Parameter identifiability of fundamental pharmacodynamic models

Issues of parameter identifiability of routinely used pharmacodynamics models are considered in this paper. The structural identifiability of 16 commonly applied pharmacodynamic model structures was analyzed analytically, using the input-output approach. Both fixed-effects versions (non-population, no between-subject variability) and mixed-effects versions (population, including between-subject variability) of each model structure were analyzed. All models were found to be structurally globally identifiable under conditions of fixing either one of two particular parameters. Furthermore, an example was constructed to illustrate the importance of sufficient data quality and show that structural identifiability is a prerequisite, but not a guarantee, for successful parameter estimation and practical parameter identifiability. This analysis was performed by generating artificial data of varying quality to a structurally identifiable model with known true parameter values, followed by re-estimation of the parameter values. In addition, to show the benefit of including structural identifiability as part of model development, a case study was performed applying an unidentifiable model to real experimental data. This case study shows how performing such an analysis prior to parameter estimation can improve the parameter estimation process and model performance. Finally, an unidentifiable model was fitted to simulated data using multiple initial parameter values, resulting in highly different estimated uncertainties. This example shows that although the standard errors of the parameter estimates often indicate a structural identifiability issue, reasonably “good” standard errors may sometimes mask unidentifiability issues

Modeling as a Tool to Support Self-Management of Type 1 Diabetes

Type 1 diabetes (T1D) is an auto-immune disease characterized by insulin-deficiency. Insulin is a metabolic hormone that is involved in lowering blood glucose (BG) levels in order to control BG level to a tight range. In T1D this glycemic control is lost, causing chronic hyperglycemia (excess glucose in blood stream). Chronic hyperglycemia damages vital tissues. Therefore, glycemic control must be restored. A common therapy for restoring glycemic control is intensive insulin therapy, where the missing insulin is replaced with regular insulin injections. When dosing this compensatory insulin many factors that affect glucose metabolism must be considered. Linkura is a company that has developed tools for monitoring the most important factors, which are meals and exercise. In the Linkura meal and exercise tools, the nutrition content in meals and the calorie consumption during exercise are estimated. Another tool designed to aid control of BG is the bolus calculator. Bolus calculators use input of BG level, carbohydrate intake, and insulin history to estimate insulin need. The accuracy of these insulin bolus calculations suffer from two problems. First, errors occur when users inaccurately estimate the carbohydrate content in meals. Second, exercise is not included in bolus calculations. To reduce these problems, it was suggested that the Linkura web tools could be utilized in combination with a bolus calculator. For this purpose, a bolus calculator was developed. The bolus calculator was based on existing models that utilize clinical parameters to relate changes in BG levels to meals, insulin, and exercise stimulations. The bolus calculator was evaluated using data collected from Linkura's web tools. The collected data showed some inconsistencies which cannot be explained by any model.  The performance of the bolus calculator in predicting BG levels using general equations to derive the clinical parameters was inadequate. Performance was increased by adopting an update-algorithm where the clinical parameters were updated daily using previous data. Still, better model performance is prefered for use in a bolus calculator.   The results show potential in developing bolus calculator tools combined with the Linkura tools. For such bolus calculator, further evaluation on modeling long-term exercise and additional safety features minimizing risk of hypoglycemia are required

Predicting QRS and PR interval prolongations in humans using nonclinical data

Risk of cardiac conduction slowing (QRS/PR interval prolongations in monitored electrocardiograms) is assessed in nonclinical studies, where the current AstraZeneca strategy involves ensuring high margins to in vitro effects and statistical tests to identify in vivo effects. This thesis aims to improve QRS/PR risk assessment using pharmacokinetic-pharmacodynamic modelling for describing QRS/PR effects and evaluating translation to human effects. Data for six compounds were collected from the literature and previously performed in vitro (sodium/calcium channel), in vivo (guinea pig/dog) and clinical AstraZeneca studies. Mathematical models were developed and evaluated to describe and compare effects across compounds and species. Key results were that proportional drug effect models often suffice for small QRS/PR changes (up to 20%), while larger effects require nonlinear models. Heartrate correction and circadian rhythm models reduced residuals primarily for describing baseline PR intervals, with highest impact in humans followed by dogs and guinea pigs. Meaningful (10%) human QRS/PR changes correlated to low levels of sodium channel block (3-7%) and calcium channel binding (13-21%) and to small effects in guinea pigs and dogs (QRS 2.3-4.6% and PR 2.3-10%). This suggests that worst case human effects can be predicted by assuming four times greater effects at the same concentration from dog/guinea pig. Small changes in vitro and in vivo consistently translate to meaningful PR/QRS changes in humans across compounds. Accurate characterisation of concentration-effect relationships therefore require a model-based approach. Although the presented work is limited by the small number of investigated compounds, it provides a starting point for predicting human risk using routine QRS/PR data to improve the safety of new drugs

Modeling as a Tool to Support Self-Management of Type 1 Diabetes

Type 1 diabetes (T1D) is an auto-immune disease characterized by insulin-deficiency. Insulin is a metabolic hormone that is involved in lowering blood glucose (BG) levels in order to control BG level to a tight range. In T1D this glycemic control is lost, causing chronic hyperglycemia (excess glucose in blood stream). Chronic hyperglycemia damages vital tissues. Therefore, glycemic control must be restored. A common therapy for restoring glycemic control is intensive insulin therapy, where the missing insulin is replaced with regular insulin injections. When dosing this compensatory insulin many factors that affect glucose metabolism must be considered. Linkura is a company that has developed tools for monitoring the most important factors, which are meals and exercise. In the Linkura meal and exercise tools, the nutrition content in meals and the calorie consumption during exercise are estimated. Another tool designed to aid control of BG is the bolus calculator. Bolus calculators use input of BG level, carbohydrate intake, and insulin history to estimate insulin need. The accuracy of these insulin bolus calculations suffer from two problems. First, errors occur when users inaccurately estimate the carbohydrate content in meals. Second, exercise is not included in bolus calculations. To reduce these problems, it was suggested that the Linkura web tools could be utilized in combination with a bolus calculator. For this purpose, a bolus calculator was developed. The bolus calculator was based on existing models that utilize clinical parameters to relate changes in BG levels to meals, insulin, and exercise stimulations. The bolus calculator was evaluated using data collected from Linkura's web tools. The collected data showed some inconsistencies which cannot be explained by any model.  The performance of the bolus calculator in predicting BG levels using general equations to derive the clinical parameters was inadequate. Performance was increased by adopting an update-algorithm where the clinical parameters were updated daily using previous data. Still, better model performance is prefered for use in a bolus calculator.   The results show potential in developing bolus calculator tools combined with the Linkura tools. For such bolus calculator, further evaluation on modeling long-term exercise and additional safety features minimizing risk of hypoglycemia are required

Modeling as a Tool to Support Self-Management of Type 1 Diabetes

Type 1 diabetes (T1D) is an auto-immune disease characterized by insulin-deficiency. Insulin is a metabolic hormone that is involved in lowering blood glucose (BG) levels in order to control BG level to a tight range. In T1D this glycemic control is lost, causing chronic hyperglycemia (excess glucose in blood stream). Chronic hyperglycemia damages vital tissues. Therefore, glycemic control must be restored. A common therapy for restoring glycemic control is intensive insulin therapy, where the missing insulin is replaced with regular insulin injections. When dosing this compensatory insulin many factors that affect glucose metabolism must be considered. Linkura is a company that has developed tools for monitoring the most important factors, which are meals and exercise. In the Linkura meal and exercise tools, the nutrition content in meals and the calorie consumption during exercise are estimated. Another tool designed to aid control of BG is the bolus calculator. Bolus calculators use input of BG level, carbohydrate intake, and insulin history to estimate insulin need. The accuracy of these insulin bolus calculations suffer from two problems. First, errors occur when users inaccurately estimate the carbohydrate content in meals. Second, exercise is not included in bolus calculations. To reduce these problems, it was suggested that the Linkura web tools could be utilized in combination with a bolus calculator. For this purpose, a bolus calculator was developed. The bolus calculator was based on existing models that utilize clinical parameters to relate changes in BG levels to meals, insulin, and exercise stimulations. The bolus calculator was evaluated using data collected from Linkura's web tools. The collected data showed some inconsistencies which cannot be explained by any model.  The performance of the bolus calculator in predicting BG levels using general equations to derive the clinical parameters was inadequate. Performance was increased by adopting an update-algorithm where the clinical parameters were updated daily using previous data. Still, better model performance is prefered for use in a bolus calculator.   The results show potential in developing bolus calculator tools combined with the Linkura tools. For such bolus calculator, further evaluation on modeling long-term exercise and additional safety features minimizing risk of hypoglycemia are required

PKPD modelling of PR and QRS intervals in conscious dogs using standard safety pharmacology data

Introduction: Pharmacokinetic-pharmacodynamic (PKPD) modelling can improve safety assessment, but few PKPD models describing drug-induced QRS and PR prolongations have been published. This investigation aims to develop and evaluate PKPD models for describing QRS and PR effects in routine safety studies. Methods: Exposure and telemetry data from safety pharmacology studies in conscious beagle dogs were acquired. Mixed effects baseline and PK-QRS/PR models were developed for the antiarrhythmic compounds AZD1305, flecainide, quinidine and verapamil and the anti-muscarinic compounds AZD8683 and AZD9164. RR interval correction and circadian rhythms were investigated for predicting baseline variability. Individual PK predictions were used to drive the pharmacological effects evaluating linear and non-linear direct and effect compartment models. Results: Conduction slowing induced by the tested anti-arrhythmics was direct and proportional at low exposures, whilst time delays and non-linear effects were evident for the tested antimuscarinics. AZD1305, flecainide and quinidine induced QRS widening with 4.2, 10 and 5.6 % µM-1 unbound drug. AZD1305 and flecainide also prolonged PR with 13.5 and 11.5 % µM- 1 . PR prolongations induced by the anti-muscarinics and verapamil were best described by Emax models with maximal effects ranging from 55 to 95 %. RR interval correction and circadian rhythm improved PR but not QRS modelling. However, circadian rhythm had minor impact on estimated drug effects. Discussion: Baseline and drug-induced effects on QRS and PR intervals can be effectively described with PKPD models using routine data, providing quantitative safety information to support drug discovery and development

A Markov model of fibrosis development in nonalcoholic fatty liver disease predicts fibrosis progression in clinical cohorts

Disease progression in nonalcoholic steatohepatitis (NASH) is highly heterogenous and remains poorly understood. Fibrosis stage is currently the best predictor for development of end-stage liver disease and mortality. Better understanding and quantifying the impact of factors affecting NASH and fibrosis is essential to inform a clinical study design. We developed a population Markov model to describe the transition probability between fibrosis stages and mortality using a unique clinical nonalcoholic fatty liver disease cohort with serial biopsies over 3 decades. We evaluated covariate effects on all model parameters and performed clinical trial simulations to predict the fibrosis progression rate for external clinical cohorts. All parameters were estimated with good precision. Age and diagnosis of type 2 diabetes (T2D) were found to be significant predictors in the model. Increase in hepatic steatosis between visits was the most important predictor for progression of fibrosis. Fibrosis progression rate (FPR) was twofold higher for fibrosis stages 0 and 1 (F0-1) compared to fibrosis stage 2 and 3 (F2-3). A twofold increase in FPR was observed for T2D. A two-point steatosis worsening increased the FPR 11-fold. Predicted fibrosis progression was in good agreement with data from external clinical cohorts. Our fibrosis progression model shows that patient selection, particularly initial fibrosis stage distribution, can significantly impact fibrosis progression and as such the window for assessing drug efficacy in clinical trials. Our work highlights the increase in hepatic steatosis as the most important factor in increasing FPR, emphasizing the importance of well-defined lifestyle advise for reducing variability in NASH progression during clinical trials

Modeling and simulation approaches for cardiovascular function and their role in safety assessment

Systems pharmacology modeling and pharmacokinetic-pharmacodynamic (PK/PD) analysis of drug-induced effects on cardiovascular (CV) function plays a crucial role in understanding the safety risk of new drugs. The aim of this review is to outline the current modeling and simulation (M&S) approaches to describe and translate drug-induced CV effects, with an emphasis on how this impacts drug safety assessment. Current limitations are highlighted and recommendations are made for future effort in this vital area of drug research