TY  - JOUR
A1  - Gomez, Christophe
A1  - Hartung, Niklas
T1  - Stochastic and deterministic models for the metastatic emission process
BT  - Formalisms and Crosslinks
JF  - Cancer Systems Biology
N2  - Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.
KW  - Poisson process
KW  - Structured population equation
KW  - Metastasis
KW  - Mathematical modeling
Y1  - 2018
SN  - 978-1-4939-7493-1
SN  - 978-1-4939-7492-4
U6  - https://doi.org/10.1007/978-1-4939-7493-1_10
SN  - 1064-3745
SN  - 1940-6029
VL  - 1711
SP  - 193
EP  - 224
PB  - Humana Press Inc.
CY  - Totowa
ER  - 
TY  - JOUR
A1  - Melin, Johanna
A1  - Parra-Guillen, Zinnia Patricia
A1  - Hartung, Niklas
A1  - Huisinga, Wilhelm
A1  - Ross, Richard J.
A1  - Whitaker, Martin J.
A1  - Kloft, Charlotte
T1  - Predicting Cortisol Exposure from Paediatric Hydrocortisone Formulation Using a Semi-Mechanistic Pharmacokinetic Model Established in Healthy Adults
JF  - Clinical Pharmacokinetics
N2  - Background and objective Optimisation of hydrocortisone replacement therapy in children is challenging as there is currently no licensed formulation and dose in Europe for children under 6 years of age. In addition, hydrocortisone has non-linear pharmacokinetics caused by saturable plasma protein binding. A paediatric hydrocortisone formulation, Infacort (R) oral hydrocortisone granules with taste masking, has therefore been developed. The objective of this study was to establish a population pharmacokinetic model based on studies in healthy adult volunteers to predict hydrocortisone exposure in paediatric patients with adrenal insufficiency. Methods Cortisol and binding protein concentrations were evaluated in the absence and presence of dexamethasone in healthy volunteers (n = 30). Dexamethasone was used to suppress endogenous cortisol concentrations prior to and after single doses of 0.5, 2, 5 and 10 mg of Infacort (R) or 20 mg of Infacort (R)/hydrocortisone tablet/hydrocortisone intravenously. A plasma protein binding model was established using unbound and total cortisol concentrations, and sequentially integrated into the pharmacokinetic model. Results Both specific (non-linear) and non-specific (linear) protein binding were included in the cortisol binding model. A two-compartment disposition model with saturable absorption and constant endogenous cortisol baseline (Baseline (cort),15.5 nmol/L) described the data accurately. The predicted cortisol exposure for a given dose varied considerably within a small body weight range in individuals weighing < 20 kg. Conclusions Our semi-mechanistic population pharmacokinetic model for hydrocortisone captures the complex pharmacokinetics of hydrocortisone in a simplified but comprehensive framework. The predicted cortisol exposure indicated the importance of defining an accurate hydrocortisone dose to mimic physiological concentrations for neonates and infants weighing < 20 kg.
Y1  - 2018
U6  - https://doi.org/10.1007/s40262-017-0575-8
SN  - 0312-5963
SN  - 1179-1926
VL  - 57
IS  - 4
SP  - 515
EP  - 527
PB  - Springer
CY  - Northcote
ER  -