Combination of "generalized Trotter operator splitting" and "quadratic adaptive algorithm" method for tradeoff among speedup, stability, and accuracy in the Markov chain model of sodium ion channels in the ventricular cell model.

The fast hybrid operator splitting (HOS) and stable uniformization (UNI) methods have been proposed to save computation cost and enhance stability for Markov chain model in cardiac cell simulations. Moreover, Chen-Chen-Luo's quadratic adaptive algorithm (CCL) combined with HOS or UNI was used to improve the tradeoff between speedup and stability, but without considering accuracy. To compromise among stability, acceleration, and accuracy, we propose a generalized Trotter operator splitting (GTOS) method combined with CCL independent of the asymptotic property of a particular ion-channel model. Due to the accuracy underestimation of the mixed root mean square error (MRMSE) method, threshold root mean square error (TRMSE) is proposed to evaluate computation accuracy. With the fixed time-step RK4 as a reference, the second-order GTOS combined with CCL (30.8-fold speedup) for the wild-type Markov chain model with nine states (WT-9 model) or (7.4-fold) for the wild-type Markov chain model with eight states (WT-8 model) is faster than UNI combined with CCL (15.6-fold) for WT-9 model or (1.2-fold) for WT-8 model, separately. Besides, the second-order GTOS combined with CCL has 3.81% TRMSE for WT-9 model or 4.32% TRMSE for WT-8 model more accurate than 72.43% TRMSE for WT-9 model or 136.17% TRMSE for WT-8 model of HOS combined with CCL. To compromise speedup and accuracy, low-order GTOS combined with CCL is suggested to have the advantages of high precision and low computation cost. For high-accuracy requirements, high-order GTOS combined with CCL is recommended. Graphical abstract.

Combination of "quadratic adaptive algorithm" and "hybrid operator splitting" or uniformization algorithms for stability against acceleration in the Markov model of sodium ion channels in the ventricular cell model.

The Markovian model has generally been used for cardiac electrophysiological simulations. However, the Markovian model is so stiff that speeding up the computation of the algorithms with variable time-steps always results in simulation instability. In particular, the unstable simulations always occur at a low voltage rate or current change, while transition rates in the Markovian model are changing markedly. The uniformization (UNI) method allows for a Markovian model simulation with high stability but also a high computation cost. To save computation costs with variable time-steps, we propose a speed increasing idea that is a compromise to the trade-off between stability and acceleration by combining Chen-Chen-Luo's "quadratic adaptive algorithm" (CCL) method with "hybrid operator splitting" (HOS) into the solver (CCL + HOS solver). The computation cost of this CCL + HOS solver is approximately 24 times lower than the CCL + UNI solver, and the CCL + HOS solver can function 295 times faster in comparison to the HOS solver with a fixed time-step (DT). The suggested optimal solver should be CCL + HOS solver with a maximum time-step at 0.1 ms due to its high speed with low error. Additionally, the CCL method has much better performance and stability than the hybrid method in this single-cell model simulation.

Combination of multi-variable quadratic adaptive algorithm and hybrid operator splitting method for stability against acceleration in the Markov model of sodium ion channels in the ventricular cell model.

Markovian model is widely used to study cardiac electrophysiology and drug screening. Due to the stiffness of Markov model for single-cell simulation, it is prone to induce instability by using large time-steps. Hybrid operator splitting (HOS) and uniformization (UNI) methods were devised to solve Markovian models with fixed time-step. Recently, it is shown that these two methods combined with Chen-Chen-Luo's quadratic adaptive algorithm (CCL) can save markedly computation cost with adaptive time-step. However, CCL determines the time-step size solely based on the membrane potential. The voltage changes slowly to increase the step size rapidly, while the values of state variables of Markov sodium channel model still change dramatically. As a result, the system is not stable and the errors of membrane potential and sodium current exceed 5%. To resolve this problem, we propose a multi-variable CCL method (MCCL) in which state occupancies of Markov model are included with membrane potential as the control quadratic parameters to determine the time-step adaptively. Using fixed time-step RK4 as a reference, MCCL combined with HOS solver has 17.2 times speedup performance with allowable errors 0.6% for Wild-Type Na+ channel with 9 states (WT-9) model, and it got 21.1 times speedup performance with allowable errors 3.2% for WildType Na+ channel with 8 states (WT-8) model. It is concluded that MCCL can improve the simulation instability problem induced by a large time-step made with CCL especially for high stiff Markov model under allowable speed tradeoff.

Advance of exosomes in ischemic stroke / 中国病理生理杂志

Stroke is one of the major causes of death and disability in China and even worldwide.At present, treatment of stroke has been traditionally focused on reducing death of ischemic cells.However,clinical trials have shown that none of neuroprotective drugs tested achieve clinical benefit after acute stroke.Exosomes are 30~100 nm extracellular vesicles derived from cells with cell membrane structure.Many studies suggest exosomes play essential roles in intercellular communication by transferring their cargo between source and target cells in brain.Emerging data show that exsomes also make a contribution to brain recovery via regulating highly interactive process pathway after stroke.Here,we review these advances and highlight the potential therapeutic functions of exosomes in brain remodeling after stroke.