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Hyperthermia and ablation 255

level may be adjusted to provide for a local overheating of the tumor, while avoiding
in as much as possible the damage of the neighboring healthy tissue.

Thermal ablation of a kidney tumor
EMF ablation, either RF or MW, is used to extirpate kidney cancer (Mayo Clinic),
and its success may rely on a preoperative assessment, where numerical simulation is a
useful, convenient, affordable, and accurate mean. On the other hand, the structure of
the kidney is complex (Layton, 2013; TBQ Editors, 2013), and some of its functions
are still not fully elucidated. At this time, a consistent physical model for it is still a
desideratum, and some convenient, reasonable yet realistic assumptions are required.
Along this line, the kidney and the tumor (tissue and capillaries) are assumed here to
be a saturated porous media (Durlofsky and Brady, 1987; Truskey et al., 2004), hemo-
dynamically connected to the local, embedded hepatic arterial and venous trees
(Bachmann et al., 1965). A one-temperature model, meaning that the solid phase of
the porous medium and the plasma are in local thermal equilibrium, would be a fair
realistic choice. The actual multiscale, directional blood flow is replaced by an equiva-
lent directional flow whose convective contribution to the heat transfer replaces the
average perfusion-related source term in the energy equation as per the bioheat
homogenization-based analysis (Chapter 1: Physical, Mathematical, and Numerical
Modeling ), which is a more common approach. The two methods lead to different
predictions, and to evidence discrepancies, we consider the RF ablation (Knavel and
Brace, 2013; Zagoria, 2004). An order of magnitude analysis of the time scales of the
three concurring “physics” may suggest stationary forms for the EMF and the hemo-
dynamic flow and transient form for the heat transfer (Dobre et al., 2017).

Mathematical modeling
Medical image-based reconstruction techniques fused with CAD constructs
(Chapter 2: Shape and Structure Morphing of Systems with Internal Flows) might
render (if possible) the complex morphology of the kidney, resulting in a computa-
tional domain. Here, to prove the concept and to provide a glimpse in the pending
physics, a CAD computational domain [e.g., by using Dassault Systemes, 2016] that
mimics as realistically as possible an adult kidney may be found satisfactory (Fig. 8.1).
Each kidney receives a renal artery but up to six arteries may exist (Bacmann). The
renal artery here splits into two daughters to supply the kidney: the upper (UD), and
lower (LD) divisions (Wacker et al., 2018), which in turn split into two smaller arteries
each. These constructs mimic the natural morphological branching (bifurcations,
lengths, and diameters of the “mother”/“daughters” segments), consistently with the
allometric laws (Chapter 1: Physical, Mathematical, and Numerical Modeling and
Chapter 2: Shape and structure morphing of systems with internal flows) (Bejan, 2000;