Decay estimates for time-fractional and other non-local in time subdiffusion equations in R^d
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in R d . An important special case is the timefractional diffusion equation, which has seen much interest during the last years, mostly due to its applications in the modeling of anomalous diffusion processes. We follow three different approaches and techniques to study this particular case: (A) estimates based on the fundamental solution and Young’s inequality, (B) Fourier multiplier methods, and (C) the energy method. It turns out that the decay behaviour is markedly different from the heat equation case, in particular there occurs a critical dimension phenom…
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
Abstract We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the solution tends to the fundamental solution, (iii) optimal L 2 -decay of mild solutions in all dimensions, (iv) L 2 -decay of weak solutions via energy methods. The first result relies on a delicate analysis of the definition of classical solutions. After proving the representation formula we carefully analyze the integral representation to obtain the quantitative decay rates of (ii). Next we use Fourier analysis techniques to obtain the optimal dec…
Muscle Free Fatty-Acid Uptake Associates to Mechanical Efficiency During Exercise in Humans
Intrinsic factors related to muscle metabolism may explain the differences in mechanical efficiency (ME) during exercise. Therefore, this study aimed to investigate the relationship between muscle metabolism and ME. Totally 17 healthy recreationally active male participants were recruited and divided into efficient (EF; n = 8) and inefficient (IE; n = 9) groups, which were matched for age (mean ± SD 24 ± 2 vs. 23 ± 2 years), BMI (23 ± 1 vs. 23 ± 2 kg m−2), physical activity levels (3.4 ± 1.0 vs. 4.1 ± 1.0 sessions/week), and V˙O2peak (53 ± 3 vs. 52 ± 3 mL kg−1 min−1), respectively, but differed for ME at 45% of V˙O2peak intensity during submaximal bicycle ergometer test (EF 20.5 ± 3.5 vs. I…
Myocardial blood flow and adenosine A2Areceptor density in endurance athletes and untrained men
Previous human studies have shown divergent results concerning the effects of exercise training on myocardial blood flow (MBF) at rest or during adenosine-induced hyperaemia in humans. We studied whether these responses are related to alterations in adenosine A2A receptor (A2AR) density in the left-ventricular (LV) myocardium, size and work output of the athlete's heart, or to fitness level. MBF at baseline and during intravenous adenosine infusion, and A2AR density at baseline were measured using positron emission tomography, and by a novel A2AR tracer in 10 healthy male endurance athletes (ET) and 10 healthy untrained (UT) men. Structural LV parameters were measured with echocardiography.…
Perfusion heterogeneity does not explain excess muscle oxygen uptake during variable intensity exercise
Previous research investigating endurance sports from a physiological perspectivehas mainly used constant or graded exercise protocols, although the nature ofsports like cross-country skiing and road cycling leads to continuous variations inworkload. Current knowledge is thus limited as regards physiological responses tovariations in exercise intensity. Therefore, the overall objective of the present thesiswas to investigate cardiovascular and metabolic responses to fluctuations inexercise intensity during exercise. The thesis is based on four studies (Studies I-IV);the first two studies use a variable intensity protocol with cardiorespiratory andblood measurements during cycling (Study I) …
Skeletal muscle blood flow and flow heterogeneity during dynamic and isometric exercise in humans
The effects of dynamic and intermittent isometric knee extension exercises on skeletal muscle blood flow and flow heterogeneity were studied in seven healthy endurance-trained men. Regional muscle blood flow was measured using positron emission tomography (PET) and an [15O]H2O tracer, and electromyographic (EMG) activity was recorded in the quadriceps femoris (QF) muscle during submaximal intermittent isometric and dynamic exercises. QF blood flow was 61% ( P = 0.002) higher during dynamic exercise. Interestingly, flow heterogeneity was 13% ( P = 0.024) lower during dynamic compared with intermittent isometric exercise. EMG activity was significantly higher ( P < 0.001) during dynamic e…