**6. Conclusion**

264 Biomarker

3. Stress response: biomarker increases against stressor, and its rate is linearly depend on

As the most simple and well-consistent with these assumptions, the logistic function is adopted as the basis of this model. The logistic function is a nonlinear ordinary differential equation consisting of the first order of exponential increasing term and the second order of

where *x*, *t*, *a*, and *b* are all positive values representing the concentration of biomarker, time, and increasing and decreasing coefficient respectively. This formula is called a logistic function or growth curve, and it has been applied to describe the exponential growth in the number of bacteria and its decaying, caused by environmental deterioration accompanying

0 9 18 27 36 45 54 63 72 81

0 9 18 27 36 45 54 63 72 81

*dx/dt = (a-bx)x* (1)

[min]

[min]

4. Recovering: biomarker decrease to the basal level after the removal of the stressor.

1. Continuity: biomarker changes continuously in the time series, 2. Homeostasis: biomarker secretion has its upper and lower limits, and

nonlinear decreasing term, as in

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Fig. 11. Simulated biomarker secretion in session A and B.

Concentration

(Simulation)

(b)

Concentration

(Simulation)

(a)

the duration of the stressor, which means non-linear increase of IgA

In this chapter, the salivary biomarker researches as a new metric for human mental stress, its background, methods, experiments, and kinetic model approaches were introduced. Although there are numbers of technical limitation and problems to be solved, biomarkers introduced in this manuscript can be useful and unique measures for human mental states. Stress estimation by salivary biomarkers has a great methodological advantage, because saliva can be collected less-stressfully and in a noninvasive manner unlike blood and urine. Moreover it is the one and the only secretory fluid that can be collected at anytime and by anyone including children and patients in need of nursing care.

On the other hand, mathematical model approach lead us an idea of the estimation of optimal work/break schedule in the limited time avoiding excessive secretion of biochemical substances: for an instance, when one has to take a long-distance drive and reach at a destination within a limited period of time, one could estimate the optimal timing of the stop for the rest. It might be useful for a stress management in the working place as well, such as VDT workload and monitoring work. The molecular analysis techniques are advancing day by day, real-time monitoring of such a tiny amount of biomarkers might be available in the near future. Remember the difficulty of self-management of stress and the necessity of introducing objective criteria. Biomarkers introduced in this manuscript can be a possible solution, even though it still remains in the initial step.
