This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. Several intuitive, visual models of system dynamics are developed.įor the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which provides information towards control of the dissipative process. The Bloch equation also describes a system of three coupled harmonic oscillators, providing additional perspective on dissipative systems. The technique by which the oxygen saturation in the blood is determined is called pulse oximetry.Trajectories for initial vector M 0 acted upon by propagator e − Γ t are displayed in the coordinates developed as the natural system for describing propagator dynamics. Your oxygen saturation levels may also be lower if you live in an area with high elevation. Your health care provider will let you know what levels are acceptable. If you have a lung disease like COPD or pneumonia, your normal oxygen saturation level may be lower. Measurement of heart rate and oxygen level with pulse oximetry are very important factors in accessing the condition of the human cardiovascular system.įor most people, a normal pulse oximeter reading for their oxygen saturation level is between 95% and 100%. If you have an existing lung condition, check with your doctor about what your readings should be. The oxygen level may be lower in some people with lung conditions, even when they feel fine. On the other hand, the percentage of arterial blood saturated with oxygen helps determine the effectiveness of a patient’s respiratory system. Heart rate varies significantly between individuals based on fitness, age, and genetics. Athletes typically have lower heart rates than less active people.īabies have a much higher heart rate, around 120 bpm, while older children have a heart rate of around 90 bpm. The heart rate of a healthy adult at rest is around 75 (☑5) (or more for women) beats per minute (bpm). The purpose is to examine how the patient’s heart rate and oxygen saturation change and then processed and displayed them in charts. Heart rate and oxygen level are a pair of biometric data that are monitored to provide information about the health of the body.
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