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We evaluated the safety and feasibility of high-intensity interval training via a novel telemedicine ergometer (MedBIKE™) in children with Fontan physiology.
The MedBIKE™ is a custom telemedicine ergometer, incorporating a video game platform and live feed of patient video/audio, electrocardiography, pulse oximetry, and power output, for remote medical supervision and modulation of work. There were three study phases: (I) exercise workload comparison between the MedBIKE™ and a standard cardiopulmonary exercise ergometer in 10 healthy adults. (II) In-hospital safety, feasibility, and user experience (via questionnaire) assessment of a MedBIKE™ high-intensity interval training protocol in children with Fontan physiology. (III) Eight-week home-based high-intensity interval trial programme in two participants with Fontan physiology.
There was good agreement in oxygen consumption during graded exercise at matched work rates between the cardiopulmonary exercise ergometer and MedBIKE™ (1.1 ± 0.5 L/minute versus 1.1 ± 0.5 L/minute, p = 0.44). Ten youth with Fontan physiology (11.5 ± 1.8 years old) completed a MedBIKE™ high-intensity interval training session with no adverse events. The participants found the MedBIKE™ to be enjoyable and easy to navigate. In two participants, the 8-week home-based protocol was tolerated well with completion of 23/24 (96%) and 24/24 (100%) of sessions, respectively, and no adverse events across the 47 sessions in total.
The MedBIKE™ resulted in similar physiological responses as compared to a cardiopulmonary exercise test ergometer and the high-intensity interval training protocol was safe, feasible, and enjoyable in youth with Fontan physiology. A randomised-controlled trial of a home-based high-intensity interval training exercise intervention using the MedBIKE™ will next be undertaken.
Recovery is a key goal for individuals, and services’ recovery orientation can facilitate this process. The independent mental health sector is increasingly important in Ireland, particularly in counselling and suicide prevention. We aimed to evaluate Pieta House as a recovery-oriented service through clients’ self-rated recovery; and clients’ and therapists’ evaluation of the service.
Clients completing therapy over a 3-month period were invited to complete the Recovery Assessment Scale (RAS) and the Recovery Self Assessment-Revised (RSA-R). Therapists completed the RSA-R staff version.
Response rate was 36.7% for clients (n=88), 98% for therapists (n=49). Personal recovery was endorsed by 73.8% of clients, with highest agreement for factors ‘Willingness to Ask for Help’ (84.5%), and ‘Reliance on Others’ (82.1%). A smaller number agreed with factors ‘Personal Confidence and Hope’ (61.3%) and ‘No Domination by Symptoms’ (66.6%). Clients’ and therapists’ evaluation of the service showed high levels of agreement with factors of ‘Choice’ (90.9% clients, 100% therapists); ‘Life Goals’ (84.1% clients, 98% therapists) and ‘Individually Tailored Services’ (80.6% clients, 79.6% therapists). Client involvement in service management had the lowest level of agreement (36.4% clients, 30.6% therapists). Clients’ self-rated recovery correlated with their rating of the service (correlation value 0.993, p=0.01).
Clients’ self-rated recovery and the recovery orientation of Pieta House were rated highly, with areas for improvement in service user involvement, peer support and advocacy. The correlation of personal recovery and recovery orientation of the service may merit further study.
The concept of a differentiable function of several variables is introduced and explored. As part of this project, linear transformations between Euclidean spaces are studied and the Spectral Theorem for self-adjoint transformations is established. This is used to diagnose the nature of a critical point of a smooth real-valued function of several variables. The implicit and inverse function theorems are proven.
The Riemann integral of a function of one variable is defined and explored. Included here are the definitions of the logarithm and exponential functions. Improper integrals are explored. Lebesgue's Theorem giving a necessary and sufficient contion for Riemann integrability is established and the Riemann-Stieltjes integral is defined and investigated.
Differential forms constitutes an approach to multivariable calculus that simplifies the study of integration over surfaces of any dimension in Rp. This topic introduces algebraic techniques into the study of higher dimensional geometry and allows us to recapture with rigor the results obtained in the preceding chapter.
There are many approaches to defining and exploring differential forms, all leading to the same objective. One is to just define a form as a symbol with certain properties. That was the approach taken when I first encountered the subject. Though this appeals to many and ultimately leads to the same objective, it strikes me as inconsistent with the approach we have taken. So in this chapter I have decided to follow the approach in  where a form is defined in terms that are more in line with what I think is the background of readers of this book. The reader might also want to look at , , and  where there are different approaches.
Here we will define differential forms and explore their algebraic properties and the process of differentiating them. The first definition extends that of a surface as given in the preceding chapter.
Definition. Let q ≥ 1. A q-surface domain or just a surface domain is a compact Jordan subset R of Rq such that int R is connected and R = cl (int R). A q-surface in Rp is a pair where R is a q-surface domain and is a function from R into Rp that is smooth on some neighborhood of R. The trace of is the set. If G is an open subset of Rp and, we say is a q-surface in G; let Sq(G) be the collection of all q-surfaces contained in G.
The derivative of a function of one variable is defined and its basic properties are explored. This includes tests for the nature of a critical point. These results are used to establish l'Hopital's Rule and Taylor's Theorem.
This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.
In this chapter we begin the study of p-dimensional Euclidean space, Rp, but in this beginning we will carry it a step further. We want to discuss differentiation and integration on Rp, but first we need to extend the notions of sequential convergence, the properties of sets, and the concept of continuity to the higher dimensional spaces. The effort to explore these concepts in Rp, however, is not greater than what is required to explore these notions in what are called metric spaces. In many respects the abstract spaces are easier to cope with than Rp. Moreover some of what we have already done is properly couched in metric spaces. Indeed, the material of §4.1 can be set there with little additional effort. Nevertheless during this venture into abstraction the main set of examples will be Euclidean space.
We start with the concept of distance between points. This must be general enough to encompass a variety of circumstances, but it should conform to the intuitive notion we all have of what is meant by distance. Since this is done at the start of the first section, it would be profitable before proceeding for the reader to reflect on what properties (s)he thinks should be included in an abstract concept of distance; then you can compare your thoughts with the definition that starts the following section.
The treatment of metric spaces here is based on Chapter 1 of .
Definitions and Examples
Definition. A metric space is a pair of objects, (X, d), where X is a set and d is a function d : X × X → [0,∞) called a metric, that satisfies the following for all x, y, z in X:
Condition (a) is sometimes called the symmetric property and says that the distance from x to y is the same as the distance from y to x. The second property says the obvious: the distance from a point to itself is 0 and the only point at a distance zero from x is x itself.