# Non Compartment Modelling

Session objectives

By the end of this session, students will be able to:

• Define non-compartment modeling

• Discuss the advantages, disadvantages, and applications of non-compartment models

• Compute various pharmacokinetic parameters

## Introduction

The labyrinthine domain of drug behavior within the human body presents a formidable challenge to pharmacy students. Among the pivotal methodologies that aid in comprehending this complexity, lies the non-compartment modeling approach, a versatile tool in pharmacokinetic studies. By shunning the assumption of distinct compartmental structures, non-compartment models leverage differential equations, integral equations, and other function-based forms to unveil the intricate behavior of drugs. This facilitates a profound insight into drug pharmacokinetics, encompassing distribution, metabolism, elimination, and beyond.

## Non Compartment Modelling

Non-compartment modeling emerges as a mathematical technique that unveils the pharmacokinetics of drugs without tethering to compartmental boundaries within the body. While compartmental models segment the body into distinct partitions, non-compartment models embrace a more abstract approach, employing differential equations, integral equations, or other functional forms to capture the bewildering dance of drugs within the human organism. This unlocks a more profound understanding of drug kinetics, encompassing the realms of absorption, distribution, metabolism, and excretion.

## Advantages of Non Compartment Modelling for Aspiring Pharmacists

### Precision in Drug Dosage Optimization

The arsenal of non-compartment modeling empowers pharmacy students to meticulously optimize drug dosages. Scrutinizing drug concentration-time profiles, students can determine the most efficacious dosing regimen, seamlessly integrating factors such as the drug’s half-life, clearance, and volume of distribution. This artistry ensures that patients receive the precise medication dosage, fostering optimal therapeutic outcomes.

### Penetrating the Mysteries of Drug Behavior

Embracing non-compartment modeling, pharmacy students embark on a comprehensive voyage to unravel the secrets of drug behavior within the human corpus. By probing the kinetics of drug absorption, distribution, metabolism, and excretion, students can prophesy drug concentrations across temporal milestones and diverse bodily compartments. This prescient knowledge proves instrumental in predicting drug efficacy, potential adversities, and the labyrinth of drug-drug interactions.

### Charting the Course of Pharmacokinetic Parameter

Estimation Non-compartment modeling bestows upon pharmacy students the power to gauge essential pharmacokinetic parameters, such as clearance and volume of distribution, from drug concentration-time data. These vital metrics shed light on the terrain of drug disposition, equipping students to tailor drug therapies catering to each patient’s unique pharmacokinetic tapestry.

## Unraveling the Limitations of Non Compartment Modelling

Elusive Biological Interpretation Among the shadows encircling non-compartment modeling lies the challenge of direct biological interpretation. Unlike compartmental models, which epitomize physiological compartments, the non-compartmental paradigm ventures into abstract territory, making it arduous to establish direct links between model parameters and specific biological processes.

The Data Conundrum: Complexity and Precision Non-compartment models often lay claim to copious and precise data for the accurate estimation of model parameters. Pharmacy students may grapple with the pursuit of such data, especially in clinical settings where the drug concentration-time profiles of patients might be scant.

Bridled Horizons of Extrapolation Non-compartment models may boast of impressive prowess, yet their extrapolation capacities might be subject to restraint, particularly when it comes to predicting drug behavior beyond the confines of available data. In such instances, more sophisticated models or experimental data might be requisites for rendering reliable prognoses.

## Non Compartment Modelling: Illuminating Avenues in Pharmacy Practice

### Alchemy of Drug Development and Formulation

Within the realm of drug development and formulation, non-compartment modeling unveils its transformative influence. By comprehending the essence of drug kinetics and behavior, pharmacy students artfully engineer drug formulations that orchestrate optimal therapeutic outcomes, harmonizing with the symphony of minimal side effects.

### Symphony of Individualized Drug Dosing

Non-compartment modeling imparts upon pharmacy students the finesse of individualized drug dosing, choreographed in harmony with each patient’s bespoke pharmacokinetic tapestry. This personalized serenade of drug therapy amplifies treatment efficacy and extinguishes the embers of adverse reactions.

### Interpretative Artistry of Therapeutic Drug Monitoring

The saga of therapeutic drug monitoring, entailing the measurement of drug concentrations in patients’ circulatory channels, attains artistic grandeur under the tutelage of non-compartment modeling. Pharmacy students master the interpretative symphony of drug concentration data, perfecting dosage regimens, and crafting sagacious clinical decisions.

## First moment (Mean Residence Time):

• It is referred to as MRT

• Explains plasma drug conc-time profile.

• Mathematically,

• Area under moment curve

(C1 x t) Vs time

• Numerical value of AUMC is higher than AUC.

• AUMC is also calculated by trapezoid met

• Blood samples are collected for a long period to obtain measurable conc. (ct).

• AUMC is calculated using,

• Terminal portion of curve – determines plasma elimination rate constant (ƛ𝑍 ) of the drug.

## Second moment (Variance of Mean Residence Time):

• It is referred to as VRT.

• Explains plasma drug conc-time profile.

• Mathematically,

• A plot of (𝐶1 x 𝑡2) Vs time is drawn.

• It is difficult to calculate area from time (𝑐1) to infinity.

• Hence calculation is restricted to MRT.

AUC & MRT are generally used in the pharmacokinetic analysis, because higher moments are prone to an unacceptable level of computational errors.

## Non-compartment Models – Pharmacokinetic Parameters

### 1. Mean Residence Time (MRT)

• It is defined as the average time that a drug resides in the body before being eliminated.

• Units = hour.

• Represents time for elimination of 63.2 % of drug when given by i.v. bolus injection

• It is the analogy of statistical moment to plasma drug elimination half-life (50 %).

• Drug elimination from the body takes place by 1st order phases,

Assumes that drug
follows one compartment open model

• k10 transformed to t1/2  (1 to h)

If drug follows two compartment open model:

• Drug equilibration takes place slowly into peripheral compartment

• MRT can be used.

From urinary excretion data,

This is accurate if renal excretion is the major route of elimination.

### 2. Apparent volume of distribution at steady state

Vol. of distribution:
considered at steady state

â

Independent of
elimination

Solely reflects the anatomic space occupied by the drug & relative degree of drug binding in blood & extravascular space.

For constant i.v. infusion:

R= infusion rate

T=duration of infusion

### 3. Drug clearance

It is defined as the reciprocal of the zero moment of conc-time curve after a single i.v. injection.

• Single i.v. injection:

• i.v. infusion at constant rate:

• Single oral dose:

• Multiple oral dosage regimen:

• Rearranging eq. 20:

Steady-state plasma drug conc. (c1ss) is a function of infusion rate (R) and total body clearance (Cl)

### 4. Mean Absorption Time (MAT)

• Mean time required for drug to reach systemic circulation from time of drug administration.

• In non-compartmental models, MAT is mathematically defined as the differences in the MRT after different modes of administration.

• Absorption follows first-order kinetics,

• If absorption follows zero-order kinetics,

### 5. Bioavailability (F)

• It is defined as the ratio of zero moments of i.v. and extravascular administration normalized for doses.

• For i.v. bolus injection, F=1.

• Absolute bioavailability,

Where, AUC = zero moment curve, µg.h/ml

D = dose of drug administered

• Relative bioavailability, 𝐹r may be expressed by comparing the zero moments of a product with a standard product.

## Summary

• Non-compartmental approach is to study the time course changes of drug concentration in the body based on the statistical moment theory and it is regarded as a model-independent method

• It is highly applied in the evaluation of bioavailability and bioequivalence

• The pharmacokinetic parameters mainly estimated by non-compartment model is

– Peak plasma drug concentration, Cmax;- Time of peak plasma drug concentration, tmax and Area under the curve, AUC

• It involves simple algebraic equations. So the derivation of equations for obtaining pharmacokinetic parameters is easy

• The main disadvantage is that it applies only in linear pharmacokinetics

• Statistical moments consider the time course changes of plasma drug concentration as a statistical distribution phenomenon and terms are mean area, mean residence time and variance of mean residence time and of urinary excretion rate

## Conclusion:

The Odyssey Continues Non-compartment modeling stands tall as a potent ally in the pharmacy student’s quest to demystify drug pharmacokinetics and sculpt bespoke drug therapies. Its allure lies in the finesse of drug dosage optimization, the profundity of drug behavior comprehension, and the power of pharmacokinetic parameter estimation. And yet, as with any odyssey, pharmacy students must chart their course wisely, steering clear of the snares of abstraction and data complexities, as they navigate the expansive realm of non-compartment modeling.

## FAQs:

Guided by Non-Compartment Modeling, how does individualized drug dosing flourish?

Within the tutelage of non-compartment modeling, pharmacy students unlock the elusive keys to individual pharmacokinetic parameters, engendering a symphony of tailored drug dosages, and bequeathing patients with treatment efficacy that sings in harmony with their uniqueness.

In the Tapestry of Drug Formulation, can non-compartment models weave their magic?

Indeed, the mastery of non-compartment models wields influence in the realm of drug development and formulation studies, infusing the alchemy of design with the essence of optimal drug delivery and therapeutic magic.

Embarking on the Odyssey: The Perils and Promise Pharmacy students might encounter challenges that the non-compartmental odyssey entails, from the scarcity of data to the intricacies of interpreting model parameters within the realms of clinical practice. Nevertheless, armed with knowledge and understanding, they unfurl the sails of potential, harnessing the full spectrum of non-compartment modeling in their pursuit of pharmacy research and the sanctity of patient care.

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Biopharmaceutics Notes PDF