NumaIRE Module

This is a macro-scale IRE solver based on solving Laplace's equation with a deposition-dependent electric conductivity (using a similar approach to e.g. Garcia et al, 2014).

The IRE protocol is formed of a sequence of pairings of in situ needles. For instance, six needles may be attached to the generator and placed in the liver, preferably to be parallel. The protocol may be, say, nine consecutive pairings of needles with one as acting an anode and another as a cathode. The remainder are inert for that protocol step.

As each step is treated as a steady-state problem, we use timestepping to move from one pair to the next - in the example above, we use nine timesteps.

Global Parameters

Parameter	Location	Type	Default	Description
Anode	Simulation	Integer Array (size N)	-	This is a list of boundary IDs, one for each timestep, indicating the erstwhile anode boundary (req)
Cathode	Simulation	Integer Array (size N)	-	This is a list of boundary IDs, one for each timestep, indicating the erstwhile cathode boundary (req)
Potential Consecutive Values	Simulation	Real Array (size 2xN)	-	The first row lists potential values on the anode, the second those on the cathode

The Anode, Cathode and Potential Consecutive Values arrays must be the same length, with the PCV array having two rows.

AlternatingBCSolver (libnuma-ire)

This is an upstream version of NumaAlternating, working with two lists of embedded boundaries, switching between a Dirichlet condition and no condition at all. It searches for boundary conditions with an Alternating Boundary Condition parameter set to TRUE and turns them on when the BC's Body Id matches the current Anode or Cathode value.

AlternatingBoundaryCondition

This is a user-defined function that returns the potential Dirichlet condition value based on whether the boundary element to which it is being applied is an anode or a cathode (zero otherwise, but when used in conjunction with the AlternatingBCSolver, this will be ignored).

CoverageCurveOutputSolver

The coverage curve output solver calculates, for each energy deposition level $ E $, the cumulative volume of tumour which has experienced maximum deposition above that level. This is a common way of reporting IRE efficacy as, for a chosen death threshold, the lesion size can be read off a plot.

At each timestep, it outputs a file, "coverage_TTT.txt", where TTT is the timestep. Each line has the format: Threshold (V/cm), Fraction of tumour volume. This solver contains a simple example of succinctly integrating a function over a domain, which may be a useful starting point for other authors.

Parameter	Location	Type	Default	Description
E	-	Variable	-	Most recent energy deposition at a point (req)
Max E	-	Variable	-	Maximum energy deposition at a point (req)
Minimum Coverage	Solver	Real	-	Lowest energy level to calculate (req)
Maximum Coverage	Solver	Real	-	Higher energy level to calculate (req)
Divisions	Solver	Integer	-	Number of energy levels (req)
Tumour	Material	Logical	FALSE	Whether or not this cell should be counted as tumour tissues, that is, whether it contributes to the totals

MaxESolver

Provides the maximum energy deposition over previous time as a variable (MaxE), along with energy deposition at present time (E), electric conductivity based on energy deposition (Electric Conductivity) and survival, based on the Garcia et al, 2014 model relating pulse number to death threshold. Note that the constants here are not based on in vivo human studies, so improved values should be used when available.

Parameter	Location	Type	Default	Description
Joule Heating	-	Variable	-	Output Joule Heating of, say, Elmer's electric potential solver
Pulse Number	Solver	Integer	-	Number of pulses at each protocol step (req)
E0	Solver	Real	399600.0	Modelling parameter in Garcia et al, 2014
A0	Solver	Real	144100.0	Modelling parameter in Garcia et al, 2014
K1	Solver	Real	0.03	Modelling parameter in Garcia et al, 2014
K2	Solver	Real	0.06	Modelling parameter in Garcia et al, 2014