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PK/PD Modeling

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So after the allometric scaling, we are going to talk about PK/PD modeling, that is to integrate PK and PD into one set of math expression, to describe the time course of the effect or response. Now PK/PD modeling helps to identify the biological processes involved in the mechanism of drug action. Now in contrast with small molecules, the molecular mechanism of action of therapeutic proteins is generally better understood. Now after the basic model or PK/PD model is built, then we can use the basic model with the incorporation of other factors, such as dose, molecular size, or receptor metabolism. We can predict the drug effect under new conditions.
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Essentially, there are a few PK/PD models that I’m going to cover here. First is the direct link PK/PD model, the indirect link PK/PD model, the indirect response PK/PD model, the cell lifespan model, and the complex response model.
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Now before PK/PD modeling, let me talk about the pharmacological response. There are several types of pharmacological response, one is continuous response, for example, the heart rate, the blood pressure. That is continuous. And also graded response. For example, pain severity, mild, moderate, severe pain. That’s graded response. Or the binary response, presence/absence, life/death, that’s binary response. Now for PK/PD modeling, we are referring to continuous response. Direct link model.
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Concentrations of the plasma compartment and the effect site equilibrated very quickly. And therefore, plasma concentration reflect the effect site of concentration. They are proportional but they are not necessarily the same. Therefore, the site of action is within the well-perfused central compartment. There’s no temporal delay of the response. And the Emax model is frequently used to model the effect. This model fits many small, fits many small molecules. And again the response is mediated through the direct interaction of the drug and the receptor at the effect site. So this is the Emax model. It described the response and the concentration relationship. And this is the Emax model equation. So within 20% to 80% of the maximum response, there is a linear relationship.
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And this is the maximum response. And here is the C50, that is the concentration that elicits 50% of the maximum response. So let’s look at this model. Let’s see, let’s say here we have a happy face. The drug is injected intravenously. The drug becomes distributed in the first compartment or the so-called central compartment. Which is then distributed into the second compartment or the peripheral compartment. Now the drug concentration in the central compartment equilibrated rapidly with the site of action. And it is the concentration or the biologics concentration in the central compartment that brings about the effect.
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And because the quick or rapid equilibration between the central compartment and the effect compartment, the effect and the concentration in the plasma are directly related. And that’s why we called it a direct link model. Let’s look at one example of them. This is when monoclonal antibody. This is the plasma concentration. And this is the reduction of the free IgE and that is the response, just for simplicity. And please note that response, the scale is kind of reversed because 0 is at the top and 100% response is at the bottom. Let’s look at the plasma concentration. At high concentration, high response. At low concentration, low response. So there is a direct link between the concentration and the response.
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So this is a direct link model.

PK/PD modeling has already been used extensively in pre-clinical and clinical drug development. However, few examples exist within the literature on the application of modeling to enable the appropriate engineering and testing of biological therapeutics. Benefits of PK/PD modeling for biologics include to elucidate biochemical process and mechanism of biologics action, to guide decision and selection of drug candidates for streamlining biologics development, and to optimize clinical dosing regimen. Five commonly applied models are presented for discussion.

Benefits of PK/PD modeling for biologics include elucidating biochemical process and mechanism of biologics action, to guide decision and selection of drug candidates for streamlining biologics development, and to optimize patient dosing regimen. Five models are presented, Direct link PK/PD model, Indirect link PK/PD model, direct response PK/PD model, Cell lifespan model, and Complex response model. Direct link model is illustrated with an anti-IgE antibody, assuming that the effect site is within the central compartment, and therefore no delay of pharmacological response occurs. For model assessment, Emax model is applied for continuous pharmacological response in direct link modeling.

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