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Karsten Knobloch,1 Amol Saxena,2 Wolfgang Schaden3 1SportPraxis Professor Knobloch, Hannover, Germany; 2Department of Sports Medicine, Sutter-Palo Alto, Palo Alto, CA, USA; 3Ludwig Boltzmann Institute for Experimental and Clinical Traumatology, AUVA Research Center, Vienna, AustriaCorrespondence: Karsten Knobloch, SportPraxis Professor Knobloch, Heiligerstrasse 3, Hannover, 30159, Germany, Email knobloch@sportpraxis-knobloch.deAbstract: This case report describes a novel and unique combination of both electromagnetic and electrohydraulic focused extracorporeal shockwave therapy (ESWT) and extracorporeal magnetotransduction therapy (EMTT) for accelerated healing in a calcaneus epiphyseal fracture with delayed healing in an adolescent Parkour athlete. After a 2.5m jump, the 14-year-old experienced significant heel pain, however avoided telling his parents. After eight weeks, the initial imaging using ultra low dose weight-bearing cone beam CT (WBCT) revealed a calcaneus non-union situation adjacent to the open calcaneal physis. To improve and accelerate bony healing substantially, we chose to apply both combined focused electromagnetic (Storz Ultra, Storz Medical AG, Tägerwillen, CH) and focused electrohydraulic (MTS, Konstanz, Germany) ESWT in a fractioned fashion plus EMTT (Storz Magnetolith, Tägerwillen, CH) in five consecutive weekly sessions while allowing the patient to fully weight bear. The follow-up WBCT after six weeks revealed a near to total healing of the delayed union and being pain-free. Notably, combination therapy with focused ESWT and EMTT did not result in early closure of the calcaneal epiphysis. We conclude that combined focused electromagnetic and electrohydraulic ESWT and EMTT facilitate bony healing in adolescent calcaneal apophyseal fractures without any adverse effects on the open physis. Evidence level IV (case report).Keywords: ESWT, shockwave therapy, EMTT, epiphysis, non, union

When steam power cycles are modeled, thermodynamic properties as functions of pressure and temperature are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, such calculations require cumbersome iterative calculations, because temperature and volume are the independent variables in the formulation for this region. In order to reduce the computing time, the International Association for the Properties of Water and Steam (IAPWS) adopted a set of backward equations for volume as a function of pressure and temperature in region 3. The necessary numerical consistency is achieved by dividing the region into 20 subregions, plus auxiliary subregions near the critical point in which the consistency requirements are relaxed due to the singular behavior at the critical point. In this work, we provide complete documentation of these equations, along with a discussion of their numerical consistency and the savings in computer time. The numerical consistency of these equations should be sufficient for most applications in heat-cycle, boiler, and steam-turbine calculations; if even higher consistency is required, the equations may be used to generate guesses for iterative procedures. [DOI: 10.1115/1.3028630]

When steam power cycles are modeled, thermodynamic properties as functions of enthalpy and entropy are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, these calculations require cumbersome two-dimensional literation of temperature T and specific volume v from specific enthalpy h and specific entropy s. While these calculations are not frequently required, the computing time can be significant. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for p(h,s) in region 3. For calculating properties as a function of h and s in the part of the two-phase region that is important for steam-turbine calculations, a backward equation [T.sub.sat](h,s) is provided. In order to avoid time-consuming iteration in determining the region for given values of h and s, equations for the region boundaries were developed. The numerical consistency of the equations documented here is sufficient for most applications in heat-cycle, boiler, and steam-turbine calculations. [DOI: 10.1115/1.2719267]

In modeling advanced steam power cycles, thermodynamic properties as functions of pressure and enthalpy (p,h) or pressure and entropy (p,s) are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, these calculations require cumbersome two-dimensional iteration of temperature T and specific volume u from (p,h) or (p,s). While these calculations in region 3 are not frequently required, the computing time can be significant. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for T(p,h), v(p,h), T(p,s), and u(p ,s) in region 3, along with boundary equations for the saturation pressure as a function of enthalpy, [P.sub.3sat](h), and of entropy, [P.sub.3sa]t(S). Using the new equations, two-dimensional iteration can be avoided. The numerical consistency of temperature and specific volume obtained in this way is sufficient for most uses. This paper summarizes the need and the requirements for these equations and gives complete numerical information. In addition, numerical consistency and computational speed are discussed. [DOI: 10.1115/1.2181598]

In modeling steam power cycles, thermodynamic properties as functions of the variables enthalpy and entropy are required in the liquid and the vapor regions. It is difficult to perform these calculations with IAPWS-IF97, because they require two-dimensional iterations calculated from the IAPWS-IF97 fundamental equations. While these calculations are not frequently required, the relatively large computing time required for two-dimensional iteration can be significant in process modeling. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for pressure as a function of enthalpy and entropy p(h,s) as a supplement to the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97) in 2001. These p(h,s) equations are valid in the liquid region 1 and the vapor region 2. With pressure p, temperature T(h,s) can be calculated from the IAPWS-IF97 backward equations T(p,h). By using the p(h,s) equations, the two dimensional iterations of the IAPWS-IF97 basic equations can be avoided. The numerical consistency of pressure and temperature obtained in this way is sufficient for most heat cycle calculations. This paper summarizes the need and the requirements for the p(h,s) equations and gives complete numerical information about the equations. Moreover, the achieved quality of the equations and their use in the calculation of the backward function T(h, s) is presented. The three aspects, numerical consistency with the IAPWS-IF97 basic equations, consistency along subregion boundaries, and computational speed important for industrial use are discussed. [DOI: 10.1115/1.1915392]