10.3 COUPLED NONLINEAR OSCILLATORS: MODEL OF CIRCADIAN RHYTHMS In Section 9.3.2,
ID: 2076423 • Letter: 1
Question
10.3 COUPLED NONLINEAR OSCILLATORS: MODEL OF CIRCADIAN RHYTHMS In Section 9.3.2, we pointed to the phenomenon distinguishing feature as a of nonlinear oscillators that are coupled together. Since the body contains a number of pacemakers and we have evolved to adapt to the 24-hour rhythm of the light-dark cycle, it follows that several of these circadian oscillators must be entrained to the extemal zeitgeber (or, if translated literally from German, "time giver"). There is a large body of evidence to support this notion. For example, in subjects who have been isolated from all extemal time cues for over 2 months, the sleep-wake and body temperature rhythms become internally desynchronized, with the temperature oscillator assuming a periodicity that is slightly longer than 24 hours and the sleep-wake cycle being prolonged to approximate ly 30 hours. Other physiological rhythms in these subjects then tend to be entrained to either the temperature of two coupled van der Pol oscillators to represent the temperature and sleep-wake pacemakers. Under normal circumstances, both oscillators are entrained to the extemal 24-hour zeitgeber. However, under conditions that simulate temporal isolation, the model exhibits the complex variations in periodicities and relative phasing between the temperature and sleep-wake rhythms that closely resemble empirical measurements. The schematic diagram in Figure 10.17a shows the temperature and sleep-wak oscillators and the mutual coupling between them. Kronauer and coworkers found that it to assume that the synchronizing zeitgeber is applied directly to the sleep- was necessary wake oscillator instead of the temperature system in order to obtain realistic phase relations between them during zeitgeber entrainment. We represent the outputs of the temperature and sleep-wake oscillators by x and respectively. The zeitgeber output is represented by z. The by the following pair of coupled van der Pol equations: model is c (0.50 (0.60 In the above equations, the scaling factor k 24/2r) is introduced so that the intrinsic periods of the (uncoupled) temperature and sleep-wake oscillators would equal 24 hours if the respective angular freq uenciesco, and were each set equal to unity. Similarly, a, is set equal to unity so that the zeitgeber period is 24 hours. The parameters p, and p, represent the stiffness" of the temperature and sleep-wake oscillators, respectively. They determine the of the transient duration of adjustment in phase of each oscillator to that ofthe time constants zeitgeber following release from entrainment or after reentrainment. In our simulations, A, and py are each assigned the value of0.1. F and Fo represent the strengths of the coupling between the temperature and sleep-wake oscillators. Fa and Fo are assigned the values of -0.04 and -0.16, respectively. The relative magnitudes of these values imply that the temperature oscillator has a stronger influence on the sleep-wake oscillator than vice versa. Fa is assigned the value of unity. The SIMULINK implementation of this modelExplanation / Answer
Here we are considering the human body as the subject and I have given the necessary values.
Normal human body temperature, also known as normothermia or euthermia, is the typical temperature range found in humans. The normal human body temperature range is typically stated as 36.5–37.5 °C (97.7–99.5 °F). Though for specific purposes you may consider it to be 37°C.
Please note that the temperature does not remain constant throughout the body and is weighted average of temperatures in
Human Activity on the other hand is calculated in terms of energy requirements.
Energy requirements are calculated from the factorial estimates of PAL. They are converted into energy units (i.e. joules and calories) by multiplying the PAL value by the BMR. In order to express requirements as energy units per kilogram of body weight, this is divided by the weight used in the equations to predict BMR.
For example to calculate the average energy requirement of a female population 20 to 30 years of age with a moderately active lifestyle and a mean body weight of 55 kg ,
BMR (calculated with the predictive equation): 5.45 MJ/day (1 302 kcal/day).
PAL (mid-point of the moderately active lifestyle): 1.85.
Energy requirement: 5.45 × 1.85 = 10.08 MJ/day (2 410 kcal/day), or 10.08/55 = 183 kJ/kg/day (44 kcal/kg/day).
Hope it helps :)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.