within those 5 liters at the top of the tank are going to be removed from the tank every time we pull the net through. So, what’s going to happen over time as we observe the concentration of fish in this tank? We start with 200 fish, concentration of 10 fish per liter. During the first hour, we will remove enough fish such that the concentration declines to 44. We removed 44 fish from the tank. Giving us a concentration of 7.8 fish per liter. Now intuitively you might say why didn’t we remove 50 fish? Initially, there are 50 fish in those 5 liters that we clear out in the yellow squares up at the top of the tank.

Why didn’t we remove 50 fish during their first hour? And that relates to the concept of first order elimination. The concentration is constantly declining as we’re scooping fish out of the tank. So we won’t remove 50. We’d remove somewhat less because as we’re pulling that net through the tank, the concentration of fish is constantly declining. It’s not the average concentration during that hour was 44 fish rather than 50. During the second hour the fish we would remove down to 121 fish have a concentration of only 6 fish. We would have removed only 35 .

So every hour we remove fewer and fewer fish because the concentration is declining but the volume of water that our that our net passes through is constant. The third hour we have 94 fish remaining. A concentration of four point seven and we’ve removed only 27 fish. That’s the fish tank model and how it relates to the fact that as the concentration of fish in the tank declines, the rate of elimination of fish declines proportionally.