Nonlinear dynamics in clinical pharmacology: the paradigm of cortisol secretion and suppression

Panos Macheras: a pioneering scientist in pharmaceutical science

Professor Panos Macheras is a pioneering scientist in pharmacokinetics, pharmacodynamics and biopharmaceutics. His many important contributions to pharmaceutical science are reviewed.

Estimating parameters of nonlinear dynamic systems in pharmacology using chaos synchronization and grid search

Bridging fundamental approaches to model optimization for pharmacometricians, systems pharmacologists and statisticians is a critical issue. These fields rely primarily on Maximum Likelihood and Extended Least Squares metrics with iterative estimation of parameters. Our research combines adaptive chaos synchronization and grid search to estimate physiological and pharmacological systems with emergent properties by exploring deterministic methods that are more appropriate and have potentially superior performance than classical numerical approaches, which minimize the sum of squares or maximize the likelihood. We illustrate these issues with an established model of cortisol in human with nonlinear dynamics. The model describes cortisol kinetics over time, including its chaotic oscillations, by a delay differential equation. We demonstrate that chaos synchronization helps to avoid the tendency of the gradient-based optimization algorithms to end up in a local minimum. The subsequent analysis illustrates that the hybrid adaptive chaos synchronization for estimation of linear parameters with coarse-to-fine grid search for optimal values of non-linear parameters can be applied iteratively to accurately estimate parameters and effectively track trajectories for a wide class of noisy chaotic systems.

Mechanisms of cortisol - Substance use development associations: Hypothesis generation through gene enrichment analysis

There are many theories about the mechanisms of associations between hypothalamic-pituitary-adrenal (HPA) function (indexed by cortisol) and substance use. However, the potential for genes that contribute to both HPA function and substance use to confound the association (e.g., genetic confounding) has largely been ignored. We explore the potential role of genetics in cortisol-substance use associations, build a conceptual framework placing theories and mechanisms for how cortisol and substance use are related into a developmental progression, and develop new hypotheses based on our findings. We conclude that the relationship between cortisol function and substance use is complex, occurs at multiple levels of analysis, and is bidirectional at multiple phases of the substance use progression. Additionally, there is potential for genetic confounding in cortisol-substance use associations, and thus a need for genetically informed designs to investigate how and why cortisol function is associated with substance use phenotypes from initiation through disorder. Gene-environment interplay and developmental context are likely to impact the effectiveness of prevention and intervention efforts to reduce substance use problems.

The Non-Linear Child: Ontogeny, Isoniazid Concentration, and NAT2 Genotype Modulate Enzyme Reaction Kinetics and Metabolism

N-acetyltransferase 2 (NAT2) catalyzes the acetylation of isoniazid to N-acetylisoniazid. NAT2 polymorphism explains 88% of isoniazid clearance variability in adults. We examined the effects of clinical and genetic factors on Michaelis-Menten reaction kinetic constants of maximum velocity (V_max) and affinity (K_m) in children 0–10 years old. We measured the rates of isoniazid elimination and N-acetylisoniazid production in the blood of 30 children. Since maturation effects could be non-linear, we utilized a pharmacometric approach and the artificial intelligence method, multivariate adaptive regression splines (MARS), to identify factors predicting NAT2 V_max and K_m by examining clinical, genetic, and laboratory factors in toto. Isoniazid concentration predicted both V_max and K_m and superseded the contribution of NAT2 genotype. Age non-linearly modified the NAT2 genotype contribution until maturation at ≥ 5.3 years. Thus, enzyme efficiency was constrained by substrate concentration, genes, and age. Since MARS output is in the form of basis functions and equations, it allows multiscale systems modeling from the level of cellular chemical reactions to whole body physiological parameters, by automatic selection of significant predictors by the algorithm.

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We identified the NAT2 K_m and V_max in children treated with isoniazid.

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Artificial intelligence (AI) algorithms were used to find predictors of K_m and V_max.

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Isoniazid concentration affected V_max and K_m, and superseded NAT2 genotype.

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Age non-linearly modified NAT2 genotype contribution until maturation at ≥ 5.3 years.

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AI output is in the form of equations that allow multiscale systems modeling.

The effects of maturation on drug metabolism have not been studied for the type phase II enzymes such as NAT2, which metabolizes the drug isoniazid. Genes have been found to control speed of isoniazid metabolism. Studies to characterize affinity and maximum velocity for isoniazid metabolism in people were last performed in two individuals' livers in the 1960s. We identified NAT2 affinity and maximum velocity in 30 tuberculosis children treated with isoniazid. Artificial intelligence methods found that metabolism was affected by the drug's concentration more than by genes, which were affected by age up to 5.3 years.

Serum drug concentrations predictive of pulmonary tuberculosis outcomes

BACKGROUND

Based on a hollow-fiber system model of tuberculosis, we hypothesize that microbiologic failure and acquired drug resistance are primarily driven by low drug concentrations that result from pharmacokinetic variability.

METHODS

Clinical and pharmacokinetic data were prospectively collected from 142 tuberculosis patients in Western Cape, South Africa. Compartmental pharmacokinetic parameters of isoniazid, rifampin, and pyrazinamide were identified for each patient. Patients were then followed for up to 2 years. Classification and regression tree analysis was used to identify and rank clinical predictors of poor long-term outcome such as microbiologic failure or death, or relapse.

RESULTS

Drug concentrations and pharmacokinetics varied widely between patients. Poor long-term outcomes were encountered in 35 (25%) patients. The 3 top predictors of poor long-term outcome, by rank of importance, were a pyrazinamide 24-hour area under the concentration-time curve (AUC) ≤ 363 mg·h/L, rifampin AUC ≤ 13 mg·h/L, and isoniazid AUC ≤ 52 mg·h/L. Poor outcomes were encountered in 32/78 patients with the AUC of at least 1 drug below the identified threshold vs 3/64 without (odds ratio = 14.14; 95% confidence interval, 4.08-49.08). Low rifampin and isoniazid peak and AUC concentrations preceded all cases of acquired drug resistance.

CONCLUSIONS

Low drug AUCs are predictive of clinical outcomes in tuberculosis patients.

Father contributions to cortisol responses in infancy and toddlerhood

The current study is one of the first prospective examinations of longitudinal associations between observed father caregiving behaviors and child cortisol reactivity and regulation in response to emotional arousal. Observations of father and mother caregiving behaviors and child cortisol levels in response to challenges at 7 months and 24 months of child age were collected. Analyses were based on a subsample of children from the Family Life Project who lived with both their biological mothers and fathers and for whom there was at least partial cortisol data (7 months: n = 717; 24 months: n = 579). At the challenge conducted at 7 months of child age, 49.0% of the sample were girls; racial composition of the sample was 25.8% African American and 74.2% European American. At the challenge conducted at 24 months of child age 49.9% of the sample were girls; racial composition was 24.7% African American and 75.3% European American. We conducted analyses across assessment points simultaneously using mixed linear modeling for repeated measures data to test for differential effects of fathering across infancy and toddlerhood. Concurrent measures of father negativity were positively associated with greater increases in child cortisol levels in response to emotion challenge at 7 months (p = .01) and with higher overall levels of cortisol at 24 months (p < .001). However, there was no evidence that father caregiving during infancy independently predicted later cortisol activity during toddlerhood.

Physiologically motivated time-delay model to account for mechanisms underlying enterohepatic circulation of piroxicam in human beings

The study was conducted to formulate a physiologically motivated time-delay (PM TD) mathematical model for human beings, which incorporates disintegration of a drug formulation, dissolution, discontinuous gastric emptying and enterohepatic circulation (EHC) of a drug. Piroxicam, administered to 24 European, healthy individuals in 20 mg capsules Feldene Pfizer, was used as a model drug. Plasma was analysed for piroxicam by a validated high-performance liquid chromatography method. The PM TD mathematical model was developed using measured plasma piroxicam concentration-time profiles of the individuals and tools of a computationally efficient mathematical analysis and modeling, based on the theory of linear dynamic systems. The constructed model was capable of (i) quantifying different fractions of the piroxicam dose sequentially disposable for absorption and (ii) estimating time delays between time when the piroxicam dose reaches stomach and time when individual of fractions of the piroxicam dose is disposable for absorption. The model verification was performed through a formal proof, based on comparisons of observed and model-predicted plasma piroxicam concentration-time profiles. The model verification showed an adequate model performance and agreement between the compared profiles. Accordingly, it confirmed that the developed model was an appropriate representative of the piroxicam fate in the individuals enrolled. The presented model provides valuable information on factors that control dynamic mechanisms of EHC, that is, information unobtainable with the models proposed for the EHC analysis previously.

Mathematical modeling of the hypothalamic-pituitary-adrenal system activity

Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans. The aim of this work was to explore in greater detail the role of this system in normal, homeostatic, conditions, since it is the first and unavoidable step in further understanding of the role of this complex neuroendocrine system in pathophysiological conditions. Neither the underlying mechanisms nor the physiological significance of this system are fully understood yet.