Against a backdrop of global antibiotic resistance and increasing awareness of the importance of the human microbiota, there has been resurgent interest in the potential use of bacteriophages for therapeutic purposes, known as phage therapy. A number of phage therapy phase I and II clinical trials have concluded, and shown phages don't present significant adverse safety concerns. These clinical trials used simple phage suspensions without any formulation and phage stability was of secondary concern. Phages have a limited stability in solution, and undergo a significant drop in phage titre during processing and storage which is unacceptable if phages are to become regulated pharmaceuticals, where stable dosage and well defined pharmacokinetics and pharmacodynamics are de rigueur. Animal studies have shown that the efficacy of phage therapy outcomes depend on the phage concentration (i.e. the dose) delivered at the site of infection, and their ability to target and kill bacteria, arresting bacterial growth and clearing the infection. In addition, in vitro and animal studies have shown the importance of using phage cocktails rather than single phage preparations to achieve better therapy outcomes. The in vivo reduction of phage concentration due to interactions with host antibodies or other clearance mechanisms may necessitate repeated dosing of phages, or sustained release approaches. Modelling of phage-bacterium population dynamics reinforces these points. Surprisingly little attention has been devoted to the effect of formulation on phage therapy outcomes, given the need for phage cocktails, where each phage within a cocktail may require significantly different formulation to retain a high enough infective dose. This review firstly looks at the clinical needs and challenges (informed through a review of key animal studies evaluating phage therapy) associated with treatment of acute and chronic infections and the drivers for phage encapsulation. An important driver for formulation and encapsulation is shelf life and storage of phage to ensure reproducible dosages. Other drivers include formulation of phage for encapsulation in micro- and nanoparticles for effective delivery, encapsulation in stimuli responsive systems for triggered controlled or sustained release at the targeted site of infection. Encapsulation of phage (e.g. in liposomes) may also be used to increase the circulation time of phage for treating systemic infections, for prophylactic treatment or to treat intracellular infections. We then proceed to document approaches used in the published literature on the formulation and stabilisation of phage for storage and encapsulation of bacteriophage in micro- and nanostructured materials using freeze drying (lyophilization), spray drying, in emulsions e.g. ointments, polymeric microparticles, nanoparticles and liposomes. As phage therapy moves forward towards Phase III clinical trials, the review concludes by looking at promising new approaches for micro- and nanoencapsulation of phages and how these may ad...

We study the wave equation on a bounded domain M in $\mathbb{R}^m$ or on a compact Riemannian manifold with boundary. Assume that we do not know the coefficients of the wave equation but are given only the hyperbolic Robin-to-Dirichlet map that corresponds to physical measurements on a part of the boundary. In this paper we show that at a fixed time $t_0$ a wave can be cut off outside a suitable set. That is, if $N\subset M$ is a union of balls in the travel time metric having centers at the boundary, then we can modify a given Robin boundary value of a wave such that at time $t_0$ the modified wave is arbitrarily close to the original wave inside N and arbitrarily small outside N. Also, at time $t_0$ the time derivative of the modified wave is arbitrarily small in all of M. We apply this result to construct a sequence of Robin boundary values so that at a time $t_0$ the corresponding waves converge to a delta distribution $\delta_{\widehat{x}}$ while the time derivative of the waves converge to zero. Such boundary values are generated by an iterative sequence of measurements. In each iteration step we apply time reversal and other simple operators to measured data and compute boundary values for the next iteration step. A key feature of this result is that it does not require knowledge of the coefficients in the wave equation, that is, of the material parameters inside the media. However, we assume that the point $\widehat{x}$ where the wave focuses is known in travel time coordinates, and $\widehat{x}$ satisfies a certain geometrical condition

There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this, there is no “gold standard” for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modeling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges.

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