Pharmacokinetics, Mathematical Model in Drug Design

Pharmacokinetics

A drug's pharmacokinetic action refers to how it travels into, through, and out of the body, which impacts its effectiveness. An ADME is the interaction between a drug and its metabolism, absorption, distribution, and excretion (pharmacokinetics). These phases are as follows:

• Absorption - An absorption is described as the process by which the drug is moved from the point of administration to the area where it acts.
• Distribution - A drug's journey through the bloodstream to reach varied tissues in the body is described by its distribution.
• Metabolism - Describes what happens when a drug is broken down.
• Excretion - Is the process by which we eliminate it from our bodies.

Here are some details about each phase:

Absorption

In the process of absorption, drugs from their administration site enter the bloodstream. Several factors contribute to the amount and rate of absorption of drugs, including:

• Drug-food interaction
• Chemical interaction and formulations of drug
• Route of administration

In the bloodstream, bioavailability is the percentage of the drug's active form that reaches the target site after administration (e.g., oral, intravenous, inhalation). As the active form of a medicine is delivered immediately to the systemic circulation, intravenous administration of the drug does not require absorption and has 100% bioavailability. As a result, oral medications do not absorb well and do not reach the site of action as much as those administered injectable. The systemic circulation of many drugs administered orally is affected by metabolization within the intestinal wall or the liver. Drug absorption is reduced due to this first-pass metabolism.

Distribution

The process of drug distribution plays a significant role in drug efficacy and toxicity because it affects the amount of drug that reaches active sites. As it moves through the body, a drug becomes absorbed into tissues such as muscle, fat, and brain tissue. Furthermore, factors such as blood flow, lipophilicity, molecule size, and interactions between the drug and components of blood, including plasma proteins, could also contribute to this effect. As an example, warfarin, a highly protein-bound drug, is only able to exert its therapeutic effects in the bloodstream to a very small degree. Warfarin could be dislodged from the protein-binding site if a highly protein-bound drug is taken with it, and there could be an increase in the amount of warfarin reaching the bloodstream. Additionally, certain organs have anatomical barriers which prevent certain drugs from penetrating the brain, such as the blood-brain barrier. Molecular weight, small size, and lipophilicity are some of the characteristics of medicines that allow them to cross the blood brain barrier better.

Metabolism

Approximately 70-80% of all clinically used drugs are bio-transformed or metabolized by CYP450 enzymes.

How are drugs metabolized?

• A person's genetic makeup may have an impact on how quickly they metabolize drugs.
• Having a decreased liver function can lead to intolerability; the elderly may metabolize drugs more slowly, and newborns or infants may have immature liver function, requiring special consideration when administering drugs.
• It is possible to decrease drug metabolism by inhibiting enzymes or to increase drug metabolism by inducing enzymes in response to drug interactions.

As CYP450 enzymes metabolize drugs, they produce inactive metabolites, which have no pharmacological activity. However, certain medications, such as codeine, are inactive and become pharmacologically active when they are converted in the body. Prodrugs are such medications. Codeine's metabolic pathway CYP2D6, which has genetic variations, can cause serious clinical outcomes in patients that have genetic variations in this pathway. There are usually higher levels of active drugs in the serum of CYP2D6 poor metabolizers (PMs). A greater level of inactive drug is present in the serum of pregnant women taking codeine, which could result in lower efficacy. However, fast-metabolizing UMs will quickly convert codeine into morphine, leading to toxic levels of morphine.

Mathematical Model in Drug Design

An underlying physical-chemical phenomenon is represented by a model. Formulation design, process design, scaling-up, and monitoring and control of the commercial process can all be done using models based on mathematical-models in the pharmaceutical industry. There are numerous benefits to modeling. The following are some of them.

• Reduction of experiment cost
• Improvement of product and production quality
• Enhancing process understanding

A model can be described in two ways: qualitatively or quantitatively. Three types of quantitative models exist: mechanistic, empirical, and hybrid. Using the knowledge pyramid in Figure, we can see that understanding and information obtained from an empirical model increases as the model becomes more mechanistic. Mechanical models derive from first-principles, depend on equations to account for physical/chemical phenomena, and are either steady-state (i.e., dynamic) or time-dependent. Process knowledge can be represented effectively using mechanical models. The input-output dynamics within a unit operation is represented by a set of differential equations. An understanding of constraints and of the constraints' constraints is necessary for model building. This requires the availability of balance equations (e.g., mass balance equations, energy balance equations).



Using mechanistic models can sometimes lead to predictions that are beyond what the input data indicate, provided that the underlying assumptions are valid. Mechanistic models are usually a bottleneck because it is difficult to come up with equations that accurately represent the system as well as its associated parameters. Additionally, input-output dynamics can be represented through empirical modeling. Complex systems in which mechanistic models are not feasible are particularly well suited to these models. A system is viewed as a "black box" and empirical models rarely describe its underlying physical and chemical properties. Models based on observational data only describe the input-output dynamics.

Empiric models have the disadvantage of having limited applicability due to the variation in data used to derive them. As a result, extrapolating these models beyond the current data range is not possible. The advantage of empirical models over mechanistic models is that they are relatively simple to build and solve. Typically, empirical models are used in the pharmaceutical industry to gain a deeper understanding of processes and to control them, such as for the programming of PAT-based tools. The advantage of models based on mechanical principles is their wide range of prediction capabilities. However, not every component of the pharmaceutical industry can be modelled from first principles.

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