Splenic contraction is enhanced by exercise at simulated high altitude

Purpose Splenic contraction increases circulating hemoglobin (Hb) with advantages during hypoxia. As both hypoxia and exercise have been shown to be important separate triggers of splenic contraction we aimed to investigate if the spleen response to simulated high altitude (HA) is enhanced by superimposing exercise. Method Fourteen healthy volunteers (seven females) performed the following protocol in a normobaric environment sitting on an ergometer cycle: 20 min rest in normoxia; 20 min rest while breathing hypoxic gas simulating an altitude of 3500 m; 10 min exercise at an individually set intensity while breathing the hypoxic gas; 20 min rest in hypoxia; and finally 20 min rest in normoxia. Spleen measurements were collected by ultrasonic imaging and venous Hb measured at the end of each intervention. Result Mean ± SD baseline spleen volume during normoxic rest was 280 ± 107 mL, the volume was reduced by 22% during rest in hypoxia to 217 ± 92 mL (p < 0.001) and by 33% during exercise in hypoxia (189 mL; p < 0.001). Hb was 140.7 ± 7.0 g/L during normoxic rest and 141.3 ± 7.4 g/L during hypoxic rest (NS), but increased by 5.3% during hypoxic exercise (148.6 ± 6.3 g/L; p < 0.001). Spleen volume and Hb were stepwise changed back to baseline at cessation of exercise and return to normoxia. Conclusion Splenic contraction is induced by hypoxia and further enhanced by superimposing exercise, and reduced when exercise ceases, in a step-wise manner, showing that the tonic but partial contraction observed in long-term field expeditions to HA may occur also in the short term. This “graded response” may be beneficial during acclimatization to HA, to cope with moderate chronic hypoxia during rest while allowing additional enhancement of oxygen carrying capacity to overcome short bouts of extreme hypoxia caused by exercise.

Partial Contraction Analysis of Coupled Fractional Order Systems

Contraction theory regards the convergence between two arbitrary system trajectories. In this article we have introduced partial contraction theory as an extension of contraction theory to analyze coupled identical fractional order systems. It can, also, be applied to study the synchronization phenomenon in networks of various structures and with arbitrary number of systems. We have used partial contraction theory to derive exact and global results on synchronization and antisynchronization of fractional order systems.

Contractive analogs

This chapter deals with contractive completions of partial operator matrices. Since the norm of a submatrix is always less or equal to the norm of the matrix itself, every partial matrix which admits a contractive completion has to be partially contractive (or a partial contraction), that is, all its fully specified submatrices are contractions. The discussions cover contractive operator-matrix completions; linearly constrained completion problems; the operator-valued Nehari and Carathéodory problems; Nehari's problem in two variables; Nehari and Carathéodory problems for functions on compact groups; the Nevanlinna–Pick problem; the operator Corona problem; joint operator/Hilbert–Schmidt norm control extensions; an L1 extension problem for polynomials; superoptimal completions and approximations of analytic functions; and model matching. Exercises and notes are provided at the end of the chapter.