Recirculatory Pharmacokinetic Modeling

Theoretical Examination Seeking Tangible Physical Meanings of Slopes and Intercepts of Plasma Concentration-Time Relationships in Minimal Physiologically Based Pharmacokinetic Models

In minimal physiologically based pharmacokinetic (mPBPK) models, physiological (e.g., cardiac output) and anatomical (e.g., blood/tissue volumes) variables are utilized in the domain of differential equations (DEs) for mechanistic understanding of the plasma concentration-time relationships [Formula: see text]. Although fundamental biopharmaceutical variables in terms of distribution (e.g., [Formula: see text] and [Formula: see text]) and elimination kinetics (e.g., [Formula: see text]) in mPBPK provide greater insights in comparison to classical compartment models, an absence of kinetic elucidation of slopes and intercepts in light of such DE model parameters hinders more intuitive appreciation of [Formula: see text]. Therefore, this study seeks the tangible physical meanings of slopes and intercepts of the plasma concentration-time relationships in one- and two-tissue mPBPK models (i.e., m2CM and m3CM), with respect to time parameters that are readily understandable in PK analyses, i.e., the mean residence ([Formula: see text]) and transit ([Formula: see text]) times. Utilizing the explicit equations (EEs) for the slopes, intercepts, and areas of each exponential phase in the m2CM and m3CM, we theoretically and numerically examined the limiting/boundary conditions of such kinetic properties, based on the ratio of the longest tissue [Formula: see text] to the [Formula: see text] in the body (i.e., [Formula: see text]) that is useful for dissecting complex PBPK systems. The kinetic contribution of the area of each exponential phase to the total drug exposure was assessed to identify the elimination phase between the terminal and non-terminal phases of the [Formula: see text] in the m2CM and m3CM. This assessment provides improved understanding of the complexities inherent in all PBPK profiles and models.

The Performance of an Artificial Neural Network Model in Predicting the Early Distribution Kinetics of Propofol in Morbidly Obese and Lean Subjects

BACKGROUND

Induction of anesthesia is a phase characterized by rapid changes in both drug concentration and drug effect. Conventional mammillary compartmental models are limited in their ability to accurately describe the early drug distribution kinetics. Recirculatory models have been used to account for intravascular mixing after drug administration. However, these models themselves may be prone to misspecification. Artificial neural networks offer an advantage in that they are flexible and not limited to a specific structure and, therefore, may be superior in modeling complex nonlinear systems. They have been used successfully in the past to model steady-state or near steady-state kinetics, but never have they been used to model induction-phase kinetics using a high-resolution pharmacokinetic dataset. This study is the first to use an artificial neural network to model early- and late-phase kinetics of a drug.

METHODS

Twenty morbidly obese and 10 lean subjects were each administered propofol for induction of anesthesia at a rate of 100 mg/kg/h based on lean body weight and total body weight for obese and lean subjects, respectively. High-resolution plasma samples were collected during the induction phase of anesthesia, with the last sample taken at 16 hours after propofol administration for a total of 47 samples per subject. Traditional mammillary compartment models, recirculatory models, and a gated recurrent unit neural network were constructed to model the propofol pharmacokinetics. Model performance was compared.

RESULTS

A 4-compartment model, a recirculatory model, and a gated recurrent unit neural network were assessed. The final recirculatory model (mean prediction error: 0.348; mean square error: 23.92) and gated recurrent unit neural network that incorporated ensemble learning (mean prediction error: 0.161; mean square error: 20.83) had similar performance. Each of these models overpredicted propofol concentrations during the induction and elimination phases. Both models had superior performance compared to the 4-compartment model (mean prediction error: 0.108; mean square error: 31.61), which suffered from overprediction bias during the first 5 minutes followed by under-prediction bias after 5 minutes.

CONCLUSIONS

A recirculatory model and gated recurrent unit artificial neural network that incorporated ensemble learning both had similar performance and were both superior to a compartmental model in describing our high-resolution pharmacokinetic data of propofol. The potential of neural networks in pharmacokinetic modeling is encouraging but may be limited by the amount of training data available for these models.

Bolus pharmacokinetics: moving beyond mass-based dosing to guide drug administration

Despite the common approach of bolus drug dosing using a patient's mass, a more tailored approach would be to use empirically derived pharmacokinetic models. Previously, this could only be possible though the use of computer simulation using programs which are rarely available in clinical practice. Through mathematical manipulations and approximations, a simplified set of equations is demonstrated that can identify a bolus dose required to achieve a specified target effect site concentration. The proposed solution is compared against simulations of a wide variety of pharmacokinetic models. This set of equations provides a near-identical solution to the simulation approach. A boundary condition is established to ensure the derived equations have an acceptable error. This approach may allow for more precise administration of medications with the use of point of care technology and potentially allows for pharmacokinetic dosing in artificial intelligence problems.

Plasma concentration based response surface model predict better than effect-site concentration based model for wake-up time during gastrointestinal endoscopy sedation

BACKGROUND

Sedation for esophagogastroduodenoscopy (EGD) and colonoscopy is characterized by rapid patient induction and emergence. The drugs midazolam and alfentanil have long been used for procedural sedation; however, the relationship between plasma or effect-site concentrations (Cp or Ce, respectively) and emergence remains unclear. The aim of this study is to develop patient wake-up prediction models for both Cp and Ce using response surface modeling, a pharmacodynamics tool for assessing patients' responses.

METHODS

The Observer's Alertness/Sedation (OAA/S) score was used to monitor sedation depth during the examinations. Concentration pairs of midazolam and alfentanil were calculated for each of Cp and Ce using pharmacokinetic simulation software. Response surface models were developed using the Greco construct. Temporal analysis was done by comparing model-predicted wake-up time with true patient wake-up time.

RESULTS

Thirty-three patients with an average body mass index of 21.85 ± 2.3 kg/m² were pooled for analysis. The average duration of examination were 2.9 ± 1.4 min for EGD and 6.6 ± 2.7 min for colonoscopy. Seventy-five concentration pairs of midazolam and alfentanil were obtained for each Cp and Ce. The Cp-based Greco response surface model showed significant synergy between midazolam and alfentanil and was a better predictor of patient wake-up time, with an average deviation of 1.0 ± 3.9 min, while the Ce model show time deviation greater than 20 min.

CONCLUSION

The early phases of drug distribution are unique and complicated by nonsteady-state concentrations, and our study revealed that Ce-based wake-up time prediction is more difficult under these circumstances.

An introduction to physiologically-based pharmacokinetic models

Physiologically-based pharmacokinetic (PBPK) models represent drug kinetics in one or more 'real' organs (and hence require submodels of organs/tissues) and they describe 'whole-body' kinetics by joining together submodels with drug transport by blood flow as dictated by anatomy. They attempt to reproduce 'measureable' physiological and/or pharmacokinetic processes rather than more abstract rate constants and volumes. PBPK models may be built using a 'bottom-up' approach, where parameters are chosen from first principles, literature, or in vitro data as opposed to a 'top-down' approach, where all parameters are estimated from data. The basic principles of PBPK models are described, focusing on the equations for three individual organs: a single flow-limited compartment describing distribution only, a membrane-limited compartment describing distribution, and a single flow-limited compartment with elimination. These organ models are linked to make a basic three-compartment physiological model of the whole body. PBPK models are particularly suited to scaling kinetics across body size (e.g., adult to neonate) and species (e.g., animal to first-in-man) as physiology and pharmacology can be represented by independent parameters. Maturation models can be incorporated as for compartmental models. PBPK models are now available in commercial software packages, and are perhaps now more accessible than ever. Alternatively, even complex PBPK models can be represented in generic differential equation-solving software using the simple principles described here. The relative ease of constructing the code for PBPK models belies the most difficult aspect of their implementation-collecting, collating, and justifying the data used to parameterize the model.