In noncommutative phase space, wave functions and energy spectra are derived for the three-dimensional (3D) Klein–Gordon oscillator in a background magnetic field. The raising and lowering operators for this system are derived from the Heisenberg equations of motion for a 3D nonrelativistic oscillator. The coherent states are obtained as the eigenstates of the lowering operators and it is found that the coherent states are not the minimum uncertainty states due to the noncommutativity of the space. It is also pointed out that in the semiclassical limit, quantum matrix elements give solutions to the semiclassical equations.

There is increasing evidence that diabetic cardiomyopathy increases the risk of cardiac arrhythmia and sudden cardiac death. While the detailed mechanisms remain incompletely understood, the loss of mitochondrial function, which is often observed in the heart of patients with diabetes, has emerged as a key contributor to the arrhythmogenic substrates. In this mini review, the pathophysiology of mitochondrial dysfunction in diabetes mellitus is explored in detail, followed by descriptions of several mechanisms potentially linking mitochondria to arrhythmogenesis in the context of diabetic cardiomyopathy.

BackgroundOxidative stress–mediated Ca2+/calmodulin‐dependent protein kinase II (CaMKII) phosphorylation of cardiac ion channels has emerged as a critical contributor to arrhythmogenesis in cardiac pathology. However, the link between mitochondrial‐derived reactive oxygen species (mdROS) and increased CaMKII activity in the context of cardiac arrhythmias has not been fully elucidated and is difficult to establish experimentally.Methods and ResultsWe hypothesize that pathological mdROS can cause erratic action potentials through the oxidation‐dependent CaMKII activation pathway. We further propose that CaMKII‐dependent phosphorylation of sarcolemmal slow Na+ channels alone is sufficient to elicit early afterdepolarizations. To test the hypotheses, we expanded our well‐established guinea pig cardiomyocyte excitation‐contraction coupling, mitochondrial energetics, and ROS‐induced‐ROS‐release model by incorporating oxidative CaMKII activation and CaMKII‐dependent Na+ channel phosphorylation in silico. Simulations show that mdROS mediated‐CaMKII activation elicits early afterdepolarizations by augmenting the late Na+ currents, which can be suppressed by blocking L‐type Ca2+ channels or Na+/Ca2+ exchangers. Interestingly, we found that oxidative CaMKII activation–induced early afterdepolarizations are sustained even after mdROS has returned to its physiological levels. Moreover, mitochondrial‐targeting antioxidant treatment can suppress the early afterdepolarizations, but only if given in an appropriate time window. Incorporating concurrent mdROS‐induced ryanodine receptors activation further exacerbates the proarrhythmogenic effect of oxidative CaMKII activation.ConclusionsWe conclude that oxidative CaMKII activation–dependent Na channel phosphorylation is a critical pathway in mitochondria‐mediated cardiac arrhythmogenesis.

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum-momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.

For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the motion of the charged particle along the magnetic field has the effect to increase the magnetic field. In the classical limit, matrix elements of the velocity operator related to the probability give a clear physical picture: Along an effective magnetic field the mechanical momentum is conserved and the motion perpendicular to the effective magnetic field follows a round orbit. If using the velocity operator defined by the coordinate operators, the motion becomes complicated. Key words: non-commutative phase space，Dirac equation，velocity operator，magnetic field PACS: 02.40.Gh，03.65.-w，11.10.Nx IntroductionTo resolve the problem of infinite energies in quantum field theory, the idea of space-time non-commutativity was proposed [1]. Discoveries in string theory and M-theory that effects of noncommutative(NC) spaces may appear near the string scale and at higher energies [2-4] greatly motivate the studies in these areas. Recently, a lot of problems have been investigated on the theory of NC spaces such as the quantum Hall effects [5][6][7][8][9], the harmonic oscillator [10][11][12][13][14], the coherent states [15], the thermodynamics [16], the classical-quantum relationship [17], the motion of the spin-1/2 particle under a uniform magnetic field [18], various kinds of relativistic oscillators [19, 20,23,24], etc. In [18], the particle is confined to the plane the applied magnetic field is perpendicular to. Here in this article, we discuss the case that the particle is allowed to move off the plane.In the next section, we derive the energy spectrum and wave functions in 3D NC phase space. It is shown that the NC 3D phase space induces an effective magnetic field in a new direction. Matrix elements of velocity and momentum operators give solutions to the semiclassical equations of motion. The final section is the summary.

Background: Oxidative stress-mediated CaMKII phosphorylation of cardiac ion channels has emerged as a critical contributor to arrhythmogenesis in cardiac pathology. However, the link between mitochondrial-derived reactive oxygen species (mdROS) and increased CaMKII activity in the context of cardiac arrhythmias has not been fully elucidated and is difficult to establish experimentally. Methods: We hypothesize that pathological mdROS can cause erratic action potentials through the oxidation-dependent CaMKII activation pathway. We further propose that CaMKII dependent phosphorylation of sarcolemmal slow sodium channels alone is sufficient to elicit early afterdepolarizations. To test the hypotheses, we expanded our well-established guinea pig cardiomyocyte e xcitation- c ontraction coupling, m itochondrial e nergetics and R OS- i nduced- R OS- r elease model by incorporating oxidative CaMKII activation and CaMKII-dependent Na + channel phosphorylation in silico . Results: Simulations show that mdROS mediated-CaMKII activation elicits early afterdepolarizations (EADs) by augmenting the late Na + currents ( I Na,L ), which can be suppressed by blocking L-type Ca 2+ channels or Na + /Ca 2+ exchangers. Interestingly, we found that oxidative CaMKII activation-induced EADs sustain even after mdROS has returned to its physiological levels. Moreover, mitochondrial-targeting antioxidant treatment can suppress the EADs, but only if given in an appropriate time window. Incorporating concurrent mdROS-induced RyRs activation further exacerbates the proarrhythmogenic effect of oxidative CaMKII activation. Conclusions: We conclude that oxidative CaMKII activation-dependent Na channel phosphorylation is a critical pathway in mitochondria mediated cardiac arrhythmogenesis.

Intraoperative imaging of living tissue at the cell level by endomicroscopy might help surgeons optimize surgical procedures and provide individualized treatments. However, the resolution of the microscopic image is limited by the motion of living tissue caused by heartbeat and respiration. An active motion compensation (AMC) strategy has been recognized as an effective way to reduce, or even eliminate, the influence of tissue movement for intravital fluorescence microscopy (IVM). To realize the AMC system, a high-speed sensor for measuring the motion of tissues is needed. At present, state-of-the-art commercialized displacement sensors are not suitable to apply in minimally invasive imaging instruments to measure the motion of living tissues because of the size problem, range of measurement or the update rate. In this study, a compact high-speed image-based method for measuring the longitudinal motion of living tissues is proposed. The complexity of the proposed method is the same as that of the traditional wide-field fluorescent microscopy (WFFM) system, which makes it easy to be miniaturized and integrated into a minimally invasive imaging instrument. Experimental results reveal that the maximum indication error, range of measurement and the sensitivity of the laboratory-built experimental prototype is 150 μm, 6 mm and −211.46 mm−1 respectively. Experimental results indicate that the proposed optical method is expected to be used in minimally invasive imaging instruments to build an AMC system.