Parameter estimation and change-point detection from Dynamic Contrast Enhanced MRI data using stochastic differential equations

Hybrid Invasive Weed Optimization Algorithm for Parameter Estimation of Pharmacokinetic Model

Given that the traditional methods of estimating pharmacokinetic parameters are constrained by the sensitivity of their initial value and incapability of evolutionary algorithm to determine search range, this paper proposes a hybrid invasive weed optimization (HIWO) algorithm by combining the Hooke–Jeeves (HJ) and invasive weed optimization (IWO) algorithm. Using the HIWO algorithm for the parameter optimization by the experiment of extravascular administration two-compartment model, we can see that the proposed method is not only better than traditional feathering method (FM) in terms of numerical stability, but also better than HJ and IWO in terms of error minimization. The experimental results show that HIWO algorithm is a feasible method to optimize the pharmacokinetic parameters, which has higher precision and stronger robustness than the other techniques.

A Simple, Realistic Stochastic Model of Gastric Emptying

Several models of Gastric Emptying (GE) have been employed in the past to represent the rate of delivery of stomach contents to the duodenum and jejunum. These models have all used a deterministic form (algebraic equations or ordinary differential equations), considering GE as a continuous, smooth process in time. However, GE is known to occur as a sequence of spurts, irregular both in size and in timing. Hence, we formulate a simple stochastic process model, able to represent the irregular decrements of gastric contents after a meal. The model is calibrated on existing literature data and provides consistent predictions of the observed variability in the emptying trajectories. This approach may be useful in metabolic modeling, since it describes well and explains the apparently heterogeneous GE experimental results in situations where common gastric mechanics across subjects would be expected.

Classification in postural style based on stochastic process modeling

We address the statistical challenge of classifying subjects as hemiplegic, vestibular or normal based on complex trajectories obtained through two experimental protocols designed to evaluate potential deficits in postural control. The classification procedure involves a dimension reduction step where the complex trajectories are summarized by finite-dimensional summary measures based on a stochastic process model for a real-valued trajectory. This allows us to retrieve from the trajectories information relative to their temporal dynamic. A leave-one-out evaluation yields a 79% performance of correct classification for a total of n=70 subjects, with 22 hemiplegic (31%), 16 vestibular (23%) and 32 normal (46%) subjects.

Parameter Estimation of Population Pharmacokinetic Models with Stochastic Differential Equations: Implementation of an Estimation Algorithm

Population pharmacokinetic (PPK) models play a pivotal role in quantitative pharmacology study, which are classically analyzed by nonlinear mixed-effects models based on ordinary differential equations. This paper describes the implementation of SDEs in population pharmacokinetic models, where parameters are estimated by a novel approximation of likelihood function. This approximation is constructed by combining the MCMC method used in nonlinear mixed-effects modeling with the extended Kalman filter used in SDE models. The analysis and simulation results show that the performance of the approximation of likelihood function for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for the analysis of population pharmacokinetic data.

A review on estimation of stochastic differential equations for pharmacokinetic/pharmacodynamic models

This paper is a survey of existing estimation methods for pharmacokinetic/pharmacodynamic (PK/PD) models based on stochastic differential equations (SDEs). Most parametric estimation methods proposed for SDEs require high frequency data and are often poorly suited for PK/PD data which are usually sparse. Moreover, PK/PD experiments generally include not a single individual but a group of subjects, leading to a population estimation approach. This review concentrates on estimation methods which have been applied to PK/PD data, for SDEs observed with and without measurement noise, with a standard or a population approach. Besides, the adopted methodologies highly differ depending on the existence or not of an explicit transition density of the SDE solution.