Function for solving the forward problem with the 3-layer model. More...

#include "header.h"

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void	calc_diffusion_curve_layer (int nt, int nz, int nr, int iprobe, int jprobe, int iz1, int iz2, int nolayer, double dt, double dr, double sdelay, double sduration, double alpha_so, double theta_so, double kappa_so, double alpha_sp, double theta_sp, double kappa_sp, double alpha_sr, double theta_sr, double kappa_sr, double dfree, double t, double s, double invr, char imagebasename, double image_spacing, double *p)
	Calculates the concentration as a function of space and time and returns the probe concentration as a function of time; also outputs the concentration as images if that option was chosen. More...

Detailed Description

Function for solving the forward problem with the 3-layer model.

This file is similar to model.c for fit-layer except that it can output the concentration as images. The concentration is calculated on an nz*(nr+1) grid for is for z: 0 -> zmax and r: 0 -> rmax. If this concentration grid were output as an image it would be rectangular of aspect ratio about 1:2, with the maximum intensity at the left side of the image (source at r=0). Instead the output images are nearly square with the source (r=0) in the middle column of the images. The left side of the images are a mirror of the right side. I.e. the output images have dimensions of nz*(2*nr-1) and are for z: 0 -> zmax and r: -rmax -> rmax.

Author: David Lewis, CABI, NKI

Copyright: GNU Public License

Date: 2012-2013

Definition in file model.c.

Function Documentation

void calc_diffusion_curve_layer	(	int	nt,
		int	nz,
		int	nr,
		int	iprobe,
		int	jprobe,
		int	iz1,
		int	iz2,
		int	nolayer,
		double	dt,
		double	dr,
		double	sdelay,
		double	sduration,
		double	alpha_so,
		double	theta_so,
		double	kappa_so,
		double	alpha_sp,
		double	theta_sp,
		double	kappa_sp,
		double	alpha_sr,
		double	theta_sr,
		double	kappa_sr,
		double	dfree,
		double *	t,
		double *	s,
		double *	invr,
		char *	imagebasename,
		double	image_spacing,
		double *	p
	)

Calculates the concentration as a function of space and time and returns the probe concentration as a function of time; also outputs the concentration as images if that option was chosen.

This function solves the diffusion equation in each layer $ k $ ,

$\frac{\partial c_k(\vec r, t)}{\partial t} = D_{free} \theta_k \nabla^2{c_k(\vec r, t)} + s/\alpha_k - \kappa_k c_k(\vec r, t) \quad ,$

subject to the continuity conditions at the interfaces between layers

$c(\vec r_k, t) = c(\vec r_{k+1}, t) \quad$

$\alpha_k \theta_k \nabla c(\vec r_k, t) = \alpha_{k+1} \theta_{k+1} \nabla c(\vec r_{k+1}, t) \quad$

and the boundary condition $c(\vec r, t) = 0$ (total absorption) at the top, the bottom, and the side of the cylinder, where

$c_k(\vec r, t)$ = concentration in layer $ k $

$D_{free}$ = free diffusion coefficient

$\theta_k$ = permeability in layer $ k $

$s_k(\vec r, t)$ = source in layer $ k $

$\alpha_k$ = extracellular volume fraction in layer $ k $

$\kappa_k$ = nonspecific clearance factor in layer $ k $

This function calls convolve3() to compute the Laplacian in cylindrical coordinates.

Parameters

[in]	nt	Number of support points in time
[in]	nz	Number of rows of concentration matrix
[in]	nr	Number of columns of concentration matrix
[in]	iprobe	z-index of probe location
[in]	jprobe	r-index of probe location
[in]	iz1	z-index of SR-SP boundary
[in]	iz2	z-index of SP-SO boundary
[in]	nolayer	Flag for whether to model a single homogeneous environment (true) or to model a 3-layer environment
[in]	dt	Spacing in time ( $t_{i+1} = t_i + \Delta t$ )
[in]	dr	Spacing in r (in this program, $\Delta z = \Delta r$ )
[in]	sdelay	Source delay (time before source starts)
[in]	sduration	Duration of source
[in]	alpha_so	Extracellular volume fraction in SO layer
[in]	theta_so	Permeability in SO layer
[in]	kappa_so	Nonspecific clearance factor in SO layer
[in]	alpha_sp	Extracellular volume fraction in SP layer
[in]	theta_sp	Permeability in SP layer
[in]	kappa_sp	Nonspecific clearance factor in SP layer
[in]	alpha_sr	Extracellular volume fraction in SR layer
[in]	theta_sr	Permeability in SR layer
[in]	kappa_sr	Nonspecific clearance factor in SR layer
[in]	dfree	Free diffusion coefficient
[in]	t	Time array
[in]	s	Source array
[in]	invr	Array for values
[out]	p	Probe array (concentration as a function of time)

Definition at line 101 of file model.c.

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Detailed Description

Function Documentation