# Improved Smart Pillow for Remote Health Care System
## 1 Introduction
### Evolution of Measurement of Core Body Temperature (MCBT)
\(T_{1}\), \(T_{3}\) form a channel with thermal resistance \(R_{1}\) while \(T_{2}\) and \(T_{4}\) forms the other with thermal resistance \(R_{2}\). The rubber sponge is selected as an insulation layer and copper is chosen for its good conduction properties. The upper side of probe with \(T_{1}\) and \(T_{2}\) will be closest to the skin. If CBT is \(T_{c}\), \(R_{s}\) is the thermal resistance of skin and the subcutaneous tissue. Figure 1: The diagram of ZHF, with the sensor with the silicone rubber and under the heater. The heat flow for the two channels is:  
\[q_{1}=\frac{T_{1}-T_{3}}{R_{1}}=\frac{T_{c}-T_{1}}{R_{s}},q_{2}=\frac{T_{2}-T_{4} }{R_{2}}=\frac{T_{c}-T_{2}}{R_{s}} \tag{1}\]  
\(R_{s}\) is variable depending on the subject, so it is removed from the formula and \(T_{c}\) is the target:  
\[T_{c}=T_{1}+\frac{(T_{1}-T_{2})(T_{1}-T_{3})}{K(T_{2}-T_{4})-(T_{1}-T_{2})},K= \frac{R_{1}}{R_{2}} \tag{2}\]  
Theoretically, \(R\) is proportional to the height of rubber sponge if the material is homogenous, so \(K\) can be calculated via measurable heights, but the heat flux dose exists in both a vertical and horizontal direction. \(K\) can be attained by experimental work and calculated as:  
\[K=\frac{(T_{c}-T_{2})(T_{1}-T_{3})}{(T_{c}-T_{1})(T_{2}-T_{4})} \tag{3}\]  
[PERSON] et al. [8] suggest that \(K\) is sensitive to ambient temperature, and [PERSON] et al. [9] find that the thickness of skin and subcutaneous tissue layer affects the results. Both sources review the performance of DHF equipment they manufactured. [PERSON] et al. concluded that the results of DHF and ZHF are very similar, with the correlation coefficient between the two methods being 0.970 (\(p<0.001\)). [PERSON] et al. determined the system had the potential for reliable continuous CBT measurement in rest and could reflect CBT variations during exercise. Notably, the distinct difference between ZHF and DHF is with or without a heater, but DHF still needs to wire all the sensors to a Micro-Controller Unit (MCU) to detect the thermal equilibrium. Considering the strict insulation that DHF needs, it is not possible to embed the MCU inside the rubber sponge, which reduces the convenience and flexibility of DHF. The other issue of DHF is the initialization time, as without a heater, DHF needs more time to reach thermal equilibrium compared to ZHF, with experimental results showing the initial time for ZHF is about 15 min and DHF is 25 min. [PERSON] et al. [10] tried to improve the DHF by employing multiple Artificial Neural Networks (ANN), as they modeled the relationship among human body temperature, skin temperature and the ambient temperature for ANN, but the balance of computational load and reaction time became an issue when applying ANNs. [PERSON] et al. [11] optimized a wearable deep body thermometer based on DHF in its structure. They first simulated the improved structure in theory by finite element analysis method, then implementing the prototype and verifying the efficiency in experiment by mimicking skin temperature. They found that the improved structure of thermometer can reach an accuracy error rate about 0.3 \({}^{\circ}\)C, with a similar result to Draeger based on ZHF. [PERSON] et al. [12] present various body temperature measurement techniques and discuss the types of wearable devices for patient monitoring. [PERSON] [13] described a framework combining a smart-phone app and Wearable Sensors for Smart Healthcare  
Figure 2: The diagram of DHF, with the copper material situated around the rubber sponge. Monitoring System (SW-SHMS) for elderly people. One of the main layers in the proposed system is the patient layer, also named wearable devices, which includes skin temperature sensors and Bluetooth is the preferred wireless communication protocol. They are concerned with the latency and packet loss. A smart aging system is presented by [PERSON] et al. [14], as they employ the hidden wellness parameter to implement well-being monitoring and anomaly detection.