Interaction of the immune system with a target population of, e.g., bacteria, viruses, antigens, or tumor cells must be considered as a dynamic process. We describe this process by a system of two ordinary differential equations. Although the model is strongly idealized it demonstrates how the combination of a few proposed nonlinear interaction rules between the immune system and its targets are able to generate a considerable variety of different kinds of immune responses, many of which are observed both experimentally and clinically. In particular, solutions of the model equations correspond to states described by immunologists as "virgin state," "immune state" and "state of tolerance." The model successfully replicates the so-called primary and secondary response. Moreover, it predicts the existence of a threshold level for the amount of pathogen germs or of transplanted tumor cells below which the host is able to eliminate the infectious organism or to reject the tumor graft. We also find a long time coexistence of targets and immune competent cells including damped and undamped oscillations of both. Plausibly the model explains that if the number of transformed cells or pathogens exeeds definable values (poor antigenicity, high reproduction rate) the immune system fails to keep the disease under control. On the other hand, the model predicts apparently paradoxical situations including an increased chance of target survival despite enhanced immune activity or therapeutically achieved target reduction. A further obviously paradoxical behavior consists of a positive effect for the patient up to a complete cure by adding an additional target challenge where the benefit of the additional targets depends strongly on the time point and on their amount. Under periodically pulsed stimulation the model may show a chaotic time behavior of both target growth and immune response. (c) 1995 American Institute of Physics.

We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles (individuals) in the stochastic system. The main expansions of the model are distinguishing cancer cells by phenotype and genotype, including environment-dependent phenotypic plasticity that does not affect the genotype, taking into account the effects of therapy and introducing a competition term which lowers the reproduction rate of an individual in addition to the usual term that increases its death rate. We illustrate the new setup by using it to model various phenomena arising in immunotherapy. Our aim is twofold: on the one hand, we show that the interplay of genetic mutations and phenotypic switches on different timescales as well as the occurrence of metastability phenomena raise new mathematical challenges. On the other hand, we argue why understanding purely stochastic events (which cannot be obtained with deterministic models) may help to understand the resistance of tumours to therapeutic approaches and may have non-trivial consequences on tumour treatment protocols. This is supported through numerical simulations.

No abstract

As a leading cause of death and morbidity, heart failure (HF) is responsible for a large portion of healthcare and disability costs worldwide. Current approaches to define specific HF subpopulations may fail to account for the diversity of etiologies, comorbidities, and factors driving disease progression, and therefore have limited value for clinical decision making and development of novel therapies. Here we present a novel and data-driven approach to understand and characterize the real-world manifestation of HF by clustering disease and symptom-related clinical concepts (complaints) captured from unstructured electronic health record clinical notes. We used natural language processing to construct vectorized representations of patient complaints followed by clustering to group HF patients by similarity of complaint vectors. We then identified complaints that were significantly enriched within each cluster using statistical testing. Breaking the HF population into groups of similar patients revealed a clinically interpretable hierarchy of subgroups characterized by similar HF manifestation. Importantly, our methodology revealed well-known etiologies, risk factors, and comorbid conditions of HF (including ischemic heart disease, aortic valve disease, atrial fibrillation, congenital heart disease, various cardiomyopathies, obesity, hypertension, diabetes, and chronic kidney disease) and yielded additional insights into the details of each HF subgroup’s clinical manifestation of HF. Our approach is entirely hypothesis free and can therefore be readily applied for discovery of novel insights in alternative diseases or patient populations.

Rivaroxaban has been investigated in the EINSTEIN-Jr program for the treatment of acute venous thromboembolism (VTE) in children aged 0 to 18 years and in the UNIVERSE program for thromboprophylaxis in children aged 2 to 8 years with congenital heart disease after Fontanprocedure. Physiologically-based pharmacokinetic (PBPK) and population pharmacokinetic (popPK) modeling were used throughout the pediatric development of rivaroxaban according to the learn-andconfirm paradigm. The development strategy was to match pediatric drug exposures to adult exposure proven to be safe and efficacious. In this analysis, a refined pediatric popPK model for rivaroxaban based on integrated EINSTEIN-Jr data and interim PK data from Part A of the UNIVERSE phase 3 study was developed and the influence of potential covariates and intrinsic factors on rivaroxaban exposure was assessed. The model adequately described the observed pediatric PK data. PK parameters and exposure metrics estimated by the popPK model were compared to the predictions from a previously published pediatric PBPK model for rivaroxaban. 91% of the individual post-hoc clearance estimates were found within the 5 th to 95 th percentile of the PBPK model predictions. In patients below 2 years, however, clearance was underpredicted by the PBPK model. The iterative and integrative use of PBPK and popPK modeling and simulation played a major role in the establishment of the bodyweight-adjusted rivaroxaban dosing regimen that was ultimately confirmed to be a safe and efficacious dosing regimen for children aged 0 to 18 years with acute VTE in the EINSTEIN-Jr phase 3 study.