Muehsam David J, Pilla Arthur A
Department of Biomedical Engineering, Columbia University, New York, New York, USA.
Bioelectromagnetics. 2009 Sep;30(6):462-75. doi: 10.1002/bem.20494.
We have previously employed the Lorentz-Langevin model to describe the effects of weak exogenous magnetic fields via the classical Lorentz force on a charged ion bound in a harmonic oscillator potential, in the presence of thermal noise forces. Previous analyses predicted that microT-range fields give rise to a rotation of the oscillator orientation at the Larmor frequency and bioeffects were based upon the assumption that the classical trajectory of the bound charge itself could modulate a biochemical process. Here, it is shown that the thermal component of the motion follows the Larmor trajectory. The results show that the Larmor frequency is independent of the thermal noise strength, and the motion retains the form of a coherent oscillator throughout the binding lifetime, rather than devolving into a random walk. Thermal equilibration results in a continual increase in the vibrational amplitude of the rotating oscillator towards the steady-state amplitude, but does not affect the Larmor orbit. Thus, thermal noise contributes to, rather than inhibits, the effect of the magnetic field upon reactivity. Expressions are derived for the ensemble average of position and the velocity of the thermal component of the oscillator motion. The projection of position and velocity onto a Cartesian axis measures the nonuniformity of the Larmor trajectory and is illustrated for AC and combined AC/DC magnetic fields, suggesting a means of interpreting resonance phenomena. It is noted that the specific location and height of resonances are dependent upon binding lifetime and initial AC phase.
我们之前运用洛伦兹 - 朗之万模型来描述弱外磁场通过经典洛伦兹力对束缚在简谐振子势中的带电离子的影响，其中存在热噪声力。先前的分析预测，微特斯拉范围的磁场会使振子取向以拉莫尔频率旋转，并且生物效应是基于束缚电荷本身的经典轨迹可以调节生化过程这一假设。在此表明，运动的热分量遵循拉莫尔轨迹。结果表明，拉莫尔频率与热噪声强度无关，并且在整个束缚寿命期间，运动保持为相干振子的形式，而不会演变为随机游走。热平衡导致旋转振子的振动幅度朝着稳态幅度持续增加，但不影响拉莫尔轨道。因此，热噪声有助于而非抑制磁场对反应性的影响。推导了振子运动热分量的位置和速度的系综平均值的表达式。位置和速度在笛卡尔轴上的投影测量了拉莫尔轨迹的不均匀性，并针对交流磁场和交流/直流组合磁场进行了说明，这暗示了一种解释共振现象的方法。需要注意的是，共振的具体位置和高度取决于束缚寿命和初始交流相位。
