Fingertip Model for Blood Flow and Temperature - Computational Biomechanics of the Musculoskeletal System - page 314

23.6 PRedIcTIon of TeMPeRaTURe oScIllaTIonS
afTeR THe conTRalaTeRal coolIng TeST
For the computation of Darcy's velocity, we adopted the following empirical equation to compute
the permeability, which is determined by the porosity ϕ :

D ϕ

ϕ

23

k = 180(1 (23.25)

− )

2

where D is the diameter of the microvessels. The temperatures of larger arteries and veins were set
to be constant, and were the same as those in the DTM simulation.
The porosity j in the model is defined as the volume ratio of microvessels to the tissue volume,
which varies with the density of the capillary network. For this, values of 0.2, 0.5, and 0.6 were
adopted as the porosities of bone, tissue, and the fingertip when the human hand is in a thermally
comfortable state. Vasodilation and vasoconstriction in the tissue are two important control pro-
cesses of the human thermoregulatory system, and they may be modeled as sinusoidal variation in
porosity from the thermal neutral value. If the mean skin temperature is assumed to be the sensory
signal for vasomotion, the periodic change in porosity can be expressed as follows (Tang et al. 2013):

n

∑

ϕϕ =1+sin (2 A π f ⋅ t ) ⋅ e

(-32)/50 T

(23.26)

0 i i

i = 1

where j 0 is the value in the thermal neutral state, f i is a frequency of internal activity such as
endothelial regulation that leads to vasomotion, A i is the amplitude of the corresponded frequency,
and n is the number of internal activities including neurogenic and endothelial oscillations. 32°C
is adopted as the thermal neutral temperature of skin. Without consideration of internal activities,
j will become an exponential function of the single variable T , as shown in Figure 23.11. It can be
seen that if the initial porosity is set to be 0.5, the porosity at 25°C will become 0.4. If the initial
porosity is set to be 0.6, the porosity at 25°C will become 0.5, which gives reasonable variation
ranges.

0.8

φ 0 = 0.6
φ 0 = 0.5

0.7

0.6

0.5

0.4

0.3

0.2

0 5 10 15 20 25 30 35 40

Temperature

fIgURe 23.11 Variation in porosity with tissue temperature without considering periodic vasomotion
according to Equation 23.26.