The patient is a 57-year-old with persistent left hip pain . The patient failed conservative treatment modalities including activity modifcations, various anti-inflammatory medications as wellas intra-articular injections. He opted for total hip arthroplasty in spite of his BMI (41.5 kg/m2) after lengthy discussion of the high risk nature of his surgery and the potential complications. Postoperatively, his pain was greatly improved . Unfortunately he had developed a foot drop after the surgery. He was intact to light touch in the distribution of the deep peroneal nerve, although somewhat decreased from the contralateral side. As his surgical approach was via a modifed lateral, it was felt that this was likely due to retractor placement. He is 4 months out from hisindex procedure with slight improvement in his ability to dorsiflex the foot. He continues with aggressive physical therapy as well as utilization of an ankle-foot-orthotic (AFO) to assist with optimal foot positioning. He has been counseled about the nature of the injury as well as the likely prognosis. He understands that it may take a full year before it is known to what extent he will resolve his nerve palsy.

Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected phage–bacterial interactions as seen during laboratory manipulation of phages. The most basic mathematical descriptor of phages is their titer, that is, their concentration within stocks, experimental vessels, or other environments. Various phenomena can serve to modify phage titers, and indeed phage titers can vary as a function of how they are measured. An important aspect of how changes in titers can occur results from phage interactions with bacteria. These changes tend to vary in degree as a function of bacterial densities within environments, and particularly densities of those bacteria that are susceptible to or at least adsorbable by a given phage type. Using simple mathematical models one can describe phage–bacterial interactions that give rise particularly to phage adsorption events. With elaboration one can consider changes in both phage and bacterial densities as a function of both time and these interactions. In addition, phages along with their impact on bacteria can be considered as spatially constrained processes. In this chapter we consider the simpler of these concepts, providing in particular detailed verbal explanations toward facile mathematical insight. The primary goal is to stimulate a more informed use and manipulation of phages and phage populations within the laboratory as well as toward more effective phage application outside of the laboratory, such as during phage therapy. More generally, numerous issues and approaches to the quantification of phages are considered along with the quantification of individual, ecological, and applied properties of phages.

Structural heart disease intervention is a major area of development in cardiology. A desire to minimise the invasiveness of interventions and reduce patient exposure to risk have been the main drivers in developing catheter-based intervention in preference to open-heart surgery. Over the past 9 years, transcatheter aortic valve implantation (TAVI) has become the standard treatment for patients deemed inoperable or high risk for conventional aortic valve replacement, with evidence of its potential in those at intermediate risk. Mitral valve interventions are also moving forward in development. Percutaneous balloon mitral valvuloplasty (BMV) is a catheter-based technique that achieves commisurotomy in the context of pliable mitral stenosis in patients with rheumatic heart disease and has replaced surgery as the favoured approach. BMV also has an important role in patients with signifcant mitral stenosis during pregnancy. Percutaneous mitral valve repair encompasses several catheter-based techniques to either diminish annular dilatation or correct poor mitral valve leaflet coaptation in patients with severe mitral regurgitation at too high risk for conventional surgical mitral valve repair or replacement. In patients who have undergone previous cardiac surgery and valve replacement, paravalvular regurgitation may occur following detachment of the surgical valve ring through stitch failure, wear and tear or after endocarditis. The risk of re-do valve replacement surgery is high and may be prohibitive, leading to a preference for an initial catheter-based strategy of plugging residual gaps external to the sewing ring in order to obtain valve competence.