Electrochemical Treatment of Tumors

1
Electrochemical Treatment of Tumors

• Speaker Hao-Kai Ken

2
Motivation

• The electrochemical treatment of tumors implies
  that diseased tissue is treated with direct
  current through the use of metallic electrodes
  inserted in the tumor.
• When tissue is electrolyzed, two competing
  reactions take place at the anode oxygen
  evolution and chlorine production.

3
Model definition
4

• This simplified model considers only a 1D model
  of the transport between two points, that is,
  between the two electrodes. The material balance
  for the species i is given by

• where ci is the concentration (mol/m3), Di give
  the diffusivities (m2/s), zi equals the charge,
  Umi represents the mobility ((molm2)/(J s)),
  and Ri is the production term for species i
  (mol/(m3 s)), F denotes Faradays constant
  (As/mol), and V is the potential (V).

5

• The mobility, umi, can be expressed in terms of
  Di, R and T as
• The conservation of electric charge is obtained
  through the divergence of the current density

6

• At the electrode surface (r ra) you specify the
  fluxes for the ionic species that are included in
  the electrode reactions, H and Cl-.
• For the inert ionic species, Na, the transport
  through the electrode surface equals zero. The
  expression for molar fluxes at the boundary for
  the reacting species is

where Ni is the flux, ?ij represents the
stoichiometric coefficient for the ionic species
i in reaction j, and nj is the number of
electrons in reaction j.
7

• Introducing dimensionless pressure, P p/pb, and
  concentration, Cc/cb, (where b denotes the
  reference concentration), you can express the
  current density for the two reactions. For the
  oxygen evolution reaction it is

where j0,I is the exchange current density (A/m2)
and Eeq,I is the standard electrode potential
(V). The chlorine evolution reaction is given by
the expression
8

• Using the input values nI nI 1, ?H,I 1, and
  ?Cl,I 1 gives the fluxes at the electrode
  surface

9

• At the exterior boundary, assume the
  concentration is constant, ci ci0, and the
  potential is set to
• The initial concentration is constant according
  to ci ci0. You obtain the initial potential
  profile from the solution of the domain equations
  and boundary conditions at t 0, yielding

• where t denotes time.

where V0,ra is the potential satisfying jI jII
j0 and ?0 is the conductivity at t 0.
10

• where V0,ra is the potential satisfying jI jII
  j0 and ?0 is the conductivity at t 0.

11
Model Navigator

• Start COMSOL Multiphysics.
• In the Model Navigator select Axial symmetry (1D)
  from the Space dimension list.
• Select the application mode
• Chemical Engineering ModulegtMass
  balancegtNernst-PlanckgtTransient analysis.
• Locate the Dependent variables edit field and
  enter V cNa cH cCl. Click OK.

12
(No Transcript)
13
Constant
14
Scalar expression
15
Geometry modeling

• Select DrawgtSpecify ObjectsgtLine.
• Type 1e-3 6e-2 in the r edit field, then click
  OK.
• Click the Zoom Extents button on the Main toolbar
  to zoom the geometry

16
(No Transcript)
17
Subdomain setting
18
(No Transcript)
19
(No Transcript)
20
Jtot_ora
21
(No Transcript)
22
Boundary Conditions
23
(No Transcript)
24
(No Transcript)
25
-0.4977-0.2567log(t100)
26
(No Transcript)
27
(No Transcript)
28
Mesh generation

• From the Mesh menu open the Free Mesh Parameters
  dialog box.
• Click the Custom mesh size button, go to the
  Global page and set the Maximum element size to
  5e-3.
• Click the Boundary tab.
• Select Boundary 1 and type 1e-5 in the Maximum
  element size edit field.
• Select Boundary 2 and type 1e-4 in the Maximum
  element size edit field.
• Click Remesh, then click OK.

29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
Solution
33
Postprocessing and Visualization

• Open the Domain Plot Parameters dialog box from
  the Postprocessing menu.
• On the General page, select Interpolated times
  and type 06003600 in the Times edit field.
• Click the Line/Extrusion tab and type the
  expression for pH in the Expression edit field
  -log10(cH1e-3).
• Click the Line Settings button, click to select
  the Legend check box, and click OK.
• Click Apply to generate the plot.

34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)