In the assembly of a sheet model, additional cables are laid down
on top of the first cable.
Nodes are numbered along the x-axis in each cable, although the
origin node numbers for each cable are (1,NX+1, 2*NX+1 ... (NY-1)*NX+1)
and the terminal node numbers are (NX, 2*NX, 3*NX ... NY*NX).
In the assembly of parallelpiped models, sets of sheets are laid
on top of one another. The corner node numbers for the origin
sheet are: 1 (lower left corner), NX (lower right corner),
(NY-1)*NX+1 (upper left corner) and NX*NY (upper right corner).
Node numbering for the sheet just above the origin sheet starts at
(NY*NX)+1. The corner node numbers in the top level sheet are:
sheet are:
NX*NY*(NZ-1)+1 (lower left corner),
NX*NY*(NZ-1)+NX (lower right corner),
NX*NY*(NZ-1)+NX*(NY-1)+1 (upper left corner)
and NX*NY*NZ (upper right corner).
After cables are laid down, connections are made between nodes
to form the different models.
A 5-point finite difference stencil is used to connect nodes
in sheet models.
A 7-point finite difference stencil is used to connect nodes
in parallelpiped models.
Boundary nodes are set as connections to node number 0.
the specified conductivity is analogous to the term with
in units of and in units of .
With and , the conductivity
parameter would be .
The region concept can also be used to generate an independent mask
file for each region. The mask can then be used to create inhomogeneous
distributions of model parameters in the creation of xxx.inp files
for use in dart simulations.
Specification of percent resistive inhomogeneity
na3d allows randomly distributed point barriers as one
form of nonuniform anisotropy.
A value between 0.0 and 1.0 will be taken as the fraction of connections
at which a high resistance is to be assigned.
A value between 1.0 and 2.0 will be taken as the fraction of
transverse connections
at which a high resistance is to be assigned. Transverse connections are
determined as those connections with cable radius less than 90
of the cable radius for the longitudinal fiber direction.
1. na3d -cx 1.0 -dx 0.01 -gl 4.0e-5 test
A cable with 101 nodes spaced 0.01 cm apart
and a longitudinal conductivity of 0.00004 S/m will be assembled
and stored files test.keys, test.cond and test.pts.
2. na3d
-cx 0.1 -dx 0.01
-cy 0.1 -dy 0.01
-gl 4.0e-5 -gt 4.0e-6
test
A sheet with 11*11=121 nodes spaced 0.01 cm apart,
conductivities of 0.00004 S/m (longitudinal fiber direction)
and 0.000004 S/m (transverse fiber direction)
will be assembled
and stored files test.keys, test.cond and test.pts.
3. na3d
-cx 0.1 -dx 0.01
-cy 0.1 -dy 0.01
-cz 0.1 -dz 0.01
-gl 4.0e-5 -gt 4.0e-6
test
A parallelpiped with 11*11*11=1331 nodes spaced 0.01 cm apart,
conductivities of 0.00004 S/m (longitudinal fiber direction)
and 0.000004 S/m (transverse fiber direction)
will be assembled.
4. na3d
-nx 10 -dx 0.01
-ny 10 -dy 0.01
-nz 10 -dz 0.01
-gl 4.0e-5 -gt 4.0e-6
test
A parallelpiped with 10*10*10=1000 nodes spaced 0.01 cm apart,
conductivities of 0.00004 S/m (longitudinal fiber direction)
and 0.000004 S/m (transverse fiber direction)
will be assembled.
5. na3d
-nx 10 -dx 0.01
-ny 10 -dy 0.01
-gl 4.0e-5 -gt 4.0e-6
-f 0.10
test
A sheet model with 10*10=100 nodes spaced 0.01 cm apart,
in which 10 of the connections in the model will be assigned
conductivities of 10*gt to represent point barriers.
6. na3d
-nx 10 -dx 0.01
-ny 10 -dy 0.01
-gl 4.0e-5 -gt 4.0e-6
-f 1.10
test
A sheet model with 10*10=100 nodes spaced 0.01 cm apart,
in which 10 of the connections aligned with the
transverse fiber direction in the model will be assigned
conductivities of 10*gt to represent point barriers.
7. na3d
-nx 10 -dx 0.01
-ny 10 -dy 0.01
-gl 4.0e-5 -gt 4.0e-6
-lrg 0
-lbx 0.0 -lby 0.0
-lcx 0.03 -lcy 0.03
-lgl 1.0e-6 -lgt 1.0e-6
-lrc
test
A sheet model with 10*10=100 nodes spaced 0.01 cm apart,
in which the grid of nodes in the region (x:0.00,0.03; y:0.00,0.03)
are prescribed different conductivities from those of the rest
of the model.
SPECIFICATIONS
Specification of geometry
na3d
builds models as sets of interconnected cables using descriptions
of the desired spacing between nodes in x-, y- and z-directions
and of the desired model dimensions.
In the assembly of a cable model, nodes are laid down on a line
between two endpoints.
Node numbering is sequential from the origin (node 1) to the
terminal (node NX). Specification of conductivity parameters
na3d
will assemble conductivity matrix entries for every connection
in the model using specified tissue conductivities.
na3d expects the longitudinal and transverse
conductivities to be specified as input.
Conductivities are specified in units of S/m .
From these conductivities and the specified fiber directions
relative to the model axes, conductivities in the x-, y- and
z-directions are determined. For example, in the standard cable
equation: Specification of fiber directions
na3d
allows specification of the fiber orientation for the full model
or for regions within the model. Specification of regional parameter definition
na3d
allows specification of unique conductivity parameters for
regions whose boundaries are specified in rectangular coordinates.
Regional parameter definition is useful to define areas
of low conductivity in models with nonuniform anisotropy
or conductive inhomogeneity and in models in which the
interstitial and extracellular volume conductors are included. COMMANDS
EXAMPLES
na3d works like a number of UNIX filter functions and provides no
internal manipulation. All operations are specified at the command line.