Page 73 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

50 BIOMECHANICS OF THE HUMAN BODY

Silicone Rubber
Strain Relief

2-Wire Lead With
Twisted Shield
Water Resistant Probe
Epoxy Length
as
Desired
Glass Fiber
Reinforcement
Thermistor
(0.25 mm Dia.)

0.3 mm, Nominally

FIGURE 2.7 Sketch of a thermistor bead probe. [From Xu et al. (1998), with permission.]

process are described as

∂ T 1 ∂ ⎛ ∂ T ⎞
ρC t = k t ⎜ r t ⎟ + ωρCT −( a T +) q p
t
t ∂ rr ∂ ⎝ r ∂ ⎠ (2.18)
t = 0 0 T = T r ()
t
ss
where q is the pulse heating deposited locally into the tissue through a very small thermistor bead
p
probe as q p =P δ(0) for t ≤ t ; q =0 for t > t . P is the deposited power, and δ(0) is the Dirac delta
p
p
p
function. Before the measurement, the steady-state temperature distribution T (r) in the sample
ss
should satisfy the one-dimensional steady-state conduction equation without the pulse heating. The
governing equation for T (r) is given by
ss
1 d ⎛ dT ⎞
CT
0 = k t r ss + ωρ ( a − T ) (2.19)
ss
r dr ⎝ dr ⎠
Subtracting Eq. (2.19) from Eq. (2.18), and introducing θ= T − T , one obtains
t ss
∂ θ 1 ∂ ⎛ ∂ θ⎞
C +
ρC = k t ⎜ r ⎟ + ωρ θ q p
t ∂ rr ∂ ⎝ r ∂ ⎠ (2.20)
t = 0 θ = 0