Biomedical Engineering Reference
In-Depth Information
out interference from individual, environmental and anatomical variations
(Fig. 1.43).
Heat-Conduction Formulas at the Skin Surface.
Under a thermally
neutral condition (around 29
◦
C in the nude, or around 25
◦
C in half-body
exposure), we can write static heat-conduction formulas for the skin sur-
face [67,68]. The parameters of skin-temperature control are composed of
three heat-flux components from the body - radiation (
Qr
), basic evapora-
tion (
Qe
), and heat convection (
Qf
) - and three heat-production components
- conduction from deep body (
Qc
), metabolic heat production (
Qm
), and
blood-flow convected heat (
Qb
). In the thermally neutral condition, equili-
brium is established at the skin surface:
Qr
+
Qe
+
Qf
=
Qc
+
Qm
+
Qb .
(1.5)
The parameters are expressed by the following equations:
Qr
=
Krε
(
Ts
4
Tw
4
)=0
.
805
10
−
10
(
Ts
4
Tw
4
)
,
−
×
−
(1.6)
10
−
2
(
Ts
Ta
)
1
.
25
/D
0
.
25
,
Qf
=0
.
58
×
−
(1.7)
10
−
2
,
Qe
=1
.
85
×
(1.8)
10
−
2
(
Tc
Qc
=
Kc
(
Tc
−
Ts
)
/
3
d
=0
.
93
×
−
Ts
)
/d ,
(1.9)
2
(
Ts−Tm
)
/
10
=1
.
44
10
−
2
Qm
=
Mo
×
S
×
×
×
S
×
2(
Ts
−
Tm
)
/
10
,
(1.10)
Qb
=
αρcV s
(
Tb
−
Ts
)
×
S,
(1.11)
10
−
3
(kcal/m
2
hK);
Ts
(K) is the skin temperature;
Tw
(K) is the wall temperature;
ε
=0
.
98 (emissivity of skin);
D
(cm) is the dia-
meter of a model;
Ta
(K) is the room temperature;
Kc
=0
.
168 (kcal/mhK)
(thermal conductivity of skin);
d
(cm) is the depth of the core temperature
point from the skin surface;
Tm
= 309 (K) (standard tissue temperature);
S
(cm) is the thickness of the skin;
α
=0
.
8 (counter current heat exchange ratio
in warm conditions);
ρc
=0
.
92 (cal/mlK) (heat capacity of blood);
Tb
= 310
(K) (blood temperature in the core); and
Vs
(ml/100 g tissue min) is the
skin blood-flow rate.
These equations become a basic mathematical model for skin temperature
analysis. We can obtain the following and calculate the blood-flow rate of
cutaneous and subcutaneous tissue (
Vs
):
Vs
=[
Krε
(
Ts
4
where
Kr
=4
.
88
×
Tw
4
)+0
.
58
10
−
2
D
−
0
.
25
(
Ts
Ta
)
1
.
25
−
×
×
−
10
−
2
2
(
Ts−Tm
)
/
10
]
/
+1
.
85
×
−
Kc
(
Tc
−
Ts
)
/
3
d
−
Mo
×
S
×
αρcS
(
Tb− Ts
)
.
(1.12)
