b0calc.cc

/*  b0calc.cc

    Mark Jenkinson, FMRIB Image Analysis Group

    Copyright (C) 2001 University of Oxford  */

/*  Part of FSL - FMRIB's Software Library
    http://www.fmrib.ox.ac.uk/fsl
    fsl@fmrib.ox.ac.uk
    
    Developed at FMRIB (Oxford Centre for Functional Magnetic Resonance
    Imaging of the Brain), Department of Clinical Neurology, Oxford
    University, Oxford, UK
    
    
    LICENCE
    
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// B0 Calculation program - intended for use with the Virtual Scanner


#include <iostream>
#include <string>
#include "newimage/newimageall.h"
#include "utils/options.h"

#define _GNU_SOURCE 1
#define POSIX_SOURCE 1

using namespace Utilities;  
using namespace NEWIMAGE;

// Global constants

string title="b0calc\nB0 field calculation program\nCopyright(c) 2001, University of Oxford (Mark Jenkinson)";
string examples="b0calc -i <input> -o <output> [options]";

Option<bool> verbose(string("-v,--verbose"), false, 
		     string("switch on diagnostic messages"), 
		     false, no_argument);
Option<bool> help(string("-h,--help"), false,
		  string("display this message"),
		  false, no_argument);
Option<bool> calcxyz(string("--xyz"), false,
		  string("calculate and save all 3 field components (i.e. x,y,z)"),
		  false, no_argument);
Option<bool> direct_conv(string("--directconv"), false,
		  string("use direct (image space) convolution, not FFT"),
		  false, no_argument);
Option<float> delta(string("-d"), -9.45e-6,   // chi_tissue - chi_air
		  string("Delta value (chi_tissue - chi_air): default=-9.45e-6"),
		  false, requires_argument);
Option<float> chi0(string("--chi0"), +4e-7,   // chi of air
		  string("Value for susceptibility of air: default=+4e-7"),
		  false, requires_argument);
Option<float> b0z(string("--b0"), 1.0,
		  string("Value for zeroth-order b0 field (z-component): default=1"),
		  false, requires_argument);
Option<float> b0x(string("--b0x"), 0.0,
		  string("Value for zeroth-order b0 field (x-component): default=0"),
		  false, requires_argument);
Option<float> b0y(string("--b0y"), 0.0,
		  string("Value for zeroth-order b0 field (y-component): default=0"),
		  false, requires_argument);
Option<float> gx(string("--gx"), 0.0,
		  string("Value for zeroth-order x-gradient field (per mm): default=0"),
		  false, requires_argument);
Option<float> gy(string("--gy"), 0.0,
		  string("Value for zeroth-order y-gradient field (per mm): default=0"),
		  false, requires_argument);
Option<float> gz(string("--gz"), 0.0,
		  string("Value for zeroth-order z-gradient field (per mm): default=0"),
		  false, requires_argument);
Option<float> extendboundary(string("--extendboundary"), 1.0,
		  string("Relative proportion to extend voxels at boundary: default=1"),
		  false, requires_argument);
Option<string> inname(string("-i,--in"), string(""),
			 string("filename of input image (usually a tissue/air segmentation)"),
			 true, requires_argument);
Option<string> outname(string("-o,--out"), string(""),
			 string("filename of B0 output volume"),
			 true, requires_argument);

/////////////////////////////////////////////////////////////////////////////

// % Sphere simulation (including Lorentz Correction)
// % cx=100; cy=100; cz=100;
// % a = 60;
// % [xs,ys,zs]=ndgrid((-(cx-1)):(cx-1),(-(cy-1)):(cy-1),(-(cz-1)):(cz-1));
// % rs=sqrt(xs.^2+ys.^2+zs.^2);
// % mu=(rs<=a);
// % mus=(round(rs)==a);      % surface voxels
// % musdotn=mus.*zs./max(rs,1e-8);         % surface normals (in z)
// % bztheory = (1-mu)/3.*(a^3).*(3*zs.^2 - rs.^2)./max((rs.^5) + mu,1e-8);

/////////////////////////////////////////////////////////////////////////////

float arctan(float num, float den)
{
  if (fabs(den)>1e-8) { 
    return atan(num/den);
  } else {
    return atan2(num,den);
  }
}


float arcsinh(float num, float den)
{
  if (fabs(den)>1e-8) { 
    return asinh(num/den);
  } else {
    return log(num + sqrt(num*num + den*den)) - log(den);
    // uses asinh(x) = log(x + sqrt(x*x+1))
  }
}

volume<float> partbzkernel(const volume<float>& obj, 
			   float xoff, float yoff, float zoff,
			   const string& b0type)
{
  // This function returns F(x';x) as described in the technical report
  //  where xoff = x' - x , yoff = y' - y , etc
  int nx, ny, nz;
  nx = obj.xsize();  ny = obj.ysize();  nz = obj.zsize();
  float dx, dy, dz;
  dx = obj.xdim();  dy = obj.ydim();  dz = obj.zdim();
  volume<float> kernel(2*nx-1,2*ny-1,2*nz-1);
  for (int z1=-(nz-1); z1<=(nz-1); z1++) {
    for (int y1=-(ny-1); y1<=(ny-1); y1++) {
      for (int x1=-(nx-1); x1<=(nx-1); x1++) {
	// the following are x' in F(x';x)  (as always use F(x+offset;x))
	float x = x1*dx+xoff, y = y1*dy+yoff, z = z1*dz+zoff;
	float r = sqrt(x*x + y*y + z*z);
	if (b0type=="0,0,1") {
	  kernel(x1+nx-1,y1+ny-1,z1+nz-1) = arctan(x*y,z*r);
	} else if (b0type=="1,0,0") {
	  kernel(x1+nx-1,y1+ny-1,z1+nz-1) = -arcsinh(y,sqrt(x*x+z*z));
	} else if (b0type=="0,1,0") {
	  kernel(x1+nx-1,y1+ny-1,z1+nz-1) = -arcsinh(x,sqrt(y*y+z*z));
	} else if (b0type=="z,0,x") {
	  kernel(x1+nx-1,y1+ny-1,z1+nz-1) = (x-xoff)*arctan(x*y,z*r)
	    + x*arctan(z*y,x*r) + zoff*arcsinh(y,sqrt(x*x+z*z)) 
	    - y*arcsinh(z,sqrt(y*y+x*x));
	} else if (b0type=="0,z,y") {
	  kernel(x1+nx-1,y1+ny-1,z1+nz-1) = (y-yoff)*arctan(x*y,z*r)
	    + y*arctan(z*x,y*r) + zoff*arcsinh(x,sqrt(y*y+z*z)) 
	    - x*arcsinh(z,sqrt(y*y+x*x));
	} else if (b0type=="-x,0,z") {
	  kernel(x1+nx-1,y1+ny-1,z1+nz-1) = -xoff*arcsinh(y,sqrt(x*x+z*z))
	    -zoff*arctan(x*y,z*r);
	} else {
	  cerr << "Unknown b0 type requested:: " << b0type << endl;
	  exit(-1);
	}
      }
    }
  }
  cerr << "." << endl;
  // apply 1/(4*pi) factor - as it is more efficient here
  kernel *= 1.0/(4.0*M_PI);
  return kernel;
}


volume<float> calculate_kernel(const volume<float>& obj, 
			       const string& b0type="0,0,1")
{
  // Combines the partial voxel Bz solutions to get a full solution
  // Answer is for position x,y,z (relative to voxel centre) 
  //   given a voxel of size (dx,dy,dz)
  cout << "Calculating kernel" << endl;
  float dx2, dy2, dz2;
  dx2 = obj.xdim()/2.0;  dy2 = obj.ydim()/2.0;  dz2 = obj.zdim()/2.0;
  volume<float> kernel;
  kernel = partbzkernel(obj,dx2,dy2,dz2,b0type);
  kernel -= partbzkernel(obj,-dx2,dy2,dz2,b0type);
  kernel -= partbzkernel(obj,dx2,-dy2,dz2,b0type);
  kernel -= partbzkernel(obj,dx2,dy2,-dz2,b0type);
  kernel += partbzkernel(obj,dx2,-dy2,-dz2,b0type);
  kernel += partbzkernel(obj,-dx2,dy2,-dz2,b0type);
  kernel += partbzkernel(obj,-dx2,-dy2,dz2,b0type);
  kernel -= partbzkernel(obj,-dx2,-dy2,-dz2,b0type);
  return kernel;
}
  
/////////////////////////////////////////////////////////////////////////////

volume<float> gradientfield(const volume<float>& chi, const string& dir)
{
  int nx, ny, nz;
  nx = chi.xsize()/2;  ny = chi.ysize()/2;  nz = chi.zsize()/2;
  float dx, dy, dz;
  dx = chi.xdim();  dy = chi.ydim();  dz = chi.zdim();
  volume<float> gfield;
  gfield = chi * 0.0f;
  for (int z1=0; z1<chi.zsize(); z1++) {
    for (int y1=0; y1<chi.ysize(); y1++) {
      for (int x1=0; x1<chi.xsize(); x1++) {
	if (dir=="x") {
	  gfield(x1,y1,z1)=(x1-nx)*dx;
	} else if (dir=="y") {
	  gfield(x1,y1,z1)=(y1-ny)*dy;
	} else if (dir=="z") {
	  gfield(x1,y1,z1)=(z1-nz)*dz;
	} else {
	  cerr << "Unknown direction '"<<dir<<"' specified in gradientfield" 
	       << endl;
	  return gfield;
	}
      }
    }
  }
  return gfield;
}

/////////////////////////////////////////////////////////////////////////////


volume<float> convolve3_complex(const volume<float>& chi, 
				const volume<float>& kernel,
				complexvolume& kernelc)
{
  // assumes that kernel has size >= (2*nx-1,2*ny-1,2*nz-1)
  // also uses kernelc unless it has the wrong size
  int nx,ny,nz;
  nx = chi.xsize();  ny=chi.ysize();  nz=chi.zsize();
  complexvolume chi1c;
  cout << "zero pad" << endl;
  chi1c.re() = kernel*0.0f;
  chi1c.im() = chi1c.re();
  chi1c.re().setROIlimits(0,0,0,nx-1,ny-1,nz-1);
  chi1c.re().activateROI();
  chi1c.re().copyROIonly(chi);
  chi1c.re().deactivateROI();
  cout << "Forward FFT" << endl;
  fft3(chi1c);
  {
    if (!samesize(kernelc.re(),kernel)) {
      cout << "Forward FFT" << endl;
      kernelc.re() = kernel;
      kernelc.im() = kernel*0.0f;
      fft3(kernelc);
    }
    cout << "Kernel multiplication" << endl;
    {
      volume<float> tmp;
      tmp = chi1c.re() * kernelc.re() - chi1c.im() * kernelc.im();
      chi1c.im() = chi1c.re() * kernelc.im() + chi1c.im() * kernelc.re();
      chi1c.re() = tmp;
    } // destroy tmp
  } // destroy kernelc
  cout << "Inverse FFT" << endl;
  ifft3(chi1c);
  cout << "select ROI" << endl;
  chi1c.re().setROIlimits(nx-1,ny-1,nz-1,2*nx-2,2*ny-2,2*nz-2);
  chi1c.re().activateROI();
  volume<float> bz;
  bz = chi*0.0f;
  bz.copyROIonly(chi1c.re());
  return bz;
}


volume<float> direct_convolve(const volume<float>& source, 
			      const volume<float>& kernel)
{ 
  extrapolation oldex = source.getextrapolationmethod();
  if ((oldex==boundsassert) || (oldex==boundsexception)) 
    { source.setextrapolationmethod(constpad); }
  if (    (( (kernel.maxz() - kernel.minz()) % 2)==1) || 
	  (( (kernel.maxy() - kernel.miny()) % 2)==1) ||
	  (( (kernel.maxx() - kernel.minx()) % 2)==1) ) 
    {
      cerr << "WARNING:: Off-centre convolution being performed as kernel"
	   << " has even dimensions" << endl;
    }
  volume<float> result(source);
  result = 0.0f;
  int midx, midy, midz;
  midz=(kernel.maxz() - kernel.minz())/2;
  midy=(kernel.maxy() - kernel.miny())/2;
  midx=(kernel.maxx() - kernel.minx())/2;
  for (int z=source.minz(); z<=source.maxz(); z++) {
    for (int y=source.miny(); y<=source.maxy(); y++) {
      for (int x=source.minx(); x<=source.maxx(); x++) {
	if (source(x,y,z)>0.0) {
	  for (int mz=kernel.minz(); mz<=kernel.maxz(); mz++) {
	    for (int my=kernel.miny(); my<=kernel.maxy(); my++) {
	      for (int mx=kernel.minx(); mx<=kernel.maxx(); mx++) {
		result(x+mx-midx,y+my-midy,z+mz-midz) += kernel(mx,my,mz);
	      }
	    }
	  }
	}
      }
    }
  }
  source.setextrapolationmethod(oldex);
  return result;
}


volume<float> convolve3(const volume<float>& chi, 
			const volume<float>& kernel,
			complexvolume& kernelc)
{
  if (direct_conv.value()) {
    return direct_convolve(chi,kernel);
  }
  return convolve3_complex(chi,kernel,kernelc);
}


/////////////////////////////////////////////////////////////////////////////

volume4D<float> BzField(const volume4D<float>& chi1, 
			float gx, float gy, float gz,
			float b0x, float b0y, float b0z)
{
  // Implements the first order perturbation solution which is:
  //    Bz(1) = delta/(1+chi0) . ( (1+chi0)/(3+chi0) . chi1.Bz(0) - { ...
  //                        (d2G/dxdz)*(chi1.Bx(0)) + ...
  //                        (d2G/dydz)*(chi1.By(0)) + (d2G/dz2)*(chi1.Bz(0)) } )
  // NOTE: 1/3 in first term comes from using the Lorentz Correction
  //       which is -2/3 . (chi / (1 + chi)) . Bz
  cout << "Calculating Bz field" << endl;
  volume4D<float> bz;
  volume<float> kernel, chi1b0;
  complexvolume fftkernel, dummy;
  string kernelstr="";
  float tol = 0.001*fabs(delta.value())*fabs(b0z);
  for (int t=chi1.mint(); t<=chi1.maxt(); t++) {
    // Start with the (1/(3+chi0) * chi1 * B_0(z)) term (non-convolved)
    bz.addvolume(b0z * chi1[t] / (3.0 + chi0.value()) * (1 + chi0.value()));
    if (fabs(gx)>tol) bz[t] += gx * gradientfield(chi1[t],"x")* chi1[t];
    if (fabs(gy)>tol) bz[t] += gy * gradientfield(chi1[t],"y")* chi1[t];
    if (fabs(gz)>tol) bz[t] += gz * gradientfield(chi1[t],"z")* chi1[t];
    // convolve appropriate kernels and B_0*chi1 terms
    //  x-gradient term
    if (fabs(gx)>tol) {
      if (kernelstr != "z,0,x") {
	kernelstr = "z,0,x";
	kernel = calculate_kernel(chi1[t],kernelstr);
	fftkernel = dummy;
      }
      bz[t] -=  gx * convolve3(chi1[t],kernel,fftkernel);
    }
    //  y-gradient term
    if (fabs(gy)>tol) {
      if (kernelstr != "0,z,y") {
	kernelstr = "0,z,y";
	kernel = calculate_kernel(chi1[t],kernelstr);
	fftkernel = dummy;
      }
      bz[t] -=  gy * convolve3(chi1[t],kernel,fftkernel);
    }
    //  z-gradient term
    if (fabs(gz)>tol) {
      if (kernelstr != "-x,0,z") {
	kernelstr = "-x,0,z";
	kernel = calculate_kernel(chi1[t],kernelstr);
	fftkernel = dummy;
      }
      bz[t] -=  gz * convolve3(chi1[t],kernel,fftkernel);
    }
    //  constant B_x term
    if (Max(fabs(b0x),Max(fabs(gx),fabs(gz)))>tol) {
      chi1b0 = b0x * chi1[t];
      if (fabs(gx)>tol) chi1b0 += gx * gradientfield(chi1[t],"z")* chi1[t];
      if (fabs(gz)>tol) chi1b0 -= gz * gradientfield(chi1[t],"x")* chi1[t];
      if (kernelstr != "1,0,0") {
	kernelstr = "1,0,0";
	kernel = calculate_kernel(chi1[t],kernelstr);
	fftkernel = dummy;
      }
      bz[t] -= convolve3(chi1b0,kernel,fftkernel);
    }
    //  constant B_y term
    if (Max(fabs(b0y),fabs(gy))>tol) {
      chi1b0 = b0y * chi1[t];
      if (fabs(gy)>tol) chi1b0 += gy * gradientfield(chi1[t],"z")* chi1[t];
      if (kernelstr != "0,1,0") {
	kernelstr = "0,1,0";
	kernel = calculate_kernel(chi1[t],kernelstr);
	fftkernel = dummy;
      }
      bz[t] -= convolve3(chi1b0,kernel,fftkernel);
    }
    //  constant B_z term
    if (Max(fabs(b0z),Max(fabs(gx),Max(fabs(gy),fabs(gz))))>tol) {
      chi1b0 = b0z * chi1[t];
      if (fabs(gx)>tol) chi1b0 += gx * gradientfield(chi1[t],"x")* chi1[t];
      if (fabs(gy)>tol) chi1b0 += gy * gradientfield(chi1[t],"y")* chi1[t];
      if (fabs(gz)>tol) chi1b0 += gz * gradientfield(chi1[t],"z")* chi1[t];
      if (kernelstr != "0,0,1") {
	kernelstr = "0,0,1";
	kernel = calculate_kernel(chi1[t],kernelstr);
	fftkernel = dummy;
      }
      bz[t] -= convolve3(chi1b0,kernel,fftkernel);
    }
  }
  // multiply everything by for delta/(1+chi0) (first order general coefficient)
  bz *= (delta.value()/(1.0 + chi0.value()));
  return bz;
}


volume4D<float> BzField(const volume4D<float>& chi1)
{
  return BzField(chi1,gx.value(),gy.value(),gz.value(),
		 b0x.value(),b0y.value(),b0z.value());
}

volume4D<float> ByField(volume4D<float>& chi1)  // chi1 is const (but needs swapping)
{
  volume4D<float> by;
  // flip object axes
  chi1.swapdimensions(3,1,2);
  by = BzField(chi1,gz.value(),gx.value(),gy.value(),
		 b0z.value(),b0x.value(),b0y.value());
  // restore original axes
  chi1.swapdimensions(2,3,1);
  by.swapdimensions(2,3,1);
  return by;
}

volume4D<float> BxField(volume4D<float>& chi1)  // chi1 is const (but needs swapping)
{
  volume4D<float> bx;
  // flip object axes
  chi1.swapdimensions(2,3,1);  
  bx = BzField(chi1,gy.value(),gz.value(),gx.value(),
		 b0y.value(),b0z.value(),b0x.value());
  // restore original axes
  chi1.swapdimensions(3,1,2);
  bx.swapdimensions(3,1,2);
  return bx;
}


/////////////////////////////////////////////////////////////////////////////

int do_calculation()
{
  volume4D<float> bz, chi;
  read_volume4D(chi,inname.value());
  if (calcxyz.value()) { bz.addvolume(BxField(chi)); }
  if (calcxyz.value()) { bz.addvolume(ByField(chi)); }
  bz.addvolume(BzField(chi));
  save_volume4D(bz,outname.value());
  return 0;
}

/////////////////////////////////////////////////////////////////////////////


int main(int argc, char* argv[])
{
  OptionParser options(title, examples);

  try {
    options.add(inname);
    options.add(outname);
    options.add(gx);
    options.add(gy);
    options.add(gz);
    options.add(b0x);
    options.add(b0y);
    options.add(b0z);
    options.add(delta);
    options.add(chi0);
    options.add(calcxyz);
    options.add(extendboundary);
    options.add(direct_conv);
    options.add(verbose);
    options.add(help);
    
    options.parse_command_line(argc, argv);

    if ( (help.value()) || (!options.check_compulsory_arguments(true)) )
      {
	options.usage();
	exit(EXIT_FAILURE);
      }
        
  }  catch(X_OptionError& e) {
    options.usage();
    cerr << endl << e.what() << endl;
    exit(EXIT_FAILURE);
  } catch(std::exception &e) {
    cerr << e.what() << endl;
  } 
  return do_calculation();
}