Biomedical Engineering Reference
In-Depth Information
the impact of large vessels with relatively long equilibration
lengths. [40, 98] have analyzed various types of vessels, includ-
ing counter-current networks, by modeling them discretely, and
have established some relations concerning the equilibration
and entrance lengths. They consequently developed the DIscrete
VAsculature (DIVA) model [98] as they concluded that it can
be important to model vessels individually. The DIVA model
has been extended [129] to also cover highly thermo-conductive
thin structures such as pacemaker wires (resulting in faster and
more accurate simulations) and 1D boundary conditions (e.g.,
water-cooled ablation catheters).
Although it has been shown that detailed vessel networks
can be relevant at more than just the local scale [173], the neces-
sary information for segmentation is not readily available from
standard medical imaging. It has been proposed that incomplete
segmented vessel information from a specific patient can be
extended by artificially grown (counter-current) vessel trees [38,
98] using fractals or a potential steered growth approach.
Large vessels have been modeled in [84, 109, 114, 177, 183],
sometimes up to explicitly solving the Navier-Stokes equation
to obtain a realistic flow distribution. [183] has even developed a
special meshing technique for this purpose. [63] has shown that
the impact of vessels can be interpreted as superdiffusion and
suggests modeling it with a nonlocal term. [36] has studied how
the convection coefficient relating the blood temperature in the
vessel to the temperature distribution in the neighboring tissue
depends on the size of the heated region and the flow rate.
Multiple experiments have been performed to compare vari-
ous blood-flow models with reality. Some of them are reviewed
in [97], which itself presents experiments testing the Pennes
model and an effective conductivity model (extending the
numerical analysis in [96]) and finds supporting evidence for
both approaches. The importance of large vessels is analyzed,
and the concept of thermally significant vessels is examined in
detail. [27] compares the Pennes, the Weinbaum-Jiji, and the
simplified Weinbaum-Jiji models to experimental data, con-
cluding that the Pennes model should be used in the vicinity of
vessels with diameters larger than 0.5 mm, while elsewhere the
Weinbaum-Jiji models, which are found to deliver comparable
results, are to be preferred. Similar results have been obtained
by [2]. [78] deduces from experiments that vessels with diam-
eters larger than 0.2 mm are thermally significant. A detailed
numerical experiment [155] simulating a branching vasculature
model with 10 generations of vessels concludes that (1) vessels
have a strong impact, (2) the flow rate and influx temperature
are important, while the diameter and Nusselt number play a
lesser role, (3) arteries have a stronger impact than veins, and (4)
which vessels are relevant has to be decided on a case-by-case
basis. [39] compares the modeling of vessels using convective
boundary conditions and detailed flow simulation with experi-
ments, finding only minor differences for the specific case
studied. [148] has compared the Pennes model with the model
by Jain (perfusion dependent conductivity [85]) and a simple
Dirichlet boundary condition approach at vessel surfaces,
concluding that the Dirichlet boundary might be appropriate
for large vessels, while the Jain model is most suited for small
vasculature.
The thermal solver implemented in HYCAT allows the flex-
ible combination of convective flow distributions (from CFD
calculations) or variable boundary conditions in major vessels
with complex flow patterns (e.g., aorta), DIVA-like discrete ves-
sel modeling for smaller vessels, and an effective thermal con-
ductivity model for the microvasculature [122]. MRI perfusion
maps can be used to account for inhomogeneous tissue perfu-
sion within a tissue.
The temperature dependence of tissue parameters is discussed
in [14, 23, 79, 106,122, 159]. [122] suggest a first-order approxi-
mation to the impact of temperature on the SAR distribution.
The impact of skin temperature and the temperature of the
hypothalamus on the perfusion rate is considered in [14, 107],
including sweating. The influence of tissue damage on the tis-
sue parameters can be found in [79, 159]. Refer to Section 7.9 in
this chapter for more information on the modeling of tempera-
ture and tissue damage dependent tissue parameters, where the
effects related to evaporation are also discussed. [195] describes
how the tissue water content varies with temperature. [134] has
developed a thermo-pharmacokinetic model describing the
interaction between temperature and the concentration of vaso-
dilating agents and their effects.
Whole-body models have been proposed [25, 26, 59, 88] to
account for nonlocal thermoregulation, heart rate dynamics,
heat radiation at the surface, moisture at the skin's surface and
sweating, clothing, skin blood flow effects, and changes of the
body core temperature. [26] has presented an interesting model
of a limb heated by a hyperthermia applicator. While the limb
is simulated in detail (including a separate simulation of arte-
rial and venous blood temperature along the limb, sweating, and
temperature-dependent tissue parameters, with muscle perfu-
sion reacting with a time delay to temperature increases and the
skin perfusion depending on the local as well as the averaged skin
temperature), the rest of the body is considered by coupling the
limb to a whole-body model. However, such whole-body models
require a large number of additional parameters, introducing fur-
ther uncertainty and making their routine application tedious. A
simple model for body core heating due to the absorption of EM
energy by blood has been proposed by [81] and is implemented in
the thermal solver of HYCAT. Such a model could easily be cou-
pled to more complex models of whole-body thermoregulation.
Various numerical methods can be used to obtain the tem-
perature distribution. If only the steady state is required, the
problem is essentially reduced to solving a Poisson equation.
Various methods are routinely applied to solve the discretized
equation [46]: Jacobi's method, successive over relaxation, con-
jugate gradient, or fast Fourier transformation based methods.
[50] has developed a nonlinear, elliptic, multilevel FEM method
to solve nonlinear heat equations. For the discretization, finite
differences, finite element, and boundary element [164] meth-
ods are used. [17] uses a hybrid approach, modeling the vessels
with FDTD and the tissues with FEM. To obtain the transient
temperature field evolution, FDTD or FEMTD (Finite Element
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