Page 255 - Computational Modeling in Biomedical Engineering and Medical Physics

244 Computational Modeling in Biomedical Engineering and Medical Physics

The EMF heating effect that seems to accompany the MFT, is described by the
energy equation
@T
ρC p 1 rUq 5 Q 1 Q perfusion 1 Q met ; ð7:12Þ
@t
where ρ is the mass density, C p is the specific heat at constant pressure, T is the temperature,
2 3
q 52 krT [W/m ]isthe heatflux, k is the thermal conductivity, Q [W/m ] is the heat
3
source (EMF source, volumetric loss density), and Q met [W/m ]is the metabolicheatsource
3
(neglected here). The bioheat term, Q perfusion [W/m ] (Chapter 1: Physical, Mathematical
and Numerical Modeling) accounts for the heat in/outflow through perfusion. It will be
concluded later that it may be ignored. The thermal properties of the constituent anatomical
regions, listed in Table 7.4, are volume-weighted average values.
The anatomic structure is initially in thermal equilibrium (37 C) and heating starts

when the applicators are energized. The boundary condition that closes the heat trans-
fer problem is convection

q 0 5 hT ext 2 Tð Þ; ð7:13Þ
2 2
where q 0 [W/m ] is the inward heat flux, h is the heat transfer coefficient (2 W/[m K]),
and T ext is the ambient temperature (20 C).

Insignificant heating by MFT is seen after 15 min, when the temperature rise seems
to stabilize, Fig. 7.14C. The procedure may take longer (60 80 min), but the situa-
tion is unlikely to change. The occurrence of the bioheat term could only strengthen
this inference, because the perfusion driven convection would act to cool the regions
down to the biological equilibrium temperature—unaffected by the MFT power level,
3
here B79.4 W/m (Baerov et al., 2020).
The applicators themselves may warm up thetissue, whichcould producemildlocal
heating. However, this effect depends also on the frequency used but MFT (100 Hz) is not
used for a thermal effect. It may then be inferred that MFT is a safe method for healing
bone tissue even when an implant is present, a plate with screws, or an external fixation.
From the understanding of the underlying physics and processes, the optimization
of the pending equipment and procedures, and the evaluation of the possible side
effects, mathematical and numerical modeling are valuable means that may add pre-
dictive value to the medical diagnose associated with the MS and therapy methods.
The structural and functional complexities of the anatomic entities under analysis
require consistent models related to computational domains—from simpler CAD
constructs to detailed anatomic reconstructions—that may produce relevant results.
For each aspect of concern, some solutions compete with the multiscale nature
(space and time) of the problems and the available computational resources.
Thereforeitisalwaystofindthe trade-offthatsatisfactorilyaccommodatesall these
constraints and objectives intractable computational endeavors.