/// <summary>
/// Create a DiffusionParameters object from OpticalProperties object and a ForwardModel
/// choice.
/// </summary>
/// <param name="op">OpticalProperties object</param>
/// <param name="fm">ForwardModel enum</param>
/// <returns>new DiffusionParameters object</returns>
public static DiffusionParameters Create(OpticalProperties op, ForwardModel fm)
{
var mua = op.Mua;
var mutr = op.Mua + op.Musp;
var cn = GlobalConstants.C / op.N;
var D = 1 / (3 * mutr);
var A = CalculatorToolbox.GetCubicAParameter(op.N);
var mueff = Math.Sqrt(3 * op.Mua * mutr);
var zb = 2 / (3 * mutr) * A;
double musTilde;
double gTilde;
switch (fm)
{
case ForwardModel.SDA:
default:
musTilde = op.Musp;
gTilde = op.G;
break;
case ForwardModel.DeltaPOne:
musTilde = op.Musp * (1 - op.G * op.G) / (1 - op.G);
gTilde = op.G / (op.G + 1);
break;
}
var mutTilde = op.Mua + musTilde;
var zp = 1 / mutTilde;
return(new DiffusionParameters(A, mueff, zb, zp, mutTilde, musTilde, mutr, gTilde, D, cn, mua));
}
// Steady-State Domain...
///// <summary>
///// Steady-State centerline Photon Hitting Density by the Green's function multiplication
///// </summary>
///// <param name="ops">optical properties object</param>
///// <param name="rhos">Source Detector separation</param>
///// <param name="rProbe">Radial distance from source to "iterogation" location</param>
///// <param name="z">Depth being probed</param>
///// <returns>The Photon Hitting Density at specified location</returns>
//public IEnumerable<double> SteadyStatePointSourceCenterlinePHD(IEnumerable<OpticalProperties> ops, IEnumerable<double> rProbes,
// IEnumerable<double> rhos, IEnumerable<double> zs)
//{
// foreach (var op in ops)
// {
// DiffusionParameters dp = DiffusionParameters.Create(op, ForwardModel.SDA);
// foreach (var rProbe in rProbes)
// {
// foreach (var rho in rhos)
// {
// foreach (var z in zs)
// {
// var r11 = DiffusionBase.Radius1(rProbe, z, dp.zp);
// var r12 = DiffusionBase.Radius2(rProbe, z, dp.zp, dp.zb);
// var r21 = DiffusionBase.Radius1(rho - rProbe, z, 0.0);
// var r22 = DiffusionBase.Radius2(rho - rProbe, z, 0.0, dp.zb);
// var fluence1 = DiffusionBase.SteadyStatePointSourceImageGreensFunction(dp, r11, r12);
// var fluence2 = DiffusionBase.SteadyStatePointSourceImageGreensFunction(dp, r21, r22);
// yield return (fluence1 * fluence2);
// }
// }
// }
// }
//}
public static IEnumerable <Complex> TimeFrequencyDomainFluence2SurfacePointPHD(
this IForwardSolver myForwardSolver,
double timeModulationFrequency,
IEnumerable <OpticalProperties> ops,
IEnumerable <double> rhoPrimes, IEnumerable <double> zs)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, ForwardModel.SDA);
Complex k =
(
(op.Mua * dp.cn + Complex.ImaginaryOne * timeModulationFrequency * 2 * Math.PI) /
(dp.D * dp.cn)
).SquareRoot();
foreach (var rho in rhoPrimes)
{
foreach (var z in zs)
{
var r21 = CalculatorToolbox.GetRadius(rho, z);
var r22 = CalculatorToolbox.GetRadius(rho, z + 2 * dp.zb);
yield return
(DiffusionGreensFunctions.TemporalFrequencyPointSourceImageGreensFunction(dp, r21, r22, k));
}
}
}
}
/// <summary>
/// Evaluates the temporal frequency radially resolved reflectance using the distribution of
/// the source-image point source configuration.
/// </summary>
/// <param name="dp">DiffusionParameters object</param>
/// <param name="rho">radial location</param>
/// <param name="k">wavevector</param>
/// <param name="fr1">Fresnel Moment 1</param>
/// <param name="fr2">Fresnel Moment 2</param>
/// <returns></returns>
public override Complex TemporalFrequencyReflectance(DiffusionParameters dp,
double rho, Complex k, double fr1, double fr2)
{
var dpLocalReal = DiffusionParameters.Copy(dp);
var dpLocalImag = DiffusionParameters.Copy(dp);
Func <DiffusionParameters, double, Complex, double, Complex>
kernelFunc = (dpLocal, r, kLocal, zp) =>
{
dpLocal.zp = zp;
return
(_pointSourceForwardSolver.TemporalFrequencyReflectance(
dpLocal, r, kLocal, fr1, fr2));
};
return
((CalculatorToolbox.EvaluateDistributedExponentialLineSourceIntegral(
zp => kernelFunc(dpLocalReal, rho, k, zp).Real,
dp.mutTilde)
+ Complex.ImaginaryOne *
CalculatorToolbox.EvaluateDistributedExponentialLineSourceIntegral(
zp => kernelFunc(dpLocalImag, rho, k, zp).Imaginary,
dp.mutTilde)
) *
dp.musTilde);
}
/// <summary>
/// Evaluate the temporally-radially resolved fluence using the point source-image configuration
/// </summary>
/// <param name="dp">DiffusionParameters object</param>
/// <param name="rho">radial location</param>
/// <param name="z">depth location</param>
/// <param name="t">time</param>
/// <returns>fluence</returns>
public override double TemporalFluence(
DiffusionParameters dp, double rho, double z, double t)
{
return(DiffusionGreensFunctions.TemporalPointSourceImageGreensFunction(dp,
CalculatorToolbox.GetRadius(rho, z - dp.zp),
CalculatorToolbox.GetRadius(rho, z + dp.zp + 2 * dp.zb),
t));
}
// this method builds an R(rho, ft) array and then uses FFT to generate R(rho, t)
private double[] DetermineROfTimeFromROfFtForFixedRho(double rho, IOpticalPropertyRegion[] regions,
out double[] FFTTimeSequence)
{
// get ops of top tissue region
var op0 = regions[0].RegionOP;
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op0.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op0.N);
var diffusionParameters = GetDiffusionParameters(regions);
var layerThicknesses = GetLayerThicknesses(regions);
int numFreq = 512; // Kienle used 512 and deltaFreq = 0.1
// Kienle says deltaFrequency depends on source-detector separation
var deltaFrequency = 0.1; // 100 MHz
if (rho <= 3)
{
deltaFrequency = 0.5; // so far I've found this value works for smaller rho
}
var F = numFreq * deltaFrequency; // 51 GHz
var deltaTime = 1.0 / (numFreq * deltaFrequency); // 0.02 ns => T = 10 ns
// var homoSDA = new PointSourceSDAForwardSolver(); // debug with h**o SDA
// var rOfTime = new Complex[numFreq]; // debug array
// considerations: 2n datapoint and pad with 0s beyond (deltaTime * numFreq)
var rOfFt = new Complex[numFreq];
double[] ft = Enumerable.Range(0, numFreq).Select(x => x * deltaFrequency).ToArray();
FFTTimeSequence = Enumerable.Range(0, numFreq).Select(x => x * deltaTime).ToArray();
for (int i = 0; i < numFreq; i++)
{
// normalize by F=(numFreq*deltaFrequency)
rOfFt[i] = TemporalFrequencyReflectance(rho, ft[i], diffusionParameters, layerThicknesses, fr1, fr2) * F;
// rOfTime[i] = homoSDA.ROfRhoAndTime(regions[1].RegionOP, rho, t[i]); // debug array
}
// to debug, use R(t) and FFT to see if result R(ft) is close to rOfFt
//var dft2 = new MathNet.Numerics.IntegralTransforms.Algorithms.DiscreteFourierTransform();
//dft2.Radix2Forward(rOfTime, FourierOptions.NoScaling); // convert to R(ft) to compare with rOfFt
//var relDiffReal = Enumerable.Zip(rOfTime, rOfFt, (x, y) => Math.Abs((y.Real - x.Real) / x.Real));
//var relDiffImag = Enumerable.Zip(rOfTime, rOfFt, (x, y) => Math.Abs((y.Imaginary - x.Imaginary) / x.Imaginary));
//var maxReal = relDiffReal.Max();
//var maxImag = relDiffImag.Max();
//var dum1 = maxReal;
//var dum2 = maxImag;
//dft2.Inverse(rOfTime, FourierOptions.NoScaling); // debug convert to R(t)
// end debug code
// FFT R(ft) to R(t)
//var dft = new MathNet.Numerics.IntegralTransforms.Algorithms.DiscreteFourierTransform();
//dft.Inverse(rOfFt, FourierOptions.NoScaling); // convert to R(t)
Fourier.Inverse(rOfFt, FourierOptions.NoScaling);
var rOfTime = new double[FFTTimeSequence.Length];
rOfTime = rOfFt.Select(r => r.Real / (numFreq / 2)).ToArray();
return(rOfTime);
}
// protected methods
/// <summary>
/// Calculates the reflectance based on the integral of the radiance over the backward hemisphere...
/// </summary>
/// <param name="surfaceFluence">diffuse fluence at the surface</param>
/// <param name="surfaceFlux">diffuse flux at the surface</param>
/// <param name="mediaRefractiveIndex">refractive index of the medium</param>
/// <returns></returns>
protected static double GetBackwardHemisphereIntegralDiffuseReflectance(
double surfaceFluence, double surfaceFlux, double mediaRefractiveIndex)
{
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(
mediaRefractiveIndex);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(
mediaRefractiveIndex);
return(GetBackwardHemisphereIntegralDiffuseReflectance(surfaceFluence, surfaceFlux,
fr1, fr2));
}
private double StationaryFlux(double rho, double z, DiffusionParameters dp)
{
var dpLocal = DiffusionParameters.Copy(dp);
return(CalculatorToolbox.EvaluateDistributedExponentialLineSourceIntegral(
zp =>
{
dpLocal.zp = zp;
return _pointSourceForwardSolver.StationaryFlux(rho, z, dpLocal);
},
dp.mutTilde) *
dp.musTilde);
}
/// <summary>
/// Evaluation of the temporally and radially resolved fluence rate using the distribution of
/// source-image point sources.
/// </summary>
/// <param name="dp">DiffusionParameters object</param>
/// <param name="rho">radial location</param>
/// <param name="z">depth location</param>
/// <param name="t">time</param>
/// <returns>fluence rate</returns>
public override double TemporalFluence(
DiffusionParameters dp, double rho, double z, double t)
{
var dpLocal = DiffusionParameters.Copy(dp);
return(CalculatorToolbox.EvaluateDistributedExponentialLineSourceIntegral(
zp =>
{
dpLocal.zp = zp;
return _pointSourceForwardSolver.TemporalFluence(dpLocal, rho, z, t);
},
dp.mutTilde) *
dp.musTilde);
}
public override IEnumerable <double> ROfRho(
IEnumerable <OpticalProperties> ops,
IEnumerable <double> rhos)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, this.ForwardModel);
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op.N);
foreach (var rho in rhos)
{
yield return(StationaryReflectance(dp, rho, fr1, fr2));
}
}
}
public override double ROfFx(IOpticalPropertyRegion[] regions, double fx)
{
// get ops of top tissue region
var op0 = regions[0].RegionOP;
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op0.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op0.N);
var diffusionParameters = GetDiffusionParameters(regions);
var layerThicknesses = GetLayerThicknesses(regions);
// check that embedded source is within top layer, otherwise solution invalid
if (diffusionParameters[0].zp > layerThicknesses[0])
{
throw new ArgumentException("Top layer thickness must be greater than l* = 1/(mua+musp)");
}
return(SpatialFrequencyReflectance(2 * Math.PI * fx, diffusionParameters, layerThicknesses, fr1, fr2));
}
/// <summary>
/// Modulation frequency-dependent reflectance. Modified from Pham et al, Appl. Opt. Sept 2000
/// to include spatial modulation, as described in Cuccia et al, J. Biomed. Opt. March/April 2009
/// </summary>
/// <param name="op">optical properties of the medium</param>
/// <param name="fx">spatial frequency</param>
/// <param name="ft">modulation frequency (GHz)</param>
/// <returns></returns>
public override Complex ROfFxAndFt(OpticalProperties op, double fx, double ft)
{
double A = CalculatorToolbox.GetCubicAParameter(op.N);
double wOverC = Math.PI * ft * op.N / GlobalConstants.C;
double mutr = op.Mua + op.Musp;
Complex D = 1 / (3 * mutr * (1.0 + Complex.ImaginaryOne * wOverC / mutr));
Complex mueff =
(
3.0 * op.Mua * mutr -
3.0 * wOverC * wOverC +
Complex.ImaginaryOne * (1 + op.Mua / mutr) * 3.0 * mutr * wOverC +
4.0 * Math.PI * Math.PI * fx * fx
).SquareRoot();
Complex temp = mueff * D;
return(3 * A * op.Musp * D / (temp + 1.0 / 3.0) / (temp + A));
}
public override IEnumerable <Complex> ROfRhoAndFt(IEnumerable <OpticalProperties> ops,
IEnumerable <double> rhos, IEnumerable <double> fts)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, this.ForwardModel);
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op.N);
foreach (var rho in rhos)
{
foreach (var ft in fts)
{
Complex k = ((op.Mua * dp.cn + Complex.ImaginaryOne * ft * 2 * Math.PI) /
(dp.cn * dp.D)).SquareRoot();
yield return(TemporalFrequencyReflectance(dp, rho, k, fr1, fr2));
}
}
}
}
public static IEnumerable <double> SteadyStateFluence2SurfacePointPHD(
this IForwardSolver myForwardSolver,
IEnumerable <OpticalProperties> ops,
IEnumerable <double> rhoPrimes, IEnumerable <double> zs)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, ForwardModel.SDA);
foreach (var rho in rhoPrimes)
{
foreach (var z in zs)
{
var r21 = CalculatorToolbox.GetRadius(rho, z);
var r22 = CalculatorToolbox.GetRadius(rho, z + 2 * dp.zb);
yield return
(DiffusionGreensFunctions.StationaryPointSourceImageGreensFunction(dp, r21, r22));
}
}
}
}
///// <summary>
///// Modified from a code of Fred's written in Matlab
///// </summary>
///// <param name="dp">diffusion parameters object</param>
///// <param name="k">complex diffusion constant, ((mua*cn +i*(ft*2*pi))/(D*cn)).^0.5</param>
///// <param name="rho">source-detector separation</param>
///// <param name="rProbe">radius from source</param>
///// <param name="y">omitted</param>
///// <param name="z">depth</param>
///// <param name="ft">temporal frequency</param>
///// <returns></returns>
//public static double DepthProbFrequencyDomainPhotonMigration(DiffusionParameters dp, Complex k,
// double rho, double rProbe, double z, double ft)
//{
// var r11 = DiffusionBase.Radius1(rho, z, dp.zp);
// var r12 = DiffusionBase.Radius2(rho, z, dp.zp, dp.zb);
// var r21 = DiffusionBase.Radius1(rProbe - rho, z, 0.0);
// var r22 = DiffusionBase.Radius2(rProbe - rho, z, 0.0, dp.zb);
// var phi1 = SDAForwardSolver.TemporalFrequencyFluence(dp, k, r11, r12);
// var phi2 = SDAForwardSolver.TemporalFrequencyFluence(dp, k, r21, r22);
// return (phi1 * phi2).Modulus; // see Kienle and Patterson, JOSA A 14(1), 246-254,1997
//}
public static IEnumerable <double> TemporalFrequencyPointSourceCenterlinePHD(
this IForwardSolver myForwardSolver, IEnumerable <OpticalProperties> ops,
IEnumerable <double> rProbes, IEnumerable <double> rhos,
IEnumerable <double> zs, IEnumerable <double> fts)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, ForwardModel.SDA);
foreach (var rProbe in rProbes)
{
foreach (var rho in rhos)
{
foreach (var z in zs)
{
var r11 = CalculatorToolbox.GetRadius(rProbe, z - dp.zp);
var r12 = CalculatorToolbox.GetRadius(rProbe, z + dp.zp + 2 * dp.zb);
var r21 = CalculatorToolbox.GetRadius(rho - rProbe, z);
var r22 = CalculatorToolbox.GetRadius(rho - rProbe, z + 2 * dp.zb);
foreach (var ft in fts)
{
Complex k =
(
(op.Mua * dp.cn + Complex.ImaginaryOne * ft * 2 * Math.PI) /
(dp.D * dp.cn)
).SquareRoot();
var phi1 = DiffusionGreensFunctions.TemporalFrequencyPointSourceImageGreensFunction(
dp, r11, r12, k);
var phi2 = DiffusionGreensFunctions.TemporalFrequencyPointSourceImageGreensFunction(
dp, r21, r22, k);
yield return((phi1 * phi2).Magnitude);
}
}
}
}
}
}
public static IEnumerable <double> TemporalPointSourceCenterlinePHD(
this IForwardSolver myForwardSolver,
IEnumerable <OpticalProperties> ops, IEnumerable <double> rProbes,
IEnumerable <double> rhos, IEnumerable <double> zs, IEnumerable <double> ts)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, ForwardModel.SDA);
foreach (var rProbe in rProbes)
{
foreach (var rho in rhos)
{
foreach (var z in zs)
{
var r11 = CalculatorToolbox.GetRadius(rProbe, z - dp.zp);
var r12 = CalculatorToolbox.GetRadius(rProbe, z + dp.zp + 2 * dp.zb);
var r21 = CalculatorToolbox.GetRadius(rho - rProbe, z);
var r22 = CalculatorToolbox.GetRadius(rho - rProbe, z + 2 * dp.zb);
foreach (var t in ts)
{
Func <double, double> integrandConvolve =
tau =>
{
return
(DiffusionGreensFunctions.TemporalPointSourceImageGreensFunction
(dp, r11, r12, tau) *
DiffusionGreensFunctions.TemporalPointSourceImageGreensFunction
(dp, r21, r22, t - tau));
};
yield return(FunctionMath.Integrate(
integrandConvolve, Meta.Numerics.Interval.FromEndpoints(0.0, t)));
}
}
}
}
}
}
// this method builds an R(fx, ft) array and then uses FFT to generate R(fx, t)
private double[] DetermineROfTimeFromROfFtForFixedFx(double fx, IOpticalPropertyRegion[] regions, out double[] FFTTimeSequence)
{
// get ops of top tissue region
var op0 = regions[0].RegionOP;
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op0.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op0.N);
var diffusionParameters = GetDiffusionParameters(regions);
var layerThicknesses = GetLayerThicknesses(regions);
int numFreq = 512; // Kienle used 512 and deltaFreq = 0.1
// Kienle says deltaFrequency depends on source-detector separation
var deltaFrequency = 0.5; // 500 MHz good for all fx
var F = numFreq * deltaFrequency; // 51 GHz
var deltaTime = 1.0 / (numFreq * deltaFrequency); // 0.02 ns => T = 10 ns
// considerations: 2n datapoint and pad with 0s beyond (deltaTime * numFreq)
var rOfFt = new Complex[numFreq];
double[] ft = Enumerable.Range(0, numFreq).Select(x => x * deltaFrequency).ToArray();
FFTTimeSequence = Enumerable.Range(0, numFreq).Select(x => x * deltaTime).ToArray();
for (int i = 0; i < numFreq; i++)
{
// normalize by F=(numFreq*deltaFrequency)
rOfFt[i] = SpatialAndTemporalFrequencyReflectance(2 * Math.PI * fx, ft[i], diffusionParameters, layerThicknesses, fr1, fr2) * F;
}
// FFT R(ft) to R(t)
//var dft = new MathNet.Numerics.IntegralTransforms.Algorithms.DiscreteFourierTransform();
//dft.Radix2Inverse(rOfFt, FourierOptions.NoScaling); // convert to R(t)
Fourier.Radix2Inverse(rOfFt, FourierOptions.NoScaling);
var rOfTime = new double[FFTTimeSequence.Length];
rOfTime = rOfFt.Select(r => r.Real / (numFreq / 2)).ToArray();
return(rOfTime);
}
/// <summary>
/// Evaluate the stationary radially resolved z-flux with the point source-image
/// configuration
/// </summary>
/// <param name="rho">radial location</param>
/// <param name="z">depth location</param>
/// <param name="dp">DiffusionParamters object</param>
/// <returns></returns>
public double StationaryFlux(double rho, double z, DiffusionParameters dp)
{
var zSource = z - dp.zp;
var zImage = z + dp.zp + 2 * dp.zb;
return
(DiffusionGreensFunctions.StationaryPointSourceImageGreensFunctionZFlux(dp,
CalculatorToolbox.GetRadius(rho, zSource), zSource,
CalculatorToolbox.GetRadius(rho, zImage), zImage));
}
/// <summary>
/// Evaluate the stationary radially resolved fluence with the point source-image
/// configuration
/// </summary>
/// <param name="rho">radial location</param>
/// <param name="z">depth location</param>
/// <param name="dp">DiffusionParameters object</param>
/// <returns>fluence</returns>
public override double StationaryFluence(double rho, double z, DiffusionParameters dp)
{
return(DiffusionGreensFunctions.StationaryPointSourceImageGreensFunction(dp,
CalculatorToolbox.GetRadius(rho, z - dp.zp),
CalculatorToolbox.GetRadius(rho, z + dp.zp + 2 * dp.zb)));
}
public Complex TemporalFrequencyZFlux(
DiffusionParameters dp, double rho, double z, Complex k)
{
var zSource = z - dp.zp;
var zImage = z + dp.zp + 2 * dp.zb;
return(DiffusionGreensFunctions.TemporalFrequencyPointSourceImageGreensFunctionZFlux(dp,
CalculatorToolbox.GetRadius(rho, zSource), zSource,
CalculatorToolbox.GetRadius(rho, zImage), zImage,
k));
}
public override Complex TemporalFrequencyFluence(DiffusionParameters dp, double rho,
double z, Complex k)
{
return(DiffusionGreensFunctions.TemporalFrequencyPointSourceImageGreensFunction(dp,
CalculatorToolbox.GetRadius(rho, z - dp.zp),
CalculatorToolbox.GetRadius(rho, z + dp.zp + 2 * dp.zb),
k));
}
/// <summary>
/// Evaluate the temporally-radially resolved z-flux using the point source-image configuration
/// </summary>
/// <param name="dp">DiffusionParameters object</param>
/// <param name="rho">radial location</param>
/// <param name="z">depth location</param>
/// <param name="t">time</param>
/// <returns></returns>
public double TemporalFlux(
DiffusionParameters dp, double rho, double z, double t)
{
var zSource = z - dp.zp;
var zImage = z + dp.zp + 2 * dp.zb;
return(DiffusionGreensFunctions.TemporalPointSourceImageGreensFunctionZFlux(dp,
CalculatorToolbox.GetRadius(rho, zSource), zSource,
CalculatorToolbox.GetRadius(rho, zImage), zImage,
t));
}