Duck Physical Properties of Tissues

A Comprehensive Reference Book
1. Auflage 2013
ISBN: 978-1-4832-8842-0
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 336 Seiten

This unique reference book describes quantitatively the measured and predicted values of all the physical properties of mammalian tissue. Reported measurements are thoroughly documented and are complemented by a range of empirical mathematical models which describe the observed physical behavior of tissue.**Intended as a broad-ranging reference, this volume gives the bioengineer, physicist, radiologist, or physiologist access to a literature which may not be known in detail. It will also be of value for those concerned with the study of a range of environmental radiation hazards.Most extensive compilation of values of physical properties of tissue**Presents data for thermal, optical, ultrasonic, mechanical, x-ray, electrical, and magnetic resonance properties**Comprehensive bibliography

Autoren/Hrsg.

Duck, Francis

Leseproben

Chapter 2

Thermal Properties of Tissue

Publisher Summary

This chapter discusses thermal conduction through tissue and its heat capacity. A variety of methods may be used to measure the thermal properties of tissue samples; the techniques used may be categorized as invasive or noninvasive, and in each case, it may enable steady-state or non-steady-state measurements to be made. Also, a set of semi-invasive techniques has been investigated in which temperatures have been measured using cutaneous and subcutaneous thermocouples with surface heat fluxes provided by various non-invasive sources. On the other hand, totally noncontact methods use external radiation to heat tissue and observe the subsequent time-course of skin temperature with a radiometer. The thermal conductivity, k, of tissues at temperatures above freezing may increase while showing a very slight positive temperature coefficient. It is generally recognized that tissues may be considered more accurately for thermal analysis as being composed of water, protein, and fat. Subsequently, thermal conductivity may then be expressed as , and ?n are thermal conductivity, density, and mass fraction of the nth component respectively and ? the density of the composite material. While for temperatures below freezing, the specific heat of tissues, C, varies markedly with temperature in a manner depending strongly on the tissue water content. For the calculation of thermal capacities, the following equation may be used: where ?n is the mass fraction of the nth component and Cn its specific heat.

Heat transport in materials may occur by conductive, convective or radiative processes. In this chapter, thermal conduction through tissue is described, together with its heat capacity. Convective heat transport is discussed only when relating thermal conductivity to tissue perfusion. The properties of tissues related to radiant heat are dealt with in Chapter 3.

2.1 Thermal conductivity, thermal diffusivity and thermal inertia

2.1.1 Terminology and definitions

The thermal conductivity, k, of a substance is defined as the quantity of heat, Q, transmitted due to a unit temperature gradient, in a direction normal to a surface of unit area in unit time under steady–state conditions and where heat transfer is dependent only on the temperature gradient.

(2.1)

where ?T/?x is the temperature gradient in the direction of heat flow, and A the cross–sectional area. The negative sign indicates that the heat flux is in the direction of decreasing temperature. The SI unit for thermal conductivity is watt per metre kelvin (W m-1 K-1). Other units, and conversion factors are given in Table 2.1.

Table 2.1

Conversion factors for thermal units

Where steady–state conditions are not relevant, the quantity thermal diffusivity, a = k/?C, is used, where C is the specific heat capacity and ? is the density, a is related to the spatial and temporal variation of temperature, T, in the medium by

(2.2)

The numeric value of a determines the relative time rate of temperature change, and is thus a measure of the ability of a thermally perturbed system to relax back to steady–state conditions. The SI unit for a is metre2 per second (m2 s-1). Other units, and conversion factors are given in Table 2.1.

Living tissue is perfused, and the passage of blood modifies the heat transfer process. Furthermore, metabolic processes generate heat within the tissue. A formulation taking these factors into account has been given by Pennes (1948) and Perl (1962) as follows:

(2.3)

where mb, Cb and Tb are the mass flow rate, specific heat and temperature of the perfusing blood respectively, and Qm is the rate of metabolic heat production. Equation 2.3 is the so–called bio–heat equation. The measurement of thermal conductivity using thermal clearance methods has been widely used as a technique to estimate tissue blood flow both of the skin and of deeper tissue. A practical quantity, the effective thermal conductivity, keff, is used under these circumstances to give an equation with a parameter which is flow dependent.

(2.4)

keff is found to vary proportionally with the square root of the perfusion rate (Jain 1979).

An equivalent effective thermal diffusivity, aeff = keff/?C, can also be defined.

Another thermal quantity, that of thermal inertia, was introduced by Buettner (1951) in considering the thermal response of skin during exposure to radiation. The temperature rise, ?T, at the surface of an opaque semi–infinite solid following irradiation during time t is:

(2.5)

where H is the irradiating intensity and A the surface absorptance. The product k?C is termed the thermal inertia and has SI units of watt2 second per metre4 kelvin2 (W2 s m-4 K-2). Other units and conversion factors are given in Table 2.1.

2.1.2 Measurement of thermal conductivity

An extensive review of methods which may be used to measure the thermal properties of materials is given by Touloukian (1964), and a useful summary of methods relevant for biological materials given in a general survey by Bowman (1975). The techniques used may be categorised as invasive or non–invasive, and in each case may enable steady–state or non–steady–state measurements to be made. Historically, many measurements of k were made using a guarded hot plate (e.g. Poppendiek , 1966). The experimental geometry is intended to ensure that heat flow between two conductive plates is entirely in the axial direction of the specimen. Equation 2.1 is applied directly to calculate k. The method has been applied exclusively to samples of tissue. More recently, invasive probes have been developed which involve the implantation within the specimen of heat sources (or sinks) which may also serve as temperature sensors. Invasive thermal diffusion methods use a heated thermocouple (e.g. Grayson , 1971) or a thermistor probe (Chen , 1981; Balasubramaniam and Bowman, 1977; Valvano , 1984). The thermistor probe, typically 0.5 mm diameter, is inserted into the tissue through a hypodermic needle, which is then removed to minimise the heat conduction along the metal. The thermistor is first used passively to measure the ambient temperature, and then heated. The electrical power required to maintain the thermistor at a steady temperature is related to the effective thermal conductivity of the surrounding tissue (Valvano , 1984). Alternatively, the time change of temperature following a transient pulse of energy to the probe is analysed (Chen , 1981). In either case the method depends upon adequate modelling of the thermal characteristics of the probe and surrounding tissue. In spite of the possible criticism that some tissue damage may occur during probe insertion and cause some modification in thermal behaviour, reliable values have been obtained using these probes in both perfused and non–perfused tissues.

A set of ‘semi–invasive’ techniques has been investigated in which temperatures have been measured using cutaneous and subcutaneous thermocouples with surface heat fluxes provided by various non–invasive sources. Henriques (1947) and Hensel and Bender (1956) describe the use of contact heating. Other techniqes have used electromagnetic irradiation: for instance infrared (Dersken , 1957), microwave (Cook, 1952) or optical radiation (Kraning, 1973).

Completely non–invasive methods depend upon the fact that when two homogeneous solids initially at different temperatures are brought into contact the interface temperature takes an intermediate value dependent upon the thermal inertias of the two contacting bodies. Tanasawa and Katsuda (1972) have used a technique based upon that described by Vendrik and Vos (1957). Totally non–contact methods use external radiation to heat tissue, and observe the subsequent time–course of skin temperature with a radiometer. Results of measurements of k?C using this method of measurement have been reported by Lipkin and Hardy (1954), Dersken (1957) and Kraning (1973) and have been used to give estimates of k using the assumption that ?C for tissue has the same value as that for water.

2.1.3 Historical background

Earliest measurements of the conduction of heat through skin were reported by Klug in 1874. Bordier (1898) showed that beef muscle conducted heat almost twice as well as fat. A value of 5 × 10-4 cal cm-1 s-1 °C-1 was given by Lefevre (1901) for the average conductivity of peripheral tissues in man, based on the assumption that the thermal gradient extended 20 mm inwards from the skin surface. Subsequent work has been tabulated by Chato (1969) and with...