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diffusionmatrix.cpp
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diffusionmatrix.cpp
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/************************************************************************
diffusionmatrix - Coefficients for time-dependent Greens function method
TWS July 2012, updated March 2017
**************************************************************/
#define _CRT_SECURE_NO_DEPRECATE
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "nrutil.h"
float expBessi0(float x);
float erfcc(float x);
void gbartx(int isp, float dist1, float req1, float *gtx, float *gbartx);
void diffusionmatrix(void)
{
extern int mxx,myy,mzz,nnt,nnv,nseg,nsp,nnodbc,slsegdiv,nsl1,nsl2;
extern int contourmethod;
extern int *mainseg,**tisspoints,*diffsolute,*permsolute;
extern float req,fac,deltat,pi1,fact,fact1,fact2;
extern float *axt,*ayt,*azt,*diff,*ds,*rseg;
extern float **gtt,**gbartt;
extern float ***gbarvv,***gvt,***gbarvt;
extern float ***gbarvc,***gtc,***gbartc;
extern float **gbarvtsum,**gbarttsum,**gttsum,*gttsum1,*gbarttsum1;
extern float *xsl0,*xsl1,*xsl2;
extern float **start,**scos,**ax,*x,*y;
int isl1,isl2,isl12,gvtsegdiv,gvtsegdiv1;
int i,j,j1,k,k1,iseg,jseg,ix,iy,iz,jx,jy,jz,jxyz,isp,it,itp,jtp;
int nit=10000; //number of points in time integration of gbarvv - integral converges slowly with nit!
float dist1,dist2,fact3,fact4,b2fact,c2fact,tint,integrand,dummy,gbarvc1,a1fact,a2fact,req1;
float gvt0,gbarvt0,gbarvv0;
float xmin,ymin,xmax,ymax,**cos;
//***** May need to increase up to 10.*req if instability occurs
float lsegmax = 2.*req; //length criterion for subdividing segments in calculation of gvv, gvt
cos = matrix(1,3,1,3);
printf("Computing diffusion coefficient matrices...");
for(isp=1; isp<=nsp; isp++) if(diffsolute[isp]){
fact = 4.*diff[isp]*deltat;
fact1 = 1./(sqrt(fact*pi1)*fact*pi1);
fact2 = 1./(4.*pi1*diff[isp]);
// tissue ~ tissue matrices gtt and gbartt, based on relative positions of tissue points
printf("gtt,gbartt...");
req1 = req; //based on tissue volume
for(jx=1; jx<=mxx; jx++) for(jy=1; jy<=myy; jy++) for(jz=1; jz<=mzz; jz++){
jxyz = jx + (jy - 1)*mxx + (jz - 1)*mxx*myy;
if(jxyz == 1){ //self-interaction
a1fact = req/sqrt(fact);
a2fact = SQR(req)/fact;
gtt[jxyz][isp] = fact1*3./(16.*a2fact*a2fact*a2fact)*(1. - 6.*a2fact + (2.*a2fact - 1.)*exp(-4.*a2fact)
+ 4.*sqrt(pi1)*a1fact*a2fact*(1. - erfcc(2.*a1fact)));
gbartt[jxyz][isp] = 1./(4.*pi1*diff[isp]*req)*3./40*(16. - (16. - 10/a2fact)*(1. - erfcc(2.*a1fact))
- 1./sqrt(pi1*a2fact)*(-1./SQR(a2fact) + 10./a2fact + (1./SQR(a2fact) - 6./a2fact + 8.)*exp(-4.*a2fact)));
}
else{
dist2 = SQR(axt[1]-axt[jx]) + SQR(ayt[1]-ayt[jy]) + SQR(azt[1]-azt[jz]);
dist1 = sqrt(dist2);
gbartx(isp,dist1,req1,>t[jxyz][isp],&gbartt[jxyz][isp]);
}
}
gttsum1[isp] = 0.;
gbarttsum1[isp] = 0.;
for(itp=1; itp<=nnt; itp++){
ix = tisspoints[1][itp];
iy = tisspoints[2][itp];
iz = tisspoints[3][itp];
gbarttsum[itp][isp] = 0.;
gttsum[itp][isp] = 0.;
for(jtp=1; jtp<=nnt; jtp++){
jx = tisspoints[1][jtp];
jy = tisspoints[2][jtp];
jz = tisspoints[3][jtp];
jxyz = 1 + abs(ix - jx) + abs(iy - jy)*mxx + abs(iz - jz)*mxx*myy;
gbarttsum[itp][isp] += gbartt[jxyz][isp];
gttsum[itp][isp] += gtt[jxyz][isp];
}
gttsum1[isp] += gttsum[itp][isp];
gbarttsum1[isp] += gbarttsum[itp][isp];
}
// vessel ~ vessel matrix gbarvv
if(permsolute[isp]){
printf("gbarvv...");
for(i=1; i<=nnv; i++){
iseg = mainseg[i];
gvtsegdiv = ds[iseg]/lsegmax + 1.;
req1 = pow(SQR(rseg[iseg])*ds[iseg]/gvtsegdiv*0.75,0.333333); //based on vessel segment volume - Jan. 2015
for(j=1; j<=nnv; j++){
jseg = mainseg[j];
gvtsegdiv1 = ds[jseg]/lsegmax + 1.;
req1 = FMAX(pow(SQR(rseg[jseg])*ds[jseg]/gvtsegdiv1*0.75,0.333333),req1); //based on other vessel segment volume
if(i == j){ //self-interaction
gbarvv[i][j][isp] = 0.;
for(it=0; it<=nit; it++){ //integration using trapezium rule
if(it == 0) integrand = 0.5/(2.*pi1*SQR(rseg[iseg])*ds[iseg]);
else{
tint = it*deltat/nit;
fact3 = 4.*diff[isp]*tint;
fact4 = 1./(sqrt(fact3*pi1)*fact3*pi1);
b2fact = SQR(rseg[iseg])/fact3;
c2fact = SQR(ds[iseg])/fact3;
integrand = fact4/2./b2fact*(1. - expBessi0(2.*b2fact))
/c2fact*(exp(-c2fact) - 1. + sqrt(pi1*c2fact)*(1. - erfcc(sqrt(c2fact))));
if(it == nit) integrand *= 0.5;
}
gbarvv[i][j][isp] += integrand*deltat/nit;
}
}
else{ //subdivide each vessel segment in gvtsegdiv pieces - April 2015
gbarvv[i][j][isp] = 0.;
for(k=1; k<=gvtsegdiv; k++){
for(j1=1; j1<=3; j1++) x[j1] = ax[j1][i] + scos[j1][iseg]*ds[iseg]*((k - 0.5)/gvtsegdiv - 0.5);
for(k1=1; k1<=gvtsegdiv1; k1++){
for(j1=1; j1<=3; j1++) y[j1] = ax[j1][j] + scos[j1][jseg]*ds[jseg]*((k1 - 0.5)/gvtsegdiv1 - 0.5);
dist2 = SQR(x[1] - y[1]) + SQR(x[2] - y[2]) + SQR(x[3] - y[3]);
dist1 = sqrt(dist2);
gbartx(isp,dist1,req1,&dummy,&gbarvv0); //use tissue interaction for different vessels
gbarvv[i][j][isp] += gbarvv0/gvtsegdiv/gvtsegdiv1;
}
}
}
}
}
// tissue ~ vessel matrices gvt and gbarvt: subdivide each vessel segment in gvtsegdiv pieces - April 2015
printf("gvt,gbarvt...");
for(i=1; i<=nnv; i++){
iseg = mainseg[i];
gvtsegdiv = ds[iseg]/lsegmax + 1.;
req1 = pow(SQR(rseg[iseg])*ds[iseg]/gvtsegdiv*0.75,0.333333);
req1 = FMAX(req,req1); //based on larger of tissue volume and segment volume - Jan 2015
gbarvtsum[i][isp] = 0.;
for(itp=1; itp<=nnt; itp++){
gvt[i][itp][isp] = 0.;
gbarvt[i][itp][isp] = 0.;
for(k=1; k<=gvtsegdiv; k++){
for(j=1; j<=3; j++) x[j] = ax[j][i] + scos[j][iseg]*ds[iseg]*((k - 0.5)/gvtsegdiv - 0.5);
dist2 = SQR(x[1] - axt[tisspoints[1][itp]])
+ SQR(x[2] - ayt[tisspoints[2][itp]])
+ SQR(x[3] - azt[tisspoints[3][itp]]);
dist1 = sqrt(dist2);
gbartx(isp,dist1,req1,&gvt0,&gbarvt0);
gvt[i][itp][isp] += gvt0/gvtsegdiv;
gbarvt[i][itp][isp] += gbarvt0/gvtsegdiv;
}
gbarvtsum[i][isp] += gbarvt[i][itp][isp];
}
}
}
}
// vessel ~ contour matrix gbarvc, tissue ~ contour matrices gtc and gbartc
// this is needed only if contour method 2 is used, otherwise disable to save time
if(contourmethod == 2){
xmin = 0.;
xmax = sqrt(SQR(xsl1[1]-xsl0[1]) + SQR(xsl1[2]-xsl0[2]) + SQR(xsl1[3]-xsl0[3]));
ymin = 0.;
ymax = sqrt(SQR(xsl2[1]-xsl0[1]) + SQR(xsl2[2]-xsl0[2]) + SQR(xsl2[3]-xsl0[3]));
for(i=1; i<=3; i++){ //set up matrix of direction cosines
cos[1][i] = (xsl1[i]-xsl0[i])/xmax;
cos[2][i] = (xsl2[i]-xsl0[i])/ymax;
}
cos[3][1] = cos[1][2]*cos[2][3] - cos[1][3]*cos[2][2];
cos[3][2] = cos[1][3]*cos[2][1] - cos[1][1]*cos[2][3];
cos[3][3] = cos[1][1]*cos[2][2] - cos[1][2]*cos[2][1];
for(isp=1; isp<=nsp; isp++) if(diffsolute[isp]){
printf("gbarvc,gtc,gbartc...");
for(isl1=1; isl1<=nsl1; isl1++) for(isl2=1; isl2<=nsl2; isl2++){
for(i=1; i<=3; i++) x[i] = xsl0[i] + (isl1-1)*(xsl1[i]-xsl0[i])/(nsl1-1) + (isl2-1)*(xsl2[i]-xsl0[i])/(nsl2-1);
isl12 = isl1 + (isl2 - 1)*nsl1;
for(i=1; i<=nnv; i++){ //add contributions from vessel sources. Subdivide subsegments.
gbarvc[isl12][i][isp] = 0.;
iseg = mainseg[i];
for(k=1; k<=slsegdiv; k++){
for(j=1; j<=3; j++) y[j] = ax[j][i] + scos[j][iseg]*ds[iseg]*(-0.5 + (k-0.5)/slsegdiv);
dist2 = SQR(x[1] - y[1]) + SQR(x[2] - y[2]) + SQR(x[3] - y[3]);
dist1 = sqrt(dist2);
gbartx(isp,dist1,req1,&dummy,&gbarvc1);
gbarvc[isl12][i][isp] += gbarvc1/slsegdiv;
}
}
for(itp=1; itp<=nnt; itp++){ //add contributions from tissue sources
dist2 = SQR(x[1] - axt[tisspoints[1][itp]])
+ SQR(x[2] - ayt[tisspoints[2][itp]])
+ SQR(x[3] - azt[tisspoints[3][itp]]);
dist1 = sqrt(dist2);
gbartx(isp,dist1,req1,>c[isl12][itp][isp],&gbartc[isl12][itp][isp]);
}
}
}
}
printf("done\n");
}