# Sensor Systems

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methods:temperature:corebodytemperature

# Core Body Temperature

Measuring the body temperature of a person is not as easy as it seems. The methods to measure temperature in the mouth or under the armpit are always a compromise for the real core body temperature. Nowadays, there are applications where we need 24/7 monitoring of temperature in daily life with a sub degree precision. These applications are related sleep and chronobiology research. There is a promising method that uses the measured heat flow on the human skin to estimate the temperature of the inner body.

This project is partially developed as a student project.

## Background

The measurement of the temperature of a human body is used for many applications. It is not only used to detect fever, but also to measure the “circadian rhythm ”, which is the day-night variation of human physiology1). Also for sleep studies, also temperature of the core body and the extremities (arms, legs) plays a crucial role. The most common method to measure temperature is a mercury thermometer or an electric component like an NTC or thermistor. To measure fever, we can accept some inaccuracy and therefore it is possible to measure in either the ear, rectum or arm-pit2). For core body temperature estimation to measure day-night rhythms we need a higher accuracy on degree level. This can no longer be done with a mercury thermometer under the armpit or in the mouth. Also for applications where we want to measure temperature in real life, at normal work, it is problematic to use classical thermometers.

## The heat flux method

One method to measure the core body is the use of the heat flow method3)4). This method is based on the understanding of a temperature measurement illustrated in figure 1. Fig. 1: A thermal model for a skin temperature measurement

The human body can be seen as a heater with a buffered temperature $T_{Core}$. This is the temperature of interest, but cannot be measured directly for practical reasons . This core body temperature is defined somewhere in the thorax, and will not be the same in all body parts and body surface. There is a thermal resistance between the core and the point of measurement $T_{1}$. We call the effective thermal resistance RCore. We can only measure at a certain location where we measure $T_{1}$. This $T_{1}$ is not equal to $T_{Core}$ because there is a heat flow through $R_{Core}$. The heat flow is dependent on the body parameters $T_{Core}$ and $R_{Core}$, but also on the environmental temperature and the thermal resistance of the probe.

What we measure is

\begin{equation} T_{1} = T_{External} + \left ( T_{Core} - T_{External} \right ) \frac{R_{Shunt}}{R_{Core}+R_{Shunt}} \label{eq:TemperatureEquation} \end{equation}

where in fact $R_{Core}$ is unknown. The thermal resistance RShunt is unknown as well, but could be determined by calibration. In the heat flow method we avoid the need for the quantitative value of the thermal resistors. If we make $T_{External}$ equal to $T_{Core}$, then the heat flow becomes zero. In practice this works as follows: if we put a heater on the human skin and we heat until $T_{1} = T_{2}$, then we know that the heat flow is zero. So, when the heat flow is zero ($T_{1} = T_{2}$), we know that the core body temperature is equal to the imposed temperature of the heater, so equal to $T_{2}$.

This can be technically implemented as shown in figure 2. On the bottom is the human skin. We have two temperature sensors (thermistors) “1”. Medium “3” is a probe material with a similar thermal resistance as the human body. Number “2” is a heater. Note that now the outside temperature is not important anymore, we simply heat until $T_{1} = T_{2}$. Fig. 2: Construction of the heat flow probe from Kobayashi et.al.

1)
Michael Smolensky, Lynne Lamberg, The Body Clock Guide to Better Health: How to Use your Body's Natural Clock to Fight Illness and Achieve Maximum Health Paperback, Henry Holt and Company (2001)((Kurt Kräuchi , How is the circadian rhythm of core body temperature regulated? Clin Auton Res (2002) 12:147–149 http://www.chronobiology.ch/wp-content/uploads/publications/2002_02.pdf
2)
P. Fulbrook, Core temperature measurement: A comparison of rectal, axillary and pulmonary artery blood temperature, In: Intensive and Critical Care Nursing, Volume 9, 1993, Issue 4, Pages 217-225
3)
T. Kobayashi, T. Nemoto, A. Kamiya, and T. Togawa, Improvement of deep body thermometer for man. Annals of Biomedical Engineering, 1975, 3, 181-188
4)
Medical body core thermometer, United States Patent Application 20050043631 http://www.google.com/patents/US20050043631 