Two-stage explicit Runge-Kutta type methods using derivatives for the system y'(t) _ f (y(t)), y(to) = yo are considered. Derivatives in the first stage have the standard form, but in the second stage, they have the form included in the limiting formula. The kthorder Taylor series method uses derivatives f', f1,... , f ( k ). Though the values of derivatives can be easily obtained by using automatic differentiation, the cost increases proportional to square of the order of differentiation. Two-stage methods considered here use the derivatives up to f ('3) in the first stage and f, f' in the second stage. They can achieve kth-order accuracy and construct embedded formula for the error estimation.
Purpose:
Consensus articles that explore rehabilitation exercise for heart failure (HF) mainly focus on stable patients with chronic HF. Results from investigations that focus on the relationship between clinical outcomes and exercise during rehabilitation of patients with acute heart failure (AHF) have produced insufficient data. The aim of this study was to evaluate the correlation between clinical outcomes and dyspnea during in-hospital early rehabilitation in patients with AHF.
Methods:
Dyspnea was measured using a 5-point Likert scale (5PLS) during rest and at the initiation of upright sitting and standing. Dyspnea was defined as 5PLS ≥2. The primary endpoint was combined all-cause death or rehospitalization for HF.
Results:
A total of 221 patients were included in this study; 81 patients (37%) died or were hospitalized during the follow-up period. In patients with dyspnea during upright sitting and standing, the event-free ratio was significantly lower compared with patients without dyspnea (P = .008 and P < .001, respectively). Body mass index (hazard ratio [HR] = 0.91, P = .011), noninvasive positive pressure ventilation usage (HR = 1.96, P = .042), and 5PLS ≥2 at the initiation of standing (HR = 2.63, P = .008) were detected as predictors of primary endpoint. New York Heart Association class IV at admission (OR = 3.17, P = .0114) and pre-admission Katz ADL index <6 (OR = 3.76, P = .0007) were isolated as risk factors for dyspnea when standing.
Conclusions:
Dyspnea during standing was associated with unfavorable events in patients with AHF as a comprehensive indicator.
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